Occurrence and treatment of bone atrophic non-unions investigated by an integrative approach

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.

Computational design and evaluation of the mechanical and electrical behavior of a piezoelectric scaffold: a preclinical study

Piezoelectric scaffolds have been recently developed to explore their potential to enhance the bone regeneration process using the concept of piezoelectricity, which also inherently occurs in bone. In addition to providing mechanical support during bone healing, with a suitable design, they are supposed to produce electrical signals that ought to favor the cell responses. In this study, using finite element analysis (FEA), a piezoelectric scaffold was designed with the aim of providing favorable ranges of mechanical and electrical signals when implanted in a large bone defect in a large animal model, so that it could inform future pre-clinical studies. A parametric analysis was then performed to evaluate the effect of the scaffold design parameters with regard to the piezoelectric behavior of the scaffold. The designed scaffold consisted of a porous strut-like structure with piezoelectric patches covering its free surfaces within the scaffold pores. The results showed that titanium or PCL for the scaffold and barium titanate (BT) for the piezoelectric patches are a promising material combination to generate favorable ranges of voltage, as reported in experimental studies. Furthermore, the analysis of variance showed the thickness of the piezoelectric patches to be the most influential geometrical parameter on the generation of electrical signals in the scaffold. This study shows the potential of computer tools for the optimization of scaffold designs and suggests that patches of piezoelectric material, attached to the scaffold surfaces, can deliver favorable ranges of electrical stimuli to the cells that might promote bone regeneration.

Suppression of DNMT2/3 by proinflammatory cytokines inhibits CtBP1/2-dependent genes to promote the occurrence of atrophic nonunion

Failure of bone healing after fracture often results in nonunion, but the underlying mechanism of nonunion pathogenesis is poorly understood. Herein, we provide evidence to clarify that the inflammatory microenvironment of atrophic nonunion (AN) mice suppresses the expression levels of DNA methyltransferases 2 (DNMT2) and 3A (DNMT3a), preventing the methylation of CpG islands on the promoters of C-terminal binding protein 1/2 (CtBP1/2) and resulting in their overexpression. Increased CtBP1/2 acts as transcriptional corepressors that, along with histone acetyltransferase p300 and Runt-related transcription factor 2 (Runx2), suppress the expression levels of six genes involved in bone healing: BGLAP (bone gamma-carboxyglutamate protein), ALPL (alkaline phosphatase), SPP1 (secreted phosphoprotein 1), COL1A1 (collagen 1a1), IBSP (integrin binding sialoprotein), and MMP13 (matrix metallopeptidase 13). We also observe a similar phenomenon in osteoblast cells treated with proinflammatory cytokines or treated with a DNMT inhibitor (5-azacytidine). Forced expression of DNMT2/3a or blockage of CtBP1/2 with their inhibitors can reverse the expression levels of BGLAP/ALPL/SPP1/COL1A1/IBSP/MMP13 in the presence of proinflammatory cytokines. Administration of CtBP1/2 inhibitors in fractured mice can prevent the incidence of AN. Thus, we demonstrate that the downregulation of bone healing genes dependent on proinflammatory cytokines/DNMT2/3a/CtBP1/2-p300-Runx2 axis signaling plays a critical role in the pathogenesis of AN. Disruption of this signaling may represent a new therapeutic strategy to prevent AN incidence after bone fracture.

Animal models of impaired long bone healing and tissue engineering- and cell-based in vivo interventions

Bone healing after injury typically follows a systematic process and occurs spontaneously under appropriate physiological conditions. However, impaired long bone healing is still quite common and may require surgical intervention. Various complications can result in different forms of impaired bone healing including nonunion, critical-size defects, or stress fractures. While a nonunion may occur due to impaired biological signaling and/or mechanical instability, a critical-size defect exhibits extensive bone loss that will not spontaneously heal. Comparatively, a stress fracture occurs from repetitive forces and results in a non-healing crack or break in the bone. Clinical standards of treatment vary between these bone defects due to their pathological differences. The use of appropriate animal models for modeling healing defects is critical to improve current treatment methods and develop novel rescue therapies. This review provides an overview of these clinical bone healing impairments and current animal models available to study the defects in vivo. The techniques used to create these models are compared, along with the outcomes, to clarify limitations and future objectives. Finally, rescue techniques focused on tissue engineering and cell-based therapies currently applied in animal models are specifically discussed to analyze their ability to initiate healing at the defect site, providing information regarding potential future therapies. In summary, this review focuses on the current animal models of nonunion, critical-size defects, and stress fractures, as well as interventions that have been tested in vivo to provide an overview of the clinical potential and future directions for improving bone healing.

