Centre for Mathematical Medicine and Biology

CMMB Conference 2012


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Multiscale Modelling in Medicine and Biology: 3-5 September 2012


This conference, run in partnership with the Mathematical Biosciences Institute (MBI, Ohio) will bring together scientists using mathematical modelling across a range of applications in medicine and biology, and crossing spatial scales from molecules to populations of organisms. It will bring together experts working at different scales on particular systems, and include mathematical approaches to derive macroscale models from microscale, as well as computational approaches to link submodels at multiple scales. By bringing together these sometimes disparate groups, we will disseminate state-of-the-art approaches and facilitate the cross-fertilisation of ideas. For example, techniques of modelling at the (sub-) cellular scale may be applicable to the study of population interactions, dispersal and epidemics, and vice-versa.

The meeting will begin with registration from 10:30am on Mon 3 Sept, and end at 4:00pm on Wed 5 Sept. We will include 12 plenary talks over this period, and invite contributed talks and poster presentations. This schedule will allow for plenty of time for discussion and interaction between attendees. All talks and registration will be held in the Exchange buidling on Jubilee campus (see map and directions below).

Note for attendees presenting a poster: it is planned that all posters will be on display over the course of the conference in the Exchange building. Presenters will be split into two groups, A (for surnames A to I) and B (for surnames J to Z). Each poster board will have space for one A poster and one B poster, to enable adequate space for the presentations. Group A will present on Monday afternoon and Group B on Tuesday afternoon. If for any reason you need to change groups, let us know.

Confirmed speakers:



The final programme is now outlined below.


Monday 3 September

10.30 Registration and refreshments
10.55 Welcome
11.00 Steven Altschuler (UT Southwestern)
12.00 Tim Elston (North Carolina) 
13.00 Lunch
14.00 Peter Kohl (Imperial) 
15.00 Mihaela Pop (Toronto)
15.30 Refreshments
16.00 Sanjay Kharche (Liverpool) 
16.30 James Sneyd (Auckland)
17.30 Poster presentations (Group A - see note above)
19.30 Dinner in the Atrium (for those staying overnight in Newark Hall)

Tuesday 4 September

9.30 Sharon Crook (Arizona State) 
10.30 Daniele Avitabile (Nottingham)
11.00 Refreshments
11.30 Michael Stumpf (Imperial) 
12.30 Rafael Pena-Miller (Exeter) 
13.00 Lunch 
14.00 Tim Secomb (Arizona) 
15.00 Raimondo Penta (Politecnico di Milano) 
15.30 Refreshments
16.00 Kevin Thurley (Charite University Hospital, Berlin) 
16.30 Ramit Mehr (Bar-Ilan University) 
17.30 Poster presentations (Group B - see note above)
19.30 Conference dinner at the Riverbank (transport provided)  

Wednesday 5 September

9.30 Kirsten Ten Tusscher (Utrecht) 
10.30 Bettina Greese (Lund, Sweden) 
11.00 Refreshments
11.30 Andreas Schuppert (Bayer)
12.30 Lunch 
13.30 Wayne Getz (Berkeley) CANCELLED
14.00 Andrea Weisse (Edinburgh SynthSys)
14.30 Ursula Klingmüller (German Cancer Research Center) 
15.30 Refreshments and close




Plenary Speakers

Steven Altschuler - Reverse engineering cell polarity circuits

How complex signaling networks shape highly-coordinated, multistep cellular responses is poorly understood. Recently, we have developed a network-perturbation approach to investigate causal influences, or “cross-talk,” among signaling modules involved in the cytoskeletal response of neutrophils to chemoattractant. We will discuss how analyzing the effects of network disruptions provides a rational strategy for decomposing complex, dynamically evolving, signaling systems and revealing evolving paths of causal influence that shape the neutrophil polarization response.

Sharon Crook - Approaches for Model Reproducibility in Computational Science

The independent verification of results is a critical step in the scientific process, and it would seem that achieving reproducibility should be much easier for computational scientists than for experimentalists. However, problems with reproducibility have received wide attention in recent years in many fields of computational inquiry, and some refer to the inability to routinely achieve reproducibility as a true crisis in computational science. Reproducibility in computational science requires descriptions of complex models that are precise and unambiguous, and some recent approaches aimed toward achieving reproducibility include model sharing databases, suggestions for publication standards, software for tracking computational “experiments”, and simulator independent model description languages. As more computational scientists focus on complex multiscale and collaborative approaches, systemic and automated avenues for reproducibility are becoming increasingly important. In this talk, I will provide an overview of these approaches for documenting and exchanging models and their components.

Tim Elston - Models and methods for quantifying cell movement

Most cells possess the ability to change morphology or migrate in response to environmental cues. To understand the molecular mechanisms that drive cell movement requires a systems-level approach that combines computational approaches, including mathematical modeling and image analysis tools, with high resolution microscopy of living cells. Here we present several examples for how such an integrated research strategy has been successfully applied. First, we combine stochastic modeling with novel biosenors for monitoring the spatiotemporal dynamics of Rho GTPase activity to investigate the role of RhoG in cell polarization and migration. Next mathematical modeling and quantitative image analysis methods are used to establish the role of cerebral cavernous malformation (CCM) proteins in vascular tube formation. Finally, we present a novel computational method for tracking and quantifying changes in cell shape.

Ursula Klingmuller - Bridging scales: Assessing liver regeneration at different levels

The liver is a key organ for metabolism, detoxification and innate immune responses. Since it is constantly exposed to toxic substances through the gut but has to maintain its vital functions liver regeneration has to occur in a tightly controlled manner.  Multiple inputs with distinct functions at the specific phases of the regeneration process coordinate priming, proliferation and termination of liver regeneration. Interleukin (IL)6 is a key factor during the priming phase rendering quiescent hepatocytes sensitive to Hepatocyte Growth Factor (HGF). We have established an ordinary differential equation (ODE) model of IL6 induced JAK1-STAT3 signalling in primary hepatocytes. The model has been calibrated based on extensive time-resolved quantitative data generated under multiple stimulation conditions. This model enabled us assess and predict the impact of small molecular inhibitors. Furthermore, we combined interaction graph modelling and ODE modelling to elucidate wiring of HGF induced MAP kinase and PI3 kinase signalling in primary hepatocytes. The resulting information is currently being provided to a multi-scale model that will help us to unravel the importance of cellular effects on decisions at the tissue level.

Peter Kohl - Cardiac systems biology: hype or hope?

