Evaluation of dispersive ultrasound for diagnosis of blast...

Defence Research andDevelopment Canada

Recherche et developpementpour la defense Canada

Evaluation of dispersive ultrasound for diagnosis of blast-inducedtraumatic brain injury in rodents

Craig BurrellStergios StergiopoulosDRDC Toronto Research Centre

Catherine TennDRDC Suffield Research Centre

Pang ShekDRDC Toronto Research Centre

Norleen CaddyMichelle GarrettYimin SheiDRDC Suffield Research Centre

Defence Research and Development Canada

Scientific ReportDRDC-RDDC-2016-R065May 2016

Evaluation of dispersive ultrasound fordiagnosis of blast-induced traumatic braininjury in rodentsCraig BurrellStergios StergiopoulosDRDC Toronto Research Centre

Catherine TennDRDC Suffield Research Centre

Pang ShekDRDC Toronto Research Centre

Norleen CaddyMichelle GarrettYimin SheiDRDC Suffield Research Centre

Defence Research and Development CanadaScientific ReportDRDC-RDDC-2016-R065May 2016

c Her Majesty the Queen in Right of Canada, as represented by the Minister of NationalDefence, 2016

c Sa Majeste la Reine (en droit du Canada), telle que representee par le ministre de laDefense nationale, 2016

Abstract

Ultrasonic frequency dispersion was used to study primary blast-induced mild trau-matic brain injuries in rats. Transcranial ultrasonic pulses were transmitted non-invasively and the frequency-dependent variations in propagation speed were measuredin controls and shockwave-exposed animals. Rats were exposed to a single shockwaveat a pressure of 0, 141 or 223 kPa, shockwave intensities known to induce functionaldeficits and neuroinflammatory response in the same animal model. Following exposure,data was collected at 24, 48 and 72 hours. A two-class Support Vector Machine diag-nostic classifier was applied to distinguish between controls and shockwave-exposedanimals. The classifier could not reliably distinguish between these groups at theincident peak pressures and post-exposure intervals used in this study.

Significance for defence and security

Diagnosis of blast-related traumatic brain injury using low-cost, portable technologywould promote effective medical triage and timely treatment in operational contexts.The possibility of using an ultrasound-based diagnostic approach is evaluated on apopulation of shockwave-exposed rodents and non-shockwave-exposed controls. Wefound that this approach could not reliably detect shockwave-induced traumatic braininjury under the conditions studied, providing no evidence that it would be a suitablediagnostic method for military use at this time.

DRDC-RDDC-2016-R065 i

Resume

Au moyen de la dispersion frequentielle des ondes ultrasonores, nous avons etudieles traumatismes cerebraux legers attribuables a leffet primaire de souffle chez lerat. Nous avons transmis des impulsions ultrasonores transcraniennes de facon noninvasive et mesure les variations de la vitesse de propagation selon la frequence chezles animaux temoins et ceux exposes a londe de choc. Des rats ont ete exposes a uneonde de choc unique a une pression de 0, 141 kPa ou de 223 kPa, des valeurs dont onsait quelles provoquent des deficits fonctionnels et une reponse neuroinflammatoirechez ce modele animal. Nous avons recueilli des donnees 24, 48 et 72 heures apreslexposition. Une machine a vecteurs de support a deux classes pour la classificationdes diagnostics a servi a etablir la distinction entre les animaux temoins et ceuxexposes a londe de choc. Le classificateur na pas permis detablir sans equivoque ladistinction entre ces deux groupes aux pics de pression incidente et aux intervalles depost-exposition utilises dans cette etude.

Importance pour la defense et la securite

Letablissement dun diagnostic de traumatisme cerebral attribuable a un effet desouffle a laide dune technologie portative et peu coteuse favoriserait un triage medicalefficace et un traitement opportun dans les contextes operationnels. Nous avons evaluela possibilite dutiliser une methode diagnostique fondee sur les ultrasons sur unepopulation de rongeurs exposes a une onde de choc et de rongeurs temoins nayantpas subi dexposition. Nous avons constate que cette approche ne permettait pas dedetecter de faon fiable les traumatismes cerebraux causes par une onde de choc dansles conditions etudiees. Ainsi, rien ne prouve, a lheure actuelle, que cette methodediagnostique soit appropriee a lusage militaire.

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Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Significance for defence and security . . . . . . . . . . . . . . . . . . . . . . . i

Resume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Importance pour la defense et la securite . . . . . . . . . . . . . . . . . . . . . ii

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Diagnosis of blast-induced mild Traumatic Brain Injury (mTBI) . . 2

2.1.1 Injury mechanisms . . . . . . . . . . . . . . . . . . . . . . . 2

2.1.2 Diagnostic tools . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Ultrasonic tissue characterization . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Ultrasonic frequency dispersion in biological tissues . . . . . 4

2.3 Dispersive Ultrasound System (DUS) . . . . . . . . . . . . . . . . . 5

2.3.1 Preliminary studies . . . . . . . . . . . . . . . . . . . . . . . 6

3 Experimental methods and materials . . . . . . . . . . . . . . . . . . . . . 7

4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Computation of pulse transit times . . . . . . . . . . . . . . . . . . . 13

4.2.1 Timing markers . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Frequency-dependent time jitter . . . . . . . . . . . . . . . . . . . . 14

DRDC-RDDC-2016-R065 iii

4.3.1 Time jitter reduction . . . . . . . . . . . . . . . . . . . . . . 16

4.4 Effect size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.5 Data normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.6 Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . 19

4.7 Support Vector Machine (SVM) classification . . . . . . . . . . . . . 21

5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.1 Support Vector Machine (SVM) classifier results . . . . . . . . . . . 25

5.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

iv DRDC-RDDC-2016-R065

List of figures

Figure 1: The DRDC Dispersive Ultrasound System (DUS). . . . . . . . . . 6

Figure 2: Examples of received signals. . . . . . . . . . . . . . . . . . . . . . 12

Figure 3: Jitter reduction in dispersion spectra . . . . . . . . . . . . . . . . 17

Figure 4: Leading principal components of lower pressure data set. . . . . . 23

Figure 5: Leading principal components of higher pressure data set. . . . . . 24

Figure 6: Classification results for full data set in lower pressure range. . . 30

Figure 7: Classification results in lower pressure range at 72 h post-exposure. 30

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List of tables

Table 1: Dispersion trend data. . . . . . . . . . . . . . . . . . . . . . . . . 5

Table 2: Frequency set used in this study. . . . . . . . . . . . . . . . . . . . 9

Table 3: Number of animals measured at each time interval. . . . . . . . . 9

Table 4: Summary of data collected in lower pressure range. . . . . . . . . 10

Table 5: Summary of data collected in higher pressure range. . . . . . . . . 11

Table 6: Jitter reduction rates achieved by application of post-processingfilters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Table 7: Overview of leading principal components for the lower pressureand higher pressure data sets. . . . . . . . . . . . . . . . . . . . . 20

Table 8: Diagnostic classification accuracies in low and high shockwavepressure ranges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Table 9: Diagnostic classification accuracies in low and high shockwavepressure ranges for jitter-reduced data . . . . . . . . . . . . . . . . 26

Table 10: Details of classification results for full data set in lower pressurerange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Table 11: Details of classification results for 72 h post-exposure data set inlower pressure range. . . . . . . . . . . . . . . . . . . . . . . . . . 29

DRDC-RDDC-2016-R065 vii

Acknowledgements

We wish to thank Andreas Freibert and Jason Zhang for their assistance with thedesign and operation of the Dispersive Ultrasound System, and Kostas Plataniotis foradvice on machine learning algorithms.

viii DRDC-RDDC-2016-R065

1 Introduction

Traumatic Brain Injury (TBI) has been a common injury in recent military conflicts.Studies of returning United States service personnel found that 1520% suffered fromTBI [1, 2]. An epidemiological survey of US Department of Defense/Veterans Affairsdatabases found that 78% of veterans from the Iraq and Afghanistan wars werediagnosed with TBI following screening and specialized examination [3]. A majorpost-deployment survey of over 16000 Canadian Armed Forces personnel found that5.2% were assessed as having suffered a TBI, with approximately half of those casesblast-induced [4]. TBI has been called the signature wound of the Iraq and Afghanistanwars [5].

