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Novel automated approach to the quantitative analysis of dopaminergic functional images in a large cohort… Shenkov, Nikolay 2017

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Novel automated approach to the quantitative analysis ofdopaminergic functional images in a large cohort of Parkinson’spatientsbyNikolay ShenkovB.Sc., University of Richmond, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)The University of British Columbia(Vancouver)August 2017c© Nikolay Shenkov, 2017AbstractPositron Emission Computed Tomography (PET) and Single Photon Emission Computed Tomog-raphy (SPECT) are nuclear medicine imaging techniques that allow for the study of physiologi-cal processes in vivo. These techniques allow to assess the dopaminergic system in subjects withParkinson’s disease (PD), which is the system most severely affected by the disease. Parkinson’sProgression Markers Initiative (PPMI) is a multicenter, longitudinal study aimed at identifying novelbiomarkers of PD progression. This study utilizes brain SPECT/PET imaging to investigate thedopaminergic system, by examining the distribution of the dopamine transporter (DaT) or the vesic-ular monoamine transporter 2 (VMAT) in the striatum.Several imaging metrics can be used to quantify the dopaminergic tracer binding in the stria-tum. These metrics are typically calculated on regions of interest (ROIs) that require either manualplacement or coregistration with MR structural images. In the first part of this work, an automatedapproach to quantifying dopaminergic tracer binding is presented; the method consists of a newmetric, Sum Intensity (SI), evaluated over a bounding box that is automatically placed on the SPEC-T/PET images. In order to validate this metric, the correlation is computed between the SI valuesand the motor scores of PD subjects from the PPMI database. We find that sum intensity achievescorrelations as strong as the ones obtained using conventional approaches such as the putamenbinding ratio, evaluated on manually-placed ROIs, but using a simplified and operator-independentapproach.The second part of this work focuses on predicting the rate of PD progression over the fouryears during which the PD subjects were enrolled in the PPMI study. Two methods of quantifyingdisease progression are considered. The first approach uses imaging features collected at year-0 ofthe study to predict the decline in the putamen binding ratios over the next four years. The modelachieves a prediction error of 13% for the better side of the putamen, which is comparable to thetest-retest reproducibility of this metric. The second approach uses imaging and clinical featuresat year-0 to predict the clinical outcome (quantified by year-4 motor and cognitive scores). Novelcombinations of clinical and imaging features that are predictors of disease severity are identified.iiLay AbstractNuclear medicine imaging techniques such as Positron Emission Tomography can be used to studyphysiological processes in vivo. They are applied in the study of the dopaminergic system in Parkin-son’s disease (PD) patients, which is the system most severely affected by the disease.In the first part of this work, a novel algorithm is developed that is able to automatically quantifydopaminergic loss from brain images. This algorithm is applied to a large database of images of PDpatients and its performance is compared to that of standard approaches.In the second part, a statistical model is build to predict the progression of PD over four years,quantified by both clinical scores and imaging metrics. The prediction of the rate of disease pro-gression has prognostic value and can enhance disease management. New combinations of inputscores are identified as important predictors of progression.iiiPrefaceA version of Chapters 4, 5, and 6, under the title An automated method and novel metric to quantifyDaT SPECT images of Parkinsons disease patients without MRI-based regions of interest, is cur-rently in review. I was responsible for the development of the algorithms, the data analysis and themajority of manuscript composition. V. Sossi was the supervisory author involved throughout theproject.Chapter 7 represents original unpublished material.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi1 Image Formation in PET and SPECT . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Modes of Nuclear Decay in Functional Imaging . . . . . . . . . . . . . . . . . . . 21.2.1 Isomeric gamma ray emission . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Electron capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.3 Positron emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Gamma Ray Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 In SPECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.2 In PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.3 Block detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Factors Limiting the Spatial Resolution . . . . . . . . . . . . . . . . . . . . . . . 81.4.1 In SPECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4.2 In PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Corrections to PET and SPECT Data . . . . . . . . . . . . . . . . . . . . . . . . . 111.5.1 Attenuation correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.5.2 Scatter correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5.3 Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5.4 Random coincidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14v1.5.5 Partial volume effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.6 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.6.1 Filtered back-projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.6.2 Iterative reconstruction using maximum likelihood . . . . . . . . . . . . . 162 Quantifying Radioligand Binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.1 In Vitro Equilibrium Binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Compartmental Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Simplified Approach with the Binding Ratio . . . . . . . . . . . . . . . . . . . . . 202.4 Tracer Quantification in This Work . . . . . . . . . . . . . . . . . . . . . . . . . . 223 The Dopaminergic System in Parkinson’s Disease . . . . . . . . . . . . . . . . . . . 243.1 Parkinson’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 The Dopaminergic System in Parkinson’s Disease . . . . . . . . . . . . . . . . . . 253.2.1 Patterns of PD progression in the striatum . . . . . . . . . . . . . . . . . . 263.3 Clinical Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.1 UPDRS motor score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.2 Montreal Cognitive Assessment . . . . . . . . . . . . . . . . . . . . . . . 283.3.3 University of Pennsylvania Smell Identification Test . . . . . . . . . . . . 293.3.4 Geriatric Depression Scale . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Parkinson’s Progression Markers Initiative . . . . . . . . . . . . . . . . . . . . . . 294 Defining Regions of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.1 Manual Placement of ROIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 MR-defined ROIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.3 MR-template Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.4 Bounding Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5 Other Automated Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Imaging Metrics to Quantify Tracer Uptake in the Striatum . . . . . . . . . . . . . . 365.1 First- and Second-order Image Metrics . . . . . . . . . . . . . . . . . . . . . . . . 365.2 Moment Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3 Sum Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 Cross-sectional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.2.1 DaTSCAN image acquisition . . . . . . . . . . . . . . . . . . . . . . . . 396.2.2 AV-133 image acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.3 Clinical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.4 ROI placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41vi6.2.5 Image metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.2.6 Regression analysis and measurement uncertainty . . . . . . . . . . . . . . 436.2.7 Resampling procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.3.1 Motor score variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.3.2 Correlations with motor score variables (DaTSCAN images) . . . . . . . . 456.3.3 Healthy controls and age . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.3.4 Correlations with motor score (AV-133 images) . . . . . . . . . . . . . . . 486.3.5 Nonlinear fitting (DaTSCAN) . . . . . . . . . . . . . . . . . . . . . . . . 486.3.6 Nonlinear fitting (AV-133) . . . . . . . . . . . . . . . . . . . . . . . . . . 506.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 Longitudinal Analysis and Outcome Prediction . . . . . . . . . . . . . . . . . . . . . 527.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527.2 Imaging-based Model of Progression . . . . . . . . . . . . . . . . . . . . . . . . . 537.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.2.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577.3 Model of Progression Based on Clinical Scores . . . . . . . . . . . . . . . . . . . 577.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577.3.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64viiList of TablesTable 2.1 Binding ratios computed from the images shown in Figure 2.3 . . . . . . . . . . 22Table 3.1 Clinical information for the PD subjects corresponding to the DaTSCAN imagesshown in Figure 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Table 6.1 Clinical features of the 75 PD subjects used in the DaTSCAN analysis. . . . . . 41Table 6.2 Spearman correlation coefficients between image metrics and motor score. . . . 47Table 6.3 Fitted values for the parameters of the exponential model based on the DaTSCANimages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Table 6.4 Fitted values for the parameters of the exponential model based on the AV-133images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Table 7.1 Error estimates for the imaging model based on year-4 predictions. . . . . . . . 55Table 7.2 Baseline imaging and clinical characteristics for three subjects from the test set. 55Table 7.3 Mean values and standard deviations of the parameters α . . . . . . . . . . . . . 56Table 7.4 Input features and output variables for the clinical model. . . . . . . . . . . . . 59Table 7.5 Error measures for the clinical predictions. . . . . . . . . . . . . . . . . . . . . 61viiiList of FiguresFigure 1.1 Comparing brain PET and SPECT images of the dopaminergic system in healthysubjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Acceptance angle θ for an absorptive collimator. . . . . . . . . . . . . . . . . 5Figure 1.3 A schematic illustration of the block detector design [37]. . . . . . . . . . . . 8Figure 1.4 Depth-of-interaction effect for a PET system in a circular configuration. . . . . 11Figure 1.5 Partial volume effect on the striatal region of the brain. . . . . . . . . . . . . . 15Figure 2.1 The reference tissue model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.2 A parametric BPND image of a HC subject imaged with 11C-DTBZ. . . . . . . 21Figure 2.3 DaTSCAN images of a subject with Parkinson’s disease imaged over a 4-yearperiod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 3.1 DaTSCAN images of the striatum for two healthy control subjects (HC) andtwo PD subjects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 4.1 Conventional approaches of ROI placement in DaTSCAN images. . . . . . . . 32Figure 4.2 Mean HC template used for the bounding box placement . . . . . . . . . . . . 34Figure 5.1 Green contour lines in the striatal BB show voxels where the normalized inten-sity is equal to θ = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Figure 6.1 Histograms of the voxel intensities inside the BB ROIs (AV-133) for a HC sub-ject, a PD subject in early disease and an advanced PD subject. . . . . . . . . . 42Figure 6.2 The effect of using different SI intensity thresholds on the correlation of thismetric with motor score. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 6.3 Consecutive motor score measurements for three different PD subjects. . . . . 45Figure 6.4 Relationship between motor score and imaging metric computed on the lessaffected side of the brain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Figure 6.5 Relationship between image metrics computed on the MR-based ROIs and mo-tor score. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 6.6 Relationship between age and imaging metric for healthy control subjects. . . . 47Figure 6.7 Relationship between motor score and imaging metric on AV-133 scans. . . . . 49ixFigure 6.8 Modelling the relationship between imaging metric and motor score in DaTSCANimages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 6.9 Modelling the relationship between imaging metric and motor score using AV-133 images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 7.1 Diagram of the process used to fit and evaluate the imaging model. . . . . . . . 54Figure 7.2 Predictions on the test set of subjects for the imaging model. . . . . . . . . . . 55Figure 7.3 Examples of the predictions made by the imaging model for three subjects fromthe test set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 7.4 Example of a subject excluded from the clinical predictions analysis. . . . . . . 58Figure 7.5 Distribution of the observed year-4 MoCA scores. . . . . . . . . . . . . . . . . 60Figure 7.6 Predictions of clinical variables for 80 subjects drawn from the validation sets. 60Figure 7.7 Fitted coefficients of the ridge regression. . . . . . . . . . . . . . . . . . . . . 62Figure 7.8 Fitted coefficients from the univariate analysis. . . . . . . . . . . . . . . . . . 63xGlossaryBGO Bismuth GermanateBR Binding RatioCT Computed TomographyFWHM Full Width at Half MaximumGDS Geriatric Depression ScaleHC Healthy ControlHRRT High Resolution Research TomographMRI Magnetic Resonance ImagingPET Positron Emission Computed TomographyPMT photomultiplier tubePPMI Parkinson’s Progression Markers InitiativeROI Region of InterestSI Sum IntensitySPECT Single Photon Emission Computed TomographyUPSIT University of Pennsylvania Smell Identification TestxiChapter 1Image Formation in PET and SPECT1.1 OverviewIn PET and SPECT imaging a biochemically-active molecule labelled with a radionuclide is injectedinto the subject under investigation. Gamma ray photons emitted from the injected compound canbe detected, and subsequently reconstructed to form a 3D image, which allows for the estimationof the spatial distribution of the compound, called tracer, inside the body. Biological processes canbe studied in vivo by estimating the tracer concentration (the tracer uptake) in regions of interest.An important requirement, known as the tracer principle, is that a relatively small amount of thecompound should be injected into the body, so that it does not perturb the biochemical pathwayunder investigation.PET and SPECT are emission computed tomography techniques, where the goal is to recoverthe 3D spatial distribution of the tracer inside the body. These two modalities are based on differentmodes of nuclear decay which necessitates different detection mechanisms. The spatial resolutionin the produced volumetric images is also very different (for example, see Figure 1.1). In SPECT,the detector is placed at different angles around the subject. For a given angle, the detector acquiresa 2D view of the radioactivity distribution in the subject (a projection). In an idealized scenario,each detector element accepts only gamma rays that have originated from a narrow cylinder locateddirectly in front of that detector element. The gamma ray events detected by this element shouldbe proportional to the total tracer activity in the cylinder. The main axis of the cylinder definesthe line of response (LOR) for that particular element. The set of all counts collected by all thedifferent elements defines a projection. Typically, multiple projections are acquired for a complete180-degree or 360-degree view of the subject.PET systems take advantage of the simultaneous emission of two photons in opposing directionswhen a positron-electron annihilation occurs. The two photons can be detected by a pair of opposingdetector elements nearly simultaneously. In the case of PET, therefore, the LOR is defined by theaxis of the cylinder that connects the two detector elements. Although the detection mechanismsare different, in both PET and SPECT a set of projections at different angles around the subject are1PET image (DTBZ) SPECT image (DaTSCAN)Figure 1.1: Comparing brain PET and SPECT images of the dopaminergic system in healthysubjects. For each image, only the transaxial slice with maximum intensity is shown.Left: Image was obtained at the HRRT at UBC using 11C-dihydrotetrabenazine (11C-DTBZ). Right: A SPECT image using 123I-FP-CIT (also known as DaTSCAN) fromthe PPMI database. The bottom figures magnify the striatal region of the brain, whichcontains a large number of dopaminergic neurons, resulting in a high tracer uptake.acquired. The projections data are corrected and reconstructed to form a 3D image of the tracerdistribution in the body.In this thesis, an automated method to quantify tracer uptake is applied to both PET and SPECTbrain images. This chapter introduces the mechanisms of detecting the gamma ray photons producedin PET and SPECT imaging and reconstructing this data to form an image, with an emphasis on thefactors affecting the spatial resolution for the two modalities.1.2 Modes of Nuclear Decay in Functional ImagingIn this section, only the nuclear decay mechanisms that are most commonly used in brain PET orSPECT imaging are discussed. For a complete list of nuclear decay mechanisms utilized in medicalimaging, see [8].1.2.1 Isomeric gamma ray emissionWhen a radioactive parent nucleus decays, the resultant daughter nucleus might be stable (in theground state) or it might also be radioactive (in an excited state). In some cases, the daughter2product might be in a metastable or isomeric state, which has a relatively long lifetime. As a result,it can be purified from its parent nucleus and used as a gamma-ray source. Technetium-99m (Th-99m) is the most commonly used radionuclide