Large-scale microstructural simulation of load-adaptive bone remodeling in whole human vertebrae

Identification of individuals at risk of bone fractures remains challenging despite recent advances in bone strength assessment. In particular, the future degradation of the microstructure and load adaptation has been disregarded. Bone remodeling simulations have so far been restricted to small-volume samples. Here, we present a large-scale framework for predicting microstructural adaptation in whole human vertebrae. The load-adaptive bone remodeling simulations include estimations of appropriate bone loading of three load cases as boundary conditions with microfinite element analysis. Homeostatic adaptation of whole human vertebrae over a simulated period of 10 years is achieved with changes in bone volume fraction (BV/TV) of less than 5 %. Evaluation on subvolumes shows that simplifying boundary conditions reduces the ability of the system to maintain trabecular structures when keeping remodeling parameters unchanged. By rotating the loading direction, adaptation toward new loading conditions could be induced. This framework shows the possibility of using large-scale bone remodeling simulations toward a more accurate prediction of microstructural changes in whole human bones.     

Predictions of bone remodeling around dental implant systems

This study presents the implementation of a mathematical bone remodeling algorithm to bone adaptation in the premolar area of the mandible around various dental implant systems, and thus sheds a new perspective to the complex interactions in dental implant mechanics. A two-dimensional, plane strain model of the bone was built from a CT-scan. The effect of implant contour on internal bone remodeling was investigated by considering four dental implant systems with contours similar to commercially available ones and another four with cylindrical and conical cross-sections. The remodeling algorithm predicts non-homogeneous density/elastic modulus distribution; and, implant contour has some effect on how this is distributed. Bone density is predicted to increase on the tips of the threads of the implants, but to decrease inside the grooves. Threadless implants favor to develop a softer bone around their periphery, compared to implant systems that have threads. The overall contour (dimensions and the shape) of an implant affect the bone density redistribution, but the differences between different implant systems are relatively small.     

Periosteal and endosteal control of bone remodeling under torsional loading.

The shape changes that occur in the mid-diaphysis of a long bone due to adaptive remodeling induced by increasing or decreasing the axial and/or torsional loading of the bone are investigated using a simple model. In this model the mid-diaphysis of a long bone is represented as a hollow thick-walled right-circular cylinder, and different optimal strategies for bone remodeling are considered. It is shown that if such a thick-walled right-circular cylinder capable of surface remodeling is subjected to an axial compressive load and a twisting torque, then the remodeling patterns depend on whether the periosteal surface or the endosteal surface controls the limits of the remodeling process. It is shown that the effect of increasing the torque is always opposite to the effect of increasing the compressive load. Thus, similar remodeling patterns are obtained by increasing one type of loading and decreasing the other. Aside from the restriction of idealized cylindrical geometry, the only assumptions made are that the bone tissue is linearly elastic and that there exists a finite range of remodeling equilibrium stresses. Only those loading situations which maintain the bone in remodeling equilibrium are considered in this work. It follows that the results presented are independent of the specific type of rule governing the temporal evolution of the bone shape, since any such rule applies only in situations where there is active remodeling and, hence, no remodeling equilibrium.     

On the optimal shape of hip implants

The success of a total hip arthroplasty is strongly related to the initial stability of the femoral component and to the stress shielding effect. In fact, for cementless stems, initial stability is essential to promote bone ingrowth into the stem coating. An inefficient primary stability is also a cause of thigh pain. In addition, the bone adaptation after the surgery can lead to an excessive bone loss and, consequently, can compromise the success of the implant. These factors depend on prosthesis design, namely on material, interface conditions and shape. Although, surgeons use stems with very different geometries, new computational tools using structural optimization methods have been used to achieve a better design in order to improve initial stability and therefore, the implant durability. In this work, a multi-criteria shape optimization process is developed to study the relationship between implants performance and geometry. The multi-criteria objective function takes into account the initial stability of the femoral stem and the effect of stress shielding on bone adaptation after the surgery. Then, the optimized stems are tested using a concurrent model for bone remodeling and osseointegration to evaluate long-term performance. Additionally, the sensitivity to misalignments is analyzed, since femoral stems are often placed in varus or valgus position. Results show that the different criteria are contradictory resulting in different characteristics for the hip stem. However, the multi-criteria formulation leads to compromise solutions, with a combination of the geometric characteristics obtained for each criterion separately.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

A Femur-Implant Model for the Prediction of Bone Remodeling Behavior Induced by Cementless Stem

