ArticleJournal of mathematical biology2019
Bone metastasis treatment modeling via optimal control.
Article in Journal of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed, 25 citations in OpenAlex.
- Validation of polymorphic Gompertzian model of cancer through in vitro and in vivo data.PloS one · 2025Article
- The Link Between the Gut Microbiome and Bone Metastasis.International journal of molecular sciences · 2024Review
- Reclassified the phenotypes of cancer types and construct a nomogram for predicting bone metastasis risk: A pan-cancer analysis.Cancer medicine · 2024Article
- Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach.PLoS computational biology · 2024Article
- A review of mathematical modeling of bone remodeling from a systems biology perspective.Frontiers in systems biology · 2024Article
- Antigen receptor therapy in bone metastasis via optimal control for different human life stages.Journal of mathematical biology · 2021Article
- Dynamic modeling of bone remodeling, osteolytic metastasis and PK/PD therapy: introducing variable order derivatives as a simplification technique.Journal of mathematical biology · 2021Review
- Bone metastases: a comprehensive review of the literature.Molecular biology reports · 2020Review
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Authors and funding
2 authors at 1 institution in 1 country.
Funding
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Abstract
Metastatic disease is a lethal stage of cancer progression. It is characterized by the spread of aberrant cells from a primary tumor to distant tissues like the bone. Several treatments are used to deal with bone metastases formation, but they are palliative since the disease is considered incurable. Computational and mathematical models are used to understand the underlying mechanisms of how bone metastasis evolves. In this way, new therapies aiming to reduce or eliminate the metastatic burden in the bone tissue may be proposed. We present an optimal control approach to analyze some common treatments for bone metastasis. In particular, we focus on denosumab treatment, an anti-resorptive therapy, and radiotherapy treatment which has a cell killing action. We base our work in a variant of an existing model introduced by Komarova. The new model incorporates a logistic equation in order to describe the bone metastasis evolution. We provide proofs of existence and uniqueness of solutions to the corresponding optimal control problems for each treatment. Moreover, we present some numerical simulations to analyze the effectiveness of both treatments when different interactions between cancer and bone cells occur. A discussion of the obtained results is provided.
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