Related papers: Nonlinear cancer chemotherapy: modelling the Norto…
This paper primarily addresses a dataset relating to cellular, chemical and physical conditions of patients gathered at the time they are operated upon to remove colorectal tumours. This data provides a unique insight into the biochemical…
We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the…
In this paper we propose an ecological resilience point of view on cancer. This view is based on the analysis of a simple ODE model for the interactions between cancer and normal cells. The model presents two regimes for tumor growth. In…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
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…
In this work, we combine a new form of the cell survival fraction developed in [29] with the Gompertz cell growth model. The result is an equation that models the cell growth/death under a radiation dose and can be applied in a conventional…
We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic variable, representing their level of resistance to the…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…
With the advancement of treatment modalities in radiation therapy for cancer patients, outcomes have improved, but at the cost of increased treatment plan complexity and planning time. The accurate prediction of dose distributions would…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the…
Causal inference plays a fundamental role in various real-world applications. However, in the motivating non-small cell lung cancer (NSCLC) study, it is challenging to estimate the treatment effect of chemotherapy on circulating tumor DNA…
Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study the…
Despite all the advances achieved in the field of tumor-biology research, in most cases conventional therapies including chemotherapy are still the leading choices. The main disadvantage of these treatments, in addition to the low…
The evolutionary and ecological dynamics of tumors under immune responses and therapeutic interventions pose major challenges to long-term treatment success. Although treatment may initially achieve short-term disease control, resistant…
Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system,…
We develop and analyze a mathematical model of oncolytic virotherapy in the treatment of melanoma. We begin with a special, local case of the model, in which we consider the dynamics of the tumour cells in the presence of an oncolytic virus…
In this article, we focus on determining a minimum-cost treatment program aimed at maintaining the size of a cancerous tumor at a level that allows the patient to live comfortably. At each predetermined point in a treatment horizon, the…
In this paper, a methodology is proposed that enables to analyze the sensitivity of the outcome of a therapy to unavoidable high dispersion of the patient specific parameters on one hand and to the choice of the parameters that define the…