The epidemiological data on TBI are dependent upon vigilant surveillance and reliablediagnostic criteria and methods. In current practice the diagnosis of TBI is frequentlybased upon clinical observation and responses to a questionnaire on the patientshistory [6, 7]. Many alternative methods of TBI diagnosis have been proposed [8], butnone as yet have been generally accepted or widely employed. The pathobiology of thecondition is not well understood [9]. There is significant overlap between the diagnosticcriteria for TBI and those for Post-Traumatic Stress Disorder (PTSD) [1, 2].

Many TBI cases in military personnel are known to result from exposure to explosiveblasts: one study found that 63% of US Army TBI cases from Afghanistan and Iraqbetween 20012007 were associated with explosions [10]. Blast injuries have beenclassified based on the means by which the injury occurred: primary blast injury isproduced directly by a high pressure blast wave loading the body; secondary blastinjury occurs when debris impacts or penetrates the body; tertiary blast injury resultsfrom the body being thrown against other objects such as walls or vehicles; quaternaryblast injury refers to other blast-related mechanisms of injury, such as burns orradiation [11,12]. Blast-related TBIs can occur in any of the four categories [8], butmuch of the interest of the research community has focused on primary blast injury.

In this study we investigate a novel approach involving ultrasonic frequency disper-sion to assess primary blast-induced mild TBI in rodents. Defence Research andDevelopment Canada (DRDC)s Dispersive Ultrasound System (DUS) non-invasivelytransmits transcranial ultrasound pulses in several frequency bands and measuresthe frequency dispersion induced in each pulse during transit. We attempted to traina machine learning system to distinguish the dispersion patterns associated withshockwave-exposed and control animals.

DRDC-RDDC-2016-R065 1

2 Background

We first surveyed methods that have been proposed to diagnose blast-induced TBI. Wethen considered historical efforts to use ultrasound to characterize biological tissues,and briefly reviewed the few cases in which ultrasound had been used to study braintissue. Finally we discussed previous applications of dispersion of ultrasound waves.

2.1 Diagnosis of blast-induced mTBI

Diagnosis of mTBI could benefit from an understanding of the nature of the underlyinginjury. We first reviewed possible mechanisms by which brain injury may occur undershockwave loading, and then surveyed proposed diagnostic approaches.

2.1.1 Injury mechanisms

There are many potential avenues by which shockwave loading could result in injury tothe brain [8]. In direct shockwave transmission the injury results from the interactionbetween the high pressure, short duration shockwave and the brain tissues. Shearstresses on axons may produce Diffuse Axonal Injury (DAI), a condition in which theelasticity of axons is altered and their functionality impaired [13, 14].

Acoustic impedance differences in brain structures could produce shockwave reflectionsand intensity focusing inside the brain, and pressure differentials could producecavitation and bubble formation in the brains vasculature. Some studies suggest thatskull flexure in response to shockwave loading might contribute to strains on braintissues [15].

Primary blast TBI might also occur due to cerebrovascular overpressure resultingfrom torso compression [16]. Barotrauma was once a leading type of blast injury, butimprovements in personal armour have done much to improve outcomes. Nonethelessthere is evidence that shockwave loading of the torso, even with personal armour, mayresult in a blood surge into the brain. Possible consequences include diffuse cerebraledema, vasospasm, hemorrhage, and damage to the blood-brain barrier [17,18]. Thesein turn may lead to neuronal damage and cell death. Injuries resulting from suchmechanisms are expected to be diffused through the brain rather than localized [16].

Finally, shockwave loading of the head will generally result in a rapid acceleration,linear or rotational, which may result in the post-injury formation of lesions at sitescorrelated with the direction of acceleration [8].

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2.1.2 Diagnostic tools

Numerous methods to diagnose TBI have been proposed [8, 19]. In recent militaryconflicts the United States used the Military Acute Concussion Evaluation (MACE)questionnaire [6, 20]; Canada used an adapted version of the same instrument [7, 21].Notwithstanding the advantages of a standardized assessment tool of this sort, therehas been considerable interest in developing a more objective diagnostic test.

Some studies have explored the possibility of cognitive testing for TBI diagnosis [22,23];others have examined motor deficits [24]. Pupillary light reflex [25] and other aspectsof oculomotor function have also been evaluated [2628].

Much activity has focused on finding biochemical markers indicative of TBI [2931].This approach is attractive because if successful it has the potential to result in afield-usable blood test for TBI injuries. However as yet no reliable biomarkers havebeen identified.

Diagnostic methods based on the brains electrical activity have also been extensivelyexplored, in part because they can be made portable and are relatively inexpensive [19].quantitative Electroencephalography (qEEG) attempts to identify abnormal brainelectrical responses that are correlated with TBI [32,33]. This approach has provenquite successful for diagnosis of concussive TBI, but its efficacy for blast-relatedTBI is less clear [34,35]. Techniques of Rheoencephalography (REG) track cerebralhemodynamics by monitoring the electrical impedance of the blood, and may, forinstance, be sensitive to changes in intracranial pressure [36] or cerebral blood flowautoregulation [37], but as yet no studies have linked it directly to TBI diagnosis.

Advanced imaging modalities to detect TBI have been explored. Diffusion TensorImaging (DTI), an advanced form of Magnetic Resonance Imaging (MRI), has beenused to study both blast-related [38,39] and non-blast-related TBI [4042], sometimesin combination with other imaging techniques [43], and has attracted special interestbecause of its apparent sensitivity to DAI, which is invisible to many conventionalimaging techniques. Magnetoencephalography (MEG) has also been shown to beeffective at diagnosing both blast and non-blast mTBI [44]. These methods arenonetheless probably not feasible for use in a military operational context because ofthe size and cost of the associated equipment.

Optoacoustic techniques to monitor blood oxygenation have been used in animalstudies to detect blast-induced intracranial hematomas [45], and changes in braintissue stiffness following cortical impact TBI have been observed using shear waveelastography [46].

The most commonly encountered ultrasound-based method for diagnosis of TBI isTranscranial Doppler (TCD) ultrasound, which monitors cerebral hemodynamics by


non-invasively measuring blood flow velocities. A number of TCD studies of TBIpatients have correlated blood flow measures with clinical assessments and intracranialpressures [19], including cases of mild TBI [47, 48]. Others have used ultrasonicattenuation and time-of-flight measurements to monitor intracranial blood pressureand volume non-invasively [49, 50].

2.2 Ultrasonic tissue characterization

Numerous efforts have been made to study the properties of biological tissues usingultrasound. Several decades ago there was a significant amount of work published on ul-trasonic characterization of a wide variety of tissues in both animals and humans [51,52].More recently attempts have been made to use ultrasonic tissue characterization todiagnose prostate cancer [53] and to study pancreatic and lymph node tissues [54].

There have also been several recent efforts to use ultrasound to image the brain [55].Historically this has not been a common use of ultrasound because reflections of theultrasound from the skull bones significantly degrade the signal-to-noise ratio anddistort focus [56]. Transcranial ultrasound has been used to diagnose intracerebralhemorrhage [57], and high-intensity focused ultrasound has been employed to mimicthe injuries produced by blast-induced TBI [58].

