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Investigating the spinal cord atrophy measurement on MRI from two aspects : physiological variations… Wang, Chunfang 2014

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Investigating the Spinal Cord AtrophyMeasurement on MRI from TwoAspects: Physiological Variations andLongitudinal Measurement MethodsbyChunfang WangB.Eng., Huazhong University of Science and Technology, 2006M.Eng., Huazhong University of Science and Technology, 2008A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES( Biomedical Engineering )THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2014© Chunfang Wang 2014AbstractSpinal cord atrophy is a valuable biomarker in multiple sclerosis (MS) forits significant correlation with physical disability. Measurement of spinalcord atrophy on MRI may be possibly confounded by fluctuations in watercontent, and the high measurement variance in previous longitudinal studiescan be possibly reduced by registration-based methods. In this thesis, weinvestigated the effect of change in water content due to hydration status oncord cross-sectional area (CSA) measurement, and the applicability of threeregistration-based methods for longitudinal cord atrophy measurement.Our first hypothesis is that dehydration can decrease the cord CSA mea-surement on MRI. We found a mean decrease of 0.65% in CSA on scanscollected from ten controls following a dehydration protocol using two in-dependent cross-sectional CSA measurement methods. Our result demon-strates that change in water content of the cord is associated with measurablechange in cord CSA.The second main hypothesis is that registration-based methods can de-crease the variance in longitudinal cord atrophy measurement by using thesignal from multiple scans to improve robustness to image noise and artifactsand by regularization of the registration to constrain the degrees of freedom.We implemented three algorithms: boundary shift integral based on rigidregistration, Jacobian integration based on deformable registration and scalefactor computation based on constrained registration (composed of rigid andscale transformation). We evaluated the three registration-based methods bycomparing them to two cross-sectional methods, as applied to three longitu-dinal data sets: 1) images with simulated cord atrophy; 2) images acquiredin the dehydration study described above; and 3) images of 15 MS patientsover a two-year interval. Our main result was that while registration-basediiAbstractmethods achieved more accurate results on simulation data sets and overallsmaller measurement variance, they were not as sensitive, reporting no de-hydration effect and smaller magnitude of patient cord atrophy. We arguethat the limited spatial resolution of 1 mm of MR scans in our experimentis possibly the main reason and future studies of cord atrophy measurementusing registration-based methods should be conducted on MR scans with ahigh spatial resolution such as 0.5 mm.iiiPrefaceThis thesis is an original and independent work by the author, ChunfangWang. All of the experiments presented henceforth were conducted by Chun-fang Wang in the MS/MRI Research Group at the University of BritishColumbia, Point Grey campus.Chapter 2. An earlier version of the work presented in this chapterhas been published in the journal Spinal Cord. MR scans for the dehydra-tion study were collected at the MRI Research Centre, University of BritishColumbia, Point Grey campus. I performed all the cord cross-sectional areameasurements, the statistical analyses and the manuscript composition.C. Wang, R.C. Tam, E. Mackie, D.K.B. Li, and A.L. Traboulsee.Dehydration affects spinal cord cross-sectional area measurementon MRI in healthy subjects. Spinal Cord, vol. 52, pp. 616−620,2014Chapter 3. The c++ code for performing deformable registration usingsymmetric diffeomorphic demons algorithm is a refinement and extensionbased on the open source ITK implementation of this algorithm released inThe Insight Journal. Dr. Roger Tam proposed the concept for the workpresented in this chapter, and I was the lead investigator, responsible for allthe algorithm implementation, data collection and test analyses.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Multiple Sclerosis . . . . . . . . . . . . . . . . . . . . 11.1.2 Involvement of Spinal Cord Atrophy in MS . . . . . . 31.1.3 Spinal Cord Atrophy Measurement Methods . . . . . 51.2 Thesis Motivation . . . . . . . . . . . . . . . . . . . . . . . . 81.2.1 The Effect of Change in Water Content on Spinal CordCSA Measurement on MRI . . . . . . . . . . . . . . . 91.2.2 Registration-based Atrophy Measurement Methods forLongitudinal Cord Atrophy Studies . . . . . . . . . . 101.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . 121.3.1 Dehydration Effect on Cord CSA Measurement . . . . 121.3.2 Registration-based Cord Atrophy Measurement Meth-ods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12vTable of Contents1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Dehydration Decreases the Cord Cross-sectional Area Mea-surement on MRI . . . . . . . . . . . . . . . . . . . . . . . . . . 162.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . 172.2.1 Subjects and MRI Procedure . . . . . . . . . . . . . . 172.2.2 Dehydration Protocol . . . . . . . . . . . . . . . . . . 182.2.3 MR Image Analysis . . . . . . . . . . . . . . . . . . . 182.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Registration-based Cord Atrophy Measurement Methods 303.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.1 Preprocessing . . . . . . . . . . . . . . . . . . . . . . 303.1.2 Boundary Shift Integral . . . . . . . . . . . . . . . . . 343.1.3 Jacobian Integration . . . . . . . . . . . . . . . . . . . 383.1.4 Scale Factor from 3-DoF Registration . . . . . . . . . 433.1.5 Experiments Performed . . . . . . . . . . . . . . . . . 443.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.1 Scaled Scan Pairs . . . . . . . . . . . . . . . . . . . . 483.2.2 Scaled Scan Pairs with Rigid Transformation . . . . . 483.2.3 Hydration Data Set . . . . . . . . . . . . . . . . . . . 543.2.4 MS Patient Data Set . . . . . . . . . . . . . . . . . . 553.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.3.1 Boundary Shift Integral . . . . . . . . . . . . . . . . . 603.3.2 Jacobian Integration . . . . . . . . . . . . . . . . . . . 623.3.3 Scale Factor from 3-DoF Registration . . . . . . . . . 654 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71viList of Tables2.1 Statistical results of the percentage changes in CSA computedby Tench method . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Statistical results of the percentage changes in CSA computedby our in-house method (Tench method using PV2) and Jimsoftware (Horsfield method) . . . . . . . . . . . . . . . . . . . 233.1 Scale factors applied to create scaled scan pairs . . . . . . . . 463.2 Mean and SD of the errors which are the differences betweenthe percentage change rates computed by BSI, JI and SF onscaled scan pairs and their respective ground truth change rates 533.3 Mean (SD) of the errors, which are the differences of the com-puted change rates to the ground truth values . . . . . . . . . 533.4 Means and SDs of the percentage change rates computed byBSI, JI and SF along with the results of Tench and Horsfieldmethods on the scan-rescan pairs . . . . . . . . . . . . . . . . 543.5 Mean and standard deviation (SD) of the percentage changerates in cord volume computed by BSI, JI and SF along withthe results of Tench and Horsfield methods on the MS patientdata set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55viiList of Figures2.1 Cord segmentation using our in-house software . . . . . . . . 192.2 Intensity estimation of the CSF . . . . . . . . . . . . . . . . . 212.3 The percentage change in cervical cord CSA from baseline tothe other three time points computed by our in-house software(Tench method) . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4 The percentage change in cervical cord CSA from baselineto the other three time points using software Jim (Horsfieldmethod). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1 Illustration of the difference image of the baseline and follow-up images before and after rigid registration. . . . . . . . . . 323.2 Example of an idealized one dimensional cord boundary shift 353.3 Illustration of the dilated cord segmentation labeled on thebaseline cord image . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Illustration of the deformation field generated by images with3% simulated atrophy. . . . . . . . . . . . . . . . . . . . . . . 403.5 Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-based methods (Tench and Horsfield) on simulated scan pairswith rigid transformation and no scaling change . . . . . . . . 493.6 Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-based methods (Tench and Horsfield) on simulated scan pairswith rigid transformation and 1% scaling change . . . . . . . 50viiiList of Figures3.7 Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-based methods (Tench and Horsfield) on simulated scan pairswith rigid transformation and 2% scaling change . . . . . . . 513.8 Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-based methods (Tench and Horsfield) on simulated scan pairswith rigid transformation and 3% scaling change . . . . . . . 523.9 The percentage change in cord volume from baseline to therescan time point computed by the three registration-basedmethods (BSI, JI and SF) and the two segmentation-basedmethods (Tench and Horsfield) . . . . . . . . . . . . . . . . . 563.10 The percentage change in cord volume from baseline to thedehydration time point computed by the three registration-based methods (BSI, JI and SF) and the two segmentation-based methods (Tench and Horsfield) . . . . . . . . . . . . . . 573.11 The percentage change in cord volume from baseline to therehydration time point computed by the three registration-based methods (BSI, JI and SF) and the two segmentation-based methods (Tench and Horsfield) . . . . . . . . . . . . . . 583.12 The percentage change in cord volume on the scan pairs withtwo years interval computed by the three registration-basedmethods (BSI, JI and SF) and the two segmentation-basedmethods (Tench and Horsfield) . . . . . . . . . . . . . . . . . 59ixList of AbbreviationsMS multiple sclerosisEDSS expanded disability status scaleRRMS relapsing-remitting multiple sclerosisPPMS primary progressive multiple sclerosisNAWM normal appearing white matterNAGM normal appearing grey matterCOV coefficient of variationROI region of interestCSF cerebrospinal fluidPV partial volumeCSA cross-sectional areaBSI boundary shift integralJI Jacobian integrationDoF degree of freedomSF scale factorSD standard deviationAD Alzheimer’s diseasexAcknowledgementsI would like to express my sincere gratitude to my supervisor Dr. RogerTam for his patience, guidance and support throughout my studies in UBC.I could not have finished this thesis without you.Thanks to Dr. David Li and Dr. Anthony Traboulsee for their valuableclinical opinions on my experiment. A special thank to Dr. David Li for hiscontinuous support and insightful advice on my research.Thanks to Dr. Burkhard Madler, Dr. Corree Laule and Trudy Harris fortheir assistance in developing the scanning protocol. Thanks to the volun-teers for their time and effort, and also thanks to Emilie Mackie for recruitingthe volunteers for the dehydration experiment.I am very thankful to my thesis examiners: Dr. Purang Abolmaesumiand Dr. Rafeef Abugharbieh for providing their valuable time to serve onmy examination committee.I want to thank my friends in the MS/MRI Research Group: Dr. LisaTang, Youngjin Yoo, Tom Brosch and Saurabh Garg. You guys always helpme and encourage me along this journey, and your friendships are highlyappreciated.Finally, I would like to thank my mama and papa, my younger brotherand my boyfriend for their continuous love and support.xiChapter 1Introduction1.1 Background1.1.1 Multiple SclerosisPathological basis and clinical course of multiple sclerosisMultiple Sclerosis (MS) is a chronic disorder in the central nervous system,which involves inflammatory demyelination and neuroaxonal degeneration.It causes focal lesions in the white and grey matter and diffuse unevenlydistributed changes in the normal appearing white matter (NAWM) and greymatter (NAGM) in the brain and spinal cord [36]. With the inflammatorydemyelination disseminated in the central nervous system, the lesions developin association with the breakdown of the blood-brain barrier, leading toacute breakdown of myelin with a degree of axonal destruction [76]. Theseacute inflammatory lesions lead to acute relapses of neurological deficit asa result of conduction block due to the loss of myelin. With time goingon, the axonal loss evolves to be the main pathological substrate and theneuroaxonal degeneration leads to progressive disabilities over time.MS takes several clinical forms, with new symptoms occurring either indiscrete attacks (relapsing forms) or accumulating over time (progressiveforms). About 85% of cases begin with relapsing-remitting (RRMS) course,suffering from relapses (attacks of symptom flare-ups) before a slow remission(period of recovery). There is usually good recovery from such relapses as aresult of resolution of inflammation, remyelination and cortical adaptation[76]. In 15% of the patients, the onset of MS is one of progressively increasingand irreversible disability, primary progressive MS (PPMS). Within next 6to 10 years, about 65% of RRMS patients enter the secondary progressive11.1. Background(SPMS) phase and are subjected to gradual progression of physical disabilityand cognitive impairment [107]. There is also a relatively rare type of MScalled progressive-relapsing (PRMS) in which patients experience steadilyworsening symptoms and attacks during the period of remission [79, 107].MS is the most common cause of neurological disability in young adults,with a prevalence that ranges between 2 and 150 per 100,000 and varyingwidely in different regions [76]. Canada has one of the highest rates of MS inthe world, and an estimated 100,000 Canadians have MS [1]. MS is typicallydiagnosed based on the presenting symptoms in combination with supportingMRIs. There is no cure of MS, and treatments attempt to return functionafter an attack, prevent new attacks and prevent disability. There are tendisease-modifying therapies approved by Health Canada to date [2].Imaging biomarkers in MSMRI has an important role for the assessment of patients with MS, becauseof its sensitivity to MS-related abnormalities and correlation to pathologicalchanges [36]. Lesion based measures, typically the number and extent ofT2-hyperintense lesions and T1-enhancing lesions after Gadolinium enhanc-ing administration in the brain are very useful to diagnosis the disease andpredict further evolution in the early phase of MS [34, 76].Beside lesions, quantitative MRI discloses the presence of abnormalitiesin the NAWM and NAGM before the development of lesions. Reduction ofthe magnetization transfer ratio value [90], increase in the mean diffusivityon diffusion tensor MRI [82, 88] and decrease of the concentration of N-acetyl-aspartate on MR spectroscopy [80] in these regions have been used inMS research studies and they are associated with the cognitive impairment.Measuring irreversible tissue loss in the brain and spinal cord on MRI,which represents the overall destructive pathological changes in the centralnervous system has become an area with increasing interest. Atrophy of thewhite or grey matter in MS reflects the overall axonal and neuronal loss andis well associated with clinical disability and cognitive deterioration [36]. At-rophy based measures, like global whole brain atrophy, regional grey matter21.1. Backgroundatrophy and spinal cord atrophy, are among the most widely used measuresin disease monitoring and treatment trials. Both brain atrophy and spinalcord atrophy have been closely associated with disability in established MS[34]. In patients with different MS subphenotypes, brain volume quantifiedfrom T1-weighted MR images decreases on average by about 0.7%-1.0% peryear [77]. Spinal cord atrophy quantified from T2 and T1 spine images cor-relates well with measures of disability [36]. In a review study by Barkhof etal.