Magnetic Resonance Motion and Diffusion Encoding of the Heart

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Doctoral Thesis

Magnetic Resonance Motion and Diffusion Encoding of the Heart

Author(s): Stoeck, Christian T.

Publication Date: 2014

Permanent Link: https://doi.org/10.3929/ethz-a-010421819

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Magnetic Resonance Motion and

Diffusion Encoding of the Heart

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH

(Dr. sc. ETH Zurich)

presented by

Christian Torben Stoeck

Dipl. Phys. ETH

ETH Zurich, Switzerland

born on 10.06.1984

citizen of Germany

accepted on the recommendation of

examiner: Prof. Dr. Sebastian Kozerke

co-examiner: Prof. Dr. Gábor Székely

co-examiner: Dr. David Atkinson

2014

DISS. ETH NO. 22215

Abstract

Abstract

Heart failure (HF) affects 23 million patients worldwide. Fifty percent of the patients

die within five years after diagnosis. Although current diagnostic imaging tools provide

information on cardiac morphology and global function, insights into the mechanisms

involved in longitudinal myocardial structural remodeling and functional impairment

are still lacking. As a result, there has been limited advancement regarding early

diagnosis and individualized therapy management to improve patient prognosis.

Magnetic Resonance Imaging (MRI) has become a prime diagnostic imaging modality.

It is the clinical reference method to calculate cardiac mass and ejection fraction.

Besides morphological imaging, MRI offers the unique feature to non-invasively probe

microscopic tissue properties. While MRI diffusion tensor imaging has been extensively

used in stationary organs such as the brain, its application to the in-vivo heart is very

challenging due to image artifacts induced by cardiac and respiratory motion.

The present thesis is concerned with the development of efficient MRI imaging

methods to quantify local cardiac tissue deformation and microstructural changes

towards a more comprehensive and quantitative characterization of the in-vivo heart

in HF and other cardiac diseases.

Using three-dimensional (3D) myocardial MRI tagging, cardiac contraction patterns can

be assessed and quantified. Despite the availability of the method, its applicability is

severely compromised by the need for successive breathholding of the patient. In

addition spatial and temporal resolutions are limited given the timing constraints

imposed by breathhold durations. In this thesis an approach to accelerating 3D tagging

is developed and validated. To this end, a model decomposing the spatiotemporal MRI

image series using partially separable functions is exploited. Image reconstruction is

posed as a regularized least-squares inverse problem in the spatial-principal

component space. Regularization is based on low-resolution training data acquired

3

Abstract

interleaved with the undersampled data. This method, termed k-t PCA, is

demonstrated to accelerate 3D tagging sufficiently to allow for single breath hold

acquisition. Clinically relevant cardiac motion parameters such as circumferential strain

and rotation were derived and compared relative to non-accelerated imaging in

healthy hearts and patients suffering from myocardial infarction. Good agreement of

quantitative data is reported and atypical strain was found to correlate well with

impaired tissue viability in myocardial infarct patients.

A further topic of this thesis relates to MRI pulse sequence design and processing

methods for imaging myocardial microstructure in-vivo. Diffusion weighted MRI

imaging has extensively been used in stationary organs such as the brain. Suitable

pulse sequences include diffusion sensitized stimulated echo acquisition modes

(STEAM) and spin echo (SE) imaging. While the application of the STEAM and SE

methods is straightforward in static tissue, deformation of the in-vivo heart due to

cardiac contraction and respiratory motion severely compromise or inhibit data

acquisition in the beating heart. This is related to the fact that cardiac deformation is

at least an order of magnitude greater than the mean displacement of water

molecules as a result of thermal self-diffusion. In addition, STEAM echo encoding and

decoding requires two successive heartbeats and hence respiratory motion needs to

be closely controlled. As a consequence of such an imaging scheme, diffusion

weighting also becomes dependent on the evolution of cardiac strain in-between echo

encoding and decoding. To address this issue, a framework using strain data derived

from 3D tagging is presented which allows correcting for strain induced modulation of

the diffusion related signal. Using the framework, strain corrected diffusion tensor

information of the in-vivo heart could be acquired both in systole and diastole for the

first time. Data quality was found to be sufficient to derive quantitative information of

systolic and diastolic helix, transverse and sheet angle orientations offering an array of

potentially important diagnostic readouts.

A disadvantage of STEAM based imaging relates to the tight respiratory control

required. Accordingly, considerable patient cooperation is needed and overall exam

times are long. To address these shortcomings, single-shot techniques based on SE

imaging are attractive alternatives. Unfortunately, SE methods require diffusion

4

gradients of extended duration and hence become very sensitive to changes in strain

during diffusion encoding. Within the scope of this thesis, a higher order motion

compensated diffusion weighted SE approach has been developed and implemented.

It is demonstrated that compensation for velocity and acceleration of tissue is critically

important to preserve the integrity of tissue related diffusion information. In view of

the clinical application of the method it is worthwhile noting that the method works

over a wide range of heart rates as encountered in cardiac patients and hence offers a

promising approach for probing cardiac microstructure in a clinical setting.

In conclusion, significant advances in cardiac MRI have been achieved permitting to

quantify cardiac mechanics and microstructure of the beating heart. A set of new

diagnostic tools is offered to aid in studying the causes and consequences of the failing

heart and other cardiac conditions. Knowledge of the in-vivo architecture of myofiber

aggregates is of key importance to unravel changes of the mechanical and

electrophysiological properties of the heart. Furthermore and in view of the progress

being made in patient-specific cardiac simulations, the data provides essential

information to personalize in-silico cardiac analysis and interventions in the future.

5

Abstract

6

Zusammenfassung

Zusammenfassung

Weltweit leiden ca. 23 Mio. Patienten an einer Herzinsuffizienz. Fünf Prozent dieser

Patienten versterben innerhalb der ersten fünf Jahre nach erfolgter Diagnose. Trotz

der Möglichkeit, mittels bildgebender Verfahren die Morphologie und Funktion des

Herzens zu analysieren, bedarf es weiterer Fortschritte, um die Herzmechanik über

längere Zeit zu überwachen, Herzversagen früh zu erkennen und die

Patientenprognose durch individuelle Therapie zu verbessern.

Die Magnetresonanz-Tomographie (MRT) ist zu einer der wichtigsten bildgebenden

Modalitäten avanciert und gilt klinisch als Standartmethode, um Herzmuskelmasse

und Auswurffraktion zu bestimmen. Darüber hinaus können mittels MRT auch

mikroskopische Gewebeeigenschaften untersucht werden. In statischen Organen, wie

dem Gehirn, zählt die Diffusions-Tensor-Bildgebung zu den erfolgversprechenden

Methoden zur Gewebecharakterisierung. Am Herzen kann diese Methodik jedoch

nicht direkt angewendet werden, da Herz- und Atembewegung zu Bildartefakten

führen.

Die vorliegende Arbeit befasst sich mit der Entwicklung effizienter MRT

Herzbildgebungsmethoden, um lokale Gewebedeformationen und die Mikrostruktur

des Herzens, in Hinblick auf eine quantitative Charakterisierung des schlagenden

Herzens bei Herzversagen und bei anderen Herzleiden, zu bestimmen.

Mittels dreidimensionaler (3D) magnetischer Markierungen des Herzmuskels kann die

Herzbewegung nichtinvasiv detektiert und quantifiziert werden. Die Praktikabilität

dieser Methode in Patienten ist jedoch durch die Vielzahl erforderlicher Atemstopps

eingeschränkt. Hinzu kommt, dass aus Zeitgründen nur eine geringe räumliche und

zeitliche Auflösung erreicht werden kann. In der vorliegenden Arbeit wird eine

beschleunigte MRT Methode zu Bestimmung der Herzmuskelbewegung entwickelt und

validiert. Dazu wird die Trennbarkeit der räumlichen Dimensionen von der zeitlichen

7

Zusammenfassung

Dimension bei der Bildgebung ausgenutzt. Die Bildrekonstruktion wird als

regularisiertes inverses Problem im räumlichen/Hauptkomponenten-Raum formuliert.

Die Regularisierung basiert hierfür auf Bilddaten niedriger räumlicher Auflösung, die

parallel zu unterabgetasteten Aufnahmen akquiriert werden. Es wird gezeigt, dass

diese Methode es ermöglicht, innerhalb eines einzelnen Atemstopps klinisch relevante

Parameter wie die zirkumferentielle Verkürzung und die Rotation des Herzmuskels

aufzunehmen. Der Erfolg des Ansatzes wird anhand von Probanden- und

Patientenmessungen demonstriert. Eine gute Übereinstimmung der beschleunigten

Methode relativ zu konventionellen Aufnahmen wurde gefunden. Darüber hinaus

konnte eine sehr gute Korrelation zwischen atypischer Herzkontraktion und

reduzierter Gewebevitalität in Patienten mit Myokardinfarkt nachgewiesen werden.

Neben der Messung der Herzbewegung befasst sich die vorliegende Arbeit mit der

Entwicklung von MRT Pulssequenzen und Datenverarbeitungsalgorithmen zur

Bestimmung der Mikrostruktur des schlagenden Herzens. Die diffusionsgewichtete

MRT wird seit längerer Zeit erfolgreich an stationären Organen wie dem Gehirn

verwendet. Die dazu benutzten Pulssequenzen umfassen die Aufnahme stimulierter

Echos (STEAM) und Spin Echos (SE). Die Herzkontraktion und die Atembewegung

erlauben es allerdings nicht, diese Sequenzen direkt auf das Herz zu übertragen. Der

Grund hierfür liegt in den unterschiedlichen Grössenordnungen der auftretenden

Bewegungen. Während die Selbstdiffusion der Wassermoleküle auf einer Skala von

wenigen Mikrometern stattfindet, bewegt sich das Herz um mehrere Millimeter bis

Zentimeter während der Messung. Hinzu kommt, dass STEAM Sequenzen zwei

aufeinanderfolgende Herzschläge benötigen, um ein diffusionsgewichtetes Bild zu

erzeugen. Entsprechend ergeben sich Fehler des gemessenen Diffusionstensors durch

die Kontraktion des Myokardgewebes zwischen den Herzschlägen. In der vorliegenden

Arbeit wird ein Datenverarbeitungsansatz präsentiert, der unter Verwendung von 3D

Herzbewegungsaufnahmen den durch die Herzkontraktion entstandenen Fehler

reduziert. Hiermit gelang es zum ersten Mal überhaupt, die Herzmuskelstruktur des

schlagenden Herzens in der Systole und in der Diastole zu untersuchen. Die sehr gute

Qualität der Daten erlaubte es, Aussagen über die Dynamik von Herzmuskelfasern zu

8

treffen. Die Auswertung der Helix-, Transvers- und Faserlaminarangulation stellen

hierbei wichtige Parametern mit möglicher klinischer Relevanz dar.

Ein Nachteil der auf STEAM basierten, diffusionsgewichteten Bildgebung besteht in der

notwendigen und strikten Kontrolle der Atembewegung. Dies bedingt die aktive

Mitwirkung des Patienten über den langen Zeitraum der Bildaufnahme. Um den Grad

der Patientenkooperation und die Messdauer an sich zu reduzieren, wurden

diffusionsgewichtete Spin-Echo Sequenzen für die Herzbildgebung entwickelt. Jedoch

benötigen solche Sequenzen starke und lange Gradienten, welche die Empfindlichkeit

der Bildaufnahme bezüglich Bewegung stark erhöhen. Als Teil dieser Arbeit wurde eine

bewegungskompensierte Diffusionskodierung entwickelt und implementiert. Es wird

gezeigt, dass sowohl Geschwindigkeits- als auch Beschleunigungskompensation

notwendig sind, um Diffusion am Herzen akkurat zu messen. Mit Hinblick auf eine

klinische Verwendung dieser Methodik sei erwähnt, dass diese Art der

Diffusionskodierung nicht mehr auf einzelne, kurze Zeitintervalle im Herzzyklus

beschränkt ist.

Zusammenfassend wird festgehalten, dass die in dieser Arbeit entwickelten Methoden

es erlauben, Herzbewegung und Herzmuskelstruktur im schlagenden Herzen zu

untersuchen. Die vorgestellten Techniken erlauben es, zukünftig Ursachen und Folgen

der Herzinsuffizienz im Detail und longitudinal zu untersuchen. Das Wissen über die

Faserstruktur des Herzmuskels ist essentiell für das Verständnis elektrophysiologischer

Eigenschaften des Herzens. In Hinblick auf die fortschreitende Entwicklung

patientenspezifischer Behandlungsansätze spielen neue MRT Methoden auch für

digitale Organsimulationen eine entscheidende Rolle.

9

Zusammenfassung

10

Contents

Contents

Abstract ............................................................................................................ 3

Zusammenfassung ............................................................................................ 7

Contents ......................................................................................................... 11

Chapter 1 Introduction ................................................................................. 15

1.1 Motivation ......................................................................................................... 15

1.2 Outline ............................................................................................................... 17

Chapter 2 Cardiac motion and microstructure .............................................. 19

2.1 Cardiac motion ................................................................................................... 19

2.1.1 Rotation ............................................................................................................. 19

2.1.2 Contraction ........................................................................................................ 20

2.2 Cardiac microstructure ...................................................................................... 22

2.3 Link between motion and structure ................................................................... 25

Chapter 3 Myocardial motion analysis techniques ....................................... 27

3.1 Magnitude based imaging techniques ............................................................... 27

3.1.1 Inversion recovery methods .............................................................................. 27

3.1.2 SPatial Modulation of Magnetization (SPAMM) ................................................. 28

3.1.3 Strain Encoding .................................................................................................. 34

3.1.4 Motion analysis .................................................................................................. 35

3.2 Phase based imaging techniques ....................................................................... 35

3.2.1 Displacement encoding ...................................................................................... 35

3.2.2 Phase-contrast velocity encoding ...................................................................... 40

3.3 Magnitude and phase based imaging techniques .............................................. 41

3.4 Motion parameters ............................................................................................ 44

3.4.1 Rotational motion .............................................................................................. 44

3.4.2 Tissue deformation ............................................................................................ 44

11

Contents

Chapter 4 Undersampled Cine 3D Tagging for Rapid Assessment of

Cardiac Motion ...................................................................................... 47

4.1 Introduction ....................................................................................................... 47

4.2 Methods ............................................................................................................. 50

4.2.1 k-t PCA ................................................................................................................ 50

4.2.2 Computer simulation .......................................................................................... 51

4.2.3 In-vivo measurements ........................................................................................ 53

4.2.4 Data analysis ...................................................................................................... 55

4.3 Results ................................................................................................................ 57

4.3.1 Computer simulation .......................................................................................... 57

4.3.2 In-vivo measurements ........................................................................................ 58

4.4 Discussion ........................................................................................................... 63

4.5 Conclusion .......................................................................................................... 66

Chapter 5 Imaging microstructure with MRI ................................................. 67

5.1 Diffusion of water molecules.............................................................................. 67

5.2 Imaging diffusion: Stejskal-Tanner diffusion encoding ....................................... 69

5.2.1 Non-Gaussian diffusion ...................................................................................... 71

5.3 Quantitative parameters .................................................................................... 72

5.4 Imaging diffusion in the beating heart ............................................................... 75

5.4.1 Diffusion weighted imaging using spin echoes ................................................... 75

5.4.1.1 Gradient field imperfections .............................................................................. 79

5.4.2 Diffusion weighted imaging using stimulated echoes ........................................ 81

5.4.2.1 Strain effects ...................................................................................................... 84

Chapter 6 Dual-Phase Cardiac Diffusion Tensor Imaging With Strain Correction ............................................................................................. 87

6.1 Introduction ....................................................................................................... 87

6.2 Methods ............................................................................................................. 88

6.2.1 Study protocol .................................................................................................... 88

6.2.2 Myocardial tagging sequence ............................................................................. 89

6.2.3 Diffusion sequence ............................................................................................. 89

6.2.4 Tensor reconstruction ........................................................................................ 91

6.2.5 Correction for material strain ............................................................................. 92

6.2.6 Data analysis ...................................................................................................... 93

6.3 Results ................................................................................................................ 94

6.4 Discussion ......................................................................................................... 103

12

6.5 Conclusion ........................................................................................................ 105

Chapter 7 Second Order Motion Compensated Spin-Echo Diffusion Tensor Imaging of the Human Heart ................................................... 107

7.1 Introduction ..................................................................................................... 107

7.2 Methods ........................................................................................................... 109

7.2.1 Diffusion encoding ........................................................................................... 109

7.2.2 Study protocol .................................................................................................. 112

7.2.3 Data analysis .................................................................................................... 113

7.3 Results .............................................................................................................. 114

7.4 Discussion ........................................................................................................ 120

7.5 Conclusion ........................................................................................................ 122

Chapter 8 Discussion & Outlook ................................................................. 123

8.1 Discussion ........................................................................................................ 123

8.2 Outlook ............................................................................................................ 126

Abbreviations ............................................................................................... 129

Bibliography .................................................................................................. 131

List of Publications ........................................................................................ 151

Journal publications .................................................................................................... 151

Patient cases ............................................................................................................... 152

Conference proceedings ............................................................................................. 152

Acknowledgements ...................................................................................... 157

Curriculum Vitae ........................................................................................... 161

Personal information .................................................................................................. 161

Education & Affiliation ................................................................................................ 161

13

Contents

14

Chapter 1 Introduction

1. Introduction

Heart failure (HF) affects 1-2% of the population in the industrialized world, of which

50% die within the first 5 years after diagnosis. At the age of 40 the sex-independent

lifetime risk for HF amounts to 20% [1]. According to the 2012 guidelines of the

European Society of Cardiology [2], HF is defined as “abnormality of cardiac structure

or function leading to failure of the heart to deliver oxygen at a rate commensurate

with the requirements of the metabolizing tissues”. Causes leading to HF include

hypertension, chemotherapy, viral infection, valvular and congenital heart diseases.

However, 60% of all HF cases are associated with coronary artery disease (CAD), which

is the most common type of heart disease. Treatment options of HF depend on many

factors, but for end-stage HF, heart transplantation is often the only choice [3].

To fully investigate and understand the reasons for failing of the heart, it is important

to extend current clinical diagnostics and enable monitoring of cardiac contraction and

assessment of healthy and altered myocardial microstructure in-vivo.

1.1 Motivation

Magnetic Resonance imaging (MRI) has become a prime diagnostic modality. It is the

method of choice for quantifying ejection fraction (EF), left-ventricular (LV) mass and

infarct size and location by late Gadolinium enhancement (LGE) [4,5]. Moreover recent

multi-center trials have demonstrated the superiority of MRI over single photon

emission tomography (SPECT) for the assessment of cardiac perfusion [6,7].

Quantification of EF is based on multi-slice and multi-phase short-axis imaging of the

entire LV [8]. Systolic and diastolic volumes are estimated based on the identification

of endocardial borders.

15

Introduction

With more elaborate MRI pulse sequences, regional tissue strain can be assessed to

quantify ventricular function [9-11]. Full 3D coverage of the LV has, however, been

limited due to prolonged scan duration and the necessary patient cooperation when

performing multiple breath holding maneuvers. To address this limitation, image

acceleration by spatial-temporal undersampling in conjunction with sophisticated

reconstruction techniques has been introduced [12,13].

As part of the present thesis, scan acceleration methods have been developed and

applied to facilitate quantification of ventricular motion and strain using 3D tagging

sequences. It is demonstrated that spatio-temporal undersampling in conjunction with

appropriate image reconstruction algorithms permit whole-heart motion

quantification in a single breath hold.

Beyond morphological imaging, MRI offers the unique feature of non-invasively

probing tissue properties at a microscopic scale [14,15]. While Diffusion Weighted

Imaging (DWI) and Diffusion Tensor Imaging (DTI) have been well established for

stationary organs including the brain, its application to the in-vivo heart is very

challenging as cardiac and respiratory motion of the heart are orders of magnitude

greater than molecular displacements due to water self-diffusion. Using diffusion

weighted stimulated acquisition echo mode (STEAM) imaging sequences [16], the

encoding of water self-diffusion is subject to myocardial strain-induced bias [17,18].

However, by quantifying cardiac deformation during the cardiac cycle, this error can be

accounted for.

An alternative approach to diffusion weighted STEAM imaging is based on the

formation and sampling of spin echoes (SE) [19]. Spin echo sequences allow for time-

efficient diffusion encoding within a single heartbeat. Being a single-shot method, SE

sequences can be applied during free-breathing of the patient, potentially improving

compliance in a clinical setting. However, diffusion weighted SE imaging of the in-vivo

heart is highly sensitive to cardiac strain. To this end, its use is very limited even on MR

scanners with very powerful gradient systems [20].

A key theme of the present work concerns methods to account or correct for cardiac

strain effects in diffusion weighted STEAM and SE imaging of the in-vivo heart. Using

16

strain correction and/or dedicated pulse sequence designs to compensate for higher

order motion during diffusion encoding, multi-slice and multi-phase diffusion tensor

imaging of the beating heart is presented. The data permits 3D reconstruction of the

in-vivo architecture of myofiber aggregates in systole and diastole for the first time.

1.2 Outline

General cardiac anatomy and mechanical function are reviewed in Chapter 2.

Alongside the current status of knowledge of cardiac microstructure is presented and

linked to cardiac mechanics.

In Chapter 3 methods for imaging and quantifying cardiac motion using MRI are

discussed. An accelerated imaging method for time-efficient whole-heart mapping of

myocardial tissue deformation is presented in Chapter 4. Using spatiotemporal

undersampling, 3D whole-heart myocardial motion pattern could be acquired in

healthy subjects and patients with myocardial infarction in a single breath hold.

Current approaches for probing myocardial microstructure ex-vivo and in-vivo are

reviewed in Chapter 5 and their relative advantages and disadvantages are discussed.

Limitations of STEAM based sequences for cardiac imaging are addressed in Chapter 6.

A framework is proposed for assessing the dynamics of in-vivo myocardial

microstructure in systole and diastole. Chapter 7 presents the design and the

validation of an approach for higher order motion compensated SE based diffusion

imaging. This single-shot method allows for free-breathing data acquisition and hence

paves the way towards clinical use of cardiac diffusion tensor imaging. The thesis is

concluded with a discussion and an outlook of future developments and applications

of the methods.

17

Introduction

18

Chapter 2 Cardiac motion and microstructure

2. The Cardiovascular System

The heart is a muscle consisting of cardiac myocytes that contract upon an electric

stimulus. During contraction each muscle cell thickens in diameter and shortens in

length. The complex contraction pattern of the heart is established by a sophisticated

myofiber arrangement. In the following sections the cardiac contraction pattern, the

myocardial microstructure and the current understanding of linking both motion and

microstructure are reviewed. Since most of the research has been conducted on the

left ventricle (LV) the following review is focused on the LV.

2.1 Cardiac motion

During cardiac contraction the myocardium undergoes longitudinal and

circumferential shortening with concurrent radial thickening. Rotational motion of

various degrees across the LV is observed leading to torsion.

2.1.1 Rotation

Rotational motion of the healthy heart during contraction is shown in Figure 1. When

viewed from the apex to the base, the base performs a clockwise rotation and the

apex a counter-clockwise rotation in planes perpendicular to the LV long-axis. Rotation

is found to be greater at the sub-endocardial relative to sub-epicardial layer [21]. It has

been demonstrated that abnormal rotational motion pattern correlate with a number

of different pathologies [22]. Example findings are listed below:

• In aortic valve stenosis a significantly increased systolic torsion (span of basal to apical peak rotation) is seen [23,24].

• Mitral valve stenosis leads to significantly reduced torsion and basal rotation [25].

• Anterolateral infarction causes reduced apical rotation [26].

19

Cardiac motion and microstructure

• LV rotation serves as an indicator for early cardiomyopathy in Fabry disease

[27]. • Dilated cardiomyopathy leads to reduced total rotation and torsion [28,29]. • Non-compaction cardiomyopathy results in global LV rotation instead of base-

to-apex counter rotation [29]. • Increased rotation and torsion were found upon kidney transplant indicating

an improvement of cardiac function [30].

