Optimal chemotherapy schedules from tumor entropy

Abstract

We propose a model for the dynamics of an heterogeneous tumor, which consists of sensitive and resistant cells. The model is analyzed and validated using a cellular automaton whose local rules are classic and widely accepted in Biology. We then extend the model to a tumor under therapy. We consider Shannon's entropy for the tumor and analyze the problem of minimizing this entropy. From this minimization problem, we find viable therapies that maintain at low level the entropy of the tumor. These therapies could provide a valuable tool for designing protocols for disease control, maintaining a very low growth level, while the tumor remains composed mainly of sensitive cells.

A generalized q growth model based on nonadditive entropy

“…The application of the concept of entropy in mathematical modeling has recently had a significant impact in different scenarios such as solid state physics [1], optics [2], medicine [3] and many other fields [4,5,6,7,8,9]. Recently, mathematical modeling and computational simulations have been the most effective and useful tools that help universal global efforts to understand coronavirus disease (COVID-19).…”

“…The use of nonextensive statistics for modeling cancer laws and treatment purposes was reported [20,21]. This approach has been applied for radiotherapy treatment schedules [22]. Continuous and discrete growth models based in q function formalism [23,24] have been proposed to understand the interaction and the evolution of complex systems [25], and the modeling problem of power exponent growth universality [26,27].…”