VEGF gradients, receptor activation, and sprout guidance in resting and exercising skeletal muscle

Formation of vascular-like structures using a chemotaxis-driven multiphase model

We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix (ECM). We demonstrate that, within this framework, chemotaxis-driven cell migration can lead to the formation of cell clusters and vascular-like structures in 1D and 2D respectively. The influence on pattern formation of additional mechanisms commonly included in multiphase tissue models, including cell-matrix traction, contact inhibition, and cell-cell aggregation, are also investigated. Using sensitivity analysis, the relative impact of each model parameter on the simulation outcomes is assessed to identify the key parameters involved. Chemoattractant-matrix binding is further included, motivated by previous experimental studies, and found to reduce the spatial scale of patterning to within a biologically plausible range for capillary structures. Key findings from the in-depth parameter analysis of the 1D models, both with and without chemoattractant-matrix binding, are demonstrated to translate well to the 2D model, obtaining vascular-like cell patterning for multiple parameter regimes. Overall, we demonstrate a biologically-motivated multiphase model capable of generating long-term pattern formation on a biologically plausible spatial scale both in 1D and 2D, with applications for modelling in vitro vascular network formation.

Harnessing Macromolecular Chemistry to Design Hydrogel Micro- and Macro-Environments

Cell encapsulation within three-dimensional hydrogels is a promising approach to mimic tissues. However, true biomimicry of the intricate microenvironment, biophysical and biochemical gradients, and the macroscale hierarchical spatial organizations of native tissues is an unmet challenge within tissue engineering. This review provides an overview of the macromolecular chemistries that have been applied toward the design of cell-friendly hydrogels, as well as their application toward controlling biophysical and biochemical bulk and gradient properties of the microenvironment. Furthermore, biofabrication technologies provide the opportunity to simultaneously replicate macroscale features of native tissues. Biofabrication strategies are reviewed in detail with a particular focus on the compatibility of these strategies with the current macromolecular toolkit described for hydrogel design and the challenges associated with their clinical translation. This review identifies that the convergence of the ever-expanding macromolecular toolkit and technological advancements within the field of biofabrication, along with an improved biological understanding, represents a promising strategy toward the successful tissue regeneration.

Mathematical modelling with Bayesian inference to quantitatively characterize therapeutic cell behaviour in nerve tissue engineering

Cellular engineered neural tissues have significant potential to improve peripheral nerve repair strategies. Traditional approaches depend on quantifying tissue behaviours using experiments in isolation, presenting a challenge for an overarching framework for tissue design. By comparison, mathematical cell-solute models benchmarked against experimental data enable computational experiments to be performed to test the role of biological/biophysical mechanisms, as well as to explore the impact of different design scenarios and thus accelerate the development of new treatment strategies. Such models generally consist of a set of continuous, coupled, partial differential equations relying on a number of parameters and functional forms. They necessitate dedicated in vitro experiments to be informed, which are seldom available and often involve small datasets with limited spatio-temporal resolution, generating uncertainties. We address this issue and propose a pipeline based on Bayesian inference enabling the derivation of experimentally informed cell-solute models describing therapeutic cell behaviour in nerve tissue engineering. We apply our pipeline to three relevant cell types and obtain models that can readily be used to simulate nerve repair scenarios and quantitatively compare therapeutic cells. Beyond parameter estimation, the proposed pipeline enables model selection as well as experiment utility quantification, aimed at improving both model formulation and experimental design.

A combined experimental and computational framework to evaluate the behavior of therapeutic cells for peripheral nerve regeneration

Recent studies have explored the potential of tissue‐mimetic scaffolds in encouraging nerve regeneration. One of the major determinants of the regenerative success of cellular nerve repair constructs (NRCs) is the local microenvironment, particularly native low oxygen conditions which can affect implanted cell survival and functional performance. In vivo, cells reside in a range of environmental conditions due to the spatial gradients of nutrient concentrations that are established. Here we evaluate in vitro the differences in cellular behavior that such conditions induce, including key biological features such as oxygen metabolism, glucose consumption, cell death, and vascular endothelial growth factor secretion. Experimental measurements are used to devise and parameterize a mathematical model that describes the behavior of the cells. The proposed model effectively describes the interactions between cells and their microenvironment and could in the future be extended, allowing researchers to compare the behavior of different therapeutic cells. Such a combinatorial approach could be used to accelerate the clinical translation of NRCs by identifying which critical design features should be optimized when fabricating engineered nerve repair conduits.

A numerical bone regeneration model incorporating angiogenesis, considering oxygen-induced secretion of vascular endothelial growth factor and vascular remodeling

Angiogenesis is considered playing an important role in bone regeneration. Studies have shown that angiogenesis is affected by biological factors, oxygen tension, and blood flow. In this paper, we propose a bone regeneration model with angiogenesis based on the theories of mechanobiology regulation, vascular network modeling, oxygen-induced secretion of vascular endothelial growth factor (VEGF), and vascular remodeling. The results showed that this model can describe the distribution and concentration of vascular endothelial growth factor induced by oxygen tension during bone regeneration, the growth and remodeling of vascular tissue under the influence of vascular endothelial growth factor and mechanical loading, and the correspondence between vascular tissue and bone regeneration.

Modelling-informed cell-seeded nerve repair construct designs for treating peripheral nerve injuries

Millions of people worldwide are affected by peripheral nerve injuries (PNI), involving billions of dollars in healthcare costs. Common outcomes for patients include paralysis and loss of sensation, often leading to lifelong pain and disability. Engineered Neural Tissue (EngNT) is being developed as an alternative to the current treatments for large-gap PNIs that show underwhelming functional recovery in many cases. EngNT repair constructs are composed of a stabilised hydrogel cylinder, surrounded by a sheath of material, to mimic the properties of nerve tissue. The technology also enables the spatial seeding of therapeutic cells in the hydrogel to promote nerve regeneration. The identification of mechanisms leading to maximal nerve regeneration and to functional recovery is a central challenge in the design of EngNT repair constructs. Using in vivo experiments in isolation is costly and time-consuming, offering a limited insight on the mechanisms underlying the performance of a given repair construct. To bridge this gap, we derive a cell-solute model and apply it to the case of EngNT repair constructs seeded with therapeutic cells which produce vascular endothelial growth factor (VEGF) under low oxygen conditions to promote vascularisation in the construct. The model comprises a set of coupled non-linear diffusion-reaction equations describing the evolving cell population along with its interactions with oxygen and VEGF fields during the first 24h after transplant into the nerve injury site. This model allows us to evaluate a wide range of repair construct designs (e.g. cell-seeding strategy, sheath material, culture conditions), the idea being that designs performing well over a short timescale could be shortlisted for in vivo trials. In particular, our results suggest that seeding cells beyond a certain density threshold is detrimental regardless of the situation considered, opening new avenues for future nerve tissue engineering.

