Angiogenesis in bone fracture healing: a bioregulatory model

Prevascularisation with endothelial progenitor cells improved restoration of the architectural and functional properties of newly formed bone for bone reconstruction

PURPOSE

The aim of this study was to examine whether the addition of endothelial progenitor cells (EPCs) contributes to restoring the architectural and functional properties of newly formed bone for reconstruction of bone defects.

METHODS

Bone marrow-derived EPCs and mesenchymal stem cells (MSCs) were co-seeded onto demineralized bone matrix (DBM) as a prevascularized tissue-engineered bone (TEB) for the repair of segmental bone defects to evaluate the effects of prevascularization of TEB on ameliorating morphological, haemodynamic and mechanical characteristics.

RESULTS

The restoration of the intraosseous vasculature and medullary cavity was improved markedly compared to the non-prevascularized groups. The blood supply, biomechanical strength, and bone mineral density of the prevascularized group were significantly higher than those of the non-prevascularized groups during bone reconstruction.

CONCLUSIONS

The present study indicates that EPC-dependent prevascularization contributes to bone healing with structural reconstruction and functional recovery and may improve the understanding of correlation between angiogenesis and osteogenesis.

Stimulated angiogenesis for fracture healing augmented by low-magnitude, high-frequency vibration in a rat model-evaluation of pulsed-wave doppler, 3-D power Doppler ultrasonography and micro-CT microangiography

This study aimed to investigate the mechanism of low-magnitude high-frequency vibration (LMHFV) treatment on angiogenesis and blood flow for enhancement of fracture healing. Nine-month-old ovariectomized (OVX) and sham-operated (Sham) rats received closed fractures creation at the femora and were randomized into LMHFV treatment (Sham-V, OVX-V) or control (Sham-C, OVX-C) groups. Pulsed-wave Doppler indicated an increase in blood flow velocity of the femoral artery at weeks 2 (OVX pair: p = 0.030) and 4 (OVX pair: p = 0.012; Sham pair: p = 0.020) post-treatment. Significantly enhanced vascular volume (VV) at the fracture site in the vibration groups was demonstrated by 3-D high-frequency power Doppler at week 2 (Sham pair: p = 0.021) and micro-computed tomography (microCT) microangiography at weeks 2 (OVX pair: p = 0.009) and 4 (OVX pair: p = 0.034), which echoed the osteogenesis findings by radiographic and microCT analysis. VV in the OVX groups was inferior to the Sham groups. However, OVX-V showed higher percentages of angiogenic enhancement than Sham-V. Despite impaired neo-angiogenesis in osteoporotic fractures, LMHFV could increase blood flow and angiogenesis in both normal and osteoporotic fractures, thus enhancing fracture healing.

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.

MOSAIC: a multiscale model of osteogenesis and sprouting angiogenesis with lateral inhibition of endothelial cells

The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.

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.

Difference in intraosseous blood vessel volume and number in osteoporotic model mice induced by spinal cord injury and sciatic nerve resection

In the present study, we examined intraosseous blood vessel parameters of the tibial metaphysis in mice using microcomputed tomography (µCT) to investigate the relationship between post-nerve-injury osteoporosis and local intraosseous blood vessel volume and number. Mice were randomly divided into groups receiving spinal cord injury (SCI), sciatic nerve resection group (NX), or intact controls (30 mice/group). Four weeks after surgery, mice were perfused with silicone and the distribution of intraosseous blood vessels analyzed by μCT. The bone density, μCT microstructure, biomechanical properties, and the immunohistochemical and biochemical indicators of angiogenesis were also measured. The SCI group showed significantly reduced tibial metaphysis bone density, μCT bone microstructure, tibial biomechanical properties, indicators of angiogenesis, and intraosseous blood vessel parameters compared to the NX group. Furthermore, the spinal cord-injured mice exhibited significantly decreased intraosseous blood vessel volume and number during the development of osteoporosis. In conclusion, these data suggest that decreased intraosseous blood vessel volume and number may play an important role in the development of post-nerve-injury osteoporosis.

A mathematical model of adult subventricular neurogenesis

Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments.

