Modeling of biological doses and mechanical effects on bone transduction

📝 Abstract

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of Calcium, Parathyroid Hormone, Nitric Oxide and Prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (Parathyroid Hormone, Nitric Oxide, and Prostaglandin E2) as parameters of bone cell mechanosensitivity because stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in term of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable. This makes the model amenable to experimental verification.

💡 Analysis

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of Calcium, Parathyroid Hormone, Nitric Oxide and Prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (Parathyroid Hormone, Nitric Oxide, and Prostaglandin E2) as parameters of bone cell mechanosensitivity because stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in term of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable. This makes the model amenable to experimental verification.

📄 Content

1 Modeling of biological doses and mechanical effects on bone transduction

Romain Rieger, Ridha Hambli* and Rachid Jennane

PRISME Laboratory, University of Orleans 8 rue Léonard de Vinci, 45072 Orléans cedex 2, France Phone : +33 (0)238 49 40 55 Fax : +33 (0)238 41 73 83

• Corresponding author: ridha.hambli@univ-orleans.fr

Abstract

Shear stress, hormones like parathyroid and mineral elements like calcium mediate the amplitude of stimulus signal which affects the rate of bone remodeling. The current study investigates the theoretical effects of different metabolic doses in stimulus signal level on bone. The model was built considering the osteocyte as the sensing center mediated by coupled mechanical shear stress and some biological factors. The proposed enhanced model was developed based on previously published works dealing with different aspects of bone transduction. It describes the effects of physiological doses variations of Calcium, Parathyroid Hormone, Nitric Oxide and Prostaglandin E2 on the stimulus level sensed by osteocytes in response to applied shear stress generated by interstitial fluid flow. We retained the metabolic factors (Parathyroid Hormone, Nitric Oxide, and Prostaglandin E2) as parameters of bone cell mechanosensitivity because

2 stimulation/inhibition of induced pathways stimulates osteogenic response in vivo. We then tested the model response in term of stimulus signal variation versus the biological factors doses to external mechanical stimuli. Despite the limitations of the model, it is consistent and has physiological bases. Biological inputs are histologically measurable. This makes the model amenable to experimental verification.

Keywords: Osteocytes; Shear stress; Ca-PTH; NO; PGE2

Notations

ocy x : Active sensing osteocytes number. bx : Active osteocblasts number. cx : Active osteoclasts number.

Ca x : Calcium level

PTH

x

PTH level NO x : Nitric Oxide level. PGE x : Prostaglandin E2 level.

P V : Interstitial fluid velocity generated by pressure.
dz dP : Pressure gradient in the canaliculi; z denotes the axial coordinate of the canaliculi.

1. Introduction It is well admitted that mechanical strain is one of the main stimulus triggering bone remodeling.

3 Bone adaptation to its environment is influenced by both mechanical and biological stimuli (Feskanich et al., 2003; Goltzman, 1999; Heldring et al., 2007). Fluid flow imposes a shear stress on osteocytes that appears to deform the cells (Weinbaum et al., 1994).
Bonewald (2008) rewieved a cascades of transduction events into the osteocyte as a response to mechanical loading. Important signaling molecules like Nitric Oxide (NO) and Prostaglandin E2 (PGE2) influencing bone remodeling homeostasis have been shown to be produced in the osteocyte in response to fluid flow.
Weinbaum et al., (1994) were one of the first to propose a theoretical model to predict the fluid shear stress and streaming potential at the surface of osteocytic process in the lacunocanalicular porosity. Rémond et al., (2005) enhanced the model of Zeng by including mass flux. Lemaire et al., (2005) developed a more complex model based on the idea that the motion of interstitial fluid is caused by a combination of mechanical strain, electro-osmotic and osmotic actions. Few numerical studies modeling the load-induced fluid flow have been developed (Goulet et al., 2008; Gururaja et al., 2005; Roland Steck, 2003; Swan et al., 2003). Some other theoretical and numerical studies have been performed considering the osteocyte’s tissue strain amplification (Han et al., 2004; Rathbonivtch et al., 2007) or the integrin function on the mechanosensation process (Wang et al., 2007; Weinbaum, 2003). Recently, Adachi et al., (2010) developed a bone remodeling finite element model based on a stimulus function expressed in term of fluid flow in the lacunocanalicular system. The limitations of this work it that the model neglects the coupling effects with the main biological mechanisms. No biological entities were considered and the bone adaptation is purely triggered by mechanical stimulus. Some studies have attempted to explore the effect of metabolic doses regarding bone remodeling or bone diseases in numerical models. Maldonado, (2006) has developed a

4 formulation of the production of NO and PGE2 by the osteocyte and a description of the evolution of the osteocyte cell population. The osteocyte rate growth was expressed as a function of the number of osteoblasts (some osteoblasts differentiate into osteocytes) and a fluid shear stress function (mechanical loading is involving on osteocyte viability). Recently, enhanced mathematical model was developed by Peterson and Riggs (2010) to describe the bone and Calcium-Parathyroid Hormone (Ca-PTH) homeostasis. Komarova (2005) have developed a theoretical model describing the autoc

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