Around a mathematical model of the concomitant tumor resistance phenomenon

The phenomenon of concomitant resistance, discovered since 1906, traduces the inhibitory effect from a first tumor on the growth of a distant tumor. The importance of the investigation on the concomitant resistance was found following the removal of the primary tumor which could lead to dramatic clinical consequences due to the suppression of this inhibition : the post-surgery metastatic acceleration. We report here on a study of a mathematical model representing the concomitant resistance between two tumors in the same organism. First, the study involves a statistical analysis of the tumor growth in 10 mice with a population approach:the non-linear mixed effect model which is the most common tool to describe the global behavior of all individuals. The goal was to compare different softwares which implement the method, where the function NLME on R has the fastest execution time.Second, the study allows the validation of the concomitant resistance mathematical model on independent data thanks to the obtaining of a highest goodness-of-fit and a good prediction. This study not only informs on the validity of the model but also provides a non-monotony of the metastatic acceleration depending on the volume of the tumor at the day of excision