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Regional variations in growth plate chondrocyte deformation as predicted by three-dimensional multi-scale simulations.

Gao J, Roan E, Williams JL - PLoS ONE (2015)

Bottom Line: The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate.This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage.While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.

View Article: PubMed Central - PubMed

Affiliation: Departments of Mechanical Engineering, University of Memphis Memphis, Tennessee, 38152, United States of America.

ABSTRACT
The physis, or growth plate, is a complex disc-shaped cartilage structure that is responsible for longitudinal bone growth. In this study, a multi-scale computational approach was undertaken to better understand how physiological loads are experienced by chondrocytes embedded inside chondrons when subjected to moderate strain under instantaneous compressive loading of the growth plate. Models of representative samples of compressed bone/growth-plate/bone from a 0.67 mm thick 4-month old bovine proximal tibial physis were subjected to a prescribed displacement equal to 20% of the growth plate thickness. At the macroscale level, the applied compressive deformation resulted in an overall compressive strain across the proliferative-hypertrophic zone of 17%. The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate. This pattern was reversed within the outer 300 μm region at the free surface where cells were compressed by 10% in the proliferative and 26% in the hypertrophic zones, in agreement with experimental observations. This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage. While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.

No MeSH data available.


Related in: MedlinePlus

Results for two cases with the cellular Young’s modulus increased 20-fold over the instantaneous short time scale value, for cellular Poisson’s ratio = 0.50 and 0.49 in an effort to approximate long-time scale compression with a purely elastic approach to compare with the experimental values in the literature.Results are very sensitive to assumed values of cellular Poisson’s ratio and to the Young’s modulus ratio between the cell and the tightly bound territorial matrix and we do not believe this is the correct approach for modeling long-time scale events since the real value of cellular Poisson’s ratio cannot be accurately determined.
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pone.0124862.g010: Results for two cases with the cellular Young’s modulus increased 20-fold over the instantaneous short time scale value, for cellular Poisson’s ratio = 0.50 and 0.49 in an effort to approximate long-time scale compression with a purely elastic approach to compare with the experimental values in the literature.Results are very sensitive to assumed values of cellular Poisson’s ratio and to the Young’s modulus ratio between the cell and the tightly bound territorial matrix and we do not believe this is the correct approach for modeling long-time scale events since the real value of cellular Poisson’s ratio cannot be accurately determined.

Mentions: Nevertheless, if for the sake of comparison one assumes slight compressibility of the cells under equilibrium conditions, following cell shrinkage after prolonged compression (Poisson’s ratio = 0.49), it is also necessary to consider the fact that the Young’s modulus of the cell increases as the volume decreases [47], varying exponentially with the volume fraction of the remaining solid phase of the cell for long time scale events [50]. To simulate such a condition we compare two solutions (Fig 10) with the cellular Young’s modulus increased 20-fold over the instantaneous value, consistent with the increases measured experimentally [50]. The cellular strains were significantly changed under conditions of slight compressibility relative to the incompressible case, which was solved for the same 20-fold greater Young’s modulus in order to exclude the possible influence of changing the modulus. The cellular strains were more sensitive to small changes in compressibility for chondrons located in the central region than for the regions near the free surface or plane of microscopic observation.


Regional variations in growth plate chondrocyte deformation as predicted by three-dimensional multi-scale simulations.

Gao J, Roan E, Williams JL - PLoS ONE (2015)

Results for two cases with the cellular Young’s modulus increased 20-fold over the instantaneous short time scale value, for cellular Poisson’s ratio = 0.50 and 0.49 in an effort to approximate long-time scale compression with a purely elastic approach to compare with the experimental values in the literature.Results are very sensitive to assumed values of cellular Poisson’s ratio and to the Young’s modulus ratio between the cell and the tightly bound territorial matrix and we do not believe this is the correct approach for modeling long-time scale events since the real value of cellular Poisson’s ratio cannot be accurately determined.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4401775&req=5

pone.0124862.g010: Results for two cases with the cellular Young’s modulus increased 20-fold over the instantaneous short time scale value, for cellular Poisson’s ratio = 0.50 and 0.49 in an effort to approximate long-time scale compression with a purely elastic approach to compare with the experimental values in the literature.Results are very sensitive to assumed values of cellular Poisson’s ratio and to the Young’s modulus ratio between the cell and the tightly bound territorial matrix and we do not believe this is the correct approach for modeling long-time scale events since the real value of cellular Poisson’s ratio cannot be accurately determined.
Mentions: Nevertheless, if for the sake of comparison one assumes slight compressibility of the cells under equilibrium conditions, following cell shrinkage after prolonged compression (Poisson’s ratio = 0.49), it is also necessary to consider the fact that the Young’s modulus of the cell increases as the volume decreases [47], varying exponentially with the volume fraction of the remaining solid phase of the cell for long time scale events [50]. To simulate such a condition we compare two solutions (Fig 10) with the cellular Young’s modulus increased 20-fold over the instantaneous value, consistent with the increases measured experimentally [50]. The cellular strains were significantly changed under conditions of slight compressibility relative to the incompressible case, which was solved for the same 20-fold greater Young’s modulus in order to exclude the possible influence of changing the modulus. The cellular strains were more sensitive to small changes in compressibility for chondrons located in the central region than for the regions near the free surface or plane of microscopic observation.

Bottom Line: The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate.This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage.While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.

View Article: PubMed Central - PubMed

Affiliation: Departments of Mechanical Engineering, University of Memphis Memphis, Tennessee, 38152, United States of America.

ABSTRACT
The physis, or growth plate, is a complex disc-shaped cartilage structure that is responsible for longitudinal bone growth. In this study, a multi-scale computational approach was undertaken to better understand how physiological loads are experienced by chondrocytes embedded inside chondrons when subjected to moderate strain under instantaneous compressive loading of the growth plate. Models of representative samples of compressed bone/growth-plate/bone from a 0.67 mm thick 4-month old bovine proximal tibial physis were subjected to a prescribed displacement equal to 20% of the growth plate thickness. At the macroscale level, the applied compressive deformation resulted in an overall compressive strain across the proliferative-hypertrophic zone of 17%. The microscale model predicted that chondrocytes sustained compressive height strains of 12% and 6% in the proliferative and hypertrophic zones, respectively, in the interior regions of the plate. This pattern was reversed within the outer 300 μm region at the free surface where cells were compressed by 10% in the proliferative and 26% in the hypertrophic zones, in agreement with experimental observations. This work provides a new approach to study growth plate behavior under compression and illustrates the need for combining computational and experimental methods to better understand the chondrocyte mechanics in the growth plate cartilage. While the current model is relevant to fast dynamic events, such as heel strike in walking, we believe this approach provides new insight into the mechanical factors that regulate bone growth at the cell level and provides a basis for developing models to help interpret experimental results at varying time scales.

No MeSH data available.


Related in: MedlinePlus