Blood Velocity and Volumetric Flow Rate Calculated from Dynamic 4D CT
Angiography using a Time of Flight Approach
By
Joseph Barfett
A thesis submitted in conformity with the requirements for the degree of Master of Science
Graduate Department of the Institute of Medical Science University of Toronto 2014
© Joseph Barfett (2014)
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Blood Velocity and Volumetric Flow Rate Calculated from
Dynamic 4D CT Angiography using a Time of Flight Approach
Joseph John Barfett
Master of Science
Institute of Medical Science
University of Toronto
2014
Abstract
Purpose: A time of flight approach to the analysis of 4D CT angiography is examined to
calculate blood flow in arteries. Materials and Methods: Software was written to track
contrast bolus TOF along a central vessel axis. Time density curves were analyzed to
determine bolus time to peak at successive vessel cross-sections which were plotted
against vessel path length. A line of best fit was plotted through the resulting data and
1/slope provided a measurement of velocity. Results: Validation was successful in
simulation and in flow phantoms, though quality of results depended strongly on quality
of curve fit. In phantoms and in vivo, accuracy and reproducibility of measurements
improved with longer path lengths and, in vivo, depended on the avoidance of venous
contamination. Conclusions: Quantitative functional intravascular information such as
blood velocity and flow rate may be calculated from 4D CT angiography.
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Dedicated to the loving memory of Caterina Ruscio.
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Acknowledgements
I would like to firstly thank my wife and best friend Dr. Stephanie Serniwka. You’ve
given me the courage to pursue my dreams and you’ve been there for the support I’ve
depended on as I struggle through projects, courses, exams and call duties. Life is just
beginning for us and I can’t wait for it!
I owe everything to my loving family Kevin, Barbara and Kara Barfett, who have
supported and encouraged my scientific interests over the decades, from chemistry sets to
pets and model rocketry to a little bit of basement aquaculture every now and then, plus a
great deal in between… I had the best time growing up that I can imagine. No new
computer or aquarium or music lesson or sport was ever too expensive for my parents.
Your love and support is something I can never repay.
Thank you to all the teachers that have much influenced me over the years. In particular I
would like to thank my senior elementary school teacher Mrs. Adele Wolf, my high
school science department head Mrs. Elizabeth Massaro (for tolerating my late night
endeavors in the high school science lab), Christopher Clifford and Rick Santavica (who
first taught me Chemistry), as well as Rick Kitto and Tom Deslippe (who first taught me
to program a computer).
My special thanks to Dr. Argyrios Margaritis, former Department Chair of Chemical and
Biochemical Engineering at the University of Western Ontario, for beginning to mentor
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me as a high school student and then as the first student through the UWO
chemical/biochemical engineering with medicine program. I’m going to great things with
what you taught me.
Thank you as well to Dr. Tony Rupar, for all of the wonderful summers in the lab
learning to think as a scientist and a clinician. I’ve put what I’ve learned to good use and I
look forward to visiting the lab again soon.
My thanks to Dr. David Mikulis and Dr. Walter Kucharczyk, two of my many mentors in
medical imaging at the University of Toronto and two of the brightest and kindest minds
in the city. Also my sincere thanks to the many exception scientists in Toronto from
whom I have learned so much, especially Dr. Adrian Crawley, Dr. Andrea Kassner, Dr.
Timo Krings, Dr. Paul Dufort, Dr. Jeff Jaskolka and Dr. Andrew Crean.
Finally my sincere thanks to all of my friends through the years, including friends of the
four-legged variety. I’m sorry that work has kept me so focused and I look forward to
some gentler days ahead.
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Table of Contents
Abstract ii
Dedication iii
Acknowledgements iv
List of Abbreviations ix
List of Tables x
List of Figures xi
List of Equations xii
List of Appendices xiii
1.0) Introduction 1
1.1) Context on the development of volumetric CT angiography 6
1.2) Statement of hypothesis 11
1.3) Basic indicator dilution theory 12
1.4) Introduction to functional angiography 21
1.5) Intra-luminal fluid velocity from volumetric 4D CT Data 25
1.6) The Time of Flight (TOF) CT Angiography (CTA) Algorithm 29
2.0) Materials and Methods 32
2.1) Programming environment 32
2.2) CT equipment 33
2.3) Creating flow simulations for TOF CTA validation 33
2.4) Construction and scanning of CT phantoms 34
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2.5) Scanning of clinical cases 35
2.6) Algorithms for segmentation of the intravascular space 36
2.7) Creation of functional angiograms 40
2.8) The TOF CTA algorithm 41
2.9) Implementation of TOF CTA in simulations, phantoms…
and clinical series 43
3.0) Results 45
3.1) Functional angiographic maps 46
3.2) Simulated flow data for algorithm validation 55
3.3) Data from CT flow phantoms 58
3.4) In vivo TOF CTA data versus phase contrast MRA 62
3.5) In vivo TOF CTA data in major intracranial arteries
of 8 normal subjects 65
4.0) Discussion 68
4.1) Functional angiography in CT imaging 69
4.2) Limitations of functional angiography 71
4.3) TOF CTA algorithm 73
4.4) Automation of the TOF approach 74
4.5) Validation of TOF CTA software in flow simulations 76
4.6) Validation of TOF CTA in flow phantoms 77
4.7) TOF CTA in the internal carotid artery 80
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4.8) TOF CTA in the major intracerebral vessels 82
4.9) Advantages and Disadvantages of TOF CTA versus
Doppler and pcMRA 84
4.10) Further applications of TOF CTA and exploration of
the technique 85
4.11) New methods of perfusion calculation using TOF CTA 91
4.12) TOF CTA with dual energy CT: flow, perfusion and
capillary permeability 92
5.0) Conclusions 99
6.0) Appendix I – Python source code for creation of vascular segmentations 103
7.0) Appendix II – Python source code for TOF CTA 110
8.0) References 117
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List Of Abbreviations
ACA – anterior cerebral artery
AUC – area under curve
AVM – arteriovenous malformation
DAVF – dural arteriovenous fistulae
ECA – external carotid artery
CT – computed tomography
CTA – computed tomography angiography
ICA – internal carotid artery
MCA – middle cerebral artery
MRA – magnetic resonance angiography
MRI – magnetic resonance imaging
MTT – mean transit time
PCA – posterior cerebral artery
pcMRA – phase contrast magnetic resonance angiography
TAC – time attenuation curve
TOA – time of arrival
TOF – time of flight
TTP – time to peak
U/S - ultrasound
x
List of Tables
3.1) Calculation of bulk velocity in a simulated flow channel 56
3.2) Contrast bolus time of flight analysis in flow phantoms
subject to dynamic volumetric 4D CT at 0.6 cm pipe diameter 59
3.3) Contrast bolus time of flight analysis in flow phantoms
subject to dynamic volumetric 4D CT at 0.3 cm pipe diameter 60
3.4) Blood velocity in the internal carotid artery of 4 patients
measured by TOF CTA angiography versus phase
contrast magnetic resonance angiography 63
3.5) Blood velocity measured by TOF CTA in the major cerebral
arteries of 8 consecutive normal subjects 66
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List of Figures
1.1) Conventional CT perfusion image of the brain 9
1.2) Movement and dispersion of an indicator in a pipe 14
1.3) Indicator flow from pipes of small to larger cross-sectional area 17
1.4) Divergent flow in pipes with a stenosis 19
1.5) Models of intravascular time density curves 23
1.6) Basis of intraluminal fluid velocity calculation via the
video densitometry approach 27
2.1) 4D CT protocol used to scan the clinical Series 38
3.1) Sample renderings of functional angiograms compared to
routinely available Maximum Intensity Projections (MIPs) 47
3.2) Patient with right dural arteriovenous fistula (DAVF)
demonstrating decreased mean transit time (MTT) in the
right transverse sinus on functional angiogram 49
3.3) Axial slice and volume rendering of functional angiogram
encoding time to peak (TTP) in a patient with right
DAVF and cortical venous reflux 50
3.4) Functional versus conventional angiogram in vasospasm 51
3.5) Subclavian steal on planar and volume rendered functional angiography 53
3.6) Functional angiogram encoding TTP in a giant right cavernous
carotid aneurysm 54
3.7) Typical graphical results of a simulated TOF CTA flow calculation 57
3.8) Typical results of TOF CTA calculation in a pipe flow phantom 61
3.9) TOF CTA in an example internal carotid artery 64
4.1) TOF CTA in the pulmonary circulation 87
4.2) TOF CTA in the internal iliac artery 88
4.3) TOF CTA in a case of subclavian steal 89
4.4) Distortion of the time density curve by presence of a severe stenosis 94
4.5) Hypothetical dual tracer system for intravascular flow quantification 96
xii
List of Equations
1.1) Stewart-Hamilton equation 15
1.2) Gamma variate equation 22
1.3) Quadratic curve 37
xiii
List of Appendices 1) Python source code for creation of vascular segmentations 102
2) Python source code for TOF CTA 109
1
1.0) Introduction
The imaging and measurement of blood flow in vessels and in tissues is ubiquitous in the
daily practice of diagnostic radiology and necessary for the accurate diagnosis of innumerable
pathologies across all modalities. It necessarily follows therefore that fluoroscopic angiography
(Alfonso et at. 2000; Shilfoygel et al. 1999; Shilfoygel et al. 2000), ultrasound (Allan 2000;
Shung 2006; Hoskins et al. 2010), computed tomography (CT) (Barfett et al. Jul 2010; Barfett et
al. Dec 2010; Prevrhal et al. 2011) and magnetic resonance imaging (MRI) (Zhao et al. 2007;
Meckel et al. 2013) can all provide assessment of blood flow by quantitative means via
commercially available software. The clinical practice of in vivo blood flow imaging may be
divided into the assessment of the macroscopic intravascular space (i.e. flow within the lumen of
arteries, arterioles, veins and venules) and the assessment of microvascular flow in tissues (i.e.
tissue perfusion, usually quantified in terms of mL of blood flowing into tissue and expressed
per unit volume of tissue per unit time). Both problems differ substantively, and although
technical approaches to the assessment of blood flow in vessels depends strongly upon the
modality employed, the measurement of tissue perfusion is in principle similar across modalities
(Allmendinger et al. 2012; Sourbron et al. 2011; Leiva-Salinas 2011; Abels et al. 2010; Hom et
al. 2009; Miles, Eastwood and Konig 2007; Miles and Cuenod 2007).
The calculation of tissue perfusion is generally performed using dynamic contrast
enhanced protocols (Salomon et al. 2009; Blomely et al. 1997; Allmendinger et al. 2012;
Sourbron et al. 2011) and draws heavily on the indicator dilution literature. The most common
techniques used to assess tissue perfusion are dynamic contrast enhanced computed tomography
(CT) (Miles, Eastwood and Konig 2007; Leiva-Salinas et al. 2011; Leiva-Salinas, Provenzale et
al. 2011; Michel et al. 2011; Konstas et al. 2011) and MRI (Sourbron et al. 2011) for which a
2
variety of suitable algorithms have been extensively described including the maximum slope
(Abels et al. 2010), deconvolution (Abels et al. 2010; Fieselmann et al. 2011) and Patlak
approaches (Hom et al. 2009; Ichihara et al. 2009). CT and MRI perfusion algorithms have
generally depended upon the central volume principle (Sourbron et al. 2011), which states that
microscopic blood flow in tissues can be calculated independently of intra-arterial blood flow if
blood volume and mean transit time (MTT) are known (Sourbron et al. 2011; Fieselmann et al.
2011).
Quantitative assessment of hemodynamics in macroscopic blood vessels, conversely,
depends strongly on the modality under consideration. The most commonly used clinical
technique is Doppler ultrasound (Allan et al. 2000, Shung 2006) to measure intravascular blood
velocity and the intravascular cardiac waveform via the Doppler effect (Allan et al. 2000). All
modern ultrasound systems provide Doppler capability. Examples of common situations in
which Doppler ultrasound is used include the assessment of major veins for blood clots, the
assessment of blood velocity including the velocity waveform through the cardiac cycle in
major vessels including major arteries in the abdomen, neck, head, limbs and in the portal vein,
as well as use of the technique at a tissue level to determine whether a region under examination
is indeed perfused by the circulation and hence viable or represents exogenous matter such as
debris or clotted blood (Evans et al. 2011). Ultrasound is limited however in that the technique
cannot be used to assess blood vessels surrounded by air in the lungs (Mazurek et al. 2013) and
is of limited utility in assessment of the adult brain due to sound attenuation by the skull.
Transcranial Doppler can provide a gross measurement of flow in intracranial arteries and is
notoriously user dependent, though low cost and convenient (Purkayastha et al. 2012),
functioning most optimally in the hands of experienced operators.
3
Less commonly used is the phase contrast MRI technique (pcMRA) (Zhao et al. 2007;
Yigit et al. 2011; Miyazaki M 2012; Mihai et al. 2011; Brockman et al. 2011; Mendrik et al.
2010), which nonetheless can provide rigorous assessment of intravascular hemodynamics
including mean flow and a flow waveform with the cardiac cycle. Phase contrast MRI is most
commonly used in cardiac imaging centers to measure flow in large arteries such as the
pulmonary artery and aorta (Markl et al. 2012). Because the technique can provide time-
dependent assessment of flow through-out the cardiac cycle, pcMRA can provide assessment of
retrograde flow through incompetent cardiac valves as well as diagnose intra-cardiac shunts by
detecting larger than expected differences between aortic and pulmonary arterial flow. There has
been some interest in the use of pcMRA in the brain to assess blood flow to aneurysms (Hope et
al. 2011) and other vascular lesions though the clinical utility of such information is lacking.
Quantitative assessment of the macroscopic intravascular space using CT has received
only limited attention in the literature. Although such assessment is of course clinically useful in
the evaluation of a wide array of pathology, CT scanners until recently did not support
sufficiently wide coverage to enable bolus tracking in organs of interest. Recent advances in CT
technology, particularly the development of increasingly powerful volumetric CT devices using
cone beam (Kalender et al. 2007; Klingebiel et al. 2009; Salomon et al. 2009; Luo et al. 2011;
Matsumoto et al. 2007), have enabled quantitative assessment of blood flow in the intravascular
space. To date, the CT literature has focused upon two main approaches for the assessment of
intravascular physiology. The first is the use of dynamic volumetric CT to characterize tissue
deformation with time and this has centered primarily upon cardiac motion (Tsao et al. 2010,
Ciolina et al. 2010) and the deformation of intracranial aneurysms (Mischi et al. 2005;
Hayakawa et al. 2011, Krings et al. 2009). The second and more recent technique, which has in
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particular focused upon the use of a 4D volumetric CT on larger, 8 or 16cm detector arrays, has
been the dynamic examination of contrast media flow through various vascular lesions including
stroke (Dorn et al. 2011; Divani et al. 2011), arteriovenous malformations (AVMs) and
arteriovenous fistulae (AVFs) including dural arteriovenous fistulae (DAVFs) (Salomon et al.
2009; Barfett et al. Jul 2010; Willems et al. 2011; Pekkola et al. 2009), as well as assessment
vascular endografts and their associated complications including endoleaks (Inoue et al. 2011;
Bent et al. 2010).
Truly quantitative evaluation of the intravascular space with CT, particularly with
regards to blood flow dynamics, has only been recently described (Barfett et al. Dec 2010;
Prevrhal et al. 2011). The approach has taken two forms, both of which have extended the video
densitometric approach that was first characterized in conventional angiography and has been
reviewed (Shpilfoygel et al. 1999; Shpilfoygel et al. 2000). The first is through the creation of
intravascular functional maps to encode well known functional parameters such as time of
arrival (TOA), time to peak (TTP) or maximum slope of the spatially congruent contrast bolus
intensity versus time profiles (Barfett et al. Jul 2010), and is further described in section 1.2 of
this manuscript. The second approach builds upon the first through the analysis of delay in TOA
of a contrast bolus between proximal and distal cross-sections of a vessel in comparison to the
distance between these cross-sections, a user-dependent technique capable of providing velocity
measurements (Alfonso et al. 2000; Shpilfoygel et al. 1999; Barfett et al. Dec 2010).
In brief, the data obtained by the analysis of bolus arrival in consecutive vessel cross
sections is plotted as a function of distance along the vessel centroid. A derivative can be taken
of this plot to produce mean velocity in the pipe. Final results can then be encoded back into the
corresponding cross sections from which the measurement was made to create a functional map.
5
The combination technique has been termed Time of Flight CT Angiography (TOF CTA) in our
group, with reference to its dependence upon the time of contrast bolus flight along a vessel path
length and broad similarity to TOF MRI which is also used to create angiograms. The
algorithmic approach is introduced in section 1.4 and detailed in section 2.4.
In addition to mean blood velocity and volumetric flow rate, it would be of additional
interest to discern a cardiac waveform from the traveling intraluminal bolus through the use of
CT, as is available for flow quantification for both ultrasound and MRI. Prior authors have
indeed previously described the extraction of cardiac waveforms from contrast bolus flow data
in conventional angiography (Shpilfoygel et al. 1999; Shpilfoygel et al. 2000). This was
possible, at least in part, due to the arterial injection of contrast in these cases via intra-arterial
catheters which result in a lack of bolus dispersion. Definition of cardiac waveform from
dynamic volumetric CT angiography, where the contrast bolus is administered via the venous
system and is dispersed through the heart and pulmonary circulation prior to its arterial arrival,
was not convincingly seen in the analysis performed and described in this manuscript and hence
is not examined. Due to the intravenous nature of contrast injection in CT, and the resulting
passage of the bolus through vessels, the heart and a capillary bed in the lungs prior to its arrival
in an area of interest, subtle changes in density with the heart beat that are often visible on
conventional angiography were generally obscured. This does not exclude the possibility that
future authors, with improved signal analysis tools, may be able to detect and quantify and
intravascular cardiac waveform from dynamic 4D CT angiography derived from intravenous
contrast injection.
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1.1) Context on the Development of Volumetric CT Angiography
X-rays were a fortuitous discovery of Wilhelm Röntgen on November 8, 1895 and
earned him the first Nobel Prize in physics in 1901 (Nitske 1971). Röntgen did not file patents
on his discoveries and donated his Nobel prize money to the University of Würzburg. X-Rays
are today defined as photons with wavelengths of 0.01 to 10 nanometers and are particularly
known for their ability to penetrate living tissue. Approximately two weeks after his discovery,
the first X-Ray image was produced by Röntgen himself, performed upon the hand of his wife
Anna as a subject. The first medical X-ray examinations were performed approximately one
month after publication of Röntgen’s paper “On a New Kind of Rays” on December 28, 1895.
The physics of X-Ray production in modern imaging systems has been extensively reviewed
(Huda 2009).
Although of incalculable impact on modern medicine, two dimensional X-rays do have
several limitations (Novelline 2004). Bones, being of high density, often obscure soft tissues.
This is particularly problematic in the brain which is covered by a dense skull. Routine X-Rays
are of value in the brain only by the indirect assessment of the impact extra soft tissue often has
on osseous structures. Secondly, X-Rays cannot adequately differentiate tissues of similar
density and are hence of limited value in the assessment of solid organs of the abdomen. Finally,
superimposition of important soft tissue structures limits their assessment by 2D projection.
Some of these limitations were overcome with the development of appropriate contrast agents.
With the development of barium imaging of the gastrointestinal tract and retrograde cystography
and pyelography by water soluble, iodinated contrast agents, successful imaging was performed
of both organ systems. Unfortunately, the use of iodinated contrast agents in the context of X-
7
Ray based examinations of the vascular system were generally invasive, requiring
catheterization of the vessels of interest.
It was Sir Godfrey Hounsfield (Miles and Cuenod 2007) who first demonstrated that a
series of rotational 2D X-Ray images could be analyzed by a computer to create a cross-
sectional image (Huda 2009) in a technique called Computed Tomography (CT). The first
generation of CT scanners were essentially X-ray sources and one dimensional sensors coupled
to a rotating gantry. These were single slice units that, although revolutionary at the time, were
used exclusively for morphologic characterization of anatomy and structural pathology.
Between the years of 1980 and 2000, as detectors and gantries improved and microprocessors
became more powerful (Pott et al. 1992), multislice CT scanners with ever larger detector arrays
were introduced that could acquire more images over a greater anatomic range and in a shorter
time (Kohl et al. 2005). Simultaneously, safer IV contrast media were developed (Kohl et al.
