Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

Jerez, Silvia; Díaz‐Infante, Saúl; Chen, B.

doi:10.1016/j.mbs.2018.03.006

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…SDEs introduce random parameters in the model and are used to investigate e.g. bone remodeling ( Sun et al, 2012 ; Jerez et al, 2018 ). One main advantage of continuous-time models is that they have been studied exhaustively in the last centuries, leading to many well-known numerical methods to determine their solutions, such as the finite element (FE) method ( Zienkiewicz et al, 1977 , used e.g.…”

Section: In Silico Modelingmentioning

confidence: 99%

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

Lafuente-Gracia

Borgiani

Nasello

et al. 2021

Front. Bioeng. Biotechnol.

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In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.

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Section: In Silico Modelingmentioning

confidence: 99%

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

Lafuente-Gracia

Borgiani

Nasello

et al. 2021

Front. Bioeng. Biotechnol.

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“…Bone is a living tissue [11]. ere is a process in its place to resorb old bone and form new bone to maintain its strength and health, called bone-remodeling process, and such a process occurs throughout a person's life [10,12,13]. In osteoporosis patients, the loss of bone mass occurs because the removal of older bone is more than the replacement of new bone which is an imbalance between bone resorption and bone formation [10].…”

Section: Introductionmentioning

confidence: 99%

“…In osteoporosis patients, the loss of bone mass occurs because the removal of older bone is more than the replacement of new bone which is an imbalance between bone resorption and bone formation [10]. ere are two families of cells mainly involved in the process of bone remodeling, namely, osteoclastic cells, breaking down the bone cells, and osteoblastic cells, forming the bone tissue [12,13]. Boneremodeling process is composed of four phases sequentially, which are activation, resorption, reversal, and formation [12].…”

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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“…The definition of fractional order operators can preserve hereditary and memory traits of a considered functions in a real problem. This property helps researchers to propose more accurate models of various phenomena [34,6,3,5,16,7,21]. Thus, many problems in physics, economics and other sciences have been modeled as fractional stochastic differential equations [38,44,1,4].…”

mentioning

confidence: 99%

A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay

Banihashemi¹,

Jafaria²,

Babaei³

2022

DCDS-S

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In present work, a step-by-step Legendre collocation method is employed to solve a class of nonlinear fractional stochastic delay differential equations (FSDDEs). The step-by-step method converts the nonlinear FSDDE into a non-delay nonlinear fractional stochastic differential equation (FSDE). Then, a Legendre collocation approach is considered to obtain the numerical solution in each step. By using a collocation scheme, the non-delay nonlinear FSDE is reduced to a nonlinear system. Moreover, the error analysis of this numerical approach is investigated and convergence rate is examined. The accuracy and reliability of this method is shown on three test examples and the effect of different noise measures is investigated. Finally, as an useful application, the proposed scheme is applied to obtain the numerical solution of a stochastic SIRS model.

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Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

Cited by 13 publications

References 25 publications

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

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

A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay

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