Figure 1. Cardiac rotation patterns. Three slices from combined line tagged volumes are shown for the apical mid-ventricular and basal level. The amount of rotation perpendicular to the ventricular long-axis is plotted as function of the trigger delay.

2.1.2 Contraction

During systolic contraction the healthy heart shortens by about 30%-40% in

longitudinal direction and by 15%-20% in circumferential direction [31]. In radial

20

direction, myocardium thickens by 15%-20% [31]. Figure 2 shows a systolic and

diastolic short-axis view of the heart as well as the four-chamber long axis view.

Additionally the tissue stretch over the imaged cardiac cycle is presented. In the

healthy heart the radial stretch is largest at the base while circumferential stretch is

largest at the apex [32,33]. Despite the contraction of the base towards the apex,

longitudinal stretch is fairly homogeneous along the long axis of the heart with slightly

higher values at the apex [32,33].

Radial, circumferential and longitudinal contractions form only three of the six

components of myocardial deformation tensor. The torsional motion described in the

previous section corresponds to the shear components of myocardial deformation

[34].

Figure 2. Cardiac contraction between systole and diastole. In the two-chamber short-axis view, radial stretch as well as circumferential shortening are visible. In the four-chamber long-axis view longitudinal contraction is shown. Local myocardial stretch in radial, circumferential and longitudinal direction is plotted as function of time (adapted from Figure 33).

Cardiac contraction can be impaired by various pathologies resulting in inefficient

pumping of the heart. Besides the amount of cardiac contraction, synchrony of the

contraction patterns is crucial for efficient cardiac performance. Synchrony of

contraction can be altered by various causes:

21


• In myocardial infarction cardiac output is reduced [9,35-37] and dyskinetic are-

as occur where tissue is passively stretched in an opposite direction relative to the healthy condition [38].

• In dilated cardiomyopathy circumferential contraction is reduced [39] and its magnitude more heterogeneously distributed across the LV [40].

• Hypertrophic cardiomyopathy causes reduced circumferential strain and lower diastolic strain rates [41].

• Impaired signal conduction such as Left Bundle Branch Blockage (LBBB) can re-sult in asynchronous myocardial contraction compromising both systolic and diastolic LV performance [42,43].

2.2 Cardiac microstructure

The arrangement of cardiomyocytes in the heart is fairly complex and subject of

ongoing research. In 1965, Grant proposed an interpretation of myocardial

microstructure and concluded: “The search for an accurate and detailed picture of the

muscular architecture of the left ventricle is by no means a trivial goal.” [44]:

• The myocardium forms a three dimensional functional syncytium of branch-ing and interconnecting myocytes.

• A description of the myocardial structure depends on the geometrical scale of investigation.

• Cell-bundles and layers of myocyte aggregates may be discerned but may not have a physiological implication.

• To appreciate the spatial levels at which myocardial structure can be ana-lyzed a statistical view should be employed.

Gilbert et al. reviewed old and novel models of cardiac architecture [45]. Their

notation is used in the following. Accordingly, myocytes and myofibers correspond to

single cells and myolaminae, band and sheet structures represent multiple

interconnected myocytes.

The principal direction of myocyte aggregates was found to follow a helical alignment

[45-47] at sub-endocardial and sub-epicardial level. In the endocardium the helix is

right-handed (positive angulation) and changes into a left-handed (negative

angulation) pattern at epicardium. Figure 3 shows a reconstruction of the helix pattern

obtained from an ex-vivo human heart using diffusion weighted MR imaging. The

transmural range of helix angles of the ex-vivo human heart has been found to vary

22

between -40° to +65° [48,49] and -72° to +63° [50] (microscopy). While the helix

pattern illustrates the arrangement of myocyte aggregates, single myocytes have a

length of only 50-150μm and a thickness of 10-20μm with considerable variation

between species [51,52].

Besides the helical pattern of myocyte aggregates, a transmural component has been

discussed implying crossing of endocardial fibers into the epicardium going from mid-

ventricular level to the apex and the base of the heart [53]. The corresponding in-plane

spiral pattern of myocyte aggregates is most clearly visible at the apex but extends

over the ventricle [46,49,54,55]. Figure 4 presents the principal fiber direction

measured by MRI at apical level along with an illustration of a fiber bundle following a

transmural course.

Figure 3. Reconstruction of the helix pattern of myocyte aggregates based on MR diffusion tensor imaging of the post mortem human heart. The antero-lateral side is shown. Color-coding corresponds to the helix angle of the tracked fibers.

23


Figure 4. Transmural course of myofiber aggregates. On the left an apical image of an ex-vivo human heart is shown. The image is superimposed with diffusion tensors acquired by MRI. The view is orientated from apex to base. The white line illustrates local fiber paths from the measured principal myofiber direction. On the right a fiber tracking result is shown for an endocardial seed point within the septum. Fibers cross transmurally and reappear at epicardial positon within the lateral wall. Both images are obtained upon dense tensor field interpolation [56].

As already noted by Grant [44], there are interconnections of adjacent myocytes by

collagen fibers and branching of myocytes. Myocyte bundles and myolaminae are

formed [57-59]. Imbedded in the extracellular tissue matrix [59], myocytes are

arranged in laminar sheets, with cleavage planes in-between. Typical layers consist of

four cells and may be connected by branching with neighboring layers to form larger

aggregates [55,60]. By means of electron microscopy the thickness of myolaminae in

dogs was found to be 48.4±20.4μm [60]. The coupling between layers by branching

and collagen fibers decreases significantly from epicardium to mid-wall and

endocardium [60]. The orientation and extent of myocyte sheets is heterogeneous

within the heart [55,61] and myolaminae were found not to extend the full transmural

depth from epicardium to endocardium [59]. Two predominant sheet populations

were reported in the sheep and canine heart with an angle between each other of 84°-

91° [62-64]. Both sheet populations are not necessarily separated, but are seen to

coexist in the mid-myocardium [45,65]. It is argued, that these myofiber aggregates

are part of a three-dimensional mesh and cannot be separated as global bands [66].

24

2.3 Link between motion and structure

In the embryonic heart, myocyte pattern develop after onset of cardiac contraction. In

a very elaborate study conducted by Tobita et al. [67], it was found that the amount of

load influences myocyte organization. To this end, healthy embryonic chicken hearts

were compared to embryos which underwent either left atrial ligation (reduced LV

load) or banding of the pre-developed LV (increased LV load). Reduced load was found

to delay fiber organization while increased load accelerated structural LV formation

with an increasing appearance of left-handed helical structure. These findings suggest

a “form follows function” principle of myocyte arrangement. The exact nature of this

process is, however, still the subject of ongoing research.

During contraction myocytes shorten by 13% as reported for dog hearts [68]. It is,

however, noted that the corresponding thickening of the muscle cells cannot explain

myocardial wall thickening of 30 to 50% [52] unless very steep helix angles occur which

seem implausible according to histology [47]. In order to address the discrepancy it

was proposed that the cleavage planes between different myolaminae allow for sliding

of sheets with respect to each other [69]. Using MR diffusion tensor imaging the

concept of changes in myocardial sheet architecture was analyzed in explanted rat [61]

and canine [70] hearts arrested in systole and diastole. Sheet extension in transverse

orientation was found in conjunction with a more radial alignment. In diastole,

myolaminae are arranged more tangentially to the epicardial surface whereas a more

radial orientation is assumed during systole. It has been reported that sheet normal

shear accounts for 40-60% of radial thickening [70,71]. Besides the change in sheet

angle between diastole and systole, heterogeneity of sheet reorganization across the

ventricle has been noted and associated with heterogeneous radial contraction

patterns observed in the heart [70,71]. The functional importance of myolaminae

reorientation has not only been studied in healthy hearts but was also investigated in

excised mice hearts with Duchenne muscular dystrophy. Impaired calcium reuptake

leads to incomplete relaxation of the heart in diastole which was found to correlate

with a more systolic sheet arrangement [72].

Besides local reorientation of entire myocyte aggregates during contraction, their

fundamental orientation has been reported to be essential for explaining torsion and

25


shear components of myocardial strain. In mathematical models the necessity of the

transmural course of myocytes (compare Figure 4) has been emphasized in order to

equalize myocardial strain [73,74]. In their model myocyte aggregation by collagen

structure as reported by Pope et al. [59] was not considered.

Finally, it is noted that the presence of a dissectible band structure does not exist [66].

However, the notion of local cleavage planes is accepted [55]. The presence of non-

tangential components of fiber direction has been confirmed based on histological

findings [75] and MR imaging [53].

Beyond the relation of myocardial microstructure and cardiac motion,

electrophysiological considerations are of importance. The anisotropy of the

myocardium determines the propagation direction of electrical signals, as the

propagation velocity is faster along myocytes relative to a direction perpendicular to

myocytes [76]. Upon pacing in-vivo dog hearts it was found that the activation

potential measured at the epicardial surface followed the helical alignment of the

epicardial cardiac microstructure [77]. It was even possible to map the transmural

change of helix inclination by measuring the potential propagation after pacing at

different transmural depths. In a recent study, a correlation of decreased activation

voltage with greater fiber disarray in mice with myocardial infarction was

demonstrated [78].

In almost all studies referenced herein, analysis of myocardial microstructure was

achieved with highly invasive methods ex-vivo. In the following section methods are

reviewed to analyze cardiac mechanics and microstructure non-invasively and in-vivo.

26

Chapter 3 Myocardial motion analysis techniques

3. Intracranial dynamics

Cardiovascular magnetic resonance (CMR) imaging allows investigating myocardial

motion and strain patterns non-invasively. In CMR tagging, tissue magnetization is

modulated by radio frequency (RF) irradiation resulting in defined magnitude and/or

phase patterns of the magnetization across the heart. By imaging these magnetization

patterns at different time points, the motion of material points can be tracked.

In the following chapter CMR imaging methods for assessing cardiac motion are

reviewed.

3.1 Magnitude based imaging techniques

3.1.1 Inversion recovery methods

In 1988, Zerhouni et al. [79] proposed selective inversion of longitudinal magnetization

to visualize cardiac motion. The evolution of longitudinal magnetization is governed by

a first order differential equation:

0

1

ZZ M MdMdt T

−= (3.1)

with solution:

( ) 1

00

00

1tt

TzZ

M MM t M e

M

= − −= −

(3.2)

with M0 being the magnetization at thermal equilibrium and 1T the time constant of

longitudinal relaxation. At the time point of zero-crossing of ( )ZM t tagged tissue will

appear dark in the image and hence its contrast relative to untagged tissue is

27

Myocardial motion analysis techniques

maximized. The degree of inversion and therefore the time point of zero-crossing of

the longitudinal magnetization can be manipulated by varying the flip angle of the

tagging RF pulse (Figure 5). By imaging the tagging pattern at different time points

after inversion, myocardial motion can be inferred. To capture through-plane motion,

radial tagging of the heart’s short-axis in conjunction with parallel tagging of the long

axis was suggested [33]. According to equation (3.2) and as demonstrated in Figure 5,

nulling of longitudinal magnetization by RF-inversion cannot be achieved for the entire

cardiac cycle, leading to varying contrast between tagged and untagged tissue in

diastole.

Figure 5. Flip angle of the inversion preparation pulse and resulting longitudinal magnetization as

function of the time between tagging and imaging. Simulation is based on a 1T of 1030ms for

myocardium [80].

3.1.2 SPatial Modulation of Magnetization (SPAMM)

As alternative to feature generation by slice-selective inversion, Axel et al. [81]

proposed a method of spatial modulation of magnetization by magnetic field

gradients. The SPAMM sequence diagram is shown in Figure 6 a). Accordingly,

longitudinal magnetization is tipped into the transverse plane and a field gradient

(Genc) is applied imposing a location depended magnetization phase. Thereafter,

magnetization is tipped back into the longitudinal direction resulting in cosine-

modulated longitudinal magnetization:

28

( ) 0cos( )z encM x k x M= (3.3)

with M0 being the magnetization at thermal equilibrium and enck the spatial encoding

frequency: ( )enc enck G t dtγ= ∫ . At positions where (2 1)

2encnk x π+

= the longitudinal

magnetization is zero and after applying an imaging RF pulse dark bands will appear in

the magnitude image. For magnitude based tagging analysis sharp edges of tag lines

are desired. This can be achieved by higher order polynomial tagging RF pulses [82] or

the Delays Alternating with Nutation for Tailored Excitation (DANTE) method [83],

which is based on a series of block pulses. The frequency response corresponds to a

series of Dirac functions ( )nf n fδ − ∆∑ convolved with the Fourier transform of the

envelope function. Thereby f∆ is given as the inverse of the inter-pulse delay. A linear

frequency spread is achieved by applying a gradient while exciting. Hence at periodic

position the longitudinal magnetization is tipped into the transverse plane and

subsequently spoiled by a crusher gradient.

To assess two-dimensional motion, the line tagging preparation is repeated with

orthogonal encoding gradient directions. Alternatively, tagging in polar coordinates

may be applied [84] resulting in star-shaped radial tagged pattern. Also, circular

tagging patterns can be generated by ring-shaped saturation bands [85]. Finally,

Nasiraei-Moghaddam et al. [86] extended these ideas to periodic circular and radial

tagging, achieved by constant RF-irradiation in combination with oscillating gradients

during tagging preparation.

29


Figure 6. Pulse sequence diagrams for motion encoded MRI. The encoding enck and decoding dek

gradients are in dark gray, while imaging, crusher and slice selection gradients are in light gray. The gradient coordinate system is aligned with the frequency encoding/readout direction (M), phase encoding direction (P) and slice select direction (S). After detection of the R-wave a tagging preparation block is applied followed by the imaging sequences for each individual heart phase. TE corresponds to the sequence’s echo time. a) 1-1 SPAMM/CSPAMM: Magnetization is spatially

modulated using encoding gradient enck . For CSPAMM imaging an additional image is required with a

180° phase shift of the second RF pulse (light gray). b) SENC imaging: Magnetization is modulated

using through-plane tagging. During read-out a demodulation gradient dek is applied. c)

DENSE/CDENSE imaging: Magnetization is modulated by 1-1 SPAMM tagging. During imaging the

modulation unwound using demodulation gradient de enck k= . d) Velocity encoding applies bipolar

waveform to encode velocity into the signal phase.

30

Figure 7 shows an example of a SPAMM prepared time series. To address tagline

fading over time the concept of Complementary Spatial Modulation of Magnetization

(CSPAMM) [87] has been proposed. Using equation (3.2) the longitudinal

magnetization of a 1-1 binomial SPAMM at time point TD is given as:

( ) ( )1 10 0, 1 cos

TD TDT T

z encM x t TD M e M k x e− −

= = − +

(3.4)

After tipping magnetization by flip angle α and using the complex representation of

the cosine, formula (3.4) becomes:

( ) ( ) 1 1 10 00, sin 1

2 2enc enc

TD TD TDik x ik xT T T

xyM M

M x t TD M e e e e eα− − −

−

= = − + + (3.5)

In the center of k-space the DC-peak containing signal 10 1

TDTM e

− −

is present. In

addition, two peaks at a distance of enck± from the k-space center result, containing

the tagging signal 10

2enc

TDik xTM

e e−

± . If a second data set is acquired with a 180° phase

added to the second tagging RF pulse (light grey in Figure 6 a), the sign of the harmonic

components is inverted:

( ) ( ) 1 1 10 00, sin 1

2 2enc enc

TD TD TDik x ik xT T T

xyM M


−

= = − − − (3.6)

Subtracting both images leads to cancelation of the DC-signal:

( ) ( ) 1 10 0, sin enc enc

TD TDik x ik xT T

xyM x t TD M e e M e eα− −

−

= = +

(3.7)

While the DC signal is effectively removed, tagline contrast to noise ratio (CNR) still

decreases with increasing temporal distance from the tagging preparation module due

to longitudinal relaxation of magnetization. This effect can be compensated for by

sweeping the flip angle [87].

31


Figure 7. SPAMM and CSPAMM tagging. Magnitude, phase and k-space images of 1-1 SPAMM tagged images for different trigger delays are shown on the left. In the first heart phase the blood pool is still present. Over time, tag lines fade. Similar in phase images the modulated phase is superimposed with the DC-phase of relaxed magnetization. While the modulated phase of SPAMM+ and SPAMM- has opposing signs (43ms) the phase of DC-magnetization has the same sign (673ms). In k-space the magnitude of the harmonic peaks is decaying while a DC-peak builds up. Upon subtraction of both SPAMM images the DC-peak is removed. It is noted that the magnitude images have been scaled individually for presentation, while k-space images have the same scaling.

Most current tagging acquisition schemes use two-dimensional imaging. The major

drawback of such an imaging strategy lies in its sensitivity to though-plane motion. The

heart contracts longitudinally, hence for different heart phases the myocardium is

imaged in different positions. Fischer et al. [88] proposed a slice tracking method,

32

which allows to image true myocardial contraction using 2D CPAMM imaging. Instead

of tagging the entire LV as in conventional 1-1 SPAMM only a thin slice is tagged while

a thick slab is excited during the imaging module thereby capturing potential through-

slice motion. Accordingly, resulting transverse magnetization is composed of the

tagged compartment, 1T relaxed signal from the tagged slice and signal from tissue

above and below the tagged slice. By employing the CSPAMM formalism only the

signal carrying the modulation is retrieved and, accordingly, potential through-plane

motion is captured. In order to quantify cardiac motion in three-dimensions, Ryf et al.

[89] introduced 3D acquisitions based on 3D tagging grids. With the introduction of 3D

tagging the problem of slice mismatch and through-slice motion was intrinsically

solved. However, initial implementations required a large number of successive breath

holds making the method cumbersome and practically challenging. Total scan

durations of 30-40min were reported, which are not practical in clinical routine. The

reason for the long scan duration lies in the fact that imaging the first harmonic peaks

requires a minimum spatial resolution which is given by:

1

2 enc

xk

∆ = (3.8)

which corresponds to half the tag-line distance. If higher order SPAMM is used, the

tagging modulation is no longer a pure cosine and, accordingly, higher order harmonics

need to be sampled. While for line tagging only two first harmonic peaks are present in

k-space for 2D grid tagging four peaks and 3D grid tagging 8 peaks need to be covered.

For 2D grid tagging, spiral readout trajectories have been proposed providing a

temporally efficient k-space coverage [90]. Also, localized k-space sampling schemes

only sampling k-space line in the proximity of the harmonic peaks have been proposed

[89]. These sampling schemes were further improved by the use of spatiotemporal

undersampling using k-t BLAST [13]. Further refinements of the 3D CSPAMM tagging

scheme by Rutz et al. [9] allowed reducing scan durations to three consecutive breath

holds thereby enabling studies in patients. Redundancy in k-space information was

used. Instead of imaging a 3D grid, three 3D volumes are acquired with 1D line tagging

in frequency encoding direction. The three volumes are rotated by 90° with respect to

each other and acquired with an anisotropic resolution.

33


3.1.3 Strain Encoding

Strain ENCoding (SENC) as proposed by Osman et al. [91] utilizes a 1-1 binomial

SPAMM preparation in slice-select direction (Figure 6b). Similar to equation (3.4) the

longitudinal magnetization after tagging preparation is given as:

( ) ( )0 cosz encM z M k z= (3.9)

At the time of imaging, the tissue of interest at position r

is stretched or squeezed in

tagging direction resulting in a spatial frequency ( ),v r t . Between slice excitation (with

a slice profile ( )f z ) and readout a demodulation gradient with demodulation

frequency dek− is applied. The resulting transverse magnetization after excitation

therefore reads:

( ) ( ) ( ) ( )( )1 10 0, sin 1 cos de

t tik zT T

xyM r t f z M e M v r z e e dzα− −

−

= − + ∫

(3.10)

Upon complex representation of the cosine equation (3.10) reads:

( ) ( ) ( )

( ) ( ) ( ) ( )

1

1 1

0

0 0

, , sin 1

2 2

de

de de

tik zT

xy de

t tiv r z iv r zik z ik zT T

M r t k f z M e e dz

M Mf z e e e dz f z e e e dz

α−

−

− −−− −

= − +

+

∫

∫ ∫

(3.11)

which results in:

( ) ( ) ( ) ( )( )

( )( )

1 1

1

00

0

, , sin 1 ,2

,2

t tT T

xy de de de

tT

de

MM r t k M e F k F k v r t e

MF k v r t e

α− −

−

= − + − +

+

(3.12)

with ( )F k being the Fourier transform of the slice profile. dek is adjusted by the user. If

dek is chosen close to ( ),v r t , the term ( )( ) 10,

2

tT

deM

F k v r t e−

−

approximates ( )0F

corresponding to the central lobe of the frequency response of the excitation pulse.

34

Hence it becomes the dominate part in equation (3.12). Consequently the transverse

magnetization can be approximated by:

( ) ( ) ( )( ) 10, , sin ,2

tT

xy de deM

M r t k F k v r t eα−

≈ −

(3.13)

( ),v r t can be estimated by the center of mass of ( )( ),deF k v r t−

from two

measurements with dek vk < and

dek vk > . An optimal set of dek is derived in [91] and the

discrete center of mass is approximated by

( )( )( ) ( )( )( )( ) ( )( ) ( )( )

, ,, Re ,

, ,de de de de

de de

k v k v k v k v

k v k v

k F k v r t k F k v r tr t v r t

F k v r t F k v r tµ β> > < <

> <

− + − = = − + −

. Osman et al.

[91] showed, that ( )( ),v r tβ can be linearized for the expected ranges of longitudinal

strain allowing to solve for ( ),v r t .

Similar to 2D tagging techniques slice mismatch over the cardiac cycle can be

compensated in combination with slice following [92]. For 3D strain estimation SENC

has been combined with in-plane displacement encoding [11] and tagging [93].

3.1.4 Motion analysis

A range of work has been published describing semi- or fully automatic tag line

identification and tracking utilizing prior knowledge to compensate for tagline fading,

using image filters and tag templates [94-96]. To generate deformation fields, the

space between tag lines or tag line crossings needs to be interpolated. Optical flow

methods have been used to overcome the necessity to interpolate [97,98]. Recently,

Arts et al. [99] and Wang et al. [100] have proposed localized modeling of the tagging

signal using cosine functions to derive pixel-by-pixel displacement fields based on

detecting local spatial frequency change between consecutive heart phases.

3.2 Phase based imaging techniques

3.2.1 Displacement encoding

In 1999 Aletras et al. [101] proposed a scheme termed Displacement Encoding with

Stimulated Echoes (DENSE) (Figure 6c). In contrast to SPAMM tagging, an additional

35


decoding gradient is used during the imaging module to generate a stimulated echo.

Accordingly, tissue that has displaced between the tagging and imaging module will

have a net phase:

enck xϕ = ∆ (3.14)

Cine DENSE [102] data can be obtained using fast readout methods such as echo

planar imaging (EPI) or spiral trajectories. In Figure 8, a cine DENSE imaging example is

shown. It is evident that the phase images show patterns corresponding to tissue

displacement between encoding and decoding.

Figure 8. Cine DENSE acquisition. The arrow indicates the encoding direction (Note: for better illustration the phase images were reconstructed from combined echo and anti-echo signals (cDENSE)).

Equation (3.6) describing the transverse magnetization after the imaging RF pulse is

modified to account for the decoding gradient as follows:

( ) ( ) 0 01 1 10 00 0, , sin 1

2 2enc t enc t enc t TD

TD TD TDik x ik x ik xT T T

xy t t TDM M

M x x t TD M e e e e e eα = = =− − −

− −= =

= = − + +

(3.15)

For static tissue 0t TD tx x x= == = and hence transverse magnetization is written as:

( ) ( ) 1 1 1 20 00, sin 1

2 2enc enc

TD TD TDik x i k xT T T

xyM M


− −

= = − + + (3.16)

36

10

2

TDTM

e−

represents the stimulated echo part located at the center of k-space. It is seen

that the magnitude of transverse magnetization decays exponentially with 1TD T and

is at best half of equilibrium magnetization.

The magnetization coming from longitudinal relaxation during the mixing time (TM)

between encoding and decoding is given by 10 1 enc

TDik xTM e e

−−

−

. It is apparent, that

this component has a phase linear in the spatial coordinate x with slope enck . According

to the Fourier shift theorem the linear phase in image space translates into a

displacement by enck in k-space. A third peak in k-space is present at position2 enck

representing the stimulated anti-echo. Given by 1 20

2enc

TDi k xTM

e e−

− the magnitude of the

stimulated anti-echo equals the magnitude of the stimulated echo. With a tissue

displacement of t TDx x x= = + ∆ , equation (3.16) can be written as:

( ) ( ) 1 1 1 20 00, , sin 1

2 2enc enc enc enc

TD TD TDik x x ik x i k x ik xT T T

xyM M

M x x t TD M e e e e e e eα− − −

− +∆ − ∆ − − ∆

∆ = = − + + (3.17)

For cardiac contraction x∆ does not correspond to a global displacement but depends

on the voxel position. Hence the additional linear phase introduced by encik xe− ∆ does

not lead to a global shift in k-space, but to a peak broadening.

37


Figure 9. DENSE acquisition. Echo, anti-echo, 1T and higher order harmonic peaks are present.

Depending on the size of the acquired k-space, magnitude and phase images may be contaminated by unwanted signal.

Both 1T - and anti-echo peaks can contaminate the acquired image (Figure 9). Since the

position of the undesired signal peaks depends on enck the signal can be shifted

outside the acquired k-space. However increasing enck may lead to unwanted phase

wraps for large displacements. Alternatively, the size of the acquired k-space can be

reduced by reducing the spatial resolution. With 1

enc

xk

∆ = the 1T -peak will appear at

the edge of k-space. To remove the 1T -peak complementary DENSE (cDENSE) can be

used [103]. similar to the CSPAMM approach [87]. After subtraction of the image with

complementary modulation, one obtains stimulated echo and anti-echo signals only:

( ) ( ) 1 1 20 0, , sin enc enc enc

TD TDik x i k x ik xT T

xyM x x t TD M e e M e e eα− −

− ∆ − − ∆

∆ = = +

(3.18)

38

If suppression of both 1T - and anti-echo peaks is desired the CANSEL method may be

used [104]. For this approach the phase of the second 90° pulse is not only changed

from 0° to 180° but also to ±90°. Accordingly, four images with different modulation

are acquired and equation (3.3) becomes:

( ) 0sin( )z encM x k x M= ± (3.19)

resulting in an additional cDENSE image:

( ) ( ) 1 1 20 0, , sin enc enc enc

TD TDik x i k x ik xT T

xyM M

M x x t TD e e e e ei i

α− −

− ∆ − − ∆

∆ = = −

(3.20)

After multiplication of equation (3.20) with i and addition to equation (3.18) only the

displacement encoded simulated echo signal peak remains:

( ) ( ) 10, sin 2 enc

TDik xT

xyM x t TD M e eα−

− ∆∆ = = (3.21)

A number of modifications to the original DENSE schemes have been proposed [105-

107] to improve scan efficiency and robustness to B0 field inhomogeneity. One source

of B0 inhomogeneity is deoxygenated blood inside the coronary venous system [108].

The coronary vein cross section and hence the blood volume is different for systole

and diastole [109]. To reduce the impact of venous blood induced B0 inhomogeneity it

was originally suggested to acquire an additional scan with identical parameters,

however without displacement encoding. Residual phase from this image corresponds

to local field variations and can be subtracted from the displacement encoded phase

maps for correction [101]. Alternatively the concept of peak combination HARP [110]

can be applied to DENSE. To this end, the regular DENSE acquisition is repeated with

inverted encoding/decoding gradients [111], however, doubling scan time.

Alternatively, Kim et al. proposed to remove the decoding gradient thereby using a

conventional CSPAMM imaging method [112,113]. Prior to reconstruction, the k-space

is then split into two halves containing either the stimulated echo or the stimulated

anti echo signal. After subtraction of the image phase the displacement is calculated.

39


3.2.2 Phase-contrast velocity encoding

In velocity encoded MRI the pulse sequence is designed to map velocity directly

[114,115]. Let us consider phase evolution of transverse magnetization in the presence

of a magnetic field gradient:

( ) ( ) ( )r t G t r t dtϕ γ= ⋅∫

(3.22)

with ( )r tϕ being the phase due to spatial trajectory ( )r t . The trajectory ( )r t

is

expanded using a Taylor series about the gradient waveform’s center of mass mt :

( ) ( ) ( ) ( )2 3( ;0)

1 1( )2 6r t m m m mG t r t r t t r t t r t t dtϕ γ = ⋅ + + + + ∫

(3.23)

For velocity encoding a gradient waveform is desired that refocuses static spins, i.e.

has zero net area and a first gradient moment ( )1m tG t dtγ= ∫ different from zero. A

bipolar gradient waveform as shown in Figure 6 d) fulfills these requirements. Its first

moment is given as 1bipolarM Gγ δ= ∆

withδ being the duration of a single gradient lobe

and ∆ the time from the beginning of the negative lobe to the beginning of the

positive lobe. With that the resulting phase is proportional to the velocity:

( )mG r tϕ γδ= ∆ ⋅ (3.24)

Storing the velocity information in the image phase, phase velocity imaging is similar to

DENSE prone to external phase perturbations, from concomitant fields, eddy currents

or B0 inhomogeneity. In order to compensate for B0 inhomogeneities, an additional

scan with a different encoding strength (different 1m

) is acquired. After calculating the

phase difference of such a 2-point acquisition, signal from static tissue and B0 induced

phase is canceled. Three-directional velocity data can be acquired using a 4-point

scheme [116]. The maximum encoded velocity without phase aliasing is given as:

1

encvmπ

γ=

∆

(3.25)

40

with 1m∆

being the difference in first gradient moments between two encoded

measurements. For cardiac imaging a encv of 10-25cm/s is typically used [117]. This

requires the application of strong velocity encoding gradients leading to unwanted

background phase offsets due to concomitant fields. Rapid switching of the velocity

encoding gradients can lead to residual eddy current induced phases. To compensate

for unwanted background phases, the phase of regions with static tissue can be used

for background phase correction [118]. Alternatively, phantom calibration may be used

[119] at the expense of additional scan time. Finally, magnetic field monitoring may be

employed to estimate the spatial-temporal behaviors of eddy currents to guide

background phase correction [120].

3.3 Magnitude and phase based imaging techniques

With HARmonic Phase (HARP) analysis [121] for SPAMM and CSPAMM tagging a time

efficient algorithm to tracking cardiac motion is available. The principle of HARP is

illustrated in Figure 10. The HARP method utilizes a band-pass filter in k-space in order

to isolate a single harmonic peak. According to equation (3.5) a single signal peak

remains upon filtering:

10( , ) ~2

enc

tik xTM

S x t e e−

(3.26)

Accordingly, a linear phase ramp proportional to enck is created assigning specific

phase values to material points in the spatial domain. By identifying these phase values

in different cardiac phases, the trajectory of material points can be reconstructed.

Upon acquisition of a second image with a tag pattern that is angulated to the initial

acquisition, the desired phase values are located on crossings of iso-phase lines of the

combined phase image. To find a unique solution it is assumed, that the displacement

is less than half the encoding distance.

41


Figure 10. HARP and peak combination HARP. CSPAMM data is filtered in k-space to separate signal of the harmonic peaks. Upon Fourier transformation a phase modulation pattern is obtained. For peak combined HARP, both images are multiplied with each other after taking the complex conjugate (†) of one of them. The phase modulation is doubled but potential off- resonance phase is canceled.

42

Similar to DENSE, HARP is sensitive to phase accumulation due to B0 inhomogeneities.

Ryf et al. [110] introduced peak combination HARP in order to make HARP more

resistant to field inhomogeneities (Figure 10). Based on CSPAMM tagging and equation

(3.7) the signal over time is given as:

( ) ( ) ( ) ( )( )00,

0sint

readout prephaseenc enci B x t G t x dt k xik x ik xS t M e e e dx

γ γα

′ ′+ −− ∫ = + ∫ (3.27)

with ( )readoutG t being the readout gradient, prephasek the prephasing modulation and

( )0 ,B x t the temporally and spatially varying B0 field. Equation (3.27) can be recast to:

( ) ( )( ) ( ) ( ) ( )0 00 0

, ,

0sint t

enc readout prephase enc readout prephaseik x i B x t G t xdt k x ik x i B x t G t xdt k xS t M e e dx

γ γα

′ ′ ′ ′ ′ ′+ + − − + + − ∫ ∫= + ∫

(3.28)

The time points at which the two harmonic peaks are sampled are defined as:

( )1

1 0:

t

readout prephase enct G t dt k kγ ′ ′ − = − ∫ (3.29)

( )2

2 0:

t

readout prephase enct G t dt k kγ ′ ′ − = ∫ (3.30)

It is evident, that the accumulated phase due to 0( , )B x t differs at the two k-space

positions by:

( )2

10 ,

t

peak tB x t dtϕ γ ′ ′∆ = ∫ (3.31)

Assuming a small change 1 20 ( )t tB x→∆ between 1t and 2t the phase difference becomes:

( )1 20 2 0 1( ) ,t t

peak B x t B x t tϕ γ → ∆ = ∆ + ∆ (3.32)

The major contribution of B0 stems from the temporal separation of consecutive heart

phases which is in the range of 20-40ms [90,110]:

( )1 20 2 0 1( ) ,HP HPt t

heartphase HP HP HPB x t B x t tϕ γ → ∆ = ∆ + ∆ (3.33)

with 2 2HPt t>> and HPt t∆ >> ∆ . Neglecting the change of B0 during single readouts, the

k-space can be divided in two separate k-spaces by HARP filtering the two harmonic

43


peaks and B0 phase is canceled upon taking the complex conjugate of one and

multiplication of both filtered images [110].

3.4 Motion parameters

3.4.1 Rotational motion

Rotation is measured as angular change of material points in the short-axis view

perpendicular to the LV long-axis relative to a reference heart phase. LV twist is

derived from rotation angles as:

LV apex basetwist angle angle= − (3.34)

from which LV torsion is derived as:

apex baseLV

apex base

angle angletorsion

d −

−= (3.35)

with apex based − being the distance between the apical and basal position [23].

An alternative method to estimating global rotation and LV twist parameters directly

from k-space of 2D line tagged images has been proposed. Rotation in image space

corresponds to rotation in k-space. Hence rotational motion from one heart phase to

the next can be estimated by 2D cross correlation of magnitude k-space based on the

proposed Fourier Analysis of Stimulated echoes (FAST) method [122,123].

Rotational motion has been found to be altered in patients with severe aortic stenosis

[23], acute changes in LV load [124], dilated cardiomyopathy [125], hypertrophic

cardiomyopathy [126] and hypertensive heart disease [127].

3.4.2 Tissue deformation

To characterize cardiac mechanics, material deformation in circumferential, radial and

longitudinal direction is of interest. One-dimensional circumferential, radial and

longitudinal Lagrangian strain can be calculated as:

44

( )1

refD

ref

L t LE

L−

= (3.36)

With ( )L t and refL being a contour length as function of time and at a given reference

point. To describe the full deformation, the three-dimensional strain tensor is

necessary:

xx xy xz

yx yy yz

zx zy zz

E E EE E E E

E E E

=

(3.37)

E is symmetric and after a coordinate transformation: ( ) ( )x y z r c l→ into

cylindrical coordinates (r: radial, c: circumferential, l: longitudinal) radial,

circumferential and longitudinal strain can be extracted:

rr rc rl

rc cc cl

rl cl ll

E E EE E E E

E E E

=

(3.38)

To estimate the full strain tensor from displacement fields obtained with MR one has

to calculate the spatial derivative of the displacement fields leading to the deformation

gradient tensor:

( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

, , , , , , , , ,

, , , , , , , , ,,

, , , , , , , , ,

x X Y Z t x X Y Z t x X Y Z tX Y Z

y X Y Z t y X Y Z t y X Y Z tF R t

X Y Zz X Y Z t y X Y Z t z X Y Z t

X Y Z

∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

= ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

(3.39)

in which R

denotes a position given in coordinates (X, Y, Z) and (x, y, z) correspond to

the coordinates in the reference frame of the deformed state. Hess et al. [11]

presented a computationally straightforward approach to estimate the temporal

course of the deformation gradient tensor by tracking the local canonical basis vectors

( )1 2 3, ,E E E

for each point R

from an initial reference heart phase over time to

( ) ( ) ( )( )1 2 3, ,e t e t e t

. The deformation gradient tensor can be calculated by:

45


( )( )( )( )

( )1

1

2 1 2 3

3

T

T

RT

e t

F t e t E E E

e t

−

=

(3.40)

The deformation gradient tensor can be decomposed by polar decomposition:

( ) ( ) ( )R R RF t R t U t= (3.41)

where ( )RU t corresponds to the right stretch tensor and ( ) ( )3 ; ,RR t O t R∈ ∀

. Hence

( ) ( ) ( )2T

R R RF t F t U t= (3.42)

holds. The Lagrangian strain tensor is computed from the right stretch tensor by:

( ) ( )( )212R RE t U t id= − (3.43)

It is noted, that if the spatial derivative of the velocity field is calculated, the strain rate

tensor field is obtained. Strain rate values have been used for clinical purpose as well

[41,128,129]. From strain rate tensors the strain tensor can be obtained after temporal

integration.

The analysis of tissue deformation is of great value for assessing myocardial infarction.

Improved sensitivity and specificity in detecting dysfunctional tissue has been reported

when using tagging methods relative to standard cine imaging [130]. Reduced

circumferential strain was found in dilated [131] and hypertrophic [41]

cardiomyopathies. Moreover, the timing of contraction has been analyzed by

investigating the temporal coherence of circumferential strain. As a result of impaired

signal conduction in the heart, patients with Left Bundle Branch Block (LBBB) or

anterior septal myocardial infarction (MI) presented significant dyssynchrony

[132,133].

46

Chapter 4 Undersampled Cine 3D Tagging for Rapid Assessment of Cardiac Motion1

4. Velocity measurements with MRI

4.1 Introduction

Patients with myocardial infarction (MI), coronary artery disease (CAD) or impaired

signal conduction in the heart such as left bundle branch block (LBBB) suffer from

reduced cardiac function. In patients undergoing cardiac resynchronization therapy

(CRT) [134] it is of great interest to generate a mechanical map indicating local

dyssynchrony [135]. Among the various mechanical parameters, cardiac strain and

torsion have been shown to be valuable clinical parameters in patients with MI [26]

or aortic stenosis [23,136]. Cardiovascular magnetic resonance (CMR) offers a

functional imaging modality to assess cardiac motion pattern and synchrony of

contraction [137,138] non-invasively.

Up to date multiple approaches have been used to investigate myocardial motion

such as displacement encoding with stimulated echo (DENSE) [101,139], velocity

encoding [140-142], tagging by spatial modulation of magnetization (SPAMM) [81]

and complementary spatial modulation of magnetization (CSPAMM) [87]. These

methods can either be applied in conjunction with two dimensional (2D) or three

dimensional (3D) imaging. In 2D acquisitions, multiple slices are imaged along the

left ventricle (LV) and strain maps are calculated slice-by-slice. Two-dimensional

acquisitions require additional techniques in order to compensate for through-plane

motion. To this end, slice following [88,143], acquisition of additional orthogonal

slices [144] or the encoding of through-plane displacement [145,146] (zHARP) have

1 Published in: Stoeck CT, Manka R, Boesiger P, Kozerke S. Undersampled cine 3D tagging for rapid assessment of cardiac motion. J Cardiovasc Magn Reson 2012;14:60.

47

Undersampled Cine 3D Tagging for Rapid Assessment of Cardiac Motion0F

been proposed. While reconstruction of 3D strain patterns from two bi-planar

acquisitions does require interpolation, slice-following techniques provide only a

projection of true 3D motion onto a 2D subspace. Using zHARP additional gradients

in through-slice direction are applied to estimate through-plane displacement by

solving a set of linear equations [145].

To circumvent the need for interpolation and slice-following techniques, true 3D

tagging has been proposed [147]. By applying modulation of magnetization in all

three spatial directions, through-plane motion is intrinsically captured and hence no

slice-following is needed. Furthermore, 3D acquisition provides full LV coverage and

yields an intrinsically higher signal-to-noise (SNR) compared to 2D imaging. While

cine 2D acquisitions easily fit into a single breath hold, 3D acquisitions require

multiple breath holds with long duration [147]. Further approaches attempted to

shorten scan time to four breath holds of 21 R-R intervals each [89] by only

sampling around the harmonic peaks in k-space. These efforts, however, led to a

lower spatial resolution in the two phase encoding directions. A different approach

was proposed by Zhong et al. [105] using a 3D DENSE acquisition covering the entire

left ventricle during free breathing. However, acquisition durations of up to 20 min

[10] depending on navigator efficiency were reported and hence feasibility for

routine clinical use may be questioned. Rutz et al. [9] introduced an accelerated 3D

CSPAMM method only requiring three navigator gated breath holds of 18 R-R

intervals each. This implementation was tested in a clinical study with patients

suffering from MI and LBBB [132] providing 3D maps of synchrony and magnitude of

contraction. To address issues of different breath hold levels the data obtained

from respiratory navigators was used to correct for potential offsets. In their study

the respiratory navigator was placed onto the right hemi-diaphragm and thereby

respiratory induced displacement of the heart was approximated according to a

linear relationship between liver and heart displacement [148]. The accuracy of the

linear translation from motion of the lung liver interface to the position of the heart

is still being debated. Nehrke et al. [149] reported a strong correlation of the

displacement of the right hemi-diaphragm and the heart, but also found significant

subject dependent variability in the correction coefficients especially comparing

48

inspiration and expiration. Subject dependency of the translation of breathing

induced liver motion to bulk motion of the heart has been confirmed by Moghari et

al. [150].

In general, data acquisition can be accelerated by undersampling in spatial and

temporal dimensions. Among the various approaches, two strategies have gained

significant attention. Compressed sensing (CS) [151] employs non-linear

reconstruction methods to recover information from randomly or pseudo-randomly

undersampled data. Inherently, compressed sensing algorithms require incoherent

sampling and hence become applicable if a sufficient number of phase-encodes

exists. In case of one-dimensional tagging preparation, the number of Cartesian

phase-encodes orthogonal to the tag direction can be greatly reduced providing an

efficient and simple way for scan time reduction. In consequence the degrees of

freedom to generate random sampling patterns become very limited and the

application of compressed sensing appears less favorable in this particular

application.

The second acceleration strategy involves uniform spatiotemporal undersampling in

conjunction with linear reconstruction algorithms. In k-t BLAST and k-t SENSE [13]

low spatial but full temporal resolution training data is used to unfold signal aliasing

resulting from data undersampling. The drawback of these methods relates to

temporal filtering if undersampling rates increase. To address this issue, Principal

Component Analysis (PCA) of the spatial-temporal frequency domain data was

introduced and results obtained with k-t PCA show improved temporal fidelity [12].

Although k-t undersampling has been extensively applied in CMR including cine and

real-time imaging [152,153], perfusion [154-159] and phase contrast imaging [160-

162], only few attempts of applying k-t undersampling to tagging have been

reported [163,164].

The objective of the present study was to implement and test k-t undersampled

whole-heart 3D CSPAMM tagging for rapid assessment of cardiac motion. The

performance is demonstrated on simulated data, data obtained in healthy subjects

and in patients with myocardial infarction.

49


4.2 Methods

4.2.1 k-t PCA

To reconstruct undersampled 3D tagging data, k-t PCA [31] is used. Similar to k-t

BLAST [30], acquired data is divided into 1) training data with low spatial resolution

(in phase encoding directions ky / kz) but full temporal resolution and 2) k-t

undersampled data with high spatial resolution and full temporal resolution. The

training data ptrain(x,t) is Fourier transformed to be represented in the spatial-

temporal frequency domain (x-f). Using principal component analysis ptrain(x,f) is

then decomposed into a basis of temporally dependent functions b(fj)

corresponding to the principal components (pc) and spatially dependent weighting

coefficients wtrain(x) in x-pc space according to:

( ) ( ) ( )train

Ttrain i j j ip x , f = b f w x

(4.1)

The aliased signal at point (x, fj) resulting from R-fold undersampling can be written

as:

( ) ( ) ( )1

,R

Talias j j i

i

p x f b f w x=

=∑

(4.2)

with w(xi) denoting the spatial weighting coefficients of the unaliased image. Hence

the aliased signals Palias(x,f) can be expressed as:

with and (4.3)

Finally, the unaliased spatial weighting coefficients are obtained by solving:

( )+H Hx aliasw = E E E + PψΘ Θ (4.4)

where Θ represents an estimate of wx from training data, Ψ denotes noise variance,

H conjugate transpose and + the Moore-Penrose pseudo-inverse.

50

4.2.2 Computer simulation

All simulations were performed in Matlab (The MathWorks, Natick, MA, USA). Three

orthogonal stacks with line tagging modulation in readout direction were generated

(Figure 11 a).

Undersampling factor

Matrix size kx×ky

Slices kz

Heart phases

Training profiles (ky×kz)

Rnet

3 65×15 15 24 25 (5×5) 2.3

4 65×20 15 24 25 (5×5) 3

5 65×20 15 24 25 (5×5) 3.5

8 65×16 15 24 25 (5×5) 4.4

Table 1. Parameters used for numerical simulation.

The CSPAMM method [87] was simulated to avoid tag line fading. The model

consisted of a contracting left ventricle as well as static tissue representing chest

wall and liver. Circumferential shortening and rotation as measured in a healthy

subject at basal and apical level was linearly interpolated along the long-axis to

create three-dimensional motion data. Peak circumferential shortening was 18.8%

and 17.8% for base and apex, respectively. Peak rotation was -3.2° and 10.3° for

base and apex (Figure 11 b-d). Longitudinal shortening obtained from the same in-

vivo subject was incorporated. Simulations of undersampled data acquisition were

compared to fully sampled simulated data sets with equivalent spatial and temporal

resolution. The matrix size was set according to practical values [9,132] (Table 1).

Gaussian noise was added to k-space data before undersampling resulting in a SNR

of 25 prior to undersampling. Both undersampled and training data were extracted

from the computer model (Figure 12 b). Undersampling rates of R = 3, 4, 5 and 8

were simulated. In all simulations, five training profiles were used in ky and kz

direction resulting in a total of 25 training profiles.

51


Figure 11. Numerical simulation. Three stacks with orthogonal line tag pattern were simulated (a). As input for the model, longitudinal shortening (b), rotation (c) and circumferential shortening (d) obtained from one in-vivo acquisition were used.

In order to study regional wall motion abnormalities, myocardial infarctions of

different severity were simulated. To this end, radial shortening in the lateral sector

was changed from 100% (no infarction) to 0% (completely static) in steps of 10%

(Figure 14). The reduction of myocardial motion in the infarcted zone was applied

transmurally along the entire long axis of the left ventricle. Reduction of radial

shortening directly reduced the circumferential contraction. In order to assure a

smooth transition between infarcted and healthy tissue, the infarcted tissue was

continuously “attached” to the adjacent healthy tissue, by reducing the motion

damping factor continuously over a sector of 40° on both ends of the infarcted

region.

52

Figure 12. Sequence diagram (a) and sampling pattern for k-t undersampling (b). After detection of the R-wave the tagging preparation is applied, followed by two repetitions of undersampled data and training data acquisitions for each stack.

4.2.3 In-vivo measurements

Eight healthy subjects (7 male, age: 27.5±3.5 years) and five patients with

myocardial infarction (5 male, age: 54.8±5.9 years, 1 patient with acute myocardial

infarction post percutaneous coronary intervention (PCI), 4 patients with chronic

myocardial infarction) were studied. Imaging was performed on a 1.5T Philips

Achieva System (Philips Healthcare, Best, the Netherlands) using a 5 channel cardiac

receiver array. Written informed consent was obtained from all subjects and the

protocol was approved by the institutional review and ethics boards.

