Modelling the role of angiogenesis and vasculogenesis in solid tumuour growth

Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation of bone-marrow-derived endothelial progenitor cells (EPCs) into the bloodstream. Once blood-borne, EPCs home in on the tumour site, where subsequently they may differentiate into ECs and form vascular structures. In this paper, we develop a mathematical model, formulated as a system of nonlinear ordinary differential equations (ODEs), which describes vascular tumour growth with both angiogenesis and vasculogenesis contributing to vessel formation. Submodels describing exclusively angiogenic and exclusively vasculogenic tumours are shown to exhibit similar growth dynamics. In each case, there are three possible scenarios: the tumour remains in an avascular steady state, the tumour evolves to a vascular equilibrium, or unbounded vascular growth occurs. Analysis of the full model reveals that these three behaviours persist when angiogenesis and vasculogenesis act simultaneously. However, when both vascularisation mechanisms are active, the tumour growth rate may increase, causing the tumour to evolve to a larger equilibrium size or to expand uncontrollably. Alternatively, the growth rate may be left unaffected, which occurs if either vascularisation process alone is able to keep pace with the demands of the growing tumour. To clarify further the effects of vasculogenesis, the full model is also used to compare possible treatment strategies, including chemotherapy and antiangiogenic therapies aimed at suppressing vascularisation. This investigation highlights how, dependent on model parameter values, targeting both ECs and EPCs may be necessary in order to effectively reduce tumour vasculature and inhibit tumour growth

Cancer disease: integrative modelling approaches

Cancer is a complex disease in which a variety of phenomena interact over a wide range of spatial and temporal scales. In this article a theoretical framework will be introduced that is capable of linking together such processes to produce a detailed model of vascular tumour growth. The model is formulated as a hybrid cellular automaton and contains submodels that describe subcellular, cellular and tissue level features. Model simulations will be presented to illustrate the effect that coupling between these different elements has on the tumour's evolution and its response to chemotherapy

Evolutionary history and taxonomy of the titi monkeys (callicebinae)

Titi monkeys (Callicebinae; Pitheciidae) are a diverse, species-rich group of New World primates with an extensive range across South America. They diverged from their sister clade (Pitheciinae) in the early Miocene, and thus, they comprise one of the oldest lineages of extant New World primates. To date, there has been no comprehensive molecular investigation of the phylogenetic relationships among Callicebinae species and, consequently, the evolutionary history of this diverse clade remains poorly studied. The overall goal of this PhD dissertation is, therefore, to provide insight into the evolutionary and biogeographic history of the subfamily Callicebinae using DNA sequence data. To infer phylogeny and estimate divergence times, we generated sequence data for 50+ wild-caught titi monkey specimens using multi-locus Sanger sequencing (22 nuclear and mitochondrial loci, > 14,500 bp) and reduced representation, genome-wide double-digest restriction-associated DNA (ddRAD) sequencing. A statistical biogeographical approach was employed to reconstruct the biogeography of Callicebinae and investigate the processes responsible for shaping present day distributions. Furthermore, the ddRAD sequence dataset was used to provide additional insight into phylogenetic relationships and genetic structure among taxa of the moloch group. Our phylogenetic and biogeographic results indicate that titi monkeys are divided into three distinct clades that diverged in the late Miocene through vicariance of a widespread ancestral range. Species relationships were generally recovered with strong support, and species-level diversification in the Amazonian clades was characterised by sequential founder events across river barriers in the Pleistocene. We propose a revised genus-level classification for Callicebinae that recognises three genera (Cheracebus, Callicebus, Plecturocebus) based on the results from the phylogenetic analyses, as well as morphological, karyological and biogeographic evidence. Overall, this study represents a major advance in our understanding of the evolutionary history of this strikingly poorly studied group, with implications for classification and research priorities

Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples

Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure

3D modelling of angiogenesis and vascular tumour growth

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute

Fibroblast growth factor homologous factor 1 interacts with NEMO to regulate NF-κB signaling in neurons.

Neuronal survival and plasticity critically depend on constitutive activity of the transcription factor nuclear factor-κB (NF-κB). We here describe a role for a small intracellular fibroblast growth factor homologue, the fibroblast growth factor homologous factor 1 (FHF1/FGF12), in the regulation of NF-κB activity in mature neurons. FHFs have previously been described to control neuronal excitability, and mutations in FHF isoforms give rise to a form of progressive spinocerebellar ataxia. Using a protein-array approach, we identified FHF1b as a novel interactor of the canonical NF-κB modulator IKKγ/NEMO. Co-immunoprecipitation, pull-down and GAL4-reporter experiments, as well as proximity ligation assays, confirmed the interaction of FHF1 and NEMO and demonstrated that a major site of interaction occurred within the axon initial segment. Fhf1 gene silencing strongly activated neuronal NF-κB activity and increased neurite lengths, branching patterns and spine counts in mature cortical neurons. The effects of FHF1 on neuronal NF-κB activity and morphology required the presence of NEMO. Our results imply that FHF1 negatively regulates the constitutive NF-κB activity in neurons

Mathematical and computational models of the retina in health, development and disease

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations