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

Engineering next-generation oxygen-generating scaffolds to enhance bone regeneration

In bone, an adequate oxygen (O2) supply is crucial during development, homeostasis, and healing. Oxygen-generating scaffolds (OGS) have demonstrated significant potential to enhance bone regeneration. However, the complexity of O2 delivery and signaling in vivo makes it challenging to tailor the design of OGS to precisely meet this biological requirement. We review recent advances in OGS and analyze persisting engineering and translational hurdles. We also discuss the potential of computational and machine learning (ML) models to facilitate the integration of novel imaging data with biological readouts and advanced biomanufacturing technologies. By elucidating how to tackle current challenges using cutting-edge technologies, we provide insights for transitioning from traditional to next-generation OGS to improve bone regeneration in patients.

Finite element solution of coupled multiphysics reaction-diffusion equations for fracture healing in hard biological tissues

This study proposes a computational framework to investigate the multi-stage process of fracture healing in hard tissues, e.g., long bone, based on the mathematical Bailon-Plaza and Van der Meulen formulation. The goal is to explore the influence of critical biological factors by employing the finite element method for more realistic configurations. The model integrates a set of variables, including cell densities, growth factors, and extracellular matrix contents, managed by a coupled system of partial differential equations. A weak finite element formulation is introduced to enhance the numerical robustness for coarser mesh grids, complex geometries, and more accurate boundary conditions. This formulation is less sensitive to mesh quality and converges smoothly with mesh refinement, exhibiting superior numerical stability compared to previously available strong-form solutions. The model accurately reproduces various stages of healing, including soft cartilage callus formation, endochondral and intramembranous ossification, and hard bony callus development for various sizes of fracture gap. Model predictions align with the existing research and are logically coherent with the available experimental data. The developed multiphysics simulation clarifies the coordination of cellular dynamics, extracellular matrix alterations, and signaling growth factors during fracture healing.

Mini-bones: miniaturized bone in vitro models

In bone tissue engineering (TE) and regeneration, miniaturized, (sub)millimeter-sized bone models have become a popular trend since they bring about physiological biomimicry, precise orchestration of concurrent stimuli, and compatibility with high-throughput setups and high-content imaging. They also allow efficient use of cells, reagents, materials, and energy. In this review, we describe the state of the art of miniaturized in vitro bone models, or 'mini-bones', describing these models based on their characteristics of (multi)cellularity and engineered extracellular matrix (ECM), and elaborating on miniaturization approaches and fabrication techniques. We analyze the performance of 'mini-bone' models according to their applications for studying basic bone biology or as regeneration models, disease models, and screening platforms, and provide an outlook on future trends, challenges, and opportunities.

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.

Horizontal Alveolar Ridge Splitting and Expansion

When considering placing dental implants in atrophic edentulous sites, there may be inadequate site width and little or no vertical bone loss. Any of several surgical procedures can augment these sites. Extracortical augmentation is done by applying graft material against the cortical bone. This technique expects progenitor cells to migrate outside the bony ridge's confines and form new bone. Another method entails ridge splitting and expansion to create space for osteogenesis and, when possible, implant placement. This may be a better method for horizontal ridge augmentation. The ridge is split, separating the facial and lingual cortices for a complete bone fracture. The patient's osseous cells can then migrate into the created space from the exposed medullary bone to form bone. The technique can be preferably performed flapless so the intact periosteum maintains a blood supply to ensure appropriate healing.

An in silico micro-multiphysics agent-based approach for simulating bone regeneration in a mouse femur defect model

Bone defects represent a challenging clinical problem as they can lead to non-union. In silico models are well suited to study bone regeneration under varying conditions by linking both cellular and systems scales. This paper presents an in silico micro-multiphysics agent-based (micro-MPA) model for bone regeneration following an osteotomy. The model includes vasculature, bone, and immune cells, as well as their interaction with the local environment. The model was calibrated by time-lapsed micro-computed tomography data of femoral osteotomies in C57Bl/6J mice, and the differences between predicted bone volume fractions and the longitudinal in vivo measurements were quantitatively evaluated using root mean square error (RMSE). The model performed well in simulating bone regeneration across the osteotomy gap, with no difference (5.5% RMSE, p = 0.68) between the in silico and in vivo groups for the 5-week healing period - from the inflammatory phase to the remodelling phase - in the volume spanning the osteotomy gap. Overall, the proposed micro-MPA model was able to simulate the influence of the local mechanical environment on bone regeneration, and both this environment and cytokine concentrations were found to be key factors in promoting bone regeneration. Further, the validated model matched clinical observations that larger gap sizes correlate with worse healing outcomes and ultimately simulated non-union. This model could help design and guide future experimental studies in bone repair, by identifying which are the most critical in vivo experiments to perform.

