Methods for functional regression and nonlinear mixed-effects models with applications to PET data

The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data. The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control. The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data. The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure

Bayesian latent time joint mixed-effects model of progression in the Alzheimer's Disease Neuroimaging Initiative.

IntroductionWe characterize long-term disease dynamics from cognitively healthy to dementia using data from the Alzheimer's Disease Neuroimaging Initiative.MethodsWe apply a latent time joint mixed-effects model to 16 cognitive, functional, biomarker, and imaging outcomes in Alzheimer's Disease Neuroimaging Initiative. Markov chain Monte Carlo methods are used for estimation and inference.ResultsWe find good concordance between latent time and diagnosis. Change in amyloid positron emission tomography shows a moderate correlation with change in cerebrospinal fluid tau (ρ = 0.310) and phosphorylated tau (ρ = 0.294) and weaker correlation with amyloid-β 42 (ρ = 0.176). In comparison to amyloid positron emission tomography, change in volumetric magnetic resonance imaging summaries is more strongly correlated with cognitive measures (e.g., ρ = 0.731 for ventricles and Alzheimer's Disease Assessment Scale). The average disease trends are consistent with the amyloid cascade hypothesis.DiscussionThe latent time joint mixed-effects model can (1) uncover long-term disease trends; (2) estimate the sequence of pathological abnormalities; and (3) provide subject-specific prognostic estimates of the time until onset of symptoms

Predicting the course of Alzheimer's progression.

Alzheimer's disease is the most common neurodegenerative disease and is characterized by the accumulation of amyloid-beta peptides leading to the formation of plaques and tau protein tangles in brain. These neuropathological features precede cognitive impairment and Alzheimer's dementia by many years. To better understand and predict the course of disease from early-stage asymptomatic to late-stage dementia, it is critical to study the patterns of progression of multiple markers. In particular, we aim to predict the likely future course of progression for individuals given only a single observation of their markers. Improved individual-level prediction may lead to improved clinical care and clinical trials. We propose a two-stage approach to modeling and predicting measures of cognition, function, brain imaging, fluid biomarkers, and diagnosis of individuals using multiple domains simultaneously. In the first stage, joint (or multivariate) mixed-effects models are used to simultaneously model multiple markers over time. In the second stage, random forests are used to predict categorical diagnoses (cognitively normal, mild cognitive impairment, or dementia) from predictions of continuous markers based on the first-stage model. The combination of the two models allows one to leverage their key strengths in order to obtain improved accuracy. We characterize the predictive accuracy of this two-stage approach using data from the Alzheimer's Disease Neuroimaging Initiative. The two-stage approach using a single joint mixed-effects model for all continuous outcomes yields better diagnostic classification accuracy compared to using separate univariate mixed-effects models for each of the continuous outcomes. Overall prediction accuracy above 80% was achieved over a period of 2.5 years. The results further indicate that overall accuracy is improved when markers from multiple assessment domains, such as cognition, function, and brain imaging, are used in the prediction algorithm as compared to the use of markers from a single domain only

Numerical Simulation of the Thermodependant Viscohyperelastic Behavior of Polyethylene Terephthalate Near the Glass Transition Temperature: Prediction of the Self-Heating During Biaxial Tension Test

The poly ethylene terephthalate near the glass transition temperature highlights a strongly non linear elastic and viscous behaviour when biaxially stretched at high strain rates representative of the injection stretch blow moulding process. A non linear visco-hyperelastic model, where characteristics are coupled to the temperature, has already been identified from equi-biaxial tension experimental results. The weak form of the mechanical part of the model is presented and implemented into a finite element code developed in the Matlab environment and validated by comparing numerical simulation of equibiaxial testing with the analytical solution in the isothermal case. Considering the thermal aspects, an experimental study, where PETsheets are heated using infrared (IR for short) lamps is also presented. The modeling of the IR radiation of the sheet helps to identify the thermal properties of the PET. The thermal model is then implemented in the finite element code, coupled to the 2D viscoelasticmodel. A discussion ismade to justify the accuracy of the assumption made on homogeneity of the temperature field through the thickness. The simulation of the 2D plane stress equibiaxial test shows the important influence of the thermal aspects and the coupled thermo-mechanical software is used to quantify the selfheating phenomenon in the case of the biaxial elongations of PET sheets at high strain rates. POLYM. ENG. SCI., 53:2683–2695, 2013. ª2013 Society of Plastics Engineer

Stream water age distributions controlled by storage dynamics and nonlinear hydrologic connectivity : Modeling with high-resolution isotope data

Peer reviewedPublisher PD

Fractal and multifractal analysis of PET-CT images of metastatic melanoma before and after treatment with ipilimumab

PET/CT with F-18-Fluorodeoxyglucose (FDG) images of patients suffering from metastatic melanoma have been analysed using fractal and multifractal analysis to assess the impact of monoclonal antibody ipilimumab treatment with respect to therapy outcome. Our analysis shows that the fractal dimensions which describe the tracer dispersion in the body decrease consistently with the deterioration of the patient therapeutic outcome condition. In 20 out-of 24 cases the fractal analysis results match those of the medical records, while 7 cases are considered as special cases because the patients have non-tumour related medical conditions or side effects which affect the results. The decrease in the fractal dimensions with the deterioration of the patient conditions (in terms of disease progression) are attributed to the hierarchical localisation of the tracer which accumulates in the affected lesions and does not spread homogeneously throughout the body. Fractality emerges as a result of the migration patterns which the malignant cells follow for propagating within the body (circulatory system, lymphatic system). Analysis of the multifractal spectrum complements and supports the results of the fractal analysis. In the kinetic Monte Carlo modelling of the metastatic process a small number of malignant cells diffuse throughout a fractal medium representing the blood circulatory network. Along their way the malignant cells engender random metastases (colonies) with a small probability and, as a result, fractal spatial distributions of the metastases are formed similar to the ones observed in the PET/CT images. In conclusion, we propose that fractal and multifractal analysis has potential application in the quantification of the evaluation of PET/CT images to monitor the disease evolution as well as the response to different medical treatments.Comment: 38 pages, 9 figure

Patient-Specific Method of Generating Parametric Maps of Patlak K(i) without Blood Sampling or Metabolite Correction: A Feasibility Study.

Currently, kinetic analyses using dynamic positron emission tomography (PET) experience very limited use despite their potential for improving quantitative accuracy in several clinical and research applications. For targeted volume applications, such as radiation treatment planning, treatment monitoring, and cerebral metabolic studies, the key to implementation of these methods is the determination of an arterial input function, which can include time-consuming analysis of blood samples for metabolite correction. Targeted kinetic applications would become practical for the clinic if blood sampling and metabolite correction could be avoided. To this end, we developed a novel method (Patlak-P) of generating parametric maps that is identical to Patlak K(i) (within a global scalar multiple) but does not require the determination of the arterial input function or metabolite correction. In this initial study, we show that Patlak-P (a) mimics Patlak K(i) images in terms of visual assessment and target-to-background (TB) ratios of regions of elevated uptake, (b) has higher visual contrast and (generally) better image quality than SUV, and (c) may have an important role in improving radiotherapy planning, therapy monitoring, and neurometabolism studies