A mechano-regulation model of fracture repair in vertebral bodies (original) (raw)
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Medical & Biological Engineering & Computing, 2012
In spite of the consolidated clinical use of minimally invasive percutaneous fixation techniques, little is reported in the literature providing a mechanobiological explanation for how the design of fixation devices can affect the healing process within fractured vertebrae. The aim of this study was to develop a multi-scale mechanoregulation model capable of predicting how the patterns of tissue differentiation within a vertebral fracture change in the presence or in the absence of fixation devices and how the dimensions of the device, and the materials it is made from (Ti-6Al-4V alloy and cobalt chrome alloy) can affect the outcome of the healing process. The macro-scale model simulates the spinal segment L3-L4-L5, including the fractured body of the L4 vertebra, while the micro-scale model represents a fractured portion of cancellous bone. The macro-scale model also includes a minimally invasive percutaneous fixation device. The model predicts that fixation devices significantly shorten healing times. Increasing values of the rod diameter D and decreasing values of its radius of curvature R lead to shorter durations of the healing period. Manufacturing the rods in cobalt chrome alloy is also predicted to reduce slightly the healing period by providing greater mechanical stability within the fracture callus.
Modelling bone tissue fracture and healing: a review
Engineering Fracture Mechanics, 2004
This paper reviews the available literature on computational modelling in two areas of bone biomechanics: fracture and healing. Bone is a complex material, with a multiphasic, heterogeneous and anisotropic microstructure. The processes of fracture and healing can only be understood in terms of the underlying bone structure and its mechanical role. Bone fracture analysis attempts to predict the failure of musculoskeletal structures by several possible mechanisms under different loading conditions. However, as opposed to structurally inert materials, bone is a living tissue that can repair itself. An exciting new field of research is being developed to better comprehend these mechanisms and the mechanical behaviour of bone tissue. One of the main goals of this work is to demonstrate, after a review of computational models, the main similarities and differences between normal engineering materials and bone tissue from a structural point of view. We also underline the importance of computational simulations in biomechanics due to the difficulty of obtaining experimental or clinical results.
There are obvious advantages to investigating the mechanical behavior of trabecular bone using microstructural models incorporating trabecular structure; however, they quickly become very complex and computationally intensive, even with simple models for tissue behavior. Alternatively, continuum damage mechanics (CDM) models offer the potential for characterizing the damage accumulation process and the risk of fracture in real skeletal structures. We implemented a phenomenological constitutive model based on CDM, along with a computational solution scheme, to describe the elastic and inelastic response of human vertebral trabecular bone to applied loading. Simulations using computational methods demonstrate that it is possible to obtain estimates of all model parameters from experimental data and to characterize the experimental response. The model successfully predicted damage measures, such as evolving and accumulated modulus degradation, despite the complicated nature of the material response and the limited amount of data for multiaxial material characterization. The ability to model the basic features of the response and reasonably predict the highly nonlinear behavior of low-density heterogeneous vertebral trabecular bone allows us to move closer to the goal of predicting the in vivo response or the risk of fracture in a clinical setting.
Modeling of anisotropic remodeling of trabecular bone coupled to fracture
Archive of Applied Mechanics, 2018
As a living tissue, bone is subjected to internal evolutions of its trabecular architecture under normal everyday mechanical loadings leading to damage. The repeating bone remodeling cycle aims at repairing the damaged zones in order to maintain bone structural integrity; this activity of sensing the peak stress at locations where damage or microcracks have occurred, removing old bone and apposing new bone is achieved thanks to a complicated machinery at the cellular level involving specialized cells (osteocytes, osteoclasts, and osteoblasts). This work aims at developing an integrated remodeling-to-fracture model to simulate the bone remodeling process, considering trabecular bone anisotropy. The effective anisotropic continuum mechanical properties of the trabecular bone are derived from an initially discrete planar hexagonal structure representative of femur bone microstructure, relying on the asymptotic homogenization technique. This leads to scaling laws of the effective elastic properties of bone versus effective density at an intermediate mesoscopic scale. An evolution law for the local bone apparent density is formulated in the framework of the thermodynamics of irreversible processes, whereby the driving force for density evolutions is identified as the local strain energy density weighted by the locally accumulated microdamage. We adopt a classical nonlinear damage model for high cycle fatigue under purely elastic strains, where the assumed homogeneous damage is related to the number of cycles bone experiences. Based on this model, we simulate bone remodeling for the chosen initial microstructure, showing the influence of the external mechanical stimuli on the evolution of the density of bone and the incidence of this evolution on trabecular bone effective mechanical properties. Keywords Bone remodeling • Bone damage • Discrete homogenization • Bone anisotropy • Proximal femur • FE simulations Notation B proportionality constant measuring the rate of adaptation process; B R Set of beams within the reference unit cell; C Elastic damage stiffness tensor; C 0 Virgin (undamaged) elasticity stiffness tensor;
Journal of biomechanical engineering, 2018
Vertebral fractures are common in the elderly, but efforts to reduce their incidence have been hampered by incomplete understanding of the failure processes that are involved. This study's goal was to elucidate failure processes in the lumbar vertebra and to assess the accuracy of quantitative computed tomography (QCT)-based finite element (FE) simulations of these processes. Following QCT scanning, spine segments (n = 27) consisting of L1 with adjacent intervertebral disks and neighboring endplates of T12 and L2 were compressed axially in a stepwise manner. A microcomputed tomography scan was performed at each loading step. The resulting time-lapse series of images was analyzed using digital volume correlation (DVC) to quantify deformations throughout the vertebral body. While some diversity among vertebrae was observed on how these deformations progressed, common features were large strains that developed progressively in the superior third and, concomitantly, in the midtransv...