External mechanical loading overrules cell-cell mechanical communication in sprouting angiogenesis during early bone regeneration

Sprouting angiogenesis plays a key role during bone regeneration. For example, insufficient early revascularization of the injured site can lead to delayed or non-healing. During sprouting, endothelial cells are known to be mechano-sensitive and respond to local mechanical stimuli. Endothelial cells interact and communicate mechanically with their surroundings, such as outer-vascular stromal cells, through cell-induced traction forces. In addition, external physiological loads act at the healing site, resulting in tissue deformations and impacting cellular arrangements. How these two distinct mechanical cues (cell-induced and external) impact angiogenesis and sprout patterning in early bone healing remains however largely unknown. Therefore, the aim of this study was to investigate the relative role of externally applied and cell-induced mechanical signals in driving sprout patterning at the onset of bone healing. To investigate cellular self-organisation in early bone healing, an in silico model accounting for the mechano-regulation of sprouting angiogenesis and stromal cell organization was developed. Computer model predictions were compared to in vivo experiments of a mouse osteotomy model stabilized with a rigid or a semirigid fixation system. We found that the magnitude and orientation of principal strains within the healing region can explain experimentally observed sprout patterning, under both fixation conditions. Furthermore, upon simulating the selective inhibition of either cell-induced or externally applied mechanical cues, external mechanical signals appear to overrule the mechanical communication acting on a cell-cell interaction level. Such findings illustrate the relevance of external mechanical signals over the local cell-mediated mechanical cues and could be used in the design of fracture treatment strategies for bone regeneration.

On the role of mechanical signals on sprouting angiogenesis through computer modeling approaches

Sprouting angiogenesis, the formation of new vessels from preexisting vasculature, is an essential process in the regeneration of new tissues as well as in the development of some diseases like cancer. Although early studies identified chemical signaling as the main driver of this process, many recent studies have shown a strong role of mechanical signals in the formation of new capillaries. Different types of mechanical signals (e.g., external forces, cell traction forces, and blood flow-induced shear forces) have been shown to play distinct roles in the process; however, their interplay remains still largely unknown. During the last decades, mathematical and computational modeling approaches have been developed to investigate and better understand the mechanisms behind mechanically driven angiogenesis. In this manuscript, we review computational models of angiogenesis with a focus on models investigating the role of mechanics on the process. Our aim is not to provide a detailed review on model methodology but to describe what we have learnt from these models. We classify models according to the mechanical signals being investigated and describe how models have looked into their role on the angiogenic process. We show that a better understanding of the mechanobiology of the angiogenic process will require the development of computer models that incorporate the interactions between the multiple mechanical signals and their effect on cellular responses, since they all seem to play a key in sprout patterning. In the end, we describe some of the remaining challenges of computational modeling of angiogenesis and discuss potential avenues for future research.

The vascularization paradox of non-union formation

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

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.

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

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

Angiogenesis and vessel co-option in a mathematical model of diffusive tumor growth: The role of chemotaxis

This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells. The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mechanism (CM). Namely, it is first proposed a detailed general family of models of the CM, based on a statistical mechanics approach. The key hypothesis is that the CM is composed by two components: i) the well-known bias induced by the angiogenic factor gradient; ii) the presence of stochastic changes of the velocity direction, thus giving rise to a diffusive component. Then, some further assumptions and simplifications are applied in order to derive a specific model to be used in the simulations. The tumor progression is favored by its acidic aggression towards the healthy cells. The model includes the evolution of many biological and chemical species. Numerical simulations show the onset of a traveling wave eventually replacing the host tissue with a fully vascularized tumor. The results of simulations agree with experimental measures of the vasculature density in tumors, even in the case of particularly hypoxic tumors.

Simulating flow induced migration in vascular remodelling

Shear stress induces directed endothelial cell (EC) migration in blood vessels leading to vessel diameter increase and induction of vascular maturation. Other factors, such as EC elongation and interaction between ECs and non-vascular areas are also important. Computational models have previously been used to study collective cell migration. These models can be used to predict EC migration and its effect on vascular remodelling during embryogenesis. We combined live time-lapse imaging of the remodelling vasculature of the quail embryo yolk sac with flow quantification using a combination of micro-Particle Image Velocimetry and computational fluid dynamics. We then used the flow and remodelling data to inform a model of EC migration during remodelling. To obtain the relation between shear stress and velocity in vitro for EC cells, we developed a flow chamber to assess how confluent sheets of ECs migrate in response to shear stress. Using these data as an input, we developed a multiphase, self-propelled particles (SPP) model where individual agents are driven to migrate based on the level of shear stress while maintaining appropriate spatial relationship to nearby agents. These agents elongate, interact with each other, and with avascular agents at each time-step of the model. We compared predicted vascular shape to real vascular shape after 4 hours from our time-lapse movies and performed sensitivity analysis on the various model parameters. Our model shows that shear stress has the largest effect on the remodelling process. Importantly, however, elongation played an especially important part in remodelling. This model provides a powerful tool to study the input of different biological processes on remodelling.