in nuclear medicine; it decays via isomeric emissionto its ground state with a half-life of 6.02 hours. In 88% of the time, the decay occurs by emissionof gamma rays with an energy of 140.5keV, which are utilized for imaging.Instead of emitting a gamma-ray photon, the metastable nucleus might transfer the excess en-ergy to an orbital electron from one of the inner shells, thereby ejecting it from its shell. Thiselectron is called a conversion electron. For a given nucleus, the ratio of the probability of emittinga conversion electron over the probability of emitting a gamma ray is denoted by α . This is animportant characteristic of the radionuclide, since conversion electrons are absorbed within tissuewith very high probability, contributing to the radiation dose to the patient. An outer shell electronmoves in to fill the vacancy created by the conversion electron, and characteristic X-rays or Augerelectrons are emitted. In the case of Th-99m, characteristic X-rays with energies in the range 18-21keV are emitted.1.2.2 Electron captureIn this form of decay, an electron is captured by the nucleus and combined with a proton. As aresult, a neutron is formed, together with a neutrino, carrying away some of the energy of the decay.This can be represented as follows:p++ e−→ n+ν+EAuger electrons and characteristic X-rays are emitted by the daughter product when the electronvacancy is filled. In the case of elements with large atomic number Z > 50, the emitted X-raysmight be energetic enough to be used for imaging purposes. For example, Iodine-123 (Z = 53) is aradionuclide used in brain SPECT imaging that decays via electron capture. It decays to Tellurium-123 a half-life of 13.2 hours, via electron capture (87%) of the time or via internal conversionelectron emission (13%). In the electron capture process, the predominant gamma ray carries energyof 159keV (the one primarily used for imaging purposes). The characteristic X-rays emitted in theprocess carry energy of up to 32 keV.The electron capture transition might produce a daughter product in a metastable state thatfurther decays to a stable ground state, emitting gamma rays in the process.1.2.3 Positron emissionIn positron emission, a proton in the nucleus is converted to a neutron and a positively-chargedelectron called positron (the antiparticle of the electron). The positron, together with a neutrino areemitted from the nucleus. This reaction can be represented as:p+→ n+ e++ν+E3The neutrino (ν) leaves the system without significant interaction with matter. The positron (e+)contains a large amount of kinetic energy (on average, between 250-740keV for most radionuclidesused in imaging) and decelerates rapidly, losing the majority of its kinetic energy, within a fewmillimetres in tissue via Coulomb interactions. Much of the radiation dose to the patient is dueto this deceleration process. Once the positron slows down to thermal energies, it interacts withan electron from the surrounding atoms in an annihilation reaction. As a result, two gamma rayphotons are emitted, each with energy of approximately 511keV, equal to the rest energy of anelectron or a positron. As a result of momentum conservation, the two photons leave the annihilationevent at an angle of nearly 180 degrees. This directional relationship of the two photons is utilizedin PET through a mechanism called coincidence-counting (see Section 1.3.2).Fluorine-18 is a radionuclide commonly used in PET that can decay to Oxygen-18 either positronemission (97%) or via electron capture (3%) with a half-life of 110 min, and a mean e+ energy, whenemitted from the nucleus of Emeanβ = 250keV . The relatively long half-life of18F compared to otherpositron emitters means it can be produced in an off-site facility and transported to many imagingcentres. In addition, it has a relatively low Emeanβ , which results in a shorter positron travel in tissue,which is favourable for the spatial resolution (discussed in Section 1.4.2).Another commonly-used positron emitter in PET is Carbon-11, which decays via positron emis-sion (99.8%) or electron capture (0.2%) to Boron-11 with a half-life of 20.4 min, and Emeanβ =390keV . Carbon-11 can be easily bonded to many chemical compounds that occur naturally in thebody, without altering their structure and chemical kinetics. However, its short half-life means thatit needs to be produced in a cyclotron very close to the imaging centre. On the other hand, its shorterhalf-life minimizes the radiation exposure to the patient.1.3 Gamma Ray Detection1.3.1 In SPECTIn a standard SPECT system, a gamma camera is used to detect the gamma rays emitted fromthe radionuclide injected in the patient. A gamma camera consists of a collimator, a scintillatingcrystal, an array of photomultiplier tubes (PMTS) and electronics responsible for processing of theinformation of the detected events.Absorptive collimationThe collimator is a lead sheet with holes bored through it, and it is placed in front of the scintillatingcrystal. The walls between the holes are called septa. The purpose of the collimator is to allowonly gamma rays travelling in a certain direction to pass through it. Figure 1.2 illustrates how aparallel-hole collimator works. Gamma rays emitted at an angle < θ/2 pass through the holes. Therest of the gamma rays are absorbed with high probability by the septa. The angle θ is called theacceptance angle.4𝑑l𝑏sourceseptadetector	  crystalFigure 1.2: Acceptance angle θ for an absorptive collimator. Here d is the hole diameter, b isthe distance between the source and the detector, and l is the septal length.The parallel-hole collimator projects onto the detector a gamma-ray image of the same size asthe original radioactive distribution. Other types of collimator geometries are utilized in imagingsuch as the pinhole collimator (for magnification of small organs), diverging collimator (for imagingof large organs such as the lungs on a single view), and converging collimator (used with large-areadetectors for imaging of small organs).Two fundamental properties are used to characterize collimators: (i) efficiency: the probabilityof a gamma ray emitted from the source to pass through the collimator and (ii) spatial resolution,which is characterized by the Full Width at Half Maximum (FWHM) of a radiation profile producedby a point source projected by the collimator onto the detector. There is a trade-off between the twoproperties, in terms of collimator geometry and emitted gamma ray energy:1. Larger hole size increases efficiency but it also increases the acceptance angle θ . This leadsto a worse spatial resolution.2. Increasing the septal length and thickness improve spatial resolution but decrease efficiency.3. Gamma rays with a larger energy are more likely to pass through the collimator. This in-creases detection efficiency but also increases the FWHM.Absorptive collimation is a relatively inefficient process since the majority of the potentiallyuseful radiation coming from the source is absorbed by the collimator.Scintillation crystalsThe purpose of the scintillator is to absorb the incident gamma rays and convert their energy intooptical photons. Typically, a crystal of thickness 0.6− 1.2 cm made of sodium iodide (NaI) withthallium doping and diameter of about 40 cm is used. The gamma rays interact with the crystaleither via a photoelectric interaction, depositing all of its energy in a single location (valid event), orvia Compton scattering (detector scatter event). The scattered photon might interact a second time5in the crystal, depositing its energy in a different location (leading to a localization error), or it mightescape the crystal. For typical energies used in SPECT imaging, the localization error introducedby multiple Compton interaction is smaller than 1.5mm for 90% of the photons [25].When the gamma ray deposits energy in the crystal, a lattice excitation occurs; the lattice de-excites by emitting optical photons (a scintillation event). The number of liberated optical photonsby a single incident gamma photon is Poisson-distributed, and proportional to the average energyof the gamma photon. An important characteristic of the gamma camera crystal is its quantumefficiency α , which is the probability of an incident gamma ray to interact in the crystal, given by:α = 1− exp(−µsc(E)lsc)where µsc(E) is the linear attenuation coefficient of the scintillator (energy dependent), andlsc is the scintillator thickness. For a 150keV incident gamma ray, and a NaI(Tl) scintillator withthickness lsc = 0.64 cm, the detector efficiency is 70% but it declines to 7% for an incident 511keVphoton (which is why the NaI(Tl) crystal is not used in PET).Photo-multiplier tubesThere are 30-100 PMTS attached on the back of the crystal. These convert the optical photons intoelectric current that is used to estimate the position and energy of the gamma photons. Ideally, therelationship between current amplitude and the location of the scintillation event with respect tothe centre of a given PMT would be linear. This would allow the estimation of the location of thescintillation event to be computed via a weighted average:xˆ =∑i xiSi∑i Siwhere the sum is over all PMTS, Si is the signal magnitude (current) from tube i located atposition xi. This expression can be used to estimate the xˆ coordinate of the event (and analogously,yˆ). In practice, distortion corrections are performed to take various factors into account (e.g. a singlePMT is not a point detector and there is some reflections occuring at the edge of the crystal).Photo-peak windowAn estimate of the energy of each detected gamma ray can be made by adding up the contributingsignals from the PMTS. Ideally, the spectrum of detected energies would have a single, narrowpeak, called the photopeak, corresponding to the primary gamma rays emitted by the source. Inreality, the energy spectrum has a thick tail towards lower energies, due to Compton scattering inthe scintillator and collimator, and X-rays produced when gamma photons interact with the leadmaterial of the collimator. For this reason, a photopeak window is specified around the photopeak(typically about 20keV in width). Events that fall outside the photopeak window are not acceptedas valid detection events (although they might still be recorded, see Section 1.5.2).6Gamma camera setupA single-headed SPECT system is frequently used, where a single gamma camera is mounted ona gantry that allows the camera to be positioned in different ways around the subject. Anotherpopular setup is the dual-headed system, where two gamma cameras are mounted on a gantry, andcan be rotated at different angles with respect to each other, around the subject. The dual-camerasetup allows for multiple views of the subject to be acquired at the same time; this can be especiallyuseful when applying corrections to the acquired data (e.g. see conjugate counting in Section 1.5.1).In order to acquire a complete set of projections, the gamma camera (or the pair of cameras)is typically rotated around the subject, at a fixed angular displacement. For instance, for eachDaTSCAN SPECT image analyzed in this thesis, a set of 120 projections were acquired, steppingover a 3-degree interval each time, for a complete 360-degree acquisition, using a dual-camera180-degree opposing-view setup.1.3.2 In PETCoincidence countingPET systems take advantage of the simultaneous emission of a pair of photons in opposite directionswhen the positron annihilates with an electron. When the photons are detected by opposing detectorsat nearly the same time, the system can localize the line along which the photons have originated(line of response).Each photon detection event is recorded together with a time stamp. The system processorcompares this time stamp to the ones recorded by other (opposing) detectors. When a pair ofphotons are detected sufficiently close in time to each other, a coincidence event is assumed to haveoccurred. The difference in time between the two photons needs to be within the coincidence timeinterval (typically a few nanoseconds) for the event to be accepted. In this way, localization isperformed electronically, without the use of absorptive collimation. This leads to a much greaterefficiency for a PET system compared to SPECT.1.3.3 Block detectorsPET systems utilize block detectors, introduced by Casey and Nutt [5]. Each block includes a 2-3 cm thick scintillating crystal that is separated into smaller elements by a reflective material. Agrid of PMTS are placed on the back of the crystal: for example, in the setup shown in Figure 1.3,the crystal is separated in an 8 x 8 grid of crystal elements, and coupled to a 2 x 2 grid of PMTs.The reflective material that separates the crystal elements directs the optical photons towards thePMTS. Optical photons produced in a scintillation event that occurred in a single crystal element aredetected by all PMTS that are part of the block (known as PMT sharing).The current amplitude produced by each PMT can be used to identify the crystal coordinates(x,y) where the scintillation event occurred using Anger logic:7Figure 1.3: A schematic illustration of the block detector design. Illustration taken from [37].x =(B+D)− (A+C)A+B+C+Dy =(A+B)− (C+D)A+B+C+Dwhere A,B,C and D are the integrated current amplitudes from the corresponding PMTS. Each(x,y) location is then assigned to a specific crystal element.The advantage of the block detector design is that it allows for multiple crystal elements tobe used, thereby increasing spatial resolution, while reducing the number of PMTS needed. Thisallowed for a decrease in the cost and size of the detectors without sacrificing performance char-acteristics. Many modifications of this basic block design exist; for an overview of the trade-offinvolved with block detector modifications, see [8].Each of the annihilation photons carries energy of 511 keV, which is substantially larger than theenergy of photons emitted in isomeric emission or electron capture. Sodium iodide, with µsc(E =511keV ) = 0.35cm−1, is not optimal for detecting annihilation photons; denser materials with largeratomic number are used such as Bismuth Germanate (BGO) with µsc(E = 511keV ) = 0.96cm−1.A commonly-used PET configuration is to arrange the block detectors in a ring or a polygonalarray around the patient so that coincidence counting can be performed efficiently. This configura-tion allows for data from all projection angles to be acquired at the same time. Small ring diameters(around 35 cm) are used for high-resolution brain imaging and larger ones (80-90 cm) are used forwhole-body PET imaging.1.4 Factors Limiting the Spatial ResolutionIn an imaging system, the FWHM of the point spread function (PSF) is used to quantify imageresolution. Although the FWHM is not a complete characterization of the PSF, it is often used tocompare different imaging systems. Every major component of an imaging system can be charac-terized with its own FWHM, which determines the individual component contribution to the overallsystem resolution Rsys.81.4.1 In SPECTThere are three main factors limiting the spatial resolution of a SPECT camera, the most dominantof which is the use of absorptive collimation. The collimator resolution Rcoll is approximately givenby:Rcoll ≈ d(le f f +b)le f fwhere d is the diameter of the collimator holes, b is the distance from the source to the collima-tor, and le f f = l−2µ−1 is the effective length of the collimator holes (see Figure 1.2). Here µ is thelinear attenuation coefficient of the material making up the collimator and le f f < l because some ofthe gamma rays penetrate the collimator septa.The next two factors are related to the intrinsic resolution of the gamma camera (Rint). When ascintillation event occurs at a given location, the number N of optical photons detected by a singlePMT follows a Poisson distribution, with a standard deviation√N. This means that if a numberof scintillation events occur repeatedly at exactly the same location in the crystal, the number ofoptical photons detected by that PMT (and the corresponding signal produced by the PMT) wouldvary following Poisson statistics. This would result in a distribution of estimated locations for thescintillation events spread over a certain area dependent on the variability in the number of opticalphotons. Using scintillation materials with a larger light output (number of optical photons per keVof incident gamma radiation) lead to an increase in the intrinsic spatial resolution (in addition to anincrease in the energy resolution). For instance, the light output of NaI(Tl) is 38 photons/keV, andthat of BGO is 6 photons/keV.The third factor is related to Compton scattering of the gamma rays within the detector. Ifthe scattered gamma photon also produces a scintillation event at some distance away from theprimary interaction, an error is introduced in the location estimate. For low-energy gamma raystypically used in brain SPECT (< 200keV ) the effect of multiple Compton scattering events onimage resolution is negligible.The overall SPECT system resolution Rsys is a combination of the collimator and intrinsic reso-lution and is given by:Rsys =√R2int +R2colland it is determined primarily by the collimator resolution.1.4.2 In PETA fundamental limitation to resolution in PET imaging is based on the distance the positron travelsbefore annihilation. The PET system can only detect the line along which the annihilation eventhas occurred, which is not exactly the line along which the radionuclide emitted the positron. Themaximum travel distance Rmax of emitted positrons depends on their maximum energy (Emaxβ ) whenemitted from the nucleus. For instance, for 18F , Emaxβ = 635keV , which results in Rmax ≈ 2.5mm.9However, a more useful measure is the root mean square effective range Rrange, as it better describesthe average distance travelled by the positron. For 18F , Rrange ≈ 0.3mm.Another factor related to positron physics is that the annihilation photons are never emitted atexactly 180-degrees apart. This is known as photon non-colinearity. This effect depends on thediameter D of the PET ring:R180 = 0.0022DFor a brain PET scanner with D = 40cm, R180 = 0.9mm.When discrete detector elements are used, the primary factor affecting the detector resolutionRdet is the detector width d. Due to the detector geometry in a ring configuration, assuming that thesource is located near the centre of the scanner, the shape of the point spread profile