Narrow Results

Mass balance equations typically adopted to describe tumor growth are to be closed by introducing a suitable velocity field. The first part of this paper is devoted to a critical review of some approaches devised to this aim in the relevant literature. In the second part we start from the observation that the phenomenological description of a tumor spheroid suggests to model it as a growing and deformable porous material. The concept of volume fraction and the essentials of the mechanics of multicomponent continua are then introduced and applied to the problem at hand. The system of equations regulating such a system is stated and its validity is then discussed at the light of numerical simulations.

In the following the reader will find a short description of some issues related to the modeling, analysis and simulation of large populations of living systems, a research field which is currently deserving a considerable interest, and that has been explored during the first 10 editions of the BIOMAT Summer School at Granada.

In this work, we did the construction of a fuzzy mathematical model wich it was developed to predict the pathological stage of prostate cancer.⁵ The intention is to help the specialists on the decision process about stage of the disease, to avoid surgery and intensive treatments unnecessary. The model consists on a system founded in fuzzy rules, that it combine the pre-surgical data (clinic state, PSA level and Gleason score) availing of a set of linguistic rules made with base on informations of the existents nomograms. Herewith we hoped to get the chance of the individual, with certain clinical features, be in each stage of the tumor extension: localized, advanced locally and metastatic. Simulations were made with patient's data of the Clinics Hospital/UNICAMP and the results were compared with Kattan's probabilities⁸ that are used on the medicals decisions. A software was developed from this model and is a graphic interface that makes interaction with the subroutines that make the calculations. Its source code was written in Java and software has been tested on Windows and Linux / GNU.

We present a mathematical model to investigate the role of the immune system in the Duchenne muscular dystrophy disease, based on the assumption that the immune system contributes to the tissue damage. Indeed, its interaction with the muscle tissue after an initial endogenous damage can be described as a predator-prey system showing typical oscillations. Moreover we investigate the dynamical properties of the system and we find that, for a biologically relevant parameters range, it shows two phase-transitions between qualitative different behaviors corresponding to complete recover or to a state where massive muscle regeneration and degeneration coexist.