Tagged images were acquired using an ECG triggered multi-shot EPI sequence with

sequence parameters listed in Table 2. As illustrated in the sequence diagram in

Figure 12 the tagging preparation was applied within 10 ms after the detection of

the R-wave. As the first RF pulse used for tagging preparation was applied

selectively in phase encoding direction, signal outside the field-of-view was

suppressed after CSPAMM subtraction and hence reduced field-of-view acquisition

53


could be performed [88]. The imaging sequence was repeated to acquire three

orthogonally tagged stacks. For each stack 21-24 heart phases were recorded.

Undersampling factor Fully sampled / R3 Fully sampled / R4

Matrix size kx×ky 28×15 28×20

Phase-encodes kz 15 15

Receiver bandwidth 314Hz/pixel 314Hz/pixel

Spatial resolution 3.8×7.2×7.2mm3 3.8×5.4×7.2mm3

Heart phases 21 24

Temporal resolution 30.3ms 30.3ms

EPI factor 5 5

TFE factor 5 5

TE/TR 2.8ms/6.1ms 2.8ms/6.1ms

R-R intervalsundersampled 18 18

Rnet 2.25 3

Training profiles (ky,kz) 25 (5/5) 25 (5/5)

R-R intervalstraining 6 6

R-R intervalsfull 3x18 3x18

Tag line distance 7mm 7mm

Table 2. Imaging parameters for the acquisition of fully sampled reference and undersampled data (R = 3 and 4).

Fully sampled data was acquired in three consecutive breath holds. To guarantee

similar breath hold position for each tagged stack a pencil beam respiratory

navigator placed on the right hemi-diaphragm was used. The position of the lung

liver interface was monitored at the beginning of each breath hold and

displacements within a 5 mm gating window were accepted. The breath hold was

repeated if the subject’s breath hold level was not within the given window.

Retrospective undersampling was applied with reduction factors of R=3 and 4.

Prospectively undersampled data were acquired according to the schematic shown

54

in Figure 12b in an additional breath hold. To facilitate comparison, all imaging

parameters except for undersampling factors were kept identical for fully sampled

and undersampled data acquisitions. For undersampling factors R = 3 and 4 the

corresponding sets of parameters is given in Table 2. Prior to image reconstruction,

the 5-channel coil array data were compressed into a single virtual coil data set

using the array compression method proposed by Buehrer et al. [165].

4.2.4 Data analysis

Epicardial and endocardial contours were manually drawn for each slice of interest

and a midmural contour was calculated. This contour was tracked over time using

the peak combination harmonic phase (HARP) [110,121] algorithm implemented in

an in-house software. Rotational motion and circumferential shortening was

calculated from tracked contours as previously described by Ryf et al. [166]. Curves

of circumferential shortening and rotation over the cardiac cycle were fitted by 8th

order polynomials, and maxima were found by estimating roots of the derivative.

From the mean rotation over the contour, torsion was derived by taking the

difference in peak rotation at the most apical and the most basal level [24]. Analysis

of peak circumferential shortening and rotation was performed in six sectors per

slice in 9 slices for computer simulation and 8-9 slices in in-vivo experiments.

Comparisons were performed sector-wise and are reported for the entire LV.

For simulation the tracking results from fully sampled data were used as ground

truth reference. For in-vivo measurements the mean of paired data points was used

as reference. In order to facilitate comparison the initial contour was kept the same

for the fully sampled reference and the retrospectively undersampled data in

simulation and in-vivo. In the comparison of fully sampled data with prospectively

undersampled acquisitions, contours were redrawn to account for changes in

breath hold position and/or patient motion in-between scans.

Analysis of simulated data was done by calculating the relative difference defined

as: rel R=1 R>1 R=1 R=1error = max(motion ) - max(motion ) max(motion ) - min(motion ) .

The fully sampled data was used as reference. Relative differences ± one standard

deviation are reported in % for circumferential shortening and rotation. In order to

estimate the correlation between undersampled and reference data linear

55


regression was performed correlating circumferential shortening and rotation of

reference data and undersampled data. Regression slope, offset and the

corresponding 95% confidence interval were estimated as well as the correlation

coefficient R2 and the standard error of the estimate (SEE). The SEE is given in % of

the range of motion and is defined as ( )N 2i ii=1

1SEE = x - xN - 2

′∑ with N being the

number of points, xi denoting measurement data and xi’ corresponding values

derived from linear regression. For in-vivo imaging, peak circumferential shortening

and rotation were compared using Bland Altman analysis. Mean differences and the

95% levels of agreement corresponding to 2 standard deviations (2SD) are reported.

Linear regression was performed on peak circumferential shortening and rotation.

Regression slopes, offsets, correlation coefficients and the SEE are reported.

Comparing reference data and retrospectively undersampled data, the HARP

tracking performance of contour coordinates was studied based on contour vertex

definitions in polar coordinates. Similar to the analysis of peak circumferential

shortening and rotation, Bland Altman and linear regression analysis were

performed.

Patient data are reported using bull’s-eye plots of peak circumferential shortening,

and late gadolinium enhancement (LGE). The centre of the bull’s-eye plots

represents the apex and the outer ring the base of the LV. For LGE images the

average myocardial signal intensity per slice and sector normalized to the signal

intensity measured in infarcted tissue is shown. Sectors were grouped into two

groups: 1) non-viable sectors having more than 50% of the area presenting LGE and

2) viable sectors having less or equal to 50% of the area presenting LGE. Peak

circumferential shortening was estimated for all sectors in each group and the

median, 50th percentiles and 90th percentiles were estimated and presented in box-

plots. Statistical significance of the differences in peak circumferential shortening

between both groups were estimated by a two-tailed Wilcoxon signed-rank test.

The results were Bonferroni corrected for repeated testing. A p-value less than 0.05

was considered statistically significant.

56

4.3 Results

4.3.1 Computer simulation

Normalized differences in peak circumferential shortening and rotation

between undersampling factors of R = 3, 4, 5 and 8 and fully sampled data used

as reference are shown in Figure 13a-b. Errors in circumferential shortening and

rotation were below 5% for undersampling factors of R = 3-5 and R = 3, 4,

respectively. At R = 8 errors in circumferential shortening and rotation were 2.5

and 3.1 times greater compared to data obtained with R = 4. The differences in

torsion between undersampled and fully sampled data were -0.13°, 0.42°, 0.95°

and 1.85° for R = 3, 4, 5 and 8, respectively.

Figure 13. Comparison of circumferential shortening and rotation for fully sampled reference data and retrospectively undersampled data from computer simulation. Relative differences are presented as average over the entire LV (a-b) along with slope and offset of linear regression and the corresponding correlation coefficient R2 and the standard error of the estimate (SEE) (c-j).

57


Figure 13c-j shows regression slope, offset, correlation coefficient and SEE for R

= 3, 4, 5 and 8. The 95% confidence intervals are presented as error bars for

fitted slopes and offsets.

Figure 14 shows the result of motion tracking in the presence of simulated

infarction. Peak circumferential shortening in an equatorial slice is plotted for

the reference vs. undersampled data. Linear regression was performed,

resulting in a slope of 1.01 (±0.04 95% confidence interval) and an offset of -

2.01% of the range of contraction (±4.79% 95% confidence interval).

Figure 14. Comparison of peak circumferential shortening from undersampled (R = 3) and fully sampled simulated data. Myocardium was divided into three groups: infarction (I), which covers a sector of 80° (22% of myocardium), healthy tissue (H) and infarct adjacent (A) tissue “attaching” infarcted to healthy tissue over a sector of 40° (11% of myocardium). For infarcted tissue, different degrees of immobilized tissue ranging from 0% to 100% were simulated.

4.3.2 In-vivo measurements

Figure 15 shows short axis slices reconstructed from fully sampled and 3- and 4-

fold retrospectively and prospectively undersampled data. Frames at 27 ms

after detection of the R-wave, at end systole (279 ms) and at mid diastole (559

ms) are shown.

Linear regression analysis performed on fully sampled and retrospectively

undersampled is shown in Figure 16. For each regression the equations of the

linear fit, the correlation coefficients R2 and the SEE are given. Figure 16 a-d

58

show the analysis of polar coordinates of tracked points and Figure 16 e-h

demonstrate sector-wise comparison of time curves of circumferential

shortening and rotation for R = 3 and 4.

Figure 15. Comparison of short-axis views reconstructed from fully sampled (ref) and 3- and 4-fold retrospectively (retrospect) and prospectively (prospect) undersampled data. Three different time points are shown.

59


Figure 16. Linear regression analysis for point-wise and sector-wise comparison of fully sampled (ref) and retrospectively undersampled (und) data in healthy volunteers (R=3 and 4). Point-wise comparison was performed for polar coordinates r (a, c) and φ (b, d). For circumferential

shortening (e, g) and rotation (f, h) entire motion curves were compared per sector across the entire LV.

Figure 17 shows the Bland-Altman comparison of fully sampled and

retrospectively undersampled in-vivo data for R = 3 and 4. Dashed lines

represent the mean difference (light grey) and the 95% limit of agreement

(2SD) (black). Figure 17 a-d provides the comparison of radial coordinates (r =

radius and φ = angle) of tracked contour points. Mean differences ± 2SD of r

were 0.0±3.3% and -0.2±4.1% for R=3 and 4 and -0.2±1.9° and -0.3±2.2° for φ. In

Figure 17 e-h Bland-Altman plots for peak circumferential shortening and peak

rotation are given. The mean differences ± 2SD for circumferential shortening

were -0.2±4.1% and -0.1±4.2% for R=3 and 4. For rotation, mean differences ±

2SD were 0.5±1.8° and 0.7±1.7° for R=3 and 4. The mean differences of torsion

were 0.45±2.22° (p = N.S.) and 0.05±2.24° (p = N.S.) for R=3 and 4, respectively.

Figure 18 shows the resulting Bland-Altman analysis of peak motion (a-d) and

correlation between full time curves of motion (e-h) comparing fully sampled

data with data acquired with prospective undersampling (R=3 and 4). Mean

differences ± 2SD of peak circumferential shortening were -0.14±5.18% and -

0.71±6.16% for R = 3 and 4. Mean differences of peak rotation were found to

be 0.44±1.80° and 0.73±1.67° for R = 3 and 4 while differences in torsion were

0.48±4.20° (p = N.S.) and 0.03±4.48° (p=N.S.) for R = 3 and 4, respectively.

Bull’s-eye plots of peak circumferential shortening and profiles of

circumferential shortening and rotation derived from undersampled (R = 4) and

60

fully sampled data are compared in Figure 19 for one healthy subject. Spatially

depend differences are not observed.

Figure 17. Bland Altman plots of point-wise and sector-wise comparison of fully sampled and retrospectively undersampled in-vivo data (R=3 and 4) in healthy volunteers. Mean differences (grey) and 95% levels of agreement (2SD) (black) are indicated by the dashed lines. Analysis was performed on the entire LV. Point-wise comparison was performed for the polar coordinates r (a, c) and φ b, d) for each tracked point. Circumferential shortening (e, g) and rotation (f, h) were

compared per sector.

Figure 18. In-vivo results of the comparison between fully sampled reference data (ref) and data acquired with an acceleration rate of R=3 and 4 (und). Mean differences (grey) and 95% level of agreement (2SD) (black) are shown for peak circumferential shortening (a, c) and rotation (b, d) of the entire left ventricle. Motion curves of circumferential shortening (e, g) and rotation (f, h) of undersampled and reference data are plotted against each other and linear regression was performed.

Figure 20 compares circumferential shortening obtained from undersampled

and fully sampled reference data for the five patients in relation the LGE

findings. Differences in peak circumferential shortening in sectors with more

than 50% of their area presenting LGE and sectors with less than 50% LGE were

statistically significant in all patients. Mean difference ± 2SD in torsion between

61


undersampled and fully sampled reference data in patients was 0.72±2.14°. The

SNR in the fully sampled in-vivo data was 36±12 on average.

Figure 19. Comparison of circumferential shortening for fully sampled data and 4-fold undersampled data. The first column shows maps of peak circumferential shortening for fully sampled b) and undersampled data c). Resulting motion profiles taken from an equatorial slice are shown for circumferential shortening (d, e) and rotation (f, g). The dots represent the actual data points while the line represents the polynomial fit.

62

Figure 20. Maps of peak circumferential shortening (csh) for five patients with myocardial infarction. The top row represents results from fully sampled data while the second row shows data from prospectively undersampled acquisitions. The third row shows the result of late gadolinium enhancement imaging (LGE). The myocardial signal intensity post contrast was averaged over each sector and normalized to the signal intensity from completely infarcted tissue. The bottom row shows box-plots of peak circumferential shortening for sectors with more than 50% late gadolinium enhanced signal (grey) and sectors with less than 50% late gadolinium enhanced signal (black). The box represents 50% of the data points and the error bars 90%. Statistical significance is indicated by # for p < 0.002 and * for p < 0.0002.

4.4 Discussion

In this work undersampled 3D CSPAMM tagging in combination with k-t PCA

has been implemented and validated.

The analysis of simulation results has revealed a maximum applicable

acceleration factor of four. Generally, good correlation was found between fully

sampled and retrospectively undersampled data over the entire left ventricle.

Analysis of relative differences in circumferential shortening showed a slight

decrease in error going from the apex towards the base of the heart. As motion

was normalized for each slice, this observation is associated with the low

magnitude of contraction of apical myocardium.

63


Different transmural extensions of infarcted tissue were investigated by

computer simulation. Motion analysis showed a good correlation between

undersampled and fully sampled reference data. Transmural reduction of

contraction as low as 20% could be distinguished from healthy fully contracting

tissue. Although fully infarcted tissue was simulated as well, sector-wise

analysis always showed contraction greater than 6%. This is due to the choice

of the position and size of the sectors used for analysis. Sectors with non-

contracting tissue contained slightly contracting neighbouring tissue, which

leads to a non-zero average circumferential shortening within a sector.

In-vivo comparison between fully sampled data and retrospectively

undersampled data showed good agreement as the mean difference was less

than 1% (% of range of motion). Differences between reference data and

prospectively undersampled acquisition were found to be larger in comparison

to differences seen relative to retrospectively undersampled data. This finding

is related to multiple issues. On one hand, reference data and undersampled

data were acquired in two consecutive scans. Despite the use of a gating

respiratory navigator, different breath hold levels are possible and slices used

for analysis might hence differ in position. On the other hand the fully sampled

reference data itself was acquired in three consecutive breath holds, which,

despite the use of a respiratory gating window of 5mm, can lead to stack

misalignment within the reference data. The resulting circumferential

shortening is dependent on the transmural position of the tracked contour. If

stack misalignment occurs a contour that appears to be midmural in one stack

can be positioned more epicardially or endocardially in the consecutive two

stacks from which the motion orthogonal to the first stack is derived from.

Hence a contour point is tracked at three different transmural positions.

Therefore the motion profiles obtained from fully sampled data, used as gold

standard reference in this work, might have been compromised. Image

registration was not performed in this study. The implementation of tailored

registration algorithms that can handle orthogonal tagging modulations

requires further investigation.

64

Maps of peak circumferential shortening as well as the corresponding motion

profiles were found to agree well for reference and undersampled data. The

magnitude of circumferential shortening is comparable to previously reported

values [9,132,167,168]. Besides potential motion smoothing, expressed by the

positive mean difference for rotation, a slice by slice comparison of

prospectively undersampled and fully sampled data might have been biased by

an offset in breath hold level for both acquisitions.

In this study, standard 2D single slice tagging data were not available for

reference. In order to capture through-plane motion and hence make data

comparable to 3D tagging, non-standard extensions of 2D tagging such as slice

following [143] or zHARP [145] are required. Accordingly, assessment of error in

the present work was relative to fully sampled 3D CSPAMM data only, which is

a clear limitation. Nevertheless, there have been previous records of validating

3D CSPAMM on healthy subjects and patients, which may serve as benchmark

[9,132].

Spatial resolution in each of the three orthogonal stacks in 3D CSPAMM may be

considered coarse (3.8×5.4-7.2×7.2mm3). The resolution given in readout

direction is, however, directly linked to the tagline spacing when using HARP

analysis. Higher temporal resolution (< 30ms) is desirable as this allows

separating data in x-pc space further and hence improves reconstruction

accuracy in k-t PCA. However, this results in more heart phases and hence more

RF excitations per cardiac cycle reducing the contrast-to-noise ratio of the

tagged data.

Five patients with myocardial infarction were examined using undersampled

tagging and LGE imaging. Maps of circumferential shortening derived from

reference data and prospectively undersampled data agreed well and infarcted

regions could be localized. Direct correlation of peak circumferential shortening

with the area of delayed enhancement was found to be only moderate. A

potential limitation of infarct detection is related to averaging of motion within

sectors. A six-sector per slice model [9,132] results in 16.7% of total myocardial

mass captured per sector and per slice. For example, non-viable tissue in border

zones of infarction is passively moved and compressed and hence the extent of

65


motion abnormality may be overestimated. This issue may be addressed by

increasing the number of sectors per slice and by using multiple circumferential

contours covering the entire transmural extent in future work.

Several strategies may be envisioned to shorten the relatively long breath hold

durations (~20 sec) of the present protocols. First, sampling of training data can

be fully integrated into the acquisition of undersampled data. Such a variable

density EPI approach provides shorter overall scan duration at the expense of

reduced temporal resolution. Second, the separation of training data and

undersampled data allows splitting the data acquisition into two breath holds.

Compared to the method proposed by Rutz et al. [9] the three stacks are not

acquired within three consecutive breath holds, but could be acquired within

one breath hold for high resolution undersampled and a second breath hold for

low resolution training data. Since the training data has very low spatial

resolution in the phase-encode directions (2.3×2.3 cm2), differences in breath

hold levels between acquisitions no longer pose a concern.

4.5 Conclusion

Undersampled cine 3D tagging in conjunction with k-t PCA reconstruction enables

significant reduction in scan time of whole-heart tagging and facilitates efficient

and accurate quantification of shortening, rotation and torsion of the left ventricle.

Using 3-fold undersampling the entire cine 3D tagging acquisition could be

accommodated in a single breath hold and feasibility in volunteers and patients was

demonstrated. Future work is dedicated to shorten breath hold durations further

and to apply the method in larger patient cohorts to prove clinical value.

66

Chapter 5 Imaging microstructure with MRI

5. k-t sPCA for Accelerating Cine 3D Flow Measurements

The ultimate resolution limit of MRI is dictated by the mean displacement of water

molecules due to self-diffusion [169,170]. Besides the fundamental diffusion limit,

the signal-to-noise ratio (SNR) is a key image quality criterion and scales inversely

with spatial resolution [171] according to:

y zpixel average phase phase sampleSNR x y z n n n τ∝ ∆ ∆ ∆ (5.1)

where the product x y z∆ ∆ ∆ denotes voxel volume, averagen the number of averages,

phasen the number of phase encodings in one (2D imaging) or two (3D imaging)

directions and sampleτ the sampling time. Based on equation (5.1) it follows that for

relevant scan times and SNR values, spatial resolutions on the order of a millimeter

are feasible. However, tissue is usually not composed of homogeneous material at

the scale of the imaging resolution but has structure that is much finer. Despite this

obvious limitation, insights into the microscopic structure may nevertheless be

gained, as demonstrated by Stejskal and Tanner [172] in 1965, by encoding the

diffusivity of water molecules using dedicated gradient pulses. In 1976 it was shown

that the diffusivity of water in muscle tissue does depend on the direction of

diffusion encoding gradients [173] leading to a framework of measuring anisotropic

diffusion with MRI [174].

5.1 Diffusion of water molecules

In 1905 Einstein [175] derived a unique solution to the differential equation for free

isotropic diffusion processes in solutions described by Fick [176], using the following

67

Imaging microstructure with MRI

boundary condition ( ) ( ) ( ) ( ){ }, 0; , , : 0 0 0y x t x t x t x x t= ∀ ∈ > ∪ < ∩ = and

( ),y x t dx n∞

−∞=∫ (n being the number of dissolved particles):

( )2

4,4

xDtny x t e

Dtπ

−= (5.2)

with D being the diffusion coefficient. The probability a water molecule is displaced

from x to x x+ ∆ during time t is given according to [175]:

( )( )2

41,4

x xDtp x x t e

Dtπ

+∆−

+ ∆ = (5.3)

The root mean square displacement along x direction is then determined as:

2x Dtλ = (5.4)

Equations (5.2)-(5.3) hold for free diffusion. A deviation from linearity in t in (5.4)

is expected for restricted diffusion with a spatial restriction narrower than xλ . In

case of more complex restriction the diffusion equation has to be solved with the

problem specific boundary conditions.

Assuming a short gradient pulse of duration δ after excitation in an MRI

experiment, the transverse magnetization experiences a phase accumulation

according to:

1 1G xϕ γ δ= (5.5)

If the gradient is repeated with inverted sign after a delay of δ∆ >> , while a water

molecule has traveled from 1x to 2x , the phase differenceϕ ϕ−2 1 reads:

( )2 1 2 1G x xϕ ϕ γ δ− = − (5.6)

The total transverse magnetization is given as the sum of magnetization weighted

by the probability density function p (PDF). With ( )2 1x x z− = it follows:

( ) γ δ∞ −

−∞∝ ∆∫0 , i G z

xyM M p z e dz (5.7)

68

The probability distribution can be derived using the Fourier transform of the

measured ratio 0xyM M as a function of the diffusion encoding strength q Gγ δ=

[177]. In case of a three-dimensional image and a three-dimensional probability

distribution, the parameter space has six dimensions: ( ), , , , ,x y zx y z q q q , with x, y, z

being the spatial coordinates and xq , yq , zq the coordinates in the so called q-space

[178]. A vector in q-space is represented by ( )q G t dtγ∞

−∞′ ′= ∫

with gradient G

being

prescribed in the canonical basis of the image space. To calculate the probability

distribution function, the q-space has to be populated by measurements of

( ) ∈

0 :xyM q M q q-space.

5.2 Imaging diffusion: Stejskal-Tanner diffusion encoding

Based upon work by Carr, Purcell and Hahn [169,179] describing signal attenuation

due to water self-diffusion in NMR experiments, Stejskal and Tanner [172] proposed

a spin echo based sequence with pulsed gradients (Figure 21).

Figure 21. Stejskal-Tanner diffusion encoding pulse sequence. While spatial encoding gradients are presented in light gray, diffusion encoding gradients in shown in dark gray.

If a particle is displaced, it accumulates phase according to its position in the

magnetic gradient field applied. Therefore Torrey [180] extended the Bloch

equation by a diffusion term:

69


2

2

01

1 0 00

10 0 01

10 0

TM M B M D Mt T

MT

γ

∂

= × − + +∇ ∇ ∂

(5.8)

As derived elsewhere [181] the solution for the transverse magnetization can be

written as:

( ) ( ) ( ) ( ) ω− − −′ ′ ′−∫∝

00 2

0,t T tirk t i tk t Dk t dt T

xyM r t M e e (5.9)

where the first exponential corresponds to the signal decay due to diffusion while

the second term contains Larmor precession in the main magnetic field 0B and the

gradient as well as 2T dephasing. ( )k t

represents the diffusion encoding moment:

( ) ( )0

tk t G t dtγ

′′ ′′ ′′= ∫

. The diffusion part of (5.9) at echo formation can be simplified

for the case of isotropic diffusion:

( ) ( )′ ′ ′− −∫ =

00 0

t Tk t Dk t dt bDM e M e (5.10)

with b being the measure of the sensitivity to diffusion:

( ) ( )( )2

0 0 0

TE t tb G t dt G t dt dtγ ′ ′ ′ ′= ⋅∫ ∫ ∫

(5.11)

Neglecting gradient ramp times, for the Stejskal-Tanner experiment the b-value is

calculated as:

2 2 2

3Stejskal Tannerb G δγ δ− = ∆ −

(5.12)

In the anisotropic case ( ) ( )Tk t Dk t

has to be written in its quadratic form, yielding

a b-matrix. D corresponds to the apparent diffusion tensor with its symmetric

matrix representation:

70

=

xx xy xz

yx yy yz

zx zy zz

D D DD D D D

D D D (5.13)

The elements can be determined from six diffusion weighted ( )0b ≠ images

(corresponding to six points in q-space) and one unweighted image ( )0b = . After

rotation into its eigensystem ( )1 2 3e e e the diffusion tensor matrix is cast into a

diagonal matrix. The corresponding eigenvalues ( )1 2 3λ λ λ represent the

diffusion coefficients along the tensors principal directions (Figure 22).