is a triangle(Rdet ≈ 0.5d) and turns into a rectangle near the face of one of the detectors (Rdet ≈ d). However,when the source is away from the centre of the scanner, there is an additional effect called the depth-of-interaction effect (Figure 1.4), which degrades resolution further. Assuming that the detectorsystem is arranged in a circular configuration, as the source moves away from the centre of thescanner at an increasing larger angular offset, the apparent width d′ of the detector element increasesas:d′ = dcosθ +Lsinθwhere d is the width of the detector element, L is the length of the crystal, and θ is the angularoffset from the centre of the scanner. This change in the apparent width is caused because thesystem is unable to locate the depth within the crystal at which the scintillation event has occurred.Because the stopping power requirement for the 511keV photons is significant, detectors with largercrystal length L (2-3 cm) are needed, making the depth-of-interaction effect more pronounced: itcan degrade Rdet by up to 40% at a distance of 10cm from the centre of the scanner [8].The combined PET system resolution is:Rsys =√R2det +R2180+R2rangeNote that in a PET system the detector resolution is primarily determined by the size and ge-ometry of the detector elements, as well as the positron physics. In SPECT, the resolution degradessubstantially as the object moves away from the gamma camera. A collimator with a very highresolution at the face of the detector is needed to achieve a moderate resolution at the centre of theobject being imaged.10d'w!LFigure 1.4: Depth-of-interaction effect for a PET system in a circular configuration. The sys-tem is unable to locate the exact depth within the crystal at which the scintillation eventhas occurred. For this reason, the annihilation event could have occurred anywhere insidethe area marked with dotted blue lines.1.5 Corrections to PET and SPECT Data1.5.1 Attenuation correctionAttenuation correction is the most significant correction for both PET and SPECT. It is necessarybecause gamma rays emitted at different locations in the subject have depth-dependent probabilityof emerging from the subject. For example, a 150keV gamma photon, emitted from a depth of15cm within the body would have a probability of e−15µl = 0.11 of emerging from the subject.Here µl(E = 150keV ) = 0.15cm−1 is the linear attenuation coefficient for tissue, which depends onphoton energy.Conjugate counting is an approach used in SPECT to reduce the attenuation effects. In conjugatecounting, projection data is obtained from two directly opposing views of the subject. These signalsare then combined using the geometric mean SG =√S1S2. An object that is far from the detectorin the first view would be strongly attenuated, however it would be weakly attenuated in the secondview, resulting in a partial cancellation effect when the two signals are combined.In addition, Chang’s multiplicative method [7] is a commonly used method for attenuation cor-rection. In this approach, an initial image is reconstructed without applying any attenuation cor-rection. The contours of this image are used to estimate the path length di through tissue for eachprojection. Each voxel at position (x,y,z) in the reconstructed image is then corrected by multiply-ing it by the following correction factor (ACF):11ACF(x,y,z) =N∑i e−µldi(x,y,z)where i = 1..N and N is the total number of projections.In PET imaging, the transmission probability that both of the annihilation photons will reachthe corresponding detectors is:A = e−µl(W−d)e−µld = e−µlWwhere W is the width of the subject along the LOR, and d measures how deep the annihilationoccurred within the tissue. The transmission probability A is independent of d.The results so far have assumed a constant linear attenuation coefficient, which is not realisticfor many regions of the body such as the thorax. The transmission probability becomes:A = exp[−∫ W0µl(x)dx]where the integral is along the LOR and µl(x) is now location-dependent. An attenuation mapwhich provides information about the spatial dependence of the attenuation coefficient is needed.Standard approaches to acquire the attenuation map often involve the acquisition of a transmissionscan. A transmission scan is often performed using an external point or line source, placed at variousangles around the subject. In this way, transmission profiles through the subject can be acquired,similar to a CT image. These transmission profiles can be reconstructed to provide the attenuationprofile. Two scans are typically required to obtain the attenuation profile: a blank scan, where thesubject is not present in the field of view (FOV), and a transmission scan, where the subject is in theFOV. With these two pieces of data, an attenuation map can be reconstructed, and used to computemore accurately the ACF.With the advent of hybrid PET-CT and PET-MRI scanners, attenuation maps can be constructedusing the Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) image. In an MRimage, unlike in CT, the image intensity in a given region is not directly related to the attenuationproperties of that region, so the MR image cannot be directly converted to an attenuation map.Various computer algorithms are used to construct the attenuation map for PET-MR scanners, see[57] for a review.1.5.2 Scatter correctionScatter events occur when the signal corresponding to a particular LOR includes events that haveoriginated from outside of this line of response. Scatter events result in a loss of contrast andpotentially introduces bias in the reconstructed voxels. Scatter and attenuation are part of the samephysical phenomenon; for gamma photon energies that occur in SPECT and PET imaging, the largemajority of the gamma ray interactions in tissue occur via Compton scattering.In SPECT, scatter correction can be performed by acquiring counts within the photopeak win-12dow (e.g., 125-160keV) as well as at lower-energy scatter window (e.g., 90-123keV). The resultantscatter profiles are multiplied by a weighting factor (determined experimentally) and subtractedfrom the photopeak profiles to compensate for the scatter events that are contributing to the pho-topeak profiles. This method assumes that the spatial distribution of the scatter events in the twoenergy windows is similar.In PET, only one of the two annihilation photons needs to be scattered for a scatter coincidenceevent to occur. In addition, the crystal materials have lower light output (6 optical photons perkeV of gamma radiation for BGO) resulting in lower energy resolution. To compensate for that,wider photopeak windows are used in order to increase detection efficiency, which also increasesthe scatter event fraction. In brain PET imaging, the scatter fraction may exceed 30% of the totaldetected events [58].A commonly-used scatter correction technique is the Single Scatter Simulation Technique [58],where a simulation of the scattered events is performed using the differential cross-section of Comp-ton scattering. The primary assumption of this method is that only scattered events are consideredwhere a single Compton scattering has occurred. Gamma rays that have undergone Compton scat-tering more than once are likely to have lost a large portion of their energy, so it is unlikely that theywill be accepted in the photopeak window. This correction procedure can also be integrated as partof the reconstruction algorithm.1.5.3 MotionA SPECT or a PET brain scan typically takes between 20 and 90 minutes; often patient movementoccurs during this period despite the use of head constraints. This motion could cause a loss ofimage resolution due to blur, erroneous localization of regions with high tracer uptake, and a mis-alignment between the image and the attenuation map, which may further introduce image artifactsand incorrect quantification. In brain imaging, the head motion is largely rigid (without deforma-tion) and so a rigid motion correction can be applied. In this case, optical tracking data of the headmight be acquired using an external tracking device; this data are acquired simultaneously withthe scan [46]. This motion tracking data can be used to geometrically transform the correspondingprojection data. The disadvantage of this approach is that it requires additional motion-trackingequipment.Dynamic PET data may take more than an hour to be acquired; during this time it is likely thatsome amount of motion will occur. However, each individual frame (volume image) is acquired overa relatively short time period of 1-10 minutes so motion during this single-frame acquisition can beassumed to be smaller than the inter-frame motion. To correct for possible misalignment betweenthe different frames caused by patient motion, the reconstructed 3D frames can be coregistered toeach other (typically using a rigid transformation). This is known as frame-by-frame alignment.131.5.4 Random coincidencesRandom coincidences are specific to PET; they occur when gamma photons from two separateannihilation events are detected within the same coincidence time window, and treated as a singleevent. The random coincidence count can be estimated by delaying the coincidence window (by upto 80 nanoseconds) so that only photons from separate annihilation events that have occurred about80 nanoseconds apart will be recorded. To perform the correction, this count can be subtracted fromthe uncorrected annihilation counts. It is usually assumed that the coincidence count rate is spatiallyuniform across the detector.1.5.5 Partial volume effectThe partial volume effect occurs when the intensity of a (typically small) object with high traceruptake ”spills” over the surrounding regions due to the limited system resolution. This is illustratedin Figure 1.5. The original image (left panel) is convolved with a Gaussian filter with a progressivelylarger radius, to simulate an intrinsic loss of resolution. As the filter radius increases, the ”spill-over” effect is apparent - the high intensity in the striatum is spread over the surrounding areas. Theline profile illustrates the loss in contrast caused by the partial volume effect. This is particularlyimportant when quantitative imaging is used, where accurate measurement of the intensity in a givenregion relative to the background is needed.The most robust methods of correcting for partial volume in PET and SPECT require additionalanatomical information, obtained from MRI or CT. Reference [16] describes a partial volume cor-rection as part of an iterative reconstruction algorithm applied to DaTSCAN SPECT images. Thiscorrection can take into account the distance-dependent spatial resolution in SPECT (as the radiationsource moves away from the collimator, the resolution is degraded).1.6 ReconstructionPET and SPECT detectors acquire a set of projection data that is used to reconstruct a 3D imagerepresenting the distribution of the tracer uptake in the subject.1.6.1 Filtered back-projectionA widely-used reconstruction method is the filtered back-projection; this is an analytic approachthat applies a filter on the projection data before it is back-projected. It is convenient to representa set of projection data in a sinogram p(r,φ), where each row corresponds to a single projectionprofile (acquired at an angle φ with respect to the x-axis), and r measures the distance away fromthe gamma camera (so the r coordinate is fixed with respect to the camera). The filtered back-projection algorithm consists of these steps:1. Apply a 1D Fourier transform on each projection profile along the r direction. This results ina transformed set of data P(kr,φ):14original 1.2 mm kernel 2.4 mm kernel 4.9 mm kernel0 25 50 75distance [mm]50000100000150000200000counts0 25 50 75 0 25 50 75 0 25 50 75Figure 1.5: Partial volume effect on the striatal region of the brain. This region is from theDTBZ image shown in Figure 1.1. A line profile through each image (location of theprofile marked by the red arrow) is shown in the bottom panel. The double spikes inthe original line profile are caused because the system is able to resolve the separatestructures of the striatum (putamen and caudate).P(kr,φ) = FT [p(r,φ)]2. Apply a filter H(kr) to each profile in order to amplify high frequencies and attenuate lowerfrequencies. In theory, in a noise-free environment, the ramp filter H(k) = |k| would be opti-mal in order to deconvolve the so-called 1/r blurring introduced by simple back-projection.In practice, the ramp filter introduces many high-frequency artifacts. The Hann filter is oftenused:H(k) = 0.5|k|(1+ cos( pikkcuto f f))where the choice of the frequency cutoff kcuto f f is application-dependent. This results in thefiltered data P′(kr,φ):P′(kr,φ) = H(kr)P(kr,φ)3. Apply the inverse Fourier transform on the filtered data:p′(r,φ) = FT−1[P′(kr,φ)]4. Perform conventional back-projection to find an approximation f ′(x,y) to the original activitydistribution:15f ′(x,y) =1NN∑i=1p′(xcosφi+ ysinφi,φi)where the index i is over the different projection profiles (rows in the sinogram).The main advantages of the filtered back-projection technique is its simple implementation andlow computational requirements, leading to its widespread adoption. A primary disadvantage isthe difficulty of incorporating the physical limitations of the system, such as the limited detectorresolution, directly into the reconstruction algorithm. In addition, this method is susceptible tomajor artifacts when the projection data are measured incompletely (for instance, due to a defect inthe electronics). For an in-depth discussion of filtered back-projection, see [15].1.6.2 Iterative reconstruction using maximum likelihoodAn alternative class of approaches employ the Maximum Likelihood principle; these methods formu-late the problem of reconstruction using probability theory. The goal is to find the tracer distributionwith the highest probability (maximum likelihood) of producing the observed projection data. Thisproblem cannot be solved in a closed form and iterative reconstruction methods are employed usingthe expectation maximization algorithm. These approaches are substantially more challenging toimplement and computationally demanding, in part because the forward- and back-projection stepsneed to be performed for each iteration. The ordered-subsets approach is often used to speed up thecomputation - in this approach only a subset of the projection data is used in the initial iterations.A primary advantage of this class of methods is that they can incorporate sophisticated models ofthe measurement procedure directly into the reconstruction. This flexibility results in reconstructedimages that are typically more quantitatively accurate compared to the ones reconstructed withfiltered back-projection. Reference [38] describe this approach. Variations of the ordered subsetsexpectation maximization method were used to reconstruct the 18F-DTBZ PET and the DaTSCANSPECT images used in this work (Section 6.2.2).16Chapter 2Quantifying Radioligand BindingThe biochemical processes investigated by functional imaging have a temporal component deter-mined by the rates at which these reactions occur. These reaction rates can reveal important in-formation about the underlying tissue physiology. Dynamic imaging is used to measure how thetracer concentrations change over time. In dynamic imaging, the image acquisition is split into timeframes (typically lasting a few minutes each in PET and up to one hour in SPECT). The individualframes are reconstructed (with the isotope decay taken into account) producing a time series of 3Dimages of the tracer concentration.The mathematical models used to relate the dynamic tracer concentrations and the physiologicalparameters of interest are called kinetic models. There are many different kinds of kinetic models de-pending on the physiological process under investigation. Some examples include ejection fractionmodels to study the heart function and enzyme kinetic models that describe glucose metabolism.This chapter introduces a type of model that is relevant for the brain imaging analysis presentedin this thesis - the receptor ligand assay. For instance, the the tracer 11C-dihydrotetrabenazine(DTBZ) can act as a radioligand for the vesicular monoamine transporter 2 (VMAT2), a proteinthat packages neurotransmitters such as dopamine into synaptic vesicles. Using kinetic modelling,the dynamically acquired 11C-DTBZ data can be used to estimate important parameters about theVMAT2 distribution in the brain.The first two sections in this chapter introduce the kinetic model concepts needed to characterizereceptor-ligand reactions. Section 2.3 discusses some of the practical challenges with dynamicimaging and introduce simpler imaging metrics commonly used in clinical practice. The automatedapproach developed in this work is motivated in Section In Vitro Equilibrium BindingA simple model for the reaction between a free ligand F and a receptor R in vitro is given by:R + Fkon−−→←−−koffRFwhere kon and ko f f are the reaction rate constants. The ratio KD = ko f f /kon is the equilibrium17CP CRCND CSK'1K1k'2k2k3k4Target regionReference regionFigure 2.1: The reference tissue model.dissociation constant. At equilibrium we haveKD =ko f fkon=[F ][R][RF ]The total receptor concentration in vitro is referred to as Bmax = [R] + [RF ]. Rearranging theequation above, we obtain:[RF ] =Bmax[F ][F ]+KdIf we assume that the ligand F is administered at tracer levels, so that [RF ]<< [R], this expres-sion can be further simplified into:BmaxKd=[RF ][F ]This ratio is known as the in vitro binding potential and relates the receptor density Bmax and thestrength of the receptor-ligand interaction 1/Kd .In many receptor-ligand imaging studies, an in vivo estimate of the binding potential is used asthe primary outcome. The interactions between the tracer and receptor in vivo are significantly morecomplicated. In vitro reaction kinetics assume that all receptors R are available for binding with F.Typically, in vivo only a fraction (Bavail) of the total receptor density Bmax is available to bind with F.In this case, the ratio of interest is Bavail/Kd . The next section discusses a simplified compartmentalmodel that allows for an estimate of this ratio in imaging studies.2.2 Compartmental ModellingEach compartment represents a distinct biochemical state of the tracer molecule. Figure 2.1 showsan example of a compartmental model. In this model there is one compartment that representsthe tracer concentration in the arterial blood plasma (CP), and three tissue compartments (where C18represents concentration):• reference compartment (CR): typically a reference region is selected where the target receptordensity is negligible. For example, in the case of dopamine transporter imaging, the occipitalcortex is commonly used as reference.