This talk will explore Systems Biology as an approach that, from the outset, combines reduction and integration. The role of models, both experimental and theoretical, will be discussed, and illustrated using examples of their application to cardiac structure and function research. Potentials and pitfalls of trying to integrate a complex biological system such as the heart will be considered, as will be the role of failure as a driver of scientific progress. Reference: Quinn TA, Kohl P. Systems biology of the heart: hype or hope? Ann N Y Acad Sci 2011/1245:40-43. (http://www.ncbi.nlm.nih.gov/pubmed/22211976)

Ramit Mehr - From Antibody Gene Sequences to Multiscale Modeling of the Humoral Immune Response

The immune response involves cells of various types, including B, T and Natural Killer (NK) lymphocytes expressing a large diversity of receptors which recognize foreign antigens and self-molecules. The various cell types interact through a complicated network of communication and regulation mechanisms. These interactions enable the immune system to perform the functions of danger recognition, decision, action, memory and learning. As a result, the dynamics of lymphocyte repertoires are highly complex and non-linear. The humoral (antibody-generating) immune response is one of the most complex responses, as it involves somatic hypermutation of the B cell receptor (BCR) genes and subsequent antigen-driven selection of the resulting mutants. This process has been and still is extensively studied using a variety of experimental methods – ranging from intravital imaging to studying the mutations in BCR genes – and has also been one of the most often modeled phenomena in the theoretical immunology community. The problem for modelers, however, is that until recently kinetic data on the humoral immune response were so limited that all models could fit those data. We have addressed this – and the challenge of following individual clones – by combining multiscale modeling with a novel immuno-informatical method of generation and quantification of lineage trees from B cell clones undergoing somatic hypermutation. We applied these new analyses to the study of humoral response changes in aging, chronic or autoimmune diseases and B cell malignancies. Finally, we used simulations to answer some theoretical questions regarding the evolution of BCR genes. Credit to: GITIT SHAHAF, MICHAL BARAK, NETA ZUCKERMAN AND RAMIT MEHR; The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, Israel.

Andreas Schuppert - Multi-scale modelling for translational medicine

Models supporting translational medicine aim to predict clinically relevant features from heterogeneous data assessed from preclinical experimentation. Although efficient modelling techniques for translational medicine are crucial to improve the efficiency of the current drug research and development processes, the available understanding of the respective systems is often not sufficient to establish detailed and reliable models. The most pressing challenges arise from the multi-scale challenges of translational medicine: linking bench and bedside requires crossing scales in size, from sub-cellular mechanisms via multi-cellular organs to patients, and in time, from phosphorylation via plasticity in cellular stress response to evolution of resistance on the long term scale. Apparently full mechanistic modelling across the scales in size and time is neither possible nor affordable today. Hence, concepts for efficient workarounds are required in order to support translational medicine on a case by case base. The workarounds must integrate smart data-driven modelling approaches, heterogeneous biological data and mechanistic models. In the presentation we will demonstrate the feasibility of efficient workarounds on examples from reengineering of modes of action of drugs from ‘omics data, the assessment of stress response of tumor cells on drugs as well as mapping of cellular dynamics on clinically relevant phenotypes using full genome expression analysis.

Tim Secomb - Pattern formation by angiogenesis and structural adaptation in microvascular networks

Microvascular networks contain hierarchical tree-like structures to provide efficient convective transport over large distances, combined with dense space-filling meshes to provide short diffusion distances to every point in the tissue. They are capable of restructuring in response to changing functional demands without interruption of blood flow. Their spatial patterns are not predetermined, but emerge as a result of angiogenesis and structural adaptation driven by local stimuli acting on each vessel segment. We have used theoretical models to investigate how these processes lead to functionally adequate network structures consistent with experimental observations. We show 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. The results provide a framework for understanding vascular network formation in normal or pathological conditions and for predicting effects of therapies targeting angiogenesis.

James Sneyd - Calcium and multiscale modelling

I will be discussing multiscale models of the lung and of the salivary gland, and showing how we can use such models to study the effects of calcium oscillations and waves at the level of entire organs. In lungs, the frequency of calcium oscillations appears to play an important role in controlling the contraction of airway smooth muscle, which is itself one of the principal causes of asthma. However, in the parotid gland, water secretion appears to be almost entirely independent of calcium oscillation frequency.

Michael Stumpf - Learning how to Guide the Behaviour of Cellular Systems

Biological systems have evolved intricate mechanisms by which they sense, respond to, and interact with their environment. They process extra-cellular signals and alter their behaviour in response to these stimuli. We are only beginning to comprehend some aspects of the molecular machinery underlying such cellular decision making processes. Here I will discuss how we can elucidate the structure and dynamics of biological information processing systems in the context of the innate immune response in zebrafish embryos. These are an excellent model system to study immune signalling at the whole organism level as they are optically transparent and their innate immune response appears to match closely what is observed in humans. I will briefly outline a flexible framework for the analysis of inter and intra-cellular signalling processes. I will then discuss how the same inferential framework can be employed in rationally designing synthetic regulatory and signalling networks that lead to specified cellular behaviour. There is tremendous scope for applying this approach in biomedical and biotechnological problems, and I will conclude with a brief overview of such emerging applications.

Kirsten ten Tuscher - Multiscale models in plant development; Interplay of Auxin, Plethoras and Pins

Plants grow and develop new organs throughout their life, meanwhile adjusting their size and shape to their local environment.  How plants achieve this robust yet flexible development is far from understood. Plant development is controlled through the interplay of plant hormones, of which auxin is a major player, and key developmental transcription factors, such as the Plethora family. This interplay is complex, with auxin inducing transcription of Plethora's while Plethora's impact production, degradation and transport of auxin, and both influencing the transitions from cell proliferation, to elongation and finally differentiation. Given the complexity of these interactions, with their feedbacks, non-linearity, and their effects  at a range of different space and time scales, computational models are essential for gaining a better understanding of these processes.

In this talk I will first discuss the challenges and advances in developing these models, focusing on a model for Arabidopsis root zonation and growth. Using this model, we unravel the complex dynamical interplay between auxin and Plethoras that give rise to a robust zonation of the root into dividing,elongating and differentiationg zones of cells. This zonation is essential for providing a robust balance between current growth from elongating and differentiating cells and future growth from maintaining a meristematic pool of dividing cells.

Next I will focus on the interplay between auxin and PINs, the polar transporters of auxin. It was long suspected that auxin influences its own transport, and experiments in recent years have confirmed that auxin indeed influences PIN levels and position. This has led to the proposal of models for self-organised auxin patterning.I will discuss the main categories of these models, argueing that these can explain only a subset of the auxin flux patterns found in plants, and end with a discussion on alternative mechanisms for PIN patterning.


