On a data-driven mathematical model for prostate cancer bone metastasis

Zholaman Bektemessov; Laurence Cherfils; Cyrille Allery; Julien Berger; Elisa Serafini; Eleonora Dondossola; Stefano Casarin; Zholaman Bektemessov; Laurence Cherfils; Cyrille Allery; Julien Berger; Elisa Serafini; Eleonora Dondossola; Stefano Casarin

doi:10.3934/math.20241656

AIMS Mathematics

2024, Volume 9, Issue 12: 34785-34805. doi: 10.3934/math.20241656

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Research article

On a data-driven mathematical model for prostate cancer bone metastasis

1.
Department of Mathematical and Computer Modeling, Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Almaty, 050060, Kazakhstan
2.
Laboratoire des Sciences de l'Ingénieur pour l'Environnement, UMR CNRS 7356, La Rochelle Université, La Rochelle Cedex 1, F-17042, France
3.
Center for Precision Surgery, Houston Methodist Research Institute, Houston, TX, United States
4.
David H. Koch Center for Applied Research of Genitourinary Cancers, University of Texas MD Anderson Cancer Center, Houston, TX, United States
5.
Department of Surgery, Houston Methodist Hospital, Houston, TX, United States

Received: 11 October 2024 Revised: 13 November 2024 Accepted: 18 November 2024 Published: 13 December 2024
MSC : 35Q92, 65L09, 65M60, 92C50

Prostate cancer bone metastasis poses significant health challenges, affecting countless individuals. While treatment with the radioactive isotope radium-223 ($ ^{223} $Ra) has shown promising results, there remains room for therapy optimization. In vivo studies are crucial for optimizing radium therapy; however, they face several roadblocks that limit their effectiveness. By integrating in vivo studies with in silico models, these obstacles can be potentially overcome. Existing computational models of tumor response to $ ^{223} $Ra are often computationally intensive. Accordingly, we here present a versatile and computationally efficient alternative solution. We developed a PDE mathematical model to simulate the effects of $ ^{223} $Ra on prostate cancer bone metastasis, analyzing mitosis and apoptosis rates based on experimental data from both control and treated groups. To build a robust and validated model, our research explored three therapeutic scenarios: no treatment, constant $ ^{223} $Ra exposure, and decay-accounting therapy, with tumor growth simulations for each case. Our findings align well with experimental evidence, demonstrating that our model effectively captures the therapeutic potential of $ ^{223} $Ra, yielding promising results that support our model as a powerful infrastructure to optimize bone metastasis treatment.
- prostate cancer,
- bone metastasis,
- tumor growth,
- PDE model,
- simulation,
- in vivo-in silico modeling,
- parameter estimation,
- inverse problems
Citation: Zholaman Bektemessov, Laurence Cherfils, Cyrille Allery, Julien Berger, Elisa Serafini, Eleonora Dondossola, Stefano Casarin. On a data-driven mathematical model for prostate cancer bone metastasis[J]. AIMS Mathematics, 2024, 9(12): 34785-34805. doi: 10.3934/math.20241656

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Abstract

Prostate cancer bone metastasis poses significant health challenges, affecting countless individuals. While treatment with the radioactive isotope radium-223 ($ ^{223} $Ra) has shown promising results, there remains room for therapy optimization. In vivo studies are crucial for optimizing radium therapy; however, they face several roadblocks that limit their effectiveness. By integrating in vivo studies with in silico models, these obstacles can be potentially overcome. Existing computational models of tumor response to $ ^{223} $Ra are often computationally intensive. Accordingly, we here present a versatile and computationally efficient alternative solution. We developed a PDE mathematical model to simulate the effects of $ ^{223} $Ra on prostate cancer bone metastasis, analyzing mitosis and apoptosis rates based on experimental data from both control and treated groups. To build a robust and validated model, our research explored three therapeutic scenarios: no treatment, constant $ ^{223} $Ra exposure, and decay-accounting therapy, with tumor growth simulations for each case. Our findings align well with experimental evidence, demonstrating that our model effectively captures the therapeutic potential of $ ^{223} $Ra, yielding promising results that support our model as a powerful infrastructure to optimize bone metastasis treatment.

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