相关论文: Adjoint method for a tumor invasion PDE-constraine…

We present a multi-species partial differential equation (PDE) model for tumor growth and a an algorithm for calibrating the model from magnetic resonance imaging (MRI) scans. The model is designed for glioblastoma (GBM) brain tumors. The…

This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in…

In this paper, we study the global dynamics of a general reaction-diffusion model based on acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. A key feature of this model is the density-limited tumor…

The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…

This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

Early assessment of tumor therapeutic response is an important topic in precision medicine to optimize personalized treatment regimens and reduce unnecessary toxicity, cost, and delay. Although diffusion MRI (dMRI) has shown potential to…

The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…

The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…

This review provides open-access computational tools that support a range of mathematical approaches to analyse three related scalar reaction-diffusion models used to study biological invasion. Starting with the classic Fisher-Kolmogorov…

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

The prediction of absorption, distribution, metabolism, excretion, and toxicity (ADMET) of small molecules from their molecular structure is a central problem in medicinal chemistry with great practical importance in drug discovery.…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

We consider the inverse problem of parameter estimation in a diffuse interface model for tumour growth. The model consists of a fourth-order Cahn-Hilliard system and contains three phenomenological parameters: the tumour proliferation rate,…

We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…

The tumor microenvironment (TME) significantly impacts cancer prognosis due to its immune composition. While therapies for altering the immune composition, including immunotherapies, have shown exciting results for treating hematological…

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

Cancer research has shifted from a purely gene-centric view to a more holistic understanding that recognizes the critical role of the tumour microenvironment, where mechanics and metabolism are key drivers of disease progression. However,…