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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

Distribution of the axial logarithmic strain and deformation of the chondrons.(A) A non-uniform distribution of axial logarithmic strain, in the y-direction, exists within the ‘m’ shape growth plate in the mesoscopic model. Chondrocytes were not included in this model. The distribution of strain was significantly different at these locations from the central or internal regions of the growth plate and reached values approaching double the nominal engineering strain of 20%; (B) Deformed chondrons obtained from the microscale model with cellular detail is overlaid on a deformed macroscale model displaying only the growth plate. Chondrons buckled within 300 μm of free surfaces, but not within the growth plate interior when 20% overall compressive strain was applied across the macroscale model. Deformed models are not scaled up. The ‘m’ shape growth plate exhibited transverse outward buckling deformation of 125 μm at the edge. The contour plot is obtained by extrapolating the integration point values to the nodes and then averaging.
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pone.0124862.g004: Distribution of the axial logarithmic strain and deformation of the chondrons.(A) A non-uniform distribution of axial logarithmic strain, in the y-direction, exists within the ‘m’ shape growth plate in the mesoscopic model. Chondrocytes were not included in this model. The distribution of strain was significantly different at these locations from the central or internal regions of the growth plate and reached values approaching double the nominal engineering strain of 20%; (B) Deformed chondrons obtained from the microscale model with cellular detail is overlaid on a deformed macroscale model displaying only the growth plate. Chondrons buckled within 300 μm of free surfaces, but not within the growth plate interior when 20% overall compressive strain was applied across the macroscale model. Deformed models are not scaled up. The ‘m’ shape growth plate exhibited transverse outward buckling deformation of 125 μm at the edge. The contour plot is obtained by extrapolating the integration point values to the nodes and then averaging.

Mentions: The axial (Y-axis) logarithmic strain distribution along the bone long axis direction in the mesoscale model of the growth plate was highly non-uniform and reached peak strains of 40% in the proliferative zone near the free boundary (Fig 4A). Chondrons, the primary functional and structural units of the growth plate, deformed by buckling near the free surfaces where the cartilage bulged outward while remaining straight in the interior regions (Fig 4B). The shape of the mammillary process also influenced the degree of buckling at the free surface. Flat growth plate exhibited greater buckling deformations of chondrons near the periphery where the maximum transverse (outward) displacement was 158 μm as compared with 125 μm for the ‘m’ shape growth plate (flat plate results are not shown).


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

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

Distribution of the axial logarithmic strain and deformation of the chondrons.(A) A non-uniform distribution of axial logarithmic strain, in the y-direction, exists within the ‘m’ shape growth plate in the mesoscopic model. Chondrocytes were not included in this model. The distribution of strain was significantly different at these locations from the central or internal regions of the growth plate and reached values approaching double the nominal engineering strain of 20%; (B) Deformed chondrons obtained from the microscale model with cellular detail is overlaid on a deformed macroscale model displaying only the growth plate. Chondrons buckled within 300 μm of free surfaces, but not within the growth plate interior when 20% overall compressive strain was applied across the macroscale model. Deformed models are not scaled up. The ‘m’ shape growth plate exhibited transverse outward buckling deformation of 125 μm at the edge. The contour plot is obtained by extrapolating the integration point values to the nodes and then averaging.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0124862.g004: Distribution of the axial logarithmic strain and deformation of the chondrons.(A) A non-uniform distribution of axial logarithmic strain, in the y-direction, exists within the ‘m’ shape growth plate in the mesoscopic model. Chondrocytes were not included in this model. The distribution of strain was significantly different at these locations from the central or internal regions of the growth plate and reached values approaching double the nominal engineering strain of 20%; (B) Deformed chondrons obtained from the microscale model with cellular detail is overlaid on a deformed macroscale model displaying only the growth plate. Chondrons buckled within 300 μm of free surfaces, but not within the growth plate interior when 20% overall compressive strain was applied across the macroscale model. Deformed models are not scaled up. The ‘m’ shape growth plate exhibited transverse outward buckling deformation of 125 μm at the edge. The contour plot is obtained by extrapolating the integration point values to the nodes and then averaging.
Mentions: The axial (Y-axis) logarithmic strain distribution along the bone long axis direction in the mesoscale model of the growth plate was highly non-uniform and reached peak strains of 40% in the proliferative zone near the free boundary (Fig 4A). Chondrons, the primary functional and structural units of the growth plate, deformed by buckling near the free surfaces where the cartilage bulged outward while remaining straight in the interior regions (Fig 4B). The shape of the mammillary process also influenced the degree of buckling at the free surface. Flat growth plate exhibited greater buckling deformations of chondrons near the periphery where the maximum transverse (outward) displacement was 158 μm as compared with 125 μm for the ‘m’ shape growth plate (flat plate results are not shown).

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