Related papers: Mathematical modeling of Buruli ulcer spread
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…
Diffusion models are a special type of generative model, capable of synthesising new data from a learnt distribution. We introduce DISPR, a diffusion-based model for solving the inverse problem of three-dimensional (3D) cell shape…
We consider a porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion.…
We consider the classical problem of droplet impact and droplet spread on a smooth surface in the case of an ideal inviscid fluid. We revisit the rim-lamella model of Roisman et al. [\textit{Proceedings of the Royal Society of London.…
Accurately modeling the spatiotemporal evolution of tumor morphology from baseline imaging is a pre-requisite for developing digital twin frameworks that can simulate disease progression and treatment response. Most existing approaches…
We consider the problem of droplet impact and droplet spreading on a smooth surface in the case of a viscous Newtonian fluid. We revisit the concept of the rim-lamella model, in which the droplet spreading is described by a system of…
Currently, free flaps and pedicled flaps are assessed for reperfusion in post-operative care using colour, capillary refill, temperature, texture and Doppler signal (if available). While these techniques are effective, they are prone to…
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and…
While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic…
We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
Increasing numbers of patients with disabilities or elderly people with mobility issues often suffer from a pressure ulcer. The affected areas need regular checks, but they have a difficulty in accessing a hospital. Some remote diagnosis…
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…
State-of-the-art models for aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method to numerically solve particle growth kinetics. In this method, particles that are smaller than the critical size are…
Out-of-distribution (OOD) detection is essential to improve the reliability of machine learning models by detecting samples that do not belong to the training distribution. Detecting OOD samples effectively in certain tasks can pose a…
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a pressure gradient generated by the death and birth of cells,…
Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of…