Size does matter: an integrative in vivo-in silico approach for the treatment of critical size bone defects

Impacts of permeability and effective diffusivity of porous scaffolds on bone ingrowth: In silico and in vivo analyses

The permeability and the effective diffusivity of a porous scaffold are critical in the bone-ingrowth process. However, design guidelines for porous structures are still lacking due to inadequate understanding of the complex physiological processes involved. In this study, a model integrating the fundamental biological processes of bone regeneration was constructed to investigate the roles of permeability and effective diffusivity in regulating bone deposition in scaffolds. The in silico analysis results were confirmed in vivo by examining bone depositions in three diamond lattice scaffolds manufactured using selective laser melting. The findings show that the scaffolds with better permeability and effective diffusivity had deeper bone ingrowth and greater bone volume. Compared to permeability, effective diffusivity exhibited greater sensitivity to the orientation of porous structures, and bone ingrowth was deeper in the directions with higher effective diffusivity in spite of identical pore size. A 4.8-fold increase in permeability and a 1.6-fold increase in effective diffusivity by changing the porous structure led to a 1.5-fold increase in newly formed bone. The effective diffusivity of the porous scaffold affects the distribution of osteogenic growth factor, which in turn impacts cell migration and bone deposition through chemotaxis effects. Therefore, effective diffusivity may be a more suitable indicator for porous scaffolds because our study shows changes in this parameter determine changes in bone distribution and bone volume.

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

An in silico model predicts the impact of scaffold design in large bone defect regeneration

Large bone defects represent a clinical challenge for which the implantation of scaffolds appears as a promising strategy. However, their use in clinical routine is limited, in part due to a lack of understanding of how scaffolds should be designed to support regeneration. Here, we use the power of computer modeling to investigate mechano-biological principles behind scaffold-guided bone regeneration and the influence of scaffold design on the regeneration process. Computer model predictions are compared to experimental data of large bone defect regeneration in sheep. We identified two main key players in scaffold-guided regeneration: (1) the scaffold surface guidance of cellular migration and tissue formation processes and (2) the stimulation of progenitor cell activity by the scaffold material composition. In addition, lower scaffold surface-area-to-volume ratio was found to be beneficial for bone regeneration due to enhanced cellular migration. To a lesser extent, a reduced scaffold Young's modulus favored bone formation. STATEMENT OF SIGNIFICANCE: 3D-printed scaffolds offer promising treatment strategies for large bone defects but their broader clinical use requires a more thorough understanding of their interaction with the bone regeneration process. The predictions of our in silico model compared to two experimental set-ups highlighted the importance of (1) the scaffold surface guidance of cellular migration and tissue formation processes and (2) the scaffold material stimulation of progenitor cell activity. In addition, the model was used to investigate the effect on the bone regeneration process of (1) the scaffold surface-area-to-volume ratio, with lower ratios favoring more bone growth, and (2) the scaffold material properties, with stiffer scaffold materials yielding a lower bone growth.

Three-dimensional-printed polycaprolactone scaffolds with interconnected hollow-pipe structures for enhanced bone regeneration

Three-dimensional (3D)-printed scaffolds are widely used in tissue engineering to help regenerate critical-sized bone defects. However, conventional scaffolds possess relatively simple porous structures that limit the delivery of oxygen and nutrients to cells, leading to insufficient bone regeneration. Accordingly, in the present study, perfusable and permeable polycaprolactone scaffolds with highly interconnected hollow-pipe structures that mimic natural micro-vascular networks are prepared by an indirect one-pot 3D-printing method. In vitro experiments demonstrate that hollow-pipe-structured (HPS) scaffolds promote cell attachment, proliferation, osteogenesis and angiogenesis compared to the normal non-hollow-pipe-structured scaffolds. Furthermore, in vivo studies reveal that HPS scaffolds enhance bone regeneration and vascularization in rabbit bone defects, as observed at 8 and 12 weeks, respectively. Thus, the fabricated HPS scaffolds are promising candidates for the repair of critical-sized bone defects.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