[9] which compared many of the MRI biomarkers that have been used totrack neuroprotection and repair after treatment in MS clinical trials, theyfound that atrophy of whole brain volume and spinal cord on serial MRIare able to demonstrate established and probable response to treatment,respectively, over the course of one year [9].1.1.2 Involvement of Spinal Cord Atrophy in MSSpinal cord atrophy, especially the cervical cord atrophy, is thought to havestrong effect on the locomotor disability in MS. The cervical cord is foundto be significantly smaller in patients with progressive MS, and a strongassociation of spinal cord area and clinical disabilities measured by ExpandedDisability Status Scale (EDSS) score [60] has been demonstrated [46, 59,61, 65, 66]. Cohen et al. [25] found that the cross sectional area (CSA) ofcervical cord most strongly correlates with EDSS (r = -0.52, p = 0.02) in MS,when comparing with other MR measures like cord lesion volume, cerebralgrey matter volume, cerebral white matter volume, whole brain volume andwhole brain lesion volume. A study of 117 patients with SPMS [44] foundthat only cervical cord CSA correlates with EDSS score. A recent studyon 440 patients of a mixed cohort of different MS subtypes [73] reportedthat cervical cord CSA was the most significant MR imaging parameter forexplaining physical disability, as measured with the EDSS score.The relative clinical importance of cervical cord atrophy in MS may re-flect both anatomical and pathological considerations. The cervical cord con-tains all the descending corticospinal fibers which are destined from motortargets in the trunk, arms and legs [25]. It is a cross-road for all cerebrospinal31.1. Backgrounddescending and spinocerebellar ascending pathways. Pathological changes tothe small cervical cord disproportionally affects a myriad of central nervoussystem functions. A histopathological study by De Luca et al. [28] foundthat there were significant reductions in cord area, axon density and fibrediameter in the corticospinal and sensory tracts and these pathological ab-normalities relate closely to functional disabilities. Pathological studies ofspinal cord atrophy suggested that it is the overall axonal degeneration thatis responsible for spinal cord atrophy in MS rather than the tissue loss insidethe individual lesions [33].Accelerated atrophy occurs in the spinal cord in MS at all stages of thedisease, from presentation with clinically isolated symptoms to advancedprogressive forms [19, 77]. Previous cross-sectional studies have found thatupper cervical cord CSA is significantly smaller in patients with SPMS andPPMS compared with healthy controls, and correlates with EDSS [35, 46,61, 65, 66]. The estimated annual atrophy rate of CSA is reported to bearound 1.6% from longitudinal cord atrophy studies in patients with SPMS[43, 46] and around 5% in patients with PPMS [4]. While the spinal cordatrophy in progressive MS is evident, the detection of cord atrophy in RRMShas been more elusive. Multiple cross-sectional studies have found that cordCSA is not reduced in RRMS patients compared to controls [14, 15, 59, 75?] and that could be used to separate progressive MS and RRMS patients[15], while longitudinal studies were able to detect the cervical cord atrophyin RRMS patients over three years [87] and over two years [72].Longitudinal studies provide valuable information with higher statisti-cal power than cross-sectional studies, because they measure within subjectdifference and can overcome the population variance in cord size. However,longitudinal studies on cord atrophy are limited with only a handful studiesconducted [4, 43, 46, 65, 87, 97]. Rashid et al. found a decrease in CSAover 3 years in early RRMS [87], while most cross-sectional studies in thissubgroup [15, 75, 86] have shown no significant difference in CSA betweenRRMS patients and control groups. Longitudinal studies using a mixed co-hort of PPMS, SPMS and RRMS [4, 67, 89, 97] observed significant cordatrophy over the study duration, but correlation between decrease in CSA41.1. Backgroundand EDSS progression was only presented in one study [67]. Furthermore,high scan-rescan variability observed greatly lowered the statistical power ofthe results in previous longitudinal studies.Quantification of spinal cord atrophy is a useful biomarker for monitoringdisease progression and therapeutic drug effects in MS. Lin et al. reportedthat the change in CSA was significantly related to changes in clinical dis-ability in a cohort of the interferon β-1a(Rebif) treatment trial over fouryears [67]. Kalkers et al. found that neuroprotective agents riluzole appearto be more effective in reducing the rate of cervical cord atrophy in the shortterm [53]. Lucas et al. examined the intrathecal injection of triamcinoloneacetonide therapy outcome in progressive MS using upper cervical cord at-rophy and showed a negative correlation between the degree of cord atrophyand treatment benefit [71]. Spinal cord atrophy is thought to be more im-portant than lesion measures in clinical trials when the therapy aim is toprevent disability, especially in progressive MS [77].1.1.3 Spinal Cord Atrophy Measurement MethodsMeasurement of cord atrophy is usually performed on T1-weighted MR scanswith a 3D acquisition sequence. The measurement is conducted at the C2to C5 level, since significant decreases of cord volume are mainly observedin the upper cervical region rather than in the lower thoracic and lumbarareas [59]. Because of the simplicity of the cylinder cord shape, the processof monitoring cord atrophy can be reduced to performing 2D cross sectionalarea measurement. The average CSA of a normal cervical cord is about80 mm2 [66].There has been a range of techniques proposed to measure cord CSA onMRI. Manual outlining on axially acquired gradient echo images were ini-tially produced to estimate cord CSA [57]. A sequential two-year longitudi-nal study of 60 MS patients established a scan-rescan coefficient of variation(COV) of 6%, rendering this method unsuitable for serial monitoring [69].Losseff et al. proposed a semi-automated intensity-based contouring algo-rithm to delineate the cord to measure the CSA [70]. The method is applied51.1. Backgroundto a short length of cord of five slices with the most caudal slice locatedat the C2/C3 intervertebral disc. On each axial image, the operator man-ually defines a region of interest (ROI) which locates the cord to estimatethe mean cord intensity, and then defines another ROI which locates theCSF to estimate the mean CSF intensity. Voxels affected by partial volumeaveraging at cord–CSF interface would have intensity midway between themean cord and CSF intensities on average. Thus, the boundary is detectedby thresholding and region growing with the provided seed point at the in-terface [99]. The scan-rescan COV for an experienced operator is around0.79% [70]. The accuracy of this method is limited by a systematic overes-timation of 4.5%-10% [99] because they do not measure the partial volumeissue on the cord boundary. This method has been employed in a numberof cross-sectional and longitudinal studies [5, 43, 97] and is able to detectsignificant reductions in CSA in SPMS patients over 12 months [4, 43, 97].Coulon et al. developed an automatic surface-based segmentation algo-rithm to obtain the segmentation of the cord and then estimate the cordvolume and CSA [26]. The algorithm optimizes a B-spline surface modelfitting to the cord such that intensity gradient is maximized globally whilemaintaining a smooth tube-like shape constraint to the detected cord edge[99]. With the surface model obtained, it is possible to automatically correctfor alignment of the cord cross-section relative to the acquisition plane, andfor curvature of the cord. However, this method provides less repeatableresults with scan-rescan COV of 1.3%. Furthermore, there is an overall un-derestimation since the procedure tended to ignore voxels affected by partialvolume. Hickman et al. employed this method in their study and found thatthe computed CSA measure at C2/C3 intervertebral disc had significant de-crease over one year in a mixed cohort of PPMS, SPMS and RRMS patients[48].Tench et al. used edge detection to identify the cord–CSF boundary[100], and for the first time addressed the computation of partial volume.For each axial slice image between C1 and C2 level, a Sobel edge detectoris applied with non-maximal suppression to locate all the edges. On axialslice images where the cord has been successfully isolated by the detected61.1. Backgroundedges, the operator places a seed point and the cord region is segmentedby region growing. All the voxels strictly within the cord are assigned anarea value equal to the pixel size; while for voxels on the boundary, they arepartial volumed by the cord and surrounding CSF and each contributes afraction f of the pixel size to the total CSA, which is computed by the localintensities. The total CSA for each slice is then corrected for cord inclinationby the cosine of the angle between the cord axis and vertical axis. The scan-rescan COV of Tench’s method is reported to be 0.55%. There have beentwo clinical studies using this method [86, 100].Horsfield et al. proposed to parametrize the cord cylinder-like surface byits center line and the radii. They realized the segmentation of the cord overan extended length with rather few user inputs. For each axial slice image,the cord is considered as a polygonal shape and the radii are considered as aperiodically varying function of θ, which is the angle of the radii subtended tothe positive x axis. The segmentation process then uses the intensity gradientto update the radii, and refines the center-line to be the centre of the area oneach slice. The optimal surface model is obtained by optimizing the functionusing a multi-scale approach. Measurement of the average CSA is thenderived as the volume divided by the length, where the length and volume canboth computed by integrals of the parametric model. They integrated theiralgorithm in Jim software package (Version 5.0, Xinapse System, Northants,United Kingdom; http://www.xinapse.com/home.php), and a number ofrecent cord atrophy studies were conducted using Jim [25, 59, 89, 103].Chen et al. presented a fully automated spinal cord segmentation al-gorithm which combines deformable registration with topology preservingintensity classification. Their method firstly align an intensity atlas to thetarget image to be segmented by deformable registration, and apply thedeformation on a topology atlas and statistical atlas associated with the in-tensity atlas, which provides the initialization for the segmentation. Thecord segmentation is achieved by iteratively evolving the topology atlas toconvergence [22]. The result of cord atrophy measurement using this methodis consistent with the results reported by Horsfield et al [50]. This methodhas been applied by Oh et al. in two spinal cord atrophy studies [81, 82].71.2. Thesis MotivationRecently De Leener et al. developed a robust, accurate and automaticspinal cord segmentation algorithm based on the propagation of a deformablemodel [27]. The algorithm firstly detects the spinal cord position and orien-tation using a circular Hough transform on multiple axial slices and buildsan initial elliptical tubular mesh. Then a low-resolution deformable modelis propagated along the spinal cord with a local contrast-to-noise adaptationat each iteration. Finally, a refinement process and a global deformationare applied on the propagated mesh to provide an accurate segmentation ofthe spinal cord. This method can manage MR images with poor contrastbetween the spinal cord and CSF by adjusting constraints in the deformablemodel. Results suggested that the achieved accuracy by this method washigher than the manual segmentation, and was slightly higher to the accu-racy obtained by Horsfield’s method [50].With the computed spinal cord segmentation, spinal cord atrophy is ei-ther defined as a measure of change in CSA relative to an age-matched nor-mal control population in cross-sectional studies, or a measure of change inCSA over a period of time in longitudinal studies. In cross-sectional studies,total intracranial volume [47, 75], thecal sac absolute volume [47], the largestskull cross-sectional area [102], and the length of the cord [47, 59, 81] havebeen used to normalize the cord volume to remove inter-subject variationsin cord size in cross-sectional studies. Normalization by the length of thecord has been demonstrated to improve the ability to detect group differenceand strength the clinical-radiological correlations [47, 59, 81]. In longitudinalstudies, the cord CSA or volume measurement is usually carried out at alltime points and then the measurement at each time pint is subtracted toestimate the amount of atrophy over the scanning interval.1.2 Thesis MotivationThere are many challenges in evaluating cervical cord atrophy measurementon MRI, like the small size of the cord, limited resolution of the spine MRimages, involuntary patient motion introduced image artifacts and physiolog-ical fluctuations like water content change. Spinal cord is a small structure81.2. Thesis Motivationwith a diameter around 8 mm, and on current MR images using a spatialresolution of 1mm, the cord is bounded to a region size of less than 100voxels and about 30% of cord area is partial volumed with the surroundingCSF [75]. Furthermore, the magnitude of the cord annual atrophy rate inMS is small with around -1.6% per year reported in SPMS patients. Theserequire the measurement method with high sensitivity and precision, becausesmall absolute errors in the measurement methods can translate into largerelative errors in the results and thus make the small cord changes difficultto detect. For example, the inconsistent findings of reduced CSA in RRMSpatients compared to control subjects may be attributed to the variationsin water content of the cord, which mask out the changes in CSA due tocord tissue loss. Moreover, in the few longitudinal cord atrophy studies con-ducted, the limited scan-rescan reproducibility (with large COV) and highmeasurement variance of the segmentation-based methods hindered the sta-tistical value of their results. We want to address these problems from twoaspects: to investigate the variations due to water content in cord CSA mea-surement and to develop registration-based methods for longitudinal cordatrophy measurement.1.2.1 The Effect of Change in Water Content on SpinalCord CSA Measurement on MRIChange in tissue water content can have significant effects on the spinalcord volume, which has a high composition of water. In MS, edema as-sociated with acute lesions and anti-inflammatory therapy can change thewater content of the cord, and therefore change the cord volume. In normalconditions, the body hydration level makes the total body weight fluctuateby approximately 3% [106], which can potentially change the water contentof the spinal cord. This is particular relevant to the cord volume or CSAmeasurement on MRI, because the MRI signal is primary derived from thehydrogen atoms in water [45]. Change in water content of the cord will berepresented as change over the cord region on spine MR images, which caneventually affect the CSA measurement on the spine MR images.91.2. Thesis MotivationHowever, it is unknown how does the change in water content affect cordCSA measurement and whether the effect would cause substantial variationin the spinal cord atrophy studies. No previous studies has been conducted toinvestigate the effect of change in water content on cord CSA measurement.Considering the small magnitude of cord atrophy rate in MS, the question ofhow does the change in water content affect the CSA measurement requiresexamination. In this thesis, we aim to investigate the dehydration effect oncord CSA measurement. Dehydration caused by restricted fluid intake hasbeen reported to decrease the whole brain volume as measured on MRI by upto 0.55% [31, 94]. Based on the decrease in brain volume following dehydra-tion from previous studies [31, 55, 56, 98], we hypothesize that dehydrationwould lead to a decrease in cord CSA measurement as well.1.2.2 Registration-based Atrophy Measurement Methodsfor Longitudinal Cord Atrophy StudiesScans from multiple time points can be used to directly measure the changein spinal cord volume or area without an accurate estimate of the absolutesize at each time point. Changes can be directly assessed between serialscans using registration-based change analysis methods. This strategy hasbeen proven successfully for reducing measurement variance in longitudinalbrain atrophy measures compared to segmentation-based methods.Boundary shift integral (BSI) [38, 64], and SIENA [96] employ the rigidregistration and approximate the brain volume change by measuring the in-tensity difference (BSI) or intensity profile distance (SIENA) between eachcorresponding pair of edge voxels of the rigidly registered baseline and re-peat images. These two techniques can significantly reduce the variancefrom segmentation errors by assessing