Shear stress is known to play a leading role in endothelial cell (EC) migration and hence, vascular remodelling. Vascular remodelling is, however, more complicated than only EC migration. To achieve a better understanding of this process, we developed a computational model in which, shear stress mediated EC migration has the leading role and other factors, such as avascular regions and EC elongation, are also accounted for. We have tested this model for different vessel shapes during remodelling and could study the role that each of these factors play in remodelling. This model gives us the possibility of addition of other factors such as biochemical signals and angiogenesis which will help us in the study of vascular remodelling in both development and disease.

Lipid availability determines fate of skeletal progenitor cells via SOX9

The avascular nature of cartilage makes it a unique tissue^1–4, but whether and how the absence of nutrient supply regulates chondrogenesis remains unknown. Here, we show that obstruction of vascular invasion during bone healing favours chondrogenic over osteogenic differentiation of skeletal progenitor cells. Unexpectedly, this process is driven by a decreased availability of extracellular lipids. When lipids are scarce, skeletal progenitors activate FoxO transcription factors, which bind to the Sox9 promoter and increase its expression. Besides initiating chondrogenesis, SOX9 acts as a regulator of cellular metabolism by suppressing fatty acid oxidation, and thus adapts the cells to an avascular life. Our results define lipid scarcity as an important determinant of chondrogenic commitment, reveal a role for FoxOs during lipid starvation, and identify SOX9 as a critical metabolic mediator. These data highlight the importance of the nutritional microenvironment in the specification of skeletal cell fate.

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

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

The endothelial tip-stalk cell selection and shuffling during angiogenesis

Angiogenesis is a critical, fine-tuned, multi-staged biological process. Tip-stalk cell selection and shuffling are the building blocks of sprouting angiogenesis. Accumulated evidences show that tip-stalk cell selection and shuffling are regulated by a variety of physical, chemical and biological factors, especially the interaction among multiple genes, their products and environments. The classic Notch-VEGFR, Slit-Robo, ECM-binding integrin, semaphorin and CCN family play important roles in tip-stalk cell selection and shuffling. In this review, we outline the progress and prospect in the mechanism and the roles of the various molecules and related signaling pathways in endothelial tip-stalk cell selection and shuffling. In the future, the regulators of tip-stalk cell selection and shuffling would be the potential markers and targets for angiogenesis.

Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies

Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.

Agent-based computational model of retinal angiogenesis simulates microvascular network morphology as a function of pericyte coverage

OBJECTIVE

Define a role for perivascular cells during developmental retinal angiogenesis in the context of EC Notch1-DLL4 signaling at the multicellular network level.

METHODS

The retinal vasculature is highly sensitive to growth factor-mediated intercellular signaling. Although EC signaling has been explored in detail, it remains unclear how PC function to modulate these signals that lead to a diverse set of vascular network patterns in health and disease. We have developed an ABM of retinal angiogenesis that incorporates both ECs and PCs to investigate the formation of vascular network patterns as a function of pericyte coverage. We use our model to test the hypothesis that PC modulate Notch1-DLL4 signaling in endothelial cell-endothelial cell interactions.

RESULTS

Agent-based model (ABM) simulations that include PCs more accurately predict experimentally observed vascular network morphologies than simulations that lack PCs, suggesting that PCs may influence sprouting behaviors through physical blockade of endothelial intercellular connections.

CONCLUSIONS

This study supports a role for PCs as a physical buffer to signal propagation during vascular network formation-a barrier that may be important for generating healthy microvascular network patterns.

