From Topological Analyses to Functional Modeling: The Case of Hippocampus

Hybrid-feature based spherical quasi-conformal registration for AD-induced hippocampal surface morphological changes

BACKGROUND AND OBJECTIVE

Establishing accurate one-to-one morphological correspondence between different hippocampal surfaces is a solid foundation for the analysis of AD-induced hippocampal morphological changes. However, owing to the large variations between hippocampal surfaces, exiting registration work either fails to obtain the accurate matching of local and overall morphological features or does not preserve the bijectivity during parametric mapping. For this reason, this study proposes a hybrid-feature based spherical quasi-conformal registration (HSQR) method that can effectively maintain the diffeomorphic property while meeting the hybrid-feature matching constraints in the spherical parameter domain.

METHODS

The HSQR algorithm is primarily achieved through hippocampal surface hybrid feature extraction and spherical quasi-conformal registration. First, hybrid features for a comprehensive morphological description of the hippocampal surface were established, which included essential anatomical features (landmarks) and mean curvature (intensity) features to ensure the accuracy of surface morphology alignment. Second, spherical parameterization was applied to genus-0 closed surfaces, such as the hippocampus, which maximized the preservation of the original local surface morphology through area-preserving properties. Third, a novel spherical quasi-conformal registration algorithm that can handle large deformations is established. It transforms a 3D spherical parameter domain into a 2D plane parameter domain using iterative local stereo projection to improve the efficiency of the registration algorithm. Subsequently, by controlling the Beltramin coefficient, the hybrid morphological features could be aligned while ensuring bijection before and after registration.

RESULTS

Using a cohort including 161 patients with amyloid-β (Aβ) positive Alzheimer disease (AD), 234 Aβ positive mild cognitive impairment (MCI) and 266 Aβ negative cognitively unimpaired (CU) individuals from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, we set up the experiment which indicated that the HSQR-based whole bilateral hippocampal atrophy features demonstrated the stronger statistical power for group morphological differences of CU vs. MCI with q-value: 0.0453 for left hippocampus and 0.0401 for right hippocampus and group morphological differences of AD vs. MCI with q-value: 0.0282 for left hippocampus and 0.0421 for right hippocampus.

CONCLUSIONS

Our registration algorithm may provide a solid foundation for the accurate quantification of hippocampal surface morphological changes for the differential diagnosis and tracking of AD.

Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0

There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.

Grid Cell Percolation

Grid cells play a principal role in enabling cognitive representations of ambient environments. The key property of these cells-the regular arrangement of their firing fields-is commonly viewed as a means for establishing spatial scales or encoding specific locations. However, using grid cells' spiking outputs for deducing geometric orderliness proves to be a strenuous task due to fairly irregular activation patterns triggered by the animal's sporadic visits to the grid fields. This article addresses statistical mechanisms enabling emergent regularity of grid cell firing activity from the perspective of percolation theory. Using percolation phenomena for modeling the effect of the rat's moves through the lattices of firing fields sheds new light on the mechanisms of spatial information processing, spatial learning, path integration, and establishing spatial metrics. It is also shown that physiological parameters required for spiking percolation match the experimental range, including the characteristic 2/3 ratio between the grid fields' size and the grid spacing, pointing at a biological viability of the approach.

Spatial representability of neuronal activity

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.