A hybrid model of the role of VEGF binding in endothelial cell migration and capillary formation

Computational models for generating microvascular structures: Investigations beyond medical imaging resolution

Angiogenesis, arteriogenesis, and pruning are revascularization processes essential to our natural vascular development and adaptation, as well as central players in the onset and development of pathologies such as tumoral growth and stroke recovery. Computational modeling allows for repeatable experimentation and exploration of these complex biological processes. In this review, we provide an introduction to the biological understanding of the vascular adaptation processes of sprouting angiogenesis, intussusceptive angiogenesis, anastomosis, pruning, and arteriogenesis, discussing some of the more significant contributions made to the computational modeling of these processes. Each computational model represents a theoretical framework for how biology functions, and with rises in computing power and study of the problem these frameworks become more accurate and complete. We highlight physiological, pathological, and technological applications that can be benefit from the advances performed by these models, and we also identify which elements of the biology are underexplored in the current state-of-the-art computational models. This article is categorized under: Cancer > Computational Models Cardiovascular Diseases > Computational Models.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.

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.

In vitro models for evaluation of periodontal wound healing/regeneration

Periodontal wound healing and regeneration are highly complex processes, involving cells, matrices, molecules and genes that must be properly choreographed and orchestrated. As we attempt to understand and influence these clinical entities, we need experimental models to mimic the various aspects of human wound healing and regeneration. In vivo animal models that simulate clinical situations of humans can be costly and cumbersome. In vitro models have been devised to dissect wound healing/regeneration processes into discrete, analyzable steps. For soft tissue (e.g. gingival) healing, in vitro models range from simple culture of cells grown in monolayers and exposed to biological modulators or physical effectors and materials, to models in which cells are 'injured' by scraping and subsequently the 'wound' is filled with new or migrating cells, to three-dimensional models of epithelial-mesenchymal recombination or tissue explants. The cells employed are gingival keratinocytes, fibroblasts or endothelial cells, and their proliferation, migration, attachment, differentiation, survival, gene expression, matrix production or capillary formation are measured. Studies of periodontal regeneration also include periodontal ligament fibroblasts or progenitors, osteoblasts or osteoprogenitors, and cementoblasts. Regeneration models measure cellular proliferation, attachment and migration, as well as gene expression, transfer and differentiation into a mineralizing phenotype and biomineralization. Only by integrating data from models on all levels (i.e. a single cell to the whole organism) can various critical aspects of periodontal wound healing/regeneration be fully evaluated.

The tumor as an organ: comprehensive spatial and temporal modeling of the tumor and its microenvironment

BACKGROUND

Research related to cancer is vast, and continues in earnest in many directions. Due to the complexity of cancer, a better understanding of tumor growth dynamics can be gleaned from a dynamic computational model. We present a comprehensive, fully executable, spatial and temporal 3D computational model of the development of a cancerous tumor together with its environment.

RESULTS

The model was created using Statecharts, which were then connected to an interactive animation front-end that we developed especially for this work, making it possible to visualize on the fly the on-going events of the system's execution, as well as the effect of various input parameters. We were thus able to gain a better understanding of, e.g., how different amounts or thresholds of oxygen and VEGF (vascular endothelial growth factor) affect the progression of the tumor. We found that the tumor has a critical turning point, where it either dies or recovers. If minimum conditions are met at that time, it eventually develops into a full, active, growing tumor, regardless of the actual amount; otherwise it dies.

CONCLUSIONS

This brings us to the conclusion that the tumor is in fact a very robust system: changing initial values of VEGF and oxygen can increase the time it takes to become fully developed, but will not necessarily completely eliminate it.

A phase II study of erlotinib in combination with bevacizumab versus chemotherapy plus bevacizumab in the first-line treatment of advanced non-squamous non-small cell lung cancer

BACKGROUND

Molecularly targeted agents for non-small cell lung cancer (NSCLC) can provide similar efficacy to chemotherapy without chemotherapy-associated toxicities. Combining two agents with different modes of action could further increase the efficacy of these therapies. The TASK study evaluated the efficacy and safety of the epidermal growth factor receptor tyrosine kinase inhibitor erlotinib in combination with the anti-angiogenic agent bevacizumab as first-line therapy in unselected, advanced non-squamous NSCLC patients.

METHODS

Patients were recruited from December 2007 to September 2008. Planned sample size was 200 patients, a total of 124 patients were randomized. Patients were randomized using a minimization algorithm 1:1 to receive bevacizumab (iv 15 mg/kg day 1 of each 21-day cycle) plus chemotherapy (gemcitabine/cisplatin or carboplatin/paclitaxel standard doses, 4-6 cycles) (BC arm) or bevacizumab plus erlotinib (p.o. 150 mg/day; BE arm) until disease progression or unacceptable toxicity. The primary endpoint was progression-free survival (PFS). If the hazard ratio (HR) of PFS for BE relative to BC was above 1.25 at the pre-planned interim analysis in favor of BC, the study would be re-evaluated. Secondary endpoints included overall survival, response rate and safety.

RESULTS

All randomized patients (n = 63 BE; n = 61 BC) were evaluated for the efficacy analyses. At the updated interim analysis, median PFS was 18.4 weeks (95% confidence interval [CI] 17.0-25.1) versus 25.0 weeks (95% CI 20.6-[not reached]) for BE versus BC, respectively (HR for death or disease progression, BE relative to BC, 2.05, p = 0.0183). The incidence of death was 19% for BE treatment compared with 11.5% for BC treatment. The HR for PFS at the updated interim analysis was above 1.25, therefore patients on the BE arm were permitted to change arms or switch to another drug and the study was terminated. Adverse events reported were as expected.

CONCLUSIONS

The TASK study did not show a benefit in terms of PFS for the combination of erlotinib with bevacizumab in unselected first-line advanced non-squamous NSCLC compared with chemotherapy plus bevacizumab.