A mechanobiological model of orthodontic tooth movement

Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. In order to optimize orthodontic treatment, it is important to identify and study the biological processes involved. This article presents a mechanobiological model using partial differential equations to describe cell densities, growth factor concentrations, and matrix densities occurring during orthodontic tooth movement. We hypothesize that such a model can predict tooth movement based on the mechanobiological activity of cells in the PDL. The developed model consists of nine coupled non-linear partial differential equations, and two distinct signaling pathways were modeled: the RANKL-RANK-OPG pathway regulating the communication between osteoblasts and osteoclasts and the TGF-β pathway mediating the differentiation of mesenchymal stem cells into osteoblasts. The predicted concentrations and densities were qualitatively validated by comparing the results to experiments reported in the literature. In the current form, the model supports our hypothesis, as it is capable of conceptually simulating important features of the biological interactions in the alveolar bone-PDL complex during orthodontic tooth movement.

In vivo osteogenic response to different ratios of BMP-2 and VEGF released from a biodegradable porous system

Bone regeneration and vascularization with porous PLGA scaffolds loaded with VEGF (0.35 and 1.75 μg) and BMP-2 (3.5 and 17.5 μg), incorporated in PLGA microspheres, or the combination of either dose of BMP-2 with the low dose of VEGF were investigated in an intramedullary femur defect in rabbits. The system was designed to control growth factor (GF) release and maintain the GFs localized within the defect. An incomplete release was observed in vitro whereas in vivo VEGF and BMP-2 were totally delivered during 3 and 4 weeks, respectively. A weak synergistic effect of the dual delivery of VEGF and BMP-2 (high dose) was found by 4 weeks. However, the absence of an apparent synergistic long-term effect (12 weeks) of the combination over BMP-2 alone suggests that more work has to be done to optimize VEGF dose, sequential presentation, and the ratio of the two GFs to obtain a beneficial bone repair response.

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.

Influence of high-frequency cyclical stimulation on the bone fracture-healing process: mathematical and experimental models

Mechanical stimulation affects the evolution of healthy and fractured bone. However, the effect of applying cyclical mechanical stimuli on bone healing has not yet been fully clarified. The aim of the present study was to determine the influence of a high-frequency and low-magnitude cyclical displacement of the fractured fragments on the bone-healing process. This subject is studied experimentally and computationally for a sheep long bone. On the one hand, the mathematical computational study indicates that mechanical stimulation at high frequencies can stimulate and accelerate the process of chondrogenesis and endochondral ossification and consequently the bony union of the fracture. This is probably achieved by the interstitial fluid flow, which can move nutrients and waste from one place to another in the callus. This movement of fluid modifies the mechanical stimulus on the cells attached to the extracellular matrix. On the other hand, the experimental study was carried out using two sheep groups. In the first group, static fixators were implanted, while, in the second one, identical devices were used, but with an additional vibrator. This vibrator allowed a cyclic displacement with low magnitude and high frequency (LMHF) to be applied to the fractured zone every day; the frequency of stimulation was chosen from mechano-biological model predictions. Analysing the results obtained for the control and stimulated groups, we observed improvements in the bone-healing process in the stimulated group. Therefore, in this study, we show the potential of computer mechano-biological models to guide and define better mechanical conditions for experiments in order to improve bone fracture healing. In fact, both experimental and computational studies indicated improvements in the healing process in the LMHF mechanically stimulated fractures. In both studies, these improvements could be associated with the promotion of endochondral ossification and an increase in the rate of cell proliferation and tissue synthesis.

Simulation of fracture healing in the tibia: mechanoregulation of cell activity using a lattice modeling approach

In this study, a three-dimensional (3D) computational simulation of bone regeneration was performed in a human tibia under realistic muscle loading. The simulation was achieved using a discrete lattice modeling approach combined with a mechanoregulation algorithm to describe the cellular processes involved in the healing process-namely proliferation, migration, apoptosis, and differentiation of cells. The main phases of fracture healing were predicted by the simulation, including the bone resorption phase, and there was a qualitative agreement between the temporal changes in interfragmentary strain and bending stiffness by comparison to experimental data and clinical results. Bone healing was simulated beyond the reparative phase by modeling the transition of woven bone into lamellar bone. Because the simulation has been shown to work with realistic anatomical 3D geometry and muscle loading, it demonstrates the potential of simulation tools for patient-specific pre-operative treatment planning.