Contributed Talks

Daniele Avitabile (Nottingham) - Coarse-grained bifurcation analysis in agent-based models: lifting from continuous microscopic to discrete macroscopic states

Coarse-grained bifurcation analysis is a numerical technique to explore parameter dependence in multiscale models: in systems where a fine-scale description is available, but a closed form coarse-level model is impractical, it is possible to perform a macroscopic bifurcation analysis using short bursts of appropriately-initialised microscopic simulations. In this talk, I will discuss the application of coarse-grained bifurcation analysis to cases when the macroscopic variables are real numbers, such as densities or ensemble averages, but the microscopic variables are integers representing discrete states of the system (examples include kinetic models and agent-based models of biological and sociological systems). In such cases, initialising the fine-scale simulations is a nontrivial task, as noise can affect considerably the stochastic continuation. I will present a strategy for initialising microscopic simulations, based on a set of precomputed weights. This new "lifting" procedure results in a considerable improvement of the convergence properties of the coarse-grained solver and requires the solution of a minimization problem at each continuation step. I will then show a set of numerical experiments for an agent-based model of opinion formation.

Bettina Greese (Lund, Sweden) - Modelling cell polarity in the plant root

We study the mechanisms underlying cell polarity in the plant root by combining mathematical/computational modelling with experimental techniques. Our aim is to further understand the interplay between an auxin gradient and the polarization of epidermal cells. Auxin is an important plant hormone, which is involved in the regulation of many aspects of development. It is transported in a characteristic pattern through the root, which is determined by the specific locations of its transport mediators. Acropetal transport (downwards) in the internal tissue and basipetal transport (upwards) in the epidermal tissue, together with auxin production in the root tip, are responsible for the establishment of an auxin gradient in the root. This gradient in turn provides cues for developmental processes. For instance, the polarization of ROP proteins towards the basal (root-tip oriented) ends of the outer membrane in epidermal cells is suggested to be an outcome of the auxin gradient. As a consequence of high ROP concentrations, the outgrowth of root hairs occurs near the basal end of epidermal cells, which we use as a marker for cell polarity when comparing model predictions and experimental results. Our mechanistic models are systems of differential equations that describe the time evolution of the active and inactive form of ROP and account for the influence of auxin. We analyze the models first in a single one-dimensional cell, then in a row of cells reflecting an epidermal cell file, and finally in a two-dimensional setting reflecting a root with reversed fountain type of gradient. The model parameters are tuned to the biological wild-type situation, and perturbations of the system are used as a validation step. In our study, we contribute to the understanding of the establishment of cell polarity in the root epidermis.

Sanjay Kharche (Liverpool) - Low Energy Cardioversion Using Feedback Stimuli in Human Atria

Low amplitude feedback induced stimulation has been proposed as a low energy atrial cardioversion method. Beatbox, a novel cardiac simulation envi-ronment, was used to study this method in the human atria. The human atrial action potential (AP) cell model by Courtemanche et al. was adopted in this study. Chronic atrial fibrillation (CAF) was simulated by reducing ICaL current conductance by 50% and increasing IK1 current conduc-tance by 100%. Single cell models for control and CAF were incorporated into spatial models using a reaction-diffusion formulation. In 2D sheet models and in the 3D model, re-entry was induced using the phase distribu-tion method. The feedback stimulation method to eliminate such CAF induced re-entry involved localized registration of electrical activity which induced application of global external defibrillating stimuli. In multiple parameter sweep simulations, the optimal registration electrode location and stimulus amplitude were explored. Using forward Euler integration methods, a time step of 0.05 ms and a space step of 0.33 mm were used in all simula-tions. CAF reduced AP duration (APD90) from 306 ms (control) to 145 ms in agreement with experimental data. Under control conditions, re-entrant waves self-terminated in the 2D and 3D models. Re-entrant waves were highly localized and persistent under CAF conditions. Under CAF condi-tions, a single threshold amplitude shock of 4.5 pA/pF eliminated the stable re-entry. However, with feedback stimulation of lower amplitude stimuli of 1 pA/pF, the re-entrant waves migrated out of the 2D tissue. In 3D CAF simu-lation, feedback control induced stimuli also caused the re-entrant wave to migrate to anatomical boundaries eventually eliminating the re-entry. The mechanism and efficacy for eliminating re-entrant waves by the feed-back control method is affected by anatomical features in the 3D model. The optimization feedback control parameters in the 3D anatomy warrant further studies.

Rafael Pena-Miller (Exeter) - Multidrug combinations: on the short-lived potency of antibiotic synergism

A common strategy to dealing with the evolution of antibiotic resistance and to increase the efficacy of antimicrobial treatments is to use multidrug combination therapies. In particular, synergistic drug combinations whereby the combined effect is greater than the predicted individual effect are highly prized. These treatments, however, are also associated with the strongest selection for resistance and hence for escape from inhibition by antibiotics. In this talk we use mathematical models to show that the nature of the interaction profile depends on the population structure and therefore is a dynamic property of the system. Using optimality theory we demonstrate that when designing optimal therapies the effects of natural selection should be accounted for, and as the bacteria we are trying to kill the best treatment strategies have to be adaptive in time. We demonstrate our theoretical predictions using experimental evolution and functional genomics.

Raimondo Penta (Politecnico di Milano) - Multiscale modelling of fluid and drug transport coupling in the tumor microvasculature

A system of differential equations for coupled fluid and drug transport in the tumor vasculature is presented. The starting point are the fluid and solute balance equations stated in the physical domain. The geometry of the problem is characterized by the intercapillary distance (the microscale), where the Kedem-Katchalsky conditions account for the interplay between the osmotic pressure and the drug transport across the capillary walls. Under assumption of periodic microstructure, a multiple scales analysis is performed to formulate continuum equations describing the fluid and drug transport coupling at the tumor length scale (the macroscale). The geometrical complexity of the resulting model is dramatically reduced while the role of both the vascular geometry (determined by the differential cell problems on the microscale), the drug concentration field and related parameters on the fluid dynamics in the tumor is captured. This approach represents one more step towards a numerically feasible mathematical model that can accurately describe drug tranport in tumor microvasculature and to provide an insight to the biophysical processes at the relevant scale and possibly support anti-cancer strategies.

Mihaela Pop (Toronto) - Myocardial remodelling in post-infarction: insights from 3D MRI-based computer models, experiments and histopathology in swine

Heart attack is a major cause of death in the industrialized world, motivating the development of non-invasive tools (e.g. imaging and computer modelling) towards improved personalized treatment. MRI is the gold-standard imaging method used to evaluate the extent, location, and severity of myocardial remodelling in patients with prior infarction, in which structural and electrical alterations in the border zone adjacent to dense scars could trigger lethal arrhythmia. MRI-based computer models could be powerful tools for understanding 3D propagation of action potential through the myocardium (normal and border zone) and for treatment planning. However, prior to integration into clinical applications, such predictive models have to be properly validated using experimental techniques selected to reflect the electrophysiological phenomena at spatio-temporal scales similar to those considered in simulations. In this work, we address the challenge of constructing realistic 3D MRI-based models from pathologic swine hearts (which are translatable to human hearts) associated with inducibility of arrhythmias; advantages and limitations of solving forward problems by using monodomain macroscopic mathematical approach are also presented. The computer model was enriched with experiments (i.e. electrophysiology data), allowing us to validate the predicted activation times. Moreover, quantitative analysis using histopathology performed in these swine hearts, demonstrated myocardial remodelling in the dense scar and border zone (due to collagen deposition and alteration of electrical coupling via gap junctions), and provided a way of tuning computer model parameters (e.g. conductivity, anisotropy ratio). Future work will focus on extending our MRI-based computer model applicability to in-vivo patients with chronic infarction for a better understanding of electrical wave propagation and arrhythmia inducibility; it is foreseen that the management and treatment planning based on predictive computer models will have immediate impact on the quality of life in this patient population.

