Computational modeling of bone fracture non-unions: four clinically relevant case studies

Model-Based Design to Enhance Neotissue Formation in Additively Manufactured Calcium-Phosphate-Based Scaffolds

In biomaterial-based bone tissue engineering, optimizing scaffold structure and composition remains an active field of research. Additive manufacturing has enabled the production of custom designs in a variety of materials. This study aims to improve the design of calcium-phosphate-based additively manufactured scaffolds, the material of choice in oral bone regeneration, by using a combination of in silico and in vitro tools. Computer models are increasingly used to assist in design optimization by providing a rational way of merging different requirements into a single design. The starting point for this study was an in-house developed in silico model describing the in vitro formation of neotissue, i.e., cells and the extracellular matrix they produced. The level set method was applied to simulate the interface between the neotissue and the void space inside the scaffold pores. In order to calibrate the model, a custom disk-shaped scaffold was produced with prismatic canals of different geometries (circle, hexagon, square, triangle) and inner diameters (0.5 mm, 0.7 mm, 1 mm, 2 mm). The disks were produced with three biomaterials (hydroxyapatite, tricalcium phosphate, and a blend of both). After seeding with skeletal progenitor cells and a cell culture for up to 21 days, the extent of neotissue growth in the disks' canals was analyzed using fluorescence microscopy. The results clearly demonstrated that in the presence of calcium-phosphate-based materials, the curvature-based growth principle was maintained. Bayesian optimization was used to determine the model parameters for the different biomaterials used. Subsequently, the calibrated model was used to predict neotissue growth in a 3D gyroid structure. The predicted results were in line with the experimentally obtained ones, demonstrating the potential of the calibrated model to be used as a tool in the design and optimization of 3D-printed calcium-phosphate-based biomaterials for bone regeneration.

Early Resistance Rehabilitation Improves Functional Regeneration Following Segmental Bone Defect Injury

Mechanical loading is integral to bone development and repair. The application of mechanical loads through rehabilitation are regularly prescribed as a clinical aide following severe bone injuries. However, current rehabilitation regimens typically involve long periods of non-loading and rely on subjective patient feedback, leading to muscle atrophy and soft tissue fibrosis. While many pre-clinical studies have focused on unloading, ambulatory loading, or direct mechanical compression, rehabilitation intensity and its impact on the local strain environment and subsequent bone healing have largely not been investigated. This study combines implantable strain sensors and subject-specific finite element models in a pre-clinical rodent model with a defect size on the cusp of critically-sized. Animals were enrolled in either high or low intensity rehabilitation one week post injury to investigate how rehabilitation intensity affects the local mechanical environment and subsequent functional bone regeneration. The high intensity rehabilitation animals were given free access to running wheels with resistance, which increased local strains within the regenerative niche by an average of 44% compared to the low intensity (no-resistance) group. Finite element modeling demonstrated that resistance rehabilitation significantly increased compressive strain by a factor of 2.0 at week 1 and 4.45 after 4 weeks of rehabilitation. The resistance rehabilitation group had significantly increased regenerated bone volume and higher bone bridging rates than its sedentary counterpart (bone volume: 22.00 mm3 ± 4.26 resistance rehabilitation vs 8.00 mm3 ± 2.27 sedentary; bridging rates: 90% resistance rehabilitation vs 50% sedentary). In addition, animals that underwent resistance running had femurs with improved mechanical properties compared to those left in sedentary conditions, with failure torque and torsional stiffness values matching their contralateral, intact femurs (stiffness: 0.036 Nm/deg ± 0.006 resistance rehabilitation vs 0.008 Nm/deg ± 0.006 sedentary). Running on a wheel with no resistance rehabilitation also increased bridging rates (100% no resistance rehabilitation vs 50% sedentary). Analysis of bone volume and von Frey suggest no-resistance rehabilitation may improve bone regeneration and hindlimb functionality. These results demonstrate the potential for early resistance rehabilitation as a rehabilitation regimen to improve bone regeneration and functional recovery.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

A Multidisciplinary Journey towards Bone Tissue Engineering

Millions of patients suffer yearly from bone fractures and disorders such as osteoporosis or cancer, which constitute the most common causes of severe long-term pain and physical disabilities. The intrinsic capacity of bone to repair the damaged bone allows normal healing of most small bone injuries. However, larger bone defects or more complex diseases require additional stimulation to fully heal. In this context, the traditional routes to address bone disorders present several associated drawbacks concerning their efficacy and cost-effectiveness. Thus, alternative therapies become necessary to overcome these limitations. In recent decades, bone tissue engineering has emerged as a promising interdisciplinary strategy to mimic environments specifically designed to facilitate bone tissue regeneration. Approaches developed to date aim at three essential factors: osteoconductive scaffolds, osteoinduction through growth factors, and cells with osteogenic capability. This review addresses the biological basis of bone and its remodeling process, providing an overview of the bone tissue engineering strategies developed to date and describing the mechanisms that underlie cell-biomaterial interactions.

