Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer's disease.

We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their cortical surface geometry and associated cortical thickness map. The proposed model is based upon a reformulation of the classification problem as a regularized multivariate functional linear regression model. This allows us to adopt a direct approach to the estimation of the most discriminant direction while controlling for its complexity with appropriate differential regularization. Our approach does not require prior estimation of the covariance structure of the functional predictors, which is computationally prohibitive in our application setting. We provide a theoretical analysis of the out-of-sample prediction error of the proposed model and explore the finite sample performance in a simulation setting. We apply the proposed method to a pooled dataset from Alzheimer's Disease Neuroimaging Initiative and Parkinson's Progression Markers Initiative. Through this application, we identify discriminant directions that capture both cortical geometric and thickness predictive features of Alzheimer's disease that are consistent with the existing neuroscience literature.

Preliminary investigations into human neurofluid transport using multiple novel non-contrast MRI methods.

We discuss two potential non-invasive MRI methods to study phenomena related to subarachnoid cerebrospinal fluid (CSF) motion and perivascular fluid transport, and their association with sleep and aging. We apply diffusion-based intravoxel incoherent motion (IVIM) imaging to evaluate pseudodiffusion coefficient, D*, or CSF movement across large spaces like the subarachnoid space (SAS). We also performed perfusion-based multi-echo, Hadamard encoded arterial spin labeling (ASL) to evaluate whole brain cortical cerebral blood flow (CBF) and trans-endothelial exchange (Tex) of water from the vasculature into the perivascular space and parenchyma. Both methods were used in young adults (N = 9, 6 F, 23 ± 3 years old) in the setting of sleep and sleep deprivation. To study aging, 10 older adults (6 F, 67 ± 3 years old) were imaged after a night of normal sleep and compared with the young adults. D* in SAS was significantly (p < 0.05) reduced with sleep deprivation (0.016 ± 0.001 mm2/s) compared to normal sleep (0.018 ± 0.001 mm2/s) and marginally reduced with aging (0.017 ± 0.001 mm2/s, p = 0.029). Cortical CBF and Tex were unchanged with sleep deprivation but significantly lower in older adults (37 ± 3 ml/100 g/min, 578 ± 61 ms) than in young adults (42 ± 2 ml/100 g/min, 696 ± 62 ms). IVIM was sensitive to sleep physiology and aging, and multi-echo, multi-delay ASL was sensitive to aging.

Patient-specific computational fluid dynamic simulation of cerebrospinal fluid flow in the intracranial space.

BACKGROUND: Abnormal cerebrospinal fluid (CSF) flow is associated with a variety of poorly understood neurological disorders such as Alzheimer's Disease and hydrocephalus. The lack of comprehensive understanding of the fluid and solid mechanics of CSF flow remains a critical barrier in the development of diagnostic assessment and potential treatment options for these diseases. We have developed a whole brain, patient-specific computational fluid dynamics (CFD) simulation of CSF flow in the cranial cavity as a step towards comprehensive understanding of CSF dynamics and how they relate to neurodegenerative diseases. METHODS: A patient-specific 3D geometry of the CSF filled spaces was segmented from structural MRI. Patient-specific boundary conditions were measured using phase contrast MRI. A rigid wall three-dimensional CFD simulation was conducted using only patient-specific waveforms as boundary conditions. Deformation of brain tissue is accounted for using volumetric flowrate boundary conditions calculated via the conservation of mass. Phase contrast MRI measurement of maximum velocity at the cerebral aqueduct was used to validate the simulation with excellent agreement. RESULTS: The CSF dynamics across the cardiac cycle are presented, illustrating the relationship between arterial flow and CSF flow. Flow in and out of the ventricles was shown to have a slight phase delay (∼20 % of the cardiac cycle) from flow in the subarachnoid space. Intracranial pressure dynamics are presented, with pressure in the Lateral Ventricles demonstrating less significant transient effects than pressure in the subarachnoid space. CONCLUSIONS: This work presents a quantitatively validated whole-brain simulation of CSF flow for a single healthy subject. The computational methodology improves over the state of the art by eliminating non-physiological boundary conditions and unnecessary assumptions about the mechanical properties of brain tissue, providing an essential step towards clinically useful tools for assessing the development of neurodegenerative disorders.

Cross-Sectional and Longitudinal Hippocampal Atrophy, Not Cortical Thinning, Occurs in Amyloid-Negative, p-Tau-Positive, Older Adults With Non-Amyloid Pathology and Mild Cognitive Impairment.

Introduction: Alzheimer's disease (AD) is a degenerative disease characterized by pathological accumulation of amyloid and phosphorylated tau. Typically, the early stage of AD, also called mild cognitive impairment (MCI), shows amyloid pathology. A small but significant number of individuals with MCI do not exhibit amyloid pathology but have elevated phosphorylated tau levels (A-T+ MCI). We used CSF amyloid and phosphorylated tau to identify the individuals with A+T+ and A-T+ MCI as well as cognitively normal (A-T-) controls. To increase the sample size, we leveraged the Global Alzheimer's Association Interactive Network and identified 137 MCI+ and 61 A-T+ MCI participants. We compared baseline and longitudinal, hippocampal, and cortical atrophy between groups. Methods: We applied ComBat harmonization to minimize site-related variability and used FreeSurfer for all measurements. Results: Harmonization reduced unwanted variability in cortical thickness by 3.4% and in hippocampal volume measurement by 10.3%. Cross-sectionally, widespread cortical thinning with age was seen in the A+T+ and A-T+ MCI groups (p < 0.0005). A decrease in the hippocampal volume with age was faster in both groups (p < 0.05) than in the controls. Longitudinally also, hippocampal atrophy rates were significant (p < 0.05) when compared with the controls. No longitudinal cortical thinning was observed in A-T+ MCI group. Discussion: A-T+ MCI participants showed similar baseline cortical thickness patterns with aging and longitudinal hippocampal atrophy rates as participants with A+T+ MCI, but did not show longitudinal cortical atrophy signature.