Simulation of bone remodeling around a femoral prosthesis using a model that accounts for biological and mechanical interactions

Effect of different constraining boundary conditions on simulated femoral stresses and strains during gait

Finite element analysis (FEA) is commonly used in orthopaedic research to estimate localised tissue stresses and strains. A variety of boundary conditions have been proposed for isolated femur analysis, but it remains unclear how these assumed constraints influence FEA predictions of bone biomechanics. This study compared the femoral head deflection (FHD), stresses, and strains elicited under four commonly used boundary conditions (fixed knee, mid-shaft constraint, springs, and isostatic methods) and benchmarked these mechanics against the gold standard inertia relief method for normal and pathological femurs (extreme anteversion and retroversion, coxa vara, and coxa valga). Simulations were performed for the stance phase of walking with the applied femoral loading determined from patient-specific neuromusculoskeletal models. Due to unrealistic biomechanics observed for the commonly used boundary conditions, we propose a novel biomechanical constraint method to generate physiological femur biomechanics. The biomechanical method yielded FHD (< 1 mm), strains (approaching 1000 µε), and stresses (< 60 MPa), which were consistent with physiological observations and similar to predictions from the inertia relief method (average coefficient of determination = 0.97, average normalized root mean square error = 0.17). Our results highlight the superior performance of the biomechanical method compared to current methods of constraint for  both healthy and pathological femurs.

Evaluating the effect of functionally graded materials on bone remodeling around dental implants

OBJECTIVES

This study evaluates the potential for osseointegration and remodeling of customized dental implants made from Titanium-Hydroxyapatite Functionally Graded Material (Ti-HAP FGM) with optimized geometry, using the finite element method (FEM).

METHODS

The study utilized CT scan images to model and assemble various geometrical designs of dental implants in a mandibular slice. The mechanical properties of Ti-HAP FGMs were computed by varying volume fractions (VF) of hydroxyapatite (0-20%), and a bone remodeling algorithm was used to evaluate the biomechanical characteristics of the ultimate bone configuration in the peri-implant tissue.

RESULTS

The findings of the FEA reveal that osseointegration improves with changes in the density and mechanical properties of the bone surrounding Ti-HAP implants, which are influenced by the varying VF of hydroxyapatite in the FGM.

SIGNIFICANCE

Increasing the hydroxyapatite fraction improves osseointegration, and appropriate length and diameter selection of Ti-HAP dental implants contribute to their stability and longevity.

Analysis of the uniqueness and stability of solutions to problems regarding the bone-remodeling process

Simulation of the bone remodeling process is extremely important because it makes possible the structure forecast of one or several bones when anomalous situations, such as prosthesis installation, occur. Thus, it is necessary that the mathematical model to simulate the bone remodeling process be reliable; that is, the numerical solution must be stable regardless of initial density field for a phenomenological approach to model the process. For several models found in the literature, this characteristic of stability is not observed, largely due to the discontinuities present in the property values of the models (e.g., Young's modulus and Poisson's ratio). In addition, checkerboard formation and the lazy zone prevent the uniqueness of the solution. To correct these difficulties, this study proposes a set of modifications to guarantee the uniqueness and stability of the solutions, when a phenomenological approach is used. The proposed modifications are: (a) change the rate of remodeling curve in the lazy zone region and (b) create transition functions to guarantee the continuity of the expressions used to describe Young's modulus and Poisson's ratio. Moreover, the stress smoothing process controls the checkerboard formation. Numerical analysis is used to simulate the solution behavior from each proposed modification. The results show that, when all proposed modifications are applied to the three-dimensional models simulated here, it is possible to observe the tendency toward a unique solution.