Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data

International audienceWe introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic trajectories, the temporal sources are defined as monotonic and time-reparametrized Gaussian Processes. To account for the non-stationarity of brain images, we model the spatial sources as sparse codes convolved at multiple scales. The method was tested on synthetic data favourably comparing with standard blind source separation approaches. The application on large-scale imaging data from a clinical study allows to disentangle differential temporal progression patterns mapping brain regions key to neurodegeneration, while revealing a disease-specific time scale associated to the clinical diagnosis

Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data

We introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic trajectories, the temporal sources are defined as monotonic and time-reparametrized Gaussian Processes. To account for the non-stationarity of brain images, we model the spatial sources as sparse codes convolved at multiple scales. The method was tested on synthetic data favourably comparing with standard blind source separation approaches. The application on large-scale imaging data from a clinical study allows to disentangle differential temporal progression patterns mapping brain regions key to neurodegeneration, while revealing a disease-specific time scale associated to the clinical diagnosis

Monotonic Gaussian Process for Spatio-Temporal Disease Progression Modeling in Brain Imaging Data

International audienceWe introduce a probabilistic generative model for disentangling spatio-temporal disease trajectories from series of high-dimensional brain images. The model is based on spatio-temporal matrix factorization, where inference on the sources is constrained by anatomically plausible statistical priors. To model realistic trajectories, the temporal sources are defined as monotonic and time-reparametrized Gaussian Processes. To account for the non-stationarity of brain images, we model the spatial sources as sparse codes convolved at multiple scales. The method was tested on synthetic data favourably comparing with standard blind source separation approaches. The application on large-scale imaging data from a clinical study allows to disentangle differential temporal progression patterns mapping brain regions key to neurodegeneration, while revealing a disease-specific time scale associated to the clinical diagnosis

Disease Progression Modeling and Prediction through Random Effect Gaussian Processes and Time Transformation

The development of statistical approaches for the joint modelling of the temporal changes of imaging, biochemical, and clinical biomarkers is of paramount importance for improving the understanding of neurodegenerative disorders, and for providing a reference for the prediction and quantification of the pathology in unseen individuals. Nonetheless, the use of disease progression models for probabilistic predictions still requires investigation, for example for accounting for missing observations in clinical data, and for accurate uncertainty quantification. We tackle this problem by proposing a novel Gaussian process-based method for the joint modeling of imaging and clinical biomarker progressions from time series of individual observations. The model is formulated to account for individual random effects and time reparameterization, allowing non-parametric estimates of the biomarker evolution, as well as high flexibility in specifying correlation structure, and time transformation models. Thanks to the Bayesian formulation, the model naturally accounts for missing data, and allows for uncertainty quantification in the estimate of evolutions, as well as for probabilistic prediction of disease staging in unseen patients. The experimental results show that the proposed model provides a biologically plausible description of the evolution of Alzheimer's pathology across the whole disease time-span as well as remarkable predictive performance when tested on a large clinical cohort with missing observations.Comment: 13 pages, 2 figure

Modeling and inference of spatio-temporal protein dynamics across brain networks

Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is usually challenging, due to the lack of a well defined time axis for the pathology. This issue is addressed by disease progression models (DPM) where long-term progression trajectories are estimated via time reparametrization of individual observations. However, due to their loose assumptions on the dynamics, DPM do not provide insights on the bio-mechanical properties of MP propagation. Here we propose a unified model of spatio-temporal protein dynamics based on the joint estimation of long-term MP dynamics and time reparameterization of individuals observations. The model is expressed within a Gaussian Process (GP) regression setting, where constraints on the MP dynamics are imposed through non--linear dynamical systems. We use stochastic variational inference on both GP and dynamical system parameters for scalable inference and uncertainty quantification of the trajectories. Experiments on simulated data show that our model accurately recovers prescribed rates along graph dynamics and precisely reconstructs the underlying progression. When applied to brain imaging data our model allows the bio-mechanical interpretation of amyloid deposition in Alzheimer's disease, leading to plausible simulations of MP propagation, and achieving accurate predictions of individual MP deposition in unseen data