the changes directly using intensityinformation. Voxel morphometry-based method Jacobian integration (JI)employs deformable registration and quantifies the change at each voxel byits Jacobian determinant of the deformation field obtained from deformableregistration between the rigidly registered baseline and repeat images. In-tegration of the Jacobian determinant at each voxel over the object region101.2. Thesis Motivationis used to estimate volume change. These registration-based methods havebeen shown to be more robust and accurate than segmentation-based meth-ods by being less sensitive to image quality and imaging system changes andachieving a higher precision with smaller variance in brain atrophy studies[6, 32]. By increasing measurement precision and statistical power, samplessizes can be reduced, which in turn reduces the length and cost of clinicaltrials.Although registration-based methods have been widely used with greatsuccess to measure longitudinal brain volume atrophy, none of the longi-tudinal spinal cord methods uses a registration-based longitudinal changeanalysis strategy. Current cord atrophy measurement methods as reviewedin Section 1.1.3 all require a segmentation of the spinal cord for each subjectin the study. As most of the segmentation-based methods are prone to seg-mentation errors that can be of the order of the amount of cord atrophy seenin MS (with detectable percentage change of 1.16% for Horsfield’s methodand of 0.27% for Tench’s method), we could not help to think whether simi-lar registration-based atrophy measurement methods would be applicable tospinal cord atrophy measurement in longitudinal studies.In this thesis, we applied three registration-based measurement methodsto measure longitudinal cord atrophy. Our hypothesis is that the registration-based measurement methods can reduce the variability in the longitudinalcord atrophy measurement. The cord CSA is inherently small with 30% of itsarea is partial volumed with the surrounding CSF on MR scans with a spatialresolution of 1 mm. The variability in the measurement using segmentation-based cross-sectional methods are mostly derived from the image noise andthe partial volume region. With regularization using different types of trans-formation, registration-based measurement methods may counteract the ex-tend of partial volume as well as enhance the signal to noise by directlylooking at the difference.111.3. Thesis Contributions1.3 Thesis Contributions1.3.1 Dehydration Effect on Cord CSA MeasurementWe designed the scanning protocol with the radiologists and collected T1-weighted MR scans from 10 volunteer subjects at four time points with adehydration and rehydration protocol. We implemented the CSA measure-ment method based on Tench’s method and test two modifications for partialvolume computation. We measured the CSA on all the MR scans at fourtime points using Tench’s method with three different partial volume compu-tation approaches. We also used the Horsfield method which is integrated inJim software to segment the cord and measure the CSA on all the scans. Wecalculated the percentage change in CSA from baseline to each subsequenttime point for all the measurements obtained by Tench method and Hors-field method. Then we used statistical analyses (one-tailed Wilcoxon ranktest) to assess the significance of the changes to determine the dehydrationeffect. We found that dehydration does have significant effect on the cordCSA measurement. A significant decrease in CSA after dehydration was ob-served in the CSA measurement obtained using Tench method (one-tailedWilcoxon rank test p = 0.018) and there was a similar magnitude of decreasein CSA measure obtained using Horsfield method which was close to signifi-cance (one-tailed Wilcoxon rank test p = 0.052). A mean decrease of 0.65%in CSA was observed after dehydration in the results of both methods, whichwas consistent with the results from previous studies of dehydration effecton brain volume measurement.1.3.2 Registration-based Cord Atrophy MeasurementMethodsThe idea of the registration-based cord atrophy measurement method is toestimate the change in cord size by the intensity differences between corre-sponding voxels assessed from registration. We explored ways to improvethe sensitivity of the longitudinal atrophy measurement methods using reg-istration with different levels of regularization in forms of three types of121.3. Thesis Contributionstransformation: rigid registration, deformable registration and constrainedregistration.First, we used rigid registration to align the input images and calculatedthe boundary shift integral to estimate the cord atrophy. The boundary shiftintegral algorithm assumes that a change in cord volume is associated withan exact shift in the cord–CSF boundary. Measurement of the cord atrophycan be estimated by the cord boundary shift, which can be computed by theintegral of intensity differences within specified intensity window betweencorresponding voxels over the cord boundary.Second, we used deformable registration seeking to improve the sensitiv-ity and calculated the integration of Jacobian determinants of voxels overthe cord region in the deformation field to estimate the cord atrophy. Thedeformation field obtained from deformable registration can be used to visu-alize the structural change between the baseline and follow-up images, andis therefore used to quantify the local change by the Jacobian determinantof each voxel. Integration of the Jacobian determinants of the voxels overthe cord region is calculated to estimate the cord atrophy.Third, we used constrained registration with three parameters (two trans-lations and one scaling factor) seeking to improve the robustness of the mea-surement by adding constraints in the registration. The uniform scale factorin the x and y axes obtained from constrained registration is used to estimatethe change in cord size.We evaluated these three registration-based methods on the following testdata sets, 1) two sets of scan pairs with simulated atrophy created by scalingto quantify the measurement precision, 2) the scan–rescan pairs to quantifythe measurement reproducibility, 3) the dehydration scan pairs with demon-strated dehydration effect and an MS patient data set with reported cordatrophy over a two-year interval to quantify the measurement sensitivity. Wecompared the results obtained by three registration-based methods on thetest data sets to the results obtained by two segmentation-based methods[50, 100], which are currently utilized as standard approaches in spinal cordatrophy studies in MS.The three registration-based methods obtained accurate results on the131.4. Thesis Outlinedata set with simulated atrophy. On the data set with rigid transformationand simulated atrophy, the errors in change rates computed by the threeregistration-based methods are with significant smaller variance than thatof the two segmentation-based methods. The scan-rescan reproducibilitycomputed by the three registration-based methods were comparable to thatof the two segmentation-based methods. However, registration-based meth-ods were not able to detect the dehydration effect (0.65% decrease in cordvolume) on the dehydration scan pairs. On the MS patient data set, al-though these registration-based methods detected significant cord atrophyover a two-year interval with smaller measurement variance, they were notas sensitive as the two segmentation-based methods, reporting much smallermagnitudes of cord atrophy rate.To the best of our knowledge, it is the first time that the applicabilityof registration-based methods to measure longitudinal spinal cord atrophyis investigated. Although registration-based methods achieved smaller mea-surement variance than the segmentation-based methods on the test datasets, they are not as sensitive. We argue that the limited spatial resolutionof 1 mm and the inherently small size of the cord are probably the mainreasons for the limited sensitivity of registration-based methods. MR scanswith a spatial resolution of less than 1 mm, and which are able to differen-tiate the grey matter and white matter over the cord region, are requiredfor future studies on longitudinal spinal cord atrophy measurement usingregistration-based methods.1.4 Thesis OutlineAn outline of this thesis is listed as follows:Chapter2 We assessed the dehydration effect to the cord CSA measure-ment on MR scans acquired with a dehydration protocol using two cord CSAmeasurement methods. Significance analysis of the results and discussionabout the dehydration effect are presented in this chapter.141.4. Thesis OutlineChapter3 We presented three registration-based atrophy measurementtechniques and their results on the test data sets. Discussion of each methodand its results are also provided.Chapter4 We summarized this thesis and highlighted the main conclu-sions that can be drawn from our experiments.15Chapter 2Dehydration Decreases theCord Cross-Sectional AreaMeasurement on MRI2.1 IntroductionMRI is commonly used to measure spinal cord atrophy in studies of neu-rodegenerative diseases such as MS [66, 70, 105]. Atrophy of the spinalcord, in particular the cervical cord [59], has been shown to contribute tophysical disability in MS [33, 66]. Most previous MS cord studies haveused the correlation between the CSA of the cord and the EDSS score,a measure of locomotor disability in MS patients, as an indicator of thestrength of the relationship between atrophy and disability [66, 105]. Signif-icant correlations between CSA and EDSS have been found in PPMS andSPMS patients in previous cross-sectional studies and longitudinal studies[4, 47, 52, 67, 91, 102]. In mixed cohorts of progressive MS and RRMSpatients, cord CSA has been found to be significantly smaller compared tohealthy control subjects [47, 66, 70, 102]. However, there have been contra-dictory findings in patients with early MS. A number of studies have foundthat cord CSA is not reduced in RRMS patients [15, 59, 75] compared withcontrols and could be used to separate progressive and RRMS patients [15],while others have shown that cord atrophy is detectable in RRMS patients[87, 97].The inconsistent findings of cord involvement in early MS may be due tomany reasons. The average CSA of a normal adult cervical cord is around162.2. Materials and Methods80 mm2. Most current MRI studies of the cord use a spatial resolution of1 mm2 in each plane, which is around 1% of the cord CSA. Since atrophy isa slow process, with an annual atrophy rate of around −1.6% observed inSPMS patients [43], a high methodological sensitivity is essential to accu-rately estimate the true rate of change on current MRI data.Variation in water content may probably confound the CSA measurementon MRI, because MRI signals are primarily derived from the hydrogen atomsin water [45]. Change in water content due to hydration status can affectbrain morphology as observed on MRI [29, 55, 56]. Duning et al. reportedthat a cohort of 20 healthy volunteers showed a significant decrease in brainvolume of 0.55% (SD = 0.69) after dehydration by restricted fluid intakefor 16 hours and an increase of 0.72% (SD = 0.21) after rapid rehydration[31]. Kempton et al. observed a significant increase in ventricular volumefollowing dehydration via a thermal exercise protocol in two studies of seven[56] and ten [55] healthy subjects. Dehydration can potentially affect the sizeof the spinal cord, which, similar to the brain, also has high water content.Considering the small magnitude of cord atrophy in diseases such as MS,the question of whether cord CSA measurement on MRI is susceptible todehydration requires examination. The goal of this study is to estimate howmuch variation in CSA can be expected due to dehydration to the degreethat would not be considered unusual in daily functioning.2.2 Materials and Methods2.2.1 Subjects and MRI ProcedureThe subjects recruited for this study are 10 volunteers, aged 21 to 32, withno symptoms of neurological disorders or spine problems. The subjects gaveinformed consent in accordance with institutional regulations. Images wereacquired using a Philips Achieva 3T MRI scanner (Philips Medical Systems,Best, The Netherlands) with a dedicated cervical spine receiver coil. Thesequence is a sagittal 3D T1-weighted turbo field echo sequence with param-eters: TR = 8.206 to 8.290 ms, TE = 3.790 to 3.834 ms, flip angle = 8◦, pixel172.2. Materials and Methodsspacing = 0.976× 0.976 mm, slice thickness = 1.000 mm, and dimensions =256 × 256 × 60 pixels. Due to the inclusion of other cord sequences in thesame session, there was insufficient time to acquire brain scans, which wouldhave necessitated a coil change.2.2.2 Dehydration ProtocolWe employed a similar dehydration and rehydration protocol to that usedby Duning et al. to study the effect on whole brain volume [31]. For eachsubject, MR scans were obtained at four time points over two days: 1)baseline, 2) rescan after one hour, 3) the next morning after fasting for atleast 14 hours, 4) after drinking 1.5L of water over the course of one hour.The subjects were asked not to exercise strenuously during the two days oftheir participation in the study.2.2.3 MR Image AnalysisThe cord CSA in each scan was measured using two established semi-automaticmethods. One is an in-house method that is a modified version of the tech-nique by Tench et al. [100]. The other is an independent method by Horsfieldet al. [50] which we used for cross-validation.Modified Tench methodSimilar to the Tench approach, the user interacts with our in-house softwareby marking the region of the cord to be measured in a sagittal view, thensegmenting a number of consecutive axial slices while guided by an edge mapthat in most cases includes a well-defined contour of the cord, as shown inFigure 2.1(b). The operator places a seed point inside the cord on each sliceand initiates a region growing process that is bounded by the contour, asshown in Figure 2.1(c). In the present study, we used a single sagittal land-mark on the most inferior and posterior point of the C2/C3 intervertebraldisc, and the eight slices superior to the landmark were used to compute anaverage CSA.182.2. Materials and MethodsFigure 2.1: a) An axial image of the cervical cord surrounded by CSF. b)Edge map which includes a well-defined contour of the cord. The user-placedseed point is shown. c) Segmented cord region bounded by the edge contour.We have made a number of improvements over the basic implementationof Tench method to allow the user to have greater control over the edge mapand to improve the robustness of the partial volume computation. We usea Canny edge detector [21] which incorporates noise reduction, suppressionof gradients that are not local maximum, and hysteresis thresholding withtwo thresholds. Hysteresis thresholding works by first applying a higher,more restrictive threshold to extract the strongest edges in the image, whichtypically includes a good part of the cord boundary, then applying a sec-ond, lower threshold that is used exclusively to link the strong edges alreadyfound. Our software interface allows the operator to interactively adjustthe higher threshold, and the lower threshold is internally set to half of theupper threshold, and the resulting edge image is immediately displayed tothe user as an overlay. This simple procedure effectively removes spuriousedges within and around the cord that can interfere with region-growing andpartial volume computation.192.2. Materials and MethodsPartial volume computationFor each segmented axial slice, all of the pixels strictly inside the cord areassigned an area value equal to the pixel size (1 × 0.976 mm = 0.976 mm2)while each boundary pixel is assigned a value that is a fraction of the pixelsize, modeled as partial volume (PV) between the cord and surrounding cere-brospinal fluid(CSF). The PV fraction f is calculated using Equation (2.1)f = (Iedge − ICSF)/(Icord − ICSF) (2.1)where Iedge is the intensity of the boundary pixel, ICSF and Icord are theintensities of the CSF and cord. The fraction f is then multiplied by thepixel size to obtain the contribution of the boundary pixel to the slice area.We tried three approaches to estimate the intensity of CSF ICSF and theintensity of the cord Icord in Equation (2.1). The first approach, denoted byPV1, is to interpolate the image and estimate ICSF and Icord at a distance ofone voxel width from the edge voxel along their gradient directions on bothsides. The second approach, denoted by PV2, is to interpolate the imageand estimate ICSF and Icord by four sample points neighboring the edge voxelalong their gradient directions on both sides, as shown in Figure 2.2. The firstpoint is located at a distance of one voxel width from the edge voxel along itsgradient direction, and three more sample locations are computed from thefirst point, with one further along the line of the strongest gradient, and theother two perpendicular to it. If a sample location falls on an edge pixel asdetermined by the Canny detector, it is unlikely to be a “pure” sample and istherefore discarded. The third approach, denoted by PV3, uses the medianintensity value of the cord region on each slice to approximate ICSF and themedian intensity value of the CSF region on each slice to approximate ICSF;the cord region is determined by the one pixel eroded region of the cordsegmentation and the CSF region is determined by the one pixel dilatedregion of the cord segmentation minus itself.The CSA for each slice is calculated by summing the contributions fromthe interior and boundary pixels. A correction factor is then applied tothe CSA value to compensate for the fact that the cord is rarely perfectly202.2. Materials and MethodsFigure 2.2: Four CSA sample points (yellow) in a T-shaped neighborhood ofthe boundary pixel (red). The mean intensity of the CSF sample points isused with the mean intensity of four cord sample points, computed similarlywith a neighborhood inside the cord, to compute a partial volume estimatefor the border pixel.perpendicular to the axial image plane, resulting in an overestimation ofthe area. Using the same procedure preformed by Tench et al. [100], thecorrection factor is the cosine of the angle between the medial axis of the cord,as estimated by fitting a straight line through the centers of the segmentedslices, and the perpendicular to the axial plane.Horsfield methodIn the method by Horsfield et al.