2.2.1 Ultrasonic frequency dispersion in biological tissues

In this paper we approach the diagnosis of TBI using the phenomenon of ultrasonicfrequency dispersion. Different ultrasound frequencies propagate through the brainand intracranial tissues at different rates; the rate for a given frequency is dependentupon the density and elastic properties of the tissues. If the relevant properties ofthe tissues are altered when a TBI is sustained, the condition may be detectable viaalterations in the frequency dependence of the observed ultrasound propagation rate.Variations in the elastic properties of rat brain tissues following cortical impact TBIhave been reported [46].

Frequency dispersion of ultrasound in human tissues has been studied to some extent.Biological materials of particular interest in the context of transcranial ultrasoundinclude brain tissue, skull bone (including the cancellous diploe bone found betweenthe exterior and interior ivory table layers of the skull), cerebrospinal fluid, and skin,in addition to other less prevalent tissues. Table 1 gives published frequency dispersiondata for some relevant materials. The data are sparse and in some cases there is onlya single published value stated without any indication of precision. The dispersiontrend, , gives the rate at which propagation speed varies with frequency:

v(f) = v(f0) + (f f0), (1)


where f0 is a reference frequency. Note that in stating a dispersion trend these sourcesassume that propagation speed varies linearly with frequency; in general this is nottrue, but it may be a good approximation in the vicinity of the reference frequency.Note also the large published value for the cancellous diploe bone in the skull; despiteits small depth (a few mm [59]) this bone layer would, based on these data, be expectedto contribute significantly to the observed frequency dispersion; it would be unlikelyto change, however, in response to a closed-head TBI injury.

Table 1: Dispersion trend data. In the last column, the first reference is for thedispersion trend value, the second for the base frequency and speed, and the third forthe speed range.

Tissue Dispersion Base Base Speed SourceTrend Frequency Speed Range

(m/(sMHz)) (MHz) (m/s) (m/s)Brain 1.2 1.0 1562 15101572 [60]; [60]; [61]Skull, diploe 300 0.5 2240 21902870 [62]; [63]; [62]Skull, ivory table slight 1.7 2960 20603030 [62]; [63]; [62]

Measurements of attenuation of ultrasound in human tissues are more common thandirect measurements of frequency dispersion [51,52,64]. The attenuation and dispersionare related to one another via the Kramers-Kronig relations [6567], and models havebeen developed to derive one from the other [6870]. Nonetheless it remains true thatempirical data on ultrasonic dispersion in human tissues are limited.

2.3 Dispersive Ultrasound System (DUS)

Defence Research and Development Canada (DRDC) has developed the DispersiveUltrasound System (DUS) for diagnosis of TBI in a military context [7173]. TheDUS, pictured in Figure 1, is a small, portable device consisting of a pair of ultrasonictransducers, a signal processing unit, and a user interface. It produces ultrasoundpulses across a range of center frequencies, where the duration, bandwidth, andamplitude of each pulse are configurable. To collect data the two transducers arepositioned bilaterally on the head; one transducer transmits a series of transcranialpulses and the other receives them. The signal strength is consistent with that usedin standard medical ultrasound applications. The transcranial pulses are repeated ata number of different center frequencies and the frequency dispersion induced in thepulses is measured (see Section 4 below).


Figure 1: The DRDC Dispersive Ultrasound System (DUS). The data acquisitionand analysis unit is pictured on the left; on the right is a fluid container with attachedultrasound probes, and a temperature monitor.

2.3.1 Preliminary studies

Preliminary studies were conducted to ascertain the extent to which the DUS coulddistinguish between different propagation media on the basis of ultrasound pulsestraversing the media.

The first test involved transmitting ultrasound pulses through five different fluids ofsimilar density and viscosity and then using the DUS to automatically identify thembased on previously learned examples. The fluids (deionized water, apple juice, fruitjuice blend, grape juice, and orange juice) were temperature-controlled in a cylindricalcontainer measuring 10 cm high and 5.2 cm in diameter (as shown in Figure 1). Foreach fluid, ultrasound pulses of 12 different center frequencies were transmitted fromone side to the other and the propagation times measured. This process was repeated300 times to test stability, which was found to be good. A SVM classifier (see Section4.7 below) was trained on a subset of the data and then used to classify the remainingdata. The system was found to correctly identify the five fluids with an overall accuracyof 99%.

A second test was conducted but in this case the DUS was used to distinguish betweendifferent concentrations of cranberry juices diluted with water. The system was trainedon two cases: no dilution and 50% dilution. It was found that the system could


subsequently identify the 50% dilution fluid with perfect consistency, but that itmisidentified the undiluted fluid approximately one-quarter of the time. To test thebehaviour of the system when presented with dilutions other than those used to trainit, we also attempted to classify a 5% dilution fluid (identified as no dilution for 90%of cases) and a 25% dilution fluid (identified as no dilution for approximately 60% ofcases).

Together, these preliminary studies suggested that the DUS could with good consis-tency distinguish similar media on the basis of ultrasound pulse propagation times.These findings were the impetus for conducting the more complex study which is themain subject of this report.

3 Experimental methods and materials

Animals: Male Sprague-Dawley rats (200225 g) were kept for at least one weekbefore experiments commenced. The animals were housed in a room with a 12 hlight-dark cycle (lights on at 0600h). Room temperature was maintained at 21 2 Cand relative humidity was 48 3%. Food and water was available ad libitum. Inconducting this research the authors adhered to the Guide to the Care and Use ofExperimental Animals [74] and The Ethics of Animal Investigation [75] publishedby the Canadian Council of Animal Care.

Shock wave exposure: A custom-built blast simulator (approx. 30.5 cm in diameterand 5.79 m in length) located at DRDC Suffield Research Centre was used forproducing the shock. The shock tube consists of two sections: a driver section filledwith high-pressure gas, and a low-pressure driven (or test) section. The two sides areseparated by a layered acetate diaphragm. Reaching a critical, controlled high-pressurein the driver causes rupturing of the diaphragm, the high-pressure gas expands into thetest section driving a shock wave into this section. Compressed helium and varyingthickness of clear acetate sheets were employed to obtain the desired target pressure.The peak pressures were determined by using a modified Friedlander equation to fit thepressure curves obtained by pressure sensors in the blast simulator. The anaesthetizedanimal was placed into a customized restraint which was inserted into the shock tubesuch that only the animals head was extended into the tube for a side-on, head-onlyexposure. The head of the animal was located 4.3 m downstream of the diaphragmand directly across from one of the pressure sensors mounted into the wall of the shocktube allowing for an estimation of the blast pressure that the animal was exposed to.

Animals were exposed to a single shock wave with an intensity of 0, 141 1.3 kPa(20.5 0.2 psi), or 223 2.8 kPa (32.3 0.4 psi). These pressure levels were chosenas they have shown to consistently induce functional deficits (such as cognitive andmotor impairments as well as sleep disturbances) in shockwave exposed animals


in our laboratory settings [7678]. Traumatic brain injuries are known to trigger aneuroinflammatory cascade which contributes to the brain injury as well as long termneuronal damage and cognitive impairment.

Other studies using the same animal model with head-only exposure have also shownevidence of brain injury at these pressure levels or lower. For instance, similar shockwave peak pressures (145 kPa and 232 kPa) have been associated with bihemisphericblood-brain barrier disruption and sub-millimeter lesion formation up to 48 h afterexposure [17]. Shock wave studies at slightly lower pressures (100200 kPa) haveproduced evidence of acute brain injury and cerebrovascular inflammation, also outto 48 h post-exposure [79, 80]. Behavioural and neurochemical changes have also beenreported following shockwave exposures comparable to our lower pressure insult [81,82],and even lower levels have produced evidence of a neuroinflammatory response thatpersists for at least 72 h (at 117 kPa) [83] and of significant memory and locomotivedeficits (at 110 kPa) [84]. Levels somewhat higher than those used in this study(241 kPa) have been associated with acute axonal degeneration, neuronal death, andblood-brain barrier disruption, though these peak pressures also caused 25% mortalityin the rats [85].