The vascularization paradox of non-union formation

Despite major research efforts to elucidate mechanisms of non-union formation, failed fracture healing remains a common complication in orthopedic surgery. Adequate vascularization has been recognized as a crucial factor for successful bone regeneration, as newly formed microvessels guarantee the supply of the callus tissue with vital oxygen, nutrients, and growth factors. Accordingly, a vast number of preclinical studies have focused on the development of vascularization strategies to stimulate fracture repair. However, recent evidence suggests that stimulation of blood vessel formation is an oversimplified approach to support bone regeneration. This review discusses the role of vascularization during bone regeneration and delineates a phenomenon, for which we coin the term “the vascularization paradox of non-union-formation”. This view is based on the results of a variety of experimental studies that suggest that the callus tissue of non-unions is indeed densely vascularized and that pro-angiogenic mediators, such as vascular endothelial growth factor, are sufficiently expressed at the facture site. By gaining further insights into the molecular and cellular basis of non-union vascularization, it may be possible to develop more optimized treatment approaches or even prevent the non-union formation in the future.

Self-Oxygenation of Tissues Orchestrates Full-Thickness Vascularization of Living Implants

Bioengineering of tissues and organs has the potential to generate functional replacement organs. However, achieving the full-thickness vascularization that is required for long-term survival of living implants has remained a grand challenge, especially for clinically sized implants. During the pre-vascular phase, implanted engineered tissues are forced to metabolically rely on the diffusion of nutrients from adjacent host-tissue, which for larger living implants results in anoxia, cell death, and ultimately implant failure. Here it is reported that this challenge can be addressed by engineering self-oxygenating tissues, which is achieved via the incorporation of hydrophobic oxygen-generating micromaterials into engineered tissues. Self-oxygenation of tissues transforms anoxic stresses into hypoxic stimulation in a homogenous and tissue size-independent manner. The in situ elevation of oxygen tension enables the sustained production of high quantities of angiogenic factors by implanted cells, which are offered a metabolically protected pro-angiogenic microenvironment. Numerical simulations predict that self-oxygenation of living tissues will effectively orchestrate rapid full-thickness vascularization of implanted tissues, which is empirically confirmed via in vivo experimentation. Self-oxygenation of tissues thus represents a novel, effective, and widely applicable strategy to enable the vascularization living implants, which is expected to advance organ transplantation and regenerative medicine applications.

The application of Bonelike® Poro as a synthetic bone substitute for the management of critical-sized bone defects - A comparative approach to the autograft technique - A preliminary study

The effective treatment of non-unions and critical-sized defects remains a challenge in the orthopedic field. From a tissue engineering perspective, this issue can be addressed through the application bioactive matrixes to support bone regeneration, such as Bonelike®, as opposed to the widespread autologous grafting technique. An improved formulation of Bonelike® Poro, was assessed as a synthetic bone substitute in an ovine model for critical-sized bone defects. Bone regeneration was assessed after 5 months of recovery through macro and microscopic analysis of the healing features of the defect sites. Both the application of natural bone graft or Bonelike® Poro resulted in bridging of the defects margins. Untreated defect remained as fibrous non-unions at the end of the study period. The characteristics of the newly formed bone and its integration with the host tissue were assessed through histomorphometric and histological analysis, which demonstrated Bonelike® Poro to result in improved healing of the defects. The group treated with synthetic biomaterial presented bone bridges of increased thickness and bone features that more closely resembled the native spongeous and cortical bone. The application of Bonelike® Poro enabled the regeneration of critical-sized lesions and performed comparably to the autograph technique, validating its octeoconductive and osteointegrative potential for clinical application as a therapeutic strategy in human and veterinary orthopedics.

Fibrodysplasia Ossificans Progressiva: What Have We Achieved and Where Are We Now? Follow-up to the 2015 Lorentz Workshop

Fibrodysplasia ossificans progressiva (FOP) is an ultra-rare progressive genetic disease effecting one in a million individuals. During their life, patients with FOP progressively develop bone in the soft tissues resulting in increasing immobility and early death. A mutation in the ACVR1 gene was identified as the causative mutation of FOP in 2006. After this, the pathophysiology of FOP has been further elucidated through the efforts of research groups worldwide. In 2015, a workshop was held to gather these groups and discuss the new challenges in FOP research. Here we present an overview and update on these topics.