• non-displaceable target compartment (CND). This represents the fraction of the tracer that isin the target region but it is not specifically bound to the receptor of interest. The tracer mightbe free (not bound to any compound) or bound non-specifically to other proteins or lipids.• specific compartment (CS): this is the tracer fraction in the target region that is specificallybound to the target (e.g. the dopamine transporter).Note that the concentrations CND and CS cannot be separated from each other in an image of thetracer concentration since they occupy the same physical space (the target region). Instead, a singleconcentration CND+CS is measured.The rate constants K1, ...k4 describe the transport (flux) of the tracer from one compartmentto another and have units of min−1. Typically, tracer kinetic models assume first-order processes,where the flux from a given compartment is linearly proportional to its concentration. For instance:f luxS→ND = k4×CSgives the amount of the tracer that is leaving the specific compartment S and ”flowing into” thenon-displaceable compartment ND per minute.A system of first-order coupled differential equations can be used to describe the tracer concen-trations over time:dCNDdt= K1CP− k2CND+ k4CS− k3CNDdCSdt=−k4CS+ k3CNDdCRdt= K1CP− k2CRThis system can be solved to relate the observed concentrations (CND +CS and CR) to the pa-rameters of interest - the rate constants. At equilibrium we have:dCSdt= 0 =>k3k4=CSCND.This is the ratio of the specifically-bound tracer at equilibrium to that of the nondisplaceabletracer in tissue; it is called the non-displaceable binding potential (BPND ). Note that it is closelyrelated to the in vivo binding potential:19BPND =fNDBavailKdwhere fND =C f reeCNDis the fraction of the tracer in the non-displaceable compartment that is free(and is therefore available to interact with the receptor). There are several practical advantages ofusing BPND as an outcome measure in receptor-ligand imaging studies:1. It is related to the available receptor density Bavail . In a disease state receptors are frequentlyover- or under-expressed, and BPND can be used to assess the underlying pathology.2. The rate constants k3 and k4 are correlated with each other. BPND has a lower overall errorcompared to the rate constants, making it a more robust measurement [29].3. When a reference region can be identified that is devoid of specific binding, BPND can be es-timated directly from the dynamic imaging data, without the need for blood plasma samplingto measure CP.The proper use of BPND depends on the assumptions that (i) the tracer-receptor reaction is re-versible over the time-scales of the dynamic scan and (ii) the nondisplaceable uptake is independentof subject groups.There are many different approaches to compute BPND . Typically, a weighted non-linear leastsquares model is fitted in order to estimate BPND based on the measured tracer concentrations:CND(t)+CS(t) and CR(t). In order to reduce the number of parameters to be estimated, it is assumedthat K1/k2 = K′1/k′2.It is particularly convenient to transform compartmental models into a linearized form as thisallows efficient estimate of the kinetic parameters using standard least squares techniques. Graphicalmethods, such as the Logan graphical analysis, perform such a linearization, and are applied to thestudy of reversible radioligands [40]. The Logan method is widely used in brain imaging due to itssimplicity and because it can be used to estimate kinetic parameters without specifying a particularcompartmental model.Figure 2.2 shows an example of a 11-C DTBZ BPND image of a Healthy Control (HC) subject. Inthis case, the binding potential is computed voxel-wise, so each voxel has an estimated BPND value;this is referred to as a parametric BPND image. In this thesis, BPND calculations are not performed,however, the concepts described here justify the use of simpler quantification approaches, whendynamic data is not available.2.3 Simplified Approach with the Binding RatioThe kinetic modelling approach outlined in the previous section requires dynamic scanning sessionsthat can last more than 1 hour. This results in a more complicated acquisition protocol (and morepotential sources of error) and increased discomfort for the patient. These considerations are ofparticular relevance when the analysis is to be applied in large clinical studies of Parkinson’s disease.20Figure 2.2: A parametric BPND image of a HC subject imaged with 11C-DTBZ.These studies often include patients with fairly advanced disease, who may not tolerate prolongedimaging sessions.A widely-used, simplified imaging metric to approximate BPND is the Binding Ratio:BRT =CT −CRCRwhere CT and CR are the average tracer concentration in the target and reference regions respectively.If the biochemical system has reached equilibrium (dCT/dt = 0 and dCR/dt = 0) at the time ofimage acquisition, then a single static acquisition is sufficient for the BR to be computed (in whichcase it closely approximates BPND ).For instance, in the case of DaT imaging with DaTSCAN, the tracer binding in the putamenand caudate is of interest. Regions of Interest (ROIS) are placed on the target (putamen or caudate)and the reference (occipital cortex) regions. These ROIs might be placed manually on the SPECTimage or based on anatomical information from other modalities such as MRI. It takes about 4hours for DaTSCAN to reach equilibrium in the striatum, so images are typically acquired 4.5hours post injection. The tracer uptake values within the ROIs are averaged in order to computeBRputamen and BRcaudate. Figure 2.3 shows an example with geometric ROIs manually placed ona DaTSCAN image of a subject with Parkinson’s disease (PD). The corresponding BR values arelisted in Table 2.1. A pattern common to PD subjects is that the binding ratios in both the caudateand the putamen decline monotonically (ignoring measurement error) as disease progresses, whichis associated with dopaminergic neuron degeneration (further discussed in Chapter 3).21Screening Year 1Year 2 Year cortexFigure 2.3: DaTSCAN SPECT images of a subject with Parkinson’s disease imaged over a4-year period. Green circles show the geometric ROIs placed on the target regions -putamen and caudate. White circles show the reference region ROIs placed on the oc-cipital cortex. A single transaxial slice is shown for each image; the actual geometricregions extend over 8 slices.Table 2.1: Binding ratios computed from the images shown in Figure 2.3. (B) is the better(less affected) side of the brain, and (W) is the worse side.Region Caudate (B) Caudate (W) Putamen (B) Putamen (W)Screening 1.72 1.56 1.00 0.56Year 1 1.87 1.17 0.40 0.59Year 2 1.71 1.21 0.57 0.39Year 4 0.87 0.85 0.32 0.232.4 Tracer Quantification in This WorkA consistent and accurate estimate of the BRs requires a careful placement of ROIs. The conven-tional ROI placement procedures (reviewed in Chapter 4) can be time consuming and can introducesignificant complications, especially when the analysis is to be applied in multi-center studies, thatuse scanners with different image resolution.In addition, when evaluating the BR over fixed-size anatomically-based or geometric ROIs, in-formation of the disease-induced alteration of the functional size is lost. For example, in Figure 2.3,it can be observed that the size of the high-activity area, which denotes preserved functional activity(marked by the green contour lines in the images), decreases rapidly over the four years, especiallyfor the less-affected side of the striatum.In this work, a new imaging metric, termed Sum Intensity (SI), is introduced, together with amuch simplified ROI placement approach. The SI metric (Section 5.3) captures the change in thesize of the functionally active region in the striatum, as well as the tracer binding magnitude (relatedto image intensity). SI is evaluated within a bounding box automatically placed over the striatal re-gion in SPECT and PET images (Section 4.4); this simplified ROI definition method eliminates the22need for MRI acquisition or manual ROI placement. In order to validate this metric, the correla-tion is computed between the SI values and clinical measures of severity of PD subjects the PPMIdatabase (Chapter 6).23Chapter 3The Dopaminergic System inParkinson’s DiseaseThis chapter introduces some of the pathological characteristics of Parkinson’s disease, as they relateto the dopaminergic imaging studies in this work. Section 3.3 provides an overview of the clinicalexams commonly used to quantify motor dysfunction, cognitive impairment, olfactory function anddepression in PD subjects. These clinical scores are later combined with imaging features in orderto model longitudinal progression of the disease in Chapter 7. The Parkinson’s Progression MarkerInitiative, which holds the primary set of clinical and imaging data investigated in this thesis, isintroduced in Section 3.43.1 Parkinson’s DiseaseParkinson’s disease (PD) is a progressive, neurodegenerative disease with an incidence proportionof 105 per 100,000 for women and 133 per 100,000 for men between the ages of 70− 79 [26].The motor symptoms of PD include tremor, limb rigidity, bradykinesia (slowness of movement),hypokinesia (reduction in movement), abnormal facial expression and freezing (inability to initiatea voluntary movement). Cognitive impairment occurs frequently among PD patients (in 15−38%of subjects by year 3 since diagnosis [6]), and depression and dementia are common in older PDpatients. Age is a risk factor for PD; the incidence proportion for the age group of 60−69 is nearlythree times larger than that of the 50−59 age group.The main pathological feature of PD is the loss of dopaminergic neurons in the substantia nigra(SN). These neurons transmit dopamine (a neurotransmitter) from SN to the putamen and caudatenucleus, forming the nigrostriatal pathway. The bodies of these neurons are in the SN, and theyproject to the putamen and, to a lesser extent, to the caudate nucleus. In addition, there is alsoaccumulation of Lewy bodies in the affected brain regions - these are spherical protein aggregatesconsisting primarily of alpha-synuclein [13]. Lewy bodies are not specific to Parkinson’s disease;they are also found in a number of other neurodegenerative diseases including Alzheimer’s disease.Currently, there is no cure for the disease. The most common symptomatic treatment involves24levodopa (L-3,4-dihydroxyphenylalanine) or dopamine agonists. Levodopa is a chemical precursorto dopamine. Unlike dopamine, levodopa can cross the blood-brain barrier. Once inside the brain,levodopa is converted to dopamine by the aromatic L-amino acid decarboxylase enzyme. Levodopaalleviates many of the motor symptoms of PD. However, after several years of treatment with thedrug, most PD patients develop involuntary movement called dyskinesias which substantially affecttheir quality of life [13].A dopamine agonist is a compound that activates the dopamine receptors, and in this way itmimics the activity of dopamine. Unlike levodopa, dopamine agonist drugs do not need to beconverted into dopamine for their action to take place. They are commonly used for treatment ofearly motor symptoms in PD subjects.3.2 The Dopaminergic System in Parkinson’s DiseaseNeuroimaging techniques such as PET and SPECT have been used extensively to study the neu-ropathological mechanisms of PD, and more recently, to detect PD. The tracers used to study thedopaminergic system in this work are:• N-ω-fluoropropyl-2β -carbomethoxy-3β -(4-iodophenyl)tropane (FP-CIT) is a cocaine ana-logue with high affinity for the dopamine transporter (DaT). DaT is a membrane protein thattransports dopamine out of the synaptic cleft and back into the cytosol, and in this way DaTterminates the neurotransmitter signal. [123-I] FP-CIT (also known as DaTSCAN) is the firstFDA-approved SPECT tracer to investigate the DaT distribution in the striatum. It is oftenused to differentiate essential tremor from tremor due to Parkinsonism [3] and to estimate PDprogression [43].In addition, DaTSCAN has a weaker affinity for the serotonergic transporter (SERT). Recentwork has investigated the ability of DaTSCAN to quantify extrastriatal SERT expression [45].• Dihydrotetrabenazine (DTBZ) is a compound with strong affinity for the vesicular monoaminetransporter 2 (VMAT2). VMAT2 is a membrane protein that transports neurotransmitters suchas dopamine and serotonin from cytosol into the synaptic vesicles in the presynaptic neurons.The synaptic vesicles are then released into the synaptic cleft, thereby conveying the neuro-transmitter signal to the postsynaptic neurons.As a radiotracer, [11-C] DTBZ was first developed by the group of David Kuhl at the Univer-sity of Michigan [21]. There exist two enantiomers of DTBZ, and only the positive isomerhas a high affinity for VMAT2. DTBZ can also be labelled with 18-F (known as AV-133).The work presented in this thesis focuses on the dopaminergic system, which is the one mostseverely impacted in PD. However, the serotonergic, noradrenergic and cholinergic systems arealso affected by the disease and can be studied via PET and SPECT imaging. For a review of theneuroimaging methods used to study PD, see [49].25Table 3.1: Motor scores for the two PD subjects whose DaTSCAN images are shown in Fig-ure 3.1. Both subjects are male, and 68-years-old when they were enrolled in the PPMIstudy (year-0). Year-4 corresponds to the motor score exams performed four years intothe study. Definition for the MS components are in Section 3.3.1.Subject Better MS Worse MS Common MS1 (year 0) 1.67 3.00 2.671 (year 4) 7.00 7.00 3.002 (year 0) 10.67 18.33 12.002 (year 4) 14.00 24.33 Patterns of PD progression in the striatumThere are several aspects of PD progression [37] that are particularly important for the work pre-sented here:• In PD subjects, the degradation of the dopaminergic system follows the rostrocaudal axis inthe striatum. The region to be affected the most (at least in early disease) is the posteriorputamen, followed by the anterior putamen, and then by the caudate. This can be seen inthe striatal images of subjects 1 and 2 shown in Figure 3.1. In the case of subject 1 (earlydisease), the tracer uptake in the putamen on the more affected side is substantially reduced,but the caudate uptake is largely preserved. In subject 2 (advanced disease), both the putamenand caudate regions are substantially affected.• The second pattern has to do with the disease asymmetry. For most of the PD patients at onsetof clinical symptoms, one side of the body is substantially more affected than the other. Thisasymmetry is also observed in the brain, where the contralateral side of the striatum is moreaffected (e.g. reduced DaTSCAN uptake). This continues until advanced disease stages arereached when the two sides of the body (and the striatum) are affected to a similar extent.These patterns in the striatum are distinct from the dopaminergic loss that occurs in healthyaging. This is illustrated by the images of subjects 3 and 4. While the uptake in the scan ofsubject 4 is substantially reduced compared to the one of subject 3, this reduction is relativelyuniform over the entire striatum, and it is symmetric. This suggests that, while healthy agingis a risk factor for PD, the mechanisms of PD degeneration are distinct from those of healthyaging [13].• The pathological changes in the brain begin years before the start of the clinical symptoms.Typically, by the time the disease is diagnosed, the uptake in the more affected putamen isreduced by about 50%.26PDHCFigure 3.1: DaTSCAN images of the striatum for two healthy control subjects (HC) and twoPD subjects. The transaxial slice with maximum total intensity is shown for each image.In all cases, the intensity is normalized using the occipital cortex as reference. Note thatthe upper two images use a different intensity range on the colour map compared to thelower ones, since the uptake in HC subjects is substantially larger.3.3 Clinical Exams3.3.1 UPDRS motor scoreThe Movement Disorder Society-sponsored revision of the Unified Parkinson’s Disease RatingScale (MDS-UPDRS) is a widely-used scale to monitor the progression of the disease clinically[23]. It consists of four sections:1. Evaluation of non-motor experiences of daily living (cognitive impairment, depression, apa-thy, daytime sleepiness).2. Evaluation of motor experiences of daily living (speech, eating tasks, tremor, freezing).3. Motor examination, which is performed by a clinician.4. Motor complications (impact of dyskinesias, motor fluctuations).The analysis in this thesis is focused on part III of the scale. This part contains 18 items, andthere are five possible scores for each item, between 0 (normal) and 4 (severe), so a healthy subjectwould have a total MS of 0. The items can be split into lateral (e.g. the ”kinetic tremor of hands”would have separate scores for the left and right hands) and common items (all other terms such asgait). The complete list of items is as follows:• Lateral: rigidity of hands and legs, finger and toe tapping, pronation/supination, leg agility,postural tremor of hands, kinetic tremor of hands, rest tremor amplitude.27• Common: speech, facial expression, neck rigidity, arising from chair, gait, freezing of gait,posture, postural stability, global spontaneity of movement, constancy of rest tremor.Each subject has 3 MS components: better side (lateral), worse side (lateral) and commoncomponent. In the cross-sectional analysis in this work (Chapter 6), a combined better + commonscore is correlated with an image metric computed on the contralateral side of the striatum. Forexample, if the left side of the body is less affected by disease, then the left + common score iscorrelated against an image metric computed on the right side of the striatum.PD medication that alleviates the motor symptoms has a profound effect on the motor score.For the purposes of the analysis presented here, accurate MS assessment needs to be performed inthe ”off state”, i.e. when medication has been withdrawn for at least 12 hours before the exam.Examples of the motor score components for the two PD subjects from Figure 3.1 are shown inTable 3.1. Some observations about these scores are as follows:• The overall score is smaller for subject 1, which also corresponds to a better-preserved striataldopaminergic function (Figure 3.1).