Designing optimal calcium phosphate scaffold-cell combinations using an integrative model-based approach

Bone formation is a very complex physiological process, involving the participation of many different cell types and regulated by countless biochemical, physical and mechanical factors, including naturally occurring or synthetic biomaterials. For the latter, calcium phosphate (CaP)-based scaffolds have proven to stimulate bone formation, but at present still result in a wide range of in vivo outcomes, which is partly related to the suboptimal use and combination with osteogenic cells. To optimize CaP scaffold selection and make their use in combination with cells more clinically relevant, this study uses an integrative approach in which mathematical modeling is combined with experimental research. This paper describes the development and implementation of an experimentally informed bioregulatory model of the effect of calcium ions released from CaP-based biomaterials on the activity of osteogenic cells and mesenchymal stem cell driven ectopic bone formation. The amount of bone formation predicted by the mathematical model corresponds to the amount measured experimentally under similar conditions. Moreover, the model is also able to qualitatively predict the experimentally observed impaired bone formation under conditions such as insufficient cell seeding and scaffold decalcification. A strategy was designed in silico to overcome the negative influence of a low initial cell density on the bone formation process. Finally, the model was applied to design optimal combinations of calcium-based biomaterials and cell culture conditions with the aim of maximizing the amount of bone formation. This work illustrates the potential of mathematical models as research tools to design more efficient and cell-customized CaP scaffolds for bone tissue engineering applications.

Feasibility of treating irradiated bone with intramedullary delivered autologous mesenchymal stem cells

Background. We aimed to explore (i) the short-term retention of intramedullary implanted mesenchymal stem cells BMSCs and (ii) their impact on the bone blood flow and metabolism in a rat model of hindlimb irradiation. Methods. Three months after 30 Gy irradiation, fourteen animals were referred into 2 groups: a sham-operated group (n = 6) and a treated group (n = 8) in which ¹¹¹In-labelled BMSCs (2 × 10⁶ cells) were injected in irradiated tibias. Bone blood flow and metabolism were assessed by serial ^99mTc-HDP scintigraphy and 1-wk cell retention by recordings of ^99mTc/¹¹¹In activities. Results. The amount of intramedullary implanted BMSCs was of 70% at 2 H, 40% at 48 H, and 38% at 168 H. Bone blood flow and bone metabolism were significantly increased during the first week after cell transplantation, but these effects were found to reduce at 2-mo followup. Conclusion. Short-term cell retention produced concomitant enhancement in irradiated bone blood flow and metabolism.

Combined in vivo/in silico study of mechanobiological mechanisms during endochondral ossification in bone healing

Mechanobiological theories have been introduced to illustrate the interaction between biology and the local mechanical environment during bone healing. Although several theories have been proposed, a quantitative validation using histomorphometric data is still missing. In this study, in vivo histological data based on an ovine animal experiment was quantified and used to validate bone healing simulations focussing on the endochondral ossification process. The bone formation at different callus regions (periosteal and endosteal bone at the medial and lateral side) was analyzed from in vivo data and quantitatively compared with in silico results. A histomorphometric difference was found in medial and lateral hard callus formation 3 weeks after osteotomy. However, the same amount of new bone was formed on both sides between week 3 and 6. Using a parametric approach, distinct ranges for mechanical strain levels regulating tissue formation were found, for which the in silico prediction agrees with the in vivo endochondral ossification both in pattern and quantity. According to this finding, a strain range of 1 to 8% seems to be conducive for cartilage formation while bone formation may be facilitated by strains up to 4%. This study demonstrates the potential of a thorough validation of in silico results for gaining a better understanding of mechanobiological mechanisms during bone healing.

Continuum-level modelling of cellular adhesion and matrix production in aggregates

Key regulators in tissue-engineering processes such as cell culture and cellular organisation are the cell-cell and cell-matrix interactions. As mathematical models are increasingly applied to investigate biological phenomena in the biomedical field, it is important, for some applications, that these models incorporate an adequate description of cell adhesion. This study describes the development of a continuum model that represents a cell-in-gel culture system used in bone-tissue engineering, namely that of a cell aggregate embedded in a hydrogel. Cell adhesion is modelled through the use of non-local (integral) terms in the partial differential equations. The simulation results demonstrate that the effects of cell-cell and cell-matrix adhesion are particularly important for the survival and growth of the cell population and the production of extracellular matrix by the cells, concurring with experimental observations in the literature.

The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3 mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.

