Related papers: A Coupled Diffusion Approximation for Spatiotempor…
Advection-diffusion equations describe a large family of natural transport processes, e.g., fluid flow, heat transfer, and wind transport. They are also used for optical flow and perfusion imaging computations. We develop a machine learning…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from first principles, we rigorously derive a system of partial…
We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional…
The reconstruction of physically valid transport fields from subject-specific imaging data is a fundamental challenge in image-based computational modeling due to measurement noise, modeling uncertainties and discretization errors. Without…
High-fidelity, high-resolution numerical simulations are crucial for studying complex multiscale phenomena in fluid dynamics, such as turbulent flows and ocean waves. However, direct numerical simulations with high-resolution solvers are…
Platelet adhesion and aggregation are essential for primary hemostasis, forming a clot that quickly stops initial bleeding. Despite this critical role, the dynamic interactions of platelet receptors with exposed collagen and von Willebrand…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
Blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites (vasculogenesis). A successful theoretical model of two dimensional experimental vasculogenesis has been recently proposed,…
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…
There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution…
Computational fluid dynamics (CFD) can be used for evaluation of hemodynamics. However, its routine use is limited by labor-intensive manual segmentation, CFD mesh creation, and time-consuming simulation. This study aims to train a deep…
An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation…
Spatiotemporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. In general, spatiotemporal forecasting problems involve complex interactions,…
Emerging connected-vehicle (CV) data shows great potential in urban traffic monitoring and forecasting. However, prior CV-based studies on arterial traffic measures prediction are limited to simulated high-penetration scenarios or small…
We present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a {linearly viscoelastic,…
We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls…
This study investigates the hemodynamic behavior of blood flow in the aortic arch across anemic, diabetic, and healthy conditions using computational fluid dynamics (CFD) simulations with a non-Newtonian Carreau viscosity model. Velocity…
We report the key findings from numerical solutions of a model of transport within an established perfusion bioreactor design. The model includes a complete formulation of transport with fully coupled convection-diffusion and scaffold cell…
In this paper, we have proposed STC-GEF, a novel Spatio-Temporal Cross-platform Graph Embedding Fusion approach for the urban traffic flow prediction. We have designed a spatial embedding module based on graph convolutional networks (GCN)…