Kevin Thurley (Charite University Hospital, Berlin) - Spatiotemporal regulation of paracrine cytokine signals shapes immune responses

The adaptive immune system depends on the coordinated action of immune cells, which communicate by small signalling proteins called cytokines. Many cytokines are pleiotropic, i.e. they are released by and act on different cell types, leading to complex spatiotemporal dynamics. In a previous investigation (Busse et al, PNAS 2010), we found that spatial cytokine gradients between cells are important for decision making in the immune system. Additionally, cytokines are often secreted in a polarised fashion into the immunological synapse (IS) and act at very low (picomolar) concentrations. This raises the question how sensitive cytokine signals are, and if paracrine cytokine signals are restricted to the IS. Here we follow a multiscale approach, combining intracellular regulation of cytokine release and cytokine receptor expression with reaction-diffusion dynamics between cells. We provide analytical solutions of a steady-state model of the IS and analyse 2D and 3D in silico T cell cultures. To be specific, we consider a well-studied and physiologically important sample system: Activation of T-helper (Th) cells via Interleukin(IL)-2 and immunosuppression by regulatory T (Treg) cells. Three major results have been obtained: First, the fractions of autocrine, synaptic paracrine and bulk cytokine signalling are controlled by the geometry of the immunological synapse. Second, paracrine signals are restricted to the immediate vicinity of cytokine secreting cells. And third, Treg cells almost instantaneously deplete the cytokine from their environment, a possible mechanism of Th cell suppression and immune tolerance. Our findings suggest that the range of a cytokine signal is carefully regulated by different layers of  spatiotemporal dynamics, underlining the need for spatially resolved data from live cell imaging or capture assays. Future investigations will take into account cellular heterogeneity in cytokine release, which can potentially be studied by hierarchic stochastic modeling (Thurley and Falcke, PNAS 2011).

Andrea Weisse (SynthSys, Edinburgh) - Optimal resource allocation or greed, what determines the winning strategy for nutrient sensing?

Bistability is key to a wide range of cellular processes such as differentiation and neuronal memory. The essential feature of a bistable response is that genetically identical cells can respond in two different ways to the same stimulus. In bistable nutrient-­sensing networks, cells express the enzymes needed to take up and metabolize the nutrient at either a maximal or a basal (almost inactive) rate. One such bistable nutrient response is the galactose‐sensing network of S. cerevisiae [Acar et al., Nature, 2005, Song et al. PLoS Comput Biol, 2010]. More commonly, cells respond to nutrients in a graded fashion, gradually adapting their enzyme expression to the amount of nutrient available. Graded responses not only differ in the amount of enzymes expressed, they are also less sensitive to stochasticity than bistable ones, which can randomly switch between the two stable states [Acar et al., Nat Gen, 2008]. An example of a graded nutrient-­sensing network is the Lac‐operon in E. coli, which was shown to be optimal with respect to the costs of producing the enzymes and the benefits of taking up the sugar [Dekel & Alon, Nature, 2005]. If graded nutrient responses evolved to optimise resource allocation, then what was the selective pressure for stochastic bistable nutrient responses? We combine population- and cell-level models for nutrient uptake to study this question.



Poster Presentations

Tariq Abdulla (Loughborough) - Epithelial to Mesenchymal Transition: the roles of cell morphology, labile adhesion and junctional coupling

Epithelial to mesenchymal transition (EMT) is a fundamental process during development and disease, e.g. development of the heart valves and tumour metastasis. An extended cellular Potts model is implemented to represent the behaviour emerging from autonomous cell morphology, labile adhesion and junctional coupling. The model facilitates exploration of the interplay between cell shape changes, adhesion and migration. The simulation model is fitted to an in vitro model of endocardial EMT.

Ishan Ajmera (Nottingham) - Modelling Genetic Regulation of Phosphate Uptake in Rice

Vivi Andasari (Dundee) - Multiscale aspects of cell-cell and cell-matrix adhesion for cancer cell invasion

Adhesion, which includes cell-to-cell and cell-to-extracellular-matrix adhesion, plays an important role in cancer invasion and metastasis. These processes require interactions and signalling cross-talks between proteins and cellular components occurring at different temporal and spatial scales. Although such processes are very complex, the necessity to fully understand the mechanism of cell adhesion is crucial for cancer studies, which may contribute to improving cancer treatment strategies. For the cell-cell adhesion, we present a multiscale individual cell-based model that describes the cellular behaviour governed by intracellular proteins, mainly by E-cadherin and beta-catenin. For the cell-matrix adhesion, we propose a multiscale model for the interactions between cell and extracellular matrix driven by cell glyco-proteins integrins and extracellular matrix ligand fibronectin. A question left, is how to mathematically couple the two models that have different t  emporal and spatial scales.

Michelle Baker (Nottingham) - Developing our understanding of cytokine mediation in arthritic disease and the impact on target, dose and dose regimen

Osteoarthritis (OA) is a joint disease affecting a large proportion of the elderly population. Many of the changes associated with OA are thought to be caused or mediated by cytokines, a class of cell signalling proteins produced by cells within the cartilage and synovial fluid of articular joints. Some of these cytokines stimulate the production of enzymes which move into the surrounding extracellular matrix and degrade collagen fibres and proteoglycans, leading to degradation of the joint cartilage and eventually deterioration of the whole joint. Anti-cytokine therapy is used successfully to treat several cytokine related disorders, most notably Rheumatoid Arthritis (RA). However despite the success of these treatments in RA and the similarities between RA and OA, trials of anti-cytokine therapy for OA have not shown significant benefit. There are currently no disease modifying drugs for OA. The purpose of this research is to model the cytokine network in the joi nts and investigate possible drug targets for OA.