2005; Rieger et al. 1996; Inoue et al. 2011) which were capable of competently and routinely
assessing the vascular system. Helical mode scanning in 4 to 16 slice units became the
predominant technique and supported the reconstruction of excellent quality axial image series
depicting anatomy of clinical interest (Rieger et al. 1996) with or without oral, rectal or
intravenous contrast. There was limited support for the reconstruction of good quality coronal or
sagittal reformats in these early systems due to a frequently anisotropic voxel size at routine
diagnostic settings.
By the early 21st century, fan-beam 64-slice CT technology had become the diagnostic
and clinical mainstay (Kohl et al. 2005; Rydberg et al. 2000; Sasiadek et al. 2000). Capable of
scanning an entire patient head to toe in less than a minute using a fan beam X-ray source and a
2-4 cm detector array, 64 slice CT technology supported a sufficiently rapid performance to
8
characterize a contrast bolus in predominantly arterial or venous phase and 3D reconstructions
became widely used to depict vascular pathology (Inuoue et al. 2011). Angiographic or
venographic images of structures such as the brain, heart or liver were still acquired in helical
mode however, and so were essentially vessel cast techniques where intravenous contrast
characterized pathology by providing delineation of the vessel lumen. A limited literature has
been published on the use of 64-slice CT to characterize cerebral aneurysm deformation
(Hayakawa et al. 2011; Krings et al. 2009), which was possible due to the relatively small size
of cerebral aneurysms and ability to capture the entire aneurysm sac with a narrow detector
array. One group had achieved success in the use of 64-slice CT to examine blood flow in the
circle of Willis although results were essentially qualitative, indicating mainly the direction of
flow (Pekkola et al. 2009).
Simultaneously, since the late 1990’s, CT perfusion has become clinically entrenched for
the assessment of acute stroke (Figure 1.1) and has been widely prototyped for a variety of other
organs throughout the body (Miles and Cuenod 2007). The CT perfusion literature is extensive
and includes a variety of algorithmic approaches to making tissue perfusion calculations
including deconvolution (Fieselmann et al. 2011, Abels et al. 2010; Wintermark et al. 2008;
Miles 2004), maximum gradient and Patlak algorithms as referenced above. The central volume
principle enabled estimates of cerebral blood volume in addition to blood flow and mean transit
time which are available from the tissue residue function of a deconvolution calculation
(reviewed in Miles 2004; Fieselmann et al. 2011). Blood volume, which might be thought of as
the percentage of a tissue volume that is occupied by the intra-capillary space, is a parameter
that has been extensively described for the depiction of salvageable brain tissue in the acute
stroke setting (Wintermark et al. 2008; Rydberg et al. 2000; Miles 2004;
9
Figure 1.1 – Conventional CT perfusion image of the brain. CT perfusion is concerned exclusively with blood flow through brain tissue. Arterial and venous hemodynamics are only assessed so as to calibrate signals measured in tissue parenchyma. This case shows decreased blood flow in the right middle cerebral artery territory, indicating acute stroke. Image produced from the emergency CT at the Toronto Western Hospital.
10
Hoeffner et al. 2004; Cianfoni et al. 2007). Since blood velocity and volumetric flow rate within
arteries had not been described on 64-slice scanners, CT perfusion has relied upon the central
volume principle, definition of arterial input functions and, depending upon the application,
venous outflow functions, to calculate parameters of functional interest (Leiva-Salinas et al.
2011; Konstas et al. 2011; Miles, Eastwood and Konig 2007). These signals are measured by
region of interest placement in the intravascular space of arteries and veins that best
characterized flow in the respective vascular network to generate a time density curve (TDC)
upon which to base calculations.
Truly volumetric CT using the cone beam technique was first described in the radiation
oncology literature (Nazmy et al. 2011) where it was used in treatment planning to track lesions
that were subject to respiratory motion. Diagnostic volumetric CT imaging has been available
on a 16 cm detector array since 2008 (i.e. the Toshiba Aquilion One) and an 8 cm array since
2007 (i.e. the General Electric Lightspeed Volumetric CT), though the latter system supports
shuttling of the CT table to mimic a 16 cm scan range. The Aquilion One supports a
reconstructed temporal resolution up to 0.1 seconds. Such modern volumetric CT systems have
since been used to characterize the dynamics of contrast bolus passage in arteries and veins of
entire organs, in particular for the assessment of vascular lesions such as various vascular
occlusions, AVMs and DAVFs (Barfett et al. Jul 2010; Salomon et al. 2009; Klingebiel et al.
2009; Luo et al. 2011; Dorn et al. 2011; Willems et al. 2011). Since 2008, however, there has
been little focus on the quantitative analysis of intravascular bolus dynamics using these
systems.
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With volumetric scanners, TDCs can be obtained in all arteries and veins affecting an
organ such as the brain, heart, kidneys, pancreas and spleen or in a limb such as the hand or
foot. The development of volumetric CT angiography has thus enabled entirely new applications
in functional CT imaging, many of which are only beginning to be explored clinically.
Interestingly, these new ideas draw heavily upon the well established field of indicator dilution
theory and video densitometry. In particular, this manuscript is concerned with the calculation
of intravascular blood velocity and volumetric blood flow rate from 4D CT source data.
1.2) Statement of Hypothesis
It is proposed that quantitative functional evaluation of the intravascular space is
achievable with source data obtained from volumetric dynamic contrast enhanced CT
angiography. Specifically, this evaluation includes the generation of functional angiograms
depicting quantitative functional intravascular data such as TTP, TOA or maximum slope as
image slices, fusion images or volume renderings. Secondly, in a manner analogous to that
described in conventional angiography (Alfonso et al. 2000; Shpilfoygel et al. 1999; Shpilfoygel
et al. 2000), it is proposed that the calculation of characteristic intravasular flow parameters such
as blood velocity (in units of distance per unit time, i.e. cm/sec) and volumetric blood flow rate
(in units of blood volume per unit time, i.e. mL/min) is possible using an intravenous rather than
intra-arterial contrast bolus injection. Finally, it is proposed that the two methods may be
combined to analyze time density data in progressive vessel cross-sections along a vessel path
length, an approach that facilitates the encoding of blood velocity or flow rate into functional
angiograms for clinical evaluation in a potentially non-user dependent fashion. The completed
12
software will be useful for the further characterization of a variety of vascular lesions as
discussed in this manuscript.
1.3) Basic Indicator Dilution Theory
Sir William Harvey first described blood flow in arteries propelled by the heart as a
pump with the 1628 publication of “De Motu Cordis” or “On the Motion of the Heart and
Blood”. This 17 chapter book clearly describes blood flow through the body as a circuit, as well
as pulsatile flow in muscular systemic arteries by the left ventricle and flow into the pulmonary
artery by the right ventricle. Harvey further postulated that venous blood was a product of
systemic circulation rather than the liver as had been proposed by Galen. Through extensive
experimentation in lower life forms such as reptiles and eels, Harvey further described the
function of the ductus arteriosis, an embryologic shunt providing systemic circulation in utero
when the lungs are not functioning.
Harvey’s most famous experiment involved the tying of a tourniquet around the arm of a
volunteer. With arteries positioned deeply in tissue and veins more superficially, a tight
tourniquet would cut off circulation to a limb and the limb would become cold. If pressure was
reduced somewhat, deep arterial flow would resume and venous flow would be reduced,
resulting in a purple engorged limb. With removal of the tourniquet, blood would flow freely.
Harvey also described a flow of blood towards the heart in veins under compression. It was
impossible however to achieve retrograde flow of blood in veins back towards limbs.
It was 201 years after the publication of “De Motu Cordis” when Australian veterinarian
Hering used an indicator, in this case ferric chloride, injected into the veins of horses to measure
13
what he called circulation time (Zierler 1999). In an 1829 paper entitled “Experiments to
measure velocity of blood circulation”, Hering described the “appearance time” of an indicator
injected into a system vein at various points in the circulation including other veins and arteries.
The method employed by Hering was the cannulation of vessels and serial extraction of blood
samples for analysis.
In 1890, G.N. Stewart at Cambridge described the use of sodium chloride as an indicator
in experiments similar to Hering. In 1893, he published an 89 page article in the Journal of
Physiology describing indicator dispersion in the circulation (Figure 1.2). Stewart moved to
America and, from Western Reserve University in 1897, proposed the use of indicator dilution
to measure blood flow. Although not quite correct, Stewart’s proposal was to measure the
“dilution” of the indicator. That is, if an indicator is injected into a vessel relatively instantly,
then measuring the concentration versus time curve at some point downstream would yield a set
of data that could be integrated over the time through which indicator was recovered. The area
under the curve (AUC) is inversely proportional to the volume of blood that had diluted the
injected indicator, and hence could be used to calculate flow. In addition, after enough time had
passed for the injected indicator to reach equilibrium in the blood, the final concentration of
indicator in a sample could be used to estimate total blood volume in an organism (Stewart
initially did not consider that indicator could diffuse out of the blood pool).
In 1928 from Louisville Kentucky, building on the work of Hering and Stewart, William
Hamilton published a paper entitled “Simultaneous Determination of the Pulmonary and
Systemic Circulation Times in Man and a Figure Related to the Cardiac Output” in which he
used Stewart’s formula, recognizing however that the theorem only held true if indicator was
not re-circulated (Zierler 1999). The difficulty was that it is difficult to know in vivo at what
14
Figure 1.2 – Movement and dispersion of an indicator in a pipe. A bolus of an indicator injected into a pipe at an upstream location (black) will, as it travels, disperse, resulting in a reduced maximum concentration and a longer duration (red). This dispersion is essentially “dilution” as described by Stewart. Importantly, the integral of the concentration versus time curve at both proximal and distal points in the system will be the same, assuming that there is no recirculation and that the entire bolus remains intra-vascular.
15
point re-circulated indicator begins to confound the measurement of a time-concentration curve
at any point in a blood vessel. This was especially true using the serial sample extraction
technique that was common at the time. One way to mitigate the effects of recirculation is to
primarily consider the wash in phase of the curve, assuming that recirculation effects are of less
significance at the time of initial arrival of a bolus. Hamilton’s work thus focused on studying
the wash-in phase of the indicator, which he claimed could be fitted by an exponential on a
semi-log plot. Although Hamilton’s approach was met with enthusiasm due to its simplicity, the
approach failed to account for all physiologic measurements and was ultimately abandoned.
Importantly, however, Hamilton considered the case where indicator could diffuse out of
the vascular system into the interstitial space or tissue bed and was particularly concerned with
how such mass transfer would interfere with Stewart’s initial concept of measuring “dilution”.
Despite this noteworthy limitation, what became known as the Stewart-Hamilton equation has
remained a mainstay for the calculation of blood flow in vivo. The equation may be written as
[1.1]
where F is volumetric blood flow, I is the quantity of indicator injected, c(t) is the concentration
of indicator measured as a function of time and is integrated from time zero to T, where if
recirculation is ignored in an infinitely long pipe T = ∞.
Although the equation would hold true for any individual artery under consideration, it is
most commonly used where a single vessel is of particular physiologic significance as us true in
the central circulation. For example, in the great vessels including the vena cava, pulmonary
16
vessels or aorta, the Stewart-Hamilton equation is used as a means to measure cardiac output
and is most commonly performed invasively either by catheter based sampling or more
commonly today by thermometry where an intravenous infusion of chilled saline substitutes for
an indicator. The technique remains in routine clinical practice and is discussed in
anesthesiology textbooks (Zierler 1999).
The development of X-ray based imaging techniques and high density intravenous
contrast media enabled the logical extension of indicator dilution theory into imaging science.
On review of literature, the first identified such studies were performed in the 1950s and were
subsequently followed by extensive academic activity (Gidlund 1957). X-ray systems were
developed which permitted the time dependent assessment and tracking of contrast bolus motion
in arteries and veins. Rather than using the concentration versus time data attained from repeat
sampling of an artery or vein, continuous monitoring of a dense bolus was possible in regions of
interest (ROIs) placed around arteries producing density versus time data. The technique was
generally referred to as “video densitometry”. The resulting plots are in this manuscript referred
to as time density curves (TDCs), however are also frequently described in the literature as time
attenuation curves (TACs).
Of course initial application of the Stewart-Hamilton equation was performed in vivo
using video densitometry techniques and was used again to estimate cardiac output (Arnould et
al. 1952). Of the many intra-vascular hemodynamic parameters potentially calculated by bolus
tracking, blood velocity was one of the most important and extensively examined. Stewart-
Hamilton, being concerned with the evaluation of cardiac output, is not intended to rigorously
derive the relative flow rates in arteries connected in parallel as the integral of the TDCs in
17
Figure 1.3 – Indicator flow from pipes of small to larger cross-sectional area. In A, an indicator (grey, occupying length of L1 moving at velocity V1) moves from an inlet pipe into a second pipe of larger cross-sectional area and is hence compressed in space (now occupying length L2 and moving at V2, where L2 < L1 and V2 < V1). In B, if we assume that the two outlet pipes are of combined cross sectional area less than the inlet, then it L2 > L1 and V2 > V1. Both outlet pipes are identical in this example. Plug-flow is assumed in this example for simplicity.
18
separate arteries could be similar despite varying flow rates. This is a crucial point to intra-
vascular flow quantification and is best illustrated by a set of simple thought experiments.
Consider the case of a bolus of indicator flowing in a pipe which changes caliber. As in
Figure 1.3A, if the bolus moves from a pipe into a second pipe of larger diameter, the bolus will
be compressed in space. If the diameter of the outlet portion of the pipe is twice that of the inlet,
elementary mass conservation indicates that bulk velocity of fluid and indicator in outflow will
be half of what it is at the inflow. A bolus half as long, traveling by a detector at half the
velocity, would look identical when measured as a time concentration curve at a pipe cross
section. Figure 1.3B better illustrates the situation in vivo. Sampling could be performed either
by serial sample extraction or by continuous videodensitometric analysis.
Considering an inlet pipe of a specified diameter is split into two outflow pipes, in this
case each of equal diameter, as in Figure 1.3B. The sum of cross sectional area of the outflow
pipes may be different than that of the inlet pipe and if greater, will result in spatial compression
of the bolus and if lesser, will result in spatial elongation of the bolus. In this example, we
consider the case where unlike that in Figure 1.3A the combined outlet pipe diameter is less than
the inlet diameter and there is resulting spatial elongation of the bolus. Given that there is equal
distribution of flow into both outlets, both elongated bolus will be of equal length and will be
traveling at equal speed.
Now consider the more complex situation where flow in an inlet is divided into
two outlet pipes of equal diameter, however, there is increased resistance to flow in one of the
outlets due to the presence of a stenosis (in vivo, such difference in resistance could also
potentially be due to a smaller vessel diameter or blockage at the level of a downstream
capillary bed and the example would still hold true).
19
Figure 1.4 – Divergent flow in pipes with a stenosis. In this example, both outflow pipes are equal in cross-sectional area, however a high-resistance stenosis has been introduced into the lower pipe, resulting in reduced velocity (V3 < V2 and hence L3 < L2). Where both boluses are measured at a detector, their arrival is shifted along the time axis, however both curves would appear identical (assuming plug flow). The shorter bolus (L2) is moving proportionally more slowly (V2) as it passes the detector.
20
In this case, assume that the increased resistance due to stenosis results in a flow velocity
in the high-resistance pipe that is half that of the low-resistance pipe, and therefore the bolus in
the high-resistance pipe is half the length in space (Figure 1.4).
When measured at a detector at the end of the pipes, the boluses will be delayed from
each other, but will otherwise appear identical and have the same height (i.e. rise), with the high
resistance bolus being half the length and moving half as quickly through the pipe (Figure 1.4).
Thus the use of the Stewart-Hamilton equation would produce identical results in both outflow
pipes, because the area under the time concentration curve would the same in each case, minus
any dispersion effects caused by flow through the stenosis itself.
In the above examples, we considered the contrast bolus as a square pulse and although
useful, this assumption is not physiologic (Blomely et al. 1997; Bassingthwaighte et al. 1963;
Bassingthwaighte et al. 1966). It is known well known that a contrast bolus that is initially
injected into a pipe as a square pulse will take a Gaussian spatial distribution as it travels along a
vessel path length (Bassingthwaighte et al. 1963). If flow rate is at the extreme end of slow
laminar or rapid turbulent flow, the bolus TDC will retain a symmetrical Gaussian waveform
(Bassingthwaighte et al. 1963). In between these extremes, as is common in the laminar or
quasi-turbulent flow in arteries, the bolus TDC develops the shape of a Gaussian that is skewed
in the direction of time (i.e. skewed to the right on a typical plot) (Bassingthwaighte et al. 1963;
Bassingthwaighte et al. 1966). Thus in the context of CT angiography, where a contrast bolus is
injected into the venous system and proceeds through the heart and lungs prior to entering the
arterial circulation and traveling to the organ under examination, an intravascular region of
interest (ROI) indicates a TDC typically takes the form of a skewed Gaussian function and
requires specialized approaches for mathematical modeling.
21
Where a bolus is injected over 10-20 seconds, as is frequently the case in CT, it must be
born in mind that the spatial distribution of the bolus will be a multiple of injection time by bulk
blood velocity. For example, a bolus injected over 10 seconds into a vessel where blood is
moving at a bulk rate of 50 cm/s will have a spatial length of 500 cm. This bolus may then be
compressed or elongated depending upon cross sectional area of vessels through which it travels
as in the example above. In general, as a bolus moves into more distal arterial circulation, the
increasing total cross sectional area of the network results in spatial compression of the bolus
(Figure 1.3).
1.3) Introduction to Functional Angiography
Given that contrast remains in the vascular system after its first pass, often for several
hours after an injection, recirculation effects complicate the measured TDC, which does not
return to the baseline density of blood within the scan time of the image series (Blomley et al.
1997). TDCs can demonstrate distinct second or even third peaks due to recirculation of a bolus
that is incompletely dispersed (Blomley et al. 1997). In addition, some of the larger blood
volumes in the intravascular anatomy, such as the cardiac ventricles or the vena cava for
example, can behave as mixing tanks in indicator dilution theory, and further increase dispersion
and lengthen the wash-out phase of a TDC (Bassingthwaighte et al. 1963; Bassingthwaighte et
al. 1966).
To model these dispersion, recirculation and detention effects, a γ-variate function has
traditionally been chosen (Blomley et al. 1997; Bassingthwaighte et al. 1963; Bassingthwaighte
22
et al. 1966) rather than a Gaussian distribution. The γ-variate function excludes secondary and
tertiary peaks in the signal but does accurately model a bolus wash-out phase that is more
gradual than wash-in.
The γ-variate function, where an indicator arrives at time zero, can be written as
[1.2]
where y(t) is the concentration of indicator at time t and A, B, and C represent arbitrary
constants.
Intravascular TDCs, in the context of CT, have been studied in particular as they pertain
to the definition of arterial input functions (AIFs) and venous outflow functions for perfusion
calculations, and both are generally modeled by the γ-variate function. With an appropriate
model fit, several parameters of the curve can be readily defined including TOA, TTP, area
under the curve (AUC) and maximum gradient of the upstroke (Figure 1.5) and these may be
calculated by several possible curve fits including, but not at all limited to, the γ-variate
function.
The various curve fits that were used in this manuscript each have pros and cons.
Although the γ-variate is the most frequently used model, its accuracy can depend upon the
injection rate and was noted to provide suboptimal fits to non-physiologic curves in phantom
experiments. Two other models are hence used in this manuscript. The first is the Gaussian
function and the second the local quadratic function. While the Gaussian function is well
known, local quadratic functions are a more novel way to examine TDCs and are implemented
23
in this project specifically to help extract TTP from an irregular shaped bolus. In this
manuscript, the quadratic model is applied fitting a quadratic function to data to the portion of
the TDC that is above 50% of the maximum value (i.e. the peak).
Functional angiograms consist of the encoding functional parameters into appropriate
vascular segmentations (Riederer et al. 2009; Barfett et al. Jul 2010) for easy viewing by
clinicians and hence rely upon accurate segmentation of the intravascular space from source
data. Segmentation of the intravascular space from the extra-vascular space may be achieved,
for example, through the analysis of signal intensity changes with time in spatially congruent
voxels. Such segmentations may be performed via any number of approaches, numerous
examples of which have been published (Saring et al. 2010).