Bone fracture healing within a continuum bone remodelling framework

Bone fracture healing is a complex process which is still under research. Computer-aided patient-specific prediction of bone development, fracture risk, prevention and treatment approaches promises a significant milestone in clinical practice. With this long-term goal in mind, a novel model is presented and examined in this work in the context of continuum bone remodelling. Therein, a clear distinction is made between external mechanical stimulation and the biological healing process of an injured bone tissue. The model is implemented within a finite element framework and investigated for the example of a fractured proximal femur head. The results show promising perspectives for further application. Besides, the model offers the possibility of easily integrating other factors like age-dependency and the availability of nutrition. For the future, further studies with large clinical datasets are essential for validation.

Management of Subtrochanteric Femoral Fracture Nonunions

Compared with other proximal femoral fractures, subtrochanteric fractures are at a higher risk for nonunion because of the high deforming forces in this region, the associated increased risk of malreduction, and the risk of poor bone healing secondary to bisphosphonate use frequently associated with these fractures. Further understanding of nonunion of subtrochanteric fractures is of increasing importance given the rise in incidence of subtrochanteric hip fractures. Surgeons should be aware of risk factors for nonunion and techniques for prevention as well as surgical management and complications associated with surgical implantation devices. Surgeons should also consider using adjuncts including bone-grafting and biologic agents.

Mapping human serum-induced gene networks as a basis for the creation of biomimetic periosteum for bone repair

BACKGROUND

The periosteum is a highly vascularized, collagen-rich tissue that plays a crucial role in directing bone repair. This is orchestrated primarily by its resident progenitor cell population. Indeed, preservation of periosteum integrity is critical for bone healing. Cells extracted from the periosteum retain their osteochondrogenic properties and as such are a promising basis for tissue engineering strategies for the repair of bone defects. However, the culture expansion conditions and the way in which the cells are reintroduced to the defect site are critical aspects of successful translation. Indeed, expansion in human serum and implantation on biomimetic materials has previously been shown to improve in vivo bone formation.

AIM

This study aimed to develop a protocol to allow for the expansion of human periosteum derived cells (hPDCs) in a biomimetic periosteal-like environment.

METHODS

The expansion conditions were defined through the investigation of the bioactive cues involved in augmenting hPDC proliferative and multipotency characteristics, based on transcriptomic analysis of cells cultured in human serum.

RESULTS

Master regulators of transcriptional networks were identified, and an optimized periosteum-derived growth factor cocktail (PD-GFC; containing β-estradiol, FGF2, TNFα, TGFβ, IGF-1 and PDGF-BB) was generated. Expansion of hPDCs in PD-GFC resulted in serum mimicry with regard to the cell morphology, proliferative capacity and chondrogenic differentiation. When incorporated into a three-dimensional collagen type 1 matrix and cultured in PD-GFC, the hPDCs migrated to the surface that represented the matrix topography of the periosteum cambium layer. Furthermore, gene expression analysis revealed a down-regulated WNT and TGFβ signature and an up-regulation of CREB, which may indicate the hPDCs are recreating their progenitor cell signature.

CONCLUSION

This study highlights the first stage in the development of a biomimetic periosteum, which may have applications in bone repair.

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.