Enhanced Delta-Notch Lateral Inhibition Model Incorporating Intracellular Notch Heterogeneity and Tension-Dependent Rate of Delta-Notch Binding that Reproduces Sprouting Angiogenesis Patterns

Endothelial cells adopt unique cell fates during sprouting angiogenesis, differentiating into tip or stalk cells. The fate selection process is directed by Delta-Notch lateral inhibition pathway. Classical Delta-Notch models produce a spatial pattern of tip cells separated by a single stalk cell, or the salt-and-pepper pattern. However, classical models cannot explain alternative tip-stalk patterning, such as tip cells that are separated by two or more stalk cells. We show that lateral inhibition models involving only Delta and Notch proteins can also recapitulate experimental tip-stalk patterns by invoking two mechanisms, specifically, intracellular Notch heterogeneity and tension-dependent rate of Delta-Notch binding. We introduce our computational model and analysis where we establish that our enhanced Delta-Notch lateral inhibition model can recapitulate a greater variety of tip-stalk patterning which is previously not possible using classical lateral inhibition models. In our enhanced Delta-Notch lateral inhibition model, we observe the existence of a hybrid cell type displaying intermediate tip and stalk cells’ characteristics. We validate the existence of such hybrid cells by immuno-staining of endothelial cells with tip cell markers, Delta and CD34, which substantiates our enhanced model.

Three-dimensional computational model simulating the fracture healing process with both biphasic poroelastic finite element analysis and fuzzy logic control

A dynamic model regulated by both biphasic poroelastic finite element analysis and fuzzy logic control was established. Fuzzy logic control was an easy and comprehensive way to simulate the tissue differentiation process, and it is convenient for researchers and medical experts to communicate with one another to change the fuzzy logic rules and improve the simulation of the tissue differentiation process. In this study, a three-dimensional fracture healing model with two different interfragmentary movements (case A: 0.25 mm and case B: 1.25 mm) was analysed with the new set-up computational model. As the healing process proceeded, both simulated interfragmentary movements predicted a decrease and the time that the decrease started for case B was later than that for case A. Compared with experimental results, both cases corresponded with experimental data well. The newly established dynamic model can simulate the healing process under different mechanical environments and has the potential to extend to the multiscale healing model, which is essential for reducing the animal experiments and helping to characterise the complex dynamic interaction between tissue differentiations within the callus region.

Automated tracking and quantification of angiogenic vessel formation in 3D microfluidic devices

Angiogenesis, the growth of new blood vessels from pre-existing vessels, is a critical step in cancer invasion. Better understanding of the angiogenic mechanisms is required to develop effective antiangiogenic therapies for cancer treatment. We culture angiogenic vessels in 3D microfluidic devices under different Sphingosin-1-phosphate (S1P) conditions and develop an automated vessel formation tracking system (AVFTS) to track the angiogenic vessel formation and extract quantitative vessel information from the experimental time-lapse phase contrast images. The proposed AVFTS first preprocesses the experimental images, then applies a distance transform and an augmented fast marching method in skeletonization, and finally implements the Hungarian method in branch tracking. When applying the AVFTS to our experimental data, we achieve 97.3% precision and 93.9% recall by comparing with the ground truth obtained from manual tracking by visual inspection. This system enables biologists to quantitatively compare the influence of different growth factors. Specifically, we conclude that the positive S1P gradient increases cell migration and vessel elongation, leading to a higher probability for branching to occur. The AVFTS is also applicable to distinguish tip and stalk cells by considering the relative cell locations in a branch. Moreover, we generate a novel type of cell lineage plot, which not only provides cell migration and proliferation histories but also demonstrates cell phenotypic changes and branch information.

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.

Microvessel Chaste: An Open Library for Spatial Modeling of Vascularized Tissues

Spatial models of vascularized tissues are widely used in computational physiology. We introduce a software library for composing multiscale, multiphysics models for applications including tumor growth, angiogenesis, osteogenesis, coronary perfusion, and oxygen delivery. Composition of such models is time consuming, with many researchers writing custom software. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissues, and comparison of predictions with in vivo or in vitro experiments and alternative computational formulations. Microvessel Chaste can be used to build simulations of vessel growth and adaptation in response to mechanical and chemical stimuli; intra- and extravascular transport of nutrients, growth factors and drugs; and cell proliferation in complex 3D geometries. In addition, it can be used to develop custom software for integrating modeling with experimental data processing workflows, facilitated by a comprehensive Python interface to solvers implemented in C++. This article links to two reproducible example problems, showing how the library can be used to build simulations of tumor growth and angiogenesis with realistic vessel networks.

Multiscale Modeling of Bone Healing: Toward a Systems Biology Approach

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

Multiscale modeling methods in biomechanics

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

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

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

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

For further resources related to this article, please visit the WIREs website.

