A microstructural finite element simulation of mechanically induced bone formation

Relating Bone Strain to Local Changes in Radius Microstructure Following 12 Months of Axial Forearm Loading in Women

Work in animal models suggests that bone structure adapts to local bone strain, but this relationship has not been comprehensively studied in humans. Here, we quantified the influence of strain magnitude and gradient on bone adaptation in the forearm of premenopausal women performing compressive forearm loading (n = 11) and nonloading controls (n = 10). High resolution peripheral quantitative computed tomography (HRpQCT) scans of the distal radius acquired at baseline and 12 months of a randomized controlled experiment were used to identify local sites of bone formation and resorption. Bone strain was estimated using validated finite element (FE) models. Trabecular strain magnitude and gradient were higher near (within 200 μm) formation versus resorption (p < 0.05). Trabecular formation and resorption occurred preferentially near very high (>95th percentile) versus low (<5th percentile) strain magnitude and gradient elements, and very low strain elements were more likely to be near resorption than formation (p < 0.05). In the cortical compartment, strain gradient was higher near formation versus resorption (p < 0.05), and both formation and resorption occurred preferentially near very high versus low strain gradient elements (p < 0.05). At most, 54% of very high and low strain elements were near formation or resorption only, and similar trends were observed in the control and load groups. These findings suggest that strain, likely in combination with other physiological factors, influences adaptation under normal loads and in response to a novel loading intervention, and represents an important step toward defining exercise interventions to maximize bone strength.

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

Improved methods to analyze and compare the muscle-based influences that drive bone strength adaptation can aid in the understanding of the wide array of experimental observations about the effectiveness of various mechanical countermeasures to losses in bone strength that result from age, disuse, and reduced gravity environments. The coupling of gradient-based and gradientless numerical optimization routines with finite element methods in this work results in a modeling technique that determines the individual magnitudes of the muscle forces acting in a multisegment musculoskeletal system and predicts the improvement in the stress state uniformity and, therefore, strength, of a targeted bone through simulated local cortical material accretion and resorption. With a performance-based stopping criteria, no experimentally based or system-based parameters, and designed to include the direct and indirect effects of muscles attached to the targeted bone as well as to its neighbors, shape and strength alterations resulting from a wide range of boundary conditions can be consistently quantified. As demonstrated in a representative parametric study, the developed technique effectively provides a clearer foundation for the study of the relationships between muscle forces and the induced changes in bone strength. Its use can lead to the better control of such adaptive phenomena.

Strain energy density gradients in bone marrow predict osteoblast and osteoclast activity: a finite element study

Huiskes et al. hypothesized that mechanical strains sensed by osteocytes residing in trabecular bone dictate the magnitude of load-induced bone formation. More recently, the mechanical environment in bone marrow has also been implicated in bone׳s response to mechanical stimulation. In this study, we hypothesize that trabecular load-induced bone formation can be predicted by mechanical signals derived from an integrative µFE model, incorporating a description of both the bone and marrow phase. Using the mouse tail loading model in combination with in vivo micro-computed tomography (µCT) we tracked load induced changes in the sixth caudal vertebrae of C57BL/6 mice to quantify the amount of newly mineralized and eroded bone volumes. To identify the mechanical signals responsible for adaptation, local morphometric changes were compared to micro-finite element (µFE) models of vertebrae prior to loading. The mechanical parameters calculated were strain energy density (SED) on trabeculae at bone forming and resorbing surfaces, SED in the marrow at the boundary between bone forming and resorbing surfaces, along with SED in the trabecular bone and marrow volumes. The gradients of each parameter were also calculated. Simple regression analysis showed mean SED gradients in the trabecular bone matrix to significantly correlate with newly mineralized and eroded bone volumes R(2)=0.57 and 0.41, respectively, p<0.001). Nevertheless, SED gradients in the marrow were shown to be the best predictor of osteoblastic and osteoclastic activity (R(2)=0.83 and 0.60, respectively, p<0.001). These data suggest that the mechanical environment of the bone marrow plays a significant role in determining osteoblast and osteoclast activity.

Influence of Clinically Relevant Factors on the Immediate Biomechanical Surrounding for a Series of Dental Implant Designs

The objective of the present study was to assess the influence of various clinically relevant scenarios on the strain distribution in the biomechanical surrounding of five different dental implant macrogeometries. The biomechanical environment surrounding an implant, i.e., the cortical and trabecular bone, was modeled along with the implant. These models included two different values of the study parameters including loading conditions, trabecular bone elastic modulus, cortical/trabecular bone thickness ratio, and bone loss for five implant designs. Finite element analysis was conducted on the models and strain in the bones surrounding the implant was calculated. Bone volumes having strains in four different windows of 0–200 με, 200–1000 με, 1000–3000 με, and >3000 με were measured and the effect of each biomechanical variable and their two-way interactions were statistically analyzed using the analysis of variance method. This study showed that all the parameters included in this study had an effect on the volume of bones in all strain windows, except the implant design, which affected only the 0–200 με and >3000 με windows. The two-way interaction results showed that interactions existed between implant design and bone loss, and loading condition, bone loss in the 200–1000 με window, and between implant design and loading condition in the 0–200 με window. Within the limitations of the present methodology, it can be concluded that although some unfavorable clinical scenarios demonstrated a higher volume of bone in deleterious strain levels, a tendency toward the biomechanical equilibrium was evidenced regardless of the implant design.

In vivo model for evaluating the effects of mechanical stimulation on tissue-engineered bone repair

It has long been known that the bone adapts according to the local mechanical environment. To date, however, a model for studying the effects of functional mechanical loading on tissue-engineered bone repair in vivo has not yet been established. We have developed a rat femoral defect model, in which ambulatory loads are transduced through the implanted tissue-engineered construct to elucidate the role of the mechanical environment in functional restoration of a large bone defect. This model uses compliant fixation plates with integrated elastomeric segments, which allow transduction of ambulatory loads. Multiaxially and uniaxially compliant plates were characterized by mechanical testing and evaluated using in vivo pilot studies. In the first study, experimental limbs were implanted with multiaxial plates, which have a low stiffness in multiple loading modes. In the second study, experimental limbs were stabilized by a uniaxial plate, which allowed only axial deformation of the defect. X-ray scans and mechanical testing revealed that the multiaxial plates were insufficient to stabilize the defect and prevent fracture under ambulatory loads as a result of low flexural and torsional stiffness. The uniaxial plates, however, maintained integrity of the defect when implanted over a 12 week period. Postmortem microCT scans revealed a 19% increase in bone volume in the axially loaded limb compared with the contralateral standard control, and postmortem mechanical testing indicated that torsional strength and stiffness were increased 25.6- and 3.9-fold, respectively, compared with the control. Finite element modeling revealed high strain gradients in the soft tissue adjacent to the newly formed bone within the implanted construct. This study introduces an in vivo model for studying the effects of physiological mechanical loading on tissue-engineered bone repair. Preliminary results using this new in vivo model with the uniaxially compliant plate showed positive effects of load-bearing on functional defect repair.

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.