Related papers: Adjoint method for a tumour growth PDE-constrained…

In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, introduced in [G. Cavalleri, P. Colli, A. Miranville, E. Rocca,…

Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are…

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. In the…

This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…

We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulating this system presents a fundamental challenge: while the…

Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…

Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell-cell adhesion effects are…

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division…

A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper…

The main target of this paper is to present an efficient method to solve a nonlinear free boundary mathematical model of prostate tumor. This model consists of two parabolics, one elliptic and one ordinary differential equations that are…

In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…

We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing…

We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the…

We propose a strange-attractor model of tumor growth and metastasis. It is a 4-dimensional spatio-temporal cancer model with strong nonlinear couplings. Even the same type of tumor is different in every patient both in size and appearance,…

In this work, we investigate the population dynamics of tumor cells under therapeutic pressure. Although drug treatment initially induces a reduction in tumor burden, treatment failure frequently occurs over time due to the emergence of…

We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…

We investigate the long-time dynamics and optimal control problem of a diffuse interface model that describes the growth of a tumor in presence of a nutrient and surrounded by host tissues. The state system consists of a Cahn-Hilliard type…

The intratumor heterogeneity has been recognized to characterize cancer cells impairing the efficacy of cancer treatments. We here propose an extension of constraint-based modeling approach in order to simulate metabolism of cell…