• There is substantial bilateral asymmetry in the motor scores of subject 2 and a much smallerasymmetry for subject 1.• All components of the MS are monotonically increasing which reflects the progressive declinein motor function. However, this decline is different for each of the components. For example,for both subjects, the increase in the common component is smaller compared to the increasein the lateral components.3.3.2 Montreal Cognitive AssessmentThe Montreal Cognitive Assessment (MoCA) is a screening exam used to determine the cognitivestatus of adults [48]. It was originally developed in 2005 to detect mild cognitive impairment andmild Alzheimer’s disease, but has been extensively used since then to measure cognitive declinein other populations [11], including PD subjects. It consists of 11 tasks that are designed to as-sess attention and concentration, executive functions, memory, language, visuoconstructional skills,conceptual thinking, calculations, and orientation. The maximum score is 30 points, and score≥ 26is considered to be normal.Previous work found that the MoCA score may be susceptible to practice effects when admin-istered repeatedly, 12 months apart (which is the case in the PPMI study examined here) [11]. Inthat study, the score was found to be greater by 1 point on average for the second exam, performed12 months after the initial one. Nevertheless, in most cases this practice effect was found to berelatively small compared to any possible disease effect.283.3.3 University of Pennsylvania Smell Identification TestThe University of Pennsylvania Smell Identification Test (UPSIT) examines an individual’s olfactorysystem through smell identification [14]. The test includes 40 questions in total, and each questionincludes a strip which releases a scent when scratched with a pencil. The patient smells the scent andthen attempts to identify it through a four-choice multiple-choice question. It is the most widely-used olfactory test in the world - it has been administered to more than 500,000 people worldwide[31]. Larger UPSIT score indicates a stronger ability to identify smells, and the maximum score is40. The score declines as a function of age, and women perform better than men on average [14].Hyposmia (reduced ability to smell) is considered a risk factor for Parkinson’s disease as wellas Alzheimer’s disease. Previous study on an early-stage PD cohort has found that hyposmia ispredictive of cognitive impairment in an 18-month follow-up [27].3.3.4 Geriatric Depression ScaleThe Geriatric Depression Scale (GDS) is a questionnaire used to identify depression in adults [59].The original questionnaire involves 30 questions, but data from the short version of the scale (13questions, 1 point each) is used in this thesis. Typically, a score above 5 is considered suggestive ofdepression. Each question involves a yes/no response, and a few example are shown below:• Do you think it is wonderful to be alive?• Are you afraid that something bad is going to happen to you?• Do you feel full of energy?• Do you often get bored?Depression in PD has been previously associated with a faster motor and non-motor progressionof the disease. In a study of 105 PD subjects, with a 12-month follow-up, patients with majordepression showed a greater cognitive decline, deterioration in the activity of daily life, and fasteroverall progression [53].3.4 Parkinson’s Progression Markers InitiativeThe Parkinson’s Progression Markers Initiative (PPMI)1 is a longitudinal, multi-center study withthe goal to identify novel biomarkers of PD progression [42]. At the time of this writing, thereare 454 sporadic PD subjects and 215 healthy controls enrolled in 33 sites in the USA, Europe,Israel, and Australia. In addition, there are 81 subjects without evidence of dopaminergic deficit(SWEDDs) enrolled. These are subjects that have some of the clinical symptoms of PD, howevertheir scans do not show substantial dopaminergic dysfunction.Some examples of the kinds of data available for the subjects enrolled in the study are:1• DaTSCAN imaging for PD subjects at years 0, 1, 2 and 4 since enrolment and healthy controlsat year 0. PPMI contains the largest DaTSCAN imaging dataset in the world.• T1 structural MR images for most PD and HC subjects.• For a subset of the PD subjects, there is functional MRI, diffusion tensor MRI, and AV-133imaging available.• Clinical exams such as MDS-UPDRS, MoCA, GDS, UPSIT, Sleep Disorder, and medicalhistory. Each subject is typically enrolled in the study for 4-6 years, during which longitudinalclinical data is collected.• Results from biological assays such as DNA single nucleotide polymorphism (SNP) se-quencining and cerebrospinal fluid biomarkers.The analysis in this thesis is based on the imaging (DaTSCAN and AV-133) and clinical data inthis study.30Chapter 4Defining Regions of InterestA reliable quantification of the dopaminergic tracer distribution in the striatum requires a precise andconsistent placement of ROIS on the PET/SPECT images. The low resolution and signal-to-noiseratio of the SPECT images make this a challenging task. Conventional ROI placement approachesare reviewed in Section 4.1 and Section 4.2. The bounding box approach used in this work for auto-mated analysis is described in Section 4.4. The approaches described here are applied to DaTSCANand AV-133 images of PD subjects in Chapter 6. Other automated ROI placement approaches arereviewed in Section 4.54.1 Manual Placement of ROIsThe most commonly used approach to define ROIs in brain images is the manual placement ofgeometric ROIs. There are several approaches that differ in the exact implementation details of themanual workflow. As an example, the following workflow was used by PPMI to define the manualROIs in the DaTSCAN images:1. For each image, the transaxial slice with the highest uptake was identified.2. The eight slices (16mm thickness in total) with largest uptake surrounding that slice wereidentified and averaged to produce a single averaged slice.3. Geometric ROIs were placed on the left and right caudate, left and right putamen (circles),and the occipital cortex.For an example of this approach, see Figure 4.1. Because this placement is performed by ahuman, it is relatively robust even in cases of images of advanced PD subjects where the uptakein the striatum is very low. The main disadvantages of this method are that it is time-consumingand that the reproducibility is lower compared to automated approaches. In addition, in advanceddisease, it can be difficult to identify the putamen visually, which might lead to incorrect ROIplacement.31Figure 4.1: Conventional approaches of ROI placement in DaTSCAN images. Left panel:manual placement of geometric ROIs in the striatum and the occipital cortex. Rightpanel: a transaxial slice of an MR T1 image of the striatum is shown in the top im-age. The segmented anatomical ROIs of the putamen and caudate are overlaid on thecoregistered SPECT image in the bottom image.4.2 MR-defined ROIsThis approach uses anatomical information from a T1 MR image to define the regions in the striatumand the occipital cortex. The following outlines the steps of defining the MR-based ROIs in [28].These ROIs were also used for the cross-sectional analysis in this thesis (Chapter 6):1. Each MR image was automatically segmented to produce labelled regions in the striatum andoccipital cortex. This was done using FreeSurfer 5.3 [18–20].2. Coregistration of the SPECT and MR images of each subject was performed via a rigid trans-form using the mutual information as the objective function [10]. SPM8 was used for thecoregistration [22].3. The segmented MR regions were then overlaid on the SPECT image.Examples of using this method in the striatum are shown in the right panel of Figure 4.1. Themain advantage of this approach is that it is using additional (anatomical) information from theMR images, which can be considered the gold standard of the ROI definition. The disadvantagesinclude:• MR is not available in all SPECT centres and not all subjects can undergo MR imaging.• The coregistration and segmentation steps are complex and involve various pieces of soft-ware, with a large number of settings and parameters to choose from. Results also differsignificantly depending on the software version used. For example, the FreeSurfer segmen-tations of the striatum produced with versions 5.3 and 6.0 of the software are substantiallydifferent.32• The SPECT images suffer from partial volume effect, making it difficult to align the high-uptake regions in the striatum with the segmented anatomical regions. Approaches to dealwith this issue by performing MR-guided partial volume correction during the OSEM recon-struction of the SPECT image are presented in [17].4.3 MR-template ApproachesThere also exist hybrid approaches that use MR-based templates as the primary reference for ROIplacement, but then require substantial manual adjustment of the MR-template on a subject-by-subject basis. For example, the following describes the approach utilized by PPMI to place striatalROIs on the AV-133 PET images:1. Each PET image was coregistered to the subject’s MR T1 image.2. The MR image was normalized to Montreal Neurologic Institute space and the same trans-formation was also applied on the PET image.3. A standardized striatal template (developed previously) was placed on each MR image. Thetemplate placement was adjusted manually on a subject-by-subject basis, especially in caseswhere striatal atrophy was present.4. The adjusted template was overlaid on the PET image, defining ROIs for the posterior puta-men, anterior putamen and the caudate.Because the striatal template is standardized, this approach avoids some of the challenges of theautomatic segmentation of the individual MR images. However, because manual template adjust-ment is required for each subject, this approach can be very time-consuming.4.4 Bounding BoxPrevious image analysis was performed by the UBC PET group [36] on 11C-DTBZ images of PDsubjects acquired on the High-resolution research tomograph (HRRT) to understand the effects ofthe ROI definition method on the metric performance (quantified by its correlation with diseaseduration). This analysis suggested that using simple bounding box (BB) ROIs does not degradethe performance of some image metrics (reviewed in Chapter 5). With these results in mind, theobjectives of our effort to develop the BB placement method were:• Develop an automated method which can be applied effectively to the thousands of SPECTimages in the PPMI database.• The inputs to this algorithm should be the SPECT images only, without using MR anatomicalinformation so that its application is not limited by MR availability.The steps for placing the BB ROI on the DaTSCAN images were:33Axial	  (z	  =	  84mm) Sagittal	  (x	  =	  70mm)Figure 4.2: Axial and sagittal views of the mean HC template, together with the fitted BB.1. All healthy control DaTSCAN images (N = 210) were coregistered to each other using a nine-degrees-of-freedom linear affine transformation that includes rescaling but not deformation.The FSL FLIRT 5 tool was used for this step [33, 34].2. An average image was computed from all healthy control images to be used as a template.An (84× 54× 24)mm3 BB ROI that encompasses the entire striatum was defined on thistemplate. The HC template with the box is shown in Figure 4.2.3. Each PD SPECT image was coregistered to the average template using the same type oftransformation as in step 1. For the purposes of the BB placement, this coregistration did notneed to be exact.4. After coregistration, the images were found to be accurately aligned in the left-right andthe anterior-posterior directions. For this reason, fixed BB coordinates (based on the HCtemplate) were used to define the BB ROI along these directions across all images.5. The image alignment was not accurate along the inferior-superior direction: deviations aslarge as 20 mm were observed. Because the coordinates in the other two directions werefixed, a simple one-dimensional search was performed by varying the box coordinates in theinferior-superior direction, and searching for the box enclosing the largest total activity.6. Once the optimal box region was defined for each image, the region was split into two, corre-sponding to the left and right striatum.Geometric ROIs were also placed on the occipital cortex, as shown by the white circles inFigure 2.3. Each ROI used was a cylinder with a 10mm thickness. These were automaticallyaligned with the location of the bounding box along the inferior-superior direction and were placedat fixed coordinates along the other two dimensions.34The main disadvantage of this method is that, by definition, the bounding box includes a largenumber of extra-striatal voxels. Image metrics computed on the bounding box that deal with thisissue are described in Chapter 5.4.5 Other Automated ApproachesSeveral other approaches exist for the automated analysis of DaTSCAN images. In [44], a boxregion is automatically placed on DaTSCAN images of PD subjects from three different databases(including the PPMI database). The notable differences between their approach and the one pre-sented in this thesis are:• In Martinez-Murcia et al. [44] intensity normalization was done by dividing each voxel to the95th percentile of the image intensity distribution. In this work, the SPECT image intensitywas normalized to the average activity in the occipital cortex.• In Martinez-Murcia et al. the box coordinates were determined by applying an intensitythreshold on the intensity-normalized image. The smallest bounding box that includes allvoxels above the threshold was used as an ROI. Several different thresholds were used. Inthis work, the box coordinates were fixed along the left-right and the anterior-posterior direc-tions (after spatial coregistration) and dynamic (subject-specific) along the inferior-superiordirection.In [2] a Gaussian mixture model (GMM) was used to to identify regions of high uptake in eachDaTSCAN image. The assumption was that the image voxels belong to a mixture of two differentintensity distributions: a low-uptake and a high-uptake distribution. Then, two ellipsoidal ROIswere fitted to the high-uptake regions corresponding the left and right striatum.35Chapter 5Imaging Metrics to Quantify TracerUptake in the StriatumThe conventional metrics to quantify the tracer distribution in the striatum (BPND and the bindingratios) were reviewed in Chapter 2. This chapter provides an overview of some of the image metricsapplied to brain imaging more recently in an attempt to extract additional disease-relevant infor-mation from the images that is not captured by conventional approaches. In addition, Section 5.3discusses the Sum Intensity metric developed in this work for use with the bounding box ROI.5.1 First- and Second-order Image MetricsOne of the ways of summarizing information about the tracer distribution is by computing first- orsecond-order image metrics. First-order metrics (also known as histogram metrics) contain infor-mation about the probability distribution of the intensity values of the voxels in the image. Spatialpatterns are not contained in the histogram there is no information about the relative positions of theintensity values within the image in the intensity histogram. In the case where the image intensity isnormalized to a reference region, the binding ratio can be considered a first-order image metric, asit is directly related to the histogram mean. Second-order metrics quantify the relationship betweenpairs of voxels; texture metrics have been applied in brain imaging [37]. However, texture metricsare not considered in this work.5.2 Moment Invariants3D moment invariants (MIs) can be used to describe the spatial distribution of voxel values withinan ROI, while being invariant to rotation, translation and scaling of the distribution. The invarianceproperty is useful in the case of brain imaging due to the individual subject variation in brain size andposition within the scanner. The MI are composed of terms that quantify the variance, skewness andkurtosis of a 3D distribution of voxel values. MIs characterize the shape of the spatial distributionbut also incorporate intensity information of the voxels within the ROI.36For a given 3D distribution f (x,y,z), the moment of order n = p+q+ r is defined as:mpqr =∫ ∞−∞∫ ∞−∞∫ ∞−∞xpyqzr f (x,y,z)dxdydzIn the case of brain imaging, the 3D distribution f (x,y,z) represents the intensity of a voxellocated at position (x,y,z) within the ROI. In order to obtain invariance to position, centroids arefirst found using:x¯ =m100m000, y¯ =m010m000, z¯ =m001m000These centroids are used to construct the central moments:µpqr =∫ ∞−∞∫ ∞−∞∫ ∞−∞(x− x¯)p(y− y¯)q(z− z¯)r f (x,y,z)dxdydzSecond-order central moments represent the variance along a given axis (e.g. µ200 is the variancealong the x-axis), and the covariance between axes (e.g. µ110 between the x- and y-axes). To obtaininvariance due to rescaling, the central moments are normalized by the zero-order moment (the sumof all voxels within the image):ηpqr =µpqrµp+q+r3 +1000To obtain rotation invariance, the moments are combined in specific ways (see [51] for a deriva-tion of these combinations). The following MIs are used in this work:J1 = η200+η020+η002J2 = η200η020+η200η002+η020η002−η2101−η2110−η2011Higher-order terms (that include information about the kurtosis and skewness of the 3D distribu-tion) can also be derived, but they are not analyzed in this work. Previous work [24] on 11C-DTBZPET images obtained on the HRRT at UBC found that 3D MIs have a significant correlation withdisease duration and motor score in PD subjects. On the HRRT data, these metrics have the poten-tial to characterize the disease-induced alterations of the uptake in the striatum. In this work, thesemetrics are applied to the lower-resolution DaTSCAN SPECT images.5.3 Sum IntensityThe Sum Intensity (SI) metric was developed to work specifically with the BB ROIs that encompassa large number of extra-striatal voxels. SI is defined as:SI = v ∑j:s j>θs j37Screening Year 1Year 2 Year 5.1: DaTSCAN SPECT images of a subject with Parkinson’s disease imaged over a4-year period. Green contour lines in the striatal BB show voxels where the normalizedintensity is equal to θ = 2. The same images were used here as the ones shown inFigure 2.3.where v is the voxel volume in mm3, and the sum is over all voxels j in the ROI that have anormalized intensity above a certain threshold θ . For the intensity normalization used in this work,the voxel intensity is divided by the average intensity in the reference (occipital) region. Thereare several possible strategies to select the intensity threshold θ ; see Section 6.2 for how it wasdetermined in this work.SI can be represented graphically by the green contour lines shown in Figure 5.1 in the casewhen the intensity threshold is θ = 2. All voxel intensities inside the high activity region enclosedby the contour lines are added together to produce the sum intensity metric.By definition, SI is sensitive to both the size of the high-activity region, as well as the enclosedvoxel intensities. Note in Figure 5.1 that there is a substantial decline in the area of the high-activityregion in the striatum, especially on the more affected side. The next chapter describes a correlationanalysis between SI and clinical measures of severity.38Chapter 6Cross-sectional Analysis6.1 IntroductionChapter 2 discussed some of the conventional approaches for quantifying tracer uptake in the stria-tum in PD subjects, as well as some of the challenges of applying these approaches to large mul-ticenter studies. The BB ROI placement and the SI metric were introduced to address some ofthese challenges. In order to validate this automated approach, the following correlation analysis ispresented in this chapter:• The BB ROI placement method was applied on (i) 18F-DTBZ (AV-133) PET data of 24 PDsubjects and (ii) DaTSCAN images of 75 PD subjects and 200 HCs from PPMI. The SI metricwas computed on the BB ROIs.