Inter-species investigation of the mechano-regulation of bone healing: comparison of secondary bone healing in sheep and rat

Inter-species differences in regeneration exist in various levels. One aspect is the dynamics of bone regeneration and healing, e.g. small animals show a faster healing response when compared to large animals. Mechanical as well as biological factors are known to play a key role in the process. However, it remains so far unknown whether different animals follow at all comparable mechano-biological rules during tissue regeneration, and in particular during bone healing. In this study, we investigated whether differences observed in vivo in the dynamics of bone healing between rat and sheep are only due to differences in the animal size or whether these animals have a different mechano-biological response during the healing process. Histological sections from in vivo experiments were compared to in silico predictions of a mechano-biological computer model for the simulation of bone healing. Investigations showed that the healing processes in both animal models occur under significantly different levels of mechanical stimuli within the callus region, which could explain histological observations of early intramembranous ossification at the endosteal side. A species-specific adaptation of a mechano-biological model allowed a qualitative match of model predictions with histological observations. Specifically, when keeping cell activity processes at the same rate, the amount of tissue straining defining favorable mechanical conditions for the formation of bone had to be increased in the large animal model, with respect to the small animal, to achieve a qualitative agreement of model predictions with histological data. These findings illustrate that geometrical (size) differences alone cannot explain the distinctions seen in the histological appearance of secondary bone healing in sheep and rat. It can be stated that significant differences in the mechano-biological regulation of the healing process exist between these species. Future investigations should aim towards understanding whether these differences are due to differences in cell behavior, material properties of the newly formed tissues within the callus and/or differences in response to the mechanical environment.

A mechano-regulation model of fracture repair in vertebral bodies

In this study a multi-scale mechano-regulation model was developed in order to investigate the mechanobiology of trabecular fracture healing in vertebral bodies. A macro-scale finite element model of the spinal segment L3-L4-L5, including a mild wedge fracture in the body of the L4 vertebra, was used to determine the boundary conditions acting on a micro-scale finite element model simulating a portion of fractured trabecular bone. The micro-scale model, in turn, was utilized to predict the local patterns of tissue differentiation within the fracture gap and then how the equivalent mechanical properties of the macro-scale model change with time. The patterns of tissue differentiation predicted by the model appeared consistent with those observed in vivo. Bone formation occurred primarily through endochondral ossification. New woven bone was predicted to occupy the majority of the space within the fracture site approximately 7-8 weeks after the fracture event. Remodeling of cancellous bone architecture was then predicted, with complete new trabeculae forming due to bridging of the microcallus between the remnant trabeculae.

Reduced local blood supply to the tibial metaphysis is associated with ovariectomy-induced osteoporosis in mice

OBJECTIVE

To investigate angiogenesis of the tibial metaphysis in ovariectomized mice with microcomputed tomography, as well as to detect the expression of vascular endothelial growth factor (VEGF) in the metaphysis, and to explore the relationship between osteoporosis and local blood supply to bones.

METHODS

Sixty mice were randomly divided into an ovariectomy group (n = 30) and a control group (n = 30). Four weeks after ovariectomy, the mice were killed and the distribution of vessels in the tibial metaphysis was determined after silicone rubber perfusion. In addition, the expression of VEGF of the tibial metaphysis was immunohistochemically determined and bone mineral density, microarchitecture, and biomechanics were tested.

RESULTS

The bone mineral density, biomechanical parameters, number of microvessels, and expression of VEGF were significantly reduced in the tibial metaphysis of ovariectomized mice, whose bone microarchitecture was also disrupted.

CONCLUSION

In this study, it was found that reduced local blood supply to the tibial metaphysis may be associated with ovariectomy-induced osteoporosis.

Computational modelling of biomaterial surface interactions with blood platelets and osteoblastic cells for the prediction of contact osteogenesis

Surface microroughness can induce contact osteogenesis (bone formation initiated at the implant surface) around oral implants, which may result from different mechanisms, such as blood platelet-biomaterial interactions and/or interaction with (pre-)osteoblast cells. We have developed a computational model of implant endosseous healing that takes into account these interactions. We hypothesized that the initial attachment and growth factor release from activated platelets is crucial in achieving contact osteogenesis. In order to investigate this, a computational model was applied to an animal experiment [7] that looked at the effect of surface microroughness on endosseous healing. Surface-specific model parameters were implemented based on in vitro data (Lincks et al. Biomaterials 1998;19:2219-32). The predicted spatio-temporal patterns of bone formation correlated with the histological data. It was found that contact osteogenesis could not be predicted if only the osteogenic response of cells was up-regulated by surface microroughness. This could only be achieved if platelet-biomaterial interactions were sufficiently up-regulated as well. These results confirmed our hypothesis and demonstrate the added value of the computational model to study the importance of surface-mediated events for peri-implant endosseous healing.

