# Tumor Growth, Proliferation and Diffusion in Osteosarcoma

## TL;DR

This paper uses mathematical models to study how osteosarcoma tumors grow, spread, and proliferate in different cell lines.

## Contribution

The study applies three mathematical models to classify osteosarcoma cell lines based on growth, proliferation, and diffusion rates.

## Key findings

- Tumor growth in immunosuppressed mice follows a sublinear pattern without blow-up.
- The logistic model accurately approximates cell proliferation rates in vitro.
- A linear reaction-diffusion model describes cell line diffusion behavior.

## Abstract

Osteosarcoma is the most common primary bone cancer. According to medical and biological studies, it has a high genetic complexity, thus, to differentiate the mechanisms of appearance and evolution of this disease is a difficult task. In this paper, we use three simplest and well known mathematical models to describe the behavior of several cell lines of osteosarcoma. First, we use a potential law to describe the tumor growth in immunosuppressed mice; with it we show that the variation of tumor growth has a sublinear behavior without the blow-up phenomenon. Second, the logistic model is used to obtain a good aproximation to the rates of proliferation in cell confluency in in vitro experiments. Third, we use a linear reaction-diffusion model; with it, we describe the diffusion behavior for some cell lines. These three models allow us to give a classification of cell lines according to the rates of tumor growth and proliferation and to the diffusion coefficient. A relationship is found between the rates of the tumor growth, the diffusion coefficient and tumorigenicity. Experimental data are extracted from Lauvrak et al. (British Journal of Cancer 109(8):2228–2236, 2013).