Growth mixture model of distraction osteogenesis: effect of pre-traction stresses

Abstract

In tensional studies of bone fragments during limb lengthening, it is usually assumed that the stress level in the gap tissue before each distraction step (pre-traction stress) is rather modest. However, during the process of distraction osteogenesis, a large interfragmentary gap is generated and these pre-traction stresses may be important. To date, to the authors' knowledge, no computational study has been developed to assess the effect of stress accumulation during limb lengthening. In this work, we present a macroscopic growth mixture formulation to investigate the influence of pre-traction stresses on the outcome of this clinical procedure. In particular, the model is applied to the simulation of the regeneration of tibial defects by means of distraction osteogenesis. The evolution of pre-traction forces, post-traction forces and peak forces is evaluated and compared with experimental data. The results show that the inclusion of pre-traction stresses in the model affects the evolution of the regeneration process and the corresponding reaction forces.

Computational modeling of bone density profiles in response to gait: a subject-specific approach

“…Within the past two decades, finite element models have been recognized as a powerful tool to investigate bone and tissue growth (Huiskes et al 1987;Jacobs et al 1995). Finite element simulations can be used to predict bone growth and resorption in response to various different loading patterns that would not be feasible to study experimentally (Reina-Romo et al 2010;Weinans et al 1992). They also allow for efficient parameter studies, which can be used to identify key contributors to bone growth (Carpenter and Carter 2010a;Hambli et al 2011), bone straightening (Carpenter and Carter 2010b), bone torsion (Taylor et al 2008), or bone failure (Gitman et al 2010;Zhang et al 2010).…”

Mechanobiological Models for Bone Tissue. Applications to Implant Design

“…Gómez-Benito et al [109][110][111] developed a continuum mathematical model of the bone healing process (Figure 4.6). It was successfully applied to simulate the influence of gap size [109], amount of interfragmentary movement [111], and external fixator stiffness [110] on the fracture healing process, and distraction osteogenesis [112]. The model simulates tissue regulation and callus growth, taking into account different cellular events (i.e., mesenchymal cell migration and proliferation; mesenchymal cells' differentiation into chondrocytes, fibroblasts, and osteoblasts, death of mesenchymal stem cells, and also the endochondral ossification process), and matrix synthesis, degradation, damage, calcification and remodeling over time.…”

“…Recently, bone healing models have been applied to simulate distraction osteogenesis [97,112,116]. Distraction osteogeneis is a surgical procedure aimed at producing a large amount of bone; it is widely used in orthopedic and craniofacial surgery.…”

“…These models have successfully simulated the effect of the distraction rate in the outcome of the process. They have predicted premature union for low distraction rates [97,112], nonunion at high distraction rates [112], and successful union at moderate rates [97,112]. The latency period has also been studied in these types of models [116].…”

Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

“…Fracture and distraction repair proceed through the same cellular healing process [43], and, therefore, most existing mechano-biological models of distraction osteogenesis are based on existing models of fracture healing, either on the mechano-regulation theory presented earlier by Prendergast et al [26,[44][45][46] or on that proposed by Gómez-Benito et al [27,47,48].…”