The Convergence of Cell-Based Surface Plasmon Resonance and Biomaterials: The Future of Quantifying Bio-molecular Interactions-A Review

Cell biology is driven by complex networks of biomolecular interactions. Characterizing the kinetic and thermodynamic properties of these interactions is crucial to understanding their role in different physiological processes. Surface plasmon resonance (SPR)-based approaches have become a key tool in quantifying biomolecular interactions, however conventional approaches require isolating the interacting components from the cellular system. Cell-based SPR approaches have recently emerged, promising to enable precise measurements of biomolecular interactions within their normal biological context. Two major approaches have been developed, offering their own advantages and limitations. These approaches currently lack a systematic exploration of 'best practices' like those existing for traditional SPR experiments. Toward this end, we describe the two major approaches, and identify the experimental parameters that require exploration, and discuss the experimental considerations constraining the optimization of each. In particular, we discuss the requirements of future biomaterial development needed to advance the cell-based SPR technique.

Sex differences in cancer mechanisms

We now know that cancer is many different diseases, with great variation even within a single histological subtype. With the current emphasis on developing personalized approaches to cancer treatment, it is astonishing that we have not yet systematically incorporated the biology of sex differences into our paradigms for laboratory and clinical cancer research. While some sex differences in cancer arise through the actions of circulating sex hormones, other sex differences are independent of estrogen, testosterone, or progesterone levels. Instead, these differences are the result of sexual differentiation, a process that involves genetic and epigenetic mechanisms, in addition to acute sex hormone actions. Sexual differentiation begins with fertilization and continues beyond menopause. It affects virtually every body system, resulting in marked sex differences in such areas as growth, lifespan, metabolism, and immunity, all of which can impact on cancer progression, treatment response, and survival. These organismal level differences have correlates at the cellular level, and thus, males and females can fundamentally differ in their protections and vulnerabilities to cancer, from cellular transformation through all stages of progression, spread, and response to treatment. Our goal in this review is to cover some of the robust sex differences that exist in core cancer pathways and to make the case for inclusion of sex as a biological variable in all laboratory and clinical cancer research. We finish with a discussion of lab- and clinic-based experimental design that should be used when testing whether sex matters and the appropriate statistical models to apply in data analysis for rigorous evaluations of potential sex effects. It is our goal to facilitate the evaluation of sex differences in cancer in order to improve outcomes for all patients.

Combining in silico and in vitro models to inform cell seeding strategies in tissue engineering

The seeding density of therapeutic cells in engineered tissue impacts both cell survival and vascularization. Excessively high seeded cell densities can result in increased death and thus waste of valuable cells, whereas lower seeded cell densities may not provide sufficient support for the tissue in vivo, reducing efficacy. Additionally, the production of growth factors by therapeutic cells in low oxygen environments offers a way of generating growth factor gradients, which are important for vascularization, but hypoxia can also induce unwanted levels of cell death. This is a complex problem that lends itself to a combination of computational modelling and experimentation. Here, we present a spatio-temporal mathematical model parametrized using in vitro data capable of simulating the interactions between a therapeutic cell population, oxygen concentrations and vascular endothelial growth factor (VEGF) concentrations in engineered tissues. Simulations of collagen nerve repair constructs suggest that specific seeded cell densities and non-uniform spatial distributions of seeded cells could enhance cell survival and the generation of VEGF gradients. These predictions can now be tested using targeted experiments.

Oxygen Consumption Characteristics in 3D Constructs Depend on Cell Density

Oxygen is not only crucial for cell survival but also a determinant for cell fate and function. However, the supply of oxygen and other nutrients as well as the removal of toxic waste products often limit cell viability in 3-dimensional (3D) engineered tissues. The aim of this study was to determine the oxygen consumption characteristics of 3D constructs as a function of their cell density. The oxygen concentration was measured at the base of hepatocyte laden constructs and a tightly controlled experimental and analytical framework was used to reduce the system geometry to a single coordinate and enable the precise identification of initial and boundary conditions. Then dynamic process modeling was used to fit the measured oxygen vs. time profiles to a reaction and diffusion model. We show that oxygen consumption rates are well-described by Michaelis-Menten kinetics. However, the reaction parameters are not literature constants but depend on the cell density. Moreover, the average cellular oxygen consumption rate (or OCR) also varies with density. We discuss why the OCR of cells is often misinterpreted and erroneously reported, particularly in the case of 3D tissues and scaffolds.

Single-Cell Receptor Quantification of an In Vitro Coculture Angiogenesis Model Reveals VEGFR, NRP1, Tie2, and PDGFR Regulation and Endothelial Heterogeneity

Angiogenesis, the formation of new blood vessels from pre-existing ones, is essential for both normal development and numerous pathologies. Systems biology has offered a unique approach to study angiogenesis by profiling tyrosine kinase receptors (RTKs) that regulate angiogenic processes and computationally modeling RTK signaling pathways. Historically, this systems biology approach has been applied on ex vivo angiogenesis assays, however, these assays are difficult to quantify and limited in their potential of temporal analysis. In this study, we adopted a simple two-dimensional angiogenesis assay comprised of human umbilical vein endothelial cells (HUVECs) and human dermal fibroblasts (HDFs) and examined temporal dynamics of a panel of six RTKs and cell heterogeneity up to 17 days. We observed ~2700 VEGFR1 (vascular endothelial growth factor receptor 1) per cell on 24-h-old cocultured HDF plasma membranes, which do not express VEGFR when cultured alone. We observed 4000–8100 VEGFR2 per cell on cocultured HUVEC plasma membranes throughout endothelial tube formation. We showed steady increase of platelet-derived growth factor receptors (PDGFRs) on cocultured HDF plasma membranes, and more interestingly, 1900–2900 PDGFRβ per plasma membrane were found on HUVECs within the first six hours of coculturing. These quantitative findings will offer us insights into molecular regulation during angiogenesis and help assess in vitro tube formation models and their physiological relevance.