[50], the operator first performs angle cor-rection by rotating the volume so that its edges are parallel to the cord inthe region of interest (C1-C2 in the current study). Then the operator placeslandmarks at C1-C2 region, and on every 10th slice in-between. The soft-ware then uses these landmarks to automatically initialize a 3D surface andsegments the spinal cord by fitting the surface to the image. There are threekey parameters in the algorithm related to cord size and shape, includingnominal cord diameter, number of shape coefficients, and order of longitudi-nal variation, which can be used to customize the fitting process. We usedthe default values in our analysis because the study is of healthy subjectsand the segmentation appeared to be visually accurate.The total cervical cord volume was calculated by the software as an212.3. Resultsintegral on the final fitted surface model. The average cervical cord CSAwas then derived as the total volume divided by the length of the segmentedregion.Statistical analysisThe percentage changes in CSA from baseline to the other three time pointswere calculated for each patient, and the mean changes between from thebaseline to the other three time points were used to determine the scan-rescanreproducibility, the dehydration effect and rehydration effect. The statisticalsignificances of the changes were assessed using one-tailed Wilcoxon ranktest, with p < 0.05 as the threshold.2.3 ResultsThe cervical cord CSA of the 10 subjects at four time points were assessed bythe modified Tench method using three different PV computation approaches(PV1, PV2 and PV3 described in Section 1.1.3). The change rates from thebaseline to the other three time points calculated by PV1, PV2 and PV3are explained in Table 2.1. The scan-rescan coefficient of variation (COV) ofthe results using PV2 and PV1 were 0.634% and 0.616%, respectively. Thescan-rescan COV of the results using PV3 was 0.736%, higher than that ofPV1 and PV2. The results of PV1 and PV2 both demonstrated significantdecrease in cord CSA after dehydration with one-tailed Wilcoxon rank testp = 0.010 and p = 0.018, respectively. Results of PV3 did not demonstrateany significant change in cord CSA after dehydration (one-tailed Wilcoxonrank test p = 0.080). Since the results of PV2 had slightly smaller scan-rescan COV than the results of PV1, we chose PV2 as the partial volumecomputation approach used in our in-house software.In the results of our in-house software (Tench method using PV2), thecervical cord CSA of the 10 subjects at baseline were within the range of69.13 − 92.12 mm2. The scan-rescan coefficient of variations was 0.616%.After dehydration, we observed a mean decrease of -0.654% (SD = 0.778, p222.3. ResultsTable 2.1: Statistical results of the percentage changes in CSA computed byTench method using three different PV computation approaches (PV1, PV2and PV3). A significant reduction in cord CSA is observed after dehydration,with a return to the baseline-equivalent after rehydration.Methods Mean change% (SD)One-tailedWilcoxontest (>0)One-tailedWilcoxontest (<0)∆scan-rescan PV1 -0.256(0.821) p = 0.052 p = 0.958PV2 -0.217(0.794) p = 0.080 p = 0.934PV3 -0.084(0.989) p = 0.652 p = 0.385∆baseline PV1 -0.695(0.801) p = 0.010 p = 0.958to dehydrated PV2 -0.654(0.778) p = 0.018 p = 0.986PV3 -0.465(0.891) p = 0.080 p = 0.935∆baseline PV1 0.073(1.354) p = 0.722 p = 0.312to rehydrated PV2 0.121(1.318) p = 0.721 p = 0.313PV3 0.251(1.213) p = 0.813 p = 0.216Table 2.2: Statistical results of the percentage changes in CSA computed byour in-house method (Tench method using PV2) and Jim software (Hors-field method). For both measurement methods, a decrease in cord CSA isobserved after dehydration, with a return to the baseline-equivalent afterrehydration.Method Mean change% (SD)One-tailedWilcoxontest (>0)One-tailedWilcoxontest (<0)∆scan-rescan in-house -0.207(0.794) p = 0.080 p = 0.934Jim -0.452(1.197) p = 0.161 p = 0.862∆baseline in-house -0.654(0.778) p = 0.018 p = 0.986to dehydrated Jim -0.650(1.071) p = 0.052 p = 0.958∆baseline in-house 0.121(1.318) p = 0.721 p = 0.313to rehydrated Jim 0.057(1.129) p = 0.539 p = 0.500∆dehydrated in-house 0.782(1.208) p = 0.967 p = 0.042to rehydrated Jim 0.715(0.939) p = 0.990 p = 0.014232.4. Discussion= 0.018 for one-tailed Wilcoxon rank test) in cord CSA as shown in Figure 2.3and Table 2.2. After the rehydration procedure, the mean cord CSA was notsignificantly different from baseline (mean change = 0.121%, SD = 1.318).However, the mean change in CSA between the dehydrated and rehydratedstates was significant (mean change = 0.782%, SD = 1.208, p = 0.042 forone-tailed Wilcoxon rank test).Measured using the Jim software (Horsfield method), the cervical cordCSAs at baseline were within the range of 72.48 − 91.28 mm2. The scan-rescan COV of the results of Horsfield method was 0.899%. We observeda mean change in CSA of -0.650% (SD = 1.071, p = 0.052 for one-tailedWilcoxon rank test) after dehydration compared with baseline, as shown inFigure 2.4 and Table 2.2. After rehydration, the mean CSA measurementincreased by 0.715% (SD = 0.939, p = 0.014 for one-tailed Wilcoxon ranktest) compared to the dehydrated state, but was not significantly differentfrom baseline.2.4 DiscussionWe investigated the effect of mild to moderate dehydration and rehydrationon CSA measurement of the cervical spinal cord in healthy subjects. Wehave observed a decrease in cervical cord CSA after fasting for an overnightperiod that would not be considered unusual in daily functioning.We used two independent CSA measurement methods in our analysis toaccount for any bias introduced by either method. The two methods agreedwell on the mean change in cervical cord CSA observed after dehydration (-0.654% for the Tench method and -0.650% for the Horsfield method), which issimilar to the change of -0.550% observed by Duning et al. [31] in their studyon dehydration effect to whole brain volume. In addition, the two methodsagreed well on the mean change between the dehydrated and rehydratedstates (0.782% for the Tench method and 0.715% for the Horsfield method),which is similar to the 0.720% increase in whole brain volume that theyfound.We tried two partial volume computation approaches other than the one242.4. Discussionscan−rescan dehydration rehydration−3−2−10123Percentage change in CSA from baseline (%)Percentage change in cervical cord CSA computed by Tench methodFigure 2.3: The percentage change in cervical cord CSA from baseline to theother three time points computed by our in-house software (Tench method).Each circle represent an individual subject, and the star and error bar rep-resent the means and the standard deviations. Dehydration and rehydrationappear to affect CSA measurements.252.4. Discussionscan−rescan dehydration rehydration−3−2−10123Percentage change in CSA from baseline (%)Percentage change in cervical cord CSA computed by Horsfield methodFigure 2.4: The percentage change in cervical cord CSA from baseline to theother three time points using software Jim (Horsfield method). Each circlerepresent an individual subject, and the star and error bar represent themeans and the standard deviations. Dehydration and rehydration appear toaffect CSA measurements.262.4. Discussionexplained in Tench et al.’s paper to estimate the CSF intensity ICSF andthe cord intensity Icord in Equation(2.1), seeking to improve the accuracyof the calculated PV values. Our experiments on the PV computation em-phasize that the accuracy of PV values which contribute to around 30% ofthe cord CSA is essential to the precision and sensitivity of the cord CSAmeasurement. The results of PV computation approach using median in-tensity of voxels over the CSF and cord region to estimate ICSF and Icordon each slice did not detect any dehydration effect. The results of the othertwo PV computation approaches which locally estimate the cord intensityand CSF intensity demonstrated significant dehydration effect. The CSFintensity and cord intensity in Equation(2.1) should be estimated locally foreach edge voxel to compute the partial volume fraction.The brain and spinal cord are directly connected and have similar mech-anisms for their regulation of water balance [13, 93], so it is reasonable tospeculate that the current results reflect the cord exhibiting an incompletecompensation to fluid deficiency, similar to what has been observed in thebrain. Overall, our results lend further evidence that hydration status canaffect volumetric measures of the central nervous system on MRI.However, there are a number of limitations in our study, including thesmall size of the cord, the reproducibility of the measurement methods, andthe small sample size. To understand these limitations, it is helpful to ex-amine the precision when using each measurement method. Horsfield et al.estimated the minimum area change detectable by their method using thefollowing equation: minimum detectable change = group mean × intra-scanCOV × 1.96 = 0.87mm2 for their study. Alternatively, the detectable per-centage change can be estimated by multiplying the intra-scan COV by 1.96to obtain the change that can be detected with 95% confidence, which yields1.16% and 0.27% for the Horsfield and Tench methods, respectively, usingvalues from their published studies. As the intra-scan COV is image- andoperator-dependent, we also estimated the precision of the two methods withour current data, which resulted in detectable percentage changes of 1.08%and 0.09% for the Horsfield and Tench methods, respectively. Our estimatedchange due to dehydration was 0.65% for both methods, which meets the 95%272.4. Discussionconfidence threshold of the Tench method, but is below that of the Horsfieldmethod, which favors the former method but does not preclude the possibil-ity of the latter method detecting a systematic change. Given that the twomethods agree well on both the effects of dehydration and rehydration, andthat at least one is confirmed to have the neccessary sensitivity on this data,we conclude that the change observed was likely real. It should be notedthat because the Tench method was our own implementation, the operatorwas very familiar with the software, which may explain the better repro-ducibility, but otherwise, these results do not indicate that either method issuperior.Another limitation is that no brain scans (due to limited scanning time)were collected and a firm conclusion cannot be made about whether simi-lar magnitudes of change can be expected in both structures. In addition,while the Duning study [31] found that mean brain volume increased beyondbaseline after rehydration, the mean cord volume in our study was signifi-cantly increased only when compared to the dehydrated state, and not tobaseline. A related confounding factor is the effect of brain volume changeson cord position. The cord could in theory be shifted rostrally due to theshrinkage of the brain after dehydration and because the cord does not havefixed landmarks (one could conceivably use the peripheral nerves, but theyare very small and quite far apart), it would be very difficult to ensure thatexactly the same level of cord is being measured. However, given that thedehydration effect on brain volume is likely to be less than 1%, the cord shiftis likely to be correspondingly small, and in the absence of local injury, thecord diameter varies smoothly over its length, so we expect the effect of cordshift to be minor.While there is increasing evidence that hydration status is a confoundingfactor in the volumetric analysis of MRIs, there is little information on howto correct for such fluctuations and whether this is even possible. Traditionalmethods for monitoring hydration status, such as urinalysis, are unlikely tobe reliable due to the complex nature of the body mechanisms for water bal-ance, which involves multiple systems whose health can change over time,even in normal aging. Nonetheless, studies of the hydration effect on brain282.4. Discussionand cord measures are valuable for improving the understanding of studyresults that may be affected by changes in water content. The results of ourcurrent study have particular implications for studies of spinal cord disordersthat involve an inflammatory response. For example, previous cross-sectionalstudies have shown that cord volume in MS patients can be increased (withvarying levels of statistical significance) when compared to healthy controls,especially in early MS [59, 75]. These findings are somewhat unintuitivefor a neurodegenerative disease, but are hypothesized to reflect the presenceof inflammation and associated edema, which can induce a temporary in-crease in cord volume. Our current results help to bolster that hypothesisby demonstrating that measurable volume changes are associated with fluc-tuations in water content. In a longitudinal study of MS patients who hada spinal cord-related relapse [24], the patients showed a decline in cervicalspinal cord area of approximately 0.7% monthly during the follow-up periodof six months, even though they were improving clinically, which may beattributable to a resolution of inflammation and edema. Our current resultsshow that changes of that magnitude can occur in a short period of time, andthat frequent cord scanning after an acute episode can be a potentially usefulmethod for monitoring edema. This is especially true given that certain MStherapies, such as natalizumzab, have been shown in human subjects to havea pseudoatrophy effect on the brain [78, 92, 106] and in preclinical studiesto have a strong anti-inflammatory effect on the cord.In conclusion, we have demonstrated that hydration status affects spinalcord CSA measurements on MRI and should be considered a source of vari-ability in clinical studies of spinal cord atrophy. Our results also supportthe use of frequent MRI scanning to monitor conditions that may involvechanges in water content, such as the inflammation and edema associatedwith acute spinal cord pathology.29Chapter 3Registration-based CordAtrophy MeasurementMethods3.1 MethodsRegistration-based atrophy measurement methods, which directly quantifythe change in volume between registered image pairs by registration, havebeen proven to be more precise and sensitive than segmentation-based meth-ods in longitudinal whole brain atrophy measurement. However, none of themethods for accessing longitudinal cord atrophy uses a registration-basedchange analysis strategy. Current methods used to assess spinal cord at-rophy in patients with MS, as reviewed in Chapter 1 Section 1.1.3 , are allcross-sectional methods based on the cord segmentation. In this chapter,we described the details of the pre-processing and three registration-basedatrophy measurement methods that we implemented for longitudinal spinalcord atrophy measurement with the aim of improving the sensitivity andprecision of the measurement: boundary shift integral, Jacobian integrationand scale factor based on constrained registration (composed of rigid andscale transformation).3.1.1 PreprocessingRigid RegistrationThe baseline scan and follow-up scan need