Rafel Bordas (Oxford) - Computational Modelling of the Effect of Airway Smooth Muscle Orientation on Bronchoconstriction

Airway smooth muscle contraction is the principal mechanism that leads to bronchoconstriction. The degree of airway narrowing is a consequence both of the contraction force generated by airway smooth muscle cells and of the mechanical structure of the airway wall. There are many factors related to the structure of the airway wall that can effect airway lumen narrowing. In this study, we investigate one of these factors: the orientation of airway smooth muscle fibres around the airway wall. Finite deformation elasticity is used to model the airway as a cylinder of a given wall-thickness. The airway is embedded in a passive parenchymal layer. An active tension is generated in the airway wall in the airway smooth muscle fibre direction to represent smooth muscle contraction. We apply the model to investigate the effect of the pitch of airway smooth muscle fibres on airway resistance during muscle contraction. The required active tension generated by the muscle to produce a set change in airway resistance is seen to alter with airway pitch. These results indicate that the orientation of airway smooth muscle around the airway may be important in determining airway responsiveness to challenge.

Victor Brena-Medina (Bristol) - Mathematical Modelling of Plant Root Hair Initiation: Dynamics of Localised Patches

A mathematical analysis is undertaken of a Schnakenberg reaction-diffusion system in 1D with a spatial gradient governing the active reaction. This system has previously been proposed as a model of the initiation of hairs from the root epidermis Arabidopsis, a key cellular-level morphogenesis problem. This process involves the dynamics of the small G-proteins ROPs which bind to form a single localised patch on the cell membrane, prompting cell wall softening and subsequent hair growth. Numerical bifurcation analysis is presented as two key parameters, cell length and the overall concentration of the auxin catalyst are varied.  The results show hysteretic transitions as either parameter is increased from a boundary patch to a single interior patch, to multiple patches whose locations are carefully controlled by the auxin gradient. The results are backed up by an asymptotic analysis using semi-strong interaction theory, leading to closed form expressions for the patch locations and intensities. A close match with the numerics is found for biologically realistic parameter values. Light is also shed on the transition mechanisms using the theory of spike competition instability. The results provide further explanation of the recent agreement found between the model and biological data for both wild-type and mutants.

Laura Cattaneo (Politecnico di Milano) - Computational modeling of transport phenomena in tumor microvasculature - preliminary results

Reduced models of fluid flows or mass transport in heterogeneous media are often used to save computational resources when the system to be simulated is too complex. In this framework the immersed boundary method (IB) is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical model. To avoid resolving the complex 3D geometry of the submerged structure we take into account only the 1D geometrical description of the structure centerline, defining a fiber network. The idea of this method is to define an asymptotic problem applying a suitable rescaling and replace the immersed interface and the related conditions by an equivalent mass source term. This method is applied to the study of blood flow and drug transport through a network of capillaries surrounded by the porous interstitium of a solid tumor. Resorting to an immersed boundary method facilitates the handling of complex network pattern and simplifies the definition of the mathematical model for drug release.

Igor Chernyavsky (Nottingham) - History effects in inflammation-driven airway smooth muscle proliferation in asthma: a theoretical model

We present a mathematical model that describes the growth dynamics of a population of airway smooth muscle (ASM) cells over short and long time-scales in the normal and inflammatory environment, typically observed in asthma [1]. Each ASM cell is described as being in the proliferative or non-proliferative state. Switching between the states is modulated by a series of episodic  inflammatory events that affect the inflammatory status (e.g. eosinophil cell count). We show how an increase in the switching rate leads to different growth regimes, corresponding to the mild and severe ASM hyperplasia. Our model also demonstrates that the rate of long-term ASM hyperplasia is proportional to the frequency of acute inflammation (associated with exacerbation events in asthma), provided the airway inflammatory status is above a certain threshold. If a single inflammatory event is not strong enough to trigger the ASM remodelling, a series of these events can accumulate, leading to long-te  rm remodelling even after the removal of the original stimulus. The existence of inflammation history-dependence for a certain parameter range in our modelling framework suggests that the rate of clearance of ASM growth/recruitment factors after an acute inflammatory event can be targeted for anti-remodelling therapy in asthma. This ASM growth model may prove useful for designing new experiments or as a building block of more sophisticated multi-cellular tissue-level models.

[1]  Baker et al. (2011)  Mathematics-in-Medicine Study Group Report, Reading, 32 p.

Huguette Croisier (Nottingham) - Multiscale modelling of airway hyper-responsiveness and remodelling in asthma: focus on smooth muscle intracellular calcium dynamics

Intracellular calcium dynamics of airway smooth muscle cells (ASMC) is a key signaling pathway for airway hyper-responsiveness and remodeling in asthma. In particular, the amount of airway contraction increases with the frequency of agonist-induced calcium oscillations. We present a mathematical model of calcium dynamics in ASMC to account for experimental results obtained in human lung slices, by the inclusion of the so-called 'store-operated calcium entry' (SOCE) pathway. The model is used to study the influence of SOCE up- and down- regulation, which can be induced by inflammatory mediators present in asthma, on agonist-induced calcium oscillations. The model also provides insight into the apparent inability of a widely used drug (the SERCA blocker CPA) to 'permeabilise' lung slices, i.e. to empty the sarcoplasmic reticulum (the main calcium store) from calcium. The partial efficiency of CPA could also explain some experimental results obtained with ASMC dissociated from the lungs and cultured.

Carmen Del Vecchio (Sannio) - Equilibrium and Stability Analysis of X-Chromosome Linked Recessive Diseases Model

A mathematical model describing the population distribution of genetic diseases related to X chromosomes has been developed. The model captures the disease spread within a population according to the relevant inheritance mechanisms; moreover it allows inclusion of de novo mutations (i.e. affected sibling born to unaffected parents). The resulting dynamic system is nonlinear, discrete time and positive. This work allows the analytical study of the model’s equilibrium point, that is the distribution of the population among healthy, carrier and affected subjects. It also provides the proof of the stability properties of the equilibrium point through the Lyapunov second method in the presence of both negligible and significant mutation rates.

Casey Diekman (MBI Ohio) - Spontaneous Autoresuscitation in a Model of Respiratory Control

We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)’s conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.

This is joint work with Peter Thomas and Christopher Wilson.

Graham Donovan (Auckland) - Multiscale modelling of the asthmatic lung

Joanne Dunster (Reading) - Unravelling the blood coagulation cascade

The enzyme thrombin is central to blood coagulation, being the end product of a complicated protein cascade with multiple feedbacks that operates over multiple timescales ensuring thrombin is delivered to the right place at the right time. Here we present a reduced model for the generation of thrombin. We analyse this model using the method of matched asymptotic expansions to derive a sequence of simplified models in time that charaterise the key reactions within the cascade. Two of the simplified models found provide an excellent substitute for the full model, capturing thrombin's explosive growth and decay. Thrombin generation is hoped to be used in a clinical setting to measure bloods ability to clot. We derive approximations for key parameters that experimentalists utlise to describe thrombin generation.

