Gaussian Processes (GP) are a powerful tool to capture the complex time-variations of a dataset. In the context of medical imaging analysis, they allow a robust modelling even in case of highly uncertain or incomplete datasets. Predictions from GP are dependent of the covariance kernel function selected to explain the data variance. To overcome this limitation, we propose a framework to identify the optimal covariance kernel function to model the data.The optimal kernel is defined as a composition of base kernel functions used to identify correlation patterns between data points. Our approach includes a modified version of the Compositional Kernel Learning (CKL) algorithm, in which we score the kernel families using a new energy function that depends both the Bayesian Information Criterion (BIC) and the explained variance score. We applied the proposed framework to model the progression of neurodegenerative diseases over time, in particular the progression of autosomal dominantly-inherited Alzheimer's disease, and use it to predict the time to clinical onset of subjects carrying genetic mutation.
Directional diffusivities derived from diffusion tensor magnetic resonance imaging (DTI) measurements describe water
movement parallel to (λ||, axial diffusivity) and perpendicular to (λ⊥radial diffusivity) axonal tracts. λ|| and λ⊥ have been
shown to differentially detect axon and myelin abnormalities in several mouse models of central nervous system white
matter pathology in our laboratory. These models include experimental autoimmune encephalomyelitis (EAE), (1)
myelin basic protein mutant mice with dysmyelination and intact axons, (2) cuprizone-induced demyelination, and
remyelination, with reversible axon injury (2, 3) and a model of retinal ischemia in which retinal ganglion cell death is
followed by Wallerian degeneration of optic nerve, with axonal injury preceding demyelination. (4) Decreased λ||
correlates with acute axonal injury and increased λ⊥ indicates myelin damage. (4) More recently, we have translated this
approach to human MR, investigating acute and chronic optic neuritis in adults with multiple sclerosis, brain lesions in
adults with multiple sclerosis, and acute disseminated encephalomyelitis (ADEM) in children. We are also investigating
the use of this technique to probe the underlying structural change of the cervical spinal cord in acute and chronic T2-
hyperintense lesions in spinal stenosis, trauma, and transverse myelitis. In each of these demyelinating diseases, the
discrimination between axonal and myelin injury which we can achieve has important prognostic and therapeutic
implications. For those patients with myelin injury but intact axons, early, directed drug therapy has the potential to
prevent progression to axonal loss and permanent disability.