Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour

In this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences within the tumour mass, caused by spatial variations in proliferation and degradation, cause cell motion. We couple the behaviour of the blood vessel into the model for the oxygen tension. The model equations track the evolution of the densities of live and dead cells, the oxygen tension within the tumour, the live and dead cell speeds, the pressure and the width of the blood vessel. We present explicit solutions to the model for certain parameter regimes, and then solve the model numerically for more general parameter regimes. We show how the resulting steady-state behaviour varies as the key model parameters are changed. Finally, we discuss the biological implications of our work

As old as the hills: Pliocene palaeogeographical processes influence patterns of genetic structure in the widespread, common shrub Banksia sessilis

The impact of Quaternary glaciation on the development of phylogeographic structure in plant species is well documented. In unglaciated landscapes, phylogeographic patterns tend to reflect processes relating to persistence and stochasticity, yet other factors, associated with the palaeogeographical history of the landscape, including geomorphological events, can also have a significant influence. The unglaciated landscape of south‐western Western Australia is an ideal location to observe these ancient drivers of lineage diversification, with tectonic activity associated with the Darling Fault in the late Pliocene attributed to patterns of deep phylogeographic divergence in a widespread tree from this region. Interestingly, other species within this region have not shown this pattern and this palaeogeographical boundary therefore presents an opportunity to examine age and historical distribution of plant species endemic to this region. In this study, we assess patterns of genetic diversity and structure across 28 populations of the widespread shrub Banksia sessilis using three cpDNA markers and nine nuclear microsatellite markers. Sixteen cpDNA haplotypes were identified, comprising two major chloroplast DNA lineages that are estimated to have diverged in the Pliocene, approximately 3.3 million years ago. This timing coincides with major geomorphological processes in the landscape, including the separation of the Darling Plateau from the adjacent Swan Coastal Plain, as well as eustatic changes on the Swan Coastal Plain that are likely to have resulted in the physical isolation of historical plant lineages. Chloroplast lineages were broadly aligned with populations associated with older lateritic soils of the Darling Plateau and Geraldton sandplains or the younger sandy soils associated with the Swan Coastal Plain and Southern Coastline. This structural pattern of lateritic versus non‐lateritic division was not observed in the nuclear microsatellite data that identified three genetic clades that roughly corresponded to populations in the North, South, and Central portions of the distributions

Bayesian inference of agent-based models: a tool for studying kidney branching morphogenesis

The adult mammalian kidney has a complex, highly-branched collecting duct epithelium that arises as a ureteric bud sidebranch from an epithelial tube known as the nephric duct. Subsequent branching of the ureteric bud to form the collecting duct tree is regulated by subcellular interactions between the epithelium and a population of mesenchymal cells that surround the tips of outgrowing branches. The mesenchymal cells produce glial cell-line derived neurotrophic factor (GDNF), that binds with RET receptors on the surface of the epithelial cells to stimulate several subcellular pathways in the epithelium. Such interactions are known to be a prerequisite for normal branching development, although competing theories exist for their role in morphogenesis. Here we introduce the first agent-based model of ex vivo kidney uretic branching. Through comparison with experimental data, we show that growth factor-regulated growth mechanisms can explain early epithelial cell branching, but only if epithelial cell division depends in a switch-like way on the local growth factor concentration; cell division occurring only if the driving growth factor level exceeds a threshold. We also show how a recently-developed method, "Approximate Approximate Bayesian Computation", can be used to infer key model parameters, and reveal the dependency between the parameters controlling a growth factor-dependent growth switch. These results are consistent with a requirement for signals controlling proliferation and chemotaxis, both of which are previously identified roles for GDNF

Apresentação

Motivated by the technology of magnetically targeted drug and gene delivery, in which a magnetic field is used to direct magnetic carrier particles from the circulation to a target site, we develop a continuum model for the motion of particles (magnetic carriers) subject to an external body force (magnetic field) in a flow of a concentrated suspension of a species of neutrally buoyant particles (blood). An advection–diffusion equation describes the evolution of the carrier particles as they advect in the flow under the action of an external body force, and diffuse as a result of random interactions with the suspension of neutrally buoyant particles (shear-induced diffusion). The model is analysed for the case in which there is steady Poiseuille flow in a cylindrical vessel, the diffusive effects are weak and there is weak carrier uptake along the walls of the vessel. The method of matched asymptotic expansions is used to show that carriers are concentrated in a boundary layer along the vessel wall and, further, that there is a carrier flux along this layer which results in a sub-layer, along one side of the vessel, in which carriers are even more highly concentrated. Three distinguished limits are identified: they correspond to cases for which (i) the force is sufficiently weak that most particles move through the vessel without entering the boundary layers along the walls of the vessel and (ii) and (iii) to a force which is sufficiently strong that a significant fraction of the particles enter the boundary layers and, depending upon the carrier absorption from the vessel walls, there is insignificant/significant axial carrier flux in these layers.<br/