Mapping Tyrosine Kinase Receptor Dimerization to Receptor Expression and Ligand Affinities

Tyrosine kinase receptor (RTK) ligation and dimerization is a key mechanism for translating external cell stimuli into internal signaling events. This process is critical to several key cell and physiological processes, such as in angiogenesis and embryogenesis, among others. While modulating RTK activation is a promising therapeutic target, RTK signaling axes have been shown to involve complicated interactions between ligands and receptors both within and across different protein families. In angiogenesis, for example, several signaling protein families, including vascular endothelial growth factors and platelet-derived growth factors, exhibit significant cross-family interactions that can influence pathway activation. Computational approaches can provide key insight to detangle these signaling pathways but have been limited by the sparse knowledge of these cross-family interactions. Here, we present a framework for studying known and potential non-canonical interactions. We constructed generalized models of RTK ligation and dimerization for systems of two, three and four receptor types and different degrees of cross-family ligation. Across each model, we developed parameter-space maps that fully determine relative pathway activation for any set of ligand-receptor binding constants, ligand concentrations and receptor concentrations. Therefore, our generalized models serve as a powerful reference tool for predicting not only known ligand: Receptor axes but also how unknown interactions could alter signaling dimerization patterns. Accordingly, it will drive the exploration of cross-family interactions and help guide therapeutic developments across processes like cancer and cardiovascular diseases, which depend on RTK-mediated signaling.

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.

Assessing the Minimum Time-Period of Normoxic Preincubation for Stable Adipose Stromal Cell-Derived Vascular Networks

Introduction

Pre-vascularization of tissue engineered grafts is a promising strategy to facilitate their improved viability following in vivo implantation. In this process, endothelial cells (ECs) form capillary-like networks that can anastomose with host vasculature. Adipose-derived stromal cells (ASCs) are a commonly used cell population for tissue engineering and contain a subpopulation of ECs capable of assembling into robust vascular networks and anastomosing with the host. However, their initial vascular assembly is significantly impaired in hypoxic conditions (2% O₂). In this study, we explored the minimum period of normoxic (20% O₂) pre-treatment required to enable the formation of stable vascular networks.

Methods

ASC-derived vascular structures were allowed to preassemble in fibrin hydrogels in normoxia for 0, 2, 4, or 6 days and then transplanted into hypoxic environments for 6 days. Total vascular length, pericyte coverage, cell proliferation, apoptosis rates, and ECM production was assessed.

Results

Vascular assembly increased with time over the 6 days of culture. We found that 4 days was the minimum period of time required for stable vascular assembly. We compared the major differences in cell behavior and network structure at Days 2 and 4. Neither proliferation nor apoptosis differed, however, the Day 4 time-point was associated with a significant increase in pericyte coverage (46.1 ± 2.6%) compared to Day 2 (24.3 ± 5.3%).

Conclusions

These data suggest oxygen tension may be a mediator of EC-pericyte interactions during vascular assembly. Pre-vascularization strategies should incorporate a normoxic period of to enable successful vascular formation and development.

Identification of Key Factors in Deep O2 Cell Perfusion for Vascular Tissue Engineering

Blood vessel engineering requires an understanding of the parameters governing the survival of resident vascular smooth muscle cells. We have developed an in vitro, collagen-based 3D model of vascular media to examine the correlation of cell density, O2 requirements, and viability. Dense collagen sheets (100 μxm) seeded with porcine pulmonary artery smooth muscle cells (PASMCs) at low or high (11.6 or 23.2x106 cells/mL) densities were spiraled around a mandrel to create tubular constructs and cultured for up to 6 days in vitro, under both static and dynamic perfusion conditions. Real-time in situ monitoring showed that within 24 hours core O2 tension dropped from 140 mmHg to 20 mmHg and 80 mmHg for high and low cell density static cultures, respectively, with no significant cell death associated with the lowest O2 tension. A significant reduction in core O2 tension to 60 mmHg was achieved by increasing the O2 diffusion distance of low cell density constructs by 33% (p<0.05). After 6 days of static, high cell density culture, viability significantly decreased in the core (55%), with little effect at the surface (75%), whereas dynamic perfusion in a re-circulating bioreactor (1 ml/min) significantly improved core viability (70%, p<0.05), largely eliminating the problem. This study has identified key parameters dictating vascular smooth muscle cell behavior in 3D engineered tissue culture.

Discovery of High-Affinity PDGF-VEGFR Interactions: Redefining RTK Dynamics

Nearly all studies of angiogenesis have focused on uni-family ligand-receptor binding, e.g., VEGFs bind to VEGF receptors, PDGFs bind to PDGF receptors, etc. The discovery of VEGF-PDGFRs binding challenges this paradigm and calls for investigation of other ligand-receptor binding possibilities. We utilized surface plasmon resonance to identify and measure PDGF-to-VEGFR binding rates, establishing cut-offs for binding and non-binding interactions. We quantified the kinetics of the recent VEGF-A:PDGFRβ interaction for the first time with K_D = 340 pM. We discovered new PDGF:VEGFR2 interactions with PDGF-AA:R2 K_D = 530 nM, PDGF-AB:R2 K_D = 110 pM, PDGF-BB:R2 K_D = 40 nM, and PDGF-CC:R2 K_D = 70 pM. We computationally predict that cross-family PDGF binding could contribute up to 96% of VEGFR2 ligation in healthy conditions and in cancer. Together the identification, quantification, and simulation of these novel cross-family interactions posits new mechanisms for understanding anti-angiogenic drug resistance and presents an expanded role of growth factor signaling with significance in health and disease.