In this manuscript, both curve fits and level sets as approaches to segmentation are used
to define the intravascular space, details of which are described in the methods section 2.1. After
determining which voxels are indeed likely intravascular, a functional parameter of the time-
density series, such as maximum slope, TOA, TTP, etc. at each voxel in the intravascular
segmentation can then be calculated and encoded into the segmentation. The resulting
intravascular functional maps may be viewed as planar series, including with image fusion to
source CT data, or may be volume rendered by any suitable approach for convenient viewing by
clinicians.
24
Figure 1.5 – Models of intravascular Time Density Curves (TDC). Raw data (red dots in A-C) can be modeled by a variety of curves, of importance to this manuscript is the Gaussian distribution (A), the gamma-variate function (B) and a local quadratic function (C) fit to greater than 50% of the max data. It is usually after fitting of an appropriate model that a functional parameter of the curve may be calculated such as Time to Peak (TTP) (D), the Area Under the Curve (AUC) (E), maximum gradient (F) or the rise (G).
25
The strength of this method is its potentially complete automation. A limitation to the
technique is that although the functional angiograms produced are indeed quantitative,
expressing functional information to users in definable units, delineation of more robust
measures of blood flow such as velocity, volumetric flow rate and direction of flow must be
inferred in a visual interpretation of gradients in, for example, TTP or TOA maps. It would be
more useful to display blood flow information to users in more readily understood units such as
cm/s or mL/minute. Such hemodynamic parameters including blood velocity and volumetric
flow rate can indeed be calculated and presented to the user as discussed below.
1.5) Intraluminal Velocity from Volumetric 4D CT Data
Delay in TOA of the bolus centroid between proximal and distal points in a pipe, vessel
or other conduit can be used as a measure of average fluid velocity along the intraluminal path-
length (Shpilfoygel et al. 1999; Shpilfoygel et al. 2000) (Figure 1.6). This velocity, if multiplied
by the cross sectional area of the conduit, may be used to calculate volumetric flow rate. Of
course a positive velocity of fluid flow indicates bulk flow in the forward direction while a
negative rate indicates motion in the retrograde direction. The caveat to initial implementation
of the technique was the limitation of 2 dimensional imaging systems such as fluoroscopy to
characterize 3 dimensional vascular structures. Crucial to blood velocity measurements in vivo
is accurate knowledge of distance over which a bolus is tracked. Long and straight arteries, like
the internal carotid arteries, aorta or arteries in the arms and legs, for example, were more
amenable to such analysis than more complex structures such as the middle cerebral arteries,
posterior cerebral arteries, etc. Secondly, in order to calculate volumetric blood flow rates, the
cross sectional diameter of the vessel had to be assumed from the 2 dimensional projection.
26
Many of these effects have been mitigated by the introduction of CT, which enables accurate
measurement of both vessel diameter and vessel path length. CT however, as discussed below,
introduces different problems into the calculation.
In performing video densitometric velocity calculations, several assumptions must be
introduced regarding the bolus, all of which are reasonable. First of all, we must assume that the
bolus is well mixed in the blood pool, as is usually the case in vivo with water soluble contrast
agents that have passed through the veins, heart and lungs prior to entering the systemic arterial
circulation. It is important to note however that if cardiac output is reduced or if flow in the
aorta is sufficiently reduced by a vascular lesion such as coarctation or dissection, settling of
contrast could potentially occur in the dependent aspect of the aorta and this could confound
measurements. This settling generally only affects large vessels such as the aorta. Prior authors
have indicated that adequate mixing of contrast in the blood pool is a reasonable assumption in
most circumstances (Lieber et al. 2009).
The second important assumption is that the injection of contrast does not change the
viscosity of blood to such an extent as to significantly reduce flow. Inevitably, the injection of a
contrast bolus will influence hemodynamics to some extent (Mulder et al. 2010). This can occur
because blood becomes more viscous (which can limit the development of turbulent flow) and
because preload on the heart is increased by the volume of the bolus. The extent of this effect
depends of course on the dose of contrast which is applied during the dynamic acquisition.
Finally, we assume that TTP is an adequate measure of bolus centroid. In the arterial
circulation this is a reasonable assumption, however it may not be so reasonable in the venous
system where flow through the capillary beds of end organs further disperses and distorts the
bolus. The choice of a feature of the curve upon which to track a bolus is somewhat arbitrary
27
and different groups have chosen different features, all of which work to reasonable accuracy
(Barfett et al. Jul 2010; Matsumoto et al. 2007; Prevrhal et al. 2011; Riederer et al. 2009). In this
manuscript we chose to examine TTP as a surrogate measure of bolus centroid due to both its
straightforward delineation as well as its relative immunity to recirculation issues which make
true bolus centroid difficult to determine with the degree of accuracy we will later see that is
necessary for in vivo applications.
In this manuscript, we will primarily consider laminar flow conditions, which are known
to be characteristic of blood flow in vessels distal to the aorta and especially in the brain
(Mendrik et al. 2010; Wootton et al. 1999). In order to make appropriate calculations as above,
we consider regions of interest placed at proximal and distal points in a vessel so as to enclose
the entire luminal cross-sectional area (i.e. Figure 1.6).
28
Figure 1.6 - Basis of intraluminal fluid velocity calculation via the video densitometry approach. Intraluminal velocity may be measured by indicator dilution theory if we assume that the indicator is well mixed. Where a bolus is passing through a pipe, the delay in arrival of bolus centroid between proximal and distal regions in the pipe may be divided into the distance between the regions to obtain mean bulk velocity. Where recirculation effects are important, time to peak (TTP) may be used as a reasonable surrogate measure of bolus centroid. It is important that these regions be orthogonal to the pipe's central axis and that their border includes the entire pipe lumen.
29
A contrast bolus moving through the lumen is depicted at the corresponding vessel cross
sections as appropriate TDCs. These curves may be analyzed to obtain the time in seconds
corresponding to any particular feature of the curve such as TTP (Siebert et al. 2012). Since we
are concerned with average velocity, where laminar flow conditions are assumed, we are
interested primarily in timing of the bolus centroid, which may be estimated from TTP. In
simplest terms, the distance between the ROIs we choose, divided by the delay in bolus centroid
arrival between the points, is a measure of mean bulk velocity of fluid within the lumen.
While it is true that TOA of a bolus in a well developed laminar flow in a pipe would
tend to measure peak velocity rather than average velocity, drag effects of red blood cells in vivo
mitigate this issue and peak velocity at the central axis in arteries is approximately 1.5x average
flow (Bassingthwaighte et al. 1963; Bassingthwaighte et al. 1966) rather than twice average
flow. If rather than average velocity in the lumen, we aimed to calculate the maximum velocity
of the parabolic flow profile in fully developed laminar flow, we might consider TOA of the
bolus upstroke, as defined for example by the time at which a time density series reaches 10% of
its subsequent peak (i.e. 10% above baseline) (Riederer et al. 2009).
The approach of placing user-defined ROIs at proximal and distal points in a vessel is
useful as it does produce quantitative estimates of blood velocity, flow rate (when multiplied by
area of the vessel cross section, typically in our examples as defined by the ROI itself) and will
indicate direction of flow by a positive or a negative final velocity. Given the trivial calculation
of volumetric flow rate from velocity, we have focused on velocity in the experiments presented
in this manuscript. Ideally, blood velocity and blood flow information would be clinically
available without user interaction with the scan to produce appropriate calculations. The TOF
CTA technique introduced below, in the form used in this manuscript, relies on mouse clicks
30
along a vessel centroid in its current implementation. Where a segmentation of the intravascular
space is performed automatically and a skeletonization is used to define vessel centroids, full
automation of TOF CTA is likely achievable.
1.6) The Time of Flight CT Angiography (TOF CTA) Algorithm
Conventional angiography, being a two dimensional technique, is inherently limited for
the assessment of three dimensional vessel path length. Some authors have used rotational
angiography as a means of overcoming this limitation. With appropriate projection of the spatial
distribution of a bolus and reconstruction of 3D vascular geometry, accurate blood velocity and
volumetric flow rate measurements can be obtained from rotational angiography. These authors
were however still advantaged by a tight arterial bolus, absence of venous contamination, the
high temporal resolution of the conventional angiography, and high signal to noise ratio of the
intravascular space. CT is limited by a comparatively lower signal to noise ratio, a reduced
temporal resolution (at present), as well as dispersion of the bolus due to venous injection. This
dispersion means that spatially the bolus is often longer than the length of the detector array, 16
cm on the Aquilion One, and is always affected by venous contamination.
The TOF CTA algorithm is a combination of the above described automated functional
angiographic and TTP versus vessel path length velocity calculation approaches, relying upon
signal processing to obviate some of the inherent limitations of CT. A user-dependent definition
of vessel centroids via mouse clicks was examined for preliminary validation of the technique in
this manuscript. Algorithmic details are extensively reviewed in section 2.4. In brief,
volumetric 4D CT source data was used to generate a segmentation of the intraluminal space
under consideration, be that either flow simulation, pipe phantom or in vivo as appropriate.
31
Using this baseline functional angiogram, the user defines a vessel centroid via successive
mouse clicks that are interconnected with lines in 3D. Using planes orthogonal to these centroid
lines, the vessel is divided into sequential cross-sections. Contrast bolus TTP is then analyzed at
each vessel cross-section, denoised through a combination of data sharing between vessel cross-
sections and application of filters including the standard mean filter, and plotted against distance
along the vessel path-length. This distance versus time information of the bolus centroid is then
differentiated with respect to time to arrive at velocity. In this manuscript, a simple line was fit
to the distance versus time data, where time was represented on the y-axis, and hence the inverse
of the slope of the line (i.e. 1/m if m is slope of the line y = mx + b) indicates velocity.
The TOF CTA algorithm was first studied in a series of flow simulations defined by
passing an idealized Gaussian contrast bolus along a simulated square channel as described in
section 2.3 below. The data were next validated in a flow phantom consisting of a series of pipes
subject to volumetric 4D CT through which a bolus of iodinated contrast was passed. Finally,
the algorithm was explored in vivo, first in a series of 8 internal carotid arteries as compared to a
phase contrast MRA gold standard, secondly as measured by a single user in the major intra
cranial arteries in a series of 8 normal subjects, and finally in an exploratory manner via a small
cross-section of 4D CT studies available at our institution including a 4D CT exam of the neck
in a case of subclavian steal, in the pulmonary arteries via a cardiac perfusion series, as well as
in the internal iliac artery via a 4D CT exam performed clinically for prostate perfusion.
32
2.0) Materials and Methods
A three-step process was employed to validate the TOF CTA approach and algorithm.
Firstly, the software was tested using simulations of contrast bolus passage through an idealized
square channel. This step was crucial to the validation of software for future in vitro and in vivo
experiments.
Next, phantom experiments were conducted whereby a contrast bolus was passed
through a series of pipes connected in parallel. Flow through the pipes was achieved via a non-
pulsatile pump. Given that the velocity of water through each pipe was known a priori, the
accuracy of TOF CTA velocity measurements could be studied in a physical system under ideal
conditions.
Finally, the technique was tested in vivo in the internal carotid artery against a phase
contrast MRA gold standard (Zhao et al. 2007) in a series of 4 subjects, 8 arteries total, and then
in the major cerebral vessels in an additional series of 8 subjects including the internal carotid
arteries (ICAs), anterior cerebral arteries (ACAs), middle cerebral arteries (MCAs), posterior
cerebral arteries (PCAs) and in the vertebrobasilar system. TOF CTA was then also explored in
arteries throughout the body in interesting cases where 4D CTA source data was available in our
group.
2.1) Programming environment
Algorithms described in this manuscript was written in Python version 2.5.1, provided as
open source by the Python Software Foundation, using the Tkinter graphical user interfaces
(GUIs) which are included in the distribution. DICOM import and export was achieved using
33
the open source pydicom library. Matrix operations were performed in NumPy and curve fits
(i.e. lines, quadratics, Gaussian, γ-variate and B-splines) performed in SciPy by non-linear least
squares regression. Image processing was performed via the Python Imaging Library. Finally,
appropriate extensions to increase runtime speed were written in c/c++, compiled via GNU
GCC, and linked to Python using the built in C types module.
2.2) CT Equipment
All 4D CT studies were conducted on the Aquilion One 320 slice CT system (Toshiba
Medical, Tokyo, Japan), a cone beam volumetric CT system with 16cm detector array. Three
identical systems were employed in this research including the array at the Toronto General
Hospital, the Princess Margaret Hospital, and the Toronto Western Hospital. All systems were
properly calibrated before use. Details of scan protocol and contrast administration are provided
in section 2.4 for the phantom studies and section 2.5 for the clinical cases.
2.3) Creating flow simulations for TOF CTA validation
A square channel, 10x10 voxels in cross-section, was algorithmically defined at the
center of a 512x512 image and extended in the z direction such that the channel's central axis
was parallel to the 160 voxel z axis of a resulting 512x512x160 voxel image volume. Individual
voxels were non-isotropic (0.5mm in the x direction, 0.5mm in the y direction, 1mm in the z
direction). A series of 50 such matrices, time stamped to indicate a 0.5 second delay between
consecutive image volumes, were created where the bolus was defined via a normal distribution
(peak of 1000 Hounsfield Units (HU) and standard deviation of 50 voxels) with x/y in-plane
34
uniformity and the centroid of the bolus moved progressively along the z axis in consecutive
volumes according to a predefined velocity in voxels per second. This was repeated at six
different velocities (10, 20, 30, 40, 60 and 80 cm/s). Radial dispersion of the bolus was
neglected in this preliminary simulation. The resulting matrices were saved as DICOM volumes
for validation of the TOF CTA software.
2.4) Construction and scanning of CT phantoms
Two flow phantoms were constructed, each consisting of a single 4-way splitter with a
single input. Inflow into the splitter was achieved with a water pump (Universal Hobby Pump,
EHEIM, Dollard Des Ormeaux, Canada) and 4 parallel outflow tracks created with two
diameters of silicone tubing (0.6 cm inner diameter in the first phantom and 0.3 cm in the
second phantom), for a total of 8 flow conditions across two experiments where each splitter
valve was adjusted to create a unique output flow in the corresponding tube. In both
experiments, outflow tubes were oriented in the z axis of a 320 detector row scanner. Flow in
each outlet tube was measured over a minute 5 times in a graduated cylinder and average flow
divided by tube cross-sectional luminal area was used to attain velocity (table 1). An 18-gauge
angiocatheter was placed 10 cm proximal to the input of the splitter and 10 mL of Visipaque
320 contrast (General Electric Medical, Toronto, Canada) was injected at 2 mL/s with injection
time beginning 5 s into a 30 s continuous computed tomography (CT) examination over a 16 cm
range. CT technique of 120 kV, 300 mA, and 0.35 s tube rotation time was employed. Dynamic
volumes were reconstructed at 1 s temporal resolution and 1 mm non-overlapping slice
thickness with a standard smoothing kernel and exported for analysis.
35
2.5) Scanning of clinical cases
2.5.1) Dynamic 4D CT Scans and Protocol
With appropriate approval, the institutional records were retrospectively reviewed and
five interesting 4D CT exams of the brain selected to prototype functional angiography as
described in section 2.7. Cases were selected to include examples of a broad spectrum of
neurovascular pathology including a right choroidal AVM, a large right DAVF, vasospasm due
to subarachnoid hemorrhage, subclavian steal syndrome, and finally a giant cavernous carotid
aneurysm. Next, with informed consent, 8 internal carotid arteries in 4 patients (mean age 66.4,
range 50 – 87), were prospectively subjected to a volumetric 4D CTA examination for
calculation of internal carotid blood velocity as described in sections 2.7 and 2.8. Finally, a
series of 8 patients with normal 4D CT examinations of the brain (mean age 74.3, range 47-87)
were queried in a retrospective manner for evaluation of the TOF CTA technique in the major
intra cranial vessels.
All scans were performed with a standard brain perfusion protocol (Figure 2.1). After
arm-to-brain transit time determination via repetition of a single axial slice through the Circle of
Willis every 2 s using a 20 mL test bolus, a mask volume at 80 kV and 300 mA with 1 s rotation
time was acquired prior to injection of a further 60 mL Visipaque 320 bolus administered at 6
mL/s. A dynamic series of 23 volumes was then acquired at 80 kV, 100 mA, and a 1 second
rotation time, including a continuous 15 s arterial acquisition followed by intermittent
acquisitions every 5 s to capture the venous phase. Total scan time, including the delay after
contrast administration, was less than 90 s (slight variation noted due to transit time estimation
from the test bolus) and total radiation dose averaged at 4.7 mSv across all patients. DICOM
36
volumes were anonymized and sent to a dedicated workstation (Vitrea 2.0.1; Vital Images,
Minnetonka, MN) for further analysis.
2.5.2) Phase Contrast MRA
Quantitative pcMRA of the internal carotid arteries was performed in human subjects using the
commercial Non-invasive Optimal Vessel Analysis (NOVA) software package (Vassolinc,
Chicago, Illinois) to obtain blood flow velocity in a manner as previously described (Zhao et al.
2007) on a 3 Tesla GE MRI Scanner. In brief, a Time of Flight MRA was acquired from the
internal carotid arteries to the circle of Willis. Suitable planes were defined at the extra-cranial
portion of the internal carotid arteries and average bulk flow through the vessel and flow
waveform through the cardiac cycle were acquired with the NOVA software package using a
phase contrast technique. No intravenous contrast agents were necessary.
2.6) Algorithms for segmentation of the intravascular space
Anonymized CT volumes, each representing a 320x512x512 matrix, were downloaded
from the Vitrea workstation to an external hard-drive. Twenty-four such volumes were included
in each 4D dynamic study. Volumetric registration was performed via a rigid skull-based mutual
information approach with customized C++ code courtesy of Dr. Paul Dufort, Department of
Medical Imaging, University of Toronto. Spatially congruent voxels were sampled from each
DICOM volume to create time density series for analysis.
Two main approaches to segmentation were used in the manuscript, the first being
segmentation by curve fit to individual voxel time density series. All curve fits were performed
37
using the multivariable regression in Scipy and an allowable range specified of the regressed
parameters. Quadratic curves, Gaussian distributions and the γ-variate function were each tested
as means of segmentation, with the quadratic curve demonstrating the best initial results (Barfett
et al. Jul 2010). Where a quadratic curve has the form:
[2.1]
the variable “a” will be negative for an inverted parabola and the magnitude of “a” indicating
the width of the parabola. Thus selecting only voxels where “a” is negative and less than a
threshold creates segmentations including voxels where contrast washed in and out in a typical
intravascular manner. Other segmentations were attempted using cubic splines, 1-R2 statistics as
well as maximum gradient calculations of individual time density curves, all of which were
qualitatively found to be inferior to quadratic curve fits (Barfett et al. Jul 2010). The functional
angiograms demonstrated in this manuscript were created using segmentations based upon the
quadratic curve approach.
38
Figure 2.1 - 4D CT protocol used to scan clinical series. A modified version of the standard “neuro one” protocol on the Aquilion One was used in scanning of all patients in the clinical series. A mask volume is first acquired at 300 mAs, followed by a continuous acquisition at the expected arterial input function and discontinuous acquisition of the relatively less important venous phase. 80 kV was used throughout at 1 s rotation time with final radiation dose averaging 4.7 mSv across all patients.
39
A simple level set approach was used in this manuscript to create basis segmentations for
TOF CTA calculations (source code in Appendix Two). The level set segmentation individually
compares all time density series in spatially congruent voxels to that from a user-defined group
of voxels known to be intravascular and encodes intensity in the final segmentation based on the
degree of likeness. Although some user input is required, the level set technique has provided
the best and most reproducible results to date and outperformed quadratic fits.
In brief, the user is asked to indicate a set of points in the intravascular space via mouse
click. Although any number of points might be chosen, adding more entries to the collection
slows down the computation exponentially and so usually only 3-5 points were employed per
segmentation, chosen from different locations in the arterial system. TDCs at each user-defined
point was stored in array format. Next, at each data point under consideration in the 4D series,
the normalized time attenuation array was compared to each of the normalized user-selected
intravascular arrays (~normalized out of 1000). Normalization is important because partial
volume effects significantly change TDCs. If for example, the user chose points in small
downstream vessels, it is likely that peak enhancement will be less than that in larger more
proximal vessels and this will confound TDC comparison in the segmentation algorithm.
