An impulsive mathematical model of bone formation and resorption: effects of parathyroid hormone, calcitonin and impulsive estrogen supplement

Chaiya, Inthira; Rattanakul, Chontita

doi:10.1186/s13662-017-1206-2

Cited by 8 publications

(14 citation statements)

References 24 publications

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“…( 2010 ), Coelho et al. ( 2016 ) Grouth rate of “Para-thyroid hormone” through parathyroid gland 0.2 Chaiya ( 2017 ) Coefficient of hill function 0.5 Chaiya ( 2017 ) “Para-thyroid hormone” apoptosis rate 0.07 Chaiya ( 2017 ) Grouth rate of CT through parafollicular cells of the thyroid gland 0.3 Chaiya ( 2017 ) Coefficient of hill function 0.5 Chaiya ( 2017 ) CT apoptosis rate 0.5 Chaiya ( 2017 ) Maximum effect of bisphosphonates 1.2 Coelho et al. ( 2016 ) Maximum effect of anti-cancer therapy 0.017 Coelho et al.…”

Section: Resultsmentioning

confidence: 99%

“…( 2016 ) Maximum effect of anti-cancer therapy 0.017 Coelho et al. ( 2016 ) Activation rate of “Osteoclasts” through “Para-thyroid hormone” 0.01 Chaiya ( 2017 ) Coefficient of hill function 10 Chaiya ( 2017 ) Coefficient of hill function 10 Chaiya ( 2017 ) Activation rate of “osteoblasts” through “Para-thyroid hormone” 0.02 Chaiya ( 2017 ) Coefficient of hill function 10 Chaiya ( 2017 ) Apoptosis rate of “osteoblasts” through “Para-thyroid hormone” 0.4 Chaiya ( 2017 ) Coefficient of hill function 10 Chaiya ( 2017 ) “Osteoclasts” A-C regulator 1.15 Ayati et al. ( 2010 ), Coelho et al.…”

Section: Resultsmentioning

confidence: 99%

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Optimizing the dynamics of bone turnover with genetic algorithm

Idrees

Sohail

2022

Model. Earth Syst. Environ.

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Control systems and the modeling strategies are not only limited to engineering problems. These approaches can be used in the field of bio-mathematics as well and modern studies have promoted this approach to a great extent. The computational modeling and simulation of bone metastasis is painful yet critical after cancer invades the body. This vicious cycle is complex, and several research centers worldwide are devoted to understanding the dynamics and setting up a treatment strategy for this life-threatening behavior of cancer. Cancerous cells activation and the corresponding process of metastasis is reported to boost during the periodic waves of COVID-19, due to the inflammatory nature of the infection associated with SARS-2 and its variants. The bone cells are comprised of two types of cells responsible for bone formation and resorption. The computational framework of such cells, in spatial form, can help the researchers forecast the bone dynamics in a robust manner where the impact of cancer is incorporated into the computational model as a source of perturbation. A series of computational models are presented to explore the complex behavior of bone metastasis with COVID-19 induced infection. The finite difference algorithm is used to simulate the nonlinear computational model. The results obtained are in close agreement with the experimental findings. The computational results can help explore the vicious cycle’s fate and help set up control strategies through drug therapies.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Optimizing the dynamics of bone turnover with genetic algorithm

Idrees

Sohail

2022

Model. Earth Syst. Environ.

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“…The functions on the right-hand sides of the former four equations in system (1) are denoted by f = (f 1 , f 2 , f 3 , f 4 ) T . Let V 0 be the set of functions V : R + × R 4 + → R + having the following properties [11,[14][15][16][17]:…”

Section: Preliminariesmentioning

confidence: 99%

“…In their work, the numerical results demonstrated that the virus-free equilibrium is globally stable. In addition, several applications of the impulsive models have been studied in, e.g., [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

An application of the impulsive CSOH model for managing squirrels in the coconut farm

2019

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In this work, we formulate the mathematical model that incorporates two equations to represent the ultimate goal and controlling strategy to the traditional prey-predator model so that we can investigate the interaction between preys and predators. The model is shortly called the CSOH model. The impulsive practice is added into the model for squirrel control purposes. In particular, we are interested in pulsing the squirrel hunters into the system for every fixed period to control squirrels at the level allowing farmers to have sufficient amount of coconuts so that they can continue their business. We establish the conditions for the squirrel-free periodic solution exists and is globally stable. The numerical simulations reveal that squirrels in the coconut farm could be entirely eradicated by the pulsing strategy. However, the disappearance of squirrels on the farm is not an ecological desire because all species should be allowed to coexist in the system. Consequently, we recommend that the number of squirrel hunters pulsed into the coconut farm should be properly set by considering the time of intervention, expenditure, ecological reasons, and emotional sensitivity of village members.

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“…ey also proposed another model accounting for the effects of PTH and calcitonin on bone-remodeling process together with the effects of impulsive treatments of estrogen in [34]. However, a mathematical model of bone resorption and bone formation consisting of osteoblastic cells, osteoclastic cells, parathyroid hormone, and prolactin with the effect of impulsive treatment of estrogen has never been established.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin

Aekthong

Rattanakul

2021

International Journal of Mathematics and Mathematical Sciences

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Osteoporosis, a bone metabolic disease, is one of the major diseases occurring in aging population especially in postmenopausal women. A system of impulsive differential equations is developed in this paper in order to investigate the effects of parathyroid hormone and prolactin on bone-forming cells, namely, osteoblasts, and bone-resorbing cells, namely, osteoclasts, under the impulsive estrogen supplement. The theoretical analysis of the developed model is carried out so that we obtain the conditions on the system parameters in which the stability and permanence of the model can occur. Computer simulations are also provided to illustrate the theoretical predictions.

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An impulsive mathematical model of bone formation and resorption: effects of parathyroid hormone, calcitonin and impulsive estrogen supplement

Cited by 8 publications

References 24 publications

Optimizing the dynamics of bone turnover with genetic algorithm

Optimizing the dynamics of bone turnover with genetic algorithm

An application of the impulsive CSOH model for managing squirrels in the coconut farm

Dynamical Modelling of Bone Formation and Resorption under Impulsive Estrogen Supplement: Effects of Parathyroid Hormone and Prolactin

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