Application of a Multi-Scale Mechanobiological Model for Bone Remodeling
Journal of Medical Imaging and Health Informatics, 2014
Bone tissue is a dynamic system capable of changing its own density in response to biomechanical stimuli. The biological system studied herein consists of three cellular types, responsive osteoblasts, active osteoblasts and osteoclasts, and four types of signaling molecules, PTH, TGF-, RANKL and OPG. This article examines the biological response to a specific mechanical stimulus in a cellular model for bone remodeling. A two-dimensional example is proposed with spatial discretization performed through the finite element method. The temporal evolution of the biological variables and bone density is obtained using the Runge-Kutta method. Deformation energy served as mechanical stimulus to trigger cellular activity demonstrating the temporal evolution of density distribution in a model of a standard femur. This distribution is in agreement with other models in the literature. The main contribution of this paper is the coupling of mechanical and biological models. Another important fact is that the results can represent the local behavior of the proposed biological variables. The given example is a first step in the development of more advanced models to represent the imbalance of bone homeostasis.
2013
Bone healing is a complex biological process which is regulated by mechanical micro-environment caused by inter-fragmentary movement (IFM). IFM generated interstitial fluid flow within the fracture callus could potentially not only affect the mesenchymal stem cells migration and differentiation during the healing, but also enhance nutrient transport within the callus tissue. In this study, a three dimensional poroelastic finite element model of a human tibia was developed to study the mechanical behaviour of the fracture callus due to IFM at the early stage of fracture. The biophysical stimuli were characterised with three main parameters involved in the healing process: octahedral shear strain, interstitial fluid velocity and pressure. The proposed algorithm represents a first step towards to the development of a powerful simulation tool for fracture healing.
Journal of Biomechanics, 2006
Most long-bone fractures heal through indirect or secondary fracture healing, a complex process in which endochondral ossification is an essential part and bone is regenerated by tissue differentiation. This process is sensitive to the mechanical environment, and several authors have proposed mechano-regulation algorithms to describe it using strain, pore pressure and/or interstitial fluid velocity as biofeedback variables. The aim of this study was to compare various mechano-regulation algorithms' abilities to describe normal fracture healing in one computational model. Additionally, we hypothesized that tissue differentiation during normal fracture healing could be equally well regulated by the individual mechanical stimuli, e.g. deviatoric strain, pore pressure or fluid velocity. A biphasic finite element model of an ovine tibia with a 3mm fracture gap and callus was used to simulate the course of tissue differentiation during normal fracture healing. The load applied was regulated in a biofeedback loop, where the load magnitude was determined by the interfragmentary movement in the fracture gap. All the previously published mechano-regulation algorithms studied, simulated the course of normal fracture healing correctly. They predicted (1) intramembranous bone formation along the periosteum and callus tip, (2) endochondral ossification within the external callus and cortical gap, and (3) creeping substitution of bone towards the gap from the initial lateral osseous bridge. Some differences between the effects of the algorithms were seen, but they were not significant. None of the volumetric components, i.e. pore pressure or fluid velocity, alone were able to correctly predict spatial or temporal tissue distribution during fracture healing. However, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing. This suggests that the deviatoric component may be the most significant mechanical parameter to guide tissue differentiation during indirect fracture healing.
Scientific Reports, 2021
Methods to repair bone defects arising from trauma, resection, or disease, continue to be sought after. Cyclic mechanical loading is well established to influence bone (re)modelling activity, in which bone formation and resorption are correlated to micro-scale strain. Based on this, the application of mechanical stimulation across a bone defect could improve healing. However, if ignoring the mechanical integrity of defected bone, loading regimes have a high potential to either cause damage or be ineffective. This study explores real-time finite element (rtFE) methods that use three-dimensional structural analyses from micro-computed tomography images to estimate effective peak cyclic loads in a subject-specific and time-dependent manner. It demonstrates the concept in a cyclically loaded mouse caudal vertebral bone defect model. Using rtFE analysis combined with adaptive mechanical loading, mouse bone healing was significantly improved over non-loaded controls, with no incidence of ...
Role of mathematical modeling in bone fracture healing
Bone fracture healing is a complex physiological process commonly described by a four-phase model consisting of an inflammatory phase, two repair phases with soft callus formation followed by hard callus formation, and a remodeling phase, or more recently by an anabolic/catabolic model. Data from humans and animal models have demonstrated crucial environmental conditions for optimal fracture healing, including the mechanical environment, blood supply and availability of mesenchymal stem cells. Fracture healing spans multiple length and time scales, making it difficult to know precisely which factors and/or phases to manipulate in order to obtain optimal fracture-repair outcomes. Deformations resulting from physiological loading or fracture fixation at the organ scale are sensed at the cellular scale by cells inside the fracture callus. These deformations together with autocrine and paracrine signals determine cellular differentiation, proliferation and migration. The local repair ac...