Figure 22. Ellipsoidal representation of the diffusion tensor. ie

correspond to the tensor’s

eigenbasis; iλ represents the diffusion along ie

.

5.2.1 Non-Gaussian diffusion

In biological tissue diffusion is restricted due to membranes, cell components or

entire cells. Hence the PDF function may differ from a Gaussian distribution [182].

As a measure for the deviation from a Gaussian shape the distribution’s kurtosis can

be studied. Kurtosis can be assessed by sampling q-space and deriving the actual

PDF according to (5.7) [183]. This requires an excessive number of data acquisitions.

To address this issue, Jensen et al. proposed an approximative method [184]. Using

equation (5.7), ( )( ),ln x yM q

is expanded in q

up to fourth order [184,185]:

( )( ) ( )( ) 2, ,

1 1ln ln 0 ...6 3x y x y i j ij ii i j k l ijkl

i j i i j k l

M b M b n n D b D n n n nW = − + +

∑∑ ∑ ∑∑∑∑

(5.14)

71


with in being the ith component of the normalized direction vector along which the

gradient is applied, ijD being the i,jth component of the diffusion tensor and ijklW

the kurtosis tensor:

( )( )( ) ( ) ( )

( ) ( ) ( ) ( )

3 3 32

3

3 3 3 3

9( ) , , ,,

, , , ,

ijkl i j k l i j k l

i k j l i l j k

W T P z T z z z z d z P z T z z d z P z T z z d zP z T z zd z

P z T z z d z P z T z z d z P z T z z d z P z T z z d z

= − −⋅

−

∫ ∫ ∫∫

∫ ∫ ∫ ∫

(5.15)

The kurtosis tensor has 43 81= components and from (5.15) it is seen that it is

symmetric with respect to exchanging indices. Hence to fully characterize the

kurtosis tensor, 15 independent components need to be determined. The scalar

diffusional kurtosis in a specific direction n

is calculated as:

( )( )( )( )( )

( )

( )( )

2

4 3

2 23

1, 3

3,

iii

i j k l ijkli j k l

iji j

D TP z T n z d zK T n n n nW T

P z T n z d zD T

⋅ = − =

⋅

∑∫ ∑∑∑∑∫ ∑∑

(5.16)

For a Gaussian distribution ( )K t is zero. For a plateau in the distribution it is positive

for a more pointy distribution it is negative [186]. While kurtosis has primarily been

assessed in the brain, a recent study has shown that cardiac tissue may also exhibit

non-zero kurtosis [187,188].

5.3 Quantitative parameters

Apparent Diffusion Coefficient (ADC): The ADC corresponds to the one dimensional

diffusion constant D in equation (5.10). In anisotropic media the measurement of

the ADC depends on the diffusion encoding direction. In isotropic media a single

data point is sufficient to solve (5.10) for D. Multiple sample points increase the

precision or allow for separation of diffusion and perfusion components using the

Intra-Voxel Incoherent Motion (IVIM) model [189].

72

Mean diffusivity (MD): The MD corresponds to the trace of the diffusion tensor:

( ) ( )1 2 31 13 3

MD tr D λ λ λ= = + + (5.17)

Since the trace is invariant under basis transformation, it is sufficient to sample the

ADC with three orthogonal gradient directions [190]. For isotropic diffusion

1 2 3λ λ λ= = holds.

Fractional Anisotropy (FA): The FA is a unit-free measure of deviation of the

diffusion tensor from an ideal sphere

( )2

2

32

i avgi

ii

FAλ λ

λ

−=

∑

∑ (5.18)

with avgλ being the mean of the eigenvalues. An FA>0 corresponds to anisotropic

diffusion and is an indication for the presence of structure [191].

By acquiring samples in q-space on a sphere (Q-ball) [192,193] the orientation

density function (ODF) can be derived. Q-ball imaging does not use a model as in

DTI, but assumes that the apparent diffusion is identical for individual tissue fiber

bundles and only differs in orientation. Therefore the signal can be written in

spherical coordinates as convolution:

( ) ( ) ( )ϕ θ ϕ θ θ= ∗, ,S F R (5.19)

where ( )R θ is the response function describing the signal behavior of one fiber

bundle and ( ),F ϕ θ corresponds to the orientation density function which weights

the response function by the amount of fibers that are present pointing in a specific

direction ( ),ϕ θ . ( )R θ can be approximated from pixels with highest FA [193] and

( ),F ϕ θ is obtained upon spherical deconvolution. It was shown by Tuch et al.

[192,194] that the orientation distribution function (ODF, see equation (5.21)), can

be approximated by the Funk Radon Transform of the diffusion signal sampled on a

shell with radius q :

73


( ) ( ) 3

0q n

S qODF n d q

S⊥∈≈ ∫

(5.20)

which corresponds to the sum of the measured signals ( )

0

S qS

in directions q

orthogonal to the direction of interest n

. The model-free estimation of anisotropic

diffusion is implemented by Diffusion Spectrum Imaging (DSI) [177] and q-Space

Imaging (QSI). It is based on the Fourier relation of the MR-signal and the PDF in the

narrow pulse approximation (equation(5.7)). The ODF can be calculated from the

PDF ( ),p z ∆ by radial integration [177]:

( ) ( )0

,ODF n p rn dr∞

= ∆∫ (5.21)

When the ODF is calculated the underlying orientations of tissue structure is found

estimating the local maximal on the ODF surface for each voxel.

Given the geometry and symmetry of the left ventricle of the heart (Figure 23a), it is

appropriate to define specific angles of fiber tracts which are derived from the

eigenvectors (DTI) or from the ODF (DSI,QSI,q-Ball). The helix angle α is defined as

the angle between the projection of the myocardial fiber onto the epi/endocardial

surface and the transmural coordinate [195] while the transverse angle β is

defined as the angle between the projection of the fiber direction onto the

transmural plane and the circumferential coordinate [195] (Figure 23b). The

transmural angle β ′ is similarly defined, however, without the projection onto the

transmural plane [53].

Besides fiber bundle orientation, the angulation of myocyte aggregation in laminar

sheets can be identified based on DTI data [54,64,195]. The first and secondary

eigenvectors of the tensor point tangentially while the tertiary eigenvector

constitutes the normal vector of the myocyte sheets.

74

Figure 23. Angle definitions. a) Each position in the myocardium is represented in its cylindrical

coordinates: radial r

, circumferential c

and longitudinal z

positions. Helix α , transverse β ,

transmural β ′ and sheet γ angle definition is shown in b). The gray surfaces indicate projection

planes for the first (fiber direction) 1e

and third (sheet normal direction) 3e

eigenvector of the

diffusion tensor. The signs (±) indicate the polarity of the used angle definition.

5.4 Imaging diffusion in the beating heart

The key challenge of cardiac diffusion imaging relates to object motion. Firstly, the

heart is displaced by breathing. Secondly, the heart undergoes contraction. While

breathing motion can be compensated for by breathholding or respiratory

navigation, the compensation of effects due to cardiac contraction is more

challenging.

5.4.1 Diffusion weighted imaging using spin echoes

If the Stejskal-Tanner (Figure 21) diffusion encoding experiment is applied while the

heart is contracting, the desired signal is spoiled. This can be understood by

considering the phase accumulation of the magnetization during the application of

a magnetic field gradient:

( ) ( )0

encoding

encoding

t

t G t x t dtϕ γ= ∫ (5.22)

where encodingt is the duration of the diffusion encoding gradient, ( )G t

the gradient

waveform and ( )x t the trajectory of material points. Using Taylor approximation of

the trajectory ( )x t :

75


( ) ( )0

0

1!

nn

n t

x t x t tt n

=

∂ = ∂ ∑ (5.23)

leads to:

20 0 00 0 0

( ) ( ) ( ) ....2γϕ γ γ= = == + + +∫ ∫ ∫

encodinγ encodinγ encodinγ

encodinγ

t t t

t t t tG t x dt G t x tdt G t x t dt (5.24)

From (5.24) it is seen that the accumulated phase can be calculated based on the

initial spatial coordinates of spins, their temporal derivatives and the gradient

moments nm

:

( )

( )

( )

( )

0 0

1 0

22 0

0

encoding

encoding

encoding

encoding

t

t

t

t nn

m G t dt

m tG t dt

m t G t dt

m t G t dt

=

=

=

=

∫∫∫

∫

(5.25)

Figure 24 shows the original Stejskal-Tanner diffusion encoding sequence as well as

a modification with a single sided (with respect to the echo pulse) waveform and

corresponding 0th to 3rd gradient moments.

It is seen that the first, second and third gradient moments are significantly

different from zero, thereby inducing sensitivity of the sequence to bulk motion. If a

single voxel, which undergoes deformation due to cardiac contraction is considered,

one can express the material stretch as a distribution of velocities across the voxels

dimension which in turn leads to a phase distribution within the voxel. Accordingly,

transverse magnetization is spoiled due to cancelation of magnetic moments with

opposing phase within a voxel according to [196]:

( ) 0sin

2

2

xy xyM M

ϕ

ϕ ϕ

∆ ∆ =∆

(5.26)

76

Hence standard diffusion encoding gradient waveforms with zero net area can only

be applied when no deformation is present i.e. tissue is either not moving or rigidly

displaced at a constant velocity. This condition is only fulfilled for very short time

windows during peak systole. Since the systolic window is only 10-20ms, sufficient

b-values can only be obtained with dedicated high-performance gradient systems

which are not available clinically.

Figure 24. Stejskal-Tanner diffusion encoding with minimal total gradient duration (top) and single sided diffusion encoding (bottom). Both diffusion encoding schemes provide a b-value of 450 s/mm2 with 80 mT/m maximum gradient strength. 0th to 3rd moments of the diffusion encoding gradient are plotted for the duration of the gradient. Gradients in light gray indicate the effective gradient including the change in sign due to the 180° refocussing pulse.

In Gamper et al. [19] it was demonstrated that the use of first-order gradient

moment nulling allows prolonging the systolic time window sufficiently to permit

mapping of 2D in-plane diffusion tensors of the in-vivo heart. A general approach to

gradient moment nulling for diffusion encoding is described by Pipe et al [197].

Figure 25 illustrates a double bipolar diffusion encoding scheme with its

corresponding 0th to 3rd gradient moments.

77


Figure 25. First order motion compensated diffusion encoding. The 0th to 3rd order moments of the diffusion encoding gradient are shown. Gradients in light gray indicate the effective gradient including the change in sign due to the 180° refocussing pulse.

Despite its feasibility for imaging the in-vivo heart, the timing of the double bipolar

diffusion encoding scheme is challenging in that it requires a constant strain rate

over the duration of the diffusion encoding gradients. The use of a trigger delay

scout sequence [20], which sweeps through trigger delays during systolic

contraction was proposed to find an optimal timing window for diffusion encoding

along all required spatial directions [56,198].

To mitigate the residual sensitivity to motion, higher-order motion compensation

may be used at the expense of considerably longer diffusion gradient durations.

Figure 26 shows diffusion encoding schemes with first and second order moment

nulling. In the top row of Figure 26 the simplest waveform is presented while a

second, more time efficient, design is shown in the bottom row. In the latter case

the gap between the two gradient lobes is fixed to the duration of the positive part

of the first lobe. A detailed investigation of higher-order moment nulling for cardiac

DTI is presented in Chapter 7.

78

Figure 26. First and second-order motion compensation for diffusion encoding. The 0th to 3rd order moments of the diffusion encoding gradient are shown. Gradients in light gray indicate the effective gradient including the change in sign due to the 180° refocussing pulse.

5.4.1.1 Gradient field imperfections

Practical spin-echo based diffusion imaging requires careful considerations of

gradient field imperfections. To reduce eddy-current related effects, Reese et al.

[199] proposed a double spin-echo sequence to cancel eddy currents of specific

decay rates. Unfortunately, such schemes introduce non-zero first and second order

gradient moments thereby increasing their motion sensitivity. Alternatively, eddy

current fields may be measured and effects thereof corrected for in image

reconstruction [200,201].

Besides eddy-current related effects, concomitant fields may play a role. Assuming

quasi-stationary conditions the magnetic flux obeys:

0B∇⋅ =

(5.27)

0B∇× =

(5.28)

79


The corresponding concomitant fields lead to an effective flux field developed to

second spatial order according to Bernstein et al. [202]:

( ) ( ) ( )2

2 2 2 2 20

0

1, ,2 4

zx y z x y x y y z

GB x y z B G x G x G x x y G G z G G xy G G yz

B

= + + + + + + + − −

(5.29)

with the concomitant field component:

( ) ( )2

2 2 2 2 2

0

12 4

zc x y x y y z

GB x y G G z G G xy G G yzB

= + + + − −

(5.30)

For symmetric sequences with respect to the refocussing pulse as shown in Figure

25 and Figure 26, concomitant fields cancel due to the refocussing pulse [203]. For

asymmetric sequences as shown in the bottom row of Figure 24 the quadratic terms

in (5.30) remain leading to signal dephasing.

80

5.4.2 Diffusion weighted imaging using stimulated echoes

An alternative to spin-echo based diffusion weighted imaging is the stimulated echo

acquisition mode (STEAM) [204,205]. STEAM takes advantage of the periodicity of

cardiac motion by splitting the Stejskal-Tanner diffusion encoding scheme into two

parts (Figure 27).

Figure 27. Diffusion weighted STEAM. Encoding and decoding blocks are applied at the same trigger delay (TD) in consecutive heart beats. Imaging gradients are shown in light grey and diffusion encoding gradients in dark grey. The orientation of macroscopic magnetization at different positions along the diffusion encoding direction is shown alongside for different time points within the sequence (neglecting readout gradients).

81


Given the formation of the stimulated echo across two consecutive heart beats, the

b-value of diffusion weighted STEAM depends on the actual heart-rate. Based on

equation (5.11) the b-value is calculated:

3 3 2

2 2 2 603 30 6

b GHR

δ ζ δζγ δ

= − + −

(5.31)

with δ being the duration of the gradients slope plus its plateau, ζ the duration of

the slope and HR the heart rate (bpm). If heart rate variations occur the apparent

diffusion coefficient is given as:

actualapparent true

assumed

bD D

b= (5.32)

For example, if a heart rate of 60 bpm and a b-value of 500 s/mm2 are assumed, an

increase in heart rate by 10 bpm leads to an underestimation of D by 14%, while a

drop in heart rate by 10 bpm leads to an overestimation of D by 20%. If the current

heart rate is known for each acquisition, the diffusion tensor can be corrected for by

expanding the b-matrix in the three-dimensional case of (5.10) to multiple b-values

for each acquisition.

Besides the b-value sensitivity, the SNR of diffusion weighted STEAM is also

dependent on heart rate. Myocardial 1T is in the rage of 870 to 1300ms for 1.5T and

3T field strengths [80]. Accordingly, a considerable amount of modulated

magnetization relaxes during the R-R interval (Figure 28).

Figure 29 shows the effect of partial saturation in combination with 1T relaxation

during the mixing time for each average as a function of heart rate and field

strength. It is seen that strong signal saturation occurs after the first average

already.

82

Figure 28. Effect of T1 relaxation during the mixing time (TM). The magnetization is normalized to the thermal equilibrium value at 1.5 and 3T. On the x-axis the position of the local magnetization along the modulation and demodulation gradient is given. The time points correspond to position V (blue), VII (red) in Figure 27 as well as right before the third RF pulse (green). The loss of modulation along the longitudinal axis which translates into a reduced magnitude of transverse magnetization upon stimulated echo formation is plotted as function of the heart rate (HR).

Figure 29. Partial saturation combination with

1T relaxation during the mixing time as a function

of heart rate and field strength. Repetitive excitation leads to a 1T dependent signal saturation.

The remaining transverse magnetization relative to the thermal equilibrium magnetization at 1.5T is color-coded as a function of averages and heart rate.

83


5.4.2.1 Strain effects

Strain effects in diffusion weighted STEAM can be separated into two components.

Firstly, different strain states of tissue during modulation and demodulation and,

secondly, the temporal evolution of myocardial strain during the mixing time

[17,18].

If the heart is not in the same contractile state during echo encoding and decoding,

a phase error occurs leading to signal attenuation unrelated to diffusion [17]. During

encoding the magnetization is modulated with spatial frequency 0k . After

deformation according to y Fx= , where F is the deformation gradient tensor, the

effective spatial encoding frequency is:

10

Teffk F k−= (5.33)

The deformation gradient tensor may be decomposed into a rotation and a stretch

component:

F RU= (5.34)

assuming that spatial rotation of tissue leads to an equivalent rotation of its

diffusion properties [18]. Magnetization upon diffusion encoding can be written as:

( ) ( ), ikxM x t M t e−= (5.35)

with the initial condition:

( ) 0,0 ikxM x M e−= (5.36)

Recalling the Bloch-Torrey equation (5.8) and neglecting relaxation one obtains:

( ) ( ), ikx TD M x t M t e k Dk−∇ ∇ = − (5.37)

and with further calculation [17]:

( ) ( )( )

( )( )0

,, ,ln

, ,T

M x tM x t D M x td t k Dkdt M M x t M x t

∂∇ ∇ ∂= = = −

(5.38)

84

It is noted that k

is assumed to be constant during the encoding duration.

Equations (5.33), (5.34) and(5.38) can now be combined and integrated over time

(note that the stretch tensor U is symmetric):

( ) ( ) ( )1 1

0 000

, 1ln TM x tk U t DU t k dt

M∆ − −

= − ∆ ∫

(5.39)

From (5.39) it is seen that the observed diffusion coefficient in the presence of

material strain differs from the true diffusion coefficient [17] by:

( ) ( )1 1

0

1observedD U t DU t dt∆ − −=

∆ ∫ (5.40)

If ( ) ( )1 10U U− −≠ ∆ it follows that observedD D≠ . Additionally Tseng et al. [206]

postulated the presence of so-called sweet-spots for imaging that fulfill the

condition ( ) 1sweet spot

sweet spot

t

tU t id−

−

+∆ − =∫ , i.e. temporal average of material strain is zero. This

condition approximately holds for two time points sweet spott − , one during systolic

contraction and one during diastolic relaxation. Unfortunately these two time

points are restrictive in terms of investigating the dynamics of diffusion tensors.

Generally, the true diffusion tensor can be estimated based on equation (5.40) if

the stretch tensor is known. In Chapter 6 methods to acquire and apply myocardial

deformation fields for diffusion tensor imaging are discussed.

85


86

Chapter 6 Dual-Phase Cardiac Diffusion Tensor Imaging With Strain Correction2

6. Mean and Fluctuating Velocity Mapping by MRI and PTV

6.1 Introduction

The influence of myocardial fiber architecture on cardiac morphology and mechanics is

of significant interest. The helical organization of myocardial fibers [46,47,195,207] and

the formation of myocytes into sheets [60,62,64] by branching and interconnection

have been well described. While microscopy provides high-resolution images

[58,59,70], MR diffusion weighted imaging enables investigation of the intact organ.

Despite its lower spatial resolution compared to microscopy, MR has found application

in ex-vivo [64,207-217] and also in a small number of in-vivo [19,56,206,218-221]

studies of the heart. More recently, diffusion tensor imaging (DTI) has enabled

tractography of the myocardium both ex-vivo [222-224] and in-vivo [56,198,225].

In order to investigate differences in fiber configuration during the cardiac cycle, Chen

et al. [61] presented a comparison of ex-vivo pig hearts first arrested in diastole and

later fixated in systole. These ex-vivo findings were confirmed by Hales et al. [226].

Significant differences in helix angle and sheet angle distributions between systole and

diastole were found. Further investigations involved the study of sheet rearrangement

in myocardial pathologies [72,227].

In-vivo DTI of the human and animal heart has been performed using diffusion

weighted stimulated echo acquisition modes (STEAM) [17,18,206,221,228,229] and

2 Published in: Stoeck CT, Kalinowska A, von Deuster C, Harmer J, Chan RW, Niemann M, Manka R, Atkinson D, Sosnovik DE, Mekkaoui C, Kozerke S. Dual-Phase Cardiac Diffusion Tensor Imaging With Strain Correction. PLoS one 2014; 9(9):e107159

87

Dual-Phase Cardiac Diffusion Tensor Imaging With Strain Correction1F

first and second order motion compensated diffusion weighted spin-echoes

[19,56,198,220,225] in combination with echo-planar imaging readouts. While spin-

echo diffusion weighted imaging requires strong gradient systems in order to be

applied in the in-vivo heart, STEAM based sequence can be performed with standard

gradient hardware.

Early reports suggested that the impact of material strain is of significance in cardiac

DTI [17,18,206,218]. To this end, it was proposed to trigger STEAM encoding and

decoding to the so-called “sweet spots” of myocardial strain at which the temporal

mean of strain approaches zero [206]. Despite this insight, cardiac diffusion-weighted

STEAM at various time points in the cardiac cycle has been reported recently [221,230-

233].

The objective of the present work is to address the impact of material strain on the

diffusion tensor when imaging the in-vivo heart using the STEAM sequence. To this

end, a tensor correction scheme based on cine 3D tagging data is presented. In

addition, the diffusion weighted STEAM sequence is modified to allow for dual-phase

and slice-interleaved imaging thereby accelerating cardiac diffusion tensor imaging by

a factor of two relative to previous single-phase approaches. Differences in fiber and

sheet architecture between systole and diastole, without and with strain correction of

the in-vivo human heart are presented.

6.2 Methods

6.2.1 Study protocol

Ten subjects without any history of cardiac disease (4 male/6 female, age 27±8years,

weight 68±7kg, heart rate 66±11bpm) were imaged on a clinical 1.5T scanner (Achieva

system, Philips Healthcare, Best, The Netherlands). The scanner was equipped with a

gradient system delivering 40mT/m maximum strength and 200mT/m/ms maximum

slew rate per physical gradient axis. A 5-channel cardiac array coil was used for signal

detection.

88

Written informed consent was obtained from each subject prior to imaging, and the

study protocol was approved by the ethics committee of the canton of Zurich.

Obtained informed consent included imaging as well as publication of anonymized

data.

Short-axis balanced steady state free precession cine data with a temporal resolution

of 7ms were obtained in the 2-chamber and short-axis planes of the left ventricle (LV)

to identify the ventricular systolic (trigger delay: 277±19ms) and diastolic (trigger

delay: 627±85ms) standstill periods. For image-based shimming, a B0 field map was

acquired in the short-axis view covering the entire LV [234].

6.2.2 Myocardial tagging sequence

Three orthogonally orientated line tagged cine image volumes covering the entire LV

were acquired within three consecutive breath holds [9]. To compensate for

differences in breath hold levels a gating respiratory navigator was applied prior to the

acquisition of each stack (acceptance window 15mm). Resulting navigator offsets were

used for stack alignment during image reconstruction. In order to avoid tag line fading

during the cardiac cycle, complementary spatial modulation of magnetization

(CSPAMM) was applied requiring two signal averages, with inverted tagging

modulation [87]. Imaging parameters were as follows: FOV: 108×108×108mm3, spatial

resolution: 3.5×7.7×7.7mm3 (tagging/readout × phase encoding × phase encoding)

reconstructed to 0.96×0.96×0.96mm3, temporal resolution: 18ms and 7mm tag line

distance. To achieve a temporal resolution of 18ms, the maximum slew rate of the

gradient system (200mT/m/ms) was used for the segmented echo planar imaging-

readout (EPI factor 7, 3 excitations per heart phase).