Finite element method (FEM), mechanobiology and biomimetic scaffolds in bone tissue engineering

Techniques of bone reconstructive surgery are largely based on conventional, non-cell-based therapies that rely on the use of durable materials from outside the patient's body. In contrast to conventional materials, bone tissue engineering is an interdisciplinary field that applies the principles of engineering and life sciences towards the development of biological substitutes that restore, maintain, or improve bone tissue function. Bone tissue engineering has led to great expectations for clinical surgery or various diseases that cannot be solved with traditional devices. For example, critical-sized defects in bone, whether induced by primary tumor resection, trauma, or selective surgery have in many cases presented insurmountable challenges to the current gold standard treatment for bone repair. The primary purpose of bone tissue engineering is to apply engineering principles to incite and promote the natural healing process of bone which does not occur in critical-sized defects. The total market for bone tissue regeneration and repair was valued at $1.1 billion in 2007 and is projected to increase to nearly $1.6 billion by 2014.Usually, temporary biomimetic scaffolds are utilized for accommodating cell growth and bone tissue genesis. The scaffold has to promote biological processes such as the production of extra-cellular matrix and vascularisation, furthermore the scaffold has to withstand the mechanical loads acting on it and to transfer them to the natural tissues located in the vicinity. The design of a scaffold for the guided regeneration of a bony tissue requires a multidisciplinary approach. Finite element method and mechanobiology can be used in an integrated approach to find the optimal parameters governing bone scaffold performance.In this paper, a review of the studies that through a combined use of finite element method and mechano-regulation algorithms described the possible patterns of tissue differentiation in biomimetic scaffolds for bone tissue engineering is given. Firstly, the generalities of the finite element method of structural analysis are outlined; second, the issues related to the generation of a finite element model of a given anatomical site or of a bone scaffold are discussed; thirdly, the principles on which mechanobiology is based, the principal theories as well as the main applications of mechano-regulation models in bone tissue engineering are described; finally, the limitations of the mechanobiological models and the future perspectives are indicated.

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.

A hybrid bioregulatory model of angiogenesis during bone fracture healing

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

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

Recently developed atrophic non-union models are a good representation of the clinical situation in which many non-unions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures.

In light of the ageing population, the occurrence of bone fractures is expected to rise substantially in the near future. In 5 to 10% of these cases, the healing process does not succeed in repairing the bone, leading to the formation of delayed unions or even non-unions. In this study we used a combination of an animal model mimicking a clinical non-union situation and a mathematical model developed for normal fracture healing to investigate both the causes of non-union formation and potential therapeutic strategies that can be applied to restart the healing process. After showing that the mathematical model is able to simulate key aspects of the non-union formation, we have used it to investigate several treatment strategies. One of these strategies, the treatment of a non-union involving a transplantation of cells from the bone marrow to the fracture site, was also tested in a pilot animal experiment. Both the simulations and the experiments showed the formation of a bony union between the fractured bone ends. In addition, we used the mathematical model to explain some unexpected experimental observations. This study demonstrates the added value of using a combination of mathematical modelling and experimental research as well the potential of using cell transplantation for the treatment of non-unions.

Low oxygen tension is a more potent promoter of chondrogenic differentiation than dynamic compression

