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Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of…
Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…
Background: Radiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation. Methods: In this paper, we propose a…
Deep learning has quickly become the weapon of choice for brain lesion segmentation. However, few existing algorithms pre-configure any biological context of their chosen segmentation tissues, and instead rely on the neural network's…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…
In this study, a morphological differentiation-based method has been introduced which employs temperature distribution on the tissue surface to detect brain tumor's malignancy. According to the common tumor CT scans, two different scenarios…
We consider Bayesian inference for stochastic differential equation mixed effects models (SDEMEMs) exemplifying tumor response to treatment and regrowth in mice. We produce an extensive study on how a SDEMEM can be fitted using both exact…
In this survey article, a variety of systems modeling tumor growth are discussed. In accordance with the hallmarks of cancer, the described models incorporate the primary characteristics of cancer evolution. Specifically, we focus on…
Malignant gliomas (MGs), particularly glioblastoma, are among the most aggressive brain tumors, with limited treatment options and a poor prognosis. Maximal safe resection and the so-called Stupp protocol are the standard first-line…
Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagu\'e…
Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection-diffusion-reaction…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
Detection of brain tumor using a segmentation based approach is critical in cases, where survival of a subject depends on an accurate and timely clinical diagnosis. Gliomas are the most commonly found tumors having irregular shape and…
Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity…
We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a…
We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation…
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models.…