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Understanding the dynamical behavior of complex systems from their underlying network architectures is a long-standing question in complexity theory. Therefore, many metrics have been devised to extract network features like motifs, centrality, and modularity measures. It has previously been proposed that network symmetries are of particular importance since they are expected to underly the synchronization of a system's units, which is ubiquitously observed in nervous system activity patterns. However, perfectly symmetrical structures are difficult to assess in noisy measurements of biological systems, like neuronal connectomes. Here, we devise a principled method to infer network symmetries from combined connectome and neuronal activity data. Using nervous system-wide population activity recordings of the C.elegans backward locomotor system, we infer structures in the connectome called fibration symmetries, which can explain which group of neurons synchronize their activity. Our analysis suggests functional building blocks in the animal's motor periphery, providing new testable hypotheses on how descending interneuron circuits communicate with the motor periphery to control behavior. Our approach opens a new door to exploring the structure-function relations in other complex systems, like the nervous systems of larger animals.

Alzheimer's disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and amyloid-$beta$. Mathematical models and numerical simulations can predict the spreading patterns of misfolded proteins in this context. However, the calibration of the model parameters plays a crucial role in the final solution. In this work, we perform a sensitivity analysis of heterodimer and Fisher-Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns. We adopt advanced numerical methods such as the IMEX-DG method to accurately describe the propagating fronts in the propagation phenomena in a polygonal mesh of sagittal patient-specific brain geometry derived from magnetic resonance images. We calibrate the model parameters using biological measurements in the brain cortex for the tau protein and the amyloid-$beta$ in Alzheimer's patients and controls. Finally, using the sensitivity analysis results, we discuss the applicability of both models in the correct simulation of the spreading of the two proteins.

Water diffusion gives rise to micrometer-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. The advent of precision medicine and quantitative imaging hinges on revealing the information content of dMRI, and providing its parsimonious basis- and hardware-independent "fingerprint". Here we reveal the geometry of a multi-dimensional dMRI signal, classify all 21 invariants of diffusion and covariance tensors in terms of irreducible representations of the group of rotations, and relate them to tissue properties. Previously studied dMRI contrasts are expressed via 7 invariants, while the remaining 14 provide novel complementary information. We design acquisitions based on icosahedral vertices guaranteeing minimal number of measurements to determine 3-4 most used invariants in only 1-2 minutes for the whole brain. Representing dMRI signals via scalar invariant maps with definite symmetries will underpin machine learning classifiers of brain pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinical practice.

The surface morphology of the developing mammalian brain is crucial for understanding brain function and dysfunction. Computational modeling offers valuable insights into the underlying mechanisms for early brain folding. Recent findings indicate significant regional variations in brain tissue growth, while the role of these variations in cortical development remains unclear. In this study, we unprecedently explored how regional cortical growth affects brain folding patterns using computational simulation. We first developed growth models for typical cortical regions using machine learning (ML)-assisted symbolic regression, based on longitudinal real surface expansion and cortical thickness data from prenatal and infant brains derived from over 1,000 MRI scans of 735 pediatric subjects with ages ranging from 29 post-menstrual weeks to 24 months. These models were subsequently integrated into computational software to simulate cortical development with anatomically realistic geometric models. We comprehensively quantified the resulting folding patterns using multiple metrics such as mean curvature, sulcal depth, and gyrification index. Our results demonstrate that regional growth models generate complex brain folding patterns that more closely match actual brains structures, both quantitatively and qualitatively, compared to conventional uniform growth models. Growth magnitude plays a dominant role in shaping folding patterns, while growth trajectory has a minor influence. Moreover, multi-region models better capture the intricacies of brain folding than single-region models. Our results underscore the necessity and importance of incorporating regional growth heterogeneity into brain folding simulations, which could enhance early diagnosis and treatment of cortical malformations and neurodevelopmental disorders such as cerebral palsy and autism.

