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We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor…
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 investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony and we derive a new asymptotic model for tumor growth. We…
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation…
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…
Gliomas are the most common malignant brain tumourswith intrinsic heterogeneity. Accurate segmentation of gliomas and theirsub-regions on multi-parametric magnetic resonance images (mpMRI)is of great clinical importance, which defines…
Immunotherapy plays a major role in tumour treatment, in comparison with other methods of dealing with cancer. The Kirschner-Panetta (KP) model of cancer immunotherapy describes the interaction between tumour cells, effector cells and…
A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid…
In this work we investigate a mathematical model describing tumour growth under a treatment by chemotherapy that incorporates time-delay related to the conversion from resting to hunting cells. We study the model using values for the…
Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies.…
We developed a mathematical model to simulate the growth of tumor volume and its response to a single fraction of high dose irradiation. We made several key assumptions of the model. Tumor volume is composed of proliferating (or dividing)…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL…
Neuroblastoma is a paediatric extracranial solid cancer that arises from the developing sympathetic nervous system and is characterised by an abnormal distribution of cell types in tumours compared to healthy infant tissues. In this paper,…
We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…
We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…
Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue.…