Bone remodeling simulation is an effective tool for the prediction of long-term effect of implant on the bone tissue, as well as the selection of an appropriate implant in terms of architecture and material. In this paper, a finite element model of proximal femur was developed to simulate the structures of internal trabecular and cortical bones by incorporating quantitative bone functional adaptation theory with finite element analysis. Cementless stems made of titanium, two types of Functionally Graded Material (FGM) and flexible ‘iso-elastic’ material as comparison were implanted in the structure of proximal femur respectively to simulate the bone remodeling behaviors of host bone. The distributions of bone density, von Mises stress, and interface shear stress were obtained. All the prosthetic stems had effects on the bone remodeling behaviors of proximal femur, but the degrees of stress shielding were different. The amount of bone loss caused by titanium implant was in agreement with the clinical observation. The FGM stems caused less bone loss than that of the titanium stem, in which FGM I stem (titanium richer at the top to more HAP/Col towards the bottom) could relieve stress shielding effectively, and the interface shear stresses were more evenly distributed in the model with FGM I stem in comparison with those in the models with FGM II (titanium and bioglass) and titanium stems. The numerical simulations in the present study provided theoretical basis for FGM as an appropriate material of femoral implant from a biomechanical point of view. The next steps are to fabricate FGM stem and to conduct animal experiments to investigate the effects of FGM stem on the remodeling behaviors using animal model.     

Projection geometry and stress-reduction techniques in craniofacial surgery

Since 1981, we have been able to modify the mathematical patterns of projection geometry to reshape the skull in craniofacial surgery. Unlike burring, morcellization, rotation, and plate switching, this technique actually changes the shape of individual sections of the skull by changing their radius of curvature. The technique is an adaptation of the principles used by engineers to build complex structures such as ships' hulls, airfoils, and domes. The result is a rigid form of the desired shape that becomes permanent with healing. This has several advantages: 1. An increase in the level of safety of craniofacial procedures for remodeling the skull. This is so because there is no need to dissect normal areas as in the standard plate-switching techniques. 2. Decreased operating room time. 3. An increased range of surgical manipulations. No longer is the surgeon limited to the shape of the material present. 4. Relief of edge pressure on the frontal lobes during scalp closure. 5. Creation of a solid bony form over which the pericranial scalp flap can be draped to form new layers of bone.     

An evolutionary Wolff's law for trabecular architecture.

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of the model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.     

Comparison of different hip prosthesis shapes considering micro-level bone remodeling and stress-shielding criteria using three-dimensional design space topology optimization

Since the late 1980s, computational analysis of total hip arthroplasty (THA) prosthesis components has been completed using macro-level bone remodeling algorithms. The utilization of macro-sized elements requires apparent bone densities to predict cancellous bone strength, thereby, preventing visualization and analysis of realistic trabecular architecture. In this study, we utilized a recently developed structural optimization algorithm, design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur pre- and post-THA. The computational simulation facilitated direct performance comparison between two commercially available prosthetic implant stems from Zimmer Inc.: the Alloclassic and the Mayo conservative. The novel micro-level approach allowed the unique ability to visualize the trabecular bone adaption post-operation and to quantify the changes in bone mineral content by region. Stress-shielding and strain energy distribution were also quantified for the immediate post-operation and the stably fixated, post-remodeling conditions. Stress-shielding was highest in the proximal region and remained unchanged post-remodeling; conversely, the mid and distal portions show large increases in stress, suggesting a distal shift in the loadpath. The Mayo design conserves bone mass, while simultaneously reducing the incidence of stress-shielding compared to the Alloclassic, revealing a key benefit of the distinctive geometry. Several important factors for stable fixation, determined in clinical evaluations from the literature, were evident in both designs: high levels of proximal bone loss and distal bone densification. The results suggest this novel computational framework can be utilized for comparative hip prosthesis shape, uniquely considering the post-operation bone remodeling as a design criterion.     

Computational simulation of simultaneous cortical and trabecular bone change in human proximal femur during bone remodeling

In this study, we developed a numerical framework that computationally determines simultaneous and interactive structural changes of cortical and trabecular bone types during bone remodeling, and we investigated the structural correlation between the two bone types in human proximal femur. We implemented a surface remodeling technique that performs bone remodeling in the exterior layer of the cortical bone while keeping its interior area unchanged. A micro-finite element (μFE) model was constructed that represents the entire cortical bone and full trabecular architecture in human proximal femur. This study simulated and compared the bone adaptation processes of two different structures: (1) femoral bone that has normal cortical bone shape and (2) perturbed femoral bone that has an artificial bone lump in the inferomedial cortex. Using the proposed numerical method in conjunction with design space optimization, we successfully obtained numerical results that resemble actual human proximal femur. The results revealed that actual cortical bone, as well as the trabecular bone, in human proximal femur has structurally optimal shapes, and it was also shown that a bone abnormality that has little contribution to bone structural integrity tends to disappear. This study also quantitatively determined the structural contribution of each bone: when the trabecular adaptation was complete, the trabecular bone supported 54% of the total load in the human proximal femur while the cortical bone carried 46%.     

