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Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control

1
IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
2
INESC–ID, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 679; https://doi.org/10.3390/math8050679
Received: 25 February 2020 / Revised: 13 April 2020 / Accepted: 28 April 2020 / Published: 1 May 2020
(This article belongs to the Section Dynamical Systems)
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. View Full-Text
Keywords: bone remodelling; PK/PD; bone metastasis; model predictive control; particle swarm optimization bone remodelling; PK/PD; bone metastasis; model predictive control; particle swarm optimization
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MDPI and ACS Style

Miranda, R.; Vinga, S.; Valério, D. Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control. Mathematics 2020, 8, 679. https://doi.org/10.3390/math8050679

AMA Style

Miranda R, Vinga S, Valério D. Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control. Mathematics. 2020; 8(5):679. https://doi.org/10.3390/math8050679

Chicago/Turabian Style

Miranda, Raquel, Susana Vinga, and Duarte Valério. 2020. "Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control" Mathematics 8, no. 5: 679. https://doi.org/10.3390/math8050679

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