After the shockwave exposure, the animal was removed from the shock tube andrestraint and the recovery time from the anaesthetic was recorded. Sham controlanimals were treated in a similar manner as the other group of animals except thatthey were not exposed to the shock wave; previous studies have shown the importanceof sham animals in blast TBI investigations [86].

Dispersive ultrasound recordings: Animals were anaesthetized and a small patch(approximately 2 cm square) of the fur along the temporal region of the head wasshaved. A small amount of ultrasound gel was added to the tips of the ultrasoundprobes which were then placed along the shaved areas of the animals head. Whilethe device was in the Test mode, the probes were carefully aligned such that theultrasound signal was transmitted from one side of the head to the other. Once aquality signal was obtained and the probes were stabilized, the data collection began.The center frequencies of the transmitted pulses are given in Table 2. Data collectionwas carried out in the Train mode where the raw data was saved for future analysis.Each data collection session lasted approximately five minutes. The collected datafor each animal was labeled with a unique identification number. When the processwas finished, the information was written to the DUS disk with a time stamp addedto each of the animals identification number for data retrieval purposes. When allexperimental data had been collected, the DUS was connected to the network wherethe information could then be transferred remotely to another laboratory where itwas downloaded and analyzed.


Table 2: Frequency set used in this study.

Name Frequency(MHz)

f3 2.30f4 2.45f5 2.60f6 2.80f7 3.00f8 3.20f9 3.40f10 3.60f11 3.80f12 4.00f13 4.30f14 4.60

4 Data analysis

Using the raw time series data collected by the DUS, a nominal transit time is computedfor each ultrasound pulse. A Principal Component Analysis (PCA) is carried out onthe transit time data to reduce the dimensionality of the data representation. Finally,a portion of the data is used to train a Support Vector Machine (SVM) classifierto distinguish between two diagnostic classes: control and shockwave-exposed; theaccuracy of the classifier is then tested on the remainder of the data.

4.1 Data description

Table 3: Number of animals measured at each time interval, both before and aftershockwave exposure.

Pressure Pre-shockwave Post-shockwave(kPa) 24 h 48 h 72 h

141 1.3 - 5 (control)12 (exposed)

8 (control)10 (exposed)

9 (control)10 (exposed)

223 2.8 5 (control) 4 (exposed) - -

Tables 3 through 5 describe the data collected during the course of the study. As shownin Table 3, for the lower shockwave pressure data were only collected post-exposure,


Table 4: Summary of data collected in lower pressure range (141 1.3 kPa). Blankentries correspond to data sets which were absent or excluded based on quality controlconsiderations.

Class Animal Number of samples byLabel post-exposure interval

24 h 48 h 72 h

Control 1 602 60 60 603 60 604 1205 60 60 606 60 60 607 60 608 60 60 9 60 60 6010 120 60

Exposed 11 120 12012 60 60 6013 60 60 12014 60 60 15 120 60 6016 60 120 6017 60 60 6018 60 60 6019 60 6020 60 60 6021 60 60 6022 60 60

Total 1140 1200 1320

at 24 h, 48 h, and 72 h for both shockwave-exposed and control animals. For the studythat used the higher shockwave pressure, data were collected prior to exposure and 24h afterwards (i.e. each animal served as its own control).

Table 4 contains detail about data collected from individual animals in the lowerpressure range. In most cases sixty samples were collected for each animal duringeach data collection session, where one sample consists of ultrasonic transit timesfor all twelve active frequencies (Table 2). In some cases this process was repeated.In other cases, either no data were collected (due to technical difficulties with the


Table 5: Summary of data collected in higher pressure range (223 2.8 kPa). Blankentries correspond to data sets which were absent or excluded based on quality controlconsiderations.

Animal Number of samplesLabel Pre-exposure Post-exposure

(24 h)

23 6024 60 25 60 12026 60 27 60 12028 60 60

Total 300 360

device or challenges keeping the animals sufficiently anaesthetized to prevent headmovement) or data were excluded from the study because the received signal indicatedan obvious problem. Figure 2 illustrates some of the problems encountered with thereceived signal. Figure 2a is an example of a good quality signal as the successive timeseries are consistent with one another, indicating that the transmitting and receivingultrasound probes were stable during data collection. Figures 2b and 2c, however, areexamples of signals which were excluded from subsequent analyses on the basis oftheir problematic time series: the blurriness of Figure 2b indicates that the positionsof the ultrasound probes changed during the data collection session, and the erraticsignal in Figure 2c likely resulted from a malfunction of the DUS device. (Section 5addresses the effect on the results when these problematic time series were includedin the analysis.)


Sample number

Amplitude

1450 1500 1550 1600 1650 17003

2

1

0

1

2

3

(a)

Sample number

Amplitude

1550 1600 1650 1700 1750 18001.5

1

0.5

0

0.5

1

1.5

(b)

Sample number

Amplitude

1550 1600 1650 1700 1750 18002.5

2

1.5

1

0.5

0

0.5

1

1.5

2

2.5

(c)

Figure 2: Examples of received signals; multiple signals from a single data collectionsession are overlaid. (a) A series of signals in which there is good consistency from onepulse transmission to the next. (b) A series of signals in which the signal has driftedduring data collection, leading to an overall blurring of the signal contours. (c) A seriesof signals in which an apparent device malfunction has resulted in inconsistencies fromone pulse transmission to the next. Signals such as those depicted in Figure 2a wereincluded in the analyses; however, those shown in Figure 2b, 2c or others similar tothese were excluded.


4.2 Computation of pulse transit times

Since dispersion consists in a variable propagation speed for waves of variable frequen-cies, we made precise measurements of the propagation speedor, equivalently, thetransit time from transmission to reception of the pulsefor each frequency. In factwe computed a time which was related to but not identical with the transit time.

4.2.1 Timing markers

We first placed timing markers on both the transmitted and received pulses, withrespect to which timing measurements were made. To this end, we first identifiedthe approximate position of the received signal r[n] in the incoming data stream bycross-correlation with a model signal r[n] called the replica. The cross-correlationfunction R[n], defined as

R[n] = (r r)[n] =

m=r[m]r[n+m], (2)

peaks at that value of the relative displacement n for which r and r overlap to thegreatest extent. A replica was pre-recorded for each frequency by transmitting pulsesthrough a medium of distilled water. To reduce noise, the peak of the cross-correlationfunction was found by first identifying the peak in the cross-correlation functionenvelope (computed via a Hilbert transform) and then performing a local search inthe vicinity of the envelope peak to find the actual cross-correlation peak. The Hilberttransform of a discrete sequence x[n] is defined as [87]

H {x[n]} x[n] =

m=h[nm]x[m] (3)

where the impulse response is

h[n] =

2sin2(n/2)

n, n /= 0

0, n = 0(4)

and yields a phase-shifted version of the original function, with = /2. The localsearch for the cross-correlation function peak in the vicinity of the envelope peak wasconducted over a range of two oscillations of R[n]. This yielded a rough determination,to within one period of the pulse frequency, of the transit time.

To further increase the precision of the temporal interval, we searched forward in thevicinity of the cross-correlation peak for the signals zero-phase crossing. We linearlyinterpolated between the two sample points nearest the zero-phase crossing to place atiming marker with sub-sampling time resolution. The interval between the timingmarkers on the transmitted and received pulses was the nominal transit time for thepulse. This process was repeated for each transmitted and received pulse, yielding anarray of transit times for each frequency.