During fracture healing and microfracture treatment of cartilage defects mesenchymal stem cells (MSCs) infiltrate the wound site, proliferate extensively and differentiate along a cartilaginous or an osteogenic lineage in response to local environmental cues. MSCs may be able to directly sense their mechanical environment or alternatively, the mechanical environment could act indirectly to regulate MSC differentiation by inhibiting angiogenesis and diminishing the supply of oxygen and other regulatory factors. Dynamic compression has been shown to regulate chondrogenesis of MSCs. In addition, previous studies have shown that a low oxygen environment promotes in vitro chondrogenesis of MSCs. The hypothesis of this study is that a low oxygen environment is a more potent promoter of chondrogenic differentiation of MSCs embedded in agarose hydrogels compared to dynamic compression. In MSC-seeded constructs supplemented with TGF-beta3, GAG and collagen accumulation was higher in low oxygen conditions compared to normoxia. For normoxic and low oxygen culture GAG accumulation within the agarose hydrogel was inhomogeneous, with low levels of GAG measured in the annulus of constructs maintained in normoxic conditions. Dynamic compression did not significantly increase GAG or collagen accumulation in normoxia. However under low oxygen conditions, dynamic compression reduced GAG accumulation compared to free-swelling controls, but remained higher than comparable constructs maintained in normoxic conditions. This study demonstrates that continuous exposure to low oxygen tension is a more potent pro-chondrogenic stimulus than 1h/day of dynamic compression for porcine MSCs embedded in agarose hydrogels.

In silico design of treatment strategies in wound healing and bone fracture healing

Wound and bone fracture healing are natural repair processes initiated by trauma. Over the last decade, many mathematical models have been established to investigate the healing processes in silico, in addition to ongoing experimental work. In recent days, the focus of the mathematical models has shifted from simulation of the healing process towards simulation of the impaired healing process and the in silico design of treatment strategies. This review describes the most important causes of failure of the wound and bone fracture healing processes and the experimental models and methods used to investigate and treat these impaired healing cases. Furthermore, the mathematical models that are described address these impaired healing cases and investigate various therapeutic scenarios in silico. Examples are provided to illustrate the potential of these in silico experiments. Finally, limitations of the models and the need for and ability of these models to capture patient specificity and variability are discussed.

A mathematical model of epiphyseal development: hypothesis on the cartilage canals growth

The role of cartilage canals is to transport nutrients and biological factors that cause the appearance of the secondary ossification centre (SOC). The SOC appears in the centre of the epiphysis of long bones. The canal development is a complex interaction between mechanical and biological factors that guide its expansion into the centre of the epiphysis. This article introduces the 'Hypothesis on the growth of cartilage canals'. Here, we have considered that the development of these canals is an essential event for the appearance of SOC. Moreover, it is also considered to be important for the transport of molecular factors (RUNX2 and MMP9) at the ends of such canals. Once the canals are merged in the centre of the epiphysis, these factors are released causing hypertrophy of adjacent cells. This RUNX2 and MMP9 release occurs due to the action of mechanical loads that supports the epiphysis. In order to test this hypothesis, we use a hybrid approach using the finite element method to simulate the mechanical stresses present in the epiphysis and the cellular automata to simulate the expansion of the canals and the hypertrophy factors pathway. By using this hybrid approach, we have obtained as a result the spatial-temporal patterns for the growth of cartilage canals and hypertrophy factors within the epiphysis. The model is in qualitative agreement with experimental results previously reported by other authors. Thus, we conclude that this model may be used as a methodological basis to present a complete mathematical model of the processes involved in epiphyseal development.

Regulation of angiogenesis during osseointegration by titanium surface microstructure and energy

Rough titanium (Ti) surface microarchitecture and high surface energy have been shown to increase osteoblast differentiation, and this response occurs through signaling via the alpha(2)beta(1) integrin. However, clinical success of implanted materials is dependent not only upon osseointegration but also on neovascularization in the peri-implant bone. Here we tested the hypothesis that Ti surface microtopography and energy interact via alpha(2)beta(1) signaling to regulate the expression of angiogenic growth factors. Primary human osteoblasts (HOB), MG63 cells and MG63 cells silenced for alpha(2) integrin were cultured on Ti disks with different surface microtopographies and energies. Secreted levels of vascular endothelial growth factor-A (VEGF-A), basic fibroblast growth factor (FGF-2), epidermal growth factor (EGF), and angiopoietin-1 (Ang-1) were measured. VEGF-A increased 170% and 250% in MG63 cultures, and 178% and 435% in HOB cultures on SLA and modSLA substrates, respectively. In MG63 cultures, FGF-2 levels increased 20 and 40-fold while EGF increased 4 and 6-fold on SLA and modSLA surfaces. These factors were undetectable in HOB cultures. Ang-1 levels were unchanged on all surfaces.Media from modSLA MG63 cultures induced more rapid differentiation of endothelial cells and this effect was inhibited by anti-VEGF-A antibodies. Treatment of MG63 cells with 1 alpha,25(OH)(2)D3 enhanced levels of VEGF-A on SLA and modSLA.Silencing the alpha(2) integrin subunit increased VEGF-A levels and decreased FGF-2 levels. These results show that Ti surface microtopography and energy modulate secretion of angiogenic growth factors by osteoblasts and that this regulation is mediated at least partially via alpha(2)beta(1) integrin signaling.

Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are included. Mechanics and biology are coupled by making certain parameters of a previously established bioregulatory model dependent on local mechanical stimuli. To illustrate the potential added value of such a framework, this coupled model was applied to investigate whether local mechanical stimuli influencing only the angiogenic process can explain normal healing as well as overload-induced nonunion development. Simulation results showed that mechanics acting directly on angiogenesis alone was not able to predict the formation of overload-induced nonunions. However, the direct action of mechanics on both angiogenesis and osteogenesis was able to predict overload-induced nonunion formation, confirming the hypotheses of several experimental studies investigating the interconnection between angiogenesis and osteogenesis. This study shows that mathematical models can assist in testing hypothesis on the nature of the interaction between biology and mechanics.

Ectopic osteogenesis of mouse bone marrow stromal cells transfected with BMP 2/VEGF(165) genes in vivo

OBJECTIVE

To evaluate the osteogenic efficacy of mouse bone marrow stromal cells (mBMSC) transfected with bone morphogenetic protein 2 (BMP2) and vascular endothelial growth factor 165 (VEGF(165)) genes.

METHODS

pIRES-BMP2-VEGF(165) plasmid DNA was introduced into the mBMSC using a liposome-mediated method. The expression of BMP2 and VEGF(165) genes was assessed by reverse transcription-polymerase chain reaction (RT-PCR) and immunohistochemical analysis. Transfected cells were injected into the thigh muscle pouches of four nude mice. The osteoinductivity activity of the transfected cells was evaluated by radiographic and histological analysis at 4 weeks after injection.

RESULTS

The mRNA and proteins of both BMP2 and VEGF(165) were successfully expressed in mBMSC as confirmed by RT-PCR and immunohistochemical analysis. Ectopically formed bone tissue was clearly observed at 4 weeks after cell injection in the thigh muscle pouches of the nude mice.

CONCLUSION

mBMSC transfected with BMP2 and VEGF(165) genes can induce ectopic osteogenesis.

Dose effect of dual delivery of vascular endothelial growth factor and bone morphogenetic protein-2 on bone regeneration in a rat critical-size defect model

The dose effect of dual delivery of vascular endothelial growth factor (VEGF) and bone morphogenetic protein-2 (BMP-2) on bone regeneration was investigated in a rat cranial critical-size defect (CSD). It was hypothesized that decreasing amounts of BMP-2 would result in a dose-dependent decrease in bone formation, and that this reduction in bone formation could be reversed by adding increasing amounts of VEGF. In vitro release kinetics of VEGF or BMP-2 were examined over 28 days. Next, scaffolds were implanted within a rat cranial CSD containing different combinations of both BMP-2 and VEGF. At 12 weeks, samples were analyzed using microcomputed tomography and histology. In vitro, VEGF and BMP-2 exhibited burst release in the first 24 h followed by a significant decrease in release rate over 27 days. Overall, BMP-2 had a more sustained release versus VEGF. An in vivo dose-dependent decrease in percentage of bone fill (PBF) was observed for BMP-2. The addition of VEGF was unable to reverse this decrease in PBF, although improvements in the number of bridged defects did occur in some groups. This suggests that for this particular model simultaneous release of BMP-2 and VEGF does not increase bone formation over BMP-2 alone at 12 weeks.