• The correlation between SI and the UPDRS part III motor score was evaluated. This cor-relation was compared to those obtained when using standard approaches including (i) theputamen BR evaluated over manually placed ROIs and (ii) the J2 metric evaluated over MRI-defined ROIs.• Since both imaging and clinical scores are subject to a substantial measurement uncertainty,the relationship between image metrics and motor score was modelled via a robust nonlinearregression method that captured the uncertainty in both variables.• The decline of dopamine transporter availability in healthy aging, as quantified by SI and theputamen BR on DaTSCAN images, was also investigated.6.2 Methods6.2.1 DaTSCAN image acquisitionThe DaTSCAN dataset analyzed in this work include images of 75 PD subjects and 200 HCs fromthe PPMI database. The PD subjects were selected based on the availability of a 3T MRI used39to define the MR-based ROIs (used for the comparison with the BB ROIs). For each PD subject,the first scan (performed at screening) was analyzed. In addition, images of 72 PD subjects notincluded in the above-mentioned set were used for the optimization of the sum intensity metric (seeSection 6.2.5).All imaging centres that are part of PPMI used a standardized DaTSCAN image acquisitionprotocol. Subjects were imaged (4±0.5)h after the injection of 111-185 MBq of DaTSCAN. A totalof 120 projections (stepping 3 degrees for each projection) were acquired into a 128×128 matrix.The total scan duration was 30-45 min. Images were reconstructed using ordered subsets iterativereconstruction without any filtering. Chang’s attenuation correction method was applied using site-specific attenuation maps empirically derived from phantom data. An isotropic 3D Gaussian filterwith a 6mm radius was applied to all images. The reconstructed images were of size 91×109×91cubic voxels (voxel size 2.0mm). Additional details of the preprocessing protocols used in the PPMIstudy are provided in [30].6.2.2 AV-133 image acquisitionA total of 24 AV-133 images of PD subjects and 4 images of HCs from the PPMI database wereanalyzed. Subjects were imaged over two 10-minute sessions starting at 50± 5min and 80± 5minfollowing the injection of 222MBq of AV-133. Projection data was acquired on a 128×128 matrixand was reconstructed using ordered subsets iterative reconstruction (4 iterations, 16 subsets), withcorrections for scattered photons, randoms, decay and attenuation. When a PET/CT system wasused, the attenuation map was constructed using a low-dose CT scan. In the PET-only systems, a5-10 minute transmission scan (with a rod source) was acquired prior to the AV-133 acquisition.Five different PET and PET/CT scanners were used for the acquisition of the images, resulting invariable image resolution and voxel size, with minimum voxel volume of 17mm3(2×2×4.25mm)and a maximum of 28.6mm3(2.67×2.67×4mm).6.2.3 Clinical dataThe PD subjects underwent a UPDRS motor score examination every 2-4 months during the firstyear of their enrolment in the study. It was discovered that there is a large variability over consecu-tive motor score measures of the same subject (see Section 6.3.1). To partially remedy this, motorscores (part III of the UPDRS exam) for a given subject measured within one year of the imagingdate were averaged. Furthermore, the individual UPDRS III items were combined into (more af-fected side + common) scores, and (less affected side + common) scores as detailed in Section 3.3.1.Table 6.1 provides an overview of some of the clinical characteristics of the PD subjects used in theDaTSCAN analysis.To evaluate the effects of averaging the motor score, the DaTSCAN correlation analysis wasalso performed using a single motor score measurement - the one closest to the imaging date.40Table 6.1: An overview of the clinical features for the 75 PD subjects (46 male, 29 female)included in the analysis. Here MS stands for motor score, and DD is the disease durationsince symptoms.age left MS right MS common MS total MS DD (years)mean 62.3 8.64 7.13 8.60 24.37 1.84std. dev 7.7 6.00 5.07 3.12 9.17 1.30min 46 0.00 0.00 2.25 7.25 0.03max 82 23.25 19.5 14.25 42.75 5.386.2.4 ROI placementFor the DaTSCAN images, three different ROI placement methods (as detailed previously) wereused: (i) manual ROI placement performed by PPMI (Section 4.1), (ii) MR-based ROIs (Section 4.2)and (iii) BB ROIs (Section 4.4).Due to the variability in the image resolution and voxel size of the AV-133 scans, the BB place-ment step that involved the coregistration of each image to a common template was found to distortsome of the images along the left-right direction. Such a distortion would result in an inaccurate SIvalues, since this metric depends on the size of the high activity region. For this reason, a somewhatmodified approach was used to place the BB ROIs on the AV-133 images:1. All PET images were first smoothed with an isotropic 3D Gaussian filter with a 5mm radiusin order to bring the images to approximately the same spatial resolution.2. A BB of size (84× 54× 24)mm3 (same size as used in the DaTSCAN images) was placedautomatically on the raw PET images (without spatial coregistration). The coordinates ofthe box were determined by finding the region on the PET image with the largest total uptake,corresponding to the striatum.3. Since an occipital cortex ROI was no longer available for intensity normalization, for eachBB, the voxel intensities were normalized to the peak of the voxel distribution (Figure 6.1)inside the BB ROI. Each BB includes a large number of extra-striatal voxels, that containprimarily non-specific uptake, which is not reduced by disease. The peak of the intensityhistogram (corresponding to these extra-striatal voxels) can therefore be used as a surrogateintensity normalization ”region”.In addition, for the PET images, MR-based template ROI placement performed by PPMI (de-scribed in Section 4.3) was also included in the analysis.6.2.5 Image metricsThe image metrics used for the DaTSCAN analysis included: (i) putamen and caudate BRs eval-uated on manually-placed ROIs (provided by PPMI), (ii) the J2 moment invariant computed onMR-based ROIs and (iii) SI computed on the BB ROIs.410.5 1.0 1.5 2.0 2.5 3.0Normalized intensity0200400600800100012001400Number of voxelsHCearly PDadvanced PDFigure 6.1: Histograms of the voxel intensities inside the BB ROIs (AV-133) for a HC subject,a PD subject in early disease and an advanced PD subject. Each intensity distributionhas a peak that corresponds to the extra-striatal voxels and a long tail towards high inten-sities that includes the striatal voxels. As disease advances, the tail of the distribution isimpacted since the high uptake in the striatum is reduced, however, the peak of the dis-tribution remains relatively unaffected since it corresponds mostly to non-specific traceruptake.The putamen BR was used for the comparison with SI as it had a stronger correlation with motorscore compared to the caudate BR. The caudate BR was included in the analysis for completeness.As discussed in Section 3.2.1, the putamen is the first region in the striatum to be affected, whilethe caudate remains relatively unaffected in early PD. Given that the analysis is performed on a setof subjects with short disease durations, it is not surprising that the putamen BR is more stronglyassociated with motor progression. Both of these BR metrics were provided by PPMI.A previous analysis of the same 75 DaTSCAN images of PD subjects compared the performanceof various radiomics features in terms of the correlation strength with motor score [28]. Theseincluded grey-level co-occurrence metrics, histogram features and moment invariants, all computedon MR-based ROIs. J2 was found to have the strongest correlation with motor score. For thisreason, J2 is used here as a reference metric computed on the MR-based putamen ROI.For the SI metric, the threshold θ was selected as follows in the DaTSCAN data. For a givencandidate threshold θi in the range 1.1−3.5, the Spearman’s rank correlation was computed betweenthe motor score (better side + common) and SI(θi) on the contralateral side of the striatum. TheBB ROI method was used for this optimization, over a separate set of 72 images of PD subjectsto avoid overfitting to the imaging data used for the analysis. Figure 6.2 shows the results of theoptimization. Based on this test, intensity thresholds in the range 1.5− 2 were found to give thestrongest correlation with the clinical metric. The value of θ = 2 was used for the rest of theanalysis as visual inspection revealed that lower thresholds resulted in the inclusion of a very largenumber of voxels.421.0 1.5 2.0 2.5 3.0 3.5Intensity threshold0.4250.4000.3750.3500.3250.3000.2750.250Correlation strength (rho)Figure 6.2: The effect of using different SI intensity thresholds on the correlation of this met-ric with motor score. The solid line represents the Spearman correlation for a givenintensity threshold θi. The dashed lines represent the standard deviation of the estimatedcorrelation value ρ .For the AV-133 image analysis, the metrics included: (i) SI computed on the BB and (ii) BRsfor the posterior putamen, anterior putamen and caudate computed on the MR-based template ROIs.The SI threshold θ was computed for the AV-133 images as described above for DaTSCAN.However, because of the small number of PET images, the threshold optimization and analysiswere performed on the same set of PD subjects (N = 24), and the value θ = 1.3 was found to beoptimal.6.2.6 Regression analysis and measurement uncertaintyModels of the following form were fitted to the clinical and imaging data:Fi = Aexp[−λmi]+C+ εi (6.1)where Fi is the imaging metric (the putamen BR and SI were both used, in separate models)for the ith subject, mi is the motor score (better side + common), A, λ and C are parameters to beestimated, and εi is an error term assumed to be normally distributed. The imaging metrics werecalculated on the corresponding contralateral side of the brain. The correlation between imaging andclinical metrics was found to be stronger on the better side (Section 6.3.2); the exponential modelwas also fitted on the better side data to allow for a more precise assessment of the relationshipbetween imaging and clinical metric.The exponential model described in Equation 6.1 was used in the analysis as it was found tobe a better fit to the imaging and clinical data compared to a linear model. Disease duration sincesymptoms and age at onset were initially included in the model as independent variables but werenot found to be significant predictors. Standard nonlinear least squares minimization procedure43available from the SciPy library (version 0.19.0) was used to fit the model [35].Measurement uncertainty in the imaging and clinical variables was incorporated into the modeldescribed by Equation 6.1 using the following method. Firstly, measurement errors were assigned toeach variable. For each subject the motor score measure is an average based on multiple (typically4 or 5) clinical examinations taken within one year of the imaging date. The standard error of thesemeasurements for each subject was used as the uncertainty for mi.In terms of assigning error to the imaging metrics, test/retest variability for the binding ratio inHC subjects imaged with DaTSCAN was reported to be 7.8±4.6% in the putamen [45]. However,in longitudinal analysis of screening and year-1 imaging data from PPMI data, for a subset ofthe PD subjects the image metric values increased between screening and year-1. The medianpercent increase for the subset of subjects with an increase in the image metric was 11% for SI and16% for the putamen BR. It was assumed that this increase for both SI and the putamen BR wassolely due to test/retest variability since it is expected that the dopamine transporter density woulddecrease monotonically for PD subjects. The observed median increases were used as uncertaintyestimates for the corresponding image metrics. Using smaller imaging error estimates did not havea significant impact on the results.In the case of AV-133, previous studies estimate the test-retest error to be in the range 2−11%for the BRs in the striatum [9]. Based on this, an uncertainty of 10% was used in this work for boththe BRs and SI.6.2.7 Resampling procedureThe standard nonlinear regression procedure produces unreliable confidence intervals in the casewhere substantial measurement uncertainty is present in the data [1]. The following bootstrap pro-cedure [12] was used to obtain a more robust estimate of the uncertainty in the fitted parameters ofthe model.1. For each data point (mi,Fi) , sample a new point from a bivariate Gaussian distribution, cen-tred at the original point, with variance given by the square of the corresponding uncertaintiesin mi and Fi. This creates a perturbed dataset in order to take into account the uncertainty inthe measurement process.2. Sample with replacement from the perturbed dataset. This takes into account the samplinguncertainty that arises from the limited data sample.3. Fit a model (following Equation 6.1) to the sampled dataset.This procedure was repeated 1000 times, each time producing a model with slightly differentfitted parameters. Based on the produced ensemble of models, interquartile ranges were computedfor each of the fitted parameters: these ranges reflect both the measurement uncertainty (step 1) aswell as the sampling uncertainty (step 2). These interquartile ranges were compared to the onesobtained from the standard parametric approach, using the same nonlinear model Equation 6.1.442012-052012-062012-092012-1101020302012-012012-022012-042012-0705101520252012-062012-092012-122013-032013-062013-092014-030102030motor scoreleftrightcommonSubject 1 Subject 2 Subject 3Figure 6.3: Consecutive motor score measurements for three different PD subjects. The heightof the bar represents total motor score (measured while the subjects were off PD med-ication) and colours separate the individual components: left, right and common score.Subject 1 shows an expected increase in total motor score over time, as well as an in-crease in the individual components. In the case of subject 2, there is an abrupt drop inboth the left and common scores in the third measurement (from April 2012). Subject 3shows an abrupt increase in the total score in the third measurement (Sept 2012) mostlydue to the jump in the left component, which then appears reduced in the following ex-amination.6.3 Results and Discussion6.3.1 Motor score variabilityA large variability in the motor scores was discovered when consecutive clinical examinations (UP-DRS measurements) of a given PD subject were examined. Differences as large as 18 points wereobserved in total motor score (measured off PD medication) between examinations performed only2 months apart. Figure 6.3 provides examples of the observed variability for three subjects; subject1 shows motor score progression that is typically expected.6.3.2 Correlations with motor score variables (DaTSCAN images)Scatter plots of the investigated DaTSCAN image metrics - putamen and caudate BR (manual ROIs),J2 (putamen MRI ROIs), SI (bounding box ROIs) - against motor scores (better side + common) areshown in Figure 6.4.The behaviour of the J2 metric was different compared to the other metrics as it captured thespatial variance and covariance of the tracer distribution in addition to the voxel intensity informa-tion. The trends for SI and the putamen BR were very similar. Overall, correlation strength betweenSI and motor score was very similar to those obtained with the reference metrics.The correlation between the image metrics and (worse + common) motor scores was weakeracross all metrics, but very similar in magnitude (ρ = 0.29 for J2, −0.28 for SI and −0.28 for boththe putamen BR and the caudate BR). In addition, no significant correlation was found between anyof the examined image metrics and disease duration or age of the PD subjects.When the correlation analysis was repeated using a single exam score per subject, the correla-tions across all imaging metrics were reduced by about 30%, illustrating the impact of the motor455 10 15 20 250.250.500.751.001.251.501.75Putamen ratio (better)Manual ROI placement5 10 15 20 25Better + common [motorscore] invariant [better]MRI ROI (PUT)5 10 15 20 25Better + common [motorscore]0200040006000Sum intensity [better]Bounding box5 10 15 20 ratio (better)Manual ROI placementFigure 6.4: Relationship between motor score and imaging metric computed on the less af-fected