Multi-scale finite element model of growth plate damage during the development of slipped capital femoral epiphysis

Abstract

Slipped capital femoral epiphysis (SCFE) is one of the most common disorders of adolescent hips. A number of works have related the development of SCFE to mechanical factors. Due to the difficulty of diagnosing SCFE in its early stages, the disorder often progresses over time, resulting in serious side effects. Therefore, the development of a tool to predict the initiation of damage in the growth plate is needed. Because the growth plate is a heterogeneous structure, to develop a precise and reliable model, it is necessary to consider this structure from both macro- and microscale perspectives. Thus, the main objective of this work is to develop a numerical multi-scale model that links damage occurring at the microscale to damage occurring at the macroscale. The use of this model enables us to predict which regions of the growth plate are at high risk of damage. First, we have independently analyzed the microscale to simulate the microstructure under shear and tensile tests to calibrate the damage model. Second, we have employed the model to simulate damage occurring in standardized healthy and affected femurs during the heel-strike stage of stair climbing. Our results indicate that on the macroscale, damage is concentrated in the medial region of the growth plate in both healthy and affected femurs. Furthermore, damage to the affected femur is greater than damage to the healthy femur from both the micro- and macrostandpoints. Maximal damage is observed in territorial matrices. Furthermore, simulations illustrate that little damage occurs in the reserve zone. These findings are consistent with previous findings reported in well-known experimental works.

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

“…The fact that damage is assumed only in the deviatoric part of the model means that, for a completely damaged structure, a volumetric quasi‐incompressible contribution will remain undamaged. Thus, considering CDM, a damaged material is characterized by voids resulting in a loss of the stiffness and strength of each constituent of the mixture . Moreover, we assume that there is no damage occurring in the SMC contribution.…”

“…The damage model here is formulated in agreement with the principles of CDM applied in many mechanobiological studies . Therefore, it is assumed that apparent density of damage evolves with mechanical loadings.…”

“…Thus, considering CDM, a damaged material is characterized by voids resulting in a loss of the stiffness and strength of each constituent of the mixture. 19,44 Moreover, we assume that there is no damage occurring in the SMC contribution. Considering these features and consistently with the CMT, it is assumed that the SEF of the arterial wall is a mass averaged function; consequently, the total specific Helmholtz free energy function can be written as…”

“…To address such issue, numerical models of arterial walls, based on an appropriate finite-element (FE) damage model, can be very helpful. Over the last decades, many phenomenological and micromechanical models have been proposed to predict the damage evolution in soft 4,[15][16][17][18] and hard 19,20 tissues. The first damage model of soft tissues can be traced back to the 1970s.…”

“…Damage models can be categorized in 3 groups: (1) deterministic models in which a pseudoelastic strain energy function (SEF) with a few parameters or damage variables of continuum damage mechanics (CDM) is used to characterize the softening/damage effect, either isotropically 19,23 or anisotropically 24-26 ; (2) probabilistic models in which probabilistic damage process and/or fiber recruitment can be included 27,28 ; and (3) microstructural-based damage models of collagen fibers in which the microscopic damage behavior of individual collagen fibrils is considered and homogenized macroscopically. 29 All these formulations can be categorized as nonlocal 4 or local [15][16][17][18][19][20] damage models. In the nonlocal methodologies, an integral-type nonlocal averaging scheme is used in the constitutive equations to limit the localization phenomena of damage variables and to overcome the mesh pathology.…”