6.2.3 Diffusion sequence

Dual-phase cardiac STEAM was implemented using a reduced field-of-view technique

[235]. To avoid saturation in adjacent slices a tilted local-look pulse scheme was

incorporated (Figure 30) [236]. Residual signal from the edge of the field-of-view (black

triangles in Figure 30 c) was suppressed using regional saturation (rest) slabs. A

scheme to interleave slices (SL1 and SL2) and heart phases (SYS and DIA) was

implemented by applying the STEAM encoding block of slice 1 in systole (SL1 SYS) and

89


slice 2 in diastole (SL2 DIA) of the first R-R interval. The corresponding STEAM decoding

block including the readout was applied in the second R-R interval, respectively. The

two paired slices had a gap of 25mm, thus avoiding cross talk from the angulated

excitation due to contraction of the heart. After acquiring all signal averages of all

diffusion encoding directions, the slice order was switched to complete the acquisition

of both heart phases for each slice. Thereby two slices were acquired in two heart

phases within a single scan, hence reducing scan time relative to sequential single-

phase, single-slice acquisition by a factor of two.

Figure 30. Dual-phase cardiac DTI acquisition scheme. The first slice is encoded in systole (STEAM 1 SL1 HP1) and the second slice in diastole (STEAM 1 SL2 HP2) with preceding fat saturation (fat sat) and regional saturation (rest) (a). Corresponding STEAM decoding and readout are performed in the second R-R interval (STEAM 2). For non-diffusion weighted imaging, FID crushers are applied in the through-plane direction (dotted area) (b) while only diffusion encoding gradients are applied otherwise (dark gray). (C) Non-coplanar excitation (tilt) is used to select two angulated slabs (red) with the first RF pulses. Slice selection within these slabs is performed with the second and third RF pulses (green). Regional saturation (blue) is used to eliminate signal from the edges (black). The final slices are represented in brown, and the measured slice distribution across the left ventricle is shown in (d). The coverage from apex to base was approximately 63mm.

The acquisition of diffusion-weighted images was divided into multiple navigator-gated

breath holds (acceptance window of 5mm). Parameters of the diffusion sequence

were: 224×100mm2 field-of-view, 2×2mm2 in-plane resolution, 8mm slice thickness,

number of slices 6, TE/TR 18ms/2R-R intervals, partial Fourier factor 0.62. A single shot

EPI readout was used. The two heart phases in the diffusion protocol were triggered to

quiescent phases of systole and mid-diastole as defined on the cine images. Unipolar

diffusion gradients were played out in 10 directions on a unit-sphere [190] with a b-

90

value of 500s/mm2. To reduce echo time, FID crushers necessary in STEAM were

removed for b=500s/mm2 acquisitions, but kept for the b=0s/mm2 acquisition.

All eight signal averages of a diffusion weighted image were acquired within one

breath hold. Different diffusion weightings were obtained in consecutive breath holds.

The volunteers were allowed sufficient time to recover in-between breath holds to

ensure consistent heart rates among the data series. A total of 11 breath holds of 14-

16s duration each were acquired per slice and two heart phases, resulting in a 15-

18min total net acquisition time for six slices at two heart phases.

6.2.4 Tensor reconstruction

To compensate for residual slice mismatch due to inconsistency in breath hold levels

within the 5mm gating window and to account for eddy-current induced geometrical

distortions, all diffusion weighted images were registered to the b=0 image by means

of affine image registration (elastix toolbox [237]).

Systolic and diastolic diffusion tensors were estimated based on the modified Stejskal-

Tanner equations. To account for non-zero diffusion weighting of the “b=0s/mm2” scan

due to diffusion weighting introduced by the FID crusher gradients present in STEAM,

the signal equation was modified as:

†B S D=

(6.1)

with B being the modified b-matrix containing the b-values of the diffusion weighted

images b and the “b=0” image 0bSb

=:

0

2 2 21 1 1 1 1 1

2 2 2

2 2 2 1

2 2 2 10 0 0 0 0 1

b

diff diff diff diff diff diff

diffN diffN diffN diffN diffN diffN

S

bx by bz bxy bxz byz

Bbx by bz bxy bxz byz

b=

− = −

−

(6.2)

S

denotes the negative logarithm of the measured signal per pixel including the signal

of the “b=0” image 0bS = :

( )1 0lnT

diffN bS S S S = = −

(6.3)

91


and D

the vector containing the unknown tensor elements and the true b=0 signal 0S :

( )2 2 2 0lnT

xy xz yzx y zD D D D D D D S =

(6.4)

where x, y and z are the coordinates of the normalized diffusion direction, T the

transpose and † the Moore-Penrose pseudo inverse.

6.2.5 Correction for material strain

Material strain effects were compensated for based on the stretch history of tissue

[17,18]. From 3D tagging data, three-dimensional displacement fields were calculated

with a custom-made software utilizing the 3D SinMod algorithm [100]. The LV was

manually masked on the tagging data as well as on the acquired b=0s/mm2 image. To

compensate for mismatch and different spatial resolution of the acquired data, the

shape of the DTI mask was mapped onto the re-sliced tagging mask by means of

coherent point drift registration [238]. Having identified the position of each diffusion

tensor estimated from the DTI acquisition within the displacement field, a cube parallel

to the canonical basis in which the displacement fields and the position of the tensors

are represented, was defined at each point and tracked over the R-R interval. The time

course of the right stretch tensor was calculated from the deformation gradient field

obtained from the tracked cubes as described by Hess et al. [11]. Stretch tensors were

calculated relative to the systolic and the diastolic time points of diffusion imaging. The

strain effect on the diffusion measurement is described by

( ) ( )1 1

0

1observed trueD U D U dτ τ τ

∆ − −=∆ ∫ (6.5)

with ( )U τ being the time course of the right stretch tensor and ∆ the duration of the

R-R interval. In accordance with [17] the equation is expanded as:

( ) ( )1 1

0

1observed trueij ik lj klD U U Dτ τ

∆ − − = ∆ ∫ (6.6)

92

For validation purposes, additional DTI data were acquired during the systolic “sweet-

spot” (trigger delay: 160ms) in one of the volunteers and compared to data in end

systole (trigger delay: 305ms) and diastole (trigger delay: 620ms).

6.2.6 Data analysis

From the six slices pairs of two were grouped for the basal, medial and apical level and

mean diffusivity (MD) and fractional anisotropy (FA) in systole and diastole were

compared for each volunteer. Additionally, helix, transverse and sheet angles were

calculated using projections of the first and third eigenvectors as described in Figure 31

(a-b) [195]. To allow tracking the transmural course of the helix angle, a local

anatomical basis was defined. To this end, the shape of the LV was mapped onto an

“ideal” circular ring by means of coherent point drift mapping [238]. This procedure

allowed the definition of a locally normalized transmural position independent of

variation of local thickness of the myocardium (Figure 31 c). The helix angle alignment

was analyzed on a slice-by-slice basis. Therefore the myocardium was separated into

five layers: epicardial, sub-epicardial, mid-wall, sub-endocardial and endocardial

similarly to previously reported helix angle analysis [221]. The transmural helix

gradient from the linear fit as well as the range of the transmural course of the helix

angle are reported for basal, medial and apical levels (Figure 31 d). Transverse and

sheet angle distributions are analyzed by means of histograms for each slice similar to

the analysis of Hales et al. [226]. The standard deviation of the transverse angle

distribution is reported as measure of coherence. Sheet angle distributions were fitted

with a quadratic function (Figure 31 e) and the coefficient of the quadratic component

is presented as a measure of sheet realignment during systolic contraction.

Additionally the mean of the absolute value of the sheet angle was calculated for

basal, medial and apical levels in systole and diastole.

The tensors shown in this study have not been interpolated as in previous works

[56,198]. Statistical differences between systolic and diastolic values were tested using

a two-tailed paired student’s t-test. A p-value < 0.05 was considered statistically

significant. All tests were Bonferroni-corrected for multiple testing.

93


Figure 31. Definition of fiber and sheet angles. A local orthonormal basis is defined (a) (radial: r

,

circumferential: c

, longitudinal: z

). Helix (α), transverse (β) and sheet angle (γ) definitions are given

in (b). For angle calculation, projections of the first ( 1e

) and third ( 3e

) eigenvectors were used (grey

planes). The sign indicates the polarity of the angle. For each tensor position a normalized transmural position is defined (c). An example of the transmural course of helix angles is shown in (d) with the angle range (grey) and linear fit (green) indicated. Histograms of sheet angles (e) were fitted using a quadratic function (green line).

6.3 Results

Dual-phase cardiac DTI data was successfully acquired in all subjects. Total exam time

including subject preparation was 1.5-2 hours.

The raw data images acquired at the systolic sweet spot, in peak systole and in diastole

are presented in Figure 32. Data are shown for the “b=0”, the first three and the last

diffusion- encoding direction as well as the average of all diffusion directions. Tagging

data from the three orthogonally line-tagged stacks are given alongside. The

temporally averaged stretch tensors as calculated from the tagging data allow radial,

94

circumferential and longitudinal stretch components, which are presented as stretch

maps, to be assessed.

Figure 32. Raw data of diffusion weighted and tagging acquisitions as well as strain maps for the sweet spot, the systolic and the diastolic heart phase. The “b=0” image, the first three and the last diffusion encoding directions as well as the averaged diffusion weighted images are shown. Tagging data from the three orthogonally oriented line-tagged stacks are given alongside. The temporally averaged stretch tensors as calculated from the tagging data allow assessing radial, circumferential and longitudinal stretch components, which are presented as stretch maps.

Figure 33 a,b shows the time course of the radial, circumferential and longitudinal

stretch calculated from the right stretch tensors at the apical, medial and basal levels

for systole and diastole. The time points of acquisition of systolic and diastolic DTI data

as well as the systolic sweet spot are indicated by vertical lines in Figure 33 a,b. The

transmural course of the helix angles and transverse and sheet angle histograms in

systole (trigger delay: 305ms) and diastole (trigger delay: 620ms) (without and with

strain correction) are shown for the medial level in Figure 33 c,d. In addition, DTI data

acquired in the systolic sweet spot (trigger delay: 160ms) is overlaid. Strain correction

results in changes in the transverse and sheet angle distributions in systole. Values

obtained upon strain correction approach data acquired in the sweet spot. Differences

in diastole are found to be smaller with and without strain correction.

95


Figure 33. Time course of the measured stretch tensor. The radial, circumferential and longitudinal components of the right stretch tensors are plotted as a function of time after the R-wave. The systolic (a) and diastolic (b) timing of the DTI sequence is indicated by the vertical solid line while the systolic sweet spot is marked by the vertical dashed line. The transmural course of the helix angles and the transverse and sheet angle histograms are presented for systole (c) and diastole (d) for a medial/basal level. Systolic and diastolic (black) as well as sweet-spot (gray) data are shown before (dotted line) and after (solid line) strain correction.

In Figure 34 systolic and diastolic tensor fields at a medial level with and without strain

correction are compared. The superquadric representation of the diffusion tensor

[212] was employed while glyphs were color-coded by the helix angle. It is observed

that systolic diffusion tensors have been rearranged into the natural helical alignment

after strain correction. In diastole, however, correction effects were subtler, mainly

illustrated by small changes in the main diffusivities.

MD and FA for both heart phases, with and without strain correction, are reported in

Table 3. After strain correction, the MD was increased in systole and decreased in

diastole, both with statistical significance. The FA was significantly increased upon

strain correction in systole, but remained unchanged in diastole.

96

Figure 34. Systolic and diastolic tensor maps with and without strain correction. Diffusion tensor fields acquired in systole (A,B) and diastole (C,D) are represented by superquadric glyphs and color-coded by the helix angle before and (A,C) after strain correction (B,D). The diffusion tensor fields before and after strain correction are merged (C,E) to visualize its impact. Insets demonstrate a major realignment of the tensor field into the typical helical pattern upon strain correction in systole (B). In diastole, strain correction effects are characterized mainly by small changes in the principal diffusivities (E). systole diastole

w/o correc-tion

with cor-rection

w/o correc-tion

with correc-tion

MD [10-4mm2/s]

base 8.6±1.2* 9.5±1.3 8.5±1.0* 8.2±1.0†

medial 8.8±1.4* 10.1±1.8 9.2±1.1* 8.7±1.1†

apex 9.6±0.8* 11.2±1.2 10.1±1.1* 9.4±0.9†

FA base 0.52±0.03* 0.61±0.02 0.61±0.05 0.61±0.04

medial 0.52±0.05* 0.60±0.03 0.61±0.04 0.61±0.04

apex 0.48±0.02* 0.55±0.02 0.57±0.03 0.57±0.03†

Table 3 MD, FA at basal, medial and apical level. * indicates statistical significance (p-value <0.05) between uncorrected and corrected data and † indicates statistical significance between systole and diastole.

Figure 35 displays helix angle maps and the dependency of helix angle on the

transmural depth for systole and diastole, with and without strain correction. Data are

given as mean ± one standard deviation across the study population. While in diastole

97


only little change in helix angles is observed upon strain correction, helix angles at

basal level are significantly different with strain correction in systole. The mean

transmural helix angle range in diastole across the volunteers was reduced by 2.2±4.4°

at the basal level and increased by 2.2±6.1° at the medial level and 1.0±5.0° at the

apical level after strain correction. For systole, the transmural helix angle range was

decreased by 9.4±9.9° at the basal level, 1.6±5.3° at the medial level and 6.7±9.9° at

the apical level after strain correction. Differences in diastole were mostly not

statistically significant. In systole, statistically significant differences at the medial and

basal levels were found when comparing data without and with strain correction.

Figure 36 shows transverse angle maps and histograms of the study population.

Significant differences were observed before and after strain correction for both

systole and diastole, at each cardiac levels. Negative transverse angles were found at

the posterior RV-LV intersection. The distribution of the systolic transverse angle has a

lower variance after strain correction suggesting a more coherent fiber track. It is

noted that transverse angle distributions in systole and diastole show a similar

variance after strain correction.

Sheet angle maps and histograms are shown in Figure 37. The characteristic

distribution of sheet angle into two populations is well seen, particularly with strain

correction. Strain correction is observed to change systolic sheet distributions

markedly, in some cases producing almost inverted distributions of those obtained

without correction.

A comparison of helix, transverse and sheet angles for the systolic and diastolic heart

phase with and without strain-correction is provided in Table 4. Significant differences

in helix angle range between systole and diastole were seen in the medial and apical

levels while differences for transverse and sheet angles between systole and diastole

were found at the medial and basal levels of the heart. Sheet angle histograms are

broadened in systole compared to diastole.

98

Figure 35. Systolic and diastolic helix angles with and without strain correction. Helix angle maps in systole (left column) and diastole (right column) without and with strain correction (a). The transmural course of the helix angle is given at the basal, medial and apical levels (b). The error bars indicate one standard deviation across the study population. Statistically significant difference between the uncorrected (blue) and the corrected case (red) are indicated by * and between systole and diastole by †.

99


Figure 36. Systolic and diastolic transverse angles with and without strain correction. Transverse angle maps in systole (left column) and diastole (right column) without and with strain correction (a). Transverse angle histograms are given at the basal, medial and apical levels (b). The error bars indicate one standard deviation across the study population. Statistically significant differences between the uncorrected (blue) and the corrected case (red) are indicated by * and between systole and diastole by †.

100

Figure 37. Systolic and diastolic sheet angles with and without strain correction. Sheet angle maps in systole (left column) and diastole (right column) without and with strain correction (a). Sheet angle histograms are given at the basal, medial and apical levels (b). The error bars indicate one standard deviation across the study population. Statistically significant differences between the uncorrected (blue) and the corrected cases (red) are indicated by * and between systole and diastole by †.significant difference between the uncorrected (blue) and the corrected case (red) are indicated by * and between systole and diastole by †.

101


systole diastole

w/o correc-tion

with cor-rection

w/o cor-rection

with cor-rection

helix

ang

le

range base 72.8°±15.4°* 63.9°±11.5° 55.3°±9.3° 53.0°±9.6°

medial 77.1°±7.7° 75.2°±6.2° 55.9°±3.7° 58.1°±6.1°†

apex 81.1°±12.3° 76.0°±10.6° 55.0°±11.9° 56.0°±13.0°†

gradient [°/%depth]

base -0.93±0.18* -0.83±0.13 -0.74±0.11 -0.72±0.11

medial -1.00±0.11 -0.98±0.10 -0.73±0.06 -0.75±0.07†

apex -1.06±0.15 -1.00±0.12 -0.71±0.14 -0.71±0.16†

tran

sver

se a

ngle

mean base -3.0°±4.5°* 3.5°±4.8° -0.9°±2.3° -1.8°±2.3°†

medial 0.2°±4.3° -1.7°±3.1° -0.4°±1.1° -0.4°±1.1°

apex 0.2°±3.05°* -6.3±5.1° 1.3°±2.3° 1.3°±2.3°†

SD base 36.0°±3.8°* 29.5°±5.1° 27.7°±3.6°* 30.2°±3.4°

medial 34.0°±5.5°* 24.6°±4.1° 24.4°±3.1°* 27.2°±3.5°

apex 35.8°±3.4°* 27.3°±2.4° 25.2°±4.3°* 28.9°±3.8°

shee

t ang

le

quadratic fit [×10-6]

base -5.33±3.9* 3.7±4.2 14.9±4.9* 10.6±3.9†

medial -1.44±4.7* 9.3±4.5 18.8±3.7* 14.0±4.3

apex 3.5±5.5* 12.6±5.7 19.2±4.8* 14.2±6.7

mean

γ

base 38.0°±4.3°* 50.4°±3.5° 61.2°±5.1°* 56.9°±4.2°†

medial 41.6°±3.7°* 55.1°±4.8° 65.0°±3.6°* 60.4°±4.3°†

apex 58.7°±5.9°* 60.5°±4.1° 66.0°±4.6°* 60.9°±6.6°

Table 4. angulation analysis. Helix transverse and sheet angle analysis at basal, medial and apical level is shown prior and after strain correction. * indicates statistical significance (p-value <0.05) between uncorrected and corrected data and † indicates statistical significance between systole and diastole.

102

6.4 Discussion

In this study, dual-heart phase cardiac DTI with strain correction was successfully

implemented and applied on 10 healthy volunteers to study differences in myofiber

architecture between systole and diastole.

The slice and phase interleaving scheme permitted a reduction in scan time by a factor

of two relative to a single-phase DTI protocol, which would need to be repeated in

systole and diastole. Given that angular diffusion resolution was encoded in separate

breath held scans with the current implementation, the number of breath holds

required per dual-slice set is dictated by the number of diffusion directions. While

breath hold durations were short (14-16sec), free-breathing acquisition is nevertheless

preferred to increase acceptance in practice. To this end, respiratory navigation in

conjunction with patient feedback could be incorporated into our approach [221], or

alternatively a modified respiratory navigation scheme to increase gating efficiency

without the need for patient feedback [229] may be applied.

Local-look excitation was used to reduce the field-of-view in phase-encode direction by

a factor of 2.5 to 3 depending on slice angulation and patient size. Alternatively,

undersampling strategies may be employed including parallel imaging [239-241] or

compressed sensing [151,242]. Further reduction of scan time could also be achieved

by combining the proposed method with simultaneous excitation of multiple slices and

subsequent unfolding using parallel imaging principles [243-245].

DTI of the heart with the stimulated echo approach has previously been performed at

sweet spots in the cardiac cycle, where the effects of strain are eliminated [206,218].

The exact locations of these sweet spots is a function of the heart rate of each

volunteer, but generally falls within mid-systole and mid-diastole. More recently, DTI

of the myocardium has been described at end-systole, where the heart reaches a

quiescent or stand-still phase [221,230,233]. With the present work, it has, however,

demonstrated that DTI of the myocardium at end-systole is significantly influenced by

strain. The effect of strain on helix angle measurements is small but its impact on

measures of sheet architecture, such as sheet angle, is extremely large. Our results

confirm those of Tseng and colleagues, who likewise showed that imaging away from

103


the systolic/diastolic sweet spots produced small differences in helix angle but very

large differences in sheet angle [206,218].

The validity of strain correction was verified by comparing data acquired in systole and

diastole to data obtained in the systolic sweet spot, for which actual material strain

equals the average strain across the cardiac cycle. While no major difference was

found between the diastolic data obtained without strain correction, and the sweet

spot data, significant change was seen for systolic data upon strain correction.

In systole, longitudinal and circumferential diffusion components are underestimated

while radial diffusion components are overestimated without strain correction. This

effect leads to stretching of the diffusion tensor in radial direction and compression in

the two orthogonal directions. Consequently, after estimating the tensors’ eigenbasis,

the second and third eigenvectors are swapped leading to higher bin counts for the

sheet angle around 0°. The first eigenvector, which is predominantly aligned within the

circumferential and longitudinal plane, is rotated out of plane. Histograms of the

transverse angle demonstrate a wider spread prior to strain correction. Without strain

correction, the change in sheet angulation between systole and diastole is significantly

overestimated and fiber tracks appear less coherent. Here, the need for strain

correction in systole was clearly demonstrated.

The changes in fiber configuration between systole and diastole seen in this study

indicate a greater longitudinal alignment of myofibers during contraction. Similar

results have been described in excised rat hearts arrested in systole and diastole [61].

Likewise, histological and MR findings from excised porcine [53] and goat [209] heart

revealed that the helical fiber structure from epicardium at the apex crosses to

endocardium at a medial level and back to epicedium at the base, hypothesizing that

the presence of non-zero transverse angles are responsible for wall thickening during

contraction [53]. These findings are in agreement with the data reported here.

In the present work sheet angle histograms were generated for basal, medial and

apical levels similar to work by Hales et al. [226]. The in-vivo results presented here

show a significant change in sheet angle from systole to diastole. In the contracted

state, fewer counts of larger angulation were found, while the counts of intermediate

104

angles were increased. These results are in accordance with those of Dou et al. al

[218], who showed that sheet orientation becomes more radial in systole. Similar to

prior reports on isolated hearts [61,72,226], the changes in sheet angle histograms

were most pronounced at the basal level and less at the apical level.

A potential study limitation lies in the intrinsic coupling of the b-value of the STEAM

approach with the subject’s heart rate. While the standard deviation of heart rate

between acquisitions was only 2.6±1.1bpm, the heart rate during a breath hold

maneuver may have changed significantly. To minimize the impact of heart rate

variation on the tensor directionality, all averages of a single diffusion encoding

direction were acquired within a single breath hold.

Besides material strain, base SNR is of critical importance regarding systematic errors

in determining apparent diffusion. Magnitude averaging of the low SNR DWI data was

performed resulting in a Rician noise distribution of the averaged data. Accordingly,

signal attenuation by diffusion is biased by the SNR dependent noise floor [246]. Since

the SNR at the apex is considerably higher as compared to the base of the heart due to

its proximity to the receive coil array, the relative underestimation of apparent

diffusion measured in the apex is less compared to the value at the basal level.

6.5 Conclusion

An approach for dual-phase cardiac DTI with correction for myocardial strain has been

successfully implemented and has allowed changes in myofiber architecture between

systole and diastole to be studied in the human heart in-vivo. The results obtained with

strain correction are in agreement with experimental ex-vivo data and prior in-vivo

data in healthy volunteers. The potential of DTI to characterize myocardial anatomy in

the heart is high, but strain correction at phases other than the sweet spots will be

crucial for the accurate characterization of myocyte architecture.

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106

Chapter 7

Second Order Motion Compensated Spin-Echo Diffusion Tensor Imaging of the Human Heart3

7. Bayesian Multi-Point Velocity Encoded MRI to assess blood and CSF flow

7.1 Introduction

Ex-vivo diffusion tensor imaging (DTI) and diffusion spectrum imaging (DSI) have

provided invaluable insights into myocardial fibre architecture of the human heart

[222,247,248]. While a static view of cardiac myofiber arrangement is of interest, it

cannot address some of the crucial questions related to dynamic rearrangement of

myofiber aggregates during the cardiac cycle. Moreover, the study of longitudinal

microscopic changes of myocardium in a range of relevant cardiovascular diseases

necessitates in-vivo imaging of the human heart. Furthermore, personalized myofiber

architecture remains one of the main bottlenecks in the design of patient-specific

cardiac models for the systematic and quantitative diagnosis and prognosis of

cardiovascular patients [249,250].

Up to date only a limited number of studies have demonstrated the feasibility of

diffusion weighted imaging of the in-vivo human heart

[18,19,48,56,71,206,218,225,251-253]. The lack of data is due to the fact that in-vivo

cardiac DTI faces considerable challenges in relation to bulk motion and myocardial

strain during diffusion encoding.