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

Modelling of Tirapazamine effects on solid tumour morphology

Bioreductive drugs are in clinical practice to exploit the resistance from tumour microenvironments especially in the hypoxic region of tumour. We pre-sented a tumour treatment model to capture the pharmacology of one of the most prominent bioreductive drugs, Tirapazamine (TPZ) which is in clinical trials I and II. We calculated solid tumour mass in our previous work and then integrated that model with TPZ infusion. We calculated TPZ cytotoxicity, concentration, penetra-tion with increasing distance from blood vessel and offered resistance from micro-environments for drug penetration inside the tumour while considering each cell as an individual entity. The impact of these factors on tumour morphology is also showed to see the drug behaviour inside animals/humans tumours. We maintained the heterogeneity factors in presented model as observed in real tumour mass es-pecially in terms of cells proliferation, cell movement, extracellular matrix (ECM) interaction, and the gradients of partial oxygen pressure (pO2) inside tumour cells during the whole growth and treatment activity. The results suggest that TPZ high concentration in combination with chemotherapy should be given to get maximum abnormal cell killing. This model can be a good choice for oncologists and re-searchers to explore more about TPZ action inside solid tumour

IgG 3 + B cells are associated with the development of multiple sclerosis

Objectives Disease‐modifying therapies (DMTs) targeting B cells are amongst the most effective for preventing multiple sclerosis (MS) progression. IgG3 antibodies and their uncharacterised B‐cell clones are predicted to play a pathogenic role in MS. Identifying subsets of IgG3+ B cells involved in MS progression could improve diagnosis, could inform timely disease intervention and may lead to new DMTs that target B cells more specifically. Methods We designed a 31‐parameter B‐cell‐focused mass cytometry panel to interrogate the role of peripheral blood IgG3+ B cells in MS progression of two different patient cohorts: one to investigate the B‐cell subsets involved in conversion from clinically isolated syndrome (CIS) to MS; and another to compare MS patients with inactive or active stages of disease. Each independent cohort included a group of non‐MS controls. Results Nine distinct CD20+IgD−IgG3+ B‐cell subsets were identified. Significant changes in the proportion of CD21+CD24+CD27−CD38− and CD27+CD38hiCD71hi memory B‐cell subsets correlated with changes in serum IgG3 levels and time to conversion from CIS to MS. The same CD38− double‐negative B‐cell subset was significantly elevated in MS patients with active forms of the disease. A third CD21+CD24+CD27+CD38− subset was elevated in patients with active MS, whilst narrowband UVB significantly reduced the proportion of this switched‐memory B‐cell subset. Conclusion We have identified previously uncharacterised subsets of IgG3+ B cells and shown them to correlate with autoimmune attacks on the central nervous system (CNS). These results highlight the potential for therapies that specifically target IgG3+ B cells to impact MS progression

Colorectal tumour simulation using agent based modelling and high performance computing

450,000 European citizens are diagnosed every year with colorectal cancer (CRC) and more than 230,000 succumb to the disease annually. For this reason, significant resources are dedicated to the identification of more effective therapies for this disease. However, classical assessment techniques for these treatments are slow and costly. Consequently, systems biology researchers at the Royal College of Surgeons in Ireland (RCSI) are developing computational agent-based models simulating tumour growth and treatment responses with the objective of speeding up the therapeutic development process while, at the same time, producing a tool for adapting treatments to patient-specific characteristics. However, the model complexity and the high number of agents to be simulated require a thorough optimisation of the process in order to execute realistic simulations of tumour growth on currently available platforms. We propose to apply the most advanced HPC techniques to achieve the efficient and realistic simulation of a virtual tissue model that mimics tumour growth or regression in space and time. These techniques combine extensions of the previously developed agent-based simulation software platform (FLAME) with autotuning capabilities and optimisation strategies for the current tumour model. Development of such a platform could advance the development of novel therapeutic approaches for the treatment of CRC which can also be applied other solid tumours.This work has been partially supported by MICINN-Spain under contract TIN2011- 28689-C02-01 and TIN2014-53234-C2-1-R and GenCat-DIUiE(GRR) 2014-SGR-576. This research was also funded by the European Community’s Framework Programme Seven (FP7) Programme under contract No. 278981 680 AngioPredict and supported by the DJEI/DES/SFI/HEA Irish Centre for High- End Computing (ICHEC).Peer ReviewedPostprint (author's final draft

A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure