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Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Functional ultrasound (fUS) indirectly measures brain activity by recording changes in cerebral blood volume and flow in response to neural activation. Conventional approaches model such functional neuroimaging data as the convolution…
This study uses a one dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the…
Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the multiscale nature of the retinal vasculature and its…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…
We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is…
Blood exhibits a heterogeneous nature of hematocrit, velocity, and effective viscosity in microcapillaries. Microvascular bifurcations have a significant influence on the distribution of the blood cells and blood flow behavior. This paper…
The bidomain system of degenerate reaction-diffusion equations is a well-established spatial model of electrical activity in cardiac tissue, with "reaction" linked to the cellular action potential and "diffusion" representing current flow…
The relationship between blood flow and neuronal activity is widely recognized, with blood flow frequently serving as a surrogate for neuronal activity in fMRI studies. At the microscopic level, neuronal activity has been shown to influence…
Flow matching has recently emerged as a principled framework for learning continuous-time transport maps, enabling efficient ODE-based sampling without relying on stochastic diffusion processes. While generative modeling has shown promise…
Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced…
In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control)…
Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient-specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems, but need…
Computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations.…
Background and Objective: Hemodynamic analysis of blood flow through arteries and veins is critical for diagnosing cardiovascular diseases, such as aneurysms and stenoses, and for investigating cardiovascular parameters, such as turbulence…
We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a one-dimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics.…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…
Serotonin (5-hydroxytryptamine) is a major neurotransmitter whose release from densely distributed serotonergic varicosities shapes plasticity and network integration throughout the brain, yet its extracellular dynamics remain poorly…