Gestational diabetes mellitus is associated with increased pro-migratory activation of vascular endothelial growth factor receptor 2 and reduced expression of vascular endothelial growth factor receptor 1

Placentas from gestational diabetes mellitus (GDM) are often hypervascularized; however, participation of vascular endothelial growth factor (VEGF) and its receptors in this placental adaptation is unclear. We aimed to test whether changes in phosphorylation of tyrosine 951 or tyrosine 1175 (pY951 or pY1175) of the vascular endothelial growth factor receptor 2 (KDR) are associated with the proangiogenic state observed in placentas from GDM. We obtained placental samples from women with normal pregnancies (n = 24) or GDM (n = 18). We measured the relative expression of markers for endothelial cell number (CD31, CD34), VEGF, vascular endothelial growth factor receptor 1 (Flt-1), KDR, pY951 and pY1175 of KDR in placental homogenate. Immunohistochemistry of placental blood vessels were performed using CD34. Proliferation and migration of human umbilical vein endothelial cells (HUVEC) obtained from normal pregnancy and GDM were determined in absence or presence of conditioned medium (CM) harvested from GDM or normoglycemic HUVEC cultures. GDM was associated with more CD31 and CD34 protein compared to normal pregnancy. High number, but reduced area of placental blood vessels was found in GDM. Reduced Flt-1 levels (mRNA and protein) are associated with reduced KDR mRNA, but higher KDR protein levels in placentas from GDM. No significant changes in Y951-or Y1175-phosphorylation of KDR in placentas from GDM were found. GDM did not alter proliferation of HUVECs, but enhanced migration. Conditioned medium harvested from GDM HUVEC cultures enhanced KDR protein amount, tube formation capacity and cell migration in HUVEC isolated from normoglycemic pregnancies. The data indicate that GDM is associated with reduced expression of Flt-1 but high pro-migratory activation of KDR reflecting a proangiogenic state in GDM.

Local recording of biological magnetic fields using Giant Magneto Resistance-based micro-probes

The electrical activity of brain, heart and skeletal muscles generates magnetic fields but these are recordable only macroscopically, such as in magnetoencephalography, which is used to map neuronal activity at the brain scale. At the local scale, magnetic fields recordings are still pending because of the lack of tools that can come in contact with living tissues. Here we present bio-compatible sensors based on Giant Magneto-Resistance (GMR) spin electronics. We show on a mouse muscle in vitro, using electrophysiology and computational modeling, that this technology permits simultaneous local recordings of the magnetic fields from action potentials. The sensitivity of this type of sensor is almost size independent, allowing the miniaturization and shaping required for in vivo/vitro magnetophysiology. GMR-based technology can constitute the magnetic counterpart of microelectrodes in electrophysiology, and might represent a new fundamental tool to investigate the local sources of neuronal magnetic activity.

Growth factor-eluting technologies for bone tissue engineering

Growth factors are essential orchestrators of the normal bone fracture healing response. For non-union defects, delivery of exogenous growth factors to the injured site significantly improves healing outcomes. However, current clinical methods for scaffold-based growth factor delivery are fairly rudimentary, and there is a need for greater spatial and temporal regulation to increase their in vivo efficacy. Various approaches used to provide spatiotemporal control of growth factor delivery from bone tissue engineering scaffolds include physical entrapment, chemical binding, surface modifications, biomineralization, micro- and nanoparticle encapsulation, and genetically engineered cells. Here, we provide a brief review of these technologies, describing the fundamental mechanisms used to regulate release kinetics. Examples of their use in pre-clinical studies are discussed, and their capacities to provide tunable, growth factor delivery are compared. These advanced scaffold systems have the potential to provide safer, more effective therapies for bone regeneration than the systems currently employed in the clinic.

An imaging-based computational model for simulating angiogenesis and tumour oxygenation dynamics

Tumour growth, angiogenesis and oxygenation vary substantially among tumours and significantly impact their treatment outcome. Imaging provides a unique means of investigating these tumour-specific characteristics. Here we propose a computational model to simulate tumour-specific oxygenation changes based on the molecular imaging data. Tumour oxygenation in the model is reflected by the perfused vessel density. Tumour growth depends on its doubling time (T d) and the imaged proliferation. Perfused vessel density recruitment rate depends on the perfused vessel density around the tumour (sMVDtissue) and the maximum VEGF concentration for complete vessel dysfunctionality (VEGFmax). The model parameters were benchmarked to reproduce the dynamics of tumour oxygenation over its entire lifecycle, which is the most challenging test. Tumour oxygenation dynamics were quantified using the peak pO2 (pO2peak) and the time to peak pO2 (t peak). Sensitivity of tumour oxygenation to model parameters was assessed by changing each parameter by 20%. t peak was found to be more sensitive to tumour cell line related doubling time (~30%) as compared to tissue vasculature density (~10%). On the other hand, pO2peak was found to be similarly influenced by the above tumour- and vasculature-associated parameters (~30-40%). Interestingly, both pO2peak and t peak were only marginally affected by VEGFmax (~5%). The development of a poorly oxygenated (hypoxic) core with tumour growth increased VEGF accumulation, thus disrupting the vessel perfusion as well as further increasing hypoxia with time. The model with its benchmarked parameters, is applied to hypoxia imaging data obtained using a [(64)Cu]Cu-ATSM PET scan of a mouse tumour and the temporal development of the vasculature and hypoxia maps are shown. The work underscores the importance of using tumour-specific input for analysing tumour evolution. An extended model incorporating therapeutic effects can serve as a powerful tool for analysing tumour response to anti-angiogenic therapies.

Cells as strain-cued automata

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, "enhanced shear motility", accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10-4-10-3s-1. The transition has previously been observed in experiments conducted in vitro.

A mathematical model for lymphangiogenesis in normal and diabetic wounds

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-β and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-β and increasing the basal lymphatic endothelial cell growth rate, inter alia, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies.

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.

Applications of computational models to better understand microvascular remodelling: a focus on biomechanical integration across scales

Microvascular network remodelling is a common denominator for multiple pathologies and involves both angiogenesis, defined as the sprouting of new capillaries, and network patterning associated with the organization and connectivity of existing vessels. Much of what we know about microvascular remodelling at the network, cellular and molecular scales has been derived from reductionist biological experiments, yet what happens when the experiments provide incomplete (or only qualitative) information? This review will emphasize the value of applying computational approaches to advance our understanding of the underlying mechanisms and effects of microvascular remodelling. Examples of individual computational models applied to each of the scales will highlight the potential of answering specific questions that cannot be answered using typical biological experimentation alone. Looking into the future, we will also identify the needs and challenges associated with integrating computational models across scales.

Chitosan-aluminum monostearate composite sponge dressing containing asiaticoside for wound healing and angiogenesis promotion in chronic wound

There are many factors that delay healing in chronic wounds including lowering level of growth factors and increasing exudate level comprising high amount of tissue destructive enzymes. Asiaticoside possesses interesting wound healing and angiogenic activities that are employed to stimulate tissue regeneration in wound healing application. This study attempted to develop chitosan-aluminum monostearate (Alst) composite sponge containing asiaticoside for use as an absorbent medical dressing in chronic wound. N-methyl-2-pyrrolidone (NMP) was used to enhance homogeneity of asiaticoside in the polymer composite matrix. The sponge dressings were prepared by lyophilization and dehydrothermal treatment (DHT). Functional group interaction, crystallinity, and morphology of the prepared sponges were investigated using FT-IR, PXRD, and SEM, respectively. Physicochemical properties, porosity, hydrophilic/hydrophobic properties and mechanical property, were evaluated. Wound dressing properties, water vapor transmission rate (WVTR), fluid absorbency, oxygen permeation (OP), and bio-adhesive property, were investigated. In vitro asiaticoside release study was conducted using immersion method. Cytotoxicity was studied in normal human dermal fibroblast (NHDF) and normal human epidermal keratinocyte (NHEK). Angiogenic activity of asiaticoside was evaluated using chick-chorioallantoic membrane (CAM) assay. FT-IR and PXRD results revealed the amidation after DHT to enhance the crystallinity of the prepared sponges. The prepared sponges had high porosity comprising high Alst-loaded amount that exhibited more compact structure. Alst enhanced hydrophobicity therefore it reduced the fluid absorption and WVTR together with bio-adhesion of the prepared sponge dressings. Porosity of all sponges was more than 85% therefore resulting in their high OP. Enhancing hydrophobicity of the material by Alst and more homogeneity caused by NMP eventually retarded the asiaticoside release for 7 days. The sponge extractions were non-toxic to the cells moreover they promoted NHDF and NHEK cell proliferation. Asiaticoside and asiaticoside-contained dressings exhibited dose-dependent angiogenic activity in CAM model.

Design of growth factor sequestering biomaterials

Growth factors (GFs) are major regulatory proteins that can govern cell fate, migration, and organization. Numerous aspects of the cell milieu can modulate cell responses to GFs, and GF regulation is often achieved by the native extracellular matrix (ECM). For example, the ECM can sequester GFs and thereby control GF bioavailability. In addition, GFs can exert distinct effects depending on whether they are sequestered in solution, at two-dimensional interfaces, or within three-dimensional matrices. Understanding how the context of GF sequestering impacts cell function in the native ECM can instruct the design of soluble or insoluble GF sequestering moieties, which can then be used in a variety of bioengineering applications. This Feature Article provides an overview of the natural mechanisms of GF sequestering in the cell milieu, and reviews the recent bioengineering approaches that have sequestered GFs to modulate cell function. Results to date demonstrate that the cell response to GF sequestering depends on the affinity of the sequestering interaction, the spatial proximity of sequestering in relation to cells, the source of the GF (supplemented or endogenous), and the phase of the sequestering moiety (soluble or insoluble). We highlight the importance of context for the future design of biomaterials that can leverage endogenous molecules in the cell milieu and mitigate the need for supplemented factors.

Optimizing cardiovascular benefits of exercise: a review of rodent models

Although research unanimously maintains that exercise can ward off cardiovascular disease (CVD), the optimal type, duration, intensity, and combination of forms are yet not clear. In our review of existing rodent-based studies on exercise and cardiovascular health, we attempt to find the optimal forms, intensities, and durations of exercise. Using Scopus and Medline, a literature review of English language comparative journal studies of cardiovascular benefits and exercise was performed. This review examines the existing literature on rodent models of aerobic, anaerobic, and power exercise and compares the benefits of various training forms, intensities, and durations. The rodent studies reviewed in this article correlate with reports on human subjects that suggest regular aerobic exercise can improve cardiac and vascular structure and function, as well as lipid profiles, and reduce the risk of CVD. Findings demonstrate an abundance of rodent-based aerobic studies, but a lack of anaerobic and power forms of exercise, as well as comparisons of these three components of exercise. Thus, further studies must be conducted to determine a truly optimal regimen for cardiovascular health.

Angiotensin II evokes angiogenic signals within skeletal muscle through co-ordinated effects on skeletal myocytes and endothelial cells

Skeletal muscle overload induces the expression of angiogenic factors such as vascular endothelial growth factor (VEGF) and matrix metalloproteinase (MMP)-2, leading to new capillary growth. We found that the overload-induced increase in angiogenesis, as well as increases in VEGF, MMP-2 and MT1-MMP transcripts were abrogated in muscle VEGF KO mice, highlighting the critical role of myocyte-derived VEGF in controlling this process. The upstream mediators that contribute to overload-induced expression of VEGF have yet to be ascertained. We found that muscle overload increased angiotensinogen expression, a precursor of angiotensin (Ang) II, and that Ang II signaling played an important role in basal VEGF production in C2C12 cells. Furthermore, matrix-bound VEGF released from myoblasts induced the activation of endothelial cells, as evidenced by elevated endothelial cell phospho-p38 levels. We also found that exogenous Ang II elevates VEGF expression, as well as MMP-2 transcript levels in C2C12 myotubes. Interestingly, these responses also were observed in skeletal muscle endothelial cells in response to Ang II treatment, indicating that these cells also can respond directly to the stimulus. The involvement of Ang II in muscle overload-induced angiogenesis was assessed. We found that blockade of AT1R-dependent Ang II signaling using losartan did not attenuate capillary growth. Surprisingly, increased levels of VEGF protein were detected in overloaded muscle from losartan-treated rats. Similarly, we observed elevated VEGF production in cultured endothelial cells treated with losartan alone or in combination with Ang II. These studies conclusively establish the requirement for muscle derived VEGF in overload-induced angiogenesis and highlight a role for Ang II in basal VEGF production in skeletal muscle. However, while Ang II signaling is activated following overload and plays a role in muscle VEGF production, inhibition of this pathway is not sufficient to halt overload-induced angiogenesis, indicating that AT1-independent signals maintain VEGF production in losartan-treated muscle.

From bench to bedside: review of gene and cell-based therapies and the slow advancement into phase 3 clinical trials, with a focus on Aastrom's Ixmyelocel-T

There is a large body of preclinical research demonstrating the efficacy of gene and cellular therapy for the potential treatment of severe (limb-threatening) peripheral arterial disease (PAD), including evidence for growth and transcription factors, monocytes, and mesenchymal stem cells. While preclinical research has advanced into early phase clinical trials in patients, few late-phase clinical trials have been conducted. The reasons for the slow progression of these therapies from bench to bedside are as complicated as the fields of gene and cellular therapies. The variety of tissue sources of stem cells (embryonic, adult bone marrow, umbilical cord, placenta, adipose tissue, etc.); autologous versus allogeneic donation; types of cells (hematopoietic, mesenchymal stromal, progenitor, and mixed populations); confusion and stigmatism by the public and patients regarding gene, protein, and stem cell therapy; scaling of manufacturing; and the changing regulatory environment all contribute to the small number of late phase (Phase 3) clinical trials and the lack of Food and Drug Administration (FDA) approvals. This review article provides an overview of the progression of research from gene therapy to the cellular therapy field as it applies to peripheral arterial disease, as well as the position of Aastrom’s cellular therapy, ixmyelocel-T, within this field.

Vascular endothelial growth factor inhibitor-induced hypertension: from pathophysiology to prevention and treatment based on long-acting nitric oxide donors

Hypertension is the most common adverse effect of the inhibitors of vascular endothelial growth factor (VEGF) pathway-based therapy (VEGF pathway inhibitors therapy, VPI therapy) in cancer patients. VPI includes monoclonal antibodies against VEGF, tyrosine kinase inhibitors, VEGF Traps, and so-called aptamers that may become clinically relevant in the future. All of these substances inhibit the VEGF pathway, which in turn causes a decrease in nitric oxide (NO) and an increase in blood pressure, with the consequent development of hypertension and its final events (e.g., myocardial infarction or stroke). To our knowledge, there is no current study on how to provide an optimal therapy for patients on VPI therapy with hypertension. This review summarizes the roles of VEGF and NO in vessel biology, provides an overview of VPI agents, and suggests a potential treatment procedure for patients with VPI-induced hypertension.

Angiogenesis: an adaptive dynamic biological patterning problem

Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. Here, theoretical simulations based on experimental data are used to demonstrate that this patterning problem can be solved through over-abundant stochastic generation of vessels in response to a growth factor generated in hypoxic tissue regions, in parallel with refinement by structural adaptation and pruning. Essential biological mechanisms for generation of adequate and efficient vascular patterns are identified and impairments in vascular properties resulting from defects in these mechanisms are predicted. The results provide a framework for understanding vascular network formation in normal or pathological conditions and for predicting effects of therapies targeting angiogenesis.

The blood vessels provide an efficient system for transport of substances to all parts of the body. They are capable of growing or regressing during development, in response to changing functional needs, and in disease states. This is achieved by structural adaptation, i.e. changes in the diameters and other characteristics of existing vessels, and by angiogenesis, i.e. growth of new blood vessels. Here, we address the question: How do the processes of structural adaptation and angiogenesis lead to the formation of organized vessel networks that can supply the changing needs of the tissue? We carried out theoretical simulations of network growth and adaptation, including vessel blood flows, oxygen transport to tissue, and the generation of a growth factor in low-oxygen regions, which stimulates angiogenesis by sprouting from existing vessels. We showed that the processes of over-abundant random angiogenesis together with structural adaptation including pruning of redundant vessels can generate adequate and efficient vessel networks that are capable of continuously adapting to changing tissue needs. Our work provides insight into the biological mechanisms that are essential for formation and maintenance of functional vessel networks, and may lead to new strategies for controlling blood vessel formation in diseases.

Nonsteady state oxygen transport in engineered tissue: implications for design

Engineered tissue constructs are limited in size, and thus clinical relevance, when diffusion is the primary mode of oxygen transport. Understanding the extent of oxygen diffusion and cellular consumption is necessary for the design of engineered tissues, particularly those intended for implantation into hypoxic wound sites. This study presents a combined experimental and computation model to predict design constraints for cellularized fibrin tissues subjected to a step change in the oxygen concentration to simulate transplantation. Nonsteady state analysis of oxygen diffusion and consumption was used to estimate the diffusion coefficient of oxygen (mean±SD, 1.7×10(-9)±8.4×10(-11) m(2)/s) in fibrin hydrogels as well as the Michaelis-Menten parameters, Vmax (1.3×10(-17)±9.2×10(-19) mol·cell(-1)·s(-1)), and Km (8.0×10(-3)±3.5×0(-3) mol/m(3)), of normal human lung fibroblasts. Nondimensionalization of the governing diffusion-reaction equation enabled the creation of a single dimensionless parameter, the Thiele modulus (φ), which encompasses the combined effects of oxygen diffusion, consumption, and tissue dimensions. Tissue thickness is the design parameter with the most pronounced influence on the distribution of oxygen within the system. Additionally, tissues designed such that φ<1 achieve a near spatially uniform and adequate oxygen concentration following the step change. Understanding and optimizing the Thiele modulus will improve the design of engineered tissue implants.