Dose effect of dual delivery of vascular endothelial growth factor and bone morphogenetic protein-2 on bone regeneration in a rat critical-size defect model

The dose effect of dual delivery of vascular endothelial growth factor (VEGF) and bone morphogenetic protein-2 (BMP-2) on bone regeneration was investigated in a rat cranial critical-size defect (CSD). It was hypothesized that decreasing amounts of BMP-2 would result in a dose-dependent decrease in bone formation, and that this reduction in bone formation could be reversed by adding increasing amounts of VEGF. In vitro release kinetics of VEGF or BMP-2 were examined over 28 days. Next, scaffolds were implanted within a rat cranial CSD containing different combinations of both BMP-2 and VEGF. At 12 weeks, samples were analyzed using microcomputed tomography and histology. In vitro, VEGF and BMP-2 exhibited burst release in the first 24 h followed by a significant decrease in release rate over 27 days. Overall, BMP-2 had a more sustained release versus VEGF. An in vivo dose-dependent decrease in percentage of bone fill (PBF) was observed for BMP-2. The addition of VEGF was unable to reverse this decrease in PBF, although improvements in the number of bridged defects did occur in some groups. This suggests that for this particular model simultaneous release of BMP-2 and VEGF does not increase bone formation over BMP-2 alone at 12 weeks.

Simulation of the nutrient supply in fracture healing

The healing process for bone fractures is sensitive to mechanical stability and blood supply at the fracture site. Most currently available mechanobiological algorithms of bone healing are based solely on mechanical stimuli, while the explicit analysis of revascularization and its influences on the healing process have not been thoroughly investigated in the literature. In this paper, revascularization was described by two separate processes: angiogenesis and nutrition supply. The mathematical models for angiogenesis and nutrition supply have been proposed and integrated into an existing fuzzy algorithm of fracture healing. The computational algorithm of fracture healing, consisting of stress analysis, analyses of angiogenesis and nutrient supply, and tissue differentiation, has been tested on and compared with animal experimental results published previously. The simulation results showed that, for a small and medium-sized fracture gap, the nutrient supply is sufficient for bone healing, for a large fracture gap, non-union may be induced either by deficient nutrient supply or inadequate mechanical conditions. The comparisons with experimental results demonstrated that the improved computational algorithm is able to simulate a broad spectrum of fracture healing cases and to predict and explain delayed unions and non-union induced by large gap sizes and different mechanical conditions. The new algorithm will allow the simulation of more realistic clinical fracture healing cases with various fracture gaps and geometries and may be helpful to optimise implants and methods for fracture fixation.

Experimental-computational evaluation of human bone marrow stromal cell spreading on trabecular bone structures

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading. Only the first phase of in vitro scaffold colonization was addressed, in which cells migrate and proliferate up to the stage when the surface of the bone is covered as a monolayer, a critical prerequisite for further tissue formation. The results confirm the model's ability to represent experimentally observed cell population spreading. The key advantage of the computational model was that by incorporating complex 3D structure, cell behavior can be characterized quantitatively in terms of intrinsic migration parameters, which could potentially be used for predictions on different macro-porous scaffolds subject to additional experimental validation. This type of modeling will prove useful in predicting cell colonization and improving strategies for skeletal tissue engineering.

Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering

Scaffold biomaterials for tissue engineering can be produced in many different ways depending on the applications and the materials used. Most research into new biomaterials is based on an experimental trial-and-error approach that limits the possibility of making many variations to a single material and studying its interaction with its surroundings. Instead, computer simulation applied to tissue engineering can offer a more exhaustive approach to test and screen out biomaterials. In this paper, a review of the current approach in biomaterials designed through computer-aided design (CAD) and through finite-element modelling is given. First we review the approach used in tissue engineering in the development of scaffolds and the interactions existing between biomaterials, cells and mechanical stimuli. Then, scaffold fabrication through CAD is presented and characterization of existing scaffolds through computed images is reviewed. Several case studies of finite-element studies in tissue engineering show the usefulness of computer simulations in determining the mechanical environment of cells when seeded into a scaffold and the proper design of the geometry and stiffness of the scaffold. This creates a need for more advanced studies that include aspects of mechanobiology in tissue engineering in order to be able to predict over time the growth and differentiation of tissues within scaffolds. Finally, current perspectives indicate that more efforts need to be put into the development of such advanced studies, with the removal of technical limitations such as computer power and the inclusion of more accurate biological and genetic processes into the developed algorithms.

In silico biology of bone modelling and remodelling: regeneration

Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico. The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was regulated only by biological stimuli such as growth factors. The most recent mathematical models couple the influences of both biological and mechanical stimuli. Examples are given to illustrate the added value of mathematical regeneration research, specifically in the in silico design of treatment strategies for non-unions. Drawbacks of the current continuum-type models, together with possible solutions in extending the models towards other time and length scales are discussed. Finally, the demands for dedicated and more quantitative experimental research are presented.