Non-union: Indications for external fixation

External fixation is currently used as the definitive mode of fracture stabilisation in the management of ˜50% of long-bone non-unions. Distinction between non-union and delayed union is a diagnostic dilemma especially in fractures healing by primary bone repair. This distinction is important, as non-unions are not necessarily part of the same spectrum as delayed unions. The aetiology of a fracture non-union is usually multifactorial and the factors can be broadly categorized into mechanical factors, biological (local and systemic) factors, and infection. Infection is present in ˜40% of fracture non-unions, often after open fractures or impaired wound healing, but in 5% of all non-unions infection is present without any clinical or serological suspicion. General indications for external fixation include clinical scenarios where; 1) percutaneous correction of alignment, or mechanical stimulation of the non-union site is required; 2) fixation of juxta-articular or 'emmental' bone fragments is necessary; and 3) staged bone or soft tissue reconstruction is anticipated. Specific anatomical indications include infected non-unions of the tibia, humerus, and juxta-articular bone. External fixation is an essential tool in the management of fracture non-unions. However, with greater understanding of the outcomes associated with both external and internal fixation the relative indications are now being refined.

Nonunion fractures, mesenchymal stem cells and bone tissue engineering

Depending on the duration of healing process, 5-10% of bone fractures may result in either nonunion or delayed union. Because nonunions remain a clinically important problem, there is interest in the utilization of tissue engineering strategies to augment bone fracture repair. Three basic biologic elements that are required for bone regeneration include cells, extracellular matrix scaffolds and biological adjuvants for growth, differentiation and angiogenesis. Mesenchymal stem cells (MSCs) are capable to differentiate into various types of the cells including chondrocytes, myoblasts, osteoblasts, and adipocytes. Due to their potential for multilineage differentiation, MSCs are considered important contributors in bone tissue engineering research. In this review we highlight the progress in the application of biomaterials, stem cells and tissue engineering in promoting nonunion bone fracture healing. © 2018 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 106A:2551-2561, 2018.

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.

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.

In silico bone mechanobiology: modeling a multifaceted biological system

Mechanobiology, the study of the influence of mechanical loads on biological processes through signaling to cells, is fundamental to the inherent ability of bone tissue to adapt its structure in response to mechanical stimulation. The immense contribution of computational modeling to the nascent field of bone mechanobiology is indisputable, having aided in the interpretation of experimental findings and identified new avenues of inquiry. Indeed, advances in computational modeling have spurred the development of this field, shedding new light on problems ranging from the mechanical response to loading by individual cells to tissue differentiation during events such as fracture healing. To date, in silico bone mechanobiology has generally taken a reductive approach in attempting to answer discrete biological research questions, with research in the field broadly separated into two streams: (1) mechanoregulation algorithms for predicting mechanobiological changes to bone tissue and (2) models investigating cell mechanobiology. Future models will likely take advantage of advances in computational power and techniques, allowing multiscale and multiphysics modeling to tie the many separate but related biological responses to loading together as part of a larger systems biology approach to shed further light on bone mechanobiology. Finally, although the ever‐increasing complexity of computational mechanobiology models will inevitably move the field toward patient‐specific models in the clinic, the determination of the context in which they can be used safely for clinical purpose will still require an extensive combination of computational and experimental techniques applied to in vitro and in vivo applications. WIREs Syst Biol Med 2016, 8:485–505. doi: 10.1002/wsbm.1356

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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.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

Cell based advanced therapeutic medicinal products for bone repair: Keep it simple?

The development of cell based advanced therapeutic medicinal products (ATMPs) for bone repair has been expected to revolutionize the health care system for the clinical treatment of bone defects. Despite this great promise, the clinical outcomes of the few cell based ATMPs that have been translated into clinical treatments have been far from impressive. In part, the clinical outcomes have been hampered because of the simplicity of the first wave of products. In response the field has set-out and amassed a plethora of complexities to alleviate the simplicity induced limitations. Many of these potential second wave products have remained "stuck" in the development pipeline. This is due to a number of reasons including the lack of a regulatory framework that has been evolving in the last years and the shortage of enabling technologies for industrial manufacturing to deal with these novel complexities. In this review, we reflect on the current ATMPs and give special attention to novel approaches that are able to provide complexity to ATMPs in a straightforward manner. Moreover, we discuss the potential tools able to produce or predict 'goldilocks' ATMPs, which are neither too simple nor too complex.