4.3 Frequency-dependent time jitter

It was observed that the transit times computed using the methods just describedwere not always stable, but exhibited an occasional jitter. Close examination revealedthat the amplitude of this jitter was frequency-dependent, being equal to a multiple ofthe period of the associated frequency (t n/f ;n Z), where n 15. The sourcesof this jitter have been investigated [88]. In some cases the envelope of the cross-correlation function of the received signal pulse had multiple peaks of approximatelyequal amplitude, and small variations in the signal resulted in the algorithm jumpingfrom one peak to the other; this could produce rather large time-jitter of severalperiods. Time-jitter was also produced when the envelope was single-peaked, but thecross-correlation function within the envelope had two or more peaks of approximatelyequal amplitude; this produced time-jitter of fewer (12) periods. Finally, even whenthe cross-correlation function had a single, well-defined peak, if the phase of the signalpulse at that peak was near the signals phase-wrap boundary (where it transitionsfrom to ) then small variations in phase could be converted into a time-jitter of 1 period by the search for the zero-phase crossing described above.

The time jitter t is small compared to the overall propagation time t(f) of thetranscranial pulse centered on frequency f :

t

t(f)=

n v(f)

d f (1.5 102)n (5)

where d is the transcranial distance and v(f) is the average propagation speed alongthe pulse path, and where we have substituted d = 3 cm, v(f) = 1500 m/s, and f = 3MHz, as appropriate in the current application. Jitter can alter the overall propagationtime by a few percent.

However, of greater relevance for the performance of a diagnostic classifier basedon dispersion times is the relative size of the time jitter and the inter-frequencypropagation time differences. The time-of-arrival difference between a pulse withcenter frequency fi and a pulse with center frequency fj is

tij = |t(fi) t(fj)|

=

dv(fi) dv(fj) but v(fi) = v(f0) + (f) from (1)

= d (f)

v2(fi)+O

(f)

v(fi)

(6)

where in our application the neglected terms are (with 1 m/(sMHz) andv(fi) 1500 m/s from Table 1, and f = 0.2 MHz from Table 2) of O(104) relativeto the leading term.


For the time jitter to be smaller than the inter-frequency temporal difference (so thatthe relative ordering of arrival times is preserved under jitter) we require tij > t,which implies

>nv2(fi)

d fi (f). (7)

In our application, again taking v(fi) 1500 m/s from Table 1, fi 3 MHz andf = 0.2 MHz from Table 2, and d = 3 cm for rodents, this condition yields the limit > n (125 m/(s MHz)). Since from Table 1 we have little expectation that thislimit will be satisfied for brain tissues, we should expect time jitter to result in ashuffling of the expected order of the propagation times for nearby frequencies. Thisshuffling introduces noise and makes classification on the basis of dispersion timesmore difficult.

The diagnostic classifier, to be further described in Section 4.7 below, functions byattempting to distinguish the pattern of propagation times for control animals fromthat for shockwave-exposed animals, under the assumption that the propagation timeschange as a result of a change in the tissue properties, modeled as a change in thedispersion trend c s, where the subscripts denote control and shockwave,respectively. This change will be easier to detect if it is not obscured by time jitter.Consider t, the difference between the times-of-arrival of the pulses when thedispersion trend changes from c s:

t =

dv(f0) + c(f) dv(f0) + s(f)

= d (f)

v2(f0)+O

c(f)

v(f0)

(8)

where, again, the higher order terms are suppressed by a factor of O(104), and wherewe have defined = |c s| as the difference in dispersion trend between thecontrol tissue and the shockwave-exposed tissue. Note that f is now the differencebetween the frequency of interest and the reference frequency f0 with respect to which is defined, as in (1). In practice, f should not be too large in order to preserve theapproximation of linear dispersion assumed by (1). To prevent the effect size frombeing obscured by time jitter, then, we require that t > t, or

>nv2(f0)

d f0 (f). (9)

Taking f0 1 MHz and v(f0) 1500 m/s from Table 1, f 1 MHz, and d = 3 cmfor rodents, we find > n (75 m/(s MHz)). Again, from Table 1 the satisfaction ofthis condition appears to be unlikely for brain tissues. Therefore we should expecttime jitter to obscure the difference between the control and shockwave-exposed data,making the classification task more difficult.


Some of the jitter could be eliminated by altering the method in Section 4.2.1 forplacing timing markers. For instance, we could consider eliminating the step in whichthe timing marker is placed at the time of zero-phase of the signal, as this stepsometimes introduces a jitter of 1 period. However, in this case the timing markerwould remain at the position of the cross-correlation function peak, which is itselfsubject to uncertainty on the order of 1 period. Moreover, other sources of jitter,such as originate from ambiguities in the cross-correlation function maximum andin the peak position of the Hilbert transform envelope, would remain. Instead, weconsidered reducing the jitter in post-processing, as described in the following section.

4.3.1 Time jitter reduction

Time jitter is ultimately attributable to small variations between signals that areconverted into large differences in the placement of timing markers. Since jitter ismerely an artifact of the timing marker placement algorithm, we considered removingthe jitter by post-processing the dispersion spectra. Several different post-processingmethods were considered, of which the two most successful were:

A sliding median filter. A median filter reassigns sample values based on themedian value of adjacent samples over a specified window size. We used astandard MATLAB median filter medfilt1 with a window size of 11 samples.

A customized algorithm. Since the amplitude of time jitter in our context isexpected to be an integer multiple of the pulse period, we implemented analgorithm which removed only discontinuities which satisfied this condition. Thisapproach is more cautious than the previous one, since it will not correct possiblesources of jitter unrelated to the timing-marker placement algorithm.

An example of jitter reduction is shown in Figure 3. Figure 3a shows the original data,where the vertical axis is the propagation time and the horizontal axis is the samplenumber. Each coloured line corresponds to the data for one frequency. The jitter isevident in the sharp discontinuities from one sample value to the next. In this example,the jitter rate (that is, the fraction of sample values which differ discontinuously fromthe value immediately prior) is about 8%. Figures 3b and 3c show the same dataafter the application of the median filter and customized jitter reduction algorithms,respectively. Some discontinuities remain in each case, but most of the jitter hasbeen removed, thereby substantially reducing the noise. The outputs of the two jittercorrection algorithms differ from one another.

Table 6 shows the overall jitter reduction achieved by the application of the twoalgorithms to the data sets defined in Tables 4 and 5. The jitter rate in the uncorrecteddata is typically in the 1015% range, and this drops to the 13% range after applicationof the jitter correction algorithms. The data set with the highest jitter rate is the 24h post-exposure data set at high pressures.


f3f4f5f6f7f8f9f10f11f12f13f14

Sample number

Transcranialpropagationtime(105s)

0 10 20 30 40 50 601.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

(a)


Sample number


0 10 20 30 40 50 601.75

1.8

1.85

1.9

1.95

2

2.05

(b)


Sample number


0 10 20 30 40 50 601.75

1.8

1.85

1.9

1.95

2

2.05

(c)

Figure 3: Jitter reduction: the vertical axes show transcranial propagation timefor each frequency in Table 2 and the horizontal axes show sample number. Thedata are for Animal 14 at 24 h post-exposure (see Table 4). (a) Dispersion spectrumshowing jitter introduced by the timing marker placement algorithm. (b) Dispersionspectrum after application of median filter. (c) Dispersion spectrum after applicationof customized jitter-reduction algorithm.


Table 6: Jitter reduction rates achieved by application of post-processing filters.

Pressure Data Jitter Rate (%)(kPa) Set No reduction Median filter Custom

141 1.3 24 h 11.0 1.7 1.448 h 12.2 1.7 1.672 h 11.4 1.8 1.2

223 2.8 Pre-exposure 10.5 1.1 1.024 h 16.7 3.0 2.8

In immediately subsequent sections of this report we shall for illustrative purposesfocus on the data set without jitter correction, but in Section 5 we shall present fullresults on classification performance using both jitter-uncorrected and jitter-correcteddata sets.