An intramembranous ossification model for the in silico analysis of bone tissue formation in tooth extraction sites

The accurate modeling of biological processes allows us to predict the spatiotemporal behavior of living tissues by computer-aided (in silico) testing, a useful tool for the development of medical strategies, avoiding the expenses and potential ethical implications of in vivo experimentation. A model for bone healing in mouth would be useful for selecting proper surgical techniques in dental procedures. In this paper, the formulation and implementation of a model for Intramembranous Ossification is presented aiming to describe the complex process of bone tissue formation in tooth extraction sites. The model consists in a mathematical description of the mechanisms in which different types of cells interact, synthesize and degrade extracellular matrices under the influence of biochemical factors. Special attention is given to angiogenesis, oxygen-dependent effects and growth factor-induced apoptosis of fibroblasts. Furthermore, considering the depth-dependent vascularization of mandibular bone and its influence on bone healing, a functional description of the cell distribution on the severed periodontal ligament (PDL) is proposed. The developed model was implemented using the finite element method (FEM) and successfully validated by simulating an animal in vivo experiment on dogs reported in the literature. A good fit between model outcome and experimental data was obtained with a mean absolute error of 3.04%. The mathematical framework presented here may represent an important tool for the design of future in vitro and in vivo tests, as well as a precedent for future in silico studies on osseointegration and mechanobiology.

Mathematical modelling of angiogenesis using continuous cell-based models

In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction–diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results.

Capturing the wide variety of impaired fracture healing phenotypes in Neurofibromatosis Type 1 with eight key factors: a computational study

Congenital pseudarthrosis of the tibia (CPT) is a rare disease which normally presents itself during early childhood by anterolateral bowing of the tibia and spontaneous tibial fractures. Although the exact etiology of CPT is highly debated, 40–80% of CPT patients are carriers of a mutation in the Neurofibromatosis Type 1 (NF1) gene, which can potentially result in an altered phenotype of the skeletal cells and impaired bone healing. In this study we use a computational model of bone regeneration to examine the effect of the Nf1 mutation on bone fracture healing by altering the parameter values of eight key factors which describe the aberrant cellular behaviour of Nf1 haploinsufficient and Nf1 bi-allelically inactivated cells. We show that the computational model is able to predict the formation of a hamartoma as well as a wide variety of CPT phenotypes through different combinations of altered parameter values. A sensitivity analysis by “Design of Experiments” identified the impaired endochondral ossification process and increased infiltration of fibroblastic cells as key contributors to the degree of severity of CPT. Hence, the computational model results have added credibility to the experimental hypothesis of a genetic cause (i.e. Nf1 mutation) for CPT.

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

Making microvascular networks work: angiogenesis, remodeling, and pruning

The adequate and efficient functioning of the microcirculation requires not only numerous vessels providing a large surface area for transport but also a structure that provides short diffusion distances from capillaries to tissue and efficient distribution of convective blood flow. Theoretical models show how a combination of angiogenesis, remodeling, and pruning in response to hemodynamic and metabolic stimuli, termed "angioadaptation," generates well organized, functional networks.

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.

Systems biology of the microvasculature

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

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.

Stromal cells and stem cells in clinical bone regeneration

Stem-cell-mediated bone repair has been used in clinical trials for the regeneration of large craniomaxillofacial defects, to slow the process of bone degeneration in patients with osteonecrosis of the femoral head and for prophylactic treatment of distal tibial fractures. Successful regenerative outcomes in these investigations have provided a solid foundation for wider use of stromal cells in skeletal repair therapy. However, employing stromal cells to facilitate or enhance bone repair is far from being adopted into clinical practice. Scientific, technical, practical and regulatory obstacles prevent the widespread therapeutic use of stromal cells. Ironically, one of the major challenges lies in the limited understanding of the mechanisms via which transplanted cells mediate regeneration. Animal models have been used to provide insight, but these models largely fail to reproduce the nuances of human diseases and bone defects. Consequently, the development of targeted approaches to optimize cell-mediated outcomes is difficult. In this Review, we highlight the successes and challenges reported in several clinical trials that involved the use of bone-marrow-derived mesenchymal or adipose-tissue-derived stromal cells. We identify several obstacles blocking the mainstream use of stromal cells to enhance skeletal repair and highlight technological innovations or areas in which novel techniques might be particularly fruitful in continuing to advance the field of skeletal regenerative medicine.

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.

Do endothelial cells dream of eclectic shape?

Endothelial cells (ECs) exhibit dramatic plasticity of form at the single- and collective-cell level during new vessel growth, adult vascular homeostasis, and pathology. Understanding how, when, and why individual ECs coordinate decisions to change shape, in relation to the myriad of dynamic environmental signals, is key to understanding normal and pathological blood vessel behavior. However, this is a complex spatial and temporal problem. In this review we show that the multidisciplinary field of Adaptive Systems offers a refreshing perspective, common biological language, and straightforward toolkit that cell biologists can use to untangle the complexity of dynamic, morphogenetic systems.