Normalization mitigates this problem
Comparison was performed by taking the absolute value of the array under examination
minus the user-defined intravascular array and searching for the max value, i.e. to find potential
outliers. The maximum value in the resulting array (i.e. the largest outlier) was then compared to
a user-supplied threshold to decide whether the array was intravascular or extravascular, with a
look up table used to sum intensity into the corresponding voxel as a linear function of the
outlier’s magnitude. This comparison was made with data at every user-supplied point and the
40
results summed into the segmentation, with the exception that a maximum value above 500 in
any one comparison of the 3-5 user defined intravascular time density series completely
excluded the voxel. The result is a simple level set map defining the intra-arterial space that is
adequate for TOF CTA calculations.
Certainly more sophisticated approaches to the level sets could be employed for the
creation of intra vascular segmentations for the performance of TOF CTA (Saring et al. 2010),
however these techniques are peripheral to the thesis and were hence not explored.
2.7) Creation of Functional Angiograms
To create functional angiograms in the series of five interesting cases, various functional
parameters were encoded into each intravascular voxel through trivial analysis of the
corresponding spatially congruent time density series. These images were published prior to
implementation of the level set segmentation approach and hence are derived from quadratic
curve fits as previously described (Barfett et al. Jul 2010). Typically, TTP and maximum slope
were chosen as the parameters to be encoded. Resulting data was then scaled out of 256 for ease
of display as 256 color bitmap image files. Volume renderings were created of these 3D maps
on both the Vitrea workstation and the open source medical imaging software package OSIRIX
using native color look-up tables to assign an intensity color spectrum for functional mapping.
Fusion images between planar flow maps and the peak arterially enhanced dynamic CT volumes
were created in OSIRIX using the image fusion tool.
41
2.8) The TOF CTA algorithm
Definition of the Intraluminal Space
Intraluminal segmentations were created of the above indicated dynamic series as
previously described above (section 2.6) using a level set approach for which source code is
provided (Appendix One).
Definition of Vessel Centroids
Software was created allowing a user to define a vessel centroid by means of successive
mouse-clicks on axial slices of CT source images. These user-defined points were connected by
3D lines using a marching unit vector and the distance between points calculated with a 3D
Pythagorean approach. The sum of distances between all consecutive points indicates the total
distance along which the TOF CTA calculation was performed.
Time Of Flight CTA Algorithm
A database was associated with each spatial coordinate along the vessel centroid. In the
analysis described herein, each of these databases included the position of all contributing
coordinates in the respective vessel cross section, an array of length corresponding to the
number of CT acquisitions in the 4D series to hold the time series data, as well as the spatial
location of the database's location along the vessel centroid in Cartesian coordinates.
The algorithm iterates through each voxel of the intraluminal segmentation and locates
that voxel's nearest neighbor on the user-defined luminal centroid using a Pythagorean
comparison. The time density data of the considered intraluminal voxel was then aggregated
42
into the time density data array of the chosen database and its 3D position recorded. Voxels in
the functional segmentation were excluded if greater than 1cm away from the user defined
centroid or if a straight 3D line connecting them with the centroid passes through a voxel that is
not deemed intraluminal on the above-described segmentation.
After all time density data is assigned as above, the aggregated time density information
stored in each database was summed and divided by the number of entries in the list of 3D
contributing points to create a denoised average of the data through what is essentially a vessel
cross-section. The averaged time-density data at each database was then quantitatively analyzed
by 3 independent means to derive TTP enhancement including taking the peak of a local
quadratic fit, Gaussian fit and γ-variate fit to a normalized signal with the use of the vertex as
TTP. Local quadratic functions were defined as a curve of the form y=ax2+bx+c fit to the subset
of data contained in a time density series where attenuation was greater than 50% of its
maximum value as previously described (Barfett et al. Jul 2010).
TTP was then plotted as a function of distance along the vessel centroid (time as y axis
and distance as x axis). A line was fit to this data and the inverse of the slope used as a measure
of intraluminal fluid velocity. The velocity at each database can optionally be multiplied by
cross sectional area to attain local volumetric flow rate. Results in each database were
reassigned as intensities to the contributing voxels in each database to create functional maps.
Python source code for the TOF CTA algorithm, including a GUI to facilitate user
defined centroids along vessel path length, is presented in Appendix Two.
43
2.9) Implementation of the TOF CTA in simulations, phantoms and clinical series
The TOF CTA algorithm as above was then applied to the simulated flow data, the
physical CT flow phantom, as well as the clinical series.
In the flow simulation, a 10 cm path length was chosen for TOF CTA measurements
beginning 1cm distal to the origin of the channel. Measurements were repeated in triplicate and
recorded. Mean, standard deviation of measurements as well as the error between the
measurement and known ideal flow rate were calculated and recorded.
In the CT flow phantom, velocity measurements were made beginning 2 cm distal to the
pipe origin across all four pipes at both 0.6 cm ID and 0.3 cm ID. Measurements were repeated
with a user-defined centroid at two different path lengths (100 and 50 voxel path lengths with 1
voxel representing 1 mm of physical distance) and repeated 3 times with mean and standard
deviation recorded. 1-R2 statistics were kept describing the quality of final linear curve fit to
raw data. The correlation between pipe velocity versus accuracy of measurement and path-
length versus standard deviation of measurement was evaluated with Pearson's rho.
In the four patient clinical series in which phase contrast MRA was available for
comparison with CT, TOF CTA was performed by defining a path lengths in the ICA at the
level of the dens extending to the level of the cavernous sinus on axial cross sectional source
images. TOF CTA analysis was performed and repeated five times in each artery and compared
to phase contrast MRA. The commercial NOVA platform was used to perform phase contrast
MRA in these arteries with technique as previously described (Zhao et al. 2007).
In the series of 8 normal subjects, TOF CTA was used to calculate blood velocity in the
internal carotid arteries, the basilar artery, as well as in the middle, anterior and posterior
44
cerebral arteries. Measurements were repeated 5 times in each vessel and recorded. Results in
the internal carotid and basilar arteries were then multiplied by vessel diameter and summed to
calculate total cerebral blood flow, data from which is presented as mean and standard
deviation.
45
3.0) Results
Functional angiograms in five clinical cases are first reviewed in section 3.1. These cases
were selected to represent a broad survey of the most common cerebrovascular lesions studied
in a radiology department and include AVM, DAVF, subclavian steal, vasospasm and
aneurysm.
In cases of AVMs and DAVF, functional angiograms successfully depict the lesion of
interest in part due to the relatively significant difference in contrast arrival time in venous
structures of the brain affected by shunt and those subject to a normal cerebral capillary bed. In
the case of subclavian steal in the vertebral arteries, a relatively long path length up and down
the neck is responsible for the dramatic gradient in TTP over vessel path length. In a case of
vasospasm, we see that the functional angiographic technique also has limits. TTP and
maximum gradient in the MCA distal to the stenosis is not convincingly altered from the normal
side. Aneurysms of a sufficient size, such as the presented case of a giant carotid artery
aneurysm, demonstrate relatively gradual fill-in and wash-out.
For many applications, including vasospasm, a more rigorous quantitative approach is
required providing intra-arterial blood velocity and volumetric flow rate, resulting in
development of the TOF CTA algorithm. Data for the validation of TOF CTA in a flow
simulation is presented in section 3.2, in CT flow phantoms in section 3.3 and finally in clinical
series in sections 3.4 and 3.5.
46
3.1) Functional Angiographic Maps
Patient 1 presented with a cerebral hemorrhage and was diagnosed with a right choroidal
AVM on conventional angiography. Functional angiogram created via the maximum gradient
approach provided a segmentation of arteries and veins without bone artifacts for volume
rendering performed on both the Vitrea workstation (Figure 3.1, a and b) and in OSIRIX (Figure
3.1, c and d). The functional angiographic segmentation was then constrained to include only
those voxels where peak enhancement occurred within 15 s after contrast injection, thus
mapping only arteries to the final rendering (Figure 3.1e).
These images are contrasted to typical maximum intensity projections of 4D CT data
provided on the Aquilion One where artifact from skull remains clearly visible (Figure 3.1f) and
are provided to demonstrate the quality of segmentation that is achievable by straight forward
algorithms such as curve fitting.
Patient 2 presented with pulsatile tinnitus and was diagnosed with a dural arteriovenous
fistula on conventional Digital Subtraction Angiography. The rendered functional angiogram
(Figure 4) demonstrates decreased MTT (i.e. arterialization of flow) through the right transverse
sinus and draining veins, where intravascular MTT is used as was defined by Blomely et al.
1997. These results correspond to findings on conventional angiography (Figure 3.2).
47
Figure 3.1 - Sample renderings of functional angiograms compared to routinely available maximum intensity projections (MIPs). Subject with right choroidal AVM was subject to 4D CT examination. A and B demonstrate a volume rendered functional angiograms, C and D represent MIP rendering of same. E demonstrates functional angiogram where venous structures were excluded on basis of constraining time to peak (TTP) to the arterial phase. Low panel F demonstrates MIP images provided by the vendor which include bone artifacts.
48
The segmented intravascular voxels were next encoded with time to peak information and
are presented as a planar fusion image and volume rendering (Figure 3.3). Early TTP of the right
transverse sinus is demonstrated and gradient from high to low intensity (red to blue, where red
represents early TTP and blue late TTP) on adjacent volume rendering indicates direction of
blood flow from the transverse sinus to the cortical veins (consistent with the confirmed cortical
venous reflux seen on angiography) and thus treatment was indicated.
Patient 3 presented to our institution with subarachnoid hemorrhage and developed
cerebral artery vasospasm demonstrated on conventional and functional angiography (Figure
3.4). No perfusion abnormalities were seen in brain tissue on the functional maps generated
from the 4D CT on the vendor's native software (not shown) from the 4D CT source data.
Transcranial Doppler performed multiple times over 3 days also demonstrated increased blood
velocity (309 –382 cm/s) in the right MCA in comparison to blood velocity in the left MCA
(198–221 cm/s), which is consistent with a relative decrease in right MCA volumetric flow.
49
Figure 3.2 - Patient with right sided dural arterovenous fistula (DAVF) demonstrating decreased mean transit time (MTT) in right transverse sinus on functional angiogram. Right sided DAVF results in arterialization of flow through the right transverse sinus (scale in seconds). Functional angiogram demonstrates an arterialized in this sinus (left). Conventional angiograms show early filling of the right sided transverse sinus.
50
Figure 3.3 - Axial slice and volume rendering of functional angiogram encoding TTP showing right DAVF and cortical venous reflux. A lesion is demonstrated in an axial slice from functional angiogram encoding TTP (early TTP red, delayed TTP blue) fused to axial CT image on left (scale in seconds). On right, volume rendering of the DAVF is seen with early filling noted of the right transverse sinus (i.e. viewed from behind) and superficial cortical veins (arrow), indicating reflux (scale in seconds). Clinically, reflux of arterialized blood into the superficial cortical veins implies elevated venous pressure and hence risk of hemorrhage. This DAVF was treated successfully.
51
Figure 3.4 - Functional versus conventional angiogram in vasospasm. A patient with subarachnoid hemorrhage developed vasospasm and was subjected to 4D perfusion study of the brain. The resulting functional angiogram encoding maximum gradient was rendered for morphologic assessment (left) where stenosis of the right proximal MCA is seen as indicated by yellow circle (scale in HU/second). A conventional angiogram shown on the right provides a gold standard for assessment of vessel morphology to diagnose vasospasm.
52
Patient 4 was diagnosed with subclavian steal on conventional angiography and
volunteered for 4D CTA of the brain. TTP maps demonstrate delayed filling of the left vertebral
artery (Figure 3.5, left, where red represents early and blue represents delayed time to peak) and
volume rendering shows appropriate colorimetric gradient down to indicate retrograde left-sided
vertebral flow. The long path length of the vertebral arteries enables direction of flow to be
evaluated by the gradient in TTP on functional angiography. TOF CTA in this case is also
presented in section 4.3.
Patient 5 was followed for a giant cavernous carotid aneurysm. TTP map demonstrated
rapid peak enhancement of the intraluminal aneurysm periphery and delayed enhancement of
the core (Figure 3.6), further indicating rapid blood flow near the aneurysm wall and relative
stagnation of blood in the center of the aneurysm sac. The calculation of aneurysm wall shear
stress in relation to growth and rupture risk is a much studied subject. Characterization of intra-
aneurysmal flow characteristics may be ultimately prove useful for the calibration of finite
element models of aneurysm wall shear stress.
53
Figure 3.5 - Subclavian steal on planar and volume rendered functional angiography. Axial functional angiogram fused to axial CT slice at same level shows early TTP in arteries (red) and relatively delayed TTP in the left vertebral artery (blue) on the left. Volume rendering on the right shows gradient in vessel TTP as contrast bolus moves from the right vertebral to the basilar artery and then back down the left vertebral artery (scale in seconds).
54
Figure 3.6 - Functional angiogram encoding TTP in a giant right cavernous carotid aneurysm. Right giant cavernous carotid aneurysm shown on functional angiogram. The TTP map demonstrates delayed filling of the aneurysm centre (scale in s).
55
3.2) Simulated flow data for algorithm validation
User generated mouse clicks successfully defined the simulated vessel centroid (Figure
3.7). Simulated velocities and flow rates derived from the TOF CTA method agree with the
expected values at low velocities, particularly where local quadratic and γ-variate fits are used,
but do fail particularly with γ-variate curve fits at relatively higher velocities (Table 1).
Using all three curve fitting techniques in individual time-density series, percentage error
of less than 10% was seen up to simulated flow velocities of less than 60cm/s. The Gaussian
curve fits used to analyze individual vessel cross-sections produced the results in best agreement
with inputted data across all velocities, a result that is expected due to the use of Gaussian
distributions to simulate flight of a contrast bolus down the channel, with an error rate of only
7.1% seen at maximum flow rate of 80 cm/s. The γ-variate function performed less well,
becoming unstable at high velocity with a 26% error at 60cm/s and a128% error at 80cm/s.
At low mean bulk flow rates (40 cm/s) and even in these very ideal conditions, a 5-6%
error in velocity measurement is typical and the error tends to be an over, rather than under,
estimate. Characterizing such limits is important for the validation of software and acceptance of
data arising from physical phantoms and the in vivo series. For in vivo cases, however, as is
demonstrated in our clinical series, it is unusual for bulk flow to be greater than 40cm/s and as
such the gross errors associated with γ-variate fits at high velocity is unlikely to be a significant
limitation in this study.
56
Table 3.1 - Calculation of bulk velocity in a simulated flow channel
Curve Fit Trial 1 Trial 2 Trial 3 Mean (Std Dev) Known Error %
Local Quadratic 10.76 10.56 10.45 10.59 10 5.90 Gaussian 10.13 10.34 10.42 10.30 10 2.97 γ -Variate 9.64 9.52 9.58 9.58 10 4.20
Local Quadratic 22.43 22.04 19.65 21.37 20 6.87
Gaussian 20.82 20.8 20.32 20.65 20 3.23 γ -Variate 19.66 19.66 19.16 19.49 20 2.53
Local Quadratic 31.33 31.73 32.01 31.69 30 5.63
Gaussian 31.68 31.12 31.02 31.27 30 4.2 γ -Variate 31.84 31.2 31.34 31.46 30 4.9
Local Quadratic 41.54 42.78 42.92 42.41 40 6.03
Gaussian 42.62 42.06 42.14 42.27 40 5.68 γ -Variate 41.92 42.48 42.78 42.39 40 5.98
Local Quadratic 63.42 63.97 62.28 63.22 60 5.37
Gaussian 62.14 62.86 63.96 62.99 60 4.98 γ -Variate 71.22 76.44 79.42 75.69 60 26.16
Local Quadratic 85.46 86.44 85.39 85.76 80 7.20
Gaussian 84.04 86.64 86.46 85.71 80 7.14 γ -Variate 178.44 181.23 187.72 182.46 80 128.1
Validation of the TOF CTA software was performed in a flow simulation using local quadratic curve fits, Gaussian curve fits and γ-variate fits to estimate TTP at individual channel cross sections. Resulting measurements are shown at each simulated velocity and percentage error calculated as [100 .(measured - known) / measured]. All methods are within 10% accuracy at flows equal to or less than 40cm/s. Error increases as velocity increases in all cases (Pearson’s rho 0.99). It is important to note that some intrinsic error exists even under these very ideal conditions using the TOF technique. The γ-variate curve fits in particular become unstable at high flow rates and grossly unstable at flows 60 cm/s and greater.
57
Figure 3.7 - Typical graphical results of a simulated TOF CTA flow calculation. Image Ai shows a volume rendering from a typical time point in the simulation. A contrast bolus is simulated with Gaussian function. Aii demonstrates a user defined centroid down the course of this channel. Aiii shows TTP as a function of gradient down the channel. Image C depicts curve fits (blue, in this case quadratic functions) to individual cross sectional time density series (one such Gaussian series is shown in red) and D the intraluminal TTP plotted against distance along the centroid. Image B shows vessel cross section placement along an incorrectly placed centroid. As expected, the algorithm divides the vessel into a series of cross sections but these are often angulated. A poor quality vessel centroid can introduce artifacts into the TOF CTA measurement. Definition of a proper centroid is easiest with small vessel diameters and longer path lengths.
58
3.3) Data from CT flow phantoms
The TOF CTA technique demonstrated appropriate fluid velocities in four pipes at the
two diameters tested (Tables 3.2 and 3.3).
In 14 of the 16 flow conditions tested, the local quadratic fit provided the closest
approximation to the known fluid velocity. Visually, local quadratic functions better fit the local
time density series at pipe cross sections rather than γ-variate functions. This is likely due to the
non-physiologic nature of the contrast injection in a phantom (i.e. γ-variate is the most
commonly used function to fit first-pass intravascular time density data in vivo). In all 14 of
these 16 conditions, the most accurate velocity calculation occurred where 1-R2 was lowest of
the three curve fits. The 2 exceptions occurred at 5cm path length (the shortest condition tested)
and at larger pipe diameter, suggesting that R2 of the final curve fit may be a better indicator of
accuracy as path length becomes longer. An accurate vessel centroid may also be more difficult
to define by a user in a large luminal diameter.
Relative differences between calculated and known velocities (i.e. measurement error)
were compared and it was found that faster velocities correlated to increased error strongly at a
0.3 cm pipe diameter (Pearson’s rho 0.80 for 5 cm path length, 0.75 for 10 cm path length) and
moderately at 0.6 cm pipe diameter (Pearson’s rho 0.56 and 0.61 respectively). Using the data
derived from local quadratic function fits to the 0.3 cm ID data, functional maps of water
velocity were generated and presented as planar images and via volume rendering (Figure 3.8).
59
Table 3.2 - Contrast bolus time of flight analysis in flow phantoms subject to dynamic volumetric 4D CT at 0.6 cm pipe diameter
50 Voxel Path 100 Voxel Path
Curve Fit Velocity Known
Calculated Velocity 1-R2 Error
Calculated Velocity 1- R2
Error
Gaussian 168 161.7(23.9) 0.0029 6.3 182.1(2.1) 0.003 14 Local Quadratic 168 176.1(18.3) 0.0036 8.1 173.6(0.5) 0.0013 5.6
γ-Variate 168 160.5(15.7) 0.0023 7.5 176.6(2.0) 0.0023 8.6
Gaussian 109 95.9(8.2) 0.0015 13.1 99.4(1.4) 0.0054 9.6 Local Quadratic 109 109.5(2.2) 0.0006 0.5 112.1(0.8) 0.0006 3.1
γ-Variate 109 94.2(5.7) 0.0009 14.8 96.3(1.4) 0.0029 12.7
Gaussian 60 56.9(3.0) 0.0055 3.1 52.3(1.9) 0.033 7.7 Local Quadratic 60 62.1(2.6) 0.0004 2.1 58.5(1.1) 0.0023 1.5
γ-Variate 60 56.1(3.5) 0.0028 3.9 52.6(1.7) 0.0193 7.4
Gaussian 23 21.8(1.2) 0.0529 1.2 18.8(0.12) 0.055 4.2 Local Quadratic 23 25.2(0.5) 0.0053 2.2 23.6(0.06) 0.0046 0.6
γ-Variate 23 22.0(0.7) 0.0311 1 19.5(0.1) 0.031 3.5 TOF CTA is examined in four pipes at 0.6cm inner diameter (ID) Known fluid velocities are compared to values derived from time of flight (TOF) algorithm where each of the three different curve fits were used to calculate time to peak (TTP) in local databases along a vessel path length as indicated. A longer path length of 100 voxels (i.e. 10cm) is compared to a shorter path length of 50 voxels (i.e. 5cm). Values presented as mean of five trials with standard deviation in brackets. 1-R2 values are presented for the quality of line fit to the final Time to Peak versus Distance plots in each calculation (i.e. not fits at individual vessel cross sections). Error is the absolute value of the difference between mean and calculated velocity.