4.4 Effect size

Before proceeding, it is interesting to compare the inter-frequency time interval tijdefined in (6) to the time interval resulting from a modification of the dispersion trendt defined in (8). If the inter-frequency spacing tij is large relative to the effectsize t then the control and shockwave-exposed dispersion patterns will be nearlyidentical. To have a reasonable effect size, we might hope to have

t tij d (f)

v(f0)2 d (f)

v(fi)2

= , (10)

where, for simplicity, we have taken one of our frequencies of interest fi to be the ref-erence frequency f0. The condition (10) states that unless the change in the dispersiontrend (and this should be understood as the average or effective dispersion trendalong the whole transmission path) resulting from shockwave-exposure is comparableto the initial dispersion trend, the data for shockwave-exposed animals and for controlanimals will be nearly identical, making them difficult to distinguish with a classifier.This is the case even in the absence of time jitter. Since there is no data available onhow shockwave exposure alters the dispersion trend, it is hard to say whether thecondition (10) is likely to be satisfied. However, it is useful to know that a changein dispersion trend of O(1) is required in order to produce even a minor differencebetween the control and shockwave-exposed data.


4.5 Data normalization

Ultrasound pulse transit times are proportional to the distance the pulse travels. Sincethe animals involved in the study were of slightly different sizes, the transit timesvaried in a manner unrelated to dispersion. To reduce this effect, we normalized thetransit times computed in Section 4.2.

In a dispersive medium i, the transit time of an ultrasound pulse is ti(f) = di/vi(f),where di is the thickness of the medium and vi(f) is a function (possibly non-linear)describing the frequency dependence of the pulse speed in that medium. For a pulsethat traverses a set of N tissues, the total transit time is t(f) =

Ni=1 di/vi(f). Clearly

this time is not invariant under a change in the size of the medium di di, butrather scales linearly with the scaling factor t(f) t(f).

If we choose one frequency f0 as a reference frequency, we can compute the averagetransit time for that frequency over a set of M measurements as

t(f0) =1

M

Mk=1

tk(f0). (11)

Because each term in the sum scales linearly under an overall rescaling of size, thisaverage time does as well. We can therefore sensibly normalize our transit times bydividing each by the average transit time of some reference frequency. The resultingnormalized time t(f) = t(f)/t(f0) is invariant under the rescaling di di, which isthe property we desired. In practice we apply a normalization factor such that theaverage value of transit times for f6 (see Table 2) is unity; the data are normalizedon a session by session basis. Note that this method only removes dependence ontissue thicknesses if the scaling factor is consistent across tissues; if there is a differentscaling factor i for each tissue (that is, if the difference between animals is not justsize but also relative thickness of tissue layers along the pulse propagation path) thenthis normalization method will limit but not eliminate dependence on the scalingfactors, and a residual dependence on animal size will remain in the normalized data.It is probable that, in practice, there is some residual dependence on animal size inthe data.

4.6 Principal Component Analysis (PCA)

As indicated in Table 2, we transmitted a set of twelve frequencies. Because data ofhigh dimensionality are difficult to visualize and it was not evident that all frequencieswere providing useful information, we considered a dimensional reduction by way ofPrincipal Component Analysis (PCA). PCA is a standard statistical procedure [89]by which a set of linearly dependent initial variables are converted into a new setof linearly independent variables called principal components, where the number of


principal components is less than or equal to the number of initial variables. Theprincipal components are ordered such that each principal component accounts formore of the variability in the data than the succeeding principal component. In thisway, it is often possible to reduce the number of variables while limiting the loss ofthe information-rich data variance.

PCA was carried out separately on the lower pressure data and the higher pressuredata outlined in Tables 4 and 5, respectively. Table 7 summarizes the output of thePCA algorithm1. It is evident from Table 7 that most of the variance of the data wascontained in the first few principal components, indicating that the original data sethad a high degree of correlation between variables.

Table 7: Overview of leading principal components for the lower pressure and higherpressure data sets.

Pressure Principal Variance Cumulative(kPa) component, Explained Variance Explained

141 1.3 1 30 302 25 553 15 704 7 77

223 2.8 1 34 342 17 513 12 634 8 71

It is instructive to use PCA dimensional reduction to represent the dispersive ultra-sound data. Figure 4 shows the leading principal components for the lower pressuredata, and Figure 5 shows the same information for the higher pressure data. Figures 4aand 5a show the two leading principal components and the histograms in Figures 4band 5b show how the data cluster along the leading principal component. (Figures 4band 5b are projections of Figures 4a and 5a onto the axis of the leading principalcomponent.) Note that in both cases there was significant overlap between the controlgroup and the shockwave-exposed group; despite a few outliers, most of the dataof each class clustered together and the clusters overlapped. This suggested thatdistinguishing the control group and the shockwave-exposed group on the basis of thisdata would be a challenging task.

In our analysis we decided to retain all of the variables, reserving a dimensionally-reduced representation of the data mainly for ease of visualization, but we comment

1 We use the MATLAB implementation of the PCA algorithm. MATLAB and Statistics ToolboxRelease 2013b, The MathWorks, Inc., Natick, Massachusetts, United States.


in Section 5 on the difference between performance results of the diagnostic clas-sifier obtained using the full complement of variables and a dimensionally-reducedrepresentation.

4.7 Support Vector Machine (SVM) classification

Diagnostic classification of the dispersion data was done by means of a Support VectorMachine (SVM) [9092]. A SVM is a versatile and powerful non-linear classifier whichis widely used. With one exception (described below) we used the implementation inthe open source SVM library libsvm [93]. Separate analyses were carried out on thelower pressure and higher pressure data.

The full data set was first split into a training set and a testing set; the former was usedto train the SVM classifier and the latter to evaluate its performance. Each element ofthe data set was labeled as belonging to either Class 1 (control) or Class 2 (shockwave-exposed). The training set was formed by randomly selecting approximately 50%of the sessions for inclusion; the remaining data constituted the testing set. Notethat the division between training and testing sets was done at the level of sessionsrather than at the level of individual measurements. This was necessary because of theredundancy inherent in making multiple measurements in each session: erroneouslysplitting on the level of individual measurements would permit data from a givensession to fall into both the training and testing sets, which would bias the classifier.Division by data collection session helped ensure that the training and testing setswere independent of one another.

Both the training set and testing set were then stratified so that each contained thesame number of instances of each class [94,95]. Stratification of the training set preventsbias in the classifier, and stratification of the testing set prevents bias in reporting theclassification accuracy. Where class sizes were unequal in the initial sets, we randomlyundersampled the larger class until the class membership equalized. In most cases itwas Class 1 (control) samples which were randomly discarded during stratification,and the percentage of the initial class membership discarded was typically 2040%.

We used a radial basis function SVM kernel [92, 96]. Kernels of this type have twoparameters, C and . Performance was optimized via a grid search over the parameterspace, with the optimization measure being classification accuracy after k-fold (k = 10)cross-validation on the training set. The parameter space over which we searched wasthat suggested in the literature [96]:

5 c 15 (12)15 g 3

where the SVM parameters are C = 2c and = 2g. The grid search proceeded in twostages: first with a coarse step size of 2 through the (c, g) parameter space and then,


centered on the (c, g) value which yielded the best cross-validation result, a localizedsearch over a 4x4 region of (c, g) parameter space with a step size of 0.25 to find alocal performance peak.

The cross-validation algorithm was partly customized. Cross-validation is a procedurecommonly used in SVM training to reduce generalization error: instead of simplytraining the classifier on the training set, the training set is divided into k sections, orfolds, with k1 folds designated as the cross-validation training set and the remainingfold called the validation set. The SVM is trained on the cross-validation training setand tested on the validation set, and then this process is repeated such that each foldrotates once through the validation set. The overall cross-validation accuracy is themean of the accuracies obtained on the validation sets.

