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Background Bone healing process includes four phases: inflammatory response, soft callus formation, hard callus development, and remodeling. Mechanobiological models have been used to investigate the role of various mechanical and biological factors on bone healing. However, the effects of initial healing phase, which includes the inflammatory stage, the granulation tissue formation, and the initial callus formation during the first few days post-fracture, are generally neglected in such studies. Methods In this study, we developed a finite-element-based model to simulate different levels of diffusion coefficient for mesenchymal stem cell (MSC) migration, Young’s modulus of granulation tissue, callus thickness and interfragmentary gap size to understand the modulatory effects of these initial phase parameters on bone healing. Results The results quantified how faster MSC migration, stiffer granulation tissue, thicker callus, and smaller interfragmentary gap enhanced healing to some extent. However, after a certain threshold, a state of saturation was reached for MSC migration rate, granulation tissue stiffness, and callus thickness. Therefore, a parametric study was performed to verify that the callus formed at the initial phase, in agreement with experimental observations, has an ideal range of geometry and material properties to have the most efficient healing time. Conclusions Findings from this paper quantified the effects of the initial healing phase on healing outcome to better understand the biological and mechanobiological mechanisms and their utilization in the design and optimization of treatment strategies. It is also demonstrated through a simulation that for fractures, where bone segments are in close proximity, callus development is not required. This finding is consistent with the concepts of primary and secondary bone healing.

Bone fracture is a very common body injury. The healing process is physiologically complex, involving both biological and mechanical aspects. Following a fracture, cell migration, cell/tissue differentiation, tissue synthesis, and cytokine and growth factor release occur, regulated by the mechanical environment. Over the past decade, bone healing simulation and modeling has been employed to understand its details and mechanisms, to investigate specific clinical questions, and to design healing strategies. The goal of this effort is to review the history and the most recent work in bone healing simulations with an emphasis on both biological and mechanical properties. Therefore, we provide a brief review of the biology of bone fracture repair, followed by an outline of the key growth factors and mechanical factors influencing it. We then compare different methodologies of bone healing simulation, including conceptual modeling (qualitative modeling of bone healing to understand the general mechanisms), biological modeling (considering only the biological factors and processes), and mechanobiological modeling (considering both biological aspects and mechanical environment). Finally we evaluate different components and clinical applications of bone healing simulation such as mechanical stimuli, phases of bone healing, and angiogenesis., Highlights • Bone fracture healing is a series of biological processes, regulated by the mechanical environment and biological factors. • Conceptual models of bone fracture healing aim to understand the qualitative process and to formulate its general mechanism. • Mechanobiological models consider the effects of both mechanical environment and biological factors. • Mechanobiological regulations and mechanical stimuli effects on growth factors can potentially have clinical applications. • While important, the inflammatory phase in the bone healing process is not included in mechanobiological simulations.

A six-degree-of-freedom musculoskeletal model of the lumbar spine was developed to predict the activity of trunk muscles during light, moderate and heavy lifting tasks in standing posture. The model was formulated into a multi-objective optimization problem, minimizing the sum of the cubed muscle stresses and maximizing the spinal stability index. Two intelligent optimization algorithms, i.e., the vector evaluated particle swarm optimization (VEPSO) and nondominated sorting genetic algorithm (NSGA), were employed to solve the optimization problem. The optimal solution for each task was then found in the way that the corresponding in vivo intradiscal pressure could be reproduced. Results indicated that both algorithms predicted co-activity in the antagonistic abdominal muscles, as well as an increase in the stability index when going from the light to the heavy task. For all of the light, moderate and heavy tasks, the muscles’ activities predictions of the VEPSO and the NSGA were generally consistent and in the same order of the in vivo electromyography data. The proposed methodology is thought to provide improved estimations for muscle activities by considering the spinal stability and incorporating the in vivo intradiscal pressure data.

Iatrogenic injuries to paraspinal muscles during the posterior lumbar surgery (PLS) cause a reduction in their cross-sectional areas (CSAs) and contractile densities over time post-surgery. This study aims to quantify such alterations. Pre- and postoperative CSAs (~6 months interval) of all paraspinal muscles were measured in six patients undergoing PLS using a 3-T magnetic resonance (MR) scanner to quantify the alterations in geometrical and tissue effective contractile (non-fatty) CSAs of these muscles at all lumbar levels. To examine the presence of any confounding effects on recorded changes within ~7-month period, measurements were also carried out on ten healthy volunteers. In the healthy population, an important (~22 %) portion of CSA of the erector spinae (ES) was noncontractile at the lower lumbar levels. Negligible variations over time in both the total geometrical (

An anatomically detailed eighteen-rotational-degrees-of-freedom model of the human spine using optimization constrained to equilibrium and stability requirements is developed and used to simulate several symmetric tasks in upright and flexed standing postures. Predictions of this stability and kinematics-driven (S+KD) model for trunk muscle forces and spine compressive/shear loads are compared to those of our existing kinematics-driven (KD) model where both translational and rotational degrees-of-freedom are included but redundancy is resolved using equilibrium conditions alone. Unlike the KD model, the S+KD model predicted abdominal co-contractions that, in agreement with electromyography data, increased as lifting height increased at a constant horizontal moment arm. The S+KD model, however, could not fully explain the CNS strategy in activating antagonistic muscles for most of the remaining tasks. Despite quite distinct activities in individual muscles, both models predicted L4-L5 intradiscal pressure that matched the in vivo data, the L4-S1 compression loads, and the sum of all trunk muscle forces. For modeling applications in ergonomics, where the compressive spine loads are of interest, the two models yielded15% difference. In the field of rehabilitation, where detailed muscle forces are required, the S+KD model explained more properly the CNS strategy in activating the antagonistic muscles for some tasks.