Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control

Abstract

Bone remodelling consists of cycles of bone resorption and formation executed mainly by osteoclasts and osteoblasts. Healthy bone remodelling is disrupted by diseases such as Multiple Myeloma and bone metastatic diseases. In this paper, a simple mathematical model with differential equations, which takes into account the evolution of osteoclasts, osteoblasts, bone mass and bone metastasis growth, is improved with a pharmacokinetic and pharmacodynamic (PK/PD) scheme of the drugs denosumab, bisphosphonates, proteasome inhibitors and paclitaxel. The major novelty is the inclusion of drug resistance phenomena, which resulted in two variations of the model, corresponding to different paradigms of the origin and development of the tumourous cell resistance condition. These models are then used as basis for an optimization of the drug dose applied, paving the way for personalized medicine. A Nonlinear Model Predictive Control scheme is used, which takes advantage of the convenient properties of a suggested adaptive and democratic variant of Particle Swarm Optimization. Drug prescriptions obtained in this way provide useful insights into dose administration strategies. They also show how results may change depending on which of the two very different paradigms of drug resistance is used to model the behaviour of the tumour.

A review of mathematical modeling of bone remodeling from a systems biology perspective

“…where γ and η are growth and decay parameters, Tdensity is a relationship between the current and maximum cancer cell population, and λ is an additional relationship term to capture the effects of other cancer interactions considered (Miranda et al, 2020;Zhang and Mager, 2019;Coelho et al, 2016;Buenzli et al, 2012b;Ayati et al, 2010). For example, in the Coelho et al (2016) model, λ corresponds to the concentration of osteoclasts.…”

A review of mathematical modeling of bone remodeling from a systems biology perspective

“…Temporal biochemical models are organized based on which of two prevailing mathematical formulations are used to describe bone cell population dynamics and their biochemical signaling dynamics in the BMU. The temporal models that adopt the power law approach defined in Section 4.1 (Komarova et al, 2003;Komarova, 2005;Garzón-Alvarado, 2012;Liò et al, 2012;Graham et al, 2013;Jerez and Chen, 2015;Chen-Charpentier and Diakite, 2016;Coelho et al, 2016;Jerez et al, 2018;Camacho and Jerez, 2019;Idrees et al, 2019;Javed et al, 2019;Idrees and Sohail, 2020;Miranda et al, 2020;Camacho and Jerez, 2021;Islam et al, 2021;Cook et al, 2022) are categorized in Table 2, described in Section 5.2, and detailed in Supplementary Table S1. The temporal models that adopt the mass action kinetics approach defined in Section 4.2 (Lemaire et al, 2004;Marathe et al, 2008;Pivonka et al, 2008;Peterson and Riggs, 2010;Marathe et al, 2011;Schmidt et al, 2011;Wang et al, 2011;Buenzli et al, 2012b;Peterson and Riggs, 2012;Ross et al, 2012;Wang and Qin, 2012;Pivonka et al, 2013;Post et al, 2013;Scheiner et al, 2013;Ji et al, 2014;Scheiner et al, 2014;Berkhout et al, 2015;Eudy et a...…”

“…where γ and η are growth and decay parameters, Tdensity is a relationship between the current and maximum cancer cell population, and λ is an additional relationship term to capture the effects of other cancer interactions considered (Ayati et al, 2010;Buenzli et al, 2012b;Coelho et al, 2016;Zhang and Mager, 2019;Miranda et al, 2020). For example, in the Coelho et al (2016) model, λ in Eq.…”