Uzair Hussain

In this article we use the Natural Scenes Dataset (NSD) to train a family of feature-weighted receptive field neural encoding models. These models use a pre-trained vision or text backbone and map extracted features to the voxel space via receptive field readouts. We comprehensively assess such models, quantifying performance changes based on using different modalities like text or images, toggling finetuning, using different pre-trained backbones, and changing the width of the readout. We also dissect each model using explainable AI (XAI) techniques, such as feature visualization via input optimization, also referred to as ``dreaming'' in the AI literature, and the integrated gradients approach to calculate implicit attention maps to illustrate which features drive the predicted signal in different brain areas. These XAI tools illustrate biologically plausible features that drive the predicted signal. Traversing the model hyperparameter space reveals the existence of a maximally minimal model, balancing simplicity while maintaining performance.

The hippocampus is classically divided into mesoscopic subfields which contain varying microstructure that contribute to their unique functional roles. It has been challenging to characterize this microstructure with current magnetic resonance based neuroimaging techniques. In this work, we used diffusion magnetic resonance imaging (dMRI) and a novel surface‐based approach in the hippocampus which revealed distinct microstructural distributions of neurite density and dispersion, T1w/T2w ratio as a proxy for myelin content, fractional anisotropy, and mean diffusivity. We used the neurite orientation dispersion and density imaging (NODDI) model optimized for grey matter diffusivity to characterize neurite density and dispersion. We found that neurite dispersion was highest in the cornu ammonis (CA) 1 and subiculum subfields which likely captures the large heterogeneity of tangential and radial fibres, such as the Schaffer collaterals, perforant path, and pyramidal neurons. Neurite density and T1w/T2w were highest in the subiculum and CA3 and lowest in CA1, which may reflect known myeloarchitectonic differences between these subfields. Using a simple logistic regression model, we showed that neurite density, dispersion, and T1w/T2w measures were separable across the subfields, suggesting that they may be sensitive to the known variability in subfield cyto‐ and myeloarchitecture. We report macrostructural measures of gyrification, thickness, and curvature that were in line with ex vivo descriptions of hippocampal anatomy. We employed a multivariate orthogonal projective non‐negative matrix factorization (OPNNMF) approach to capture co‐varying regions of macro‐ and microstructure across the hippocampus. The clusters were highly variable along the medial–lateral (proximal–distal) direction, likely reflecting known differences in morphology, cytoarchitectonic profiles, and connectivity. Finally, we show that by examining the main direction of diffusion relative to canonical hippocampal axes, we could identify regions with stereotyped microstructural orientations that may map onto specific fibre pathways, such as the Schaffer collaterals, perforant path, fimbria, and alveus. These results highlight the value of combining in vivo dMRI with computational approaches for capturing hippocampal microstructure, which may provide useful features for understanding cognition and for diagnosis of disease states.

Diffusion MRI (dMRI) is an imaging technique widely used in neuroimaging research, where the signal carries directional information of underlying neuronal fibres based on the diffusivity of water molecules. One of the shortcomings of dMRI is that numerous images, sampled at gradient directions on a sphere, must be acquired to achieve a reliable angular resolution for model-fitting, which translates to longer scan times, higher costs, and barriers to clinical adoption. In this work we introduce gauge equivariant convolutional neural network (gCNN) layers for dMRI that overcome the challenges associated with the signal being acquired on a sphere with antipodal points identified. This is done by noting that the domain is equivalent to the real projective plane, ℝ P ² , which is a non-euclidean and a non-orientable manifold. This is in stark contrast to a rectangular grid which typical convolutional neural networks (CNNs) are designed for. We apply our method to upsample angular resolution for predicting diffusion tensor imaging (DTI) parameters from just six diffusion gradient directions. The symmetries introduced allow gCNNs the ability to train with fewer subjects as compared to a baseline model that involves only 3D convolutions.

The hippocampus is classically divided into mesoscopic subfields which contain varying microstructure that contribute to their unique functional roles. It has been challenging to characterize this microstructure with current MR based neuroimaging techniques. In this work, we used a novel surface-based approach in the hippocampus to show distinct microstructural distributions of myelin, neurite density and dispersion, fractional anisotropy, and mean diffusivity using diffusion MRI. To get at this issue we used the Neurite Orientation Dispersion and Density Imaging (NODDI) model optimized for gray matter diffusivity and diffusion tensor imaging (DTI). We found that neurite dispersion was highest in the Cornu Ammonis (CA) 1 and subiculum subfields which likely captures the large heterogeneity of tangential and radial fibers, such as the Schaffer collaterals, perforant path, and pyramidal neurites. Neurite density and myelin content were highest in the subiculum and lowest in CA1, which may reflect known myeloarchitecture differences between these subfields. We show macrostructural measures of gyrification, thickness, and curvature which were in line with ex vivo descriptions of hippocampal anatomy. We employed a multivariate orthogonal projective non-negative matrix factorization (OPNNMF) approach to capture co-varying regions of macro- and microstructure across the hippocampus. The clusters were highly variable along the medial-lateral (proximal-distal) direction, which is expected as there are known differences in morphology, cytoarchitectonic profiles, and connectivity. Long-axis (anterior-posterior) differences can also be seen in the OPNNMF components, where the body of the hippocampus has more parcellations than the head and tail. Finally, we show that by examining the main direction of diffusion relative to canonical hippocampal axes, we could identify microstructure that may map onto specific tangential fiber pathways, such as the Schaffer collaterals and perforant path. These results highlight the value of combining in vivo diffusion MRI with computational approaches for capturing hippocampal microstructure, which may provide useful features for understanding cognition and for diagnosis of disease states.

The hippocampus is implicated in numerous neurological disorders and the ability to detect subtle or focal hippocampal abnormalities earlier in disease progression could significantly improve the treatment of patients. Ex vivo studies with ultra-high field have revealed that diffusion MRI (dMRI) can reveal microstructural variations within the hippocampal subfields and lamina, and may also be sensitive to intra-hippocampal pathways. However, translation to lower resolution in vivo dMRI studies of the hippocampus is challenging due to its complicated geometry. One novel way to overcome some of these obstacles is by transforming the usual Cartesian coordinates in an MRI image to coordinates that are crafted to curve themselves according to the complicated geometry of the hippocampus. This procedure allows us to virtually unfold the hippocampus into a thin sheet. In this work, we introduce an algorithm to map diffusion MRI data to this sheet, allowing us to overcome the difficulties associated with the hippocampus’ complicated geometry. We demonstrate how our method can be readily integrated into existing implementations of traditional tractography methods and how it leads to enhancements in the resulting tracts. Further, our results on high quality in vivo dMRI acquisitions show that unfolding the hippocampus leads to a more anatomically plausible modelling of the connectivity of the hippocampus as probed by probabilistic tractography, revealing key elements of the polysynaptic pathway and anterior-posterior connectivity gradients.

We model an extreme mass ratio merger as a point particle radially plunging into a large Schwarzschild black hole. We assume that the mass of the point particle, μ , is much smaller than the black hole mass M . Under this assumption we can employ the Zerilli formalism modified to include a source term which arises from the energy-momentum tensor of the small object. We solve the Zerilli equation by numerically evolving initial data. Then, we ray trace the null geodesics of the event horizon from after the merger backward in time to extract the geometry of the perturbed event horizon. Further, we take advantage of the axisymmetry of the setup to locate the apparent horizon and study its geometry.

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess nontrivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have nonzero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This “first law of black hole and soliton mechanics” contains new intensive and extensive quantities associated with each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulas relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.