Numerical evaluation of the mechanical environment of a fractured long bone for osteoporotic and non-osteoporotic subjects

Competent fracture healing monitoring requires an extensive knowledge of the evolution of the mechanical environment of the healing bone during daily-life activities such as walking. Fractures are caused due to a traumatic incidence, while low trauma or fragility fractures can also occur due to osteoporosis. It is expected that the mechanical behavior of healing bones differs among osteoporotic and non-osteoporotic subjects. This work presents finite element simulations of gait analysis considering a fractured long bone at the hematoma stage. The aim is to investigate the evolution of the mechanical environment of the femur for an osteoporotic and a non-osteoporotic subject. This is the first computational study providing quantitative information for the impact of osteoporosis on the mechanical environment of the femur. It was shown, that higher deformation and equivalent stress values are calculated for osteoporotic bones during a gait cycle, while the highest values were observed in the femoral head.

Computational Modeling to Quantify the Contributions of VEGFR1, VEGFR2, and Lateral Inhibition in Sprouting Angiogenesis

Sprouting angiogenesis is a necessary process in regeneration and development as well as in tumorigenesis. VEGF-A is the main pro-angiogenic chemoattractant and it can bind to the decoy receptor VEGFR1 or to VEGFR2 to induce sprouting. Active sprout cells express Dll4, which binds to Notch1 on neighboring cells, in turn inhibiting VEGFR2 expression. It is known that the balance between VEGFR2 and VEGFR1 determines tip selection and network architecture, however the quantitative interrelationship of the receptors and their interrelated balances, also with relation to Dll4-Notch1 signaling, remains yet largely unknown. Here, we present an agent-based computer model of sprouting angiogenesis, integrating VEGFR1 and VEGFR2 in a detailed model of cellular signaling. Our model reproduces experimental data on VEGFR1 knockout. We show that soluble VEGFR1 improves the efficiency of angiogenesis by directing sprouts away from existing cells over a wide range of parameters. Our analysis unravels the relevance of the stability of the active notch intracellular domain as a dominating hub in this regulatory network. Our analysis quantitatively dissects the regulatory interactions in sprouting angiogenesis. Because we use a detailed model of intracellular signaling, the results of our analysis are directly linked to biological entities. We provide our computational model and simulation engine for integration in complementary modeling approaches.

Impact of spino-pelvic and global spinal alignment on the risk of osteoporotic vertebral collapse

Introduction

Numerous studies have reported the risk factors of osteoporotic vertebral collapse. However, whether spino-pelvic and global spinal alignments are associated with the occurrence of osteoporotic vertebral collapse remains unclear. This study aimed to investigate the association between spino-pelvic and global spinal alignments and the occurrence of osteoporotic vertebral collapse.

Methods

A total of 46 consecutive patients who underwent a nonoperative treatment for a single-level fresh osteoporotic thoracolumbar vertebral compression fracture (T10 to L3) were retrospectively reviewed. The parameters evaluated were the pelvic incidence, anterior deviation of the C7 plumb line, distance between the C7 plumb line and the center of the fractured vertebra, and kyphotic wedge angle of the fractured vertebra in a standing whole-spine radiograph at the beginning of the nonoperative treatment. As an outcome measure, the presence or absence of osteoporotic vertebral collapse was radiographically evaluated at the final follow-up. Multiple logistic regression analysis was used to determine significant risk factors of osteoporotic vertebral collapse.

Results

The mean values for each parameter were as follows: pelvic incidence, 58.0 degrees; anterior deviation of the C7 plumb line, 3.0 cm; distance between the C7 plumb line and the center of the fractured vertebra, 5.7 cm; and kyphotic wedge angle of the fractured vertebra, 14.6 degrees. Multiple logistic regression analysis revealed that the distance between the C7 plumb line and center of the fractured vertebra was a significant risk factor of osteoporotic vertebral collapse (p = 0.012; odds ratio, 1.025). The anterior deviation of the C7 plumb line (p = 0.214), pelvic incidence (p = 0.728), and kyphotic wedge angle of the fractured vertebra (p = 0.07) did not affect the occurrence of osteoporotic vertebral collapse.

Conclusions

A large distance between the C7 plumb line and center of the fractured vertebra was a significant risk factor of osteoporotic vertebral collapse. The distance approximately represents that of between gravity center of trunk cranial to the fractured vertebra and the fractured vertebra. Accordingly, the large distance may cause larger flexion moment to the fractured site, leading to stress concentration that results in insufficient bone healing.

Review on experiment-based two- and three-dimensional models for wound healing

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.