Bone Remodeling Under Vibration: A Computational Model of Bone Remodeling Incorporating the Modal Behavior of Bone

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
A. Ostadi Moghaddam ◽  
M. J. Mahjoob ◽  
A. Nazarian
Keyword(s):  
Bone Remodeling ◽  
Computational Models ◽  
Resonance Region ◽  
Frequency Domain Analysis ◽  
Bone Adaptation ◽  
Bovine Bone ◽  
Loading Frequency ◽  
Modified Model ◽  
Modal Behavior ◽  
Modal Vibration

Developing precise computational models of bone remodeling can lead to more successful types of orthopedic treatments and deeper understanding of the phenomenon. Empirical evidence has shown that bone adaptation to mechanical loading is frequency dependent, and the modal behavior of bone under vibration can play a significant role in remodeling process, particularly in the resonance region. The objective of this study is to develop a bone remodeling algorithm that takes into account the effects of bone vibrational behavior. An extended/modified model is presented based on conventional finite element (FE) remodeling models. Frequency domain analysis is used to introduce appropriate correction coefficients to incorporate the effect of bone's frequency response (FR) into the model. The method is implemented on a bovine bone with known modal/vibration characteristics. The rate and locations of new bone formation depend on the loading frequency and are consistently correlated with the bone modal behavior. Results show that the proposed method can successfully integrate the bone vibration conditions and characteristics with the remodeling process. The results obtained support experimental observations in the literature.

High Fidelity Computational Model of Bone Remodeling Cellular Mechanisms

2010 ◽  
Author(s):  
Charles L. Penninger ◽  
Andrés Tovar ◽  
Glen L. Niebur ◽  
John E. Renaud
Keyword(s):  
Bone Remodeling ◽  
Computational Models ◽  
Bone Adaptation ◽  
Daily Activities ◽  
High Fidelity ◽  
Mechanical Stimuli ◽  
Cellular Activity ◽  
Cellular Mechanisms ◽  
Mechanical Loads ◽  
Metabolic Activities

One of the most intriguing aspects of bone is its ability to grow, repair damage, adapt to mechanical loads, and maintain mineral homeostasis [1]. It is generally accepted that bone adaptation occurs in response to the mechanical demands of our daily activities; moreover, strain and microdamage have been implicated as potential stimuli that regulate bone remodeling [2]. Computational models have been used to simulate remodeling in an attempt to better understand the metabolic activities which possess the key information of how this process is carried out [3]. At present, the connection between the cellular activity of remodeling and the applied mechanical stimuli is not fully understood. Only a few mathematical models have been formulated to characterize the remolding process in terms of the cellular mechanisms that occur [4,5].

scholarly journals Predicting cortical bone adaptation to axial loading in the mouse tibia

2015 ◽  
Vol 12 (110) ◽  
pp. 20150590 ◽  
Author(s):  
A. F. Pereira ◽  
B. Javaheri ◽  
A. A. Pitsillides ◽  
S. J. Shefelbine
Keyword(s):  
Cortical Bone ◽  
Computational Models ◽  
Mechanical Load ◽  
Fluid Velocity ◽  
Structural Response ◽  
Axial Loading ◽  
Mechanical Stimulus ◽  
Bone Adaptation ◽  
Mouse Tibia ◽  
Efficient Loading

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms.

Analogy of Strain Energy Density Based Bone-Remodeling Algorithm and Structural Topology Optimization

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
In Gwun Jang ◽  
Il Yong Kim ◽  
Byung Man Kwak
Keyword(s):  
Topology Optimization ◽  
Energy Density ◽  
Bone Remodeling ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Optimization Method ◽  
Bone Adaptation ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Method

In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis,” J. Biomech. Eng., 20, pp. 1135–1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields—the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)—in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.

scholarly journals The Role of the Loading Condition in Predictions of Bone Adaptation in a Mouse Tibial Loading Model

2021 ◽  
Vol 9 ◽  
Author(s):  
Vee San Cheong ◽  
Visakan Kadirkamanathan ◽  
Enrico Dall’Ara
Keyword(s):  
Bone Remodeling ◽  
Mechanical Loading ◽  
Axial Load ◽  
Bone Adaptation ◽  
Combined Loading ◽  
Micro Ct ◽  
Loading Conditions ◽  
Physiological Loading ◽  
Physiological Load ◽  
Significant Difference