60
Table 3.3 - Contrast bolus time of flight analysis in flow phantoms subject to dynamic volumetric 4D CT at 0.3 cm pipe diameter
50 Voxel Path 100 Voxel Path
Curve Fit Velocity Known
Calculated Velocity 1-R2 Error
Calculated Velocity 1-R2
Error
Gaussian 241 189.5(5.4) 0.0002 51.5 184.1(2.8) 0.0005 56.9 Local Quadratic 241 250.4(8.4) 0.00008 9.4 235.5(3.8) 0.00015 5.5 γ-Variate 241 185.4(5.1) 0.00018 55.6 187.7(2.6) 0.0004 53.3 Gaussian 87 83.5(11.6) 0.0023 3.5 88.5(0.06) 0.002 1.5 Local Quadratic 87 89.6(5.4) 0.00089 2.6 87.8(0.3) 0.00048 0.8 γ-Variate 87 87.4(8.0) 0.00178 0.4 89.7(0.2) 0.00137 2.7 Gaussian 69 66.1(1.5) 0.0012 2.9 61.1(1.1) 0.00227 7.9 Local Quadratic 69 67.7(0.99) 0.0011 1.3 71.1(0.5) 0.00126 2.1 γ-Variate 69 63.3(1.8) 0.00072 5.7 60.2(0.8) 0.00132 8.8 Gaussian 28 25.1(0.6) 0.0072 2.9 22.6(0.06) 0.02433 5.4 Local Quadratic 28 30.5(0.2) 0.00356 2.5 28.1(0.2) 0.0032 0.1 γ-Variate 28 25.4(0.2) 0.00476 2.6 23.2(0.2) 0.0103 4.8
TOF CTA is examined in four pipes at 0.3cm inner diameter (ID) Known fluid velocities are compared to values derived from time of flight (TOF) algorithm where each of the three different curve fits were used to calculate time to peak (TTP) in local databases along a vessel path length as indicated. A longer path length of 100 voxels (i.e. 10cm) is compared to a shorter path length of 50 voxels (i.e. 5cm). Values presented as mean of five trials with standard deviation in brackets. 1-R2 values are presented for the quality of line fit to the final Time to Peak versus Distance plots in each calculation (i.e. not fits at individual vessel cross sections). Error is the absolute value of the difference between mean and calculated velocity.
61
Figure 3.8 - Typical results of TOF CTA calculation in a pipe flow phantom. The first TOF CTA images obtained in this study were of a four pipe flow phantom. Panel A shows a volume rendering and panel B a cross sectional image from TOF CTA where velocity is encoded into the color scale (scale in cm/s). A typical TTP versus distance plot used to measure velocity in one of the pipes is shown in panel C. This is an example of how functional information can be encoded into images for clinical use by a non-technical specialist.
62
3.4) In Vivo Data: TOF CTA versus phase contrast MRA
Appropriate TTP versus distance curves were generated in all 8 internal carotid arteries
under consideration using the arterial segment defined from the level of the dens to the
cavernous carotid on axial slices. Velocity measurements were recorded using the local
quadratic, Gaussian and γ-variate curve fit approaches to the TOF CTA algorithm and compared
to a pcMRA gold standard (Table 3) on the NOVA platform. pcMRA provides data as mean
velocity as well as peak and trough velocities through a cardiac cycle.
In 5 of 8 arteries, the mean measured velocity by the three curve fit methods fell within
one standard deviation of the maximum and minimum pulsatile velocities as defined by
pcMRA. In 3 arteries, measurements were slightly outside this range. This was the case in the
left ICA of patient 1 as measured by γ-variate, the right ICA of patient 3 as measured by γ-
variate, as well as the left ICA of patient three as measured by the local quadratic technique.
In every case, using all types of curve fit, TOF CTA measurements are on the same order
of magnitude as measurements using the gold standard, and did not produce any nonsensical
measurements such as negative values or bulk flows greater than 100 cm/s.
63
Table 3.4 - Internal carotid artery blood velocity in 4 patients measured by TOF CTA versus a pcMRA gold standard
Pt
Age
Lesion ICA
TOF CTA
Gaussian
(cm/s)
TOF CTA
Local Quad
(cm/s)
TOF CTA γ-
variate (cm/s)
Gold Standard
pcMRA
(cm/s)
1 62 DAVF Right 16.1 (3.2) 15.4 (4.2) 18.9 (3.3) 14.5 [12.1-16.8]
Left 13.2 (2.4) 14.8 (4.0) 15.5 (3.6) 11.8 [9.7-14.3]
2 67 DAVF Right 15.7 (3.7) 17.6 (3.2) 16.1 (2.7) 16.4 [15.5-18.3]
Left 16.8 (4.2) 18.9 (5.1) 16.5 (2.2) 20.8 [18.7-21.5]
3 71 AVM Right 14.5 (3.3) 14.7 (3.8) 11.9 (3.4) 18.4 [15.7-23.1]
Left 16.3 (2.0) 11.8 (2.6) 14.2 (2.2) 15.1 [12.3-17.2]
4 50 AVM Right 38.0 (4.6) 33.5 (6.3) 37 (5.3) 35.4 [32.6-39.0]
Left 18.3 (3.4) 19.2 (5.4) 16.8 (2.7) 17.4 [16.0-19.4]
Abbreviations: patient (Pt), time of flight computed tomography angiography (TOF CTA),
quantitative phase contrast magnetic resonance angiography (pcMRA), dural arteriovenous
fistulae (DAVF), arteriovenous malformation (AVM), internal carotid artery (ICA).
64
Figure 3.9 - TOF CTA in an example internal carotid artery. A typical TTP versus distance curve is shown (left) in an internal artery. Note that in comparison to phantoms and simulations, the data is relatively more noisy (A). TTP was encoded back into the artery and rendered for viewing as a functional angiogram encoding TTP (B) and velocity (C). Such renderings can be resized and rotated by a user in 3D.
65
Figure 3.9 demonstrates a typical ICA studied with the TOF CTA technique, where
image A shows the TTP versus distance curve in this artery (red points) fit with a straight blue
line. The lower left side image B shows the TTP versus distance curve encoded into the ICA
which is then volume rendered. In this example, a signal smoothing algorithm was not applied
to the TTP versus distance data prior to encoding and hence the progression of color gradient
from blue to red is not constant. In vivo data is inherently noisier than data from simulations or
phantom experiments. Image C shows a functional angiogram encoding blood velocity in cm/s.
3.5) TOF CTA in the major intra-cranial arteries of 8 normal subjects
Blood velocities in the major cerebral vessels were calculated in a series of 8 subjects
and are presented in Table 3.5 as the mean of 3 individual TOF CTA measurements and
standard deviation.
In general the data are reasonable, with no negative velocities recorded in this series and
even the highest velocities measured <50 cm/s, bearing in mind that we are considering a
velocity measurement which is averaged both over the cardiac cycle and includes the entire
vessel cross section rather than the peak of a parabolic flow profile.
In the ICA’s across all patients, mean flow measured 25.5 (standard deviation 10.7) cm/s
on the left and 29.1 (7.4) cm/s on the right. These values are at the low end of normal range
presented by other authors (Meckel et al. 2013), however unlike such prior studies it is also
noted that the patient population under consideration in this manuscript is comparatively elderly
(66.4 versus 23.0 years). Conversion to flow via multiplication of velocity by cross sectional
vessel area ndicates 5.6 (2.4) mL/s of flow on the left and 6.0 (2.1) mL/s of flow on the right.
66
Table 3.5 - Blood velocities were measured in the major intracranial vessels using the Time of Fight CTA technique.
Pt Lt ICA Rt ICA VB Lt PCA Rt PCA Lt MCA Rt MCA Lt ACA Rt ACA
1 17.0(1.65) 18.1(1.7 ) 15.1(1.6)
17.1(4.1) 18.7(3.9) 15.7(4.7)
27.8(3.4) 28.9(9.7) 26.7(5.3)
9.8(0.3) 8.7(2.5) 10.1 (2.8)
7.8(1.5) 9.1(3.0) 9.6(0.5)
27.5(1.1) 26.6(3.9) 25.2(2.7)
25.8(4.0) 22.9 (4.8) 24.1(4.8)
6.4(0.5) 6.5 (1.0) 6.0 (0.44)
8.5(1.5) 10.1 (1.1) 7.9 (1.4)
2 26.5(2.7) 32.5(5.9) 26.8(4.1)
23.6(1.6) 33.0(1.3) 24.5(3.1)
34.9(5.4) 35.1(6.8) 37.5(6.3)
29.4(9.8) 45.9(10.9) 23.3(6.0)
31.2(8.9) 22.2(6.7) 24.1 (4.5)
17.1(1.6) 12.6(4.6) 15.6(3.6)
12.7(2.4) 19.9(2.7) 14.3 (2.7)
15.5(2.5) 17.8(8.8) 13.5 (3.7)
13.2(4.8) 15.9(8.1) 12.4 (2.9)
3 31.6(2.1) 34.2(3.6) 28.9(1.9)
27.4(2.9) 32.5(6.1) 26.6(2.6)
21.8(2.9) 20.6(6.8) 18.2(8.7)
19.2(1.8) 19.2(4.1) 16.9(3.4)
26.0(2.4) 31.0(1.7) 18.7(2.3)
32.7(1.7) 33.5(1.1) 33.2(1.5)
45.6(3.6) 37.7(2.4) 32.1(7.3)
42.4(2.8) 37.1(3.1) 35.1(1.9)
25.3(4.5) 29.1(2.8) 24.9(1.2)
4 14.5(4.1) 14.5(2.8) 16.4 (5.8)
35.4(8.0) 54.4(10.6) 27.3(4.8)
9.0(1.2) 9.6(1.6) 8.6(1.8)
8.0(3.3) 9.2(1.1) 13.1(7.0)
13.1(5.0) 27.7(5.8) 12.6(3.5)
20.1(1.3) 23.4(5.0) 24.5(4.3)
40.3(5.6) 42.0(5.5) 63.5(9.4)
22.2(3.6) 34.2(8.2) 21.4 (5.8)
16.4(2.7) 34.2(6.3) 25.1(5.5)
5 12.7(1.2) 14.7(1.1) 13.4(1.1)
12.3(4.1) 13.4(8.1) 12.4(5.5)
7.3(2.6) 7.9(3.8) 7.1(1.7)
10.2(0.9) 15.4(0.5) 10.1(1.3)
9.0(1.9) 10.3(1.1) 9.6 (1.5)
14.1(4.3) 13.5(2.9) 11.6(2.7)
17.9(3.1) 15.4(2.9) 16.4(2.9)
7.6(1.4) 8.1(0.5) 6.9(0.7)
5.9(3.9) 6.5(4.9) 5.7(3.5)
6 27.0(8.9) 28.9(6.9) 48.8(7.8)
32.1(2.5) 39(2.1) 36.9(3.7)
25.8(4.0) 29.8(5.9) 28 (4.1)
6.5(0.8) 5.6(2.2) 6.1(0.7)
5.4(0.9) 5.4(1.7) 3.9(0.7)
32.3(4.1) 35.2(8.4) 31.6(6.1)
21.8(2.1) 22.5(5.0) 21.3(3.5)
14.3(1.2) 14.7(1.5) 13.3(1.4)
16.4(2.1) 18.2(1.3) 15.6(1.1)
7 7.4(3.0) 6.2(2.9) 5.9(1.7)
9.8(5.5) 8.3(2.9) 10.2 (5.5)
5.6(1.2) 4.9(2.9) 4.6(2.1)
10.8(2.2) 11.7(4.2) 10.0(2.8)
10.2(2.6) 11.2(1.9) 9.8(2.6)
5.1(2.6) 4.9(3.0) 4.6(3.3)
6.8(3.3) 8.2(0.9) 7.7(6.4)
11.9(2.8) 6.9(1.8) 6.6(1.5)
4.6(1.5) 4.4(0.3) 4.0(0.9)
8 44.5.3(7.8) 44.3(5.0) 35.9(3.2)
37.9(3.3) 41.1(4.2) 39.1(2.4)
40.3(3.8) 39.8(3.9) 38.5(3.7)
6.6(0.6) 5.9(0.7) 5.2(1.1)
7.6(1.5) 7.1(0.9) 7.0(0.9)
21.4(4.7) 23.4(3.3) 18.4(2.9)
23.5(5.15) 25.5(2.2) 23.1(3.5)
12.4(0.7) 13.9(1.6) 11.4(4.3)
15.4(1.7) 15.9(2.7) 13.5(4.2)
Abbreviations: patient (Pt), time of flight computed tomography angiography (TOF CTA), internal carotid artery (ICA), vetebrobasilar (VB), posterior cerebral artery (PCA), middle cerebral artery (MCA), anterior cerebral artery (ACA). Measurements across 3 trials in each vessel show reasonable reproducibility and are of reasonable magnitude. TOF CTA results presented as mean of 3 trials with standard deviation in curved brackets. In each cell, top row are results by Gaussian fit to local Time Density Curves (TDCs), middle row local quadratic fits to TDC, and bottow row γ-variate fits to TDCs. It is not known from the medical record whether patient 4 had a stenosis upstream in the left internal carotid artery as scanning of the neck vessels is not routine at our institution when CT angiography and perfusion in the brain is normal in the acute setting.
67
Coefficient of variation between subjects is decreased by conversion from velocity to volumetric
flow in the ICAs. Indeed, when ICA and basilar artery flows are summed, total cerebral blood
flow measures 14.3 (3.7) mL/s across the series (coefficient of variation 0.26), a more compact
distribution.
The ICAs and ACAs are accurately characterized by the technique due to their long path
length. In general the basilar artery is too short a segment for TOF CTA analysis using the
present software and hence the larger of the two vertebral arteries were included in each case to
improve signal to noise. With this modification, reproducible values could be obtained as
indicated in Table 4. Meaningful TOF CTA measurements in the MCA and PCA depended
strongly on the avoidance of venous contamination from the cavernous sinus and internal
cerebral veins respectively and frequently require extension of the vessel path length from the
origin in the circle of Willis into an M3 or P3 branch to obtain sufficient data for a reproducible
measurement. By extending the path length, it was possible to sample data past the venous
contamination, which is site specific to the cavernous sinus or internal cerebral veins, and so
mitigate its effect on subsequent calculations.
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4.0) Discussion
4D volumetric CT is a fundamental technical advance in CT technology that enables the
development of new post processing tools, differing from existing algorithms in kind rather than
quality. While functional imaging in CT has traditionally focused on the calculation of tissue
perfusion using the central volume principle, 4D CT for the first time enables quantitative
functional evaluation of hemodynamics in the intravascular space. A new set of techniques will
need to be defined for this analysis which will certainly require an extensive re-visitation of the
indicator dilution literature.
TOF CTA is a simple technique relying upon the tracking of a bolus during its travel
along vessels. Assuming the bolus is well-mixed, tracking the bolus centroid as it moves along
the central axis of a vessel provides a straight forward means to calculate hemodynamic
parameters such as blood velocity and volumetric flow rate. The brain is an ideal first organ for
analysis of the TOF CTA technique due to the relative availability of data and the triviality of
image registration using rigid skull-based methods (i.e. image registration is non-trivial in the
body and frequently requires correction for the effects of respiration and deformation of solid
organs). The brain however does present unique challenges in that blood vessels are generally of
small caliber. Additionally, depending on the practice pattern of an institution, it can be difficult
to define a non-invasive gold standard in a large patient series where 4D CT has also been
performed. This will be the subject of future work.
This discussion section will first review the results of functional segmentations for the
common neurovascular lesions studied herein, followed by discussion of the implementation of
TOF CTA in flow simulations, pipe flow phantoms and the preliminary in vivo data obtained
69
from examination of the TOF CTA algorithm across our clinical series. Finally, some new
prospects in functional CT research using TOF CTA are discussed.
4.1) Functional angiography in CT Imaging
With quantitative analysis of density change in spatially congruent voxels through time,
blood vessels may be successfully segmented from the rest of the field of view. Segmentation by
curve fit is an elementary and powerful means of producing such images of vascular structures
without interference from bone or calcium artifact (figure 3.1). With adequate segmentations,
physiologic information can be encoded and presented as either planar functional intravascular
maps or functional renderings. Segmentation by curve fit was used to produce the functional
angiograms shown in Figures 3.2-3.6.
Intravascular TTP, rise and maximum slope of the contrast upstroke are all typical
examples of functional parameters that may be encoded into intravascular voxels to produce a
functional angiogram. The resulting images can show early filling of a venous structure in the
case of an arteriovenous shunting lesion, including the direction of blood flow to display cortical
venous reflux (the main criterion predicting hemorrhagic transformation of a DAVF), or to
gauge the severity of such a lesion through assessment of the difference between arterial to
venous TTP and maximum gradient. Functional parameters assessed in a reconstituted vessel
distal to an occlusion or stenosis, such as that beyond an MCA infarct in the case of stroke, may
indicate degree of collateral flow to the infarcted vascular territory and serve as an adjunct to CT
perfusion in the acute setting. TTP of an intracranial aneurysm can be used to quantify the
detention time of the aneurysm sac and hence the probability of thrombosis, a parameter
particularly relevant to aneurysms of the posterior circulation and in those aneurysms treated by
70
flow diversion. Such analysis may in the future also be linked to wall shear stress. Should a
correlation between such parameters exist, the routine clinical assessment of wall shear stress
will be enabled without need for technically difficult computational modeling.
One potential limitation to the evaluation of maximum gradient in the arterial circulation
is elongation of the bolus upstroke as a function of path length in the vessel lumen due to
parabolic laminar flow effects and increased contrast dispersion, both of which are well known
(Barfett et al. 2011, Barfett et al. 2012). These effects mitigate the use of maximum gradient in
calculations to perform flow quantification in the arterial system and will be particularly
problematic at slow flow states. We have found that when evaluating gradient maps or derivates,
it is important to consider that changes in the functional map may be due to contrast dispersion
rather than alteration of blood flow.
We have opted for TTP rather than time of arrival (TOA), as has been most extensively
described in the MRI literature (Riederer et al. 2009, Saring et al. 2010), as a parameter for
functional encoding. The relative noisiness of signals generated from spatially congruent voxels
in CT data compared with MRI potentially complicates TOA calculation by curve fit. While
TOA depends strongly on only a subset of data in any early phase of a time attenuation curve,
TTP, conversely, is generally calculated by curve fit to both the contrast wash-in and wash-out
at higher HU attenuations and therefore potentially produces a more accurate and reproducible
result. Importantly, we have found in vivo and subsequently confirmed in our phantom
experiments that proximal and distal portions of the same vessel demonstrate greater difference
in TTP than in TOA (Barfett et al. Jul 2010). This is logical when we consider that a contrast
bolus subject to a typical parabolic laminar flow profile will be propelled forward more rapidly
along a pipe’s central axis than at its periphery and hence TOA tends to measure the greatest
71
velocity in a parabolic flow profile rather than bulk flow. Thus, use of TTP, a measure of the
bolus centroid, exaggerates delay between contrast arrival along a vessel path-length and leads
to more readily interpretable functional maps. The effect seems dominant at slower flow rates
and at larger vessel calibers (Barfett et al. Jul 2010).
Mean transit time (MTT) was defined in the intravascular space as full-width half-max
of a TDC curve in a review by Blomley et al. 1997. In the patient with DAVF, an MTT map was
included in addition to TTP maps (Figure 3.2). MTT in the current literature is more commonly
understood as it applies to tissue perfusion and so intravascular MTT was not emphasized in this
manuscript.