side of the brain.score variability on the correlation results.To further understand the effect of the ROI definition on metric performance, the SI and puta-men BR metrics were computed on the MR ROIs. In this case, correlations between the imagemetrics and motor scores were found to be substantially weaker (Figure 5) compared to when usingthe original BB ROIs. In the case of SI, this is likely because a large portion of the high uptake (Fig-ure 6.5, highlighted in orange on the right panel) is outside of the MR-defined region. In contrast,the BB ROI is advantageous when computing SI as it is a large ROI that captures the entire high-activity region in the striatum. At the same time the low-intensity voxels included in the box areautomatically excluded by the metric as it only captures voxels above a certain intensity threshold.Table 6.2 lists the correlations obtained for the different ROI-definition - image metric combi-nations. Note that J2 computed on the BB achieves significant correlations for both the better andthe worse sides.The threshold θ = 2 for SI was selected while using the BB ROI in the optimization procedureso it is possible that a different threshold is more appropriate when computing SI on the MR ROIs.Regardless of the choice of the threshold, however, the SI performance tends to be degraded on theMR ROIs since some of the high uptake is excluded from these ROIs.6.3.3 Healthy controls and agePrevious work has demonstrated that there is an age-related decline in dopamine transporter avail-ability in healthy subjects [39, 55]. To investigate the behaviour of SI in healthy aging, this metric465 10 15 20 25Better + common [motorscore]05001000150020002500Sum Intensity (better)MRI ROI5 10 15 20 25Better + common [motorscore]0.500.751.001.251.501.752.002.25Putamen ratio (better)MRI ROIFigure 6.5: Relationship between image metrics computed on the MR-based ROIs and motorscore. The right panel shows an example of a transaxial slice (striatum area shown only)from a DaTSCAN image of a PD subject, together with boundaries of the segmentedputamen and caudate ROIs obtained from the MR segmentation.Table 6.2: Spearman correlation coefficients between image metrics and motor score. BB =striatal bounding box, MR = putamen MR ROI, Manual = manually-placed putamen ROI.The manual ROIs used by the PPMI investigators were not provided on the PPMI website,so SI and J2 were not computed on these regions. ∗p < 0.01,∗∗ p < 0.001.metric Binding Ratio Sum Intensity J2ROI type MR BB Manual MR BB MR BBbetter side -0.20 -0.40** -0.44** -0.25 -0.42** 0.43** 0.39**worse side -0.15 -0.28 -0.28 -0.21 -0.28 0.29 0.32*was computed on the HC DaTSCAN images available from PPMI, and correlated against age (Fig-ure 6.6). The putamen BR was also included in this analysis for comparison.It is evident from the scatter plots that there is substantial inter-subject variability in the metricvalues for a given age. However, the correlation with age was stronger for SI (ρ =−0.43 for SI and−0.29 for the putamen BR). In addition, SI declined more rapidly with age; on average by about50% between the ages of 30 and 85. In contrast, putamen BR declines by 36% on average for thesame age range.30 40 50 60 70 80age02500500075001000012500Sum Intensity (average)30 40 50 60 70 80age1234Putamen Ratio (average)Bounding box Manual ROIFigure 6.6: Relationship between age and imaging metric for healthy control subjects. Foreach image, the average of the image metric on the left and on the right side of the brainwas computed.47Table 6.3: Fitted values for the parameters of the exponential model based based on theDaTSCAN images. For each parameter, the median estimate is shown, together withits interquartile range. Here A, C and λ are the original fitted parameters, and A’ and C’are the fitted parameters after normalizing the two metrics to a common mean (to allowfor a direct comparison between the fitted parameters).SI putamen BRA 4980 (4340, 6170) 1.52 (1.15, 2.74)A’ 1.66 (1.45, 2.06) 1.52 (1.15, 2.74)C 1200 (0, 2040) 0.77 (0.67, 0.84)C’ 0.40 (0, 0.68) 0.77 (0.67, 0.84)λ 0.09 (0.04, 0.23) 0.26 (0.14, 0.41)Since the volume of the striatum is observed to decline in healthy aging [50], there is likely acorresponding reduction in the volume of the high uptake region in the DaTSCAN images. SI isalso sensitive to the size of the high uptake region, which might explain the more rapid age-relateddecline observed with this metric, compared to the putamen BR. This result shows that while SIand the putamen BR are related to each other, they cannot be interpreted in the same way. Theputamen BR is a more direct measure of the dopamine transporter density in the putamen, whileSI also captures information about the size of the functional region in the striatum. In the case ofPD subjects, the disease effect on the dopamine transporter distribution likely dominates over theage-related effect, which explains why no significant correlation with age was found for that groupof subjects.6.3.4 Correlations with motor score (AV-133 images)The Spearman correlation values between motor score and BRs on the less affected side for PDsubjects were ρ =−0.48 for the posterior putamen, −0.26 for the anterior putamen and −0.20 forthe caudate. Scatterplots that illustrate the relationships between the posterior putamen BR (MR-based template ROI) and SI (bounding box) are shown in Figure 6.7. Overall, the correlation withmotor score was found to be stronger with SI computed on the BB. The difference in correlationstrength is especially large on the more affected side of the striatum. However, the more affectedposterior putamen BR is better able to separate HCs (represented by the dashed lines) and PDsubjects compared to SI. This corroborates a previous finding [37] that image metrics that achievebest separability between HCs and PD subjects are not necessarily optimal for tracking diseaseprogression in PD subjects.6.3.5 Nonlinear fitting (DaTSCAN)The results from the exponential model fitting of the DaTSCAN data, along with confidence bandsare shown in Figure 6.8. The fitted coefficients and the estimated interquartile ranges based on theresampling procedure described in Section 6.2.7 are shown in Table 6.3.48𝜌 = −0.62, 𝑝 = 0.001 𝜌 = −0.56, 𝑝 = 0.004𝜌 = −0.48, 𝑝 = 0.02 𝜌 = −0.11, 𝑝 = 0.61Figure 6.7: Relationship between motor score and imaging metric on AV-133 scans. The fourdashed lines represent the image metric values for the healthy control subjects.0 5 10 15 20 25 3002000400060008000Sum intensity [better]Bounding boxm [better + common] motor score0 5 10 15 20 25 300. ratio [better]Manual ROIm [better + common] motor scoreFigure 6.8: Modelling the relationship between imaging metric and motor score in DaTSCANimages. The exponential model fit and confidence bands are shown in red. Note thatsome data points are dominated by uncertainty in the imaging metric, while others aredominated by motor score uncertainty.Based on the plotted models in Figure 6.8, it is evident that the putamen BR declines rapidlyfor early disease (motor score m < 15), during which the better putamen is changing rapidly. Nearm = 15, the putamen BR is close to its asymptotic value (C = 0.77[0.67,0.84]) and the decline ismuch slower for more advanced disease. In contrast, the estimated median λ (the coefficient in theexponent) is smaller for SI, indicating a slower decline, however this metric continues to declinebeyond m = 15.Interquartile ranges of the fitted parameters for the same model (Equation 6.1) were also es-timated using the standard parametric approach that does not take into account the measurementerror (results not shown). These ranges were substantially smaller compared to the ones based on49Table 6.4: Fitted values for the parameters of the exponential model based on the AV-133images. Notations are identical to those was used in Table 6.3.Sum Intensity post. putamen BRA 30700 (25000, 35700) 1.20 (0.73, 1.39)A’ 1.23 (0.94, 1.42) 1.20 (0.73, 1.39)C 4200 (0, 17500) 0.02 (0, 0.83)C’ 0.17 (0, 0.70) 0.02 (0, 0.83)λ 0.03 (0.02, 0.13) 0.03 (0, 0.30)the resampling approach used in this work. In particular, the interquartile range for λ based on thestandard parametric approach was 35% smaller for both SI and the putamen BR. The resampling ap-proach captures the uncertainty due to the measurement errors in the variables, and produces moreconservative (wider) interquartile ranges that reflect this uncertainty.Both the SI and the putamen BR models are poorly fitted near m = 0, which is related to theexpected metric value for early PD subjects that do not yet exhibit motor deficit. This is illustratedby the wide confidence bands in Figure 6.8 near m = 0. This is not surprising, and reflects the lackof imaging and clinical data needed to characterize the early disease state, prior to the appearance ofsymptoms. The PPMI study has currently enrolled a group of prodromal subjects, with REM sleepdisorder or hyposmia. Incorporating this type of subjects in the image analysis might help answerquestions about the optimal image metrics to quantify early nigrostriatal degeneration.This regression analysis suggests that (i) the motor score measurement uncertainty can have alarge impact on the correlation analysis with imaging and should be minimized as much as possibleduring the clinical examination, and (ii) resampling approaches that account for the variability inboth imaging and clinical metrics might lead to more robust analyses.6.3.6 Nonlinear fitting (AV-133)The results from fitting Equation 6.1 to the AV-133 data (less affected side) are shown in Figure 6.9and the fitted parameters are in Table 6.4. Overall, the model is better fitted to the SI data comparedto the posterior putamen BR data, indicated by the smaller interquartile ranges in the estimatedparameters of the SI model.Unlike the putamen BR in the DaTSCAN data, the posterior putamen BR is predicted to declineto nearly 0 (C = 0.02[0,0.83]) for advanced disease. The posterior putamen is the first subregionin the striatum to be affected by disease, following the rostrocaudal pattern of degeneration. Thehigher spatial resolution of the AV-133 images allows for the posterior putamen to be resolved fromthe rest of the putamen, so image metrics computed on this subregion might be more sensitive tosubtle changes associated with early disease.500 10 20 30m [better + common] motor score10000200003000040000Sum IntensityBounding box0 10 20 30m [better + common] motor score0. putamenMR-based templare ROIFigure 6.9: Modelling the relationship between imaging metric and motor score using AV-133images. Labels and color-coding are identical to those used in Figure 6.8. One subjectwas excluded from both plots due to his high image metric values, however this subjectwas not excluded from the fitting procedure.6.4 ConclusionIn this chapter, the automated approach, comprised of the SI metric, evaluated over a boundingbox ROI, was validated. The correlations between motor score and SI in DaTSCAN images of PDsubjects are very similar to those obtained using reference approaches. In addition, SI has a practicaladvantage as it is automatically computed and only requires the SPECT image and a HC DaTSCANtemplate as inputs. In the case of AV-133, SI achieves substantially stronger correlations, especiallyon the less affected side of the brain. However, this result needs to be validated based on a largersample of AV-133 images, that would allow for separate sets of images to be allocated for metricoptimization and analysis, respectively.The findings in this work are based on a set of PD subjects with relatively short symptomdurations (up to 5 years). An analysis that includes subjects with longer durations is needed tobetter understand the behaviour of the SI metric and its utility in tracking disease progression. Inparticular, the optimum intensity threshold used to compute SI is likely to depend on the diseaseseverity range of the subjects analyzed as well as the scan type. Lower threshold might be bettersuited when analyzing images of subjects with advanced disease when the uptake in the striatum issignificantly reduced.SI includes information on both intensity and size of the functionally-active region; if prop-erly tuned, this metric may preserve a large dynamic range as disease progresses and may thus beadvantageous when investigating progression.51Chapter 7Longitudinal Analysis and OutcomePredictionThe analysis presented in the previous chapter has been cross-sectional, based on imaging andclinical features obtained at year-0 (baseline) of the PPMI study. The focus of this chapter is onpredicting the rate of PD progression over the four years during which the subjects were enrolledinto the study based on data acquired at baseline. The prediction of the rate of disease progressionhas prognostic value and can enhance disease management. It can also help assess the efficacy ofdisease-modifying candidate therapies: the observed rate of progression (after the therapy has beenapplied) can be compared to the predicted one. In the case of Parkinson’s disease, there are multipleways in which disease severity can be quantified. In this work, two methods are used:1. Based on imaging features collected at year-0 (baseline) of the study, the decline in the puta-men binding ratios (putamen BRs) over the next four years is predicted.2. Based on imaging and clinical features at year-0, the year-4 UPDRS motor score and MoCAcognitive score are predicted.The goals of these analyses are to (i) assess model accuracy in predicting clinical symptom pro-gression and dopamine transporter depletion using baseline data only, and (ii) identify combinationsof features that are important predictors of progression.7.1 Previous WorkReference [54] studies the longitudinal decline of DaTSCAN uptake in the striatum in 35 PD sub-jects. They found that the annual decline in the striatum BR was 0.26± 0.14 (in units of the BR),and the largest annual difference was found in the posterior putamen. Furthermore, the decline inthe posterior putamen was larger in early PD subjects compared to advanced PD subjects. However,there has been no attempt, to out best knowledge, to explain the longitudinal change in the striatalBRs based on additional imaging features acquired at the initial scan.52An analysis on clinical variables and biomarkers that are predictive of cognitive decline in PDsubjects is performed in [52]. In that work, 390 PD subjects from PPMI that had year-0 and year-2 MoCA scores and clinical assessment of cognitive impairment were included. In a multivariateregression analysis using year-0 clinical and biomarker features as inputs, and using year-2 MoCAas the outcome measure, the following features were found to be statistically significant: age, MoCAbaseline score, UPSIT score, and the Aβ − tauratio (a cerebrospinal fluid biomarker). DaTSCANimaging features (mean caudate and putamen BRs, and side-to-side asymmetry terms) were notfound to be significant. Further comparison between the results found in [52] and the ones obtainedin this thesis is made in Section 7.3.2.A review of the models of longitudinal progression of the UPDRS motor score in PD subjectsis presented in [56]. However, these models are disease-drug models that evaluate the change inthe UPDRS score between the ”on medication” and ”off medication” states over time, developedwith the purpose to locate maximum symptomatic benefit of treatment or to compare symptomaticeffects between different clinical trials. In contrast, in this work, only ”off medication” UPDRSscores are examined, and the main goal is to find associations between the inputs (baseline features)and motor scores at year-4.In [41], an analysis is performed on the change in UPDRS scores in PD subjects from PPMI.In that work, after adjustment for age, gender, disease duration, symptomatic treatment status, andbaseline UPDRS score, a larger yearly change in the UPDRS score was found to be associatedwith lower better putamen BRs and cerebrospinal fluid alpha-synuclein levels (both measured atbaseline). However, we were unable to find published effect sizes for each of these variables.7.2 Imaging-based Model of Progression7.2.1 MethodsA total of 193 PD subjects from PPMI that had completed DaTSCAN imaging over four years wereincluded in this analysis. The DaTSCAN images were processed and binding ratios for the putamenand caudate were computed by PPMI as described in Section 4.1.A hierarchical Bayesian model was used for the imaging predictions. The model includes alongitudinal component:PBRi = βit+ ci+ εi (7.1)where the index i is over each subject, t = [0,1,2,4] is a vector that contains the scan times inyears since the start of the study and PBRi are the corresponding putamen BR values for subject i. Inthis model, each subject has their own yearly change (slope) βi as well as intercept ci correspondingto the PBR value at baseline.The slope term was predicted for each subject using the following imaging terms extracted atbaseline:53Figure 7.1: Diagram of the process used to fit and evaluate the imaging model.1. The initial putamen BR (PBR0).2. The difference between the better and the worse sides: ∆0 = PBRB−PBRW .3. The difference between the caudate and putamen ratios (CBR0−PBR0).The relationship between β and these features was assumed to be linear:β = α1PBR0+α2∆0+α3(CBR0−PBR0)+ εβ (7.2)The coefficients α link the observed image features at baseline and the expected 4-year progres-sion (represented by β ). These coefficients were estimated in a training phase using both longitudi-nal and baseline data for Ntrain = 100 subjects (Figure 7.1). The fitted α were then used to predictthe yearly change βk for each subject k in the test set (Ntest = 93). For model validation, the slopesβk are used to predict the putamen BRs at year-4 (PBRk4), and compared with the measured values.The error terms εβ and εi were assumed to be normally distributed.This model was fitted separately for the better and worse sides of the striatum, so each subject khad two separate progression parameters: βBk and βWk . The STAN library was used for the parameterestimation [4]. The mean absolute error and median percent error between observed and predictedPBR values at year-4 were used to quantify model performance.7.2.2 Results and discussionThe predictions for the year-4 putamen BRs on the test set of subjects are shown in Figure 7.2, andthe corresponding error estimates are in Table 7.1. Overall, the predictions on the less affected sideof the striatum are more accurate; the median percent error of 13.6% on that side is comparableto the test-retest error for DaTSCAN (9− 16% [45]). However, for a subset of the subjects thepredictions are not accurate, and it is useful to examine individual predictions.540.00 0.25 0.50 0.75 1.00 1.25observed values0. valuesBetter putamenidentitybest fit0.00 0.25 0.50 0.75 1.00 1.25observed values0. putamenFigure 7.2: Predictions on the test set of subjects for the imaging model.Table 7.1: Error estimates for the imaging model based on year-4 predictions.better side worse sidemedian perc. error 13.8% 19.8%mean abs. error 0.13 0.12The predictions for three subjects from the test set are shown in Figure 7.3, and their clinical andimaging characteristics obtained at baseline are shown in Table 7.2. These subjects were selectedbecause all three had nearly identical PBR values at baseline, however, there were differences inother imaging and clinical scores at baseline. For instance, the caudate is better preserved in thecase of subj. 2 (larger CBR−PBR terms) and the yearly decline in PBR values is somewhat slowerfor that subject. The progression is faster for subj. 3 and it is underestimated by the model. Notethat this subject has a much smaller motor asymmetry at baseline (Better MS - Worse MS = 4.8)compared to the others.Posterior distributions for the coefficients α were also obtained (Table 7.3) in order to assessthe imaging feature contributions to the progression prediction. Larger side-to-side asymmetry wasfound to lead to a faster decline on the better side. For both sides of the striatum, a better-preservedcaudate (larger CBR−PBR term) leads to a slower decline. The model was also fitted using thebaseline PBR term only to assess the importance of the other two features, (results not shown) andTable 7.2: Baseline imaging and clinical characteristics for three subjects from the test set.Subject 1 2 3age 62 46 63.6CBR - PBR (better) 0.47 1.67 0.72CBR - PBR (worse) 0.65 1.46 1.00Better MS 8.5 9.6 14.0Worse MS 19.5 21.4 18.8550 1 2 (better)Subj 10 1 2 20 1 2 30 1 2 (worse)0 1 2 4scan year0. 