Radhia Eljazi (Heriot Watt) - tbc

Graziella Figueredo (Nottingham) - Vascular Tissue Modelling Environment

Over a number of years a multiscale model for vascular tissue has been developed and extended. The model combines (1) a fluid flow in a vessel network, (2) partial differential equations for the transport, release and uptake of diffusible substances such as oxygen; (3) cell division and reinforced random walks of cells on a regular lattice; (4) ordinary differential equations for subcellular networks that regulate the cell cycle and growth factors; and (5) integration of angiogenic and vasculogenic endothelial cells into the vascular network. This project is currently being implemented within the "Cancer, Heart and Soft Tissue Environment" (Chaste), which is part of the virtual phisiological human (VPH) Toolkit. The purpose of adding the vascular model to Chaste is to obtain a robust, open-source and extensible Vascular Tissue Modelling Environment (VTME), which allows biologists to test hypotheses on the mechanisms of vascular tissue growth and homeostasis, and to test potential new treatments for various pathologies. The strategy adopted for the development of VTME was to identify the original multiscale vascular model main functionalities and reconceptualize them to suit the Chaste methodology.

Stephanie Foan (Nottingham) - Modelling the Aging Immune System

My laboratory work seeks to characterise changes to T cells throughout life. Rather than one marked change, we observe low-level alterations that may accumulate to an increase in morbidity in the elderly. We have simulated immune aging using ordinary differential equations and aim to create a predictive model of immune system behaviour throughout life. This would provide insight into the key nodes of immunological pathways and direct future research. I work with experts in immunology and computer science and I am to improve the management of my interdisciplinary collaboration and get the most from both fields. I am also keen to expand my knowledge of multiscale modelling in order to develop my simulation work.

John Fozard (Nottingham) - Multicellular modelling of growing plant roots

Multicellular models provide an ideal framework in which to integrate processes occurring at cell and tissue scales. We describe a vertex-based model for plant tissue in which anisotropic viscous wall properties control the growth of the cells. The geometrical representation is two-dimensional, and the mechanical properties of cell walls in the plane of the simulation are discretized using finite elements. This is combined with models for cell division, polar auxin transport in the root apex, auxin responses, and other gene regulatory networks (encoded in Systems Biology Modelling Language). Cell scale geometrical data is acquired from confocal imaging and used to provide the initial state of the tissue. The simulation is implemented in a combination Python and C++, using the OpenAlea framework, in a modular fashion which allows multiple sub-models to be readily combined. The mechanical and transport models give large systems of differential equations for the evolut  ion of the tissue state; these are solved numerically, with the sparsity of the Jacobian matrix being exploited for efficient computation. We also describe a hybrid vertex-midline model, which provide a computationally efficient and highly robust method of describing uniaxial growth, whilst still explicitly including cell-level detail which is important, e.g. for auxin transport in the root tip. We show how both these models may be used to investigate root elongation and the bending of a root during a gravitropic response.

Juan Gutierrez (MBI Ohio) - Analysis of Asymptomatic Malaria as a Species Competition Problem

Half the human population, living in 100 countries, is at risk of malaria infection every year, with an estimated 350 to 500 million cases of clinical malaria annually and approx. 1% death rate. Recently, several malaria endemic countries of Latin America have experienced a significant reduction in the number of reported malaria cases, and a sense of victory permeates the public health community. However, after a close examination of reporting methods, it becomes evident that the number of cases of asymptomatic malaria is grossly underestimated. This is significant because asymptomatic individuals are capable of infecting vectors, thus offering a permanent refuge (due to lack of treatment) for the Plasmodium parasite.

Attempts to eradicate malaria need to take into account the effect of asymptomatic individuals. Malaria diagnosis via PCR revealed that a significant percentage of the population (up to 10% in certain localities) presents unreported asymptomatic malaria. Since asymptomatic individuals present levels of parasitemia capable of infecting a vector, and they do not receive treatment, they become a sizeable refuge for the parasite. This situation, in which strains that cause clinical manifestations are rapidly contained whereas mild asymptomatic strains remain in the ecosystem, can lead to a process of rapid natural selection. As the morbidity of malaria decreases, other pathologies are expected to increase as a result of chronic exposure to low levels of malaria. This epidemiological state indicates that a selection process has occurred rather quickly in favor of less virulent strains of Plasmodium vivax. I present the epidemiological analysis of this scenario, and suggest intervention measures that correlate the fast evolution of P. vivax strains with public health management.

Mainul Haque (Nottingham) - Mathematical modelling of a microRNA regulated gene network in Caenorhabditis elegans

MicroRNAs are known to regulate gene expression by repressing translation or by directing sequence-specific degradation of target mRNAs, and are therefore considered to be key regulators of gene expression. A gene regulatory pathway involving  heterochronic genes controls the temporal pattern of Caenorhabditis elegans postembryonic cell lineages. Based on experimental data, we propose and analyze a mathematical model of a gene regulatory module in this nematode involving two heterochronic genes, lin-14 and lin-28, which are both regulated by lin-4, encoding a microRNA. The conditions under which the model experiences bifurcations are investigated. We determine the parameter regimes for which the system exhibits monostability and bistability, the latter associated with a biological switch. We observe that bistability occurs without higher co-operativity of the associated Hill function, in keeping with knowledge about the regulatory behaviour of lin-14 and lin-28.  The analytical results are confirmed by numerical simulations which illustrate how the microRNA  lin-4 plays a crucial  role in determining of the qualitative dynamics of the model. A short discussion of the biological implications of our findings concludes the paper.

Tanvi Joshi (Nottingham) - PDE Model: Another approach to modelling vascular tumour growth

Vascular tumour growth has been previously modeled as a multiscale model [1,2]. Such a model is organized into three layers depending on the time and the length scales. The model is based on the hybrid cellular automaton concept. Predefined set of rules are used to decide how cells move and where newly formed daughter cells are placed. The cell cycle model is given by an ordinary differential equation. Diffusible transport of oxygen and VEGF is modeled using partial differential equations. Here, we aim to develop a model, consisting of only Partial Differential Equations (PDE), for vascular tumour growth, and test under what circumstances will such a model be equivalent to the multiscale models.

[1]M. R. Owen, T. Alarc´on, P. K. Maini, and H. M. Byrne. Angiogenesis and vascular remodelling in normal and cancerous tissues. J Math Biol, 58:689–721, Apr 2009.

[2]M. R. Owen, I. J. Stamper, M. Muthana, G. W. Richardson, J. Dobson, C. E. Lewis, and H. M. Byrne. Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy. Cancer Res., 71:2826–2837, Apr 2011.