Computational Modeling of Human Mesenchymal Stromal Cell Proliferation and Extra-Cellular Matrix Production in 3D Porous Scaffolds in a Perfusion Bioreactor: The Effect of Growth Factors

Stem cell expansion on 3D porous scaffolds cultured in bioreactor systems has been shown to be beneficial for maintenance of the original cell functionality in tissue engineering strategies (TE). However, the production of extracellular matrix (ECM) makes harvesting the progenitor cell population from 3D scaffolds a challenge. Medium composition plays a role in stimulating cell proliferation over extracellular matrix (ECM) production. In this regard, a computational model describing tissue growth inside 3D scaffolds can be a great tool in designing optimal experimental conditions. In this study, a computational model describing cell and ECM growth in a perfusion bioreactor is developed, including a description of the effect of a (generic) growth factor on the biological processes taking place inside the 3D scaffold. In the model, the speed of cell and ECM growth depends on the flow-induced shear stress, curvature and the concentrations of oxygen, glucose, lactate, and growth factor. The effect of the simulated growth factor is to differentially enhance cell proliferation over ECM production. After model calibration with historic in-house data, a multi-objective optimization procedure is executed aiming to minimize the total experimental cost whilst maximizing cell growth during culture. The obtained results indicate there are multiple optimum points for the medium refreshment regime and the initial growth factor concentration where a trade-off is made between the final amount of cells and the culture cost. Finally, the model is applied to experiments reported in the literature studying the effects of perfusion-based cell culture and/or growth factor supplementation on cell expansion. The qualitative similarities between the simulation and experimental results, even in the absence of proper model calibration, reinforces the generic character of the proposed modeling framework. The model proposed in this study can contribute to the cost efficient production of cell-based TE products, ultimately contributing to their affordability and accessibility.

Towards multi-dynamic mechano-biological optimization of 3D-printed scaffolds to foster bone regeneration

Substantial tissue loss, such as in large bone defects, represents a clinical challenge for which regenerative therapies and tissue engineering strategies aim at offering treatment alternatives to conventional replacement approaches by metallic implants. 3D printing technologies provide endless opportunities to shape scaffold structures that could support endogenous regeneration. However, it remains unclear which of the numerous parameters at hand eventually enhance tissue regeneration. In the last decades, a significant effort has been made in the development of computer tools to optimize scaffold designs. Here, we aim at giving a more comprehensive overview summarizing current computer optimization framework technologies. We confront these with the most recent advances in scaffold mechano-biological optimization, discuss their limitations and provide suggestions for future development. We conclude that the field needs to move forward to not only optimize scaffolds to avoid implant failures but to improve their mechano-biological behaviour: providing an initial stimulus for fast tissue organisation and healing and accounting for remodelling, scaffold degradation and consecutive filling with host tissue. So far, modelling approaches fall short in including the various scales of tissue dynamics. With this review, we wish to stimulate a move towards multi-dynamic mechano-biological optimization of 3D-printed scaffolds. STATEMENT OF SIGNIFICANCE: Large bone defects represent a clinical challenge for which tissue engineering strategies aim at offering alternatives to conventional treatment strategies. 3D printing technologies provide endless opportunities to shape scaffold structures that could support endogenous regeneration. However, it remains unclear which of the numerous parameters at hand eventually enhance tissue regeneration. In the last decades, a significant effort has been made in the development of computer tools to optimize scaffold designs. This review summarizes current computer optimization frameworks and most recent advances in mechano-biological optimization of bone scaffolds to better stimulate bone regeneration. We wish to stimulate a move towards multi-dynamic mechano-biological optimization of 3D-printed scaffolds.

Scleral ossicles: angiogenic scaffolds, a novel biomaterial for regenerative medicine applications