MMP-sensitive PEG diacrylate hydrogels with spatial variations in matrix properties stimulate directional vascular sprout formation

The spatial presentation of immobilized extracellular matrix (ECM) cues and matrix mechanical properties play an important role in directed and guided cell behavior and neovascularization. The goal of this work was to explore whether gradients of elastic modulus, immobilized matrix metalloproteinase (MMP)-sensitivity, and YRGDS cell adhesion ligands are capable of directing 3D vascular sprout formation in tissue engineered scaffolds. PEGDA hydrogels were engineered with mechanical and biofunctional gradients using perfusion-based frontal photopolymerization (PBFP). Bulk photopolymerized hydrogels with uniform mechanical properties, degradation, and immobilized biofunctionality served as controls. Gradient hydrogels exhibited an 80.4% decrease in elastic modulus and a 56.2% decrease in immobilized YRGDS. PBFP hydrogels also demonstrated gradients in hydrogel degradation with degradation times ranging from 10-12 hours in the more crosslinked regions to 4-6 hours in less crosslinked regions. An in vitro model of neovascularization, composed of co-culture aggregates of endothelial and smooth muscle cells, was used to evaluate the effect of these gradients on vascular sprout formation. Aggregate invasion in gradient hydrogels occurred bi-directionally with sprout alignment observed in the direction parallel to the gradient while control hydrogels with homogeneous properties resulted in uniform invasion. In PBFP gradient hydrogels, aggregate sprout length was found to be twice as long in the direction parallel to the gradient as compared to the perpendicular direction after three weeks in culture. This directionality was found to be more prominent in gradient regions of increased stiffness, crosslinked MMP-sensitive peptide presentation, and immobilized YRGDS concentration.

Myoblasts inhibit prostate cancer growth by paracrine secretion of tumor necrosis factor-α

PURPOSE

Myoblasts can form muscle fibers after transplantation. Therefore, they are envisioned as a treatment for urinary incontinence after radical prostatectomy. However, to our knowledge the safety of this treatment and the interaction of myoblasts with any remaining neighboring cancer are unknown. We investigated the interactions between myoblasts and prostate carcinoma cells in vitro and in vivo.

MATERIALS AND METHODS

Myoblasts isolated from the rectus abdominis were used in a series of co-culture experiments with prostate cancer cells and subcutaneously co-injected in vivo. Cell proliferation, cell cycle arrest and apoptosis of cancer in co-culture with myoblasts were assessed. Tumor volume and metastasis formation were evaluated in a mouse model. Tissue specific markers were assessed by immunohistochemistry, fluorescence activated cell sorting analysis, Western blot and real-time quantitative polymerase chain reaction.

RESULTS

Myoblasts in proximity to tumor provided paracrine tumor necrosis factor-α to their microenvironment, decreasing the tumor growth of all prostate cancer cell lines examined. Co-culture experiments revealed induction of cell cycle arrest, tumor death by apoptosis and increased myoblast differentiation. This effect was largely blocked by tumor necrosis factor-α inhibition. The same outcome was noted in a mouse model, in which co-injected human myoblasts also inhibited the tumor growth and metastasis formation of all prostate cancer cell lines evaluated.

CONCLUSIONS

Myoblasts restrict prostate cancer growth and limit metastasis formation by paracrine tumor necrosis factor-α secretion in vitro and in vivo.

Effects of fiber type and size on the heterogeneity of oxygen distribution in exercising skeletal muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.

Computational modelling of anti-angiogenic therapies based on multiparametric molecular imaging data

Computational tumour models have emerged as powerful tools for the optimization of cancer therapies; ideally, these models should incorporate patient-specific imaging data indicative of therapeutic response. The purpose of this study was to develop a tumour modelling framework in order to simulate the therapeutic effects of anti-angiogenic agents based upon clinical molecular imaging data. The model was applied to positron emission tomography (PET) data of cellular proliferation and hypoxia from a phase I clinical trial of bevacizumab, an antibody that neutralizes the vascular endothelial growth factor (VEGF). When using pre-therapy PET data in combination with literature-based dose response parameters, simulated follow-up hypoxia data yielded good qualitative agreement with imaged hypoxia levels. Improving the quantitative agreement with follow-up hypoxia and proliferation PET data required tuning of the maximum vascular growth fraction (VGF(max)) and the tumour cell cycle time to patient-specific values. VGF(max) was found to be the most sensitive model parameter (CV = 22%). Assuming availability of patient-specific, intratumoural VEGF levels, we show how bevacizumab dose levels can potentially be 'tailored' to improve levels of tumour hypoxia while maintaining proliferative response, both of which are critically important in the context of combination therapy. Our results suggest that, upon further validation, the application of image-driven computational models may afford opportunities to optimize dosing regimens and combination therapies in a patient-specific manner.

Generation of mechanical and biofunctional gradients in PEG diacrylate hydrogels by perfusion-based frontal photopolymerization

The spatial presentation of soluble growth factors, immobilized extracellular matrix molecules, as well as matrix rigidity, plays an important role in directed and guided cell migration. Synthetic hydrogel scaffolds offer the ability to systematically introduce gradients of these factors contributing to our understanding of how the 3D arrangement of biochemical and mechanical cues influence cell behavior. Using a novel photopolymerization technique, perfusion-based frontal photopolymerization (PBFP), we have engineered poly(ethylene glycol) diacrylate (PEGDA) hydrogel scaffolds with gradients of mechanical properties and immobilized biofunctionality. The controlled delivery of a buoyant photoinitiator, eosin Y, through a glass frit filter results in the formation and subsequent propagation of a polymer reaction front that is self-sustained and able to propagate through the monomeric mixture. Propagation of this front results in monomer depletion, leading to variations in cross-linking, as well as spatial gradients of elastic modulus and immobilized concentrations of the YRGDS cell adhesion ligand within PEGDA hydrogels. Furthermore, the magnitudes of the resulting gradients are controlled through alterations in polymerization conditions. Preliminary in vitro cell-culture studies demonstrate that the gradients generated stimulate directed 2D cell growth on the surface of PEGDA hydrogels. By day 14, fibroblast aggregates spread roughly twice as far in the direction parallel to the slope of the gradient as compared to the perpendicular direction. The presented technique has great potential in controlling gradients of mechanical properties and immobilized biofunctionality for directing and guiding 3D cell behavior within tissue-engineered scaffolds.

