Mechanobiological based long bone growth model for the design of limb deformities correction devices

A numerical study towards shape memory alloys application in orthotic management of pediatric knee lateral deviations

Exerting a constant load would likely improve orthosis effectiveness in treating knee lateral deviations during childhood and early adolescence. Shape memory alloys are potential candidates for such applications due to their so called pseudoelastic effect. The present study aims to quantitatively define the applicable mechanical loads, in order to reduce treatment duration while avoiding tissular damage and patient discomfort. This is essential for performing a more efficient design of correction devices. We use a patient-specific finite elements model of a pediatric knee to determine safe loading levels. The achievable correction rates are estimated using a stochastic three-dimensional growth model. Results are compared against those obtained for a mechanical stimulus decreasing in proportion to the achieved correction, emulating the behavior of conventional orthoses. A constant flexor moment of 1.1 Nm is estimated to change femorotibial angle at a rate of (7.4 ± 4.6) deg/year (mean ± std). This rate is similar to the achieved by more invasive growth modulation methods, and represents an improvement in the order of 25% in the necessary time for reducing deformities of (10 ± 5) deg by half, as compared with conventional orthoses.

How do bones grow? A mathematical description of the mechanobiological behavior of the epiphyseal plate

Growth modulation is an emerging method for the treatment of skeletal deformities originating in the long bones or the vertebral bodies. It requires the controlled application of mechanical loads to the affected bone, causing an alteration of the growth and ossification process occurring in a cartilaginous region called epiphyseal growth plate or physis. In order to avoid the possibility of under- or over-correction, quantification of the applied forces is necessary. Pursuing this goal, here we propose a phenomenological model of mechanobiological effects on the epiphyseal growth plate, based on the observed similarity between the mechanobiologically induced growth and viscoelastic material behavior. The model incorporates mechanical loading effects on growth direction, growth rate and ossification speed; it also allows to evaluate the occurrence of transient effects. Model consistency was tested against a rather large set of experiments existing in the literature. A generic simplified geometrical model of bones was established for this. Analytical solutions for growth and ossification evolution were obtained for different loading conditions, allowing to test the ability of the model to describe bone growth under various kinds of mechanical loading conditions. Model-predicted changes regarding epiphyseal growth plate thickness as well as longitudinal growth speed are consistent with experiments in which static tension or compression were applied to long bones. Results suggest that when the mechanical load is sinusoidally variable, conflicting data existing in the literature could be explained by a previously unconsidered effect of the the applied load initial phase. The model can accurately fit data regarding torsional loads effects on growth. Mechanobiological data for humans is very scarce. For this reason, when possible, the model parameters values were estimated, for the proposed generic geometry, after growth measurements in animal models available in the literature. Although it is not possible to assert their validity for humans, the proposed model along with the obtained parameters values give a rational foundation to be used in more advanced computational studies.

Biomechanical Analysis of Staples for Epiphysiodesis

Limb asymmetry can, and often does, cause various health problems. Blount bone staples (clips) are used to correct such uneven growth. This article analyzes the performance of a biomechanical staple during bone (tibia) growth arrest. The staples considered in this study were made of 1.4441 stainless steel, the model of tibia consisted of two materials representing corticalis and spongiosis. Hooke’s law was used for modeling materials’ behaviors for finite element analysis (FEA). The maxima of stress and total staple displacement were evaluated using the finite element method and verification of the results, along with the determination of the maximum loading (growing) force that the staples are capable of withstanding, was performed experimentally. The presented method can be used to determine the safety and usability of staples for bone growth arrest. According to our results, the design of Blount staples considered in this paper is safe and suitable for orthopedic treatment.

A tool for solving bone growth related problems using finite elements adaptive meshes

Long bones geometry changes in response to longitudinal growth in the epiphyseal plates and hydroxyapatite apposition in the periosteum. Due to its relevance for growth modulation and orthotics performance, researchers have extensively modeled these phenomena, using the finite elements method for it almost since the introduction of modern computers. This is a rather complex task that, besides the inherent difficulty of solving the models equations, requires considering a moving boundary. Here, the development of a new computational tool for its resolution is described. A generalized formulation of these problems is established based on the most common approaches taken in the literature and a novel finite elements algorithm is proposed for its resolution. The later allows a significant reduction of the spatial discretization requirements, the computational cost and the numerical errors associated with more classical approaches. The potentiality of the method is demonstrated by its application to three cases of practical interest, namely, hemiepiphysiodesis treatment, growth in the distal femur and bone remodeling around hip prosthesis. Eight relevant cases of study and an open source implementation of the proposed algorithm are also provided as supplementary material.