The partitioning of the training set into a cross-validation training set and a validationset was customized. The libsvm implementation constructs the partition by randomsampling, but in our case this was inappropriate: data were grouped together bysession, and, as mentioned earlier, bias would result if individual sessions were splitbetween training and testing sets (or, in this context, between cross-validation trainingsets and validation sets). Consequently, we customized the partitioning algorithm torespect the session-grouping of the data. When the training set consisted of data fromN sessions and k-fold cross-validation was desired, we defined the size of each fold tobe v = N/k sessions. This resulted in the total number of folds being k = N/vand, depending on the values of N and k, it could happen that k < k. (For example,if N = 20 and k = 10 (the standard value), each fold consisted of v = 2 sessions andthe total number of folds was k = 10, as desired, but if N = 25 and k = 10 then v = 3and k = 9.) This reduction in the number of folds ensured that each fold served asthe validation set once and only once during the cross-validation process. Otherwisethe cross-validation process proceeded in a standard manner.

The final SVM model was obtained by training using the optimal (c, g) parametervalues as determined by the k-fold (k = 10), stratified cross-validation process wehave just described. The data in the testing set were then classified using this SVMmodel to assess the accuracy of the classifier.

The above procedure began with the random division of the full data set into a trainingset and a testing set. We repeated this random partitioning (and the subsequent cross-validation training and testing) numerous times in order to assess the robustness ofthe classifier under perturbations in the training and testing data. When the fulldata set consisted of N data sessions, we repeated the partitioning and classificationprocedure N times. We defined the mean accuracy of the SVM classifier as the meanclassification accuracy over these iterations.


ControlShockwave-exposed

Principal

Com

pon

ent2

Principal Component 11 0.5 0 0.5 1 1.5 2

2

1.5

1

0.5

0

0.5

1

1.5

2

(a) Leading Principal Components.


Number

Principal Component 11 0.5 0 0.5 1 1.5 20

200

400

600

800

1000

1200

1400

1600

1800

2000

(b) Projection of the above onto the first Principal Component axis showingdensity of each group.

Figure 4: Leading Principal Components of lower pressure data set. The shockwave-exposed group data are shown in red and the control group data in green.



PrincipalCom

pon

ent2

Principal Component 11.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.2 0.4

1.2

1

0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

(a) Leading Principal Components.


Number

Principal Component 11.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.2 0.40

50

100

150

200

250

(b) Projection of the above onto the first Principal Component axis showingdensity of each group.

Figure 5: Leading Principal Components of higher pressure data set. The shockwave-exposed group data are shown in red and the control group data in green.


5 Results5.1 Support Vector Machine (SVM) classifier results

The principal results of the SVM classification are shown in Table 8. In the lowerpressure range, we first considered a classification task on data collected at any post-exposure interval (marked All in the table), and then considered classification taskslimited to comparisons of control and shockwave-exposed data at specific post-exposureintervals (marked 24 h, 48 h, and 72 h in the Table). At higher pressures weconsidered one classification task based on a comparison of data collected prior toshockwave exposure and at 24 hours post-exposure. The main classification results aregiven in the column No PCA, in which quality control criteria were applied to excludeproblematic raw data (as described in Section 4.1) but no principal component analysiswas applied. For comparison, in succeeding columns we also give the classificationaccuracies when a principal component analysis was done (with only the three leadingcomponents retained) and when no quality control criteria were applied to the raw data.As described above, the means and standard deviations in Table 8 were obtained byiteratively re-partitioning the data into training and testing sets N times and repeatingthe SVM model selection, training, and testing procedure for each partitioning. Thenumber of partitionings in each case was equal to the number of data sessions includedin each classification task: All (N = 54), 24 h (N = 17), 48 h (N = 18), and 72h (N = 19) at lower pressures, and N = 9 at higher pressures. (In the No qualitycontrol column the number of data sessions was enlarged to N = 69, 23, 23, and 23,respectively, at lower pressures, and N = 10 at higher pressures.)

Table 8: Diagnostic classification accuracies in low and high shockwave pressureranges.

Pressure Control Shockwave- Classification Accuracy (%)(kPa) Group exposed Group No PCA PCA ( = 3) No quality control

141 1.3 All All 51 6 56 3 55 424 h 24 h 53 10 55 13 58 648 h 48 h 53 10 55 8 48 772 h 72 h 64 9 58 9 52 9

223 2.8 Pre-exposure 24 h 39 15 47 14 47 19

In most cases the classification accuracy was consistent with random classification(50%). This indicates that at this pressure and at the stated post-exposure intervals,it was not possible to reliably distinguish between the control and shockwave-exposedgroups on the basis of the data we collected.

A few of the results in Table 8 differ from 50% by more than one standard deviation.Of these, the one with the highest mean value is that obtained at 72 h post-exposure


in the lower pressure data set, for which the mean accuracy was 64 9%. This resultwas robust under SVM model selection: a less refined tuning of the SVM classifiersparameters (obtained by carrying out only the first, coarser stage of the parameterspace grid search described in Section 4.7 above) yielded a similar classificationaccuracy of 62 8%. As indicated in Table 8, if only the three highest varianceprincipal components were retained in the data the classification accuracy dropped to58 9%, which could indicate that the differences between the control and shockwave-exposed groups are subtle rather than gross features, being confined to lower varianceprincipal components. We also observed that if the exclusion of poor quality time seriesdescribed in Section 4.1 was not done the classification result at 72 h post-exposuredropped to 52 9%, which is consistent with the intuition that inclusion of lowquality raw data will degrade the performance of a working classifier. Although thereis a significant probability that this particular result is a statistical fluctuation, itnonetheless makes a good illustrative case worth exploring to better understand thedata.

Table 9: Diagnostic classification accuracies in low and high shockwave pressureranges for jitter-reduced data, assuming no PCA and excluding low quality data.

Pressure Control Shockwave- Classification Accuracy (%)(kPa) Group exposed Group Median Filter Custom

141 1.3 All All 48 7 52 924 h 24 h 56 9 53 1548 h 48 h 50 9 46 972 h 72 h 63 9 59 14

223 2.8 Pre-exposure 24 h 41 21 29 17

The poor performance of the classifier summarized in Table 8 might be thought tobe due to the presence of time-jitter in the data, as described in Section 4.3. InTable 9, therefore, are shown the classification results obtained using jitter-reduceddata. In addition to being processed by the jitter-reduction algorithms described inSection 4.3.1, these data were filtered for quality (as in Section 4.1) and no PrincipalComponent Analysis was done; the classification results should therefore be comparedto those in the No PCA column of Table 8. It is clear that jitter reduction has nodiscernible effect on the classifiers performance. The results are again consistent withrandom classification at one standard deviation, with the exception of the median-filtered low-pressure data at 72 h post-exposure. However, even this modest statisticaldifference from randomness disappears with the custom-filtered (and cleanest) data,strongly suggesting that it is merely a statistical anomaly.

Tables 10 and 11 provide details about the classification results summarized in Table 8.For example, Table 10 shows the classification results for individual partitionings of


the lower pressure data set into training and testing subsets. For each partitioning, the(stratified) number of measurements in the training set and in the testing set is stated.The next column indicates how many of the training set examples were designatedas support vectors by the SVM classifier; the relatively high proportion of supportvectors in this case (on average, 71 14% of the training set elements have beendesignated as support vectors) indicates that there is no clean separation betweenthe control and shockwave-exposed data sets, even in the higher-dimensional featurespace of the classifier. The final column states the classification accuracy obtained foreach partitioning; it is the mean and standard deviation of this column that is givenin Table 8. The equivalent table for classification of the lower pressure ranges 72 hpost-exposure data is given in Table 11.

It is also instructive to examine the classifiers confusion matrix C, which providesmore detail about the classifiers performance. For instance, for the full lower pressuredata set described in Table 10 the confusion matrix is

CAll =

0.39 0.10 0.11 0.100.38 0.07 0.12 0.07

(13)

which is illustrated in Figure 6. In a perfect classifier the confusion matrix would bediagonal; off-diagonal elements are misclassifications. The top-right element indicateswhat fraction of control group data points were misclassified as shockwave-exposed,and the lower-left element indicates the reverse case. In this example, most of thecontrol group data points were correctly classified (0.39 0.10 out of a possible 0.5),but most of the shockwave-exposed data points were misclassified (0.12 0.07 out ofa possible 0.5 were correct): the classifier tends to classify data as being in the controlgroup.