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

Although bone has a unique restorative capacity, i.e., it has the potential to heal scarlessly, the conditions for spontaneous bone healing are not always present, leading to a delayed union or a non-union. In this work, we use an integrative in vivo - in silico approach to investigate the occurrence of non-unions, as well as to design possible treatment strategies thereof. The gap size of the domain geometry of a previously published mathematical model was enlarged in order to study the complex interplay of blood vessel formation, oxygen supply, growth factors and cell proliferation on the final healing outcome in large bone defects. The multiscale oxygen model was not only able to capture the essential aspects of in vivo non-unions, it also assisted in understanding the underlying mechanisms of action, i.e., the delayed vascularization of the central callus region resulted in harsh hypoxic conditions, cell death and finally disrupted bone healing. Inspired by the importance of a timely vascularization, as well as by the limited biological potential of the fracture hematoma, the influence of the host environment on the bone healing process in critical size defects was explored further. Moreover, dependent on the host environment, several treatment strategies were designed and tested for effectiveness. A qualitative correspondence between the predicted outcomes of certain treatment strategies and experimental observations was obtained, clearly illustrating the model's potential. In conclusion, the results of this study demonstrate that due to the complex non-linear dynamics of blood vessel formation, oxygen supply, growth factor production and cell proliferation and the interactions thereof with the host environment, an integrative in silico-in vivo approach is a crucial tool to further unravel the occurrence and treatments of challenging critical sized bone defects.

In 5–10% of fracture patients, the bone fractures do not heal in the normal healing period (delayed healing) or do not heal at all (non-union). In order to investigate the causes of impaired healing and design potential treatment strategies, we have used a combined experimental and computational approach. More specifically, large bone defects were analyzed in mouse models and simulated by a previously published computational model. After showing that the predictions of the computational model match the observations of the experimental model, we have used the computational model to investigate the underlying mechanisms of action. In particular, the results indicated that the new blood vessels do not reach the central fracture zone in time due to the large defect size, which leads to insufficient oxygen delivery, increased cell death and disrupted bone healing. The healing, however, could be rescued by adequate blood vessel ingrowth from the overlying soft tissues. Moreover, potential treatment strategies were designed based on the influence of these soft tissues. In conclusion, this study demonstrates the potential of a combined experimental and computational approach to contribute to the understanding of pathological processes like the impaired bone regeneration in large bone defects and design future treatments thereof.

Regenerative orthopaedics: in vitro, in vivo...in silico

In silico, defined in analogy to in vitro and in vivo as those studies that are performed on a computer, is an essential step in problem-solving and product development in classical engineering fields. The use of in silico models is now slowly easing its way into medicine. In silico models are already used in orthopaedics for the planning of complicated surgeries, personalised implant design and the analysis of gait measurements. However, these in silico models often lack the simulation of the response of the biological system over time. In silico models focusing on the response of the biological systems are in full development. This review starts with an introduction into in silico models of orthopaedic processes. Special attention is paid to the classification of models according to their spatiotemporal scale (gene/protein to population) and the information they were built on (data vs hypotheses). Subsequently, the review focuses on the in silico models used in regenerative orthopaedics research. Contributions of in silico models to an enhanced understanding and optimisation of four key elements-cells, carriers, culture and clinics-are illustrated. Finally, a number of challenges are identified, related to the computational aspects but also to the integration of in silico tools into clinical practice.

Evaluation of native mesenchymal stem cells from bone marrow and local tissue in an atrophic nonunion model

INTRODUCTION

It has been reported that cells or growth factors might improve bone regeneration in nonunion. However, the intrinsic potential of the nonunion tissue to regenerate bone is still unclear; in particular, it is not known whether there are progenitor cells within the nonunion. Thus, in this study, a clinically relevant model has been developed to investigate the nature of the cells in atrophic nonunion tissue and to assess their regenerative potential.

MATERIALS AND METHODS

Seventeen Wistar rats underwent the procedure to induce an atrophic nonunion at the tibial midshaft by stripping the periosteum and endosteum as well as creating a small (1.0 mm) noncritical gap. The fracture was stabilized with an external fixator. The proliferation ability of bone marrow-derived cells and nonunion tissue-derived cells was determined using colony forming assays. The differentiation potential of nonunion tissue-derived cells was also investigated.