Two sequence types have been investigated for in-vivo DTI. The STimulated Echo

Acquisition Mode (STEAM) was initially proposed for cardiac diffusion weighted

imaging (DWI) [228] and subsequently used to perform DTI during breath holds

[18,71,206,218] and during free breathing in combination with a dedicated visual

3 Manuscript under revision

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Second Order Motion Compensated Spin-Echo Diffusion Tensor Imaging of the Human Heart2F

patient feedback system [254]. The advantage of STEAM based sequences is their

feasibility on standard clinical MR systems, without the need for high-performance

gradient hardware. The nature of STEAM imaging, however, requires echo encoding

across two consecutive heart beats while the position of the heart in two consecutive

heart beat is only allowed to vary within narrow limits [254]. As a consequence of this

fact and the required motion control, exam times are very long and considerable

patient cooperation is required. In addition, there is an intrinsic weighting of the

diffusion signal due to myocardial strain [17,18]. This issue may be addressed by

imaging in the so-called “sweet spots” [206] although these limit imaging to two

predefined cardiac phases which do not coincide with end-systole and end-diastole.

Alternatively, strain correction may be applied in post-processing based on the

knowledge of the time course of myocardial strain [17].

Diffusion weighted single-shot spin-echo (SE) imaging has been proposed as an

alternative to STEAM and has been demonstrated to provide diffusion tensor

information of the in-vivo human heart [19,20,48,56,252,253,255]. The acquisition

scheme permits free-breathing imaging without the need for dedicated patient

feedback systems. However, the non-rigid component of bulk motion leads to a direct

strain encoding during the application of the diffusion gradients and this needs to be

addressed. To minimize strain effects, spin-echo DWI and DTI have primarily been

applied in diastole [251,253,256].

An approach to overcome signal attenuation caused by changes in cardiac strain is to

design higher-order motion compensated diffusion gradient waveforms, which have

been proposed as part of SE schemes for diastolic DWI [256] or as part of T2 pre-pulses

in conjunction with balanced steady-state free precession sequences [257]. The latter

variant allowed separating diffusion contrast generation from imaging. However, such

a scheme may be very sensitive to residual phase due to RF pulse imperfections and

uncompensated cardiac motion components.

Finally, image post-processing methods may be employed to correct for strain-induced

signal attenuation of conventional twice-refocused diffusion weighted SE images. To

this end, diffusion weighted images are acquired at different trigger delays during the

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diastolic rest period [251,253] and temporal filtering and projection is used to combine

image information from the set of temporally resolved images [258]. Potential

drawbacks of this approach, however, include the fact that the myocardium is thinnest

in diastole and hence partial voluming is increased. In addition, diffusion weighting is

limited to rather low b-values which reduces the diffusion related contrast and signal

attenuation due to perfusion may confound results.

Systolic cardiac DTI in humans has been proposed based on first order motion

compensated diffusion gradients incorporated into a SE sequence [19,56,259]. With

this approach, careful sequence timing is required when applied on clinical MR imaging

equipment [20]. Stronger gradient systems on animal imaging systems delivering up to

1.5T/m maximum gradient amplitudes allow for significantly reduced diffusion

gradient durations [225] and third order gradient moment nulling was investigated in

the in-vivo rat heart [260].

The objective of the present work is to propose and implement second order motion

compensated spin-echo diffusion tensor imaging of the human heart on a clinical

scanner. The reduced effect of strain on imaging fiber architecture of the in-vivo left

ventricle by second order motion compensated diffusion encoding is investigated and

compared to first order motion compensation.

7.2 Methods

7.2.1 Diffusion encoding

The signal phase accumulated during diffusion encoding is described by

( )( ) ( ) ( )0

encodingtr t G t r t dtϕ γ= ∫

with encodingt representing the duration of the diffusion

gradient, ( )G t

the gradient waveform and ( )r t

the spatial trajectory of magnetization.

Upon Taylor expansion of ( )r t

the phase can be written as:

20 0 00 0 0

( ) ( ) ( ) ....2γϕ γ γ= = == + + +∫ ∫ ∫

encodinγ encodinγ encodinγ

encodinγ

t t t

t t t tG t r dt G t r tdt G t r t dt (7.1)

with the associated nth order gradient moments nm :

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( )

( )

( )

( )

0 0

1 0

22 0

0

encoding

encoding

encoding

encoding

t

t

t

t nn

m G t dt

m tG t dt

m t G t dt

m t G t dt

=

=

=

=

∫∫∫

∫

From equation (7.1) it is evident that nulling of higher order moments results in phase

insensitivity to higher order motion (the derivatives of ( )r t

). To achieve higher order

gradient moment nulling whilst minimizing the overall gradient durations and echo

time for a given b-value, the maximum gradient amplitude is used. Figure 38 a)

illustrates a first order motion compensated (MC) gradient waveform [19,225] with

0 1 0m m= = at encodingt t= . In Figure 38 b), both first and second order motion

compensation is achieved and 0 1 2 0m m m= = = at encodingt t= .

110

Figure 38. First (a) and second (b) order motion compensated diffusion encoding using spin-echoes. Following a respiratory navigator (Nav), regional saturation (REST) is applied parallel to the imaging slice to saturate blood signal apically of the imaging slice. A spatial spectral pulse for fat suppression is used for reduced field of view imaging (LL). A variable rate selective excitation (VERSE) pulse is integrated for RF refocussing. The timing of gradients is given in ms. For each gradient waveform the 0th to 2nd moments (m0, m1, m2) are plotted as function of time.

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7.2.2 Study protocol

First and second order motion compensated diffusion tensor imaging were

implemented on a clinical 1.5T Philips Achieva System (Philips Healthcare, Best, The

Netherlands) equipped with a gradient system delivering 80mT/m per physical axis at a

slew rate of 100mT/m/ms.

Five subjects (4 female, age: 21±2years, heart rates: 66±13 beats/min, min/max heart

rates: 47/85 beats/min) with no known cardiac disease were imaged. Written

informed consent was obtained from all subjects prior to scanning and the protocol

was approved by the institutional review and ethics boards.

Diffusion imaging was performed in the short-axis view orientation. A reduced field-of-

view (FOV) technique was applied [235] employing a spectral spatial pulse for fat

suppression [261]. The duration of the 180° refocusing pulse was minimized using

variable rate selective excitation (VERSE) [262] (Figure 38). Imaging parameters were

as follows: in plane resolution: 2.7×2.7mm2, slice thickness: 6mm, field of view (FOV):

230×98mm2, TR/TE: 1R-R/73ms, flip angle: heart rate dependent Ernst angle assuming

a T1 of 1030ms [80]. The echo time was kept equal for both diffusion encoding

approaches. The only parameter changed was the waveform of the diffusion encoding

gradients.

Images were acquired during free breathing and gated using a respiratory navigator

with an acceptance window of 5mm. During contraction and during the first half of the

echo time blood below the imaging slice may move into the imaging plane and

experience the 180° refocussing pulse. Within the second half of the echo time, blood

within the imaging slices will move towards the aorta and exit the heart. To avoid

signal projection of the emptying blood pool onto the image, magnetization below the

imaging plane was saturated in a slab parallel to the imaging plane.

Diffusion weighted imaging was performed at trigger delay intervals of 10ms from the

shortest trigger delay possible (45ms) to peak systole (time point of maximal

circumferential contraction). At each trigger delay, eight signal averages of a

b=0s/mm2 image and three diffusion encoded images with the encoding direction in

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the readout, phase-encoding and through-slice direction with a b-value of 450s/mm2

were acquired. Slices were positioned at basal and apical locations (Figure 2), where

rotational motion and through-plane contraction are largest.

DTI data with ten diffusion encoding directions [190] were acquired in an additional

session in five healthy volunteers (4 female, age: 25±2years, heart rate: 71±13

beats/min, min/max heart rate: 50/87 beats/min) including one volunteer on which

DWI was performed. The sequence parameters were: in plane resolution: 2.7×2.7mm2

reconstructed to 1.35×1.35mm2, slice thickness: 6mm, field of view (FOV):

230×98mm2, TR/TE: 3R-R/73ms, flip angle: 90° and 12 signal averages. To reduce total

scan time while allowing for a TR of 3R-R intervals a slice cycling scheme with non-

coplanar excitation according to [236,263] was used. Data was acquired at 38%, 47%,

56%, 66% and 75% of peak systole employing both first and second order motion

compensated gradient schemes. Imaging slices were positioned at apical level (20% of

long-axis length from the tip of the apex), mid-ventricular and basal level (20% of long-

axis length below the mitral valve).

7.2.3 Data analysis

The apparent diffusion coefficient (ADC) was calculated for each dataset for the

different trigger delays and diffusion directions acquired. The mean ADC and the

corresponding standard deviation across the myocardium were analyzed within each

slice. The trigger delay is reported as percentage values relative to peak systole (100%

corresponds to peak systole). To avoid partial voluming effects, epicardial and

endocardial voxels were not taken into account. The duration of the plateau of the

mean diffusivity (MD) as function of trigger delay was defined using a range between

the minimum MD and 2.14×10-4mm2/s above the minimum MD. The range was

derived based on the standard deviation of MD values across volunteers within 40%

and 60% peak systole for second order motion compensation at basal and apical level.

Upon calculation of the diffusion tensors, the local helix, transverse and sheet angles

were estimated [195,264]. To do so, the mask of the LV was warped onto an ideal ring

by means of coherent point drift registration [238]. Within the ring the canonical

cylindrical basis was defined and associated to every tensor coordinate inside the LV.

For the helix angle analysis the transmural depth was normalized along the radial

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coordinate. Upon identification of the cylindrical basis, the helix angle was defined as

the angle between the diffusion tensor’s first eigenvector projected onto the local

cylindrical surface and the imaging plane. The transverse angle was defined as angle

between the component of the first eigenvector within the imaging plane and the

circumferential direction. The third eigenvector was projected onto the radial-

longitudinal plane and the angle between the projection and the imaging plane was

defined as sheet angle. To avoid partial volume effects of bright blood signal in the

b=0s/mm2 images, the averaged image of all diffusion encoding directions was

calculated and scaled (corresponding to signal attenuation caused by an ADC of 10×10-

4mm2/s). This image was used as unweighted reference signal for myofiber angle

analysis. Helix angles were calculated for each heart phase and transmural variation is

reported in box-plots representing the helix angle distribution along the

circumferential dimension at different transmural depths. The transverse angle

histograms are reported including mean±standard deviation across the myocardium

averaged across volunteers. The first eigenvector of the resulting diffusion tensors is

visualized by whisker plots. To illustrate strain-induced deviation from the

circumferential structure, the vectors are color-coded according to the local transverse

angle. Sheet angles are visualized by rendering the plane spanned by first and second

eigenvectors.

7.3 Results

An example for first and second order motion compensated DWI acquired throughout

systole is shown in supporting Figure 39. Partial motion-induced signal voids are visible

prior to complete signal cancelation. While signal voids are readily apparent with first

order motion compensation, second order motion compensation yields a wider range

of trigger delays applicable.

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Figure 39. Example time series of first and second order motion compensated (MC) diffusion weighted imaging throughout systole. Diffusion encoding was applied along in-plane (M,P) and through-plane (S) directions (white arrows). Earliest occurrences of motion induced signal voids are marked by white boxes.

115


In Figure 40 ADC values based on encoding along the readout (M), phase encode (P)

and slice select (S) directions as well as mean ADC values as a function of the trigger

delay are shown. Second order motion compensated diffusion encoding yielded a

trigger delay range of 15-77% of peak systole for the apical and 15-79% for the basal

slices on average. In comparison, for first order motion compensation, the

corresponding trigger delay windows were 30-56% (apical) and 25-50% (basal).

The standard deviation of ADCs and mean ADCs across the myocardium were found to

be lower on a wider range for second order motion compensation, relative to first

order motion compensated diffusion encoding.

Figure 41 shows helix angle maps, line plots of the first eigenvector color-coded by the

corresponding transverse angle as well as sheet structure at mid-ventricular level for

38%, 47%, 56%, 66% and 75% peak systole. For first order motion compensated

diffusion encoding, the characteristic transmural variation of helix angles is absent and

patches of high angulation (dark blue/red) are found in the myocardium for trigger

delays of 66% and 75% peak systole. Patches of large deviation from the

circumferential direction for the first eigenvector (transverse angulation of ±90°) are

visible at trigger delays greater 66% peak systole. Second order motion compensation

results in better circumferential alignment of the principal diffusion direction.

Orientation of myocardial sheets is shown by local surfaces spanned by the first and

second eigenvector. The sheet structure is seen to be more consistent for adjacent

trigger delays with second order motion compensation.

Figure 42 shows the transmural helix angle box plots for basal, mid-ventricular and

apical slices pooled across all volunteers. Second order motion compensated diffusion

encoding shows a linear dependency of the helix angles as a function of transmural

depth for all trigger delays and reduced variation along the ventricular circumference.

First order motion compensated diffusion encoding matched results from second

order motion compensated acquisition best at mid-ventricular level for trigger delays

of early to mid-systole. The root mean squared difference of helix angles across

volunteers relative to the mean over all volunteers was 15.9°/5.1° (38%), 12.3°/5.0°

(47%), 18.0°/4.3° (56%), 15.0°/2.8° (66%) and 15.8°/5.2° (75%) at the base, 7.0°/4.8°

116

(38%), 8.6°/5.4° (47%), 10.1°/4.2° (56%), 5.2°/5.2° (66%) and 6.5°/5.9° (75%) at the

mid-ventricular level and 10.1°/8.2° (38%), 11.8°/5.5° (47%), 9.8°/6.3° (56%), 15.1°/4.9°

(66%) and 11.4°/3.8° (75%) at the apex for first and second order motion

compensation. The corresponding trigger delays are given in brackets.

Figure 40 Apparent Diffusion Coefficients (ADC) for in-plane (ADC M/P) and through-plane (ADC S) encoding and mean ADC for first and second order motion compensated (MC) diffusion encoding as a function of trigger delay (in % peak systole) for an apical and basal slice location. The accepted range is indicated in green and is spanned by the horizontal dotted lines (range between minimal ADC and 2.14×10-4mm2/s above). Average ADC values across the myocardium within each slice are shown (in black) along with the corresponding standard deviation (in grey). Solid lines correspond to the mean across the volunteers and dashed lines to the standard deviation across volunteers.

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Figure 41. Helix angle maps from a mid-ventricular slice are shown for first and second order motion compensated (MC) diffusion encoding (top rows). Corresponding line plots of the first eigenvector color-coded by the transverse angle are presented (middle row). Local sheet structure is shown by 2D planes spanned by the first and second eigenvector color-coded by the sheet angle. The view corresponds to the anterior side similar to the insets in the whisker plot for transverse angle presentation. Maps are superimposed to the corresponding mean diffusion image.

Figure 43 shows the transverse angle histograms for both motion compensation

schemes averaged across volunteers. Using second order motion compensated

gradients, the standard deviation of the transverse angle is on average 51% smaller

when compared to data obtained with first order motion compensation. A transition

from negative to positive transverse angles is found when going from apex to base.

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Figure 42. The transmural helix angle analysis is presented for first order motion compensated (blue) and second order motion compensated (red) gradient waveforms. The box in the box-plot corresponds to the 50% percentile and the error bars to the 90% percentile of the helix angle distribution along the circumferential dimension as a function of transmural depth. Values presented correspond to the mean across volunteers.

Figure 43. Histograms of transverse angle are presented for first (light grey) and second (dark grey) order motion compensated diffusion encoding (MC). Plotted values correspond to the mean across volunteers and the error bars to the corresponding standard deviation. Values presented within the plots correspond to the mean ± one standard deviation of the plotted histograms.

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7.4 Discussion

In the present study, second order motion compensated cardiac diffusion imaging has

been implemented on a clinical MR system and compared to first order motion

compensation.

While MD values across the myocardium were found to be relatively constant over a

wide range of trigger delays for second order motion compensated diffusion encoding,

first order motion compensated diffusion encoding resulted in a strong dependency on

the trigger delay in accordance to previous findings [20]. Second order motion

compensated diffusion encoding not only yielded reduced variation of MD values

within the myocardium, it also reduced the standard deviation of MD values across

volunteers.

For first order motion compensated diffusion encoding, the optimal trigger delay for

DTI was found in a narrow range between 30% and 50% of peak systole, similar to

previous reports [19,20]. Tensor reconstruction suggests that the window of feasible

trigger delays is narrow. At ±30ms offset from the optimal trigger delay time, tensor

alignment deviated locally from the expected circumferential arrangement and the

characteristic transmural course of helix angles is lost in parts of the myocardium.

In this study the helix angle was calculated upon projection of the first eigenvector

onto a cylindrical surface [195]. Hence large deviations from a circumferential course

result in an overestimation of the helix angle. At the basal and mid-ventricular level,

considerable cardiac contraction in through plane direction occurs leading to a loss of

the characteristic transmural variation of helix angles for early and late systole for first

order motion compensation. The loss of transmural variation of the helix angle is also

reflected in a wider angle distribution along the circumference.

For second order motion compensated diffusion encoding, a 2.5 fold wider window of

trigger delays was found. A coherent circumferential course of myofibers with a linear

transmural course of helix angles was detected with a smaller spread in angle

distribution along the circumference. The results agree with previously reported fiber

angulations in the ex-vivo human heart [49]. The variation of transverse angles

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between apex and base agrees with previously reported STEAM based in-vivo imaging

[264] and ex-vivo studies [53,209].

In this study, the echo time was kept the same for both diffusion encoding gradient

waveforms to ensure similar T2 weighting. For first order motion compensated

encoding the echo time may, however, be reduced by 4ms.

In the second order compensation scheme used in this study, the duration of the gap

between the pairs of gradient lobes is dependent on the b-value. There is a minimum

value for this gap as it must be wide enough to accommodate the refocussing pulse.

Note that in the 2nd order compensated scheme, because the gradient’s zeroth

moment is non-zero at this time, the FID crushers around the refocussing pulse are not

required.

In this study a clinically available high performance gradient system was employed

enabling gradient durations of 43ms/50ms for first/second order motion compensated

gradient schemes. For clinical systems with lower maximum gradient strengths such as

60mT/m or 40mT/m the total gradient durations increase to 51ms/60ms and

64ms/78ms. Prolonged gradient duration increases the sensitivity to motion, since

bulk motion is more likely to deviate from its first and second order Taylor

approximation.

Diffusion weighted imaging generally suffers from low SNR. In this study a 1.5T clinical

system was used. Increasing the main magnetic field strength leads to an increase in

SNR at the cost of larger susceptibility effects in particular in the proximity of the

posterior vein [265]. To reduce susceptibility induced image distortions, the readout

duration may be shortened using parallel imaging at the cost of SNR.

In this study a rather coarse spatial resolution was used to maintain SNR while keeping

the duration of the scan session within applicable limits. Other studies have reported a

spatial resolution of 2×2×5mm3 [56,252] which further reduces sensitivity to bulk

motion for both first [19] as well as second order motion compensation.

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7.5 Conclusion

In this study second order motion compensated spin-echo diffusion encoding was

implemented and compared to first order motion compensated diffusion gradient

waveforms for systolic cardiac diffusion tensor imaging. A significantly decreased

sensitivity to bulk motion compared to first order motion compensated diffusion

gradients was found, enabling cardiac DTI from base to apex at various time points

during systolic contraction.

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Chapter 8 Discussion & Outlook

8. Summary

In this thesis, MR imaging methods have been developed, implemented and validated

which allow measuring cardiac deformation and microstructure in the beating heart.

With the new set of tools quantitative parameters such as cardiac strain and torsion as

well as helix, transverse and sheet angulation of myofiber aggregates of human hearts

have been analyzed non-invasively. The advances in the field of cardiovascular

magnetic resonance imaging presented herein are important for bench-to-bedside

translation of novel imaging approaches potentially leading to robust diagnostic tools

to monitor and guide therapy in cardiac medicine.

8.1 Discussion

In the first part of this thesis spatial-temporal undersampling of 3D myocardial tagging

was developed. Upon scan acceleration only a single breath hold was necessary to

acquire data for 3D myocardial strain analysis. Besides shortening of total scan

duration, the single breath hold acquisitions led to a reduced misalignment of image

stacks, which is of importance for data analysis. While healthy volunteers and patients

in this study tolerated the long breath hold duration, patients with shortness of breath

may have difficulties. By decomposing data acquisition into high resolution

undersampled data and low resolution training data, the benefit of better stack

alignment remains if the training data is acquired in a second breath hold. As a result

of the low spatial resolution of the training data, differences in consecutive breath

hold levels may no longer pose concerns. Alternatively, training data can be acquired

simultaneously as part of a variable density echo planar imaging (EPI) readout at the

cost of reduced temporal resolution. Besides the regular sheared grid sampling

patterns and linear reconstruction used herein, random undersampling in conjunction

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Discussion & Outlook

with non-linear compressed sensing reconstruction may be employed. These methods

rely on the sparsity of the image content itself or an appropriate transformation

thereof. It is foreseeable that the combination of parallel imaging and cosine

transformation of tagged data may outperform linear reconstruction methods. Along

this line, future work should investigate localized spatial transforms using a harmonic

basis in conjunction with partially separable functions to further compress cine tagging

data.

Crucial to the analysis of cardiac motion remains the use of advanced post-processing

methods. In the studies herein either harmonic phase analysis (HARP) or an analysis

based on local sine wave modeling (SINMOD) was used. While HARP allows tracking

cardiac motion with respect to a reference heart phase, it requires a band pass filter in

k-space, which reduces spatial resolution. In contrast, SINMOD works on the

magnitude images and can benefit from the full spatial resolution. However, it results

in relative displacement fields from one heart phase to the next leading to noise

related error integration of motion tracking. Ultimately a combination of both

methods appears promising as it allows using HARP phase data to derive a first

approximation of deformations to subsequently guide SINMOD processing of

unfiltered magnitude data for refinement of the tracking position.

In order to avoid the need for sophisticated post-processing algorithms, tissue

displacements may be encoded directly into the signal phase. Methods such as

displacement encoding with stimulated echoes (DENSE) may be used for this purpose.

Being a phase based method, however, care has to be taken to correct for B0

inhomogeneities. Furthermore, to increase spatial resolution without increasing the

displacement encoding strength, methods to suppress DC- and higher order harmonic

peaks in k-space are required.

The second part of the thesis concerned microstructural imaging of the myocardium.

Both, diffusion weighted stimulated echo acquisition mode (STEAM) and spin echo (SE)

sequences were employed. The inherent sensitivity to myocardial strain of STEAM

based imaging has been addressed and dynamics of myocardial microstructure were

analyzed. The imaging method was accelerated by interleaving imaging slices and

124

heart phases during acquisition. Still, imaging required a large number of breath holds.

Free-breathing STEAM imaging was proposed with dedicated patient feedback

hardware. For potential free-breathing acquisition the herein proposed method

requires modifications. The set of slices has to be imaged as closely as possible in time

to avoid slice mismatch due to breathing during encoding and decoding. Furthermore

the gating using respiratory navigators can be optimized for improved temporal

efficiency [266]. Additional gain in scan time may be achieved by concurrent multi-slice

excitation [244,245] in conjunction with parallel imaging reconstruction.

As an alternative to STEAM, spin-echo based diffusion weighted imaging and diffusion

tensor imaging have been investigated. It has been demonstrated that higher order

motion compensated diffusion gradients enable in-vivo DTI of the human heart during

free breathing without dedicated patient feedback. Due to the prolonged echo time,

however, multiple signal averages were necessary. For multi-slice acquisitions, a slice

interleaving scheme may be employed to increase the repetition time and hence

reduce signal saturation [267] without prolonging the total scan duration.

A general drawback of a single-shot echo-planar readout as it is commonly employed

with diffusion weighted imaging concerns the sensitivity to B0 inhomogeneities. As a

consequence, the shape of the left ventricle (LV) in the vicinity of veins appears

distorted. By acquiring a field map in addition, phase distortions due to field

inhomogeneity may be unwound and the true anatomical shape of the heart can be

recovered [268].