1 2 7.3: Examples of the predictions made by the imaging model for three subjects fromthe test set. The measured putamen BRs over the four years of the study are shown inred. The green bands represent the predictions made by the model, and the width of theband corresponds to the uncertainty in the prediction (the 68% confidence interval).Table 7.3: Mean values and standard deviations of the parameters α obtained from the poste-rior distributions of the fitted model. ∗p < 0.01,∗∗ p < 0.001.putamen (α1) asymmetry putamen (α2) putamen - caudate (α3)better side −0.11±0.02∗∗ −0.05±0.02∗ 0.03±0.01∗worse side −0.13±0.02∗∗ +0.02±0.02 0.03±0.01∗the error rates increased by 20% for the better side and by 10% for the worse side.The Bayesian approach provides a flexible framework where different model components de-scribing relationships between variables can be combined into a single model [60]. In the modeldescribed here, two components were used (longitudinal component to estimate β and baselinecomponent to estimate α), but it can easily be extended to capture a more complex structure whenmodelling disease progression. For example, one possibility is to first segment the population ofPD subjects based on clinical data and relevant genomic variation (captured by single nucleotidepolymorphisms). The coefficients α can then be estimated separately for each subgroup of PD sub-jects, allowing the model to capture possible differences in expected rate of progression betweenthe different subgroups. Such a model structure would likely require a larger number of subjects,however.A possible limitation of this model is that the longitudinal trajectory of the putamen BRs wasassumed to be linear, while it was previously shown in a study that included subjects with diseaseduration of up to 20 years that the trajectory is better described by an exponential function [47].Given the relatively short time-scales in this analysis, the linearity assumption likely does not havea substantial impact on the predictions. However, if this type of analysis is to be applied to dataacquired over a longer disease duration range, then a more flexible longitudinal trajectory would be56necessary.7.2.3 ConclusionThis analysis identifies new imaging features that are predictors of progression. These featuresdescribe the spatial pattern of dopamine transporter depletion in the striatum: (i) the side-to-sideasymmetry, and (ii) the difference between the caudate and the putamen ratios, indicative of therostrocaudal gradient. These features are consistent with the previously discussed patterns of PDprogression in the striatum (Section 3.2.1).While the mean prediction error is relatively low, the predictions are not accurate for about 22%of the subjects (note that those subjects were included in the test error computation in Table 7.1).Future work needs to identify the factors leading to atypical progression in these subjects.7.3 Model of Progression Based on Clinical Scores7.3.1 MethodsFor this model of progression, the available clinical data (MoCA cognitive and UPDRS motor scoresover four years) for the 193 PD subjects described in the imaging model were examined for possibleinconsistencies. It was assumed that motor symptoms should worsen monotonically, when exam-ined off medication. Therefore, the primary inclusion criterion was that the subjects’ year-4 motorscore should be no less than their year-0 score (both measured off medication). Following this, atotal of 44 subjects were excluded due to inconsistencies primarily in the motor scores. Figure 7.4illustrates the motor scores over time for a subject that was excluded from the analysis.The motor scores at year-0 and at year-4 were split into 3 components (better side, worse side,common) as detailed in Section 3.3.1. The complete set of input features and output variables usedin the model is listed in Table 7.4. The inputs included a combination of clinical scores that havebeen previously associated with cognitive decline [52, 53] or motor dysfunction [28, 41], as well asthe DaTSCAN imaging features (based on the caudate and putamen BRs) described in the previoussection. The BRs were used as DaTSCAN features rather than sum intensity because (i) BRs wereavailable for a larger set of subjects at the time of the analysis and (ii) one of our aims was to usethe difference between the uptake in the caudate and in the putamen as an imaging feature, and sumintensity, computed on the bounding box over the entire striatum, does not capture that difference.The output features were selected with the aim to characterize the motor function as well as thecognitive ability of the subjects at year-4. All inputs features were standardized to a median of 0and interquartile range of 1 prior to model fitting.A multivariate linear least squares with L2 regularization, known as ridge regression, was usedfor the predictive model. The objective function of ridge regression is:minW||XW −Y ||2+α||W ||2572011-082012-022012-082013-022013-082014-022014-082015-022015-081015202530total MSdose = 0Figure 7.4: Example of a subject excluded from the clinical prediction analysis. The labeldose = 0 means that, according to the PPMI records, the subject was withdrawn fromLevodopa/dopamine agonist medication for 12 hours prior to the clinical exam. For theyear-4 exams, it is possible that the subject was still on medication, leading to a substan-tially lower score compared to the baseline measurement and an unreliable estimate ofthe true motor symptom severity.where X is the n× p input matrix with p input features and n subjects, Y is the n×k matrix withk outputs, W is the p× k matrix of weights to be determined, and α is a parameter that controls theregularization strength. A value α = 0 corresponds to the ordinary least squares (OLS) problem andα → ∞ leads to the null model where W = 0.Ridge regression often outperforms OLS in cases where the OLS estimates have a large variance- that is, when small variation in the training data result in large change in the fitted coefficients [32].The additional regularization term in ridge regression tends to shrink the regression coefficients ofnon-predictive features towards zero, which reduces variance and improves test error. Regulariza-tion is especially useful in cases of multicollinearity in the input features, in which case the OLSsolution is not unique and unstable, whereas ridge regression provides stable estimates of the coef-ficients.Ten-fold cross-validation was used to train and validate the model. At each iteration, the modelwas fitted on 90% of the data (training set) and validated on the 10% held-out data (validation set)by computing the mean absolute error and median percent errors on the output variables. Duringthe training stage, the training set was further subdivided using another ten-fold cross-validation inorder to select the optimum α in the range 0.1−10 that minimizes the absolute error within that setof data. For each iteration of the cross-validation, the value of α was selected using the training setonly, and the model was used to predict the outcome variables for the 10% held-out data.To estimate the number of subjects whose outcome prediction was inaccurate, a threshold of 8points over the absolute error for the total motor score was used and a threshold of 3 points for theMoCA score. For example, if the absolute difference between the predicted and actual total motor58Table 7.4: Input features and output variables for all subjects (N = 149) included in the clin-ical model. In addition, sex (30% female, N f emale = 45) was also used as a binary inputvariable with 0 denoting a male and 1 denoting a female subject. Olfactory function wasassessed using the UPSIT score, and depression was assessed using the GDS score. Allimaging features are based on the putamen and caudate BR metrics.mean std dev min maxyear-0 inputsage 61.8 10.0 33.7 84.9sex 0.30 0 1better side MS 3.05 2.85 0.00 11.67worse side MS 10.63 4.06 1.33 23.00common MS 6.79 2.60 2.00 15.33better put 0.94 0.35 0.22 2.32caud - put (better) 1.18 0.41 0.06 2.32asymmetry put 0.27 0.27 -0.36 0.87caud - put (worse) 1.13 0.39 0.23 2.32MoCA 27.10 2.28 17.00 30.00olfactory 21.74 8.01 5.00 39.00depression 5.13 1.40 1.00 10.00year-4 outcomesbetter side MS 8.49 4.38 0.33 19.67worse side MS 16.18 4.36 5.67 27.33common MS 11.19 3.86 3.00 23.00MoCA 26.01 4.07 11.00 30.00scores for a given subject was > 8 points, then the prediction was considered inaccurate.7.3.2 Results and discussionScatter plots of predicted vs. true outcomes are shown in Figure 7.6, and the corresponding errormeasures are in Table 7.5. Overall, the motor score predictions are more accurate compared to thecognitive ones. Using the error thresholds defined previously, 26% of the subjects had an inaccuratemotor score prediction (∆ > 8), 32% had an inaccurate MoCA prediction (∆ > 3), and 10% hadinaccurate predictions for both outcomes.The larger error for the MoCA score is not surprising given the distribution of the year-4 MoCAscores (Figure 7.5). The majority of the subjects score in a relatively narrow range between 20and 30, but there is a small number of subjects with scores as low as 11, making this variable verychallenging to predict.One of the primary advantages of the linear model is that the fitted weights W (shown in Fig-ure 7.7) can be interpreted in terms of an association between inputs and outputs. When examiningthese weights, the reader should be reminded that larger motor score reflects more severe motordysfunction, while a larger cognitive score reflects better cognition.5915 20 25 30MoCA score051015202530Number of subjectsFigure 7.5: Distribution of the observed year-4 MoCA scores.0 5 10 15 2005101520predicted valueBetter side MSidentitybest fit5 10 15 20 25510152025Worse side MS5 10 15 20observed value5101520predicted valueCommon MS20.0 22.5 25.0 27.5 30.0observed value20.022.525.027.530.032.5 MoCAFigure 7.6: Predictions of clinical variables for 80 subjects drawn from the validation sets.Subjects with MoCA score < 18 were excluded from the MoCA plot to make it easier toexamine the majority of subjects (where MoCA ≥ 18). All subjects were included in thecalculation of the error measures.60Table 7.5: Error measures for the clinical predictions. The uncertainties in the mean absoluteerror are determined from the standard deviation of the error over the 10 folds of cross-validation.better MS worse MS common MS MoCAmean abs. error 2.42±0.27 2.46±0.33 2.38±0.37 2.59±0.41median perc. error 26% 13% 21% 7%Not surprisingly, the strongest predictor for a given output variable was the corresponding inputfeature measured at year-0. In addition, among the clinical variables, age, the depression score,and the better and common motor scores had a negative impact on the MoCA outcome. Among theimaging terms, the difference between the more affected caudate and putamen, and the asymmetry inthe putamen (better - worse) were associated with a better cognitive score, while a higher putamenBR (on the better side) was associated with a poorer cognitive outcome. Given the colinearityamong the input features, these findings should be interpreted with caution: they do not imply thatan increase in the putamen BR leads to a poorer cognitive outcome. That is because an increase inthe putamen BR is also associated with improved motor performance at year-0 (lower motor scores),and the combined effect of higher putamen BR and lower motor scores on the cognitive outcomewould be positive, according to the model.In order to further clarify the multivariate results, univariate analysis was also performed wherea regression model was fitted to every input feature - output variable combination. The fitted co-efficients are shown in Figure 7.8. It can be observed in that figure that a higher putamen BR wasassociated with better motor score outcome for the better and common components (lower scores),but there was no significant univariate association between the better putamen BR and the cognitiveoutcome, unlike in the multivariate regression result. A possible interpretation of the findings fromthe multivariate analysis is that the imaging features (such as the putamen BR) act as additional(correction) factors to the clinical variables measured at year-0, which are the primary predictors ofclinical outcomes.In [52], researchers did not find the motor score to be a significant predictor of the MoCA scoreat year-2, or predictive of clinically-diagnosed cognitive impairment, although they used the totalmotor score as an input feature, rather than dividing the score into components. This suggests thatusing separate motor components might enhance the predictive power of the motor score. Fur-thermore, they found that the UPSIT olfactory score to be significantly associated with the MoCAoutcome, whereas here the association between olfactory score and MoCA at year-4 was found to bevery weak. This suggests that early changes in the cognition (up to year-2) might be more stronglyassociated with olfaction. In addition, they did not find any of the DaTSCAN imaging terms to bepredictive of the MoCA score, although they did not include the difference between the caudate andthe putamen BRs as a feature into their model.From the ridge regression results, larger asymmetry in the putamen was associated with a betteroutcome on the common MS and better MS terms (smaller year-4 scores), however, this should be612 1 0 1 2 3better MScommon MSworse side MSbetter putamencaud - put (better)asymmetry putcaud - put (worse)agesexMoCAolfactorydepression better MSworse MScommon MSMoCAFigure 7.7: Fitted coefficients of the ridge regression. Each row corresponds to an input fea-ture, and the weights for the different outputs are colour-coded. The bar length representsa mean over the ten model fits performed during cross-validation, where each fit resultsin a somewhat different weight matrix W , and the error bars are the standard deviationsof these weights.considered in conjunction with the motor score terms measured at year-0, which are the primarypredictors of year-4 motor score. In addition, age might have an impact on the better and commonMS scores (worse outcome with increasing age), although this effect appears relatively small.7.3.3 ConclusionIn this section, a ridge regression model was used to predict clinical outcome at year-4 of the PPMIstudy based on baseline clinical and imaging features. For the majority of the subjects the predic-tions were found to be adequate, which suggests that in those cases there is enough informationin the year-0 features to describe the PD progression (as quantified by the clinical exams) for thenext four years. In addition, the fitted weights provide insights into the combinations of featurespredictive of motor dysfunction and cognitive decline. Although multiple models in the past havebeen used to correlate clinical and imaging features against motor performance or cognitive scores,to the best of the author’s knowledge, there have been no previous work that attempts to characterizelongitudinal cognitive and motor PD progression using baseline features.There are many ways in which this model can be improved. The most direct approach is to addadditional inputs, such as features extracted from other imaging modalities (such as diffusion MR),and cerebrospinal fluid biomarkers. More complex predictive models such as random forests mayalso be considered, to capture possible nonlinear effects and interactions between the various inputs,however, at the price of a more limited interpretability.623 2 1 0 1 2 3 4 5better MScommon MSworse side MSbetter putamencaud - put (better)asymmetry putcaud - put (worse)agesexMoCAolfactorydepression better MSworse MScommon MSMoCAFigure 7.8: Fitted coefficients from linear regression models fitted with a single feature as in-put. Error bars correspond to the standard error of each fitted coefficient (68% confidenceinterval).63Bibliography[1] J. S. Alper and R. I. Gelb. Standard errors and confidence intervals in nonlinear regression:comparison of Monte Carlo and parametric statistics. The Journal of Physical Chemistry, 94(11):4747–4751, may 1990. ISSN 0022-3654. doi:10.1021/j100374a068.[2] A. Augimeri, A. Cherubini, G. L. Cascini, D. Galea, M. E. Caligiuri, G. Barbagallo,G. Arabia, and A. Quattrone. 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