Abstract
A simple and fast computational model to describe the dynamics of tumour growth and metastasis formation is presented. The model is based on the calculation of successive generations of tumour cells and enables one to describe biologically important entities like tumour volume, time point of 1st metastatic growth or number of metastatic colonies at a given time. The model entirely relies on the chronology of these successive events of the metastatic cascade. The simulation calculations were performed for two embedded growth models to describe the Gompertzian like growth behaviour of tumours. The initial training of the models was carried out using an analytical solution for the size distribution of metastases of a hepatocellular carcinoma. We then show the applicability of our models to clinical data from the Munich Cancer Registry. Growth and dissemination characteristics of metastatic cells originating from cells in the primary breast cancer can be modelled thus showing its ability to perform systematic analyses relevant for clinical breast cancer research and treatment. In particular, our calculations show that generally metastases formation has already been initiated before the primary can be detected clinically.
Highlights
In the mathematically oriented medical literature different models are applied to describe the process of tumour growth and metastasis formation
The computational model Metastasis formation is a complex process often referred to as a cascade as each step has to be performed in a certain order
We proposed a simple model of metastasis formation based on successive series of generations of tumour cells
Summary
In the mathematically oriented medical literature different models are applied to describe the process of tumour growth and metastasis formation Most of these models fall in one of the three following categories: The first ones are discrete models on the basis of single cell interactions which are described by the aid of Mte Carlo simulations. A third interesting alternate ansatz was developed by Iwata, Kawasaki and Shigesada [4,5] which is in the following referred to as the IKS-model. They model metastasis formation from the primary tumour and from metastases from metastases and give complex analytical solutions for the density respective the abundance of metastatic colonies depending on different growth functions of the primary tumour
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