Nonlinear modeling and control strategies for bone diseases based on TGF<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>β</mml:mi></mml:math> and Wnt factors

Camacho, Ariel; Jerez, Silvia

doi:10.1016/j.cnsns.2021.105842

Cited by 3 publications

(4 citation statements)

References 40 publications

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“…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...…”

Section: Open Accessmentioning

confidence: 99%

“…This model adds explicit state variables for RANKL and OPG by setting one of the original paracrine power parameters equal to zero, namely the one corresponding to osteoblast-derived osteoclast regulation, and formulating separate equations for RANKL and OPG levels. Camacho and Jerez (2021) follows Ryser et al (2009) by dropping paracrine signal exponents to explicitly model TGF-β and Wnt as state variables in a temporal model. Camacho and Jerez (2021) also updates the cell population equations to incorporate TGF-β-induced osteoclast apoptosis and Wntinduced osteoblast proliferation.…”

Section: Power Law Modelsmentioning

confidence: 99%

“…Camacho and Jerez (2021) follows Ryser et al (2009) by dropping paracrine signal exponents to explicitly model TGF-β and Wnt as state variables in a temporal model. Camacho and Jerez (2021) also updates the cell population equations to incorporate TGF-β-induced osteoclast apoptosis and Wntinduced osteoblast proliferation. In the bone metastasis model by Garzón-Alvarado (2012), tumor-induced changes in TGF-β and parathyroid hormone-related protein (PTHrP) are added as state variables.…”

Section: Power Law Modelsmentioning

confidence: 99%

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

Cook,

Lighty,

Smith

et al. 2024

Front. Syst. Biol.

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Bone remodeling is an essential, delicately balanced physiological process of coordinated activity of bone cells that remove and deposit new bone tissue in the adult skeleton. Due to the complex nature of this process, many mathematical models of bone remodeling have been developed. Each of these models has unique features, but they have underlying patterns. In this review, the authors highlight the important aspects frequently found in mathematical models for bone remodeling and discuss how and why these aspects are included when considering the physiology of the bone basic multicellular unit, which is the term used for the collection of cells responsible for bone remodeling. The review also emphasizes the view of bone remodeling from a systems biology perspective. Understanding the systemic mechanisms involved in remodeling will help provide information on bone pathology associated with aging, endocrine disorders, cancers, and inflammatory conditions and enhance systems pharmacology. Furthermore, some features of the bone remodeling cycle and interactions with other organ systems that have not yet been modeled mathematically are discussed as promising future directions in the field.

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Section: Open Accessmentioning

confidence: 99%

Section: Power Law Modelsmentioning

confidence: 99%

Section: Power Law Modelsmentioning

confidence: 99%

See 1 more Smart Citation

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

Cook,

Lighty,

Smith

et al. 2024

Front. Syst. Biol.

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“…Among the models that focus on explicitly capturing certain autocrine and paracrine signals is the spatial extension byRyser et al (2009). This model adds explicit state variables for RANKL and OPG by setting one of the original paracrine power parameters equal to zero, namely the one corresponding to osteoblast-derived osteoclast regulation, and formulating separate equations for RANKL and OPG levels Camacho and Jerez (2021). followsRyser et al (2009) by dropping paracrine signal exponents to explicitly model TGF-β and Wnt as state variables in a temporal model.…”

mentioning

confidence: 99%

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

Cook,

Lighty,

Smith

et al. 2024

Preprint

View full text Add to dashboard Cite

Bone remodeling is an essential physiological process in the adult skeleton. Due to the complex nature of this process, many mathematical models of bone remodeling have been developed. Each of these models has unique features, but they have underlying patterns. In this review, the authors highlight the important aspects frequently found in mathematical models for bone remodeling and discuss how and why these aspects are included when considering the physiology of the bone basic multicellular unit, which is the term used for the collection of cells responsible for bone remodeling. The review also emphasizes the view of bone remodeling from a systems biology perspective. Understanding the systemic mechanisms involved in remodeling will help provide information on bone pathology associated with aging, endocrine disorders, cancers, and inflammatory conditions and enhance systems pharmacology. Furthermore, some features of the bone remodeling cycle and interactions with other organ systems that have not yet been modeled mathematically are discussed as promising future directions in the field.

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

Camacho¹,

Diaz-Ocampo²,

Jerez³

2022

Math. Model. Nat. Phenom.

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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 L1-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.

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Nonlinear modeling and control strategies for bone diseases based on TGFβ and Wnt factors

Cited by 3 publications

References 40 publications

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

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

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

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

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