Related papers: Modeling Three-dimensional Invasive Solid Tumor Gr…
We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the…
Tumor growth is constrained by spatial, mechanical, and metabolic factors whose alignment progressively breaks down across cellular, mesoscopic, and tissue scales as tumors expand. We hypothesize that this misalignment drives tumors toward…
Cancer evolves continuously over time through a complex interplay of genetic, epigenetic, microenvironmental, and phenotypic changes. This dynamic behavior drives uncontrolled cell growth, metastasis, immune evasion, and therapy resistance,…
Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to…
In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which…
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor…
Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on…
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and…
While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe…
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…
Multidrug resistance consists of a series of genetic and epigenetic alternations that involve multifactorial and complex processes, which are a challenge to successful cancer treatments. Accompanied by advances in biotechnology and…
The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we…
Cell competition is recognized to be instrumental to the dynamics and structure of the tumor-host interface in invasive cancers. In mild competition scenarios, the healthy tissue and cancer cells can coexist. When the competition is…
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…
Heterogeneity is a hallmark of all cancers. Tumor heterogeneity is found at different levels -- interpatient, intrapatient, and intratumor heterogeneity. All of them pose challenges for clinical treatments. The latter two scenarios can also…