4.2) Limitations of functional angiograms
The increased availability of functional intravascular imaging in all modalities has
resulted in renewed interest in characterizing intravascular flow physiology with CT (Barfett et
al. Jul 2010; Willems et al. 2011; Prevrhal et al. 2011). Several authors have recently attempted
this using a variety of techniques (Prevrhal et al. 2011; Barfett et al. Jul 2010; Pekkola et al.
2011). One group attempted qualitative visualization of flow using multidetector CT (Pekkola et
al. 2011), while a second utilized a projectional approach in non-pulsatile phantoms (Prevrhal et
al. 2011). The functional angiogram technique as defined in this manuscript began with the
desire for a purely quantitative approach.
Functional angiograms do have merits. We found in particular that intravascular TTP
maps could appropriately characterize shunting lesions such as AVM or DAVF. In the case of
DAVF, TTP maps can also demonstrate cortical venous reflux (Figure 3.3), which is a key
72
predictor of hemorrhage and therefore a determinant as to whether these lesions require
treatment either by either endovascular or surgical means. We found that maximum gradient is
also increased in the venous structures receiving increased blood flow from these shunts (Figure
4), though the clinical utility of this information is less certain. Further studies are required to
determine the sensitivity and specificity of demonstrating cortical venous reflux by 4DCT
versus through the use of the more invasive cerebral angiography gold standard. TTP maps were
able to demonstrate reversal of flow in the case of subclavian steal (Figure 3.5) and a central to
peripheral filling of a giant cavernous aneurysm (Figure 3.6). The latter may be particularly
interesting to study in regards to calibrating finite element models of aneurysm shear stress.
Initially it was thought by the author that the maximum gradient of the upstroke phase
(i.e. the maximum gradient) in the artery would provide a means to quantify intravascular blood
flow in a manner analogous to the maximum gradient method of calculating tissue perfusion in
CT (Abels et al. 2010). In practice we found that maximum rate of contrast enhancement in
intra-arterial voxels correlated with stenosis to some degree but was strongly influenced by
partial volume effects. For example, it has been shown in the CT literature (Paul et al. 2010) that
given two substantially different sized vessels with the same concentration of contrast
enhancement, the larger vessel will demonstrate a higher HU attenuation. As an extreme
example, if we consider both the abdominal aorta (diameter of ~ 4 cm) and a single mesenteric
artery (diameter ~ 0.5 cm), then in venous phase when contrast is evenly distributed throughout
the system, the larger aorta will appear more dense than the smaller mesenteric vessel. This is
due mainly to partial volume effects of the relatively low-density extra-vascular space
influencing the smaller vessel, rather than concentration of contrast in the lumen and therefore
flow itself. It might be erroneously assumed that larger vessels will always have higher flow
73
rates, particularly where upstream stenosis in a vessel or other vascular lesions cause significant
flow disruption.
There are algorithms in the literature which are available to correct for such partial
volume effects, however these are experimental and not generally available on commercial
scanners or workstations. This is a potential issue for further investigation.
4.3) TOF CTA algorithm
TOF CTA as described in this manuscript is a simple technique to derive functional
intravascular information including blood velocity, blood flow and the direction of blood flow
from 4D dynamic CT angiography in a potentially non-user dependent fashion. In addition to
these three key functional parameters, the technique may similarly be used to calculate other
less complex characteristics of a contrast bolus such as TTP, TOA, area under the curve and
maximum gradient. Importantly, the method supports display of such quantitative functional
information to a user by means of a functional map or volume rendering (Figures 10,11). The
algorithm relies upon an intravascular segmentation, as well as a skeletonization of that
segmentation to attain blood vessel centroids. In the software described in this manuscript, we
have given the user a tool to define vessel path-length. With this vascular centroid defined, the
TOF CTA analysis is then performed automatically.
In contrast to conventional CT perfusion, which is concerned with enhancement of the
extra-vascular tissues, TOF CTA is intended for analysis of the intraluminal compartment. This
distinction is important firstly due to the future intention for TOF CTA to evaluate primarily
vascular lesions and secondly due to the improved signal-to-noise for quantitative analysis of
74
contrast bolus passage within the vessel lumen as opposed to the tissues. For example, since the
technique is concerned strictly with assessment of the intravascular space and therefore tissue
enhancement is not a consideration, it may be possible to perform TOF CTA analysis with only
minimal doses of IV contrast.
4.4) Automation of the TOF CTA approach
A major advantage of the TOF CTA approach over the definition of user-dependent
ROIs (Barfett et al. Dec 2010) is the potential for full automation. As discussed above, TOF
CTA relies upon an accurate segmentation of the intravascular space as well as definition of
vessel centroids. CT image segmentation has been subject to intense academic activity and
several approaches have already been described in the literature (Saring et al, 2010; Oliveira et
al. 2011; Rengier et al. 2011; Song et al. 2011). A robust segmentation algorithm has been
published for cerebral vessels (Saring et al. 2010), and which may be suitable for clinical use. In
this manuscript we have made extensive use of both the curve fit approach and the level set
approach to segmentation. Curve fits were initially used to create segmentations for functional
angiograms and the results published. It was noted in evaluation of the TOF CTA algorithm that
these segmentations were frequently affected by venous contamination. For example, venous
TDCs from the cavernous sinus and internal cerebral veins could confound measurement of ICA
and PCA blood velocity, respectively. Segmentation by level set provided higher quality
segmentations that were less affected by venous contamination and proved to be suitable for
TOF CTA calculations.
The second basic requirement for the algorithm is a skeletonization of vessel centroids.
This is computationally more challenging than segmentation, however it has also been the
75
subject of intense research (Paul et al. 2010) and, hence, most medical imaging workstations
(including MATLAB) offer production quality vascular skeletonization tools. These algorithms
were initially developed for the assessment of vessel caliber and atherosclerosis and do support
branch points. With appropriate vascular segmentatons and skeletonization, it is highly likely
that the TOF CTA algorithm can be successfully automated. One algorithmic approach to such
automation would be to firstly find the major blood vessels entering the 4D volume, which
where the brain is considered would typically include the two internal carotid arteries and the
two vertebral arteries and, occasionally, the external carotid arteries and/or its branches where
they are visible. All these arteries would coexist on a single slice at the base of the volume.
After definition of the vascular inputs, the algorithm might walk down the central axes of
vessels until branch points are reached. At these branching points in the vascular segmentation,
a choice of direction might be initially chosen randomly and the choice stored in memory to
avoid repeat measurement along that path on subsequent calculations.
A crucial point to the quality of data produced by the TOF algorithm is in the choice of
signal smoothing filters used both to estimate TTP of the contrast bolus and to smooth the
resulting distance versus time plot. Again several options are available. In this manuscript, we
opted for proof of concept via a simple linear fit to the distance/time data to produce a single
velocity that summarizes flow in the vessel. This approach has advantages for preliminary
validation but would not be suitable for a production system in clinical implementation as
velocities do change from proximal to distal points in any given vessel as a function of vessel
caliber. In addition to a variety of curves which are available for to be fit to time versus distance
data, a purely numerical approach might also be taken where a signal filter is chosen and
derivatives taken from less noise filtered data rather than from a curve.
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4.5) Validation of the TOF CTA software in flow simulations
Initially the TOF CTA software was evaluated in flow simulations. This served two
purposes, firstly to ensure that the software was functioning properly and produced expected
results and secondly to evaluate the theoretical accuracy of the algorithms in their current state
against a gold standard. This analysis yielded interesting data.
Firstly, we found that in general that Gaussian curve fits to the source data provided a
better evaluation of flow velocity than γ-variate functions, though both methods were accurate
below a mean bulk flow of 40 cm/s (Table 1). The better performance of the Gaussian function
is expected given that Gaussian functions were used to generate the baseline simulation.
Importantly, even at low bulk velocities below 40 cm/s, a velocity measurement error of
approximately 5% was seen (Table 1). The primary source of error in this flow simulation was
the user dependent definition of the channel centroid, even in this case where the centroid is
trivial to define. This vessel centroid is inevitably always slightly off axis. Translated in vivo,
systematic errors of at least 5% are reasonable to expect.
This simulation provided the first evidence that choice of curve fit for individual vessel
cross-sections is a crucial issue in data quality control. Several methods were attempted prior to
settling on the local quadratic, Gaussian and γ-variate approaches, including the use of cubic
splines with various amounts of signal smoothing as well as several attempts at purely numerical
solutions to find bolus centroid. The success of these various approaches depends strongly upon
the shape of the signal to which they are fit. The splines in particular were found to be unstable
as signal shapes changed across different phantoms and anatomic configurations and thus
splines would give erratic results unless constantly recalibrated. The numerical approaches
attempted, including use of TDC feature analysis to divide the signal into subsections to be
77
analyzed independently, can work but depend to a large extent on sufficient temporal resolution
of the acquired signal (i.e. these approaches benefit from a density of data points around the
TTP). In vivo, this could translates into a higher number of scan volumes and hence a higher
radiation dose. Forcing data to fit a defined curve somewhat mitigates this problem.
The γ-variate is a good general choice of function for this application due to its extensive
use to describe signals in vivo. In particular, contrast bolus profiles in arteries and veins are
routinely modeled with the γ-variate in both the CT and MRI context (Blomley et al. 1997). In
our flow simulation, however, we found γ-variate fits to become highly unstable when modeling
velocities 60 cm/s or above. This is a systemic error that relates to the multi variable linear
regression algorithm used in SciPy to fit the curve rather than to the function itself. Fortunately,
bulk flow in arteries is rarely greater than 60 cm/s and thus the γ-variate fits performed better in
vivo than in this initial simulation. It is possible that γ-variate fits might be improved through the
addition of additional variables into the equation, however multivariate linear regression above
3 variables is non-trivial in SciPy and was hence not explored.
4.6) Validation of TOF CTA in flow phantoms
Our flow phantom is not an accurate representation of in vivo conditions for several
reasons. Firstly, the flow was non-pulsatile. Though pulsatile flow pumps are available which
replicate in vivo conditions, we do not have access to such a system at Toronto General Hospital
and so began prototyping with hobby pumps. Secondly, silicone tubing does not replicate the in
vivo arterial wall due firstly to lack of deformation with pressure change and secondly in terms
78
of surface roughness. Finally, in our phantom we did not include recirculation as part of the set
up whereas in vivo, intravascular signals are strongly affected by recirculation effects.
We found in these phantom experiments that TOF CTA did measure intraluminal flow
rates in a reproducible manner. In 14 of 16 flow conditions tested, the local quadratic function
fit to TDC of individual pipe cross sections provided the most accurate measurement of
velocity. The two exceptions occurred at the larger 0.6 cm pipe diameter and only where a
shorter 5cm path length was employed for measurement. 1-R2 statistics were kept to describe
the quality of fit of the straight line to TTP versus distance data. In all 14 of 16 flow conditions
where the local quadratic function provided the most accurate assessment of velocity, the 1-R2
value was lowest (i.e. the best fit) where quadratic functions were applied.
The simplicity of geometry in a flow phantom makes it possible to address some
fundamental questions pertaining to flow measurement with TOF CTA. The straight silicone
pipes for example provided an ideal geometry for the definition of vessel centroids. Aside from
verification of the fundamental premise, the two issues that were examined in these experiments
include an assessment of how path length influences accuracy of results (i.e. are results more
accurate if the velocity is measured over a longer path length) and secondly whether velocity is
more accurately measured at slower flow rates. The range of flow rates studied in each
experiment provided insight into this second issue.
In the Table 2, we see that the difference between measured and known velocities
correlated to fluid velocity, that is to say that in general a faster intrinsic velocity resulted in a
larger measurement error (Pearson's rho 0.61 at 0.6 cm ID and 0.75 at 0.3 cm ID, using a 100
voxel path length). This is to be expected and was indeed predicted by the flow simulation
experiments. At high velocity, the choice of curve fit at local vessel cross sections strongly
79
affected the final velocity calculation. This is especially apparent at the smaller piper diameter,
where at the maximum intraluminal velocity of 241 mm/s, calculated velocities using the γ-
variate function and Gaussian distribution were off by over 50 cm/s, an error of greater than
20%, even when 100 voxels of path length was chosen.
In regards to the effect of path length on TOC CTA measurement, we have shown that
short path lengths lead to less reproducible measurements with a higher standard deviation
between measurements (Table 2). For example, at 0.6 cm ID, it was found that standard
deviation of the TOF CTA measured velocity inversely correlated with path length, with
Pearson's rho of -0.48. A similar trend was seen at 0.3cm ID, with measured velocity inversely
correlating to path-length and Pearson's rho measuring -0.49. Taking a measurement over a
longer path-length is equivalent to including more data in the calculation and it is reasonable to
expect that the inclusion of more data would amount to a more accurate and less variable result.
The effects of path-length on measurement error seemed to be more dominant at the
larger pipe diameter. A simple explanation for this is that smaller pipes are inherently subject to
a more uniformly defined vessel centroid. If a user chooses a central path in a smaller pipe
diameter, there is less potential for error than might be present at a larger diameter. In our
experience with the TOF CTA software we have found that choice of the vessel central path
strongly influences resulting data. A path which deviates from the centroid can result in artifacts
in the flow calculation and lead to inaccuracy in final results. In the future, it is likely that
skeletonization of the vessel to automatically define the vessel centroid will help to mitigate this
problem.
In summary, phantom work demonstrates that intraluminal fluid velocities may be
measured using the TOF CTA approach and secondly, that the accuracy of these measurements
80
is improved by slower intraluminal flow rates and by taking the measurement over a longer
path-length.
4.7) TOF CTA in the internal carotid artery
The internal carotid artery (ICA) is an ideal geometry to prototype the TOF CTA
technique for several reasons. Firstly, the ICA is visible in every head CT scan and image
registration of head CT is simplified by the availability of a rigid and easily segmented skull.
Secondly, perfusion CT in the brain is a relatively common undertaking in neuroradiology
departments, whereas perfusion data in other areas of the body is rare even in the research
environment due to radiation safety and image registration issues. Finally, the ICA is generally
orthogonal to axial CT images of the brain and is of a relatively long path length through the
neck into the cranial cavity. The long path length combined with relatively large vessel size and
therefore slow flow (as compared to flow in the cerebral arteries or circle of Willis for example)
make the ICA ideal for TOF CTA analysis.
We encountered significant limitation in our patient recruitment due to the radiation
doses associated with multiphasic CT. In a study period of 12 months, we were able to recruit 4
patients to have both a 4D CT and pcMRA of the internal carotid arteries to serve as gold
standard, a total of 8 data points. During the study period, 4D CTA of the brain was rarely used
in the outpatient clinical setting as it is difficult to justify a radiation dose typical of 4D CT
examinations in patients with cerebral AVM or DAVF. Time resolved MRA is the standard of
care for the evaluation of these lesions at our institution and the relatively young age of these
patients further mitigates the role of imaging options involving ionizing radiation.
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In our series of 8 ICAs, TOF CTA demonstrated reasonable agreement with results
shown by pcMRA. Given the novelty of the technique, we were first impressed by the fact that
in 5 of 8 arteries, the TOF CTA measurement provided a result in range of the pcMRA method
using all curve fitting techniques. An important difference between pcMRA and TOF CTA is in
the fact that pcMRA is capable of providing both diastolic and systolic flow rates through the
cardiac cycle including a waveform whereas TOF CTA can only provide mean bulk flow over
the course of several heart beats.
Discrepancy between TOF CTA and phase contrast MRA may be due to several factors.
Firstly, patients who received a 4D CT of the brain on an outpatient basis had to be called back
for phase contrast MRI and were therefore scanned on different days. There is therefore
variation in terms of heart rate and blood pressure at the time of both scans. Secondly, any
number of minor quality control issues can affect either TOF CTA measurements or pcMRA
measurements. In order to make a measurement with pcMRA using the NOVA platform, the
user first defines a plane through an artery or vein and then obtains a pcMRA measurement by
defining the vessel lumen on that plane from pcMRA data. In contrast, TOF CTA takes a
measurement of fluid velocity over a path-length and in this case over the course of the ICA
from the level of the dens to the cavernous sinus. It is a well-known basic principle of fluid
dynamics that although volumetric flow rate through a vessel is constant, velocity does change
with vessel caliber. Thus one would expect a relatively more rapid flow rate in the small more
distal cavernous ICA than the larger more proximal suprabulbar ICA. The caliber of vessel, as
defined by source segmentations, can also change measurements for both pcMRA and TOF
CTA. All of these issues can confound measurements.
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It is important to note however that despite all these limitations, results obtained by TOF
CTA are reasonable and do correspond to those obtained by phase contrast MRA. All
measurements provided by TOF CTA are on the same magnitude as those of pcMRA, with no
absurd results such as average velocities of over 100cm/s or negative velocities for example.
Given the novelty of the technique, our initial results represent a meaningful step forward in
terms of validation.
Unless a patient recruitment mechanism is established to perform pcMRA routinely in
stroke patients receiving 4D CT perfusion of the brain, however, it may be necessary to explore
the further validation of the TOF CTA technique in animal models.
4.8) TOF CTA in the major intracerebral vessels
Presented in Table 4 is a cross section of TOF CTA data obtained from the analysis of
the intracranial arteries in a set of 8 consecutive patients subject to 4D CT at our institution. This
is a retrospective analysis and unfortunately does not provide such measurements against a gold
standard. Still, much useful information was obtained. Firstly, in our experience, the ICAs and
ACAs are readily suitable for the technique due to their long path length. In the case of the ICA,
however, an incompletely segmented cavernous sinus can be a source of considerable error. The
cavernous sinus, a venous structure, tends to increase TTP of corresponding vessel cross
sections and hence can reduce velocity when the slope of a line of best fit is taken from the TTP
versus distance plot. We found that switching from curve based segmentations to a level set
based approach significantly improved such venous contamination. Another possible solution to
this problem is to extend path length of the ICA measurement just beyond the cavernous sinus
into the proximal MCA to obtain a proper arterial curve fit.
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TOF CTA in the ACAs is not affected by contamination, but can be limited by
incomplete separation of the two vessels in segmentations, i.e. “kissing vessels”. The current
form of the TOF CTA software excludes points in a segmentation that fall outside a vessel, but
more sophisticated algorithms to deal with the issue of partial volume effects between adjacent
vessels would likely further improve the quality of analysis. Taking these limitations and
observations into account, it was quite trivial to obtain reproducible measurements in both the
ICAs and ACAs across all patients. It is interesting to note that patient 4 of the retrospective
series demonstrated reduced flow in the left ICA and MCA compared to the right. It is unclear
from the medical record whether this patient had an upstream stenosis in the left internal carotid
artery, as imaging of the neck vessels at our institution is not routine in the setting of acute
stroke if CT perfusion is normal.
Secondly, in general the basilar artery is too short a segment for TOF CTA analysis
using the present software and would frequently yield nonsensical or even negative flow rates,
suggesting that velocity in the basilar is too rapid to assess over such a short path length. To
correct this problem, the larger of the two vertebral arteries were included in each case to
provide sufficient path length for an accurate calculation. As we observed in the phantom study,
long path lengths correlate to more accurate measurements. Theoretically, there is no limit to the
length of vessel that can be used in these calculations, though including more than one artery in
the calculation will of course provide a mean estimate of blood velocity across multiple vessels
rather than velocity in a single vessel of interest.
Finally, meaningful TOF CTA measurements in the MCA and PCA depend strongly on
the avoidance of venous contamination and frequently require extension of the vessel axis from
the origin into a distal M3 or P3 branch to obtain adequate path length for a reproducible
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measurement. In these arteries, while path length is certainly important, overall it was found that
quality of the underlying arterial segmentation (i.e. the exclusion of venous voxels) is the most
crucial factor in determining quality of TOF CTA measurements. Even with image registration,
issues with patient motion and resulting noisiness can reduce the quality of segmentations and
hence confound measurements.
Importantly, and with the above factors in mind, reasonable results could be obtained
with TOF CTA in the major cerebral vessels. For example, flow is appropriately antegrade in all
cases and flow velocity is on the correct magnitude. We also find that in the case of the ICAs
and vertebrobasilar system, results are reasonable. For example, mean flow across all ICAs
measured 25.5 (10.7) cm/s on the left and 29.1 (7.4) cm/s on the right. Conversion to flow
indicates 5.6 (2.4) mL/s on the left and 6.0 (2.1) mL/s on the right (i.e. when velocity is
multiplied by cross sectional vessel area at the immediately infracranial carotid). Total blood
flow to the brain as measuring by ICA and basilar artery flows averaged 14.3 (3.7) mL/s or 858
mL/minute across the series. This is approximately 20% of a 5L per minute cardiac output.