to be positionally registered forregistration-based measurement methods to yield meaningful results, be-303.1. Methodscause the intensity change on MR scans derived from real cord tissue losscan be small compared with the differences caused by patient movement andcord mismatch. For example, there is rigid transformation and 2% simulatedatrophy created by scaling between Figures 3.1 (a) and 3.1 (b). Because ofthe spatial mismatch, the intensity changes due to the scaling atrophy aremasked out by the intensity changes brought by rigid transformation, asshown on their difference image Figure 3.1 (c). After rigid registration, thesetwo images are resampled as shown in Figures 3.1 (d) and 3.1 (e). The differ-ence image of these two registered images is shown in Figure 3.1 (f), whichexclusively shows the intensity changes due to scaling atrophy and makes itpossible for the change analysis to accurately assess the simulated atrophy.The steps to register the baseline scan and follow-up scan in our experi-ments are described as follows.Firstly, the baseline and follow-up scans were segmented using our in-house software described in Chapter 2 Section 1.1.3 to obtain the cord seg-mentation which contains 11 slices above and 5 slices below the C2/C3 inter-vertebra disc, with partial volume values on the cord boundary. The binarybaseline segmentation S(1) and follow-up segmentation S(2) of the size of25× 25× 17 voxels were created by cropping and using the threshold of 0.6on the partial volume region. The baseline and follow-up scans were alsocropped to be 25×25×17 axial subvolumes I(1) and I(2), respectively, usingthe cord segmentations S(1) and S(2).We assumed that rigid transformation is able to align the cord region weexamined (around a length of 16 mm) although the cord moves articulatelywith the vertebra. The baseline segmentation S(1) was dilated by one voxelslice by slice as labeled by the yellow line in Figure 3.3 (a). The dilatedcord region in the baseline image was used to provide a mask for computingthe mean square intensity difference cost function in the rigid registration toalign the baseline image I(1) and follow-up image I(2). The resulting rigidtransformation T was split into forward transformation Tfwd and backwardtransformation Tbwd. The baseline image I(1) and baseline segmentation S(1)were resampled using the backward transformation Tbwd to obtain the reg-istered baseline image I(1)r and registered baseline segmentation S(1)r . The313.1. Methodsfollow-up image I(2) and follow-up segmentation S(2) were resampled usingthe forward transformation Tfwd to obtain the registered follow-up imageI(2)r and registered follow-up segmentation S(2)r . This resampling proceduretransforms the baseline and follow-up images to a position that is halfwaybetween them to ensure that the two images being compared undergo equiv-alent processing steps.(a) An axial slice of thebaseline image(b) An axial slice of thefollow-up image(c) The difference image ofthe baseline and follow-upimages(d) An axial slice of theregistered baseline image(e) An axial slice of theregistered follow-up image(f) The difference image ofthe registered baseline andfollow-up imagesFigure 3.1: Illustration of the difference image of the baseline and follow-up images before and after rigid registration. The baseline image (a) andfollow-up image (b) are created from one control MR scan by scaling and rigidtransformation. After rigid registration, the difference image (f) exclusivelyshows the intensity difference introduced by scaling atrophy.323.1. MethodsIntensity NormalizationIn order to maximize the accuracy of registration-based change analysis, theintensity of the same tissue on the baseline scan and the follow-up scan needto be as similar as possible. We performed the intensity mapping using themean intensities of the CSF and cord on the registered baseline and follow-upimages to correct for intensity and contrast differences. Firstly the registeredbaseline segmentation S(1)r and follow-up segmentation S(2)r were convertedto binary images S(1)r b and S(2)r b using a threshold of 255*20%. The CSF maskregion was defined as the binary segmentation dilated by one voxel minusitself ((S(i)r b ⊕ B) \ S(i)r b , where i ∈ {1, 2}). We utilized the morphologicaloperator B, consisting of the origin and its nearest four neighbors in twodimensions. We calculated the mean and standard deviation of the intensitiesover the CSF region on the registered baseline and follow-up images, whichare (µ(1)CSF, σ(1)CSF) for I(1)r and (µ(2)CSF, σ(2)CSF) for I(2)r . Secondly the cord maskregion is defined as the binary segmentation eroded by one voxel (S(i)r b 	 B,where i ∈ {1, 2}). We calculated the mean and standard deviation of theintensities over the cord mask region on the registered baseline and follow-upimages, which are (µ(1)cord, σ(1)cord) for I(1)r and (µ(2)cord, σ(2)cord) for I(2)r .We performed a line fitting from the intensities of the follow-up im-age to the intensities of the baseline image using their two correspondingmean intensities (µ(2)cord, µ(1)cord) and (µ(2)CSF, µ(1)CSF). The mapping equation wasdefined by y = ax + b, where a = (µ(1)cord − µ(1)CSF)/(µ(2)cord − µ(2)CSF), b =(µ(1)CSFµ(2)cord − µ(2)CSFµ(1)cord)/(µ(2)cord − µ(2)CSF). The intensities of the registeredfollow-up image I(2)r were then normalized using the mapping equation tocreate the normalized registered follow-up image I(2)r n .The registered and normalized baseline and follow-up images I(1)r andI(2)r n were passed into the change analysis stage. Three different registration-based methods were implemented to estimate the change in cord volumewith input images of I(1)r and I(2)r n , as explained individually in the followingthree sections.333.1. Methods3.1.2 Boundary Shift IntegralThe boundary shift integral (BSI) is a widely recognized technique firstlyproposed by Fox et al. [38] to measure atrophy directly from the differenceimage of the registered serial MR images. It has been successfully used tomeasure the volume change in the whole brain [38, 64], the hippocampus[10, 12, 74], the caudate [49] and the ventricles [85]. Results from these ap-plications have shown that the BSI algorithm is able to detect the differencein the atrophy rate in these tissues to distinguish the patient and healthygroups in a range of neurological disorders including Alzheimer’s disease(AD) [11, 12, 18] and MS [6]. The rate of cerebral atrophy in patients withMS was 3 times that of aged matched controls over a 1-year period in a pre-vious study using BSI [39]. Furthermore, the whole brain atrophy assessedby BSI has been used as an outcome measure in therapeutic interventionstudies for AD [37].The boundary shift integral algorithm assumes that a change in volumeof a soft tissue object must be associated with an exact shift in the bound-ary of that object. The shift of the tissue boundary results in an exactlyequivalent shift of the signal which is constructed from the MR samples [41].Hence, if the baseline scan and follow-up scan are registered, in the areaaround the boundary of the registered scans Ibase and Ireg, the intensities ofIbase(x, y, z) and Ireg(x, y, z) should shift by an amount corresponding to theposition shift; this permits the precise measurements of boundary shifts bydetermining intensity shifts in the boundary region. The change in volumecan thus be estimated by computing the integral of all of the boundary shifts.If ibase(x) is the MR signal along the cord boundary at the location x ofthe baseline scan and ireg(x) is the MR signal at location x of a registeredfollow-up scan on which there has been a boundary shift of ∆w from thebaseline, then these two MR signals can be related by ireg(x) = ibase(x+∆w)in the region of the cord boundary [41]. Moreover, if the intensity changesmonotonically across the cord boundary, then ibase(x) and ireg(x) will takethe form shown in Figure 3.2. We can therefore define inverse functionsxbase(i) and xreg(i), related by xreg(i) = xbase(i)−∆w.343.1. MethodsFigure 3.2: Example of an idealized one dimensional cord boundary shiftbetween the intensity ibase(x) along x axis on baseline scan, and the intensityireg(x) along x axis on registered follow-up scan. An estimate of the shiftalong x axis, ∆w, may be obtained as the shaded area divided by the intensityrange (I1 − I2) . This strategy can be extended to three dimensions toestimate the cord volume loss ∆v.A simple estimate of ∆w can be obtained using ∆w = xbase(i)− xreg(i),where i may be any value within the intensity range of the cord boundaryregion [IR, IS]. In 3D T1 weighted spine MR images, the cord is brighterwhile the CSF is darker, thus IR is the intensity on the CSF side of theboundary and IS is the intensity on the cord side of the boundary. A morerobust estimated can be obtained by averaging the estimates of ∆w over anintensity range [I2, I1], as shown in Equation (3.1).∆w =1I1 − I2∫ I1I2(xbase(i)− xreg(i))di (3.1)where IR ≤ I2 < I1 ≤ IS.Equation (3.1) can alternatively be expressed as an integral with respectto x over the boundary, as written in Equation (3.2). Equation (3.1) and353.1. MethodsEquation (3.2) are equivalent by considering that both integrals evaluate thearea of the shaded region in Figure 3.2.∆w =1I1 − I2∫boundary(Clip(ibase(x), I1, I2)− Clip(ireg(x), I1, I2))dx (3.2)where IR ≤ I2 < I1 ≤ IS, and Clip(a, I1, I2) =I2 a < I2a I2 ≤ a ≤ I1I1 a > I1If we extend this strategy to three-dimensions and determine the integralnumerically by evaluating the integrand at small sampling intervals, thevolume change can be calculated as shown in Equation (3.3)∆v =KI1 − I2×∑x,y,z∈E(Clip(Ibase(x, y, z), I1, I2)− Clip(Ireg(x, y, z), I1, I2))(3.3)where K is the unit voxel volume, E is the set of voxels in the border regionof the cord, Ibase(x, y, z) and Ireg(x, y, z) are the voxel intensities on theregistered baseline and follow-up scans at (x, y, z), and the intensity rangeof the integral [I2, I1] is referred to as the intensity window.In our application to the cord, I(1)r and I(2)r n are the registered baselineand follow-up images, and S(1)r and S(2)r are the corresponding segmentationimages. The resampled segmentation images S(1)r and S(2)r were convertedto binary images S(1)r b and S(2)r b using a threshold of 255*50%. We definedthe border region E as the set of voxels that are members of the unionof S(1)r b and S(2)r b dilated by an operator B slice by slice but not membersof the intersection of S(1)r b and S(2)r b eroded by an operator B slice by slice,as explained in Equation (3.4). We utilized the morphological operator B,consisting of the origin and its nearest four neighbors in two dimensions.The region between the yellow line and blue line on Figure 3.3(b) shows theborder region E created by Equation (3.4) overlaid on the registered baselineimage I(1)r , where the outer boundary of the border region is labeled by theyellow line and the inner boundary of the border region is labeled by the363.1. Methodsblue line.E = ((S(1)r b ∪ S(2)r b )⊕B) \ ((S(1)r b ∩ S(2)r b )	B) (3.4)(a) The boundary of the dilated cordsegmentation of a baseline croppedcord image I(1) is labeled by the yel-low line. The dilated baseline cordsegmentation is used as a mask forthe rigid registration between thebaseline image I(1) and repeat imageI(2).(b) The border region is overlaid onthe registered baseline cord imageI(1)r . The outer boundary of the bor-der region is labeled by the yellowline. The inner boundary of the bor-der region is labeled by the blue line.Boundary shift integral is computedover the border region.Figure 3.3: Illustration of the dilated cord segmentation labeled on the base-line cord image I(1), and the border region labeled on the registered baselinecord image I(1)r .Intensity Window SelectionThe evaluation of BSI requires the appropriate selection of an intensity win-dow. The intensity window [I2, I1] should be selected such that it falls en-tirely within the intensity transitions associated with the boundaries of astructure. Fox et al. [38] selected the intensity window for applying the BSIto whole brain atrophy measurement by comparing simulated and measuredvolumes of brain loss over a range of intensity window parameter values.Boyes et al. [17] improved the accuracy of BSI results by determining theintensity window parameters based on comparing the BSI to segmented vol-ume differences for a range of windowing parameters. Hobbs et al. [49] used373.1. Methodsthe mean and standard deviation of different tissues involved to automati-cally calculate the intensity window. They took the median of all the specificoptima of the subjects in their data set to be the optimal intensity windowin their application using BSI to estimate caudate atrophy in a cohort study.Leung et al. [64] proposed determining the intensity window by the meanand standard deviation of CSF and GM which are estimated by the k-meansclustering in the border region of the brain in their application to measurewhole brain atrophy.For our application to compute the cord BSI, we adopted the strategyHobbs et al. proposed for automatic intensity window selection. In or-der to capture most of the tissue-type change between the cord and CSF,it was desirable to ignore changes within the same tissue type and max-imize the changes between different tissue types. Therefore, the inten-sity window for the cord boundary shift computation was chosen to be[µ(1)CSF + σ(1)CSF, µ(1)cord − σ(1)cord], where µ(1)CSF and σ(1)CSF are the mean and stan-dard deviation of intensities of the voxels in the CSF region on the registeredbaseline image I(1)r , and µ(1)cord and σ(1)cord are the mean and standard deviationof intensities of the voxels in the cord region on I(1)r .With the selected intensity window, BSI was computed using Equation(3.3) over the border region between I(1)r and I(2)r n on eight slices above theC2/C3 intervertebra disc landmark. Percentage change rate in cord volumewas calculated by dividing the computed BSI by the cord volume of thebaseline scan over eight slices.3.1.3 Jacobian IntegrationThe deformation field obtained from deformable registration makes it possi-ble to visualize structural changes that occur over time by deforming a sub-ject’s baseline scan onto their subsequent scans, and to statistically quantifylocal changes [62]. Based on the analysis of the Jacobian determinant ofthe deformation field obtained, temporal changes due to growth or atrophycan be identified [51]. This technique has been widely applied to assess theatrophy of whole brain as well as regional areas of the brain using different383.1. Methodsforms of deformable registration [11, 42, 101] .The quantification of the amount of warping applied at each voxel bythe deformation field T (x, y, z) can be locally derived from the Jacobian ma-trix ∇T (x, y, z) of the deformation in terms of determinant det(∇T (x, y, z))[23] . A Jacobian matrix ∇T (x, y, z) is obtained for each voxel by takingthe secondary derivative of the deformation field T (x, y, z), as defined inEquation (3.5) .∇T (x, y, z) =∂Tx(x,y,z)∂x∂Tx(x,y,z)∂y∂Tx(x,y,z)∂z∂Ty(x,y,z)∂x∂Ty(x,y,z)∂y∂Ty(x,y,z)∂z∂Tz(x,y,z)∂x∂Tz(x,y,z)∂y∂Tz(x,y,z)∂z (3.5)The determinant det(∇T (x, y, z)), denoted by det(J), represents an expan-sion if det(J) > 1 or a contraction if det(J) < 1 at each voxel. The change invoxel size after deformation calculated by (det(J)−1) can then be integratedover a specified region to obtain an approximation to the total volume changein this region. The estimated total volume change divided by the number ofvoxels in this region yields an average measure of volume change rate overthis region.Figures 3.4 (a) and 3.4 (b) show two images created from a spine MRI ofa control subject, with simulated atrophy between them created by scaling.The baseline image Figure 3.4 (a) is created by applying a scale factor of1.0075 on both the x and y axes of a spine MRI from a control subject toobtain 1.5% explansion in volume, and the follow-up image Figure 3.4 (b)is created by applying a scale factor of 0.9925 on both the x and y axesto the same MR scan to obtain 1.5% shrunk in volume. In this way, 3%simulated scaling atrophy is created between the baseline image and follow-up image. Figure 3.4 (c) shows the deformation field, which is obtained fromdeformable registration between the two images shown in Figures 3.4 (a) and3.4 (b), overlaid on the baseline image over the cord region. There is obviousshrinkage of the cord region, illustrated by the deformation vectors pointinginto the cord region on Figure 3.4 (c).The deformable registration aims to find the displacement s(p) at each393.1. Methods(a) An axial slice of thebaseline image(b) An axial slice of thefollow-up image(c) The deformation vec-tors of the deformationfield over the cord regionoverlaid on the baseline im-age.Figure 3.4: Illustration of the deformation field generated by images with3% simulated atrophy. The baseline image (a) and the follow-up image(b) are created from one control MR scan by scaling to create 3% atrophybetween them. After deformable registration, the deformation field over thecord region in (c) demonstrates the expected shrinkage of the cord, with themajority of the deformation vectors pointing into the cord.voxel p in order to capture the shape change (similarity) as well as constrainthe smoothness of the deformation field (regularization) from the movingimage to the fixed image. The optimization of the deformable mapping canbe summarized briefly as:1. Compute the update field u by minimizing the similarity function2. Update the deformation field s with u3. Regularize the deformation field sThe non-rigid registration algorithm employed in our experiment is thesymmetric log-domain diffeomorphic demons proposed by Vercauteren et al.[104]. The energy function to be minimized is defined in Equation (3.6),E(F,M, s) =1σ2iSim(F,M, s) +1σ2TReg(s) (3.6)where F is the fixed image, M is the moving image, s is the deformation403.1. Methodsfield, Sim(F,M, s) = 12‖F −M ◦ s‖2, Reg(s) = ‖∇s‖2, σi measures the localintensity noise, and σT controls the amount of regularization we need.In order to register F and M , we need to optimize Equation (3.6) over agiven space. The diffeomorphic demons algorithm performs the optimizationin a space of diffeomorphisms to enforce invertibility by defining an expo-nential mapping from the vector space to diffeomorphisms [104]. At eachiteration, the algorithm computes an update step u by minimizing the corre-spondence energy Ecorrs (u) = ‖F −M ◦ (s ◦ exp(u))‖2 + ‖u‖2 with respect tou using a Newton method and then maps it to the space of diffeomorphismsthrough the exponential exp(u). Updating the deformation field s with theupdate step u is thus in the form of s← s ◦ exp(u) [104].In order to easily compute the inverse of the spatial transformation, thecomplete spatial transformation s is encoded through the exponential of asmooth stationary velocity field v where s = exp(v) [7, 104], thus the inverseof the spatial transformation s−1 can be obtained by exp(−v) in the logdomain. The update step s ← s ◦ exp(u) is cast into the form of v ←log(exp(v) ◦ exp(u)) [104]. The updated transformation log(exp(v) ◦ exp(u))can then be approximated by the first two terms of the Baker-Campbell-Hausdorff formula v ← v+u+ 12 [v, u], where [v, u] is the Lie bracket: [v, u] =Jac(v)× u− Jac(u)× v [16].To make the registration framework symmetric, the global energy issymmetrized by sopt = arg mins(E(I0, I1, s) + E(I1, I0, s−1)), where s−1 =exp(−v) in the log domain, and E is defined by Equation (3.6), I0 and I1are the two input images of the registration. The symmetric update is themean of the forward and backward update steps in each iteration [30]. Theregistration is optimized using a multi-resolution scheme.To sum up, the multi-resolution symmetric log-domain diffeomorphicdemons registration is performed using the following steps :• Choose a starting deformation field v• For each resolution level, resample the deformation field v obtainedfrom the previous resolution level be the same size as the fixed imageat the current resolution level and use the resampled deformation field413.1. Methodsto initialize the registration• Iterate until convergence1. Compute the forward demons force update field uforward where I0plays the role of the fixed image F and I1 plays the role of themoving image M2. Compute the backward demons force update field ubackward whereI1 plays the role of fixed image F and I0 plays the role of themoving image M3. Compute the symmetric update step u = 12(uforward − ubackward)4. Update the current deformation field v with the symmetric updatestep u and apply the diffusion-like regularization v ← Kdiff ∗ (v+u+ 12 [v, u]), where Kdiff is a Gaussian convolution kernel with theparameter σ set to 1.05. Compute the mean square error (MSE) after applying the updateddeformation field v and compare the current MSE value with thetwo MSE values obtained from the previous two iterations. If thecurrent MSE value is not smaller than the previous two values,convergence is obtained; otherwise continue to iterateIn our application to compute the cord change rate using Jacobian in-tegration (JI), we used this deformable registration algorithm to obtain thedeformation field between the registered baseline image I(1)r and follow-upimage I(2)r n in our experiments. Firstly the resampled baseline segmentationS(1)r was converted to a binary image S(1)r b using a threshold of 255*50% andS(1)r b was dilated by two voxels slice by slice to create the dilated cord maskregion. Then the registered baseline image I(1)r and registered follow-up im-age I(2)r n were masked by the dilated cord segmentation to create two imagesI(1)rm and I(2)r nm with voxels outside the dilated cord region being zero. Themasked images I(1)rm and I(2)r nm were used as the fixed and moving images,respectively, in the deformable registration, and the numbers of iterationschosen to be 5 and 10 for the two resolution levels (full-image resolution and423.1. Methodshalf-image resolution), respectively. With the obtained deformation field,the volume change rate was calculated by the mean value of (det(J) − 1)over the core region S(1)r b .3.1.4 Scale Factor from 3-DoF RegistrationAs cord atrophy is a slow process, it is reasonable to assume that the cervicalcord will not significantly change its cylindrical shape dramatically withinthe time frame of most clinical studies. Therefore, in contrast to measuringlocal changes and summing them up as described in the boundary shiftintegral and Jacobian integration, a more strongly regularized approach tomeasuring global changes in volume can be attempted by using a constrainedrigid registration with scaling. The potential advantage of this approach isincreased robustness with respect to local artifacts.We defined a 3-DoF transformation T containing three parameters: tx,ty and scalexy, where scalexy is the scale factor in the x and y axes, andtx and ty are the translations in the x and the y axes respectively. Thetransformation uses one scale factor scalexy in the x and y axes to modela cord that changes size uniformly. We added the translations tx and ty toadjust for small translations that have not yet been corrected by the rigidregistration. The change rate of the cord size can be approximated by thescale factor scalexy obtained from the 3-DoF constrained registration.The 3-DoF constrained registration is realized in the ITK registrationframework using the mean square intensity difference as the similarity metricshown in Equation (3.7). A regular step gradient descent optimizer is usedto compute the update step u for each parameter using the gradient of theenergy function with respective to each parameter.E = ‖F −M ◦ T‖2 (3.7)The 3-DoF constrained registration is performed using the followingsteps:• Choose an initial transformation for T433.1. Methods• Iterate until convergence1. Compute the gradient ∇E of the energy function2. Compute the update step u by multiplying the gradient ∇E withthe step length L that was usually set to be the maximum steplength, u = L×∇E.3. Compare the direction of∇E of current iteration and the directionof the gradient of the previous iteration. If the directions areopposite, reduce the update step u by a relaxing factor r whichis set to be 0.2, u = r × L×∇E4. If the length of the update step u is larger than the minimum steplength, update the transformation to the new transformation T ←T +u and continue to iterate, otherwise stop and the convergenceis obtainedIn our application to measure cord change rate, the 3-DoF constrainedregistration was performed on the registered baseline and follow-up images,with I(1)r used as the fixed image and I(2)r n used as the moving image. Theresampled baseline cord segmentation S(1)r was used as the mask with onlyvoxels inside the mask region included when computing the mean squareintensity difference cost function. With the scale factor (SF) obtained afterthe constrained registration, the change rate of cord volume between baselineand follow-up scans can be computed by (scalexy2 − 1).3.1.5 Experiments PerformedIn order to assess the sensitivity and precision of these three registration-based methods which are abbreviated by BSI, JI and SF, different tests wereperformed on the scan pairs which are outlined below.Scaled scan pairsWe created a simulation data set with different levels of simulated cord at-rophy created by scaling between the scan pairs, assuming that the cord443.1. Methodschanges uniformly as it undergoes atrophy, which is not strictly true butis a useful approximation. We applied two scale factors (one leading to anincrease in volume and the other one leading to a decrease in volume) oneach baseline scan in the hydration data set (described in Section 2.2.2) tocreate two simulated images to eliminate the problem of different degrees ofblurring between the two simulated cord images introduced by interpolation.The steps to create one simulated scan pair with 2% scaling atrophy froma control scan are explained as follows. Firstly, the control scan is enlargedby increasing the voxel size by a scale factor of 1.005 in the x and y axesto create a simulated cord image with 1% increase in volume with respectto the control scan. Secondly, the control scan is shrunk by decreasing thevoxel size by a scale factor of 0.995 in both x and y axes to create the sim-ulated cord image with 1% decrease in volume with respect to the controlscan. Thus, a simplistic simulation of 2% cord atrophy, an amount typicalof a SPMS patient over the course of one year [43] is generated between thescaled scan pair.From each baseline scan, we created three scaled scan pairs with threedifferent levels of change in volume (-1%, -2% and -3%) using the scale factorslisted in Table 3.1. Measures of change were computed using BSI, JI and SFon the scaled scan pairs of each baseline scan in the hydration data set. Thedifference between the computed change rate and the ground truth valuerepresents the error of the result computed by the method. We calculatedthe mean and standard deviation of the errors obtained by BSI, JI and SFto assess the performance of these three registration-based methods on thissimulation data set.Scaled scan pairs with rigid transformationTo additionally simulate changes in patient position between scans, we cre-ated a data set with both simulated atrophy and rigid transformation tosimulate the cord tissue loss and spinal cord repositioning.From the baseline scan of each subject in the hydration data set, wecreated four simulated scan pairs with four different levels of scaling change453.1. MethodsTable 3.1: Scale factors applied to create scaled scan pairs with threedifferent levels of change in cord volume between the simulated baselineimage and follow-up image.Simulated simulated baseline simulated follow-upchange rate image (scale factor) image (scale factor)-3% 1.5% (1.0075) -1.5% (0.9925)-2% 1.0% (1.005) -1.0% (0.995)-1% 0.5% (1.0025) -0.5% (0.9975)(0%, -1%, -2% and -3%) generated by the scale factors listed in Table 3.1 ,and with rigid transformation randomly generated by rotation parametersin the range of -4 degrees and 4 degrees and translation parameters in therange of -2mm and 2mm.Measures of change rate in cord volume were computed using BSI, JI andSF on the four scaled scan pairs with rigid transformation for each subject.We also measured the change rate in cord volume on this simulation dataset using the Tench [100] and Horsfield [50] methods for comparison. Thedifference between the computed change rate and the ground truth valuerepresents the error of the result computed by the method. We calculatedthe mean and standard deviation of these errors to assess the performanceof the three registration-based methods and the two cross-sectional methodson this simulation data set.Hydration data setThe hydration data set described in Chapter 2 Section 2.2.2 is composed ofserial MR scans of 10 healthy subjects at four time points (named baseline,rescan, dehydrated and rehydrated). Cord volume change was measuredusing BSI, JI and SF on the scan pairs from the baseline to the other threetime points as described below.• Scan-rescan scan pairsThe cord size is assumed to be constant between these two scans which463.1. Methodswere taken one hour apart, so the calculated cord volume change rateshould be zero and any departure from zeros is assumed to be scan-rescan variance. Means and SDs of the results computed by BSI, JI andSF methods on the scan-rescan scan pairs were compared with resultsof the Tench and Horsfield methods to see whether registration-basedmethods are able to improve the scan-rescan reproducibility.• Dehydration scan pairsWe computed the measures of change using BSI, JI and SF from thebaseline to the dehydrated scans. A one-tailed Wilcoxon rank test wasperformed on the BSI, JI and SF measures on the dehydration scanpairs to see whether they are able to detect any dehydration effect,which was reported in the results of Tench and Horsfield methods (ex-plained in Chapter 2) and whether they can improve the measurementsensitivity.• Rehydration scan pairsThere is a return in the cord CSA after rehydration and no significantchange is observed from the baseline to the rehydrated scans in theresults of Tench and Horsfield methods. We computed the measuresof change using BSI, JI and SF on the rehydration scan pairs to seewhether registration-based methods are able to yield similar resultsas the two cross-sectional methods and whether they can improve themeasurement precision.MS patient data setThe MS patient data set used in our experiment is composed of MR scansof 15 SPMS patients selected from a negative MS clinical trail. For eachpatient in the MS patient data set, there are two 3D T1 weighted MR imagescollected at two time points with a two-year interval.There should be significant cord atrophy between the scan pairs with atwo-year interval in this MS patient data, because SPMS patients are typi-cally characterized by gradual progression of their disabilities and cognitive473.2. Resultsimpairment and steady annual cord atrophy rate has been reported in thissubtype [43]. Two-year change rate in cord volume was measured using BSI,JI and SF as well as the Tench and Horsfield methods. A one-tailed Wilcoxonrank test was performed on the change rate computed on the scan pairs inthe MS patient data set to see whether significant cord atrophy can be de-tected by these methods and whether registration-based methods are able toimprove the sensitivity and precision compared with the segmentation-basedmethods in the MS patient data set.3.2 ResultsNo failed rigid registration was detected in the preprocessing of all the scanpairs in our experiments. The rigid registration was evaluated by computingthe Dice coefficient [58] of the resampled segmentation images S(1)r b and S(2)r b .The computed Dice coefficients are in the range of 0.90 to 0.99, indicatingthat the resampled baseline and repeat scan pairs I(1)r and I(2)r are fairlyrigid registered in our experiments.3.2.1 Scaled Scan PairsTable 3.2 lists mean and SD of the differences of the percentage changerates computed by BSI, JI and SF to the ground truth values in the simu-lation scan pairs with three different degrees of scaling atrophy. The threeregistration-based methods all obtained accurate results (small mean errors)on this simulation data set with SF achieving the lowest magnitude of abso-lute errors.3.2.2 Scaled Scan Pairs with Rigid TransformationThe percentage change rates computed by BSI, JI and SF as well as Tenchand Horsfield methods for simulated scan pairs with random rigid transfor-mation and four different levels of scaling atrophy (0%, -1%, -2% and -3%)are shown in four Figures 3.5 , 3.6 , 3.7 and 3.8 , respectively.483.2. ResultsTench Horsfield BSI JI SF−2.5−2−1.5−1−0.500.511.522.5Percentage change in volume computed (%)Percentage change in cervical cord volume computed on simulated imageswith 0% scaling atrophy and rigid transformationFigure 3.5: Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-basedmethods (Tench and Horsfield) on simulated scan pairs with rigid transfor-mation and no scaling change (0%). Each circle represents a single subjectin the simulated scan pairs, and the stars and error bars represent the meansand standard deviations of the measurements. The blue line represents theground truth change rate between the two scans in the simulated scan pairs.Registration-based methods outperformed the segmentation-based methodswith smaller mean errors to the ground truth and