Jose Lourenco (Oxford) - Unifying the epidemiology and molecular evolution of dengue viruses

To explain the observed temporal dynamics and structuring in pathogen populations, mathematical models have commonly evoked strong immunological strain interactions as the predominant drivers. The effect of spatial segregation between individual hosts or groups of hosts, as well as the stochasticities therein, have often been neglected, however. By using a discrete, spatially explicit individual-based model we show that multi-strain systems can exhibit all of the characteristic dynamics, including semi-regular epidemic outbreaks and sequential strain dominance, even in the absence of immune-interactions. The inclusion of a more natural description of the stochasticities underlying host-host or host-vector contacts provides a complimentary hypothesis about the underlying causes for the oscillatory nature in incidence and variant distributions that commonly characterize the complex epidemiologies of multi-strain pathogens. We discuss these findings in the context of dengue.

Sandip Mandal (IISER, Mohali, India) - Evolution of mathematical models of malaria and development of a new predictive model

The population biology of associations between hosts and pathogens is an important problem, as it is increasingly being realized that population level processes play a major role in disease spread along with the within-host dynamics. Even with the detail knowledge from genetics, molecular and cellular biology, about the malaria parasite and its interaction with mosquito and human hosts yet, thousands of people are dying in malaria proving the lack of effective vaccines or suitable strategy to prevent it. Since the time of Sir Ronald Ross in 1911, mathematical modelling has been used as a successful technique in malaria research. Several models have been developed and being developed by researchers extending Ross's model by considering different factors, such as latent period, acquired immunity, spatial and genetic heterogeneity of host and parasite etc. Apart from this, malaria burden is also known to differ with age of human host, as both age and immunity are int  er-related factors. The prevalence pattern is also known to vary from place to place due to changes of ecological, demographic, and socioeconomic differences across host populations and environmental conditions. In this talk, I will briefly discuss the evolution of basic mathematical models of malaria in different scales, and will describe the development of a new model, which considers age dependent immunity in human host and effect of seasonal variation on the intensity of malaria transmission. Incorporation of these factors gives better understanding of malaria prevalence pattern with both age and time. In our model human population is divided into different compartments, which are easily detectable so that the model can be implemented in real life situation. The predictions of age prevalence pattern as well as the temporal variation of malaria prevalence from the model are validated with malaria prevalence data obtained from different geographical and environmental regions.

Petros Mina (Bristol) - Modelling emergence of oscillations in a population of bacterial cells

Population level measurements of phenotypic behaviour in biological systems may not necessarily reflect individual cell behaviour. To assess qualitative changes in the behaviour of a single cell, when alone and when part of a community, we developed an agent based model describing the metabolic states of a population of quorum coupled cells using differential equations. The model is biologically grounded and motivated on experimental work that shows that the population exhibits oscillatory behaviour. We investigate the nature of oscillations from the single cell level up to coupled cells via numerical simulation and bifurcation analysis. We study the effect of population size increase as well as the spatiotemporal behaviour of the model through large scale 3D simulations. The model suggests that the population establishes the oscillatory behaviour as the system's preferred stable state.

Calin Miron (Nottingham) - Multiscale modelling of the cellulosome assembly

Sunny Modhara (Nottingham) - Mathematical modelling of tip cell selection in angiogenesis

Angiogenesis is the process by which new blood vessels form during, for example, wound healing or organismal development. Endothelial cells that form blood vessels respond to growth factors that are produced in a tissue by forming capillary sprouts, proliferating and migrating into the tissue, towards the source of the growth factors. The behaviour of individual endothelial cells is also regulated by interactions with their neighbouring cells. The interaction between secreted growth factors such as VEGF, and the Delta-Notch signalling pathway has been shown to be important in tip cell selection. An agent-based computational model has previously been used to explore the dynamics of this interaction, including the role of VEGF-induced filopodial extension, but a dynamical systems approach has not been applied. Here we develop tractable ordinary differential equation (ODE) models to more fully characterise this interaction. We begin by exploring a model for the signall  ing alone (i.e. we neglect filopodial elongation), for which we identify regions of parameter space in which, there exist stable spatially homogeneous solutions (all cells are identical) and parameter regimes in which alternate cells express high (low) levels of Notch activity and VEGF receptors. We then extend the model to include simplified filopodial dynamics and show that this system can exhibit a spatial instability (corresponding to tip cell selection) even when it would not in the absence of filopodial elongation.

Kazeem Okosun Oare (Vaal Uni Tech, SA) - On the dynamics of stress and labor force productivity

In this paper, we derive and analyze a compartmental mathematical model for the dynamics of stress management and its impact on the organizational labor force productivity. We first calculate the basic stress-non-productivity reproductive number and investigate the existence and stability of equilibria. The model is found to exhibit backward bifurcation implying that for stress or the non productivity of organizational labor force to be eradicated, the basic stress-non-productivity reproductive number must be below a critical value less than one. From the sensitivity analysis we observe that increasing ( or decreasing) the progression rate from stressed individuals to stress induced non productive individuals by 10%, increases (or decreases) the basic stress-non-productivity reproductive number by 10%, and also decreasing (or increasing) the recovery rate of the stress induced non-productive individuals by 9.99%, increases (or decreases) the basic stress-non-productivity reproductive number by 9.99%.

Kayode Stephen Ojo (Federal Uni Tech, Nigeria) - Synchronization in multiscale systems

Bonsu Osei (Eastern Conneticut State) - A comparative study of seasonal and non-seasonal dynamics of Buruli ulcer

Buruli Ulcer (BU) is a debilitating affliction that produces a very scarring ulcer. The disease, which is caused by Mycobacterium Ulcerans has been postulated to be spread by a vector (waterbugs) whose breeding habits are determined by environmental factors and seasonal patterns.  In this talk, we compare the seasonal dynamics of BU to its non-seasonal counterpart and show that seasonal dynamics typically affect the number of secondary cases of BU, which is the key to the spread of any disease.

Glaucia Pereira (Imperial) - Blood rheology and thrombosis: a computational and experimental approach

Abnormal trends in blood coagulation could lead to severe diseases like the occlusion of arteries and veins, resulting from the over-coagulation around damaged zones. The mathematical modelling of such a phenomenon is a maze itself, due to the wide variety of aspects to be considered, which in a simulation environment presents an additional barrier: the compromise between accuracy and computational cost. There are numerous works that represent the clot formation and its transport [1]. Some of them combine biomechanics and biochemistry, looking for a description of the mechanical properties of both blood and thrombus and its interactions [2] during the aggregation process, under a micro or macroscopic point of view. However, the use of a rheological-based model (micro-scale modelling) might result in a more realistic representation of thrombus formation and transport, in a macro-scale framework; which should give rise to an accurate model to study the long-term consequences of such a disease. To address the problem a numerical scheme for fluid-structure interaction was improved and the results for a rheology-based model might be experimentally validated.