Given the current prolonged life expectancy, various pathologies affect increasingly the aging subjects. Regarding the musculoskeletal apparatus, bone fragility induces more susceptibility to fractures, often not accompanied by good ability of self-repairing, in particular when critical-size defects (CSD) occur. Currently orthopedic surgery makes use of allografting and autografting which, however, have limitations due to the scarce amount of tissue that can be taken from the donor, the possibility of disease transmission and donor site morbidity. The need to develop new solutions has pushed the field of tissue engineering (TE) research to study new scaffolds to be functionalized in order to obtain constructs capable of promoting tissue regeneration and achieve stable bone recovery over time. This investigation focuses on the most important aspect related to bone tissue regeneration: the angiogenic properties of the scaffold to be used. As an innovative solution, scleral ossicles (SOs), previously characterized as natural, biocompatible and spontaneously decellularized scaffolds used for bone repair, were tested for angiogenic potential and biocompatibility. To reach this purpose, in ovo Chorioallantoic Membrane Assay (CAM) was firstly used to test the angiogenic potential; secondly, in vivo subcutaneous implantation of SOs (in a rat model) was performed in order to assess the biocompatibility and the inflammatory response. Finally, thanks to the analysis of mass spectrometry (LCMSQE), the putative proteins responsible for the SO angiogenic properties were identified. Thus, a novel natural biomaterial is proposed, which is (i) able to induce an angiogenic response in vivo by subcutaneous implantation in a non-immunodeficient animal model, (ii) which does not induce any inflammatory response, and (iii) is useful for regenerative medicine application for the healing of bone CSD.

Computational modeling of human bone fracture healing affected by different conditions of initial healing stage

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.

Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds

Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen–Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

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.

Computational Modeling and Reverse Engineering to Reveal Dominant Regulatory Interactions Controlling Osteochondral Differentiation: Potential for Regenerative Medicine

The specialization of cartilage cells, or chondrogenic differentiation, is an intricate and meticulously regulated process that plays a vital role in both bone formation and cartilage regeneration. Understanding the molecular regulation of this process might help to identify key regulatory factors that can serve as potential therapeutic targets, or that might improve the development of qualitative and robust skeletal tissue engineering approaches. However, each gene involved in this process is influenced by a myriad of feedback mechanisms that keep its expression in a desirable range, making the prediction of what will happen if one of these genes defaults or is targeted with drugs, challenging. Computer modeling provides a tool to simulate this intricate interplay from a network perspective. This paper aims to give an overview of the current methodologies employed to analyze cell differentiation in the context of skeletal tissue engineering in general and osteochondral differentiation in particular. In network modeling, a network can either be derived from mechanisms and pathways that have been reported in the literature (knowledge-based approach) or it can be inferred directly from the data (data-driven approach). Combinatory approaches allow further optimization of the network. Once a network is established, several modeling technologies are available to interpret dynamically the relationships that have been put forward in the network graph (implication of the activation or inhibition of certain pathways on the evolution of the system over time) and to simulate the possible outcomes of the established network such as a given cell state. This review provides for each of the aforementioned steps (building, optimizing, and modeling the network) a brief theoretical perspective, followed by a concise overview of published works, focusing solely on applications related to cell fate decisions, cartilage differentiation and growth plate biology. Particular attention is paid to an in-house developed example of gene regulatory network modeling of growth plate chondrocyte differentiation as all the aforementioned steps can be illustrated. In summary, this paper discusses and explores a series of tools that form a first step toward a rigorous and systems-level modeling of osteochondral differentiation in the context of regenerative medicine.

Harnessing extracellular vesicles to direct endochondral repair of large bone defects

Large bone defects remain a tremendous clinical challenge. There is growing evidence in support of treatment strategies that direct defect repair through an endochondral route, involving a cartilage intermediate. While culture-expanded stem/progenitor cells are being evaluated for this purpose, these cells would compete with endogenous repair cells for limited oxygen and nutrients within ischaemic defects. Alternatively, it may be possible to employ extracellular vesicles (EVs) secreted by culture-expanded cells for overcoming key bottlenecks to endochondral repair, such as defect vascularization, chondrogenesis, and osseous remodelling. While mesenchymal stromal/stem cells are a promising source of therapeutic EVs, other donor cells should also be considered. The efficacy of an EV-based therapeutic will likely depend on the design of companion scaffolds for controlled delivery to specific target cells. Ultimately, the knowledge gained from studies of EVs could one day inform the long-term development of synthetic, engineered nanovesicles. In the meantime, EVs harnessed from in vitro cell culture have near-term promise for use in bone regenerative medicine. This narrative review presents a rationale for using EVs to improve the repair of large bone defects, highlights promising cell sources and likely therapeutic targets for directing repair through an endochondral pathway, and discusses current barriers to clinical translation. Cite this article: E. Ferreira, R. M. Porter. Harnessing extracellular vesicles to direct endochondral repair of large bone defects. Bone Joint Res 2018;7:263-273. DOI: 10.1302/2046-3758.74.BJR-2018-0006.

