4.4 Article

Optimal control for a bone metastasis with radiotherapy model using a linear objective functional

Journal

Publisher

EDP SCIENCES S A
DOI: 10.1051/mmnp/2022038

Keywords

Bone metastasis; radiotherapy; optimal control; bang-bang solutions; singular solutions

Funding

  1. Mexico CONACyT Project [CB2016-286437]

Ask authors/readers for more resources

This article presents a mathematical modeling framework to study the effects of radiation therapy on bone metastasis. By proposing an optimal control problem to describe the interactions between cancer cells and bone cells, and analyzing the different possible radiation effects on the bone and cancer cells through numerical simulations.
Radiation is known to cause genetic damage to highly proliferative cells such as cancer cells. However, the radiotherapy effects to bone cells is not completely known. In this work we present a mathematical modeling framework to test hypotheses related to the radiation-induced effects on bone metastasis. Thus, we pose an optimal control problem based on a Komarova model describing the interactions between cancer cells and bone cells at a single site of bone remodeling. The radiotherapy treatment is included in the form of a functional which minimizes the use of radiation using a penalty function. Moreover, we are interested to model the 'on' and the 'off' time states of the radiation schedules; so we propose an optimal control problem with a L (1)-type objective functional. Bang-bang or singular arc solutions are the obtained optimal control solutions. We characterize both solutions types and explicitly give necessary optimality conditions for them. We present numerical simulations to analyze the different possible radiation effects on the bone and cancer cells. We also evaluate the more significant parameters to shift from a bang-bang solution to a singular arc solution and vice versa. Additionally, we study a fractionated radiotherapy model that yields an output solution that resembles intermittent radiotherapy scheduling.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.4
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available