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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

Determination of the elastic moduli of the growth plate utilized in the models.(A) Stained histological slice (haematoxylin and eosin) of a 4-month old bovine growth plate; chondrocytes are dispersed in the reserve zone (RZ) and are stacked in tubes (chondrons) extending from the zone of proliferation (P) through the zones of maturation and hypertrophy (H). The walls of the chondron tubes (interterritorial matrix) become increasingly calcified toward the metaphyseal side. Following chondrocyte death, the walls of tubes or bars of calcified cartilage (CC) matrix form the scaffolding upon which bone is laid down (primary spongiosa); scale bar = 100 μm. (B) Distribution of the elastic modulus of the P/H zone (3-layer mesoscale and 10-layer mesocale models) and interterritorial matrix (ITM) (microscale model).
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pone.0124862.g002: Determination of the elastic moduli of the growth plate utilized in the models.(A) Stained histological slice (haematoxylin and eosin) of a 4-month old bovine growth plate; chondrocytes are dispersed in the reserve zone (RZ) and are stacked in tubes (chondrons) extending from the zone of proliferation (P) through the zones of maturation and hypertrophy (H). The walls of the chondron tubes (interterritorial matrix) become increasingly calcified toward the metaphyseal side. Following chondrocyte death, the walls of tubes or bars of calcified cartilage (CC) matrix form the scaffolding upon which bone is laid down (primary spongiosa); scale bar = 100 μm. (B) Distribution of the elastic modulus of the P/H zone (3-layer mesoscale and 10-layer mesocale models) and interterritorial matrix (ITM) (microscale model).

Mentions: Three individual layers were generated in the P/H zone of the growth plate (Fig 1B) to represent the change of elastic modulus through the thickness of the cartilage (Table 1) [36]. The elastic moduli of the individual layers of the P/H zone were adjusted iteratively (Fig 2) so that the overall effective stiffness of the 3-layer mesoscale model was 0.49 MPa, which is the same as the model with a single P/H layer (macro-scale model). An intermediate model (not shown) consisting of 10 layers in the P/Z zone was created to reduce the influence of mismatch of elastic modulus between the 3-layer P/H zone in the mesoscale model and the microscale chondron model containing 45 cells. The same iterative experimental-data-informed method was used to adjust individual layer moduli so that the overall stiffness was the same as that for the macroscale model, i.e. an effective response of 0.49 MPa. In order to obtain the effective response of the 3-layered or 10-layered mesoscale models, each multilayered mesoscale model was uniaxially compressed and a stress-strain response was obtained to compute an effective elastic modulus. This is similar to the inverse methods that we carried out in our previous work in which we determined the intrinsic elastic modulus of the bovine growth plate [34]. The resulting input material parameters of the mesoscale models are shown in Fig 2. Three-layered and 10-layered model consisted of 159,848 and 119,700 C3D8RH elements, respectively.


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

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

Determination of the elastic moduli of the growth plate utilized in the models.(A) Stained histological slice (haematoxylin and eosin) of a 4-month old bovine growth plate; chondrocytes are dispersed in the reserve zone (RZ) and are stacked in tubes (chondrons) extending from the zone of proliferation (P) through the zones of maturation and hypertrophy (H). The walls of the chondron tubes (interterritorial matrix) become increasingly calcified toward the metaphyseal side. Following chondrocyte death, the walls of tubes or bars of calcified cartilage (CC) matrix form the scaffolding upon which bone is laid down (primary spongiosa); scale bar = 100 μm. (B) Distribution of the elastic modulus of the P/H zone (3-layer mesoscale and 10-layer mesocale models) and interterritorial matrix (ITM) (microscale model).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0124862.g002: Determination of the elastic moduli of the growth plate utilized in the models.(A) Stained histological slice (haematoxylin and eosin) of a 4-month old bovine growth plate; chondrocytes are dispersed in the reserve zone (RZ) and are stacked in tubes (chondrons) extending from the zone of proliferation (P) through the zones of maturation and hypertrophy (H). The walls of the chondron tubes (interterritorial matrix) become increasingly calcified toward the metaphyseal side. Following chondrocyte death, the walls of tubes or bars of calcified cartilage (CC) matrix form the scaffolding upon which bone is laid down (primary spongiosa); scale bar = 100 μm. (B) Distribution of the elastic modulus of the P/H zone (3-layer mesoscale and 10-layer mesocale models) and interterritorial matrix (ITM) (microscale model).
Mentions: Three individual layers were generated in the P/H zone of the growth plate (Fig 1B) to represent the change of elastic modulus through the thickness of the cartilage (Table 1) [36]. The elastic moduli of the individual layers of the P/H zone were adjusted iteratively (Fig 2) so that the overall effective stiffness of the 3-layer mesoscale model was 0.49 MPa, which is the same as the model with a single P/H layer (macro-scale model). An intermediate model (not shown) consisting of 10 layers in the P/Z zone was created to reduce the influence of mismatch of elastic modulus between the 3-layer P/H zone in the mesoscale model and the microscale chondron model containing 45 cells. The same iterative experimental-data-informed method was used to adjust individual layer moduli so that the overall stiffness was the same as that for the macroscale model, i.e. an effective response of 0.49 MPa. In order to obtain the effective response of the 3-layered or 10-layered mesoscale models, each multilayered mesoscale model was uniaxially compressed and a stress-strain response was obtained to compute an effective elastic modulus. This is similar to the inverse methods that we carried out in our previous work in which we determined the intrinsic elastic modulus of the bovine growth plate [34]. The resulting input material parameters of the mesoscale models are shown in Fig 2. Three-layered and 10-layered model consisted of 159,848 and 119,700 C3D8RH elements, respectively.

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