Micromechanical study of the load transfer in a polycaprolactone-collagen hybrid scaffold when subjected to unconfined and confined compression

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 [Formula: see text]m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 [Formula: see text]m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539-548, 1997. https://doi.org/10.1016/S0021-9290(96)00140-6 ), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.

In silico clinical trials for pediatric orphan diseases

To date poor treatment options are available for patients with congenital pseudarthrosis of the tibia (CPT), a pediatric orphan disease. In this study we have performed an in silico clinical trial on 200 virtual subjects, generated from a previously established model of murine bone regeneration, to tackle the challenges associated with the small, pediatric patient population. Each virtual subject was simulated to receive no treatment and bone morphogenetic protein (BMP) treatment. We have shown that the degree of severity of CPT is significantly reduced with BMP treatment, although the effect is highly subject-specific. Using machine learning techniques we were also able to stratify the virtual subject population in adverse responders, non-responders, responders and asymptomatic. In summary, this study shows the potential of in silico medicine technologies as well as their implications for other orphan diseases.

Immediate post-extraction implants with or without pure platelet-rich plasma: a 5-year follow-up study

PURPOSE

The purpose of this study was comparison of clinical and radiographic outcomes of immediate post-extraction implants with or without the use of pure platelet-rich plasma (P-PRP) in the short- and medium-term follow-up.

METHODS

A retrospective analysis was performed to assess soft tissue healing, implant and prosthesis survival, marginal bone level changes and biological complications.

RESULTS

A total of 109 partially edentulous patients with 126 implants were included in this analysis. At 4-5 years after loading, cumulative survival rate in test group was 97.4% and in control group was 97.8%, with no significant differences. After 5 years of function, marginal bone loss (MBL) in test group was 0.8 ± 0.35 and 1.02 ± 0.27 mm for immediate and delayed loading, respectively, and in control group was 0.6 ± 0.16 and 0.8 ± 0.89 mm for immediate and delayed loading, respectively. No significant differences in MBL were observed intragroups and intergroups at any time point considered. Soft tissue healing score was significantly higher in test group compared to the control at 3 and 7 days after surgery, with significant differences.

CONCLUSIONS

P-PRP implant group showed a better soft tissue management and wound healing in the first 7 days after surgery compared to non-P-PRP implant group. In the medium-term follow-up, comparable clinical and radiographic outcomes were noticed between two groups.

Bone fracture healing in mechanobiological modeling: A review of principles and methods

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.

Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

Bone is a living part of the body that can, in most situations, heal itself after fracture. However, in some situations, healing may fail. Compromised conditions, such as large bone defects, aging, immuno-deficiency, or genetic disorders, might lead to delayed or non-unions. Treatment strategies for those conditions remain a clinical challenge, emphasizing the need to better understand the mechanisms behind endogenous bone regeneration. Bone healing is a complex process that involves the coordination of multiple events at different length and time scales. Computer models have been able to provide great insights into the interactions occurring within and across the different scales (organ, tissue, cellular, intracellular) using different modeling approaches [partial differential equations (PDEs), agent-based models, and finite element techniques]. In this review, we summarize the latest advances in computer models of bone healing with a focus on multiscale approaches and how they have contributed to understand the emergence of tissue formation patterns as a result of processes taking place at the lower length scales.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

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

The human skeleton has a remarkable regeneration capacity. Nevertheless, 5-10 % of the bone fractures fails to heal and develops into a non-union which is a challenging orthopedic complication requiring complex and expensive treatment. This review paper will discuss four different computational models, each capturing a particular clinical case of non-union: non-union induced by reaming of the marrow canal and periosteal stripping, non-union due to a large interfragmentary gap, non-union due to a genetic disorder [i.e. NF1 related congenital pseudoarthrosis of the tibia (CPT)] and non-union due to mechanical overload. Together, the four computational models are able to capture the etiology of a wide range of fracture non-union types and design novel treatment strategies thereof. Further research is required to corroborate the computational models in both animal and human settings and translate them from bench to bed side.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.