The importance of mechanical loading in bone biology and medicine

This paper discusses the premise that the skeleton is primarily a mechanical organ, and reviews the reasons that mechanical factors play a major role in bone biology. It begins by considering three basic observations: (1) Galileo's observation that bone proportions become more robust as the species' overall size increases; (2) da Vinci's observation that larger structures are inherently weaker than smaller structures subjected to the same stress; and (3) the general observation that each unit of bone mass provides structural support for about 15 units of soft tissue organ mass. Together, these observations lead to the concept that it can be advantageous to minimize bone mass, consistent with constraints on other factors. This premise is discussed here in relation to the phenomenon of bone remodeling, which is seen to serve two purposes: the adjustment of bone mass and geometry to maintain peak bone strains at their maximum tolerable values, and the continual removal of fatigue damage produced at those strain levels. Finally, it is observed that bone remodeling apparently originated approximately 250 million years ago when the first vertebrates of substantial size became weight-bearing on land, suggesting that mechanical forces associated with weight-bearing were instrumental in the evolution of bone remodeling.     

Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.     

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale (～10 μm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale (～10 cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10⁴ length scale (from ～10 μm to ～10 cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.     

Intrasac pressure changes and vascular remodeling after endovascular repair of abdominal aortic aneurysms: review and biomechanical model simulation

In this paper, we review existing clinical research data on post-endovascular repair (EVAR) intrasac pressure and relation with abdominal aortic aneurysm (AAA) size changes. Based on the review, we hypothesize that intrasac pressure has a significant impact on post-EVAR AAA size changes, and post-EVAR remodeling depends also on how the pressure has changed over a period of time. The previously developed model of an AAA based on a constrained mixture approach is extended to include vascular adaptation after EVAR using an idealized geometry. Computational simulation shows that the same mechanism of collagen stress-mediated remodeling in AAA expansion induces the aneurysm wall to shrink in a reduced sac-pressure after post-EVAR. Computational simulation suggests that the intrasac pressure of 60 mm?Hg is a critical value. At this value, the AAA remains stable, while values above cause the AAA to expand and values below cause the AAA to shrink. There are, however, variations between individuals due to different cellular sensitivities in stress-mediated adaptation. Computer simulation also indicates that an initial decrease in intrasac pressure helps the AAA shrink even if the pressure increases after some time. The presented study suggests that biomechanics has a major effect on initial adaptation after EVAR and also illustrates the utility of a computational model of vascular growth and remodeling in predicting diameter changes during the progression and after the treatment of AAAs.     

Bone remodelling of the scapula after a total shoulder arthroplasty

According to Wolff’s law, the changes in stress after a prosthesis implantation may modify the shape and internal structure of bone, thus compromising the long-term prosthesis fixation and, consequently, be a significant factor for glenoid loosening. The aim of the present study is to evaluate the changes in the bone adaptation process of the scapula after an anatomical and reverse total shoulder arthroplasty. Five finite element models of the implanted scapula are developed considering the implantation of three anatomical, cemented, all-polyethylene components; an anatomical, cementless, metal-backed component; and a reverse, all-metal component. The methodology followed to simulate the bone adaptation of the scapula was previously validated for the intact model, prior to the prosthesis implantation. Additionally, the influence of the bone quality on the adaptation process is also investigated by considering an osteoporotic condition. The results show that the stress shielding phenomenon is more concerning in cementless, metal-based components than in cemented, all-polyethylene components, regardless of the bone quality. Consequently, as far as the bone adaptation process of the bone is concerned, cemented, all-polyethylene components are better suited for the treatment of the shoulder joint.     

Assessment of Shape Changes of Mistletoe Berries: A New Software Approach to Automatize the Parameterization of Path Curve Shaped Contours

Photographs of mistletoe (Viscum album L.) berries taken by a permanently fixed camera during their development in autumn were subjected to an outline shape analysis by fitting path curves using a mathematical algorithm from projective geometry. During growth and maturation processes the shape of mistletoe berries can be described by a set of such path curves, making it possible to extract changes of shape using one parameter called Lambda. Lambda describes the outline shape of a path curve. Here we present methods and software to capture and measure these changes of form over time. The present paper describes the software used to automatize a number of tasks including contour recognition, optimization of fitting the contour via hill-climbing, derivation of the path curves, computation of Lambda and blinding the pictures for the operator. The validity of the program is demonstrated by results from three independent measurements showing circadian rhythm in mistletoe berries. The program is available as open source and will be applied in a project to analyze the chronobiology of shape in mistletoe berries and the buds of their host trees.