The in vivo mouse tibial loading model is used to evaluate the effectiveness of mechanical loading treatment against skeletal diseases. Although studies have correlated bone adaptation with the induced mechanical stimulus, predictions of bone remodeling remained poor, and the interaction between external and physiological loading in engendering bone changes have not been determined. The aim of this study was to determine the effect of passive mechanical loading on the strain distribution in the mouse tibia and its predictions of bone adaptation. Longitudinal micro-computed tomography (micro-CT) imaging was performed over 2 weeks of cyclic loading from weeks 18 to 22 of age, to quantify the shape change, remodeling, and changes in densitometric properties. Micro-CT based finite element analysis coupled with an optimization algorithm for bone remodeling was used to predict bone adaptation under physiological loads, nominal 12N axial load and combined nominal 12N axial load superimposed to the physiological load. The results showed that despite large differences in the strain energy density magnitudes and distributions across the tibial length, the overall accuracy of the model and the spatial match were similar for all evaluated loading conditions. Predictions of densitometric properties were most similar to the experimental data for combined loading, followed closely by physiological loading conditions, despite no significant difference between these two predicted groups. However, all predicted densitometric properties were significantly different for the 12N and the combined loading conditions. The results suggest that computational modeling of bone’s adaptive response to passive mechanical loading should include the contribution of daily physiological load.

scholarly journals Predicting cortical bone adaptation to axial loading in the mouse tibia

2015 ◽  
Author(s):  
Andre F Pereira ◽  
Behzad Javaheri ◽  
Andrew Pitsillides ◽  
Sandra Shefelbine
Keyword(s):  
Cortical Bone ◽  
Computational Models ◽  
Mechanical Load ◽  
Fluid Velocity ◽  
Structural Response ◽  
Axial Loading ◽  
Mechanical Stimulus ◽  
Bone Adaptation ◽  
Mouse Tibia ◽  
Efficient Loading

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on-off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's tau rank coefficient \(\tau = 0.51\), \(p<0.001\)). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to time variant stimulus. Such models could be used in the design of more efficient loading protocols and drugs therapies that target the relevant physiological mechanisms.

scholarly journals The importance of loading frequency, rate and vibration for enhancing bone adaptation and implant osseointegration

2008 ◽  
Vol 16 ◽  
pp. 65-68 ◽  
Author(s):  
A Torcasio ◽  
◽  
GH van Lenthe ◽  
H Van Oosterwyck
Keyword(s):  
Bone Adaptation ◽  
Loading Frequency ◽  
Frequency Rate

Damaged-Bone Adaptation Under Steady Homogeneous Stress

2002 ◽  
Vol 124 (3) ◽  
pp. 322-327 ◽  
Author(s):  
S. Ramtani ◽  
M. Zidi
Keyword(s):  
Theoretical Model ◽  
Bone Remodeling ◽  
Small Strain ◽  
Bone Adaptation ◽  
Damage Effect ◽  
Recent Theory ◽  
Loading History ◽  
Homogeneous Stress ◽  
Bone Microdamage ◽  
Adaptive Elasticity

In this work an extension of the adaptive-elasticity theory is proposed in order to include the contribution of bone microdamage as a stimulus. Some aspects of damaged-bone tissue adaptation, brought about by a change of the daily loading history, are investigated. In particular, under the assumption of a small strain approximation and isothermal conditions, the solution of the remodeling rate equation for steady homogeneous stress is discussed and the damage effect upon the remodeling time constant is shown. The result is both theoretical and numerical, based on a recent theory of internal damaged-bone remodeling (Ramtani, S., and Zidi, M., 1999, “Damaged-Bone Remodeling Theory: Thermodynamical Approach,” Mechanics Research Communications, Vol. 26, pp. 701–708. Ramtani, S., and Zidi, M., 2001, “A Theoretical Model of the Effect of Continum Damage on a Bone Adaption Model,” Journal of Biomechanics, Vol. 34, pp. 471–479) and motivated by the works of Cowin, S. C., and Hegedus, D. M., 1976, “Bone Remodeling I: Theory and Adaptive Elasticity,” Journal of Elasticity, Vol. 6, pp. 471–479 and Hegedus, D. H., and Cowin, S. C., 1976, “Bone Remodeling II: Small Strain Adaptive Elasticity,” Journal of Elasticity, Vol. 6, pp. 337–352.

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