smaller measurement vari-ance on this simulated scan pairs .493.2. ResultsTench Horsfield BSI JI SF−3.5−3−2.5−2−1.5−1−0.500.511.5Percentage change in volume computed (%)Percentage change in cervical cord volume computed on simulated imageswith 1% scaling atrophy and rigid transformationFigure 3.6: Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-basedmethods (Tench and Horsfield) on simulated scan pairs with rigid transfor-mation and 1% scaling change. Each circle represents a single subject inthe simulated scan pairs, and the stars and error bars represent the meansand standard deviations of the measurements. The blue line represents theground truth change rate between the two scans in the simulated scan pairs.The results obtained by BSI and JI have smaller mean errors and smallervariance than the two segmentation-based methods. Although the mean ofthe Tench results is closer to the ground truth value -1% compared withthe mean of the SF results, the standard deviation of SF results is muchsmaller. Registration-based methods are able to significantly improve themeasurement variance on this simulation scan pairs.503.2. ResultsTench Horsfield BSI JI SF−4.5−4−3.5−3−2.5−2−1.5−1−0.500.5Percentage change in volume computed (%)Percentage change in cervical cord volume computed on simulated imageswith 2% scaling atrophy and rigid transformationFigure 3.7: Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-basedmethods (Tench and Horsfield) on simulated scan pairs with rigid transfor-mation and 2% scaling change. Each circle represents a single subject inthe simulated scan pairs, and the stars and error bars represent the meansand standard deviations of the measurements. The blue line represents theground truth change rate between the two scans in the simulated scan pairs.The JI and SF results are better than the results of the two segmentation-based methods with smaller mean error and smaller variance. Although themean error of BSI results is larger than the two segmentation-based methods,the standard deviation of the BSI result is much smaller. Registration-basedmethods improve the measurement variance on this simulation scan pairs.513.2. ResultsTench Horsfield BSI JI SF−5.5−5−4.5−4−3.5−3−2.5−2−1.5−1−0.5Percentage change in volume computed (%)Percentage change in cervical cord volume computed on simulated imageswith 3% scaling atrophy and rigid transformationFigure 3.8: Percentage change rates computed by the three registration-based methods (BSI, JI and SF) along with the two segmentation-basedmethods (Tench and Horsfield) on simulated scan pairs with rigid transfor-mation and 3% scaling change. Each circle represents a single subject inthe simulated scan pairs, and the stars and error bars represent the meansand standard deviations of the measurements. The blue line represents theground truth change rate between the two scans in the simulated scan pairs.The measurement variance using BSI, JI and SF is significantly improvedwith much smaller SDs compared to the measurements using Tench andHorsfield methods.523.2. ResultsTable 3.2: Mean and SD of the errors which are the differences between thepercentage change rates computed by BSI, JI and SF on scaled scan pairsand their respective ground truth change rates.Mean (SD) of the errors (%)Methods BSI JI SF-3% -0.13 (0.37) 0.01 (0.17) 0.01 (0.02)-2% -0.08 (0.26) 0.01 (0.06) 0.01 (0.05)-1% -0.07 (0.13) -0.01 (0.07) 0.05 (0.05)Table 3.3: Mean (SD) of the errors, which are the differences of the com-puted change rates to the ground truth values, on the simulation data setwith rigid transformation and simulated atrophy. The measurement SDs us-ing the three registration-based methods are smaller than the measurementSDs using the two segmentation-based methods.Mean (SD) of the errors (%)Tench Horsfield BSI JI SF-3% 0.13 (1.02) -0.09 (1.37) 0.38 (0.25) 0.12 (0.33) 0.06 (0.25)-2% 0.09 (0.75) -0.17 (0.92) 0.27 (0.22) 0.08 (0.42) -0.01 (0.26)-1% -0.09 (0.69) -0.39 (1.24) 0.07 (0.14) -0.06 (0.21) 0.13 (0.23)0% 0.10 (1.02) -0.33 (0.96) -0.02 (0.07) -0.02 (0.36) 0.02 (0.12)The means and standard deviations of the errors of the results obtainedby BSI, JI and SF as well as Tench and Horsfield methods on the four sets ofsimulated scan pairs are provided in Table 3.3 . The registration-based meth-ods improved the measurement variance, achieving much smaller standarddeviations than the two segmentation-based methods on this simulation dataset. Their results support our hypothesis that the registration-based atro-phy measurement methods are robust to the variability in cord segmentationand can eventually improve the precision of cord atrophy measurement bydirectly assessing the change.533.2. Results3.2.3 Hydration Data SetTable 3.4: Means and SDs of the percentage change rates computed byBSI, JI and SF along with the results of Tench and Horsfield methods onthe scan-rescan pairs (labeled 1 in the table), dehydration scan pairs (la-beled 2 in the table) and rehydration scan pairs (labeled 3 in the table).The three registration-based methods have comparable reproducibility onthe scan-rescan scan pairs, compared to the results of the two segmentation-based methods. However, they did not detect any significant decrease incord volume on the dehydration scan pairs which was detected by the twosegmentation-based methods.Mean (SD) of the change rate(%)Tench Horsfield BSI JI SF1 -0.22 (0.79) -0.40 (1.26) -0.24 (0.77) -0.26 (0.61) -0.09 (0.73)2 -0.65 (0.78)* -0.65 (1.04)† 0.09 (0.68) -0.34 (0.97) -0.34 (0.71)3 0.12 (1.32) 0.06 (1.13) 0.05 (0.70) 0.00 (0.73) -0.01 (1.18)*p≤0.05, † p≤0.1The means and standard deviations of the percentage changes computedby each technique on the three sets of scan pairs in the hydration data setare presented in Table 3.4 .On the scan-rescan scan pairs, the coefficients of variance (SD divided bythe mean) of the three registration-based methods were comparable to thatof two segmentation-based methods, indicating no obvious improvement bythe registration-based methods in scan-rescan reproducibility.On the dehydration scan pairs, there was no significant change in cordvolume detected by BSI, JI and SF. Registration-based methods are notsensitive enough to detect the dehydration effect.On the rehydration scan pairs, results of BSI, JI and SF showed no changefrom zero, which is similar to the results of Tench and Horsfield methods.The results of each technique on the three sets of scan pairs in the hy-dration data set are shown in Figures 3.9, 3.10 and 3.11.543.2. Results3.2.4 MS Patient Data SetThe mean (SD) percentage change rates quantified using each techniqueon the scan pairs with a two-year interval in the MS patient data set arepresented in Table 3.5 and Figure 3.12.Table 3.5: Mean and standard deviation (SD) of the percentage changerates in cord volume computed by BSI, JI and SF along with the results ofTench and Horsfield methods on the MS patient data set. All these methodsdetected significant cord atrophy on the scan pairs with a two-year interval.However, the magnitudes of cord atrophy detected by the registration-basedmethods were smaller compared with the cord atrophy detected by the twosegmentation-based methods.Mean (SD)(%)Tench Horsfield BSI JI SF-2.53 (3.81)** -2.13 (3.59)* -0.74 (1.68)* -1.00 (1.78)* -1.45 (2.63)***p≤0.01, *p≤0.05These methods all detected significant cord atrophy over two years withthe percentage change rates computed by the three registration-based meth-ods and two segmentation-based methods all significantly below zero (p ≤0.05) in the one-tailed Wilcoxon rank test. The registration-based methodsimproved the measurement variance by obtaining smaller standard devia-tions. However, they do not seem to be as sensitive, reporting smaller mag-nitudes of atrophy compared with the atrophy detected by the segmentation-based methods. The cord atrophy previously reported in the literature isaround -1.6% in SPMS patients per year and the magnitude of cord atro-phy computed by the two segmentation-based methods over two years agreesreasonably well to the reported figure. In terms of correlation, the measure-ments using SF agreed well with the measurements using Tench method.The measurements using SF significantly correlated with the measurementsusing Tench (Spearman’s correlation coefficient r = 0.63, p = 0.01).553.2. ResultsTench Horsfield BSI JI SF−4−3−2−101234Percentage change in volume computed (%)Percentage change in cervical cord volume computed on scan−rescan scan pairsin the hydration data setFigure 3.9: The percentage change in cord volume from baseline to the rescantime point computed by the three registration-based methods (BSI, JI andSF) and the two segmentation-based methods (Tench and Horsfield). Eachcircle represents a single subject in the hydration data set, and the stars anderror bars represent the means and standard deviations. The scan-rescanvariation computed by the three registration-based methods was comparableto that computed by Tench method with similar means and SDs.563.2. ResultsTench Horsfield BSI JI SF−4−3−2−101234Percentage change in volume computed (%)Percentage change in cervical cord volume computed on dehydration scan pairsin the hydration data setFigure 3.10: The percentage change in cord volume from baseline to thedehydration time point computed by the three registration-based methods(BSI, JI and SF) and the two segmentation-based methods (Tench and Hors-field). Each circle represents a single subject in the hydration data set, andthe stars and error bars represent the means and standard deviations. Theresults of registration-based methods did not demonstrate any statisticallysignificant decrease in cord volume following dehydration.573.2. ResultsTench Horsfield BSI JI SF−4−3−2−101234Percentage change in volume computed (%)Percentage change in cervical cord volume computed on rehydration scan pairsin the hydration data setFigure 3.11: The percentage change in cord volume from baseline to the rehy-dration time point computed by the three registration-based methods (BSI,JI and SF) and the two segmentation-based methods (Tench and Horsfield).Each circle represents a single subject in the hydration data set, and the starsand error bars represent the means and standard deviations. No significantchange in cord volume was detected by the registration-based methods fromthe baseline scan to the rehydrated scan, which is similar to the results ofthe two segmentation-based methods.583.2. ResultsTench Horsfield BSI JI SF−8−6−4−202468Percentage change in volume computed (%)Percentage change in cervical cord volume computed on scan pairs with a two−year interval in the MS patient data setFigure 3.12: The percentage change in cord volume on the scan pairs withtwo years interval computed by the three registration-based methods (BSI,JI and SF) and the two segmentation-based methods (Tench and Horsfield).Each circle represents a single subject in the MS patient data set, and thestars and error bars represent the means and standard deviations. Themeans of the change rates computed by all the methods are below zero.The measurement variance is slightly improved in the results of registration-based methods. However, the magnitudes of atrophy rates computed by theregistration-based methods are smaller than the magnitudes of atrophy ratescomputed by the segmentation-based methods.593.3. Discussion3.3 DiscussionIn this study, we implemented three registration-based atrophy measure-ment techniques to measure longitudinal spinal cord atrophy from locallyregistered serial MR images. We evaluated these three registration-basedmethods on the following test data sets, 1) two sets of scan pairs with simu-lated change to quantify the measurement precision, 2) the scan-rescan scanpairs to quantify the measurement reproducibility, 3) the dehydration scanpairs with demonstrated dehydration effect and SPMS patient scan pairswith reported cord atrophy to quantify the measurement sensitivity. Wecompared the results obtained by the registration-based methods on thesetest data sets to the results obtained by two segmentation-based methodsthat are currently utilized as standard approaches in spinal cord atrophystudies in MS.Our experiments showed that the registration-based methods reducedmeasurement variance (overall smaller standard deviations) compared withthe segmentation-based methods on all the test data sets and improvedthe measurement precision, achieving less errors on the two simulated datasets. However, the registration-based methods were not as sensitive as thesegmentation-based methods, detecting no dehydration effect on the dehy-dration scan pairs and reporting reduced magnitude cord atrophy on theMS patient data set. We argue in the following sections that the limitationin sensitivity of registration-based methods on hydration data set and MSpatient data set is probably due to the limited spatial resolution of the MRscans in our experiments and the inherently small size of the cord.3.3.1 Boundary Shift IntegralThe technique BSI directly estimates the cord volume change between tworegistered images by calculating the intensity changes within specified in-tensity window at the cord–CSF boundary. The accuracy of BSI methoddepends on the chosen intensity window. Any intensity transitions that lieoutside the window do not contribute to the BSI, resulting in an underesti-mation. Brain BSI was reported to underestimate around 0.71% of simulated603.3. Discussionscaling atrophy in Boyes et al.’s study [18], and Camara et al. showed thatbrain BSI consistently underestimated atrophy by around 18% especially athigher level of atrophy on a cohort of realistic simulated images with knownamounts of atrophy [20]. The caudate BSI also had a tendency to under-report change relative to the manual measures [49]. In our experiments, BSIunderestimated the simulated scaling atrophy on the simulation data set andalso underestimated the real cord atrophy on the MS patient data set, whichcan be probably explained by the limitation of the intensity window in BSImethod. While this underestimate is significant, it is understood to be linearand does not affect the sensitivity of BSI results to differentiate AD subjectsand healthy controls [18]. As a comparison group of control subjects withserial MR scans was not available in the MS patient data set, we do notknow whether the underestimate of cord BSI would affect its sensitivity todifferentiate the control and MS patient group.The intensity mean and SD estimated on the limited samples of the cordvoxels and CSF voxels (around 85 cord voxels and 35 CSF voxels on theaxial slice of MR images with a spatial resolution of 1 mm), which are usedto decide the intensity window, are easily affected by the noise or artifacts,resulting in miscalculation of cord BSI. While the effect of noise and artifactsalso exists in brain BSI, it is likely to be cancelled out and not significant,because the whole brain region is bigger containing more voxels than the cordand the means and SDs estimated on a larger sample are more reliable. Fur-thermore, as the cord region we are examining is so small, any miscalculationin cord BSI will disproportionally affect the final result. Despite the fact thatBSI has been successfully used to measure atrophy of small structures insidethe brain like caudate nucleus and hippocampus, the mean (SD) of annualatrophy rate computed by BSI is 4.63(2.78)% for hippocampus volume of 147patients with AD in Leung et al.’s study [63] and 2.90(1.60)% for caudatenucleus volume of 16 patients with Huntington’s disease in Hobbs et al.’sstudy [49], which are both larger than the magnitude of dehydration effect(-0.65%) and two-year cord atrophy of SPMS patients (-2.13% to -2.53%)in our experiments. Moreover, the change quantified by BSI brought bycommon image non-idealities like image noise and contrast difference would613.3. Discussionpossibly exceed the disease effect of MS. Preboske et al. [85] pointed thatthe magnitudes of the error using BSI in measures of longitudinal brain at-rophy that can result from commonly encountered image non-idealities cansignificantly exceed the disease effect which range from 1% to 2.78% per yearfor brain atrophy in AD.To summarize, the precision and sensitivity of cord BSI on MR scanswith a spatial resolution of 1 mm are limited due to these conditions. MRimages with a spatial resolution less than 1 mm can probably overcome theselimitations because there would be more voxels over the cord region providingmore samples to estimate the mean and SD of the cord and CSF intensities.The effect of image noise and other image non-idealities on the cord BSIresult would be lessened, which would improve the precision of cord BSI.MR scans with higher resolution are suggested for further studies using BSIin longitudinal cord