For the 72 h post-exposure data in the lower pressure range the confusion matrix is

C72h =

0.36 0.09 0.14 0.090.22 0.10 0.28 0.10

, (14)

which is illustrated in Figure 7. The results for classifications of control group data (thefirst row) are comparable to the earlier example, but there are fewer misclassificationsof the shockwave-exposed group data (the second row).


Table 10: Details of classification results for full data set in lower pressure range.Each case corresponds to a randomized partitioning of the data into training andtesting subsets, which are then both stratified to equalize membership in the twodiagnostic classes. Testing set accuracy is stated in percent.

Case Training Set Size Testing Set Size Support Vectors Testing Set Accuracy

1 1544 1100 1302 462 1104 1540 930 513 1210 1434 927 494 1544 1100 1231 495 1214 1430 863 466 1100 1544 889 587 1654 990 634 538 1540 1104 1304 509 1760 880 1227 5010 1430 1214 1150 5011 1104 1540 872 5512 1430 1214 887 5613 1434 1210 1087 4914 1210 1434 570 5715 994 1650 836 5516 1544 1100 1145 3317 1100 1544 862 5318 1214 1430 554 5819 880 1764 387 5020 1320 1324 965 3821 990 1540 692 5422 990 1654 516 4023 1100 1544 945 5524 1430 1214 1138 4025 1210 1434 455 4826 1544 1100 1301 5127 1100 1544 688 4828 1214 1430 943 5329 880 1750 652 5230 1214 1430 1005 6031 1210 1434 997 5232 990 1654 669 5733 1540 1104 606 4934 1430 1214 808 5135 1434 1210 1148 5136 1654 990 1224 5737 1544 1100 1192 6138 1540 1104 1131 3539 1654 990 1457 4240 990 1654 788 5241 1654 990 888 4642 1324 1320 898 5543 1544 1100 1028 5244 1324 1320 1134 5245 1320 1324 696 5246 1760 880 995 6047 1650 880 1391 5148 990 1530 811 5349 994 1650 766 3750 1104 1540 996 5151 1320 1324 834 5352 1430 1214 1033 5353 990 1654 629 5454 1324 1320 1038 49


Table 11: Details of classification results for 72 h post-exposure data set in lowerpressure range. Each case corresponds to a randomized partitioning of the data intotraining and testing subsets, which are then both stratified to equalize membership inthe two diagnostic classes. Testing set accuracy is stated in percent.

Case Training Set Size Testing Set Size Support Vectors Testing Set Accuracy

1 550 550 216 612 440 440 81 463 550 440 268 664 330 440 87 535 330 220 106 646 550 440 169 607 550 330 362 788 440 330 129 529 660 440 390 7010 660 440 141 6111 440 550 309 7812 550 550 87 6413 440 550 277 6214 440 660 291 6815 660 440 334 6916 660 440 323 7017 550 440 94 5818 660 440 360 6019 550 550 314 75


Predicted Group

Shockwave-exposed

Control

Fraction

Actual Group

Control Shockwave-exposed0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 6: Classification results for full data set in lower pressure range.

Predicted Group

Shockwave-exposed

Control

Fraction

Actual Group

Control Shockwave-exposed0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 7: Classification results in lower pressure range at 72 h post-exposure.


5.2 Discussion

Possible reasons for the poor diagnostic performance of the classifier in this studyare worth examining. Interpretation of these results should take into account thatin the current study no gross pathology was noted when necropsies were performedon the animals brains, a finding consistent with other studies under similar condi-tions [17, 84, 97]. On the other hand, and as discussed in Section 3 above, there isconsiderable evidence from comparable studies carried out at similar or lower blastpressures and with the same animal model to support the view that the animals didindeed suffer at least a mild TBI. These studies have observed behavioural deficits,sleep disturbances, and markers of a neuroinflammatory response following blastexposure.

The objective of this study was to investigate whether the neurological changesunderlying these symptoms of blast exposure could be detected through their effectson the propagation of ultrasound pulses through the affected tissues. In preliminarystudies (see Section 2.3.1) we had shown that fluids could be distinguished on thebasis of dispersive ultrasound data, which suggested that the same method might alsobe able to distinguish between other propagation media as well, such as (in this case)brain tissues of shockwave-exposed and control animals.

At the outset it was difficult to assess the likelihood that this approach would becapable of identifying cases of shockwave-exposure because while relatively littleis known about responses of intracranial tissues to shockwave-exposure still less isknown about how those responses affect ultrasonic frequency dispersion. As discussedin Section 2.2.1, data on ultrasonic frequency dispersion properties of intracranialtissues is scarce and of uncertain quality. However, despite these knowledge gaps, weconsidered the problem of mild TBI diagnosis to be a sufficiently compelling one tojustify attempting an unconventional diagnostic method.

Given that the present study has proved unable to identify differences between thedispersive ultrasound spectra of shockwave-exposed and control animals, a naturalconclusion is that the neurological changes which occurred in the animals as a resultof shockwave-exposure were not of such a nature as to affect ultrasonic frequencydispersion.

Another possibility is that the severity of the injury suffered by the shockwave-exposed animals was highly variable, and that this variability prevented their beingdistinguished as a group from the control group. But this is unlikely for at leasttwo reasons. First, other studies conducted under similar conditions have found thatdespite some variability within shockwave-exposed groups, these groups can, on avariety of measures, be consistently distinguished from control animals [79, 82, 84].Second, our classification method does not require that the two diagnostic groups beclearly and consistently distinguishable. Even if only a few shockwave-exposed animals


had dispersion data which differed from the controls, or if the shockwave-exposeddata varied over a wide spectrum that blended at one end into the control group, thiswould still shift the classification accuracy away from 50%. Since we so consistentlyobserve classification accuracies consistent with 50%, the most reasonable conclusionis that the dispersive ultrasound data does not indicate any statistically significantdifferences between the two diagnostic groups.

We showed in Section 4.3 that the data input to the diagnostic classifier include acertain amount of noise, which we call time jitter, and we argued that it would beexpected to degrade the performance of the classifier. The time jitter is a consequenceof the method by which we compute the ultrasonic pulse propagation time, as describedin Section 4.2, and so we described several algorithms for smoothing the jitter inpost-processing. However, we found that even with jitter-reduced data (in whichthe jitter rate was 12%) the classifiers performance was consistent with randomclassification. From this we conclude that the poor performance of the classifier cannotplausibly be attributed to time jitter.

6 Conclusions

We examined the use of ultrasonic frequency dispersion to detect primary blast-induced mild brain injuries in rodents. We non-invasively transmitted transcranialultrasonic pulses and observed the frequency-dependent variations in propagationspeed in controls and shockwave-exposed rats. The shockwave loading onto the headof the animal had a peak pressure of 0, 141 1.3 kPa, or 223 2.8 kPa, levelsknown to induce functional deficits and neuroinflammatory response. We attemptedto distinguish between the data collected from the control and shockwave-exposedgroups using a two-class Support Vector Machine (SVM) classifier.

We found that the classification results were consistent with random classification,indicating that the classifier could not reliably distinguish between the two groups ofanimals at the incident peak pressures and post-exposure intervals that we studied.

Relatively little is known about how exposure to high intensity, short duration pressuresalters the dispersive qualities of intracranial tissues. The negative finding of this studysuggests that shockwave exposure does not significantly alter the dispersive propertiesof brain tissues, and that therefore ultrasonic frequency dispersion is not a suitablediagnostic probe for primary blast-induced mild traumatic brain injury.


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