4.9) Advantages and disadvantages of TOF CTA versus Doppler and pcMRA
TOF CTA is a distinctly different approach to the calculation of intravascular
hemodynamics compared to both Doppler ultrasound and pcMRA. The first and most
fundamental difference is that while Doppler and pcMRA can measure flow at a user specified
point in a vessel, TOF CTA requires distance of which to make a calculation. The more distance
that is given, the more accurate the calculation. Thus TOF CTA is not suitable to calculate flow
across a vessel stenosis, for example, or flow in a short vessel. A second potential disadvantage
to TOF CTA is that the flow provided is an averaged measurement over many heart beats.
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While Doppler ultrasound and pcMRA can show a changes in a flow waveform over the cardiac
cycle, TOF CTA in its current state cannot. Thus from TOF CTA it is impossible to calculate
peak systolic or diastolic flow, for example. Finally, TOF CTA will always require
administration of both IV contrast and radiation.
There are however several potential advantages to TOF CTA. Firstly, the technique is
non user dependent and will, in its production phase, likely be completely automated. Secondly,
with such automation, the technique can characterize flow in every artery in a field of view
including an organ such as the brain with a single 4D CT scan of short duration, whereas
Doppler ultrasound and pcMRA generally require a user to interrogate vessels individually.
Finally, owing to the spatial resolution of CT, TOF CTA is capable of making flow
measurements in small peripheral vessels. We have had success with the technique in measuring
flow in cortical vessels of the brain for example, or in segmental vessels of the lung, where
Doppler ultrasound and pcMRA are limited. In the correct clinical context, all techniques are
very useful. In time, TOF CTA may find a role alongside other forms of functional imaging.
4.10) Further applications of TOF CTA and exploration of the technique
Initial clinical implementation of the technique might include grading arteriovenous
malformations and other shunting lesions of the brain, calculation of blood flow rate through
coronary artery bypass grafts, calculation of blood flow in arteries of the circle of Willis in
vasospasm, and perhaps to calibrate finite element models of vessel or aneurysm wall shear
stress.
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While we were limited in the number of cases available for in vivo analysis, we have
prototyped the technique retrospectively in 4D CT examinations from a variety of patients from
the UHN database. The most interesting of these cases included a cardiac perfusion series (in
which we used the TOF CTA algorithm to estimate aortic and pulmonary artery blood velocity),
a prostatic perfusion series (used to calculate blood velocity in the iliac vessels), as well as
examination of the neck vessels in a case of subclavian steal syndrome.
First we illustrate an example of the cardiac perfusion series examined with the TOF CT
technique. Unfortunately in this case there is too great a coronary calcification burden to permit
examination of coronary arterial blood flow. The pulmonary vessels were readily examinable
however and an intravascular segmentation created with curve fits as described above. A user-
defined vessel centroid was then taken along the main, left main and segmental pulmonary
arteries branches. Resulting TOF CTA time/distance curve is shown (Figure 4.1). The gradual
trend of increasing tangent slopes to this curve indicate a decreasing blood velocity from
proximal to distal portions of the pulmonary arterial tree. This result is expected as effective
cross-sectional vascular surface areas is increased with the degree of vessel branching.
Another case we examined was from a prostatic perfusion series performed in the
context of prostate cancer, courtesy of Dr. Catherine Coolens, Princess Margaret Hospital. TOF
CTA clearly demonstrates progression of TTP along the course of the iliac vessel under
examination (Figure 4.2).
Finally, a case of subclavian steal was characterized by 4D CT prior to treatment. TOF
CTA shows antegrade blood flow in one vertebral artery and retrograde flow in the other
(Figure 4.3). Treatment was uneventful.
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Figure 4.1 - TOF CTA in the pulmonary circulation. TOF CTA performed along a user-defined centroid in the pulmonary circulation demonstrates a gradual decrease in blood velocity (i.e. increase in slope of the TTP vs. distance plot) as effective cross sectional area increases more distally in the vascular tree. Calculation of pulmonary artery blood velocity has numerous applications.
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Figure 4.2- TOF CT in the external iliac artery. A 76 year old man underwent perfusion imaging of the prostate. The source data was used to evaluate external iliac artery flow via TOF CTA.
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Figure 4.3 - TOF CTA in the vertebral arteries in a case of subclavian steal. Image A is a TTP functional angiogram of the vertebral arteries in a patient with subclavian steal syndrome. Using the TTP functional angiogram as a segmentation upon which to base TOF CTA, antegrade flow was demonstrated in the right side (image B) and retrograde flow in the left side (image C).
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There remains significant opportunity for further work to characterize the TOF CTA
algorithm in a variety of anatomic structures subject to 4D CT analysis.
Two major clinical studies are underway using TOF CTA at the time this manuscript
was submitted. The first study involves the use of TOF CTA to characterize blood flow in circle
of Willis vessels in patients undergoing perfusion CT for evaluation of vasospasm from
subarachnoid hemorrhage at St. Michael’s Hospital. At this center, CT perfusion is routinely
used for the evaluation of vasospasm and to determine the need for angioplasty of vessels in the
circle of Willis in a manner similar to other authors (Mills et al. 2013). The resulting functional
maps are noisy and difficult to interpret. TOF CTA, because it focuses on the intravascular
space where signal to noise in any given ROI is better than what is generally available in tissue,
may have some advantage in detecting subtle flow abnormalities in this population. The aim of
this study is to determine whether TOF CTA can delineate significant flow disturbance and
whether this correlates to patient symptoms and will be initially retrospective.
The second study is underway at Sunnybrook hospital where TOF CTA is being used to
calculate flow rates in coronary artery bypass grafts. Although the assessment of coronary blood
flow with the technique would be of high clinical value, such assessment is limited by both
cardiac motion and radiation dose. Relatively stationary bypass grafts, conversely, lend
themselves well to assessment with the TOF CTA technique. An approved study of 100 patients
in currently recruiting.
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4.11) New methods of perfusion calculation using TOF CTA
CT and MRI perfusion have typically relied upon the central volume principle for the
calculation of tissue perfusion parameters such as blood volume, blood flow and mean transit
time. As reviewed above in section 1.0, these calculations may be made by the maximum
gradient approach, the deconvolution approach and, as is more often the case in body perfusion,
the Patlak approach.
TOF CTA offers another approach to the calculation of tissue perfusion that remains to
be explored. As an example consider the author's recent work in perfusion of the foot for the
evaluation of critical limb ischemia (Barfett et al. Jul 2010, Barfett et al. 2012). In this instance,
the human foot is supplied by two major arteries (posterior tibial and dorsalis pedis). Using the
TOF CTA approach, it is trivial to calculate the flow rate of blood in cm/s in each artery.
Knowing artery caliber, which is available from CT, it is trivial to calculate flow rate of blood
into the foot in mL/s.
In this paper we examined the en bloc enhancement of an entire anatomic structure as a
single unit, i.e. it is possible to calculate the overall enhancement of a structure such as the foot,
minus the intravascular space, in Hounsfield units per unit volume of tissue. From here, it is
possible to subdivide the structure into a set of smaller regions of interest, each one of which
demonstrates some internal enhancement (or potentially lack thereof in the case of ischemia)
and determine the fraction of total enhancement which may be attributable to each ROI. A map
can then be created, where each ROI can be color encoded to indicate the amount to which that
ROI contributed to overall enhancement. Given that we know volumetric flow rate into the foot
via the TOF CTA technique, the data could then be appropriately calibrated so that each ROI is
assigned a fraction of overall flow in mL/s.
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This approach to perfusion is available in volumetric scanners which intrinsically can be
used to measure enhancement of a structure, including an organ, en bloc as a single unit, and
may offer technical advantages in certain clinical scenarios. We are proceeding with this method
in our work on critical limb ischemia in the diabetic population.
4.12) TOF CTA with dual energy CT: flow, perfusion and capillary permeability
Dual energy CT is an old technology which has recently become clinically available in
routine practice, with advanced dual energy CT capabilities being offered by all the major
vendors. Dual energy CT offers some unique advantages from the point of view of
characterizing intravascular physiology and potentially tissue perfusion (Karcaaltincaba et al.
2011; Nakazawa et al. 2011; Thieme et al. 2011; Zhang et al. 2012). All perfusion algorithms
rely upon a time series of data as the basis of their calculations and this is intrinsically high in
dose, especially where the body is concerned. This is a significant caveat which has limited the
use of known perfusion calculations in routine clinical practice, even in patients well enough to
hold their breath for the duration of a dynamic CT exam.
Dual energy CT offers the capability to produce material maps via either two or three
material decomposition algorithms as has been previously described (Liu et al. 2009; Gupta et
al. 2010). For example, one author has used the iodine map as a surrogate measure of lung
perfusion in the context of CT scans for pulmonary embolus (Thieme et al. 2011). Similarly,
intra-vascular iodine gradient can provide a surrogate indicator of intravascular flow rate (Zhang
LJ et al. 2011). These new methods of functional characterization in CT are powerful but again
suffer from the major limitation of contrast dispersion, which severely limits mathematically
rigorous flow calculations.
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As blood moves from the venous system where it acquires contrast, travels down a series
of blood vessels to the heart, is mixed, enters the lungs, then travels back into the heart, then into
arteries, there is substantial dispersion of contrast (Zierler 1999). An IV injection that begins as
a square wave becomes Gaussian in distribution as a result of these flow effects
(Bassingthwaighte 1963). Where recirculation and mixing in the major central vessels is
concerned, the signal takes on a more gamma variate (though as discussed by Hamilton in
general these effects are less relevant at the upstroke of the contrast bolus in any given ROI).
The extent to which intravascular or tissue contrast gradients can be used to indicate
blood flow depends on the extent of signal distortion occurs through dispersion. Consider for
example a system of two arteries arising from a common source with a stenosis at the origin of
the second artery. As a contrast bolus passes through the system, if an image is acquired early
enough in phase, the first artery will demonstrate a relatively tight gradient from origin along the
path-length, while the second will demonstrate more gradual gradient due to slow internal flow.
Although the larger gradient in the slow flowing second artery indicates slower internal flow,
gradient is only a surrogate indicator of flow because the signal is inherently distorted by
presence of the stenosis, i.e. the contrast upstroke is intrinsically flattened by these stenoses
(Figure 4.4). The same problem exists where iodine maps are used to measure tissue perfusion.
In the lungs, for example, the calculation of an iodine map from dual energy CT will show
relatively less iodine concentration in regions of hypoperfused lung. This hypoperfusion is a
surrogate measure, rather than a rigorous measure, of this decreased tissue perfusion due to the
same issue of contrast gradient distortion.
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Figure 4.4 – Distortion of the time density curve by presence of a severe stenosis. Consider a pipe phantom where a single inlet is divided into two outlet pipes of equal diameter and there is a severe stenosis at the origin of one of the outlet pipes, creating a high resistance system. Such stenoses can dramatically increase contrast dispersion and cause flattening of the resulting TDC.
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Dual energy CT offers a potential solution to this problem by means of three element
decomposition. It has recently been shown that using some mathematical assumptions, it is
possible to calculate the concentration of three substances from dual energy CT data (Liu et al.
2009; Cormode et al. 2010). Initially, a dual energy scan was used to solve the relative
concentration of both one contrast agent and background tissue in voxels of interest. In the
technique used by Liu et al, the images acquired at the two sets of images were combined to
form a theoretically third data set, and with three data sets, the relative concentrations of two
contrast agents and background tissue could be calculated. Importantly, where a single organ
such as the brain, heart, kidney or foot is concerned, these calculations could be made
potentially more accurate through even more multispectral studies involving more than two
spectral energies and the calculation of relative element concentrations by a multivariate
regression model.
Using either a dual energy or a multi-energy technqiue, with three-element
decomposition exists the flexibility to calculate concentration of two contrast agents and a
tissue. This capability has been used in the literature to calculate for example distribution of
brain, iron in hemorrhage and iodine in contrast to separate contrast from intra-cerebral
hematoma (Gupta et al. 2010). Another author has used the technique to separate iron from gold
in a novel contrast agent targeted towards atherosclerosis (Cormode et al. 2010). In the case of
TOF CTA, we could use two agents to correct for the issue of flow gradient. Consider a system
where a patient is injected with a bolus of iodine and gadolinium such that relative
concentrations of each element are ordered by a specified ratio (Figure 4.5). Consider next that a
single arterial phase multispectral image volume is acquired of a long (note this acquisition
could be in helical mode).
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Figure 4.5 – Hypothetical dual tracer system for intravascular flow quantification. Two tracers are injected in an ordered fashion. In this example, assume iodine (yellow) and gadolinium (grey) based contrast agents are injected in an increasing ratio. Where division of flow occurs into multiple vessels, relatively more rapid flow will be characterized by an elongated gradient of the tracers in space. Slow flow, such as that distal to a stenosis, will exhibit a more compact spatial distribution of the tracers. Of course such calculations can be limited by dispersion of the bolus, however where a test bolus is used to determine optimal timing of scan acquisition (as is commonly the case), dispersion is known and hence such effects can be corrected.
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Assume that a three element decomposition algorithm is used to calculate the gradient of
both iodine and gadolinium along the vessel. Both contrast agents are subject to the same
dispersion effects, however these can often be measured by a test bolus and accounted for.
Given that the difference in injection time of the agents is known a priori, it is possible to
calculate flow rate based on ratio of the agents at vessel cross sections in absolute rather than in
qualitative terms. The same idea may be extended to tissue perfusion, where a rigorous
parameter such as blood flow or MTT may be derived from the relative ratio of iodine and
gadolinium in different tissues of interest.
In essence, multispectral CT examinations involving the near simultaneous coinjection
of several contrast agents may be used as a replacement for multiphasic exams involving a
single contrast agent for the attainment of similar functional data. The advantage to
multispectral CT technique however is the potentially much lower radiation dose, particularly in
the body. Advances of this nature may permit perfusion analysis to be performed in body
tumours where radiation dose would have previously prohibited dynamic CT, particularly where
patient body habitus is a factor driving up radiation dose. Using dual energy CT, the TOF
technique may also be modified such that it can be implemented from single helical mode
acquisitions at acceptable doses of ionizing radiation. Much further work is needed to explore
such an option.
Finally, capillary permeability is an issue much discussed in the current oncology
literature as a means to quantify tumour aggressiveness and response to treatment. MRI
assessment of tumour perfusion in the body is limited by lack of resources in Canada to offer
MRI imaging to cancer patients on a frequent basis. Assessment of capillary permeability by CT
is limited by the need for 4D data to be acquired over minutes and hence exceptionally high
radiation dose, particularly in the body (see Grainger et al. 2011 review). The multispectral
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technique offers the potential for capillary permeability to be calculated with helical mode
scans. Consider a system where a bolus of iodine contrast agent is injected at time zero,
followed by an injection of a gadolinium contrast agent two minutes later. After one minute of
delay, the iodine has had time to cross leaky capillaries, whereas the gadolinium will have only
just distributed in the intravascular space. Using three material decomposition, the ratio of tissue
iodine to gadolinium may be calculated and this parameter may be used as an indicator of
capillary permeability.
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5.0) Conclusions
Intravascular functional information such as blood velocity and volumetric flow rate
have been available via both MRI and ultrasound for many years. It has been shown that with
recent advances in CT technology, this information is also available in CT using the algorithmic
approaches described herein. With the code available in Appendix Two, we have validated the
algorithm in simulated flow channels, a CT phantom, as well as in vivo in a small series. In this
manuscript, data are shown from arteries including the ICAs, major intracranial vessels,
pulmonary arteries, arteries in the pelvis, as well as vertebral arteries in the neck. In our group,
we have also explored the potential of the technique in anatomic structures including the heart,
lungs, aorta, abdominal vessels and vessels of the limbs (data not shown). Although a variety of
clinical applications may become available for TOF CTA, initial trials underway at the
University of Toronto include the assessment of blood flow in intracranial arteries of vasospasm
patients and in coronary artery bypass grafts.
TOF CTA is a rigorous approach to the calculation of intravascular blood velocity that
provides an estimation of mean velocity over many cardiac cycles. In our experiments to date,
we have seen no evidence that the technique is capable of providing peak arterial or diastolic
flow rates within the cardiac cycle, though this may be the subject of future work. Additionally,
the technique requires a path over which to make measurements, with longer paths resulting in
more accurate results, particularly at rapid flow rates. The technique would not be suitable to
measure flow at a single point, for example, across a vessel stenosis as is commonly performed
with Doppler ultrasound.
Advantages of the technique over conventional approaches to the functional assessment
of the intravascular space include an ability to assess flow in small vessels that cannot typically
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be assessed by pcMRA, including vessels distal to the circle of Willis in the brain. Additionally,
the technique can be applied to arteries that are not commonly accessible by ultrasound
including pulmonary vessels. The technique is potentially non user-dependent and can likely be
fully automated.
We have not explored the assessment of intravascular hemodynamics in venous
structures in this manuscript. As discussed in the introduction, venous TDCs are more dispersed
than their arterial counterparts and it is unclear whether TTP would represent an accurate
assessment of bolus centroid in these vessels. Although the center of mass of a bolus could be
calculated numerically, recirculation effects and delay in transit times between varying capillary
beds with common venous drainage could complicate such calculation in vivo. For example, in
the case of a unilateral stroke, blood from both cerebral hemispheres will drain into the superior
sagittal sinus, even though transit time of blood on the side of occlusion will be prolonged. The
effects of such different transit times as inputs into veins may confound TOF CTA
measurements. The use of bolus tracking to characterize venous hemodynamics will likely be
the subject of future research.
TOF CTA requires the administration of both intravenous contrast and radiation.
Intravenous contrast can be dangerous and has been known to induce both allergic reactions and
can cause worsening of renal failure in at risk patients. One advantage of TOF CTA however
derives from its strict concern with the intra-vascular space and the fact that signal to noise is far
better in the blood vessel lumen than in tissue. For example, several papers have been recently
published on the use of low doses of contrast for routine CT angiography in the at risk
population. It is certain that TOF CTA would also work well at low contrast doses.
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The issue of radiation exposure in the context of medical imaging, and CT in particular,
is the subject of intense debate. Several authors have recently convincingly argued that medical
radiation exposure contributes to cancer incidence on at least a population level. Although the
benefits of advanced functional imaging, where truly indicated, certainly outweigh the small risk
of radiation induced malignancy, the issue has garnered much attention and has made many
physicians think twice before ordering CT imaging on a routine basis.
Dynamic CT examinations of the brain are similar in overall radiation dose to diagnostic
CT angiography. The problem with 4D CT of the brain however is in the non diagnostic nature
of source images, and the potential need to repeat CT scans at diagnostic doses for the
assessment of anatomy rather than function. Two groups have proposed potential solutions to
this problem, one have reconstructed 3D CT angiograms from 4D data using an average
intensity projection technique and another using a weighted average. The reconstruction of high
quality 3D images from 4D data remains open for future work.
Radiation dose is of particular concern in CT in the body, including the thorax, abdomen
and pelvis. Although there is a wide literature on CT perfusion in lung nodules, the heart and
solid abdominal organs, the high radiation doses needed to image the body have prevented the
routine implementation of such techniques. If the acquisition of even one scan of the body
results in a concerning radiation dose to a patient, the acquisition of the many such scans needed
to characterize passage of a bolus for perfusion calculations is generally impossible. Even if
radiation dose concerns are eventually mitigated by novel iterative reconstruction techniques,
artifact from cardiac and respiratory motion complicates the assessment of TDC curves in any
particular organ of interest. Motion correction in the chest and abdomen has been the subject of
intense research into deformable image registration and has, unfortunately, met only very
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limited clinical success. We have discussed at the end of this manuscript some potential
techniques for multispectral CT to mitigate some of these problems, though much further work
is required to assess both the technical feasibility and practicality of such techniques.
In summary, TOF CTA is a new approach to functional CT imaging that draws heavily
upon prior work in indicator dilution and bolus tracking in conventional angiography. Despite
the venous nature of the contrast injection and resulting dispersion of the bolus by the time it
reaches arteries of interest, it remains possible to track the motion of contrast along vessel path
lengths on noisy 4D CT source images each individually acquired at low radiation dose. As a
result of such tracking, it is possible to perform calculations to derive many hemodynamic
parameters of interest including blood velocity and volumetric flow rate. The further
development of the technique both theoretically and in clinical trial may increase both the value
and utilization of functional CT imaging.
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6.0) Appendix One
Python Source Code for Creation of Vascular Segmentation
Below is code to create a vascular segmentation from a set of 4D CT perfusion data. Cut and
paste into an appropriate python.m file to run. Requires that numpy, scipy, pydicom and the
python imaging library are installed. Uses the native Tkinter GUI interface. The code uses a
directory of dicom volumes as its input, which is typical of the data generated by the aquilion
one. As its output, the code creates a numpy array of the times of data acquisition, a numpy data
object which contains the 4D data from a segmentation, as well as a single dicom volume
containing the segmentation itself. The resulting segmentation is ideal for performance of TOF
CTA calculations using the code in appendix two.
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from Tkinter import *
import Image, ImageDraw, ImageTk, sys
import numpy
import dicom
from tkFileDialog import askdirectory, askopenfilename
import os, os.path
import algo
import scipy
from scipy import optimize
from scipy import interpolate
from scipy import stats,math
import matplotlib.pyplot as plt
# above, all of the needed python libraries are imported. Numpy, Scipy, pydicom and PIL (python imaging library)
# are needed
#the global dicom object is defined as a 3D numpy array called dicomVolumeDataList, the dimensions are extracted
global dicomVolumeDataList, listPoints
listPoints = [] # the list of user defined points, also made global
dicomVolumeDataList = numpy.zeros([320,512,512])
#these lengths are needed so an initial blank volume may be displayed in the GUI without an error measage
xlength = dicomVolumeDataList.shape[1]
ylength = dicomVolumeDataList.shape[2]
zlength = dicomVolumeDataList.shape[0]
#as the user clicks, their points are stored to listPoints
def mouse_click_callback(event):
global displaySliceNum, askin, biggy, listPoints
print displaySliceNum, event.x, event.y
askin = [displaySliceNum, event.x, event.y] # askin is the name of the most currect chosen point, a numpy array
listPoints.append(askin)
try:
print biggy[displaySliceNum, event.x, event.y]
except:
print 'no biggy'
#if the user selects a point outside the gross intravascular segmentation, they are told so
# this is where the user laods an arbitrary volume so they can choose intra vascular points
def load_arr():
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global dicomVolumeDataList
myFile = askopenfilename()
dicomVolumeDataList = numpy.clip(dicom.ReadFile(myFile).pixel_array,0,300)
# the users work is saved, first the 4D array object containing all the time series data of the gross segmentation,
# secondly the time series that defines the CT acquisition, which is extracted from the dicom headers,
# and finally the segmentation map which is saved as SegMap. Files are stored in the working directory
def save_dicom():
global biggy, dicomVolumeDataList, fileForROI, xdata
print 'saving the file'
numpy.save('fourDdataObject',biggy)
numpy.save('timeStamp',xdata)
plan = dicom.ReadFile(fileForROI)
plan.PixelData = dicomVolumeDataList.tostring()
plan.save_as("SegMap.dcm")
canvas.bind("<Button-1>", mouse_click_callback)
# This is where the bulk of the segmentation happens. The steps are grossly defined with comments
def load_volume():
global dicomVolumeDataList, biggy, listPath, fileForROI, displaySliceNum, askin, xdata, listPoints
# get a path to all the dicom files from the user
listPath = askdirectory()
#then this function returns a list of all the dcm files
dicom_images = get_images(listPath)
#we get the number of files, which is basically the legth of the time series
vectorSize = len(dicom_images)
# we need two empty lists
# this list records an estimated intensity of each dicom volume
intens = []
# this list records the times of each volume acquisition so it can later be saved to disc
timeSteps = []
# we are going to iterate thorugh all the dicom volumes
for i in xrange (vectorSize):
print i
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if i == 0:
# if it's the first dicom volume we are loading, we get the time
plan = dicom.ReadFile(dicom_images[i])
yt = numpy.clip(plan.pixel_array-700,0,1)
localTimePoint = plan.ContentTime
g = localTimePoint.index('.')
TimeSec = (float(localTimePoint[g-2]+localTimePoint[g-1]+localTimePoint[g+1]))/10
TimeMin = float(localTimePoint[g-4]+localTimePoint[g-3])*60
TimeHour = float(localTimePoint[g-6]+localTimePoint[g-5])*60*60
startTime = TimeSec + TimeMin + TimeHour # we define the start time
####
# in this line we crop the dicomvolume to include bone and contrast enhanced blood vessel,
# basically anything between 50 and 400 hounsfield units and get an average attenuation,
# by looking at these, we are going to pick the highest density volume from the series and use that
# to take a gross segmentation of blood vessels. There will be bone in this segmentation as well, but
# we'll filter that later using the level sets. For now we want to work with a smaller amount of data
# to speed up the overall computation
intens.append(numpy.mean(numpy.clip((dicom.ReadFile(dicom_images[i]).pixel_array)-50,0,450)-yt*450))
####
# now we do the same time analysis thing for each subsequent step
plan = dicom.ReadFile(dicom_images[i])
localTimePoint = plan.ContentTime
g = localTimePoint.index('.')
TimeSec = (float(localTimePoint[g-2]+localTimePoint[g-1]+localTimePoint[g+1]))/10
TimeMin = float(localTimePoint[g-4]+localTimePoint[g-3])*60
TimeHour = float(localTimePoint[g-6]+localTimePoint[g-5])*60*60
totalTime = TimeSec + TimeMin + TimeHour
timeSteps.append(totalTime-startTime) # when we append data, we subtract the start time so that the time
# vector is in seconds, this first element would just become zero
# now we turn that time vector into an array to use in calculations
xdata = numpy.array(timeSteps)
# this next bit returns the location of the highest attenuating dicom volume in our series
biggest = 0
for i in xrange (vectorSize):
if intens[i] > biggest:
biggest = intens[i]
locBig = i
# now we load this filed
fileForROI = dicom_images[locBig]
# and segment all the voxels with values between 150 and 900, which should get us all the contrast enhanced vessels
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# all the other elements get set to zero using the clip function from numpy
peakMat = numpy.clip(dicom.ReadFile(fileForROI).pixel_array-150,0,700)-700*yt
# now we get a list of all the nonzero elements of our matrix. We will do subsequent operations only on this subset
locs = numpy.nonzero(peakMat)
# and we get the length of this list so we can iterate through it
els = len(locs[0])
# we create the empty volume of numpy objects, we are only going to fill elements that we got above with
# the time attenuation data. We want to hold it all in memory at the same time
biggy = numpy.empty([320,512,512],dtype=numpy.object)
#making the object
print "make object"
#We put in empty time density series into all the appropriate elements
for t in xrange(els-1):
biggy[locs[0][t],locs[1][t],locs[2][t]] = numpy.zeros([vectorSize], dtype ='int')
print "filling dummy object"
# now at this stage we are going to iterate through the whole list of dicom files and update the elements
# of each array at the correct time step. This is fairly quick since we are dealing with a small subset of data
for i in xrange (vectorSize): # here
g = dicom.ReadFile(dicom_images[i]).pixel_array
for t in xrange(els-1):
biggy[locs[0][t],locs[1][t],locs[2][t]][i] = g[locs[0][t],locs[1][t],locs[2][t]]
print i
#valsArr = numpy.zeros([vectorSize]) #here
#this is where we do the actual segmentation. Remember the user has created a list of points, listPoints, with
#known intravascular data. For each time density series in our known segmentation, we compare that data to all
#of the users chosen points. This is the slowest part of the whole algorithm because python is very slow with loops
#this part of the function could easily be rewritten in C/C++. Email me for instructions if needed.
for t in xrange(els):
#er = numpy.max(biggy[locs[0][t],locs[1][t],locs[2][t]])
# we get the time density data of the voxel of interest
arrToSearch = biggy[locs[0][t],locs[1][t],locs[2][t]]
fillColor = 0
# we compare that to every point in the user provided list
for yt in listPoints:
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# now we get the user defined arrays individually for each loop
modelArr = biggy[yt[0],yt[1],yt[2]]
#now we do the comparison. I've used a series of ifs as its quicker than another loop in python
#we set the final density fillColor depending on the degree of match
try:
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 350:
fillColor = 100
# note at each one of the if statements we normalize the signals, subtract the arrays and take the max
# absolute value
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 300:
fillColor = 200
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 250:
fillColor = 300
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 200:
fillColor = 400
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 150:
fillColor = 500
if numpy.max(abs(arrToSearch*1000/numpy.max(arrToSearch)-modelArr*1000/numpy.max(modelArr))) < 100:
fillColor = 600
except:
d = 8 # this does nothing, but it needs an except statement
peakMat[locs[0][t],locs[1][t],locs[2][t]] = fillColor # now we assign the resulting density
#valsArr[numpy.where(arrToSearch == er)] +=1 # here
dicomVolumeDataList = numpy.clip(peakMat,0,1)*100
# gets a list of pathnames for dicom files once user picks a directory
def get_images(path):
abs_path = os.path.abspath(path)
entries = os.listdir(abs_path)
good_entries = []
for entry in entries:
if os.path.splitext(entry)[1].lower() == '.dcm':
good_entries.append(os.path.join(abs_path, entry))
good_entries.sort()
IsADicomLoaded=True
return good_entries
#######################
# the following functions form part of the Tkinter GUI which provides image viewing
window = Tk()
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window.title('Isolate with Region Grows and Export New Dicom')
canvas = Canvas(window, width = 511, height = 511, bg='pink')
canvas.grid(row=0, column=0)
def showimage():
global displaySliceNum,displayTimePoint,dicomVolumeDataList,photo,photo2,xlength,ylength,zlength, newVol, startPolygon
MatrixOfImageToDisplay = numpy.zeros([512,512])
MatrixOfImageToDisplay[0:xlength,0:ylength] = dicomVolumeDataList[displaySliceNum,:,:]
windowVal=10
levelVal=10
photo= algo.window_and_level(dicomVolumeDataList[displaySliceNum,:,:], levelVal, windowVal)
canvas.delete()
canvas.create_image(256, 256, image=photo)
# scrolls through slices in the current volume
def scrollToSlice():
global displaySliceNum
displaySliceNum = sliceScrollbar.get()
showimage()
def ifImThenScroll(i):
scrollToSlice()
#######################
sliceScrollbar = Scale(window, orient='horizontal', from_=0, to=320, command=ifImThenScroll)
sliceScrollbar.grid(row=1, column=1)
# this button uses a 4D CT series to segment the intravascular space
button1 = Button(window,text='load a Volume and Segment', command = load_volume)
button1.grid(row=2, column=0)
# this button saves the users work in three ways. Firstly the timing of the volumetric acquisition is saved,
# secondly the 4D data saved as a numpy object array after gross segmentation of the intravascular space,
# finally the segmentation which results from level set segmentation is saved
button2 = Button(window,text='Save 4D Array Object', command = save_dicom)
button2.grid(row=3, column=0)
# this button lets user load a CT volume to pick intravascular points which are then
# used to perform a segmentation
button3 = Button(window,text='Load Vol Define IntraVascular', command = load_arr)
button3.grid(row=5, column=0)
mainloop() # sets the GUI up to receive event
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7.0) Appendix Two
Python Code for TOF CTA Calculation
The following is python code for the TOF CTA algorithm, including a GUI for the user defined
definition of a vessel centroid on which to perform TOF CTA analysis. As its input, the
software requires a dicom volume depicting an intravascular segmentation, as well as the
directory of dicom files. The time data is extracted here from the dicom headers of the
individual dicom volumes. The program output is velocity in the chosen vessel based upon
fitting of local quadratic functions, Gaussian distributions and γ-variate functions to time series
data of individual vascular cross sections. The results are graphed using Python’s matplotlib
library to enable visualization of the quality of curve fit. There is some code to back project the
velocity data into the vessels and save the resulting dicom map, however this is commented out
in the code below. It may be enabled by the user if desired.
111
from Tkinter import *
import Image, ImageDraw, ImageTk, sys
import numpy
import dicom
from tkFileDialog import askdirectory, askopenfilename
import os, os.path
import algo
import scipy
from scipy import optimize
from scipy import interpolate
from scipy import stats,math
import matplotlib.pyplot as plt
# above, all of the needed python libraries are imported. Numpy, Scipy, pydicom and PIL (python imaging library)
# are needed
#the global dicom object is defined as a 3D numpy array called dicomVolumeDataList, the dimensions are extracted
global dicomVolumeDataList, listPoints
listPoints = [] # the list of user defined points, also made global
dicomVolumeDataList = numpy.zeros([320,512,512])
#these lengths are needed so an initial blank volume may be displayed in the GUI without an error measage
xlength = dicomVolumeDataList.shape[1]
ylength = dicomVolumeDataList.shape[2]
zlength = dicomVolumeDataList.shape[0]
#as the user clicks, their points are stored to listPoints
def mouse_click_callback(event):
global displaySliceNum, askin, biggy, listPoints,dicomVolumeDataList
askin = [displaySliceNum, event.x, event.y] # askin is the name of the most currect chosen point, a numpy array
listPoints.append(askin)
## here we fill in the artery around the mouse click so we can segment it later
try:
for z in [-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10]:
for x in [-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10]:
for y in [-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10]:
if displaySliceNum+z > 0:
if dicomVolumeDataList[displaySliceNum+z,event.x+x,event.y+y] > 0:
dicomVolumeDataList[displaySliceNum+z,event.x+x,event.y+y] = 10000
112
except:
print 'no biggy'
#if the user selects a point outside the gross intravascular segmentation, they are told so
### here we load the data from file,
def load_4DarrObject():
global biggy, dicomVolumeDataList, xdata
myFile = askopenfilename()
xdata = numpy.load(myFile) # loading the time series data
myFile = askopenfilename()
biggy = numpy.load(myFile) # the object containing 4D CT data
myFile = askopenfilename()
dicomVolumeDataList = numpy.clip(dicom.ReadFile(myFile).pixel_array,0,1)*100 # the segmentation to pick arteries
##############################
# the following functions perform nonlinear regression to fit gamma variate functions to time series
# fed into gamma3FitQCTA. This is the most complex case, quadratic and Gaussian fits are just less complex
def fit_the_gamma3(v,xdata):
ydata = numpy.zeros([len(xdata)])
for i in xrange (len(xdata)):
ydata[i] = v[0]*(xdata[i]**v[1])*numpy.math.exp(-xdata[i]/v[2])
return ydata
def my_func2(v,y):
global xdata
myYdata = numpy.zeros([len(xdata)])
for i in xrange (len(xdata)):
myYdata[i] = v[0]*(xdata[i]**v[1])*numpy.math.exp(-xdata[i]/v[2])
residuals = y - myYdata
return residuals
def gamma3FitQCTA(arterialInputVector,xdata):
guess = [5,5,5]
foundVars = optimize.leastsq(my_func2,guess,args=(arterialInputVector),maxfev = 10000)
xdata2 = scipy.linspace(0, xdata[-1], num=10000)
optimumFit = fit_the_gamma3(foundVars[0],xdata2)
optimumFit2 = fit_the_gamma3(foundVars[0],xdata)
maxLoc = xdata2[list(optimumFit).index(numpy.max(optimumFit))]
return maxLoc
###############################
113
# feed a vector of points along the vessel centroid and a point of interest, function will return
# the closest point on the vessel centroid to that point of interest
def find_closest_point(centroids,x,y,z):
minDist = 1000
for point in centroids:
dist = ((point[0] - z)**2 + (point[1] - x)**2 + (point[2] - y)**2)**0.5
if dist < minDist:
closest = point
minDist = dist
return centroids.index(closest), minDist
# This is where the bulk of the TOF CTA.
def runTOFCTA():
global dicomVolumeDataList, biggy, listPath, fileForROI, displaySliceNum, askin, xdata, listPoints
print 'hi'
bigPointList = []
#############################
# takes the user defined points and connects them to create a complete centroid
first = 0
oldZ = listPoints[0][0]
oldX = listPoints[0][1]
oldY = listPoints[0][2]
for els in listPoints:
if first > 0:
myLilList = algo.threeD_bresenham(oldZ,oldX,oldY,els[0],els[1],els[2])
oldZ = els[0]
oldX = els[1]
oldY = els[2]
for ell in myLilList:
bigPointList.append(ell)
first += 1
listPoints = bigPointList
#################################
##########################################
# Here we use Pythagorous to find the distance along the vessel path length
# This is needed to make distance calculations
distVec = []
for ty in xrange (len(listPoints)):
if ty == 0:
114
distVec.append(0)
else:
a1 = listPoints[ty][0]
a2 = listPoints[ty-1][0]
b1 = listPoints[ty][1]
b2 = listPoints[ty-1][1]
c1 = listPoints[ty][2]
c2 = listPoints[ty-1][2]
distVec.append(((a1-a2)**2+(b1-b2)**2+(c1-c2)**2)**0.5)
distVec[ty] = distVec[ty] + distVec[ty-1]
###############################
numPtPath = len(listPoints)
TACvec = []
# create an empty set of time attenuation curves
for t in xrange(numPtPath):
TACvec.append(numpy.zeros([len(xdata)]))
# get the points that are close to the user defined centroid, the algorithm is more
# efficient if it only tests points in the vessel of interest
evalPts = numpy.nonzero(numpy.clip(dicomVolumeDataList-1000,0,1))
iterat = len(evalPts[0])
# time attenuation data is aggregated along the centroid
for ty in xrange(iterat):
voxel = [evalPts[0][ty],evalPts[1][ty],evalPts[2][ty]]
ptIndex, mindist = find_closest_point(listPoints,voxel[1],voxel[2],voxel[0])
TACvec[ptIndex] += biggy[voxel[0],voxel[1],voxel[2]]
TACvec[ptIndex] = TACvec[ptIndex] /2
timePeaks = []
# now find time to peak along the centroid
for ry in TACvec:
peakVal = gamma3FitQCTA(ry,xdata)
timePeaks.append(peakVal)
timePeaks = numpy.array(timePeaks)
# plot TTP versus distance along the vessel centroid, 1/slope is a measure of velocity in
115
# voxels per second
plt.plot(distVec, timePeaks)
plt.show()
# gets a list of pathnames for dicom files once user picks a directory
def get_images(path):
abs_path = os.path.abspath(path)
entries = os.listdir(abs_path)
good_entries = []
for entry in entries:
if os.path.splitext(entry)[1].lower() == '.dcm':
good_entries.append(os.path.join(abs_path, entry))
good_entries.sort()
IsADicomLoaded=True
return good_entries
#######################
# the following functions form part of the Tkinter GUI which provides image viewing
window = Tk()
window.title('tof cta')
canvas = Canvas(window, width = 511, height = 511, bg='pink')
canvas.grid(row=0, column=0)
canvas.bind("<Button-1>", mouse_click_callback)
def showimage():
global displaySliceNum,displayTimePoint,dicomVolumeDataList,photo,photo2,xlength,ylength,zlength, newVol, startPolygon
MatrixOfImageToDisplay = numpy.zeros([512,512])
MatrixOfImageToDisplay[0:xlength,0:ylength] = dicomVolumeDataList[displaySliceNum,:,:]
windowVal=10
levelVal=10
photo= algo.window_and_level(dicomVolumeDataList[displaySliceNum,:,:], levelVal, windowVal)
canvas.delete()
canvas.create_image(256, 256, image=photo)
# scrolls through slices in the current volume
def scrollToSlice():
global displaySliceNum
displaySliceNum = sliceScrollbar.get()
showimage()
116
def ifImThenScroll(i):
scrollToSlice()
#######################
sliceScrollbar = Scale(window, orient='horizontal', from_=0, to=320, command=ifImThenScroll)
sliceScrollbar.grid(row=1, column=1)
# this button uses a 4D CT series to segment the intravascular space
button1 = Button(window,text='load a Volume', command = load_4DarrObject)
button1.grid(row=2, column=0)
# this button lets user load a CT volume to pick intravascular points which are then
# used to perform a segmentation
button3 = Button(window,text='Run TOF CTA', command = runTOFCTA)
button3.grid(row=5, column=0)
mainloop() # sets the GUI up to receive events
117
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