Alzheimer's Disease Modelling and Staging through Independent Gaussian Process Analysis of Spatio-Temporal Brain Changes

International audienceAlzheimer's disease (AD) is characterized by complex and largely unknown progression dynamics affecting the brain's morphology. Although the disease evolution spans decades, to date we cannot rely on long-term data to model the pathological progression, since most of the available measures are on a short-term scale. It is therefore difficult to understand and quantify the temporal progression patterns affecting the brain regions across the AD evolution. In this work, we present a generative model based on probabilistic matrix factorization across temporal and spatial sources. The proposed method addresses the problem of disease progression modelling by introducing clinically-inspired statistical priors. To promote smoothness in time and model plausible pathological evolutions, the temporal sources are defined as monotonic and independent Gaussian Processes. We also estimate an individual time-shift parameter for each patient to automatically position him/her along the sources time-axis. To encode the spatial continuity of the brain sub-structures, the spatial sources are modeled as Gaussian random fields. We test our algorithm on grey matter maps extracted from brain structural images. The experiments highlight differential temporal progression patterns mapping brain regions key to the AD pathology, and reveal a disease-specific time scale associated with the decline of volumetric biomarkers across clinical stages

Data-driven models of dominantly-inherited Alzheimer’s disease progression

Dominantly-inherited Alzheimer's disease is widely hoped to hold the key to developing interventions for sporadic late onset Alzheimer's disease. We use emerging techniques in generative data-driven disease-progression modelling to characterise dominantly-inherited Alzheimer’s disease progression with unprecedented resolution, and without relying upon familial estimates of years until symptom onset (EYO). We retrospectively analysed biomarker data from the sixth data freeze of the Dominantly Inherited Alzheimer Network observational study, including measures of amyloid proteins and neurofibrillary tangles in the brain, regional brain volumes and cortical thicknesses, brain glucose hypometabolism, and cognitive performance from the Mini-Mental State Examination (all adjusted for age, years of education, sex, and head size, as appropriate). Data included 338 participants with known mutation status (211 mutation carriers: 163 PSEN1; 17 PSEN2; and 31 APP) and a baseline visit (age 19–66; up to four visits each, 1·1±1·9 years in duration; spanning 30 years before, to 21 years after, parental age of symptom onset). We used an event-based model to estimate sequences of biomarker changes from baseline data across disease subtypes (mutation groups), and a differential-equation model to estimate biomarker trajectories from longitudinal data (up to 66 mutation carriers, all subtypes combined). The two models concur that biomarker abnormality proceeds as follows: amyloid deposition in cortical then sub-cortical regions (approximately 24±11 years before onset); CSF p-tau (17±8 years), tau and Aβ42 changes; neurodegeneration first in the putamen and nucleus accumbens (up to 6±2 years); then cognitive decline (7±6 years), cerebral hypometabolism (4±4 years), and further regional neurodegeneration. Our models predicted symptom onset more accurately than EYO: root-mean-squared error of 1·35 years versus 5·54 years. The models reveal hidden detail on dominantly-inherited Alzheimer's disease progression, as well as providing data-driven systems for fine-grained patient staging and prediction of symptom onset with great potential utility in clinical trials

Simulating the outcome of amyloid treatments in Alzheimer's Disease from multi-modal imaging and clinical data

International audienceIn this study we investigate a novel quantitative instrument for the development of intervention strategies for disease modifying drugs in Alzheimer's disease. Our framework is based on the modeling of the spatio-temporal dynamics governing the joint evolution of imaging and clinical biomarkers along the history of the disease, and allows the simulation of the effect of intervention time and drug dosage on the biomarkers' progression. When applied to multi-modal imaging and clinical data from the Alzheimer's Disease Neuroimaging Initiative our method enables to generate hypothetical scenarios of amyloid lowering interventions. The results quantify the crucial role of intervention time, and provide a theoretical justification for testing amyloid modifying drugs in the pre-clinical stage. Our experimental simulations are compatible with the outcomes observed in past clinical trials, and suggest that anti-amyloid treatments should be administered at least 7 years earlier than what is currently being done in order to obtain statistically powered improvement of clinical endpoints