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.

Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis

BACKGROUND

The spatial distribution of vascular endothelial growth factor A (VEGF) is an important mediator of vascular patterning. Previous experimental studies in the mouse hindbrain and retina have suggested that VEGF alternative splicing, which controls the ability of VEGF to bind to heparan sulfate proteoglycans (HSPGs) in the extracellular matrix (ECM), plays a key role in controlling VEGF diffusion and gradients in tissues. Conversely, proteolysis notably by matrix metalloproteinases (MMPs), plays a critical role in pathological situations by releasing matrix-sequestered VEGF and modulating angiogenesis. However, computational models have predicted that HSPG binding alone does not affect VEGF localization or gradients at steady state.

RESULTS

Using a 3D molecular-detailed reaction-diffusion model of VEGF ligand-receptor kinetics and transport, we test alternate models of VEGF transport in the extracellular environment surrounding an endothelial sprout. We show that differences in localization between VEGF isoforms, as observed experimentally in the mouse hindbrain, as well as the ability of proteases to redistribute VEGF in pathological situations, are consistent with a model where VEGF is endogenously cleared or degraded in an isoform-specific manner. We use our predictions of the VEGF distribution to quantify a tip cell's receptor binding and gradient sensing capacity. A novel prediction is that neuropilin-1, despite functioning as a coreceptor to VEGF₁₆₅-VEGFR2 binding, reduces the ability of a cell to gauge the relative steepness of the VEGF distribution. Comparing our model to available in vivo vascular patterning data suggests that vascular phenotypes are most consistently predicted at short range by the soluble fraction of the VEGF distributions, or at longer range by matrix-bound VEGF detected in a filopodia-dependent manner.

CONCLUSIONS

Isoform-specific VEGF degradation provides a possible explanation for numerous examples of isoform specificity in VEGF patterning and examples of proteases relocation of VEGF upon release.

Module-based multiscale simulation of angiogenesis in skeletal muscle

Background

Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.

Results

We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.

Conclusions

This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.

Computational models of VEGF-associated angiogenic processes in cancer

Tumour angiogenesis allows a growing mass of cancer cells to overcome oxygen diffusion limitation and to increase cell survival. The growth of capillaries from pre-existing blood vessels is the result of numerous signalling cascades involving different molecules and of cellular events involving multiple cell and tissue types. Computational models offer insight into the mechanisms governing angiogenesis and provide quantitative information on parameters difficult to assess by experiments alone. In this article, we summarize results from computational models of tumour angiogenic processes with a focus on the molecular-detailed vascular endothelial growth factor-associated models that have been developed in our laboratory, spanning multiple scales from the molecular to whole body.

Physiologically based construction of optimized 3-D arterial tree models

We present an approach to generate 3-D arterial tree models based on physiological principles while at the same time certain morphological properties are enforced at construction time in order to build individual vascular models down to the capillary level. The driving force of our approach is an angiogenesis model incorporating case-specific information about the metabolic activity in the considered domain. Additionally, we enforce morphometrically confirmed bifurcation statistics of vascular networks. The proposed method is able to generate artificial, yet physiologically plausible, arterial tree models that match the metabolic demand of the embedding tissue and fulfill the enforced morphological properties at the same time. We demonstrate the plausibility of our method on synthetic data for different metabolic configurations and analyze physiological and morphological properties of the generated tree models.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Krogh cylinders in retinal development, panretinal hypoperfusion and diabetic retinopathy

The volume of cells that a length of capillary supplies with O(2) is called a Krogh cylinder. This geometric 'tissue unit' was named after the Danish zoophysiologist and Nobel laureate August Krogh who made important discoveries in the fields of external and internal respiration in the first half of the last century. Krogh's ideas concerning tissue O(2) distribution can be extrapolated to retinal oxygenation by larger vessels (including arterioles, arteries and even veins) and by vessel groups within higher-order 'microvascular units' (including the choroid). During retinal development, for example, the difference in pO(2) levels within arteries and capillaries determines Krogh cylinders of different radius and establishes the periarterial capillary-free zone of His. The O(2) supply to the venous end of a tissue unit may be compromised during periods of reduced perfusion, increased O(2) consumption or hypoxaemia, resulting in an 'anoxic corner' of the Krogh cylinder. A funnel of hypometabolic (and therefore hypoxia-tolerant) cells will likely intervene between the necrotic cells and unaffected cells located closer to the O(2) source. Macular perivenular whitening heralds anoxic corners and/or hypoxic funnels owing to hypoperfusion within second-order microvascular units. In eyes with extensive retinal capillary closure from diabetes, Krogh cylinders surround the medium-sized arteries and veins that form arteriovenous shunts while traversing the midperipheral retina. These isolated tissue units incorporate an outer sheath of hypoxic cells within which vascular endothelial growth factor is upregulated. This 'angiogenic sheath' expands following retinal detachment; it corresponds to the hypoxia-tolerant funnel within capillary-based tissue units and to the cerebral penumbra after stroke.

Systems biology of pro-angiogenic therapies targeting the VEGF system

Vascular endothelial growth factor (VEGF) is a family of cytokines for which the dysregulation of expression is involved in many diseases; for some, excess VEGF causes pathological hypervascularization, while for others VEGF-induced vascular remodeling may alleviate ischemia and/or hypoxia. Anti-angiogenic therapies attacking the VEGF pathway have begun to live up to their promise for treatment of certain cancers and of age-related macular degeneration. However, the corollary is not yet true: in coronary artery disease and peripheral artery disease, clinical trials of pro-angiogenic VEGF delivery have not, so far, proven successful. The VEGF and VEGF-receptor system is complex, with at least five ligand genes, some encoding multiple protein isoforms and five receptor genes. A systems biology approach for designing pro-angiogenic therapies, using a combination of quantitative experimental approaches and detailed computational models, is essential to deal with this complexity and to understand the effects of drugs targeting the system. This approach allows us to learn from unsuccessful clinical trials and to design and test novel single therapeutics or combinations of therapeutics. Among the parameters that can be varied in order to determine optimal strategy are dosage, timing of multiple doses, route of administration, and the molecular target.