In his book 'A Beautiful Question', physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

Data sets with imbalanced class sizes, where one class size is much smaller than that of others, occur exceedingly often in many applications, including those with biological foundations, such as disease diagnosis and drug discovery. Therefore, it is extremely important to be able to identify data elements of classes of various sizes, as a failure to do so can result in heavy costs. Nonetheless, many data classification procedures do not perform well on imbalanced data sets as they often fail to detect elements belonging to underrepresented classes. In this work, we propose the BTDT-MBO algorithm, incorporating Merriman-Bence-Osher (MBO) approaches and a bidirectional transformer, as well as distance correlation and decision threshold adjustments, for data classification tasks on highly imbalanced molecular data sets, where the sizes of the classes vary greatly. The proposed technique not only integrates adjustments in the classification threshold for the MBO algorithm in order to help deal with the class imbalance, but also uses a bidirectional transformer procedure based on an attention mechanism for self-supervised learning. In addition, the model implements distance correlation as a weight function for the similarity graph-based framework on which the adjusted MBO algorithm operates. The proposed method is validated using six molecular data sets and compared to other related techniques. The computational experiments show that the proposed technique is superior to competing approaches even in the case of a high class imbalance ratio.

We propose a lesion-aware graph neural network (LEGNet) to predict language ability from resting-state fMRI (rs-fMRI) connectivity in patients with post-stroke aphasia. Our model integrates three components: an edge-based learning module that encodes functional connectivity between brain regions, a lesion encoding module, and a subgraph learning module that leverages functional similarities for prediction. We use synthetic data derived from the Human Connectome Project (HCP) for hyperparameter tuning and model pretraining. We then evaluate the performance using repeated 10-fold cross-validation on an in-house neuroimaging dataset of post-stroke aphasia. Our results demonstrate that LEGNet outperforms baseline deep learning methods in predicting language ability. LEGNet also exhibits superior generalization ability when tested on a second in-house dataset that was acquired under a slightly different neuroimaging protocol. Taken together, the results of this study highlight the potential of LEGNet in effectively learning the relationships between rs-fMRI connectivity and language ability in a patient cohort with brain lesions for improved post-stroke aphasia evaluation.

Non-sensory thalamic nuclei interact with the cortex through thalamocortical and cortico-basal ganglia-thalamocortical loops. Reciprocal connections between the mediodorsal thalamus (MD) and the prefrontal cortex are particularly important in cognition, while the reciprocal connections of the ventromedial (VM), ventral anterior (VA), and ventrolateral (VL) thalamus with the prefrontal and motor cortex are necessary for sensorimotor information processing. However, limited and often oversimplified understanding of the connectivity of the MD, VA, and VL nuclei in primates have hampered development of accurate models that explain their contribution to cognitive and sensorimotor functions. The current prevalent view suggests that the MD connects with the prefrontal cortex, while the VA and VL primarily connect with the premotor and motor cortices. However, past studies have also reported diverse connections that enable these nuclei to integrate information across a multitude of brain systems. In this review, we provide a comprehensive overview of the anatomical connectivity of the primate MD, VA, and VL with the cortex. By synthesizing recent findings, we aim to offer a valuable resource for students, newcomers to the field, and experts developing new theories or models of thalamic function. Our review highlights the complexity of these connections and underscores the need for further research to fully understand the diverse roles of these thalamic nuclei in primates.

Background: Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline.

Objective: We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data.

Methods: We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs.

Results: Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model predictions. In addition, the proposed multi-fidelity Monte Carlo estimators are significantly cheaper to compute than traditional estimators, under a specified confidence level or variance.

Conclusions: The proposed pipeline for personalized and uncertainty-aware predictions of coronary hemodynamics is based on routine clinical measurements and recently developed techniques for CT myocardial perfusion imaging. The proposed pipeline offers significant improvements in precision and reduction in computational cost.

The formation, dissolution, and dynamics of multi-particle complexes is of fundamental interest in the study of stochastic chemical systems. In 1976, Masao Doi introduced a Fock space formalism for modeling classical particles. Doi's formalism, however, does not support the assembly of multiple particles into complexes. Starting in the 2000's, multiple groups developed rule-based methods for computationally simulating biochemical systems involving large macromolecular complexes. However, these methods are based on graph-rewriting rules and/or process algebras that are mathematically disconnected from the statistical physics methods generally used to analyze equilibrium and nonequilibrium systems. Here we bridge these two approaches by introducing an operator algebra for the rule-based modeling of multi-particle complexes. Our formalism is based on a Fock space that supports not only the creation and annihilation of classical particles, but also the assembly of multiple particles into complexes, as well as the disassembly of complexes into their components. Rules are specified by algebraic operators that act on particles through a manifestation of Wick's theorem. We further describe diagrammatic methods that facilitate rule specification and analytic calculations. We demonstrate our formalism on systems in and out of thermal equilibrium, and for nonequilibrium systems we present a stochastic simulation algorithm based on our formalism. The results provide a unified approach to the mathematical and computational study of stochastic chemical systems in which multi-particle complexes play an important role.