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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

Overview of the multiscale modeling approach.(A) Two idealized models were constructed consisting of epiphyseal bone, growth plate (GP) cartilage and metaphyseal bone (about 7 x 7 x 7 mm) with variations of mammillary processes: flat and ‘m’ shaped. (B) Set-up of the multiscale modeling approach. At the macroscale level, quarter models were used for analysis. About 0.69 mm thick growth plate cartilage was partitioned into two sections to represent the reserve zone (RZ) and the proliferative/hypertrophic (P/H) zone. Calcified cartilage (CC) was also included in the macroscale model. At the mesoscale, three individual layers were generated in the P/H zone to represent the gradient change of elastic modulus through the thickness of the growth plate. The microscale model of the chondron consisted of interterritorial matrix (ITM), territorial matrix (TM) and 46 chondrocytes with gradually changing cellular shape along with the same number of ITM sections. The elastic modulus of ITM increased from the RZ to the metaphyseal side to represent the gradual change of its material properties.
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pone.0124862.g001: Overview of the multiscale modeling approach.(A) Two idealized models were constructed consisting of epiphyseal bone, growth plate (GP) cartilage and metaphyseal bone (about 7 x 7 x 7 mm) with variations of mammillary processes: flat and ‘m’ shaped. (B) Set-up of the multiscale modeling approach. At the macroscale level, quarter models were used for analysis. About 0.69 mm thick growth plate cartilage was partitioned into two sections to represent the reserve zone (RZ) and the proliferative/hypertrophic (P/H) zone. Calcified cartilage (CC) was also included in the macroscale model. At the mesoscale, three individual layers were generated in the P/H zone to represent the gradient change of elastic modulus through the thickness of the growth plate. The microscale model of the chondron consisted of interterritorial matrix (ITM), territorial matrix (TM) and 46 chondrocytes with gradually changing cellular shape along with the same number of ITM sections. The elastic modulus of ITM increased from the RZ to the metaphyseal side to represent the gradual change of its material properties.

Mentions: We used a multiscale finite element submodeling approach in this study. Submodeling is useful to study a local region of a model, based on the interpolation of nodal results from its global model onto the nodes at the boundaries of the submodel [15]. This allows us to study the transmission of loads from the macroscopic structure (in millimeters) to microscopic structures (in microns). Our model (Fig 1) is comprised of a macroscale model to represent a uniaxial compression test sample (bone-growth plate-bone), a mesoscale model to represent the growth plate with its various zones, and a microscale model to represent the axial columnar organization of chondrocytes (chondrons) in the proliferative and hypertrophic zones (P/H zone).


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

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

Overview of the multiscale modeling approach.(A) Two idealized models were constructed consisting of epiphyseal bone, growth plate (GP) cartilage and metaphyseal bone (about 7 x 7 x 7 mm) with variations of mammillary processes: flat and ‘m’ shaped. (B) Set-up of the multiscale modeling approach. At the macroscale level, quarter models were used for analysis. About 0.69 mm thick growth plate cartilage was partitioned into two sections to represent the reserve zone (RZ) and the proliferative/hypertrophic (P/H) zone. Calcified cartilage (CC) was also included in the macroscale model. At the mesoscale, three individual layers were generated in the P/H zone to represent the gradient change of elastic modulus through the thickness of the growth plate. The microscale model of the chondron consisted of interterritorial matrix (ITM), territorial matrix (TM) and 46 chondrocytes with gradually changing cellular shape along with the same number of ITM sections. The elastic modulus of ITM increased from the RZ to the metaphyseal side to represent the gradual change of its material properties.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0124862.g001: Overview of the multiscale modeling approach.(A) Two idealized models were constructed consisting of epiphyseal bone, growth plate (GP) cartilage and metaphyseal bone (about 7 x 7 x 7 mm) with variations of mammillary processes: flat and ‘m’ shaped. (B) Set-up of the multiscale modeling approach. At the macroscale level, quarter models were used for analysis. About 0.69 mm thick growth plate cartilage was partitioned into two sections to represent the reserve zone (RZ) and the proliferative/hypertrophic (P/H) zone. Calcified cartilage (CC) was also included in the macroscale model. At the mesoscale, three individual layers were generated in the P/H zone to represent the gradient change of elastic modulus through the thickness of the growth plate. The microscale model of the chondron consisted of interterritorial matrix (ITM), territorial matrix (TM) and 46 chondrocytes with gradually changing cellular shape along with the same number of ITM sections. The elastic modulus of ITM increased from the RZ to the metaphyseal side to represent the gradual change of its material properties.
Mentions: We used a multiscale finite element submodeling approach in this study. Submodeling is useful to study a local region of a model, based on the interpolation of nodal results from its global model onto the nodes at the boundaries of the submodel [15]. This allows us to study the transmission of loads from the macroscopic structure (in millimeters) to microscopic structures (in microns). Our model (Fig 1) is comprised of a macroscale model to represent a uniaxial compression test sample (bone-growth plate-bone), a mesoscale model to represent the growth plate with its various zones, and a microscale model to represent the axial columnar organization of chondrocytes (chondrons) in the proliferative and hypertrophic zones (P/H zone).

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