[1] M. Hoffman and D. Monroe. Rethinking the coagulation cascade. Current Hematology Reports, 4:391–396, 2005. [2] A. L. Fogelson and R. D. Guy. Platelet-wall interactions in continuum models of platelet thrombosis: formulation and numerical solution. Mathematical Medicine and Biology, 21:293–334, 2004.

Holger Perfahl (Stuttgart) - 3D Modelling of Vascular Network Formation by an Overlapping-Sphere Approach

We present a mechanical agent-based model of vascular network formation under in vitro conditions. The model is based on in vitro experiments in which rat vessel fragments are cultivated in a matrigel and form networks. The model describes how cells divide and align in order to form a vascular network. Cell movement is given by a biased random-walk in the direction of an externally applied chemo-attractant. Different vessel cells interact with each other via an overlapping sphere approach in which the mechanical interaction is modeled by a linear elastic spring law. Cell division is triggered by an intracellular clock that models the progression through the cell cycle. The duration of the cell cycle is influenced by the concentration of a growth factor and mechanical stimulus. The progression of the cell cycle is slowed down if cells are compressed and accelerated if cells are elongated. The vessels build sprouts with a certain probability that also depends on the degree of elongation or compression. Elongated cells are more likely to divide in the vessel direction to decrease their mechanical stress, whereas compressed or undeformed cells are more likely to build sprouts. In the numerical simulations we study the influence of the parameters on different metrics that describe the vascular networks.

Eleftheria Pervolaraki (Leeds) - Computational modelling of the activity and arrhythmia of the human foetal heart

Background. Computational cardiac models facilitate the interpretation of noninvasive, high-resolution recordings, requiring cardiac geometry and electrophysiology. We deliver high-resolution human foetal heart geometry and anisotropy at different gestational ages and models of foetal ventricular electrophysiology. Methods. Cardiac 3D structure is reconstructed by MRI and its anisotropic architecture revealed by DT-MRI, on a 9.4T Bruker-BioSpin. Foetal ECG was recorded through the 5-electrode high-sensitivity Monica AN24 (Monica Healthcare) during maternal rest and activity. ECG intervals (PR, QR, RS, QS) relating to propagation times, and QT dispersion relating to ventricular APD, were extracted. Results. The 3D computational grids were reconstructed with high spatial resolution allowing interpolation to an isotropic grid suitable for excitation equations of human tissue. The smooth change in the helix angle of the primary eigenvector (“myofibre”), seen in adult human hearts, is present if the transmural angles are averaged within ventricular wall segments, but not clear at voxel level. The helix and transverse angles appear more irregular, but fibre tracking of the streamlines in the primary eigenvectors showed helical organisation of the myocardium. The hearts show low fractional anisotropy, and the irregularity in angle spatial distribution is related to the primary eigenvalues being greater than the secondary and tertiary. Quantitative histology can relate this to either a not very elongated myocardial cell shape or poorly developed mid- and sub-endocardium. PR and QR intervals, from fECG, are indices of propagation times, while QT intervals are indices of ventricular APD. PR intervals do not change after week 25 and QR intervals decrease; while there is a 2fold increase in the linear dimensions of the heart. This implies a more than 2fold increase in conduction velocity, of the order of 10cm/s. For an APD of 200ms the wavelength of a re-entrant wave would be ~2cm, making a re-entrant possible.

Ramana Pidaparti (Virginia Commonwealth University) - joint poster with Angela Reynolds

Pepe Luis Puglisi (Davis) - Feed Forward Modeling: Fixing the Force-Frequency Relationship

The force frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Several attempts were made to construct mathematical descriptions of this phenomenon. This property of the cardiac muscle is amplified by the β adrenergic stimulation. In a coordinated way the neurohumoral state alters both: frequency (acting on the SA node) and force generation (modifying the ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Failure to do so has deleterious consequences. We implemented this physiological coordination in a new version of our computer simulation of the cardiac cell: LabHEART (v5.5) where the cell parameters are updated according to the frequency of stimulation (namely: ICaL, IKs, SERCA pump and myofilaments’ Ca-sensitivity). This feed forward modeling helps to reproduce a more realistic cell behavior and it is an efficient method to use in multiscale simulation when changes in frequency are involved.

Angela Reynolds (Virginia Commonwealth University, with Ramana Pidaparti) - Multi-scale Modeling Framework for Lung Tissue Inflammation

A better understanding of the acute/chronic inflammation in airway tissues is crucial for avoiding lung injuries in patients undergoing mechanical ventilation.  Inflammation is a complex and dynamic process triggered by many mechanisms within the lung and involves multiple scales from organ to the sub-cellular level. In this study, a multiscale modeling framework is developed to address the cellular inflammation due to mechanical ventilation at the organ level. The developed multiscale modeling framework is illustrated through a case study to investigate inflammatory responses at the alveolar sac during mechanical ventilation. Currently the simulation results capture tissue deformation due to ventilation and the strain-induced and/or bacteria-associated inflammatory response (cellular level). These results will be extended to investigate the effects of altering mechanical ventilation parameters such as waveform and frequency.

Ricardo Ruiz Baier (Lausanne) - Mathematical modeling and numerical simulation of myocyte active contraction

In this work we are interested in the numerical simulation of the main mechano-chemical interactions in isolated cardiomyocytes. We formulate our coupled problem in both an Lagrangian and a fully Eulerian setting. In the latter, we track the boundary of the elastic body using a level set method with the particularity that the level set function also delivers information about the stretching of the interface. We employ a modified level set approach based on the imposition of additional constraints via Lagrange multipliers. Moreover, we consider an active strain description of the activation mechanism which is based on the assumption of a multiplicative decomposition of the deformation gradient. Several tests illustrate the applicability of the model and the numerical method for reproducing a  quantitative agreement with observed calcium-driven mechanical activation.

Amy Smith (Oxford) - Multi-scale modelling of blood flow in the coronary microcirculation: a discrete to continuum approach

Motivated by the study of microvascular diseases, our goal is to develop continuum models of blood flow through the capillaries. In particular we focus on the coronary microcirculation, since our group has acquired a large set of structural data via high-resolution imaging of vessels in the muscular walls of the heart. Initially, we look for an appropriate cut-off between branching arterioles and mesh-like capillary networks, using only geometric information without flow data. Next, considering the capillaries in isolation, we represent this dense network of vessels as a continuum by using an averaging technique called homogenisation. We show that the effective fluid transport can be described by Darcy's Law, and explicitly calculate the permeability tensor in this expression by solving a set of equations on a physiologically-realistic periodic network,  automatically constructed by sampling from statistics extracted from our data set. This enables us to explore the relationship between the underlying structure of capillary networks and the resulting averaged flow properties.

Ruth Smith (Nottingham) - Neural Field Models

Geometric visual hallucinations are