The standard treatment of locally advanced rectal cancer is neoadjuvant chemoradiotherapy before surgery. For those patients experiencing a complete clinical response after the treatment, a watch-and-wait strategy with close monitoring may be practicable. In this respect, the identification of biomarkers of the response to therapy is extremely important. Many mathematical models have been developed or used to describe tumor growth, such as Gompertz's Law and the Logistic Law. Here we show that the parameters of those macroscopic growth laws, obtained by fitting the tumor evolution during and immediately after therapy, are a useful tool for evaluating the best time for surgery in this type of cancer. A limited number of experimental observations of the tumor volume regression, during and after the neoadjuvant doses, permits a reliable evaluation of a specific patient response (partial or complete recovery) for a later time, and one can evaluate a modification of the scheduled treatment, following a watch-and-wait approach or an early or late surgery. Neoadjuvant chemoradiotherapy effects can be quantitatively described by applying Gompertz's Law and the Logistic Law to estimate tumor growth by monitoring patients at regular intervals. We show a quantitative difference in macroscopic parameters between partial and complete response patients, reliable for estimating the treatment effects and best time for surgery.

Faculty of Mathematics and Physics Charles University 5 Holešovičkách 2 18000 Prague Czech Republic

Istituto Nazionale di Fisica Nucleare Sezione di Catania 95123 Catania Italy

Istituto Oncologico del Mediterraneo 95029 Viagrande Italy

REM 95029 Viagrande Italy

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Quantitative Method for Monitoring Tumor Evolution During and After Therapy