atrophy measurement.3.3.2 Jacobian IntegrationThe technique JI uses the Jacobian determinant values of deformation fieldobtained from deformable registration over the cord region to give an averageestimate of cord change rate over time. The accuracy of JI depends on thedeformable registration algorithm applied.The deformation field for the small cord region obtained from the non-linear registration algorithm should be both plausible and smooth for theJacobian determinants to yield meaningful results. On one hand, we areseeking to obtain a plausible registration to optimally align the images bymaximizing the similarity measure. On the other hand, we need to regu-larize the registration results to provide robust and meaningful measures ofanatomical changes, because the statistical power of studies using JI to quan-tify anatomical changes largely depends on the smoothness of the Jacobiandeterminant maps associated with the deformation [40, 68].We chose the symmetric log-domain diffeomorphic demons algorithm asimplemented in ITK for our cord deformable registration application becauseof its demonstrated theoretical advantages [104] and practical efficiency. The623.3. Discussionsymmetric log-domain diffeomorphic algorithm optimizes the displacementfield using an efficient second-order minimization framework and providesdiffeomorphic transformations that are smooth in terms of Jacobian deter-minants. Thanks to the open-source implementation of this algorithm [30],we can practically modify and debug its source code. In addition, the relativeease for us to find the optimal parameters, compared to another symmetricdeformable registration algorithm SyN [8], is another practical advantage.Choosing a right combination of parameters for deformable registration isalways an application-dependent problem. In the case of symmetric log-domain diffeomorphic demons, the most important parameter to be tuned isthe sigma σ of the Gaussian kernel for regularization. We evaluated the JIresults on the simulation data set with scaling atrophy over a range of σ val-ues (between no regularization at all and σ = 2.0 with an interval of 0.2) andchose the one (σ = 1.0) which gave the lowest errors to be the parameter usedin our experiments. Meanwhile, we used the change in mean square errormerit values suggested by Peroni et al. [84] instead of the predefined itera-tion numbers in the original implementation to be the stopping criterion andthe cord deformable registration in our experiments actually converged afterno more than 10 iterations in most cases. On the contrary, there are moreparameters to be tuned using SyN beside the smoothing sigma for the Gaus-sian kernel, like the weights for the mean square error and cross-correlationsimilarity metrics, the gradient step size, the time step for integration. It ishard to find the optimal parameters using SyN for our cord application anddifferent parameter settings ended up with very different JI results.The atrophy rates provided by JI were more accurate and less variablethan those from the two segmentation-based methods on both simulationdata sets with scaling. However, on the hydration data set and MS patientdata set, JI results did not demonstrate to be superior in terms of sensitivityand precision, which is probably due to the inherent limitation of spineMRI images used in our experiments. The spinal cord is composed of whitematter and grey matter. On MR images used in our experiments, which wereT1-weighted images with a spatial resolution of 1 mm, these two internalstructures are not differentiable, making it impossible for the deformable633.3. Discussionregistration algorithm to find structural meaningful correspondence insidethe cord boundary. JI performed well on the simulation data sets becausethere are good intensity correspondences between the baseline and repeatimages which were created from the same control scan. The reduced intensitycorrespondence over the cord region on the MR images in the hydration dataset and MS patient data set resulted in the limited sensitivity to detect realcord atrophy using JI. Another reason that may underlie the underestimationof the cord atrophy on the MS patient data set could be the inclusion of thepartial volume voxels in the region of interest to be integrated.The fact that JI results critically rely on deformable registration empha-sizes that we can not directly compare atrophy rates computed using differentdeformable registration methods. As shown in Camara et al.’s paper [20], JIusing two different deformable registration algorithms (free-form deformableregistration vs. fluid registration) to quantify realistic simulated atrophyin multiple regions of brain yielded significantly different results. In ourattempt using SyN [8] as the deformation registration algorithm in our ex-periments, JI results detected significantly larger magnitude cord atrophy onthe MS patient data set with mean (SD) of atrophy rate to be -3.03(3.72)%(one-tailed Wilcoxon test p = 0.006), and the measurements significantlycorrelated with the measurements using Tench method (Spearman’s corre-lation coefficient r = 0.61, p = 0.02). However, the JI results using SyNdid not show any improvement in measurement variance and also they didnot show any improvement in measurement accuracy on the simulation datasets.To summarize, the standard resolution of the MR images used in ourexperiments accounts for the limited sensitivity of the JI technique to quan-tify cord atrophy. Future cord atrophy studies using JI are suggested tobe performed on MR images with higher resolution that are able to dif-ferentiate the GM and WM inside the cord. Additional validation of thenon-linear registration algorithm should be performed, and parameters forthe chosen deformable registration algorithm should be carefully selected toobtain meaningful JI results. Moreover, although we used a 0.5 probabilitythreshold on the resampled baseline cord segmentation to create the binary643.3. Discussionbaseline cord mask as the region of interest within which Jacobian determi-nants are integrated, other probability thresholds should be investigated, asmisclassified partial volume voxels will increase measurement errors.3.3.3 Scale Factor from 3-DoF RegistrationThe technique SF uses the scale factor obtained from the 3-DoF constrainedregistration (2 translation tx and ty, and 1 scaling factor scalexy), where weconstrain uniform scale factor scalexy on x and y axes, to measure the globalchange in cord size. The accuracy of the cord atrophy measurement usingSF depends on the scale factor obtained from optimization of the 3-DoFconstrained registration.In our experiments, SF achieved very accurate results on the simula-tion data set with scaling atrophy because the simulated atrophy generatedwas global scaling change and 3-DoF constrained registration measures theglobal change in cord size. On the simulation data set with rigid trans-formation and scaling atrophy, SF achieved more accurate results than thetwo segmentation-based methods, with smaller mean errors and smaller vari-ance. On the dehydration scan pairs, SF was able to detect a mean decreaseof 0.34% in cord volume with one-tailed Wilcoxon rank test p value of 0.12.On the MS patient data set, SF detected significant cord atrophy over twoyears with a mean atrophy rate of 1.45%, and the measurements of SF weresignificantly correlated with the measurements of Tench method with a sys-tematic underestimation.The underestimation in SF results can be explained by the uniform scalefactor scalexy on the x and y axes in the 3-DoF transformation. SF assumesthat the cord changes uniformly on the x and y axes, which might not betrue in real scenarios. Imposing a constraint of an equal scale change in thex and y dimensions regularized the optimization process, thereby reducingmeasurement variance; however, it also reduced sensitivity of this method,thus resulting in the underestimation. In addition, the interpolation doneto resample the input images at each iteration also introduced artifacts inthe merit function either by generating many local optima or by shifting653.3. Discussionthe global optimum [3]. These artifacts consequently increase the chance ofregistration converging to a wrong minimum, thereby producing inaccurateregistration results.The limited resolution of MR images used in our experiments also causedthe limited sensitivity of SF. On T1 weighted MR images with a spatial res-olution of 1 mm, the intensities inside the cord boundary are fuzzy becauseof the non-differentiable intensities of grey matter and white matter. Themean square error merit function which is computed over the small cordregion (less than 100 voxels on each slice) is easily to be affected by imagenoise and artifacts, and interpolation artifacts. Thus, the optimization ofthe 3-DoF constrained registration is likely to converge to an undesirableminimum, degrading the sensitivity. However, on MR images with higherspatial resolution, there are more voxels over the partial volume region ex-plicitly capturing the tissue loss and also the cord region inside the cordboundary would have good soft tissue contrast of the grey matter and whitematter, providing better intensity correspondence for the registration. Themerit function computed from a larger number of voxels would be robust toimage noise and artifacts, and the negative effect of interpolation artifactswould be lessened. The optimization of the 3-DoF constrained registrationwould yield more accuracy estimation of scale change.In summary, SF generated small measurement variance in longitudinalcord atrophy measurement but at the cost of lower sensitivity. AlthoughSF tends to underestimate atrophy, we do not know whether this underesti-mation will affect its sensitivity in separating MS patient group and controlgroup, since a comparison control group is not available in the MS patientdata set. Experiments on MS patients with a comparison control group andlarger sample sizes are suggested for future study to investigate longitudinalcord atrophy measurement using SF. Future studies using SF are recom-mended to be performed on high resolution MR images with resolution lessthan 1 mm in order to improve the sensitivity.66Chapter 4Conclusion4.1 SummaryWe investigated the spinal cord atrophy measurement on MRI from two as-pects. Firstly, change in water content due to hydration status affects thecord CSA measurement on MRI, whose signals are mainly derived from wa-ter. We conducted the experiment to assess the dehydration effect on cordCSA measurement. We designed the dehydration and rehydration protocoland collected the MR scans from ten healthy subjects at four time points.Two established cord CSA measurement methods were employed to measurethe cord CSA on all the MR scans. Statistical analyses of the percentagechange in CSA from baseline time point to each subsequent time point wereperformed to assess the significance of these changes to determine the de-hydration effect. Results from the two methods agree well and we haveobserved a decrease in the cervical cord CSA by 0.65% after solid and liquidfasting for an overnight period that would not be considered unusual in rou-tine research or clinical settings involving MRI. Our findings lend evidencethat change in water content due to hydration status affects the spinal cordCSA measurement and should be considered a source of variability in clinicalstudies of spinal cord atrophy.Secondly, registration-based methods were adapted for longitudinal cordatrophy measurement for the first time. Three registration-based methods(boundary shift integral, Jacobian integration and scale factor obtained from3-DoF constrained registration), were implemented to measure the changein spinal cord volume on rigid registered serial MR images. These threemethods were evaluated on two data sets with simulated atrophy, on thehydration data set with dehydration effect, and on an MS patient data set674.1. Summarywith cord atrophy over a two-year interval. Their results were compared tothe results obtained by two segmentation-based methods, which are currentlyutilized as standard approaches in spinal cord atrophy studies in MS.Our experiments showed that registration-based methods reduce the mea-surement variance with smaller standard deviations of their measurementson all the data sets over the two segmentation-based methods. However,they were not sensitive enough to detect the dehydration effect on the dehy-drated scan pairs and also detected a reduced magnitude of cord atrophy onthe MS patient data set. We argue that their results with limited sensitivityare possibly due to the limited spatial resolution of 1 mm of MR scans inour experiment and the inherently small size of the cord. Registration-basedmethods estimate the change in cord size by assessing the intensity differ-ences between corresponding voxels using registration with different levelsof regularization. In all three methods examined, regardless of whether theregistration is rigid registration (used in BSI), deformable registration (usedin JI) and 3-DoF constrained registration (used in SF), the intensity differ-ences of corresponding voxels over the cord region between the baseline andfollow-up images were the fundamental information used in all three meth-ods explored. However, on MR images used in our experiments, which wereT1-weighted images with a spatial resolution of 1 mm, the cord is boundedto a region size of less than 100 voxels on each axial slice and lacks internalcontrast between grey matter and white matter. The intensity window inBSI, which is determined by the intensity mean and standard deviation ofthe cord and surrounding CSF, is easily affected by image noise and artifacts,resulting in underestimation of cord BSI. The mean square error merit func-tion in the deformable registration (used in JI) and constrained registration(used in SF) evaluated over the cord region with poor intensity correspon-dence and a limited number of voxels, is very sensitive to artifacts introducedby image noise and interpolation done to resample the input images at eachiteration. These artifacts consequently generate many local optima or changethe global optimum, increasing the chance of registration converging to anundesirable minimum and thereby resulting in the limited sensitivity.Registration-based methods reduced the measurement variance by im-684.2. Future workposing different levels of regularization in registration but at the cost of lesssensitivity. As the cord atrophy in MS is a slow process with an annualatrophy of around 1.6% in SPMS patients reported in previous literature,the registration-based methods applied on MR images with a spatial resolu-tion of 1 mm are not able to meet the precision and sensitivity requirementsfor longitudinal spinal cord atrophy measurement. High resolution MR scanswith a spatial resolution less than 1 mm are required to conduct further stud-ies on spinal cord atrophy measurement using the three registration-basedmethods proposed.4.2 Future workThe results presented in the dehydration study provide support for our hy-pothesis that change in water content does have a significant effect on theCSA measurement on MRI. However, there are limitations in our experimentand further investigation will improve our understanding of the effect of wa-ter content to the cord measurement on MRI. In future work, brain scans canbe collected along with the spine scans to verify whether similar magnitudeof change can be expected in both structures after dehydration and providefurther information on the relationship between the dehydration effect on theMRI measurements of brain volume and cord volume. Our current studiesuse conventional T1 weighted MR images with a resolution of 1 mm. MRscans acquired using phase-sensitive inversion recovery (PSIR) imaging canprovide good grey matter and white matter contrast over the cord regionand have been used to investigate the spinal cord grey matter atrophy in MS[83, 95]. It would be interesting to investigate the dehydration effect on thevolume of spinal cord white matter and spinal cord grey matter using PSIRscans.In future studies investigating registration-based methods for longitudi-nal cord atrophy measurement, MR images with a spatial resolution below1 mm, and which are able to differentiate the white matter and grey matterover the cord region, such as PSIR scans [54], are suggested to be collectedand used to evaluate the precision and sensitivity of registration-based meth-694.2. Future workods. A larger sample size of MS patients and a comparison control group arerecommended to examine the sensitivity of the registration-based methodsin separating the patient and healthy groups. 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