So far, diffusion weighted data of the heart could only be acquired using two-

dimensional (2D) imaging methods. Accordingly, whole-heart myocardial fiber

reconstructions have required sophisticated data interpolation and extrapolation

methods with some assumptions [56,252]. Further advances should be dedicated to

developing three-dimensional (3D) data acquisitions schemes. Such multi-shot imaging

approaches do, however, need to address motion-induced phase inconsistencies to

avoid severe image artifacts. Higher-order motion compensated gradients as

presented herein inherently reduce the motion-induced phase. Accordingly and in

conjunction with low-resolution phase navigators 3D cardiac diffusion weighted

imaging may indeed be attempted in the future.

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From a hardware development perspective, dedicated gradient inserts have been

proposed delivering a maximum strength of 300mT/m at a slew rate of 200mT/m/ms

[269]. With such gradient systems, echo times can be reduced significantly leading to a

gain in signal-to-noise ratio. High performance gradient systems open the path for

single-sided diffusion encoding schemes [255] allowing for high spatial resolution DTI

in-vivo. With the use of very strong field gradients, however, spin dephasing due to

concomitant fields and image distortions due to eddy currents need to be addressed.

8.2 Outlook

Based on microstructural imaging of the myocardium, digital organ modeling is

envisioned, providing a unique opportunity to simulate treatment response prior to

intervention. The response of the heart to ablation, for example, can be simulated

based on digital models that rely on the individual patient’s cardiac anatomy and

microstructure. In a future setting, virtual ablations may be performed to guide

interventions by predicting the resulting changes of signal conduction within the

myocardium. Furthermore, modeling of electro-mechanical coupling may allow

extrapolating changes in mechanical efficiency of the heart upon intervention. The

study of effects of myocardial scaring due to infarction or interventions to manipulate

myocardial strain distribution is a possible scenario, which may help avoiding

undesired strain hot spots potentially leading to remodeling and failure of the heart.

From a clinical perspective, myocardial tagging as well as cardiac DTI are considered

essential tools to help furthering our understanding of cardiac pathophysiology. To this

end, it is of interest to investigate the link between function and form of the in-vivo

heart. Examples are dilated cardiomyopathy, which is associated with altered rotation

and radial contraction patterns or non-compaction and cardiac hypertrophy which

result from altered myocardial structure.

In the context of heart failure diagnosis, it is appealing to define a mechanical

efficiency index linking cardiac function to myocardial structure for individual patients.

In the pathological setting, atypical contraction pattern relate to microstructural

abnormalities. Based on in-vivo imaging the risk of progressive alteration in

126

contraction pattern may be predicted and intervention prior to the onset of symptoms

may be facilitated. Resulting myocardial remodeling and changes of cardiac motion can

be monitored non-invasively at regular intervals.

In regenerative medicine, stem cells are studied for post-infarction treatment. The

efficacy of treatment depends on cell origin, organization and cell delivery. While

histology is the gold standard to measure tissue alteration upon therapy post-mortem,

ejection fraction has been used as a measure of treatment success in-vivo. With

myocardial tagging, myocardial strain and torsion can be added to the array of

diagnostic readouts. Importantly, cardiac DTI now allows to perform “virtual histology”

and therefore myocardial microstructure can be quantified longitudinally in-vivo.

127


128

Abbreviations

Abbreviations in alphabetic order

ADC Apparent Diffusion Coefficient

bpm beats per minute

CAD Coronary Artery Disease

CANSEL Cosine ANd Sine acquisitions to ELiminate artifacts generating echoes

CDENSE Complementary Displacement Encoding with Stimulated Echoes

CMR Cardiovascular Magnetic Resonance

CNR Contrast to Noise Ratio

CRT Cardiac Resynchronization Therapy

CS Compressed Sensing

CSPAMM Complementary SPatial Modulation of Magnetization

DANTE Delays Alternating with Nutations for Tailored Excitation

DENSE Displacement Encoding with Stimulated Echoes

DIA DIAstole

DSI Diffusion Spectrum Imaging

DTI Diffusion Tensor Imaging

DWI Diffusion Weighted Imaging

ECG ElectroCardioGram

EF Ejection Fraction

FA Fractional Anisotropy

FAST Fourier Analysis of STimulated echoes

FID Free Induction Decay

FOV Field Of View

HARP HARmonic Phase

HF Heart Failure

129

Abbreviations

HR Heart Rate

IVIM Intra Voxel Incoherent Motion

LBBB Left Bundle Branch Block

LGE Late Gadolinium Enhancement

LV Left Ventricle

M Measurement/Frequency encoding direction

MD Mean Diffusivity

MI Myocardial Infarction

MRI Magnetic Resonance Imaging

MRT Magnet Resonanz Tomographie

N.S. Not Significant

ODF Orientation Distribution Function

P Phase encoding direction

PCA Principal Component Analysis

PDF Probability Density Function

QSI Q-Space Imaging

RF Radio Frequency

S Slice encoding direction

SD Standard Deviation

SE Spin Echo

SEE Standard Error of the Estimate

SENC Strain ENCoding

SINMOD SINe wave MODeling

SNR Signal to Noise Ratio

SPAMM SPatial Modulation of Magnetization

SPECT Single Photon Emission Computed Tomography

STEAM STimulated Echo Acquisition Mode

SYS SYStole

TE echo time

TM mixing time

TMIP Temporal Maximum Intensity Projection

TR repetition time

130

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List of Publications


Journal publications 1. Stoeck CT, Kalinowska A, von Deuster C, Harmer J, Chan RW, Niemann M, Manka R,

Atkinson D, Sosnovik DE, Mekkaoui C, Kozerke S, Dual-Phase Cardiac Diffusion Ten-sor Imaging With Strain Correction, PLoS one 2014

2. Winklhofer S, Stoeck CT, Berger N, Thali M, Manka R, Kozerke S, Alkadhi H, Stolzmann P, Post-mortem cardiac diffusion tensor imaging: detection of myocardi-al infarction and remodeling of myofiber architecture, Eur Radiol. 2014

3. Chan RW, von Deuster C, Giese D, Stoeck CT, Harmer J, Aitken AP, Atkinson D, Kozerke S, Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring, J Magn Reson. 2014

4. Sosnovik DE, Mekkaoui C, Huang S, Chen HH, Dai G, Stoeck CT, Ngoy S, Guan J, Wang R, Kostis WJ, Jackowski MP, Wedeen VJ, Kozerke S, Liao R, Microstructural impact of ischemia and bone marrow-derived cell therapy revealed with diffusion tensor magnetic resonance imaging tractography of the heart in-vivo, Circulation. 2014

5. Toussaint N, Stoeck CT, Schaeffter T, Kozerke S, Sermesant M, Batchelor PG, In-vivo human cardiac fibre architecture estimation using shape-based diffusion tensor processing, Med Image Anal. 2013

6. Wang H, Stoeck CT, Kozerke S, Amini AA, Analysis of 3D cardiac deformations with 3D SinMod, IEEE Eng Med Biol Soc. 2013

7. Weiss K, Summermatter S, Stoeck CT, Kozerke S, Compensation of signal loss due to cardiac motion in point-resolved spectroscopy of the heart, Magn Reson Med. 2013

8. Zurbuchen A, Pfenniger A, Stahel A, Stoeck CT, Vandenberghe S, Koch VM, Vogel R, Energy harvesting from the beating heart by a mass imbalance oscillation genera-tor, Ann Biomed Eng. 2013

9. Stoeck CT, Manka R, Boesiger P, Kozerke S, Undersampled cine 3D tagging for rapid assessment of cardiac motion, J Cardiovasc Magn Reson. 2012

10. Manka R, Kozerke S, Rutz AK, Stoeck CT, Boesiger P, Schwitter J, A CMR study of the effects of tissue edema and necrosis on left ventricular dyssynchrony in acute myo-cardial infarction: implications for cardiac resynchronization therapy, J Cardiovasc Magn Reson. 2012

151


11. Stoeck CT, Hu P, Peters DC, Kissinger KV, Goddu B, Goepfert L, Ngo L, Manning WJ,

Kozerke S, Nezafat R, Optimization of on-resonant magnetization transfer contrast in coronary vein MRI, Magn Reson Med. 2010

12. Toussaint N, Sermesant M, Stoeck CT, Kozerke S, Batchelor PG, In-vivo human 3D cardiac fibre architecture: reconstruction using curvilinear interpolation of diffusion tensor images, Med Image Comput Comput Assist Interv. 2010

13. Hu P, Stoeck CT, Smink J, Peters DC, Ngo L, Goddu B, Kissinger KV, Goepfert LA, Chan J, Hauser TH, Rofsky NM, Manning WJ, Nezafat R, Noncontrast SSFP pulmo-nary vein magnetic resonance angiography: impact of off-resonance and flow, J Magn Reson Imaging. 2010

14. Hu P, Chuang ML, Ngo LH, Stoeck CT, Peters DC, Kissinger KV, Goddu B, Goepfert LA, Manning WJ, Nezafat R, Coronary MR imaging: effect of timing and dose of iso-sorbide dinitrate administration, Radiology. 2010

15. Stoeck CT, Han Y, Peters DC, Hu P, Yeon SB, Kissinger KV, Goddu B, Goepfert L, Manning WJ, Kozerke S, Nezafat R, Whole heart magnetization-prepared steady-state free precession coronary vein MRI, J Magn Reson Imaging. 2009

Patient cases

1. Harmer J, Pushparajah K, Toussaint N, Stoeck CT, Chan R, Atkinson D, Razavi R, Kozerke S, In-vivo Mapping of Myofiber Architecture in the Systemic Right Ventricle, Eur Heart J. 2013

Conference proceedings 1. Stoeck CT, Kalinowska A, von Deuster C, Harmer J, Kozerke S, In-vivo dual-phase

cardiac DTI with 3D strain correction, ISMRM 2014, Milan Italy, poster presenta-tion, p. 2429

2. Deuster C, Stoeck CT, Buehrer M, Harmer J, Chan RW, Atkinson D, Kozerke S, Free-breathing cardiac DTI with simultaneous multi-slice excitation, ISMRM 2014, Milan Italy, oral presentation, p. 671

3. Harmer J, Chan RW, Stoeck CT, von Deuster C, Atkinson D, Kozerke S, Correction of Off-resonance Distortions in In-vivo Cardiac Diffusion Tensor Imaging, ISMRM 2014, Milan Italy, poster presentation, p. 4461

4. Mekkaoui C, Stoeck CT, Jackowski MP, Reese TG, Kozerke S, Sosnovik DE, Micro-structural Characterization of the Infarct Border Zone in Humans with In-vivo Diffu-sion Tensor MRI and “Gray-Zone” Late Gadolinium Enhancement, ISMRM 2014, Mi-lan Italy, oral presentation, p. 3973

5. Mekkaoui C, Jackowski MP, Stoeck CT, Thiagalingam A, Kostis WJ, Ruskin JN, Tim Reese TG, Kozerke S, Sosnovik DE, Detection of Infarcted and Arrhythmogenic Myo-

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cardium with DTI Tractography and Electroanatomical Voltage Mapping, ISMRM 2014, Milan Italy, poster presentation, p. 0239

6. Mekkaoui C, Jackowski MP, Sakadzic S, Stoeck CT, Reese TG, Kozerke S, Ott HC, Sosnovik DE, Impact of the Connective Tissue Matrix in the Myocardium on the Re-striction of Water Revealed with Diffusion Tensor MRI of a Decellularized Human Heart, ISMRM 2014, Milan Italy, poster presentation, p. 188

7. Chan RW, von Deuster C, Stoeck CT, Harmer J, Kozerke S, Atkinson D, High-Resolution Diffusion Tensor Imaging (DTI) of the Human Kidneys using a Free-Breathing Multi-Slice Targeted-FOV Approach, ISMRM 2014, Milan Italy, poster presentation, p. 2553

8. Niemann M, Stoeck CT, Manka R, Kozerke S, Revealing Ultrastructural Morphology in Hypertrophic Cardiomyopathy using Diffusion Tensor Imaging, DGK 2014, Mann-heim Germany, poster presentation

9. Stoeck CT, Deuster C, Toussaint N, Kozerke S, High-resolution multi-slice single-shot cardiac DTI using asymmetric diffusion encoding, ISMRM 2013, Salt Lake City USA, oral presentation, p. 480, summa cum laude award

10. Wang H, Stoeck CT, Kozerke S, Amini AA, 3D Left-Ventricular Deformation Analysis from 3D CSPAMM with 3D SinMod, ISMRM 2013, Salt Lake City USA, poster presen-tation, p. 1430

11. Toussaint N, Stoeck CT, Schaeffter T, Sermesant M, and Kozerke S, Cardiac Laminae Structure Dynamics from In-vivo Diffusion Tensor Imaging, ISMRM 2013, Salt Lake City USA, oral presentation, p. 484 summa cum laude award

12. von Deuster C, Stoeck CT, Giese D, Harmer J, Chan RW, Atkinson D, and Kozerke S, Concurrent dual-slice cardiac DTI of the in-vivo human heart, ISMRM 2013, Salt Lake City USA, poster presentation, p. 2099

13. Harmer J, Toussaint N, Pushparajah K, Stoeck CT, Chan RW, Razavi R, Atkinson D, Kozerke S, In-vivo Diffusion Tensor Imaging of the Systemic Right Ventricle at 3T, ISMRM 2013, Salt Lake City USA, poster presentation, p. 3098

14. Harmer J, Stoeck CT, Chan RW, Atkinson D, Kozerke S, In-Vivo High Resolution Dif-fusion Tensor Imaging of the Human Heart at 3T:Fat Suppression in the presence of B0 field inhomogeneities, ISMRM 2013, Salt Lake City USA, poster presentation, p. 3206

15. Weiss K, Summermatter S, Stoeck CT, Kozerke S, Compensation of signal loss due to cardiac motion in point-resolved spectroscopy of the heart, ISMRM 2013, Salt Lake City USA, poster presentation, p. 1363

16. Chan RW, Kozerke S, Giese D, Harmer J, Stoeck CT, von Deuster C, Aitken A, Atkin-son D, Characterization and Correction of Eddy-Current Artifacts in Unipolar and Bi-polar Diffusion Sequences using a Field-Monitoring Approach: Application to Renal Diffusion Tensor Imaging (DTI), ISMRM 2013, Salt Lake City USA, poster presenta-tion, p. 2576

17. Schneeweis C, Schnackenburg B, Stoeck CT, Berger A, Hucko T, Fleck E, Kelle S, Messroghli D, Gebker R, Characterization of myocardium and myocardial motion in

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patients considered for transaortic valve implantation (TAVI) , SCMR 2013, San Francisco USA, poster presentation

18. Stoeck CT, Toussaint N, Boesiger P, Kozerke S, Dual heart-phase cardiac DTI using Local-look STEAM, ISMRM 2012, Melbourne Australia, oral presentation, p. 227 summa cum laude award

19. Toussaint N, Stoeck CT, Kozerke S, Semesant M, Schaeffter T, Statistical Atlas of the Human Left Ventricular Fibre Architecture using In-Vivo DT-MRI, ISMRM 2012, Mel-bourne Australia, oral presentation, p. 227 magna cum laude award

20. Stoeck CT, Toussaint N, Boesiger P, Batchelor PG, Kozerke S, Sequence timing opti-mization in multi-slice diffusion tensor imaging of the beating heart, ISMRM 2011, Montréal Canada, oral presentation, p. 282

21. Stoeck CT, Nezafat R, Boesiger P, KozerkeS, 3D Whole Heart CSPAMM tagging in a single Breath hold using k-t-PCA, ISMRM 2010, Stockholm Sweden, oral presenta-tion, p. 483

22. Toussaint N, Stoeck CT, Sermesant M, Kozerke S, Batchelor P, Three-dimensional Prolate Spheroidal Extrapolation for Sparse DTI of the In-vivo Heart, ISMRM 2010, Stockholm Sweden, oral presentation, p. 758

23. Stoeck CT, Peters DC, Han Y, Kissinger KV, Goddu B, Goepfert L, Manning WJ, Kozerke S, Nezafat R, On-resonant binomial pulse preparation for magnetic transfer contrast enhanced coronary vein imaging, ISMRM 2009, Honolulu Hawaii, poster presentation, p. 1893

24. Stoeck CT, Crean A, Greenwood JP, Boesiger P, Plein S, Kozerke S, In-vivo compari-son of CSPAMM and DENSE for cardiac motion analysis, ISMRM 2009, Honolulu Hawaii, poster presentation, p. 1816

25. Hu P, Stoeck CT, Peters DC, Kissinger KV, Goddu B, Goepfert L, Rofsky N, Manning N, Nezafat R, Quantification of Pulmonary Vein Off-Resonance Frequency Through Cardiac Cycle: Implications for Non-Contrast PV MRA, ISMRM 2009, Honolulu Ha-waii, poster presentation, p. 3933

26. Stoeck CT, Kozerke S, Maredia N, Crean A, Greenwood JP, Plein S, In-vivo compari-son of DENSE and CSPAMM for cardiac motion analysis, SCMR 2009, Orlando USA, poster presentation

27. Hu P, Stoeck CT, Peters DC, Kissinger KV, Goddu B, Goepfert L, Manning WJ, Nezaf-at R, Coronary MRI with induced vasodilation using isosorbide dinitrate, SCMR 2009, Orlando USA, poster presentation

28. Stoeck CT, Peters DC, Han Y, Goddu B, Manning WJ, Kozerke S, Nezafat R, Whole Heart Coronary Vein Imaging, ISMRM 2008, Toronto Canada, poster presentation

29. Nezafat R, Stoeck CT, Bengani P, Peters DC, Hauser T, Rofsky N, Manning WJ, Non-Contrast Pulmonary Vein Angiography using Off-Resonance RF Excitation, ISMRM 2008, Toronto Canada, poster presentation

154

30. Hu P, Stoeck CT, Peters DC, Manning WJ, Nezafat R, Off-resonance effect of non-contrast pulmonary vein imaging, Magnetic Resonance Angiography Workshop 2008, Graz Austria

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156

Acknowledgements

Acknowledgements

First of all I would like to thank my thesis advisor Prof. Sebastian Kozerke. Besides

guiding me through the endeavor of conducting research in a very competitive field, I

am grateful for his insights into academic politics and his help with my first steps

towards an independent academic career. He managed to keep me on track, whenever

I was wandering off different paths. My stubbornness might have led to some gray hair

though, for which I want to apologize.

I also want to thank my co-examiners Prof. Gábor Székely and Dr. David Atkinson for

agreeing on being referees for this thesis as well as providing feedback.

This thesis marks a break point of a timeline that goes back a few years. Along my

journey in MRI-science I had the ability to meet a crowd of funny, helpful and inspiring

people. I would like to thank the people responsible getting me in touch with MRI:

Prof. Markus Rudin, Dr. Christof Baltes, Dr. Thomas Müggler and the Animal Imaging

Center crew under whose supervision I made my first MR related scientific steps. Next

stop was former head of institute Prof. Peter Bösiger, who despite not having met me

before, supported my wish to conduct my master project in Boston. He deserves my

thanks and respect, also for establishing a relaxed but successful working environment,

and not to be forgotten granting me money to book the conference accommodation

for half the institute’s staff in Honolulu within the first six months of my PhD studies.

In Boston my way crossed Prof. Warren Manning’s and Prof. Reza Nezafat’s who I

thank for their warm welcome and the ongoing support. My project advisor Reza made

science look fun and easy, with his open minded and very calm approach to nearly

everything. In the end this experience contributed significantly to my conclusion of

staying in cardiac MR upon return to Zurich.

157

Acknowledgements

At this point I will break with the motto of the cardio team and throw out a

compliment: You guys rock! At first, a big Thank you to the “old” cardio squad: Verena,

Kilian, Rudi, Johannes, Lukas and Daniel, for forming my PhD-family. A big hug to

Verena, our “chief of staff” at ETZ F 61.2, and Rudi as her deputy. I would have to

thank Johannes for his continuous IT support for the entire office, but more

importantly and together with Lukas, Kilian and Daniel for their friendship beyond

office hours. Kilian, I hereby accept the draw in our fight for desk domination. I also

want to thank Nicolas Toussaint who not only added the necessary amount of chaos to

science, but also well complimented my work on data acquisition strategies by his PhD

studies on data reconstruction and evaluation. Even considering the sorrow hours

every PhD-student has to go through, I had a great time and the cardio family played a

major role. The bar has been set high for the next generation to come, but some say

that they will be capable of handling it. The “old” cardio team has been gradually

replaced by the “new” gang: Julia, Constantin, Max, Patrick, Claudio, Christian, Georg,

Adrian, Jonas, Kerem, Zsófia and Martin Genet; and I am grateful to them, that the

tradition of having a good social environment has not come to an end. A special Thanks

goes to Constantin who was brave enough to join the cardiac-DTI team, thereby

doubling its man-power, and on top joining in for the regular night shifts and weekend

scanning sessions.

I would like to thank the MDs: Robert Manka, Markus Niemann, Alexander Gotschy,

Andrei Manoliu, Maximilian Emmert, Nikola Cesarovic, Thea Fleischmann and Miriam

Lipiski for giving me insights into the medical and not-so-medical part of clinics and

veterinary medicine. Similarly I have to thank Christina Heep, Anja Struwe, Ines Bühler

and Simone Kaufmann who have always been incredibly patient whenever I was

interfering with their tight patient schedule, acquiring some extra data or crashing the

MR-system.

Thank you to the Gastro/Diffusion team: Jelena aka. Jelly, Caro, Robert and Tobias who

I consider part of the PhD-family I “grew up” with. I keep a lot of good memories!

My gratitude also goes to Marianne Berg who has been managing the institute ever

since I started here, helping me with all administrative issues in an exceptional way,

158

Roger Lüchinger for his help whenever the MRI-scanner did not agree with me and

thought of shutting down, crashing or surprising me with some arbitrary error

messages as well as Bruno Willi responsible that IT was in order. Furthermore I would

like to thank Martin Bührer and Gérard Crelier for providing their software and

software support.

The IBT-experience would not have been the same without all the fellow PhD students

at the institute. Especially without Johanna, Max and Lars who started the same time

as I did. Not to forget the Hardware and Spectro groups that contributed to the very

appealing working and post-working environment.

Finally and most of all I want to thank my family. I would not have been able to reach

this stage, without their unconditional support and efforts, which showed me that

every challenge can be overcome. I am grateful for my aunts’, my uncles’ and

especially my grandparents’ support, insuring, that none of the doors you find along

the way is locked for me. With this I would like to thank my sister Ina, for being the

most important key. Over the years I have had many opportunities to glance at the big

picture of the world, which I consider a privilege I owe my family.

Thank You!

159

Acknowledgements

160

Curriculum Vitae

Curriculum Vitae

Personal information

Name: Christian Torben Stoeck

Date of Birth: June 10th, 1984 in Hannover, Germany

Citizenship: German

Education & Affiliation

09/2008-09/2014 PhD candidate

Supervisor: Prof. Dr. Sebastian Kozerke

Institute for Biomedical Engineering

Department of Information Technology and Electrical Engineering

ETH Zurich, Zurich, Switzerland

10/2007-10/2013 Associate in Medicine

Harvard Medical School Boston, USA

09/2007-03/2008 Diploma in Physics

ETH Zurich, Zurich, Switzerland

10/2007- 03/2008 Diploma thesis

Title: “Optimization of Coronary Vein MRI using on-resonance Magnetization Transfer”

Supervision: Prof. Dr. Sebastian Kozerke, Prof. Dr. Reza Nezafat

Beth Israel Deaconess Medical Center

Division of Cardiology

Harvard Medical School Boston, USA.

161

Curriculum Vitae

06/2005-07/2006 ERASMUS exchange

The Royal Institute of Technology / KTH Stockholm, Sweden

05/2003 High-School

Friedrich-Hecker-Gymnasium, Radolfzell am Bodensee, Germany

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Magnetic Resonance Motion and Diffusion Encoding of the Heart

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