RESULTS

Noncritical size defect nonunions were successfully induced in all of the animals. The typical characteristics of atrophic nonunions were demonstrated by radiography, micro-CT, and histology. An atrophic nonunion stimulated a systemic response in the bone marrow with an increase in bone marrow-derived mesenchymal stem cells. In contrast, cells derived from the nonunion gap were not able to form colonies. This indicated that the quiescent or inactive cells in the tissue at the atrophic nonunion gap could be induced to differentiate under osteogenic and chondrogenic conditions, but not under adipogenic conditions. Thus, these cells had the characteristics of osteochondral progenitor cells.

DISCUSSION

Although there was an increase in the systemic response in the atrophic nonunion model, the intrinsic potential of local tissue from the atrophic nonunion site was impaired. The cells derived from nonunion tissue could be stimulated to differentiate into bone under appropriate conditions. This suggested that there are progenitor cells in atrophic nonunion tissue, which have an intrinsic ability to regenerate bone, but the microenvironment in the atrophic nonunion site might be retarding their function. Consequently, physical or biological agents (such as growth factors or cells) are needed to reactivate the endogenous progenitor cells to make them regenerate bone in atrophic nonunions.

The role of osteocytes in targeted bone remodeling: a mathematical model

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. We have aimed to give a simple, yet still tractable, model that remains faithful to the underlying system based on the known literature. This model extends and complements many of the existing mathematical models for bone remodeling, but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to explore theoretically many of the qualitative features of the role of osteocytes in bone biology as presented in recent literature.

Modeling vascularized bone regeneration within a porous biodegradable CaP scaffold loaded with growth factors

Osteogenetic microenvironment is a complex constitution in which extracellular matrix (ECM) molecules, stem cells and growth factors each interact to direct the coordinate regulation of bone tissue development. Importantly, angiogenesis improvement and revascularization are critical for osteogenesis during bone tissue regeneration processes. In this study, we developed a three-dimensional (3D) multi-scale system model to study cell response to growth factors released from a 3D biodegradable porous calcium phosphate (CaP) scaffold. Our model reconstructed the 3D bone regeneration system and examined the effects of pore size and porosity on bone formation and angiogenesis. The results suggested that scaffold porosity played a more dominant role in affecting bone formation and angiogenesis compared with pore size, while the pore size could be controlled to tailor the growth factor release rate and release fraction. Furthermore, a combination of gradient VEGF with BMP2 and Wnt released from the multi-layer scaffold promoted angiogenesis and bone formation more readily than single growth factors. These results demonstrated that the developed model can be potentially applied to predict vascularized bone regeneration with specific scaffold and growth factors.

Clinical strategies at the docking site of distraction osteogenesis: are open procedures superior to the simple compression of Ilizarov?

This retrospective review reports on forty-five tibial non-unions who underwent docking site treatment for non-union using closed versus open and endoscopic strategies. In this cohort of patients, all but twelve were infected non-unions. Sixteen patients initially treated with single compression were compared to twenty-three patients treated with open revision of the docking site, and six endoscopic procedures. In the single compression group, an average of 6.4 cm of bone was resected and index lengthening was 2.01. In the open revision group, a mean of 9.4 cm was resected and the index lengthening was 1.72. In the endoscopic group, an average of 8.6 cm of bone was resected and index lengthening was 1.71. Consolidation at the docking site occurred in 41 cases out of 45 following the first procedure. There was no statistical difference between the three groups. Conclusive evidence of superiority of one modality of treatment over the other cannot be drawn from our data. The simple compression procedure requires less invasive surgery and is probably less demanding and more cost-effective in short transports, although the two cases of failure due to recurrence of sepsis were observed after this procedure. Further studies are desirable to investigate the effectiveness of open docking site grating procedures.

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 activities lead to new bone formation and stabilization of the fracture. Although experimental data are available at different spatial and temporal scales, it is not clear how these data can be linked to provide a holistic view of fracture healing. Mathematical modeling is a powerful tool to quantify conceptual models and to establish the missing links between experimental data obtained at different scales. The objective of this review is to introduce mathematical modeling to readers who are not familiar with this methodology and to demonstrate that once validated, such models can be used for hypothesis testing and to assist in clinical treatment as will be shown for the example of atrophic nonunions.

Current views on calcium phosphate osteogenicity and the translation into effective bone regeneration strategies

Calcium phosphate (CaP) has traditionally been used for the repair of bone defects because of its strong resemblance to the inorganic phase of bone matrix. Nowadays, a variety of natural or synthetic CaP-based biomaterials are produced and have been extensively used for dental and orthopaedic applications. This is justified by their biocompatibility, osteoconductivity and osteoinductivity (i.e. the intrinsic material property that initiates de novo bone formation), which are attributed to the chemical composition, surface topography, macro/microporosity and the dissolution kinetics. However, the exact molecular mechanism of action is unknown. This review paper first summarizes the most important aspects of bone biology in relation to CaP and the mechanisms of bone matrix mineralization. This is followed by the research findings on the effects of calcium (Ca²⁺) and phosphate (PO₄³⁻) ions on the migration, proliferation and differentiation of osteoblasts during in vivo bone formation and in vitro culture conditions. Further, the rationale of using CaP for bone regeneration is explained, focusing thereby specifically on the material's osteoinductive properties. Examples of different material forms and production techniques are given, with the emphasis on the state-of-the art in fine-tuning the physicochemical properties of CaP-based biomaterials for improved bone induction and the use of CaP as a delivery system for bone morphogenetic proteins. The use of computational models to simulate the CaP-driven osteogenesis is introduced as part of a bone tissue engineering strategy in order to facilitate the understanding of cell-material interactions and to gain further insight into the design and optimization of CaP-based bone reparative units. Finally, limitations and possible solutions related to current experimental and computational techniques are discussed.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.

Towards a new spatial representation of bone remodeling

Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different approaches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models. Here we develop a mathematical representation of bone remodeling that can effectively describe many aspects of the complicated geometries and spatial behavior observed. There is a sharp interface between bone and marrow regions. Also the surface of bone moves in and out, i.e. in the normal direction, due to remodeling. Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling. We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes. We exhibit simulations based on our computational model that show the motion of the interface between bone and marrow as a consequence of bone remodeling. The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo. By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling. By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo. This makes it possible to perform in silica experiments more closely resembling experimental observations.

BMPs are mediators in tissue crosstalk of the regenerating musculoskeletal system

The musculoskeletal system is a tight network of many tissues. Coordinated interplay at a biochemical level between tissues is essential for development and repair. Traumatic injury usually affects several tissues and represents a large challenge in clinical settings. The current demand for potent growth factors in such applications thus accompanies the keen interest in molecular mechanisms and orchestration of tissue formation. Of special interest are multitasking growth factors that act as signals in a variety of cell types, both in a paracrine and in an autocrine manner, thereby inducing cell differentiation and coordinating not only tissue assembly at specific sites but also maturation and homeostasis. We concentrate here on bone morphogenetic proteins (BMPs), which are important crosstalk mediators known for their irreplaceable roles in vertebrate development. The molecular crosstalk during embryonic musculoskeletal tissue formation is recapitulated in adult repair. BMPs act at different levels from the initiation to maturation of newly formed tissue. Interestingly, this is influenced by the spatiotemporal expression of different BMPs, their receptors and co-factors at the site of repair. Thus, the regenerative potential of BMPs needs to be evaluated in the context of highly connected tissues such as muscle and bone and might indeed be different in more poorly connected tissues such as cartilage. This highlights the need for an understanding of BMP signaling across tissues in order to eventually improve BMP regenerative potential in clinical applications. In this review, the distinct members of the BMP family and their individual contribution to musculoskeletal tissue repair are summarized by focusing on their paracrine and autocrine functions.

Evaluation of angiogenesis and osteogenesis

Bone regeneration has long been a major focus for tissue engineers and the importance of vascularization to the bone regeneration process has been well documented. Over the past decade, technological advances in the areas of stem cell biology, scaffold fabrication, and protein engineering have significantly enhanced our understanding of the interplay between vascularization and bone growth. This review, therefore, describes the commonly used models for investigating the complex interactions between osteoblastic cells and endothelial cells, evaluates the different tools utilized to investigate the relationship between vascularization and bone growth in vivo, and finally, summarizes possible areas of research related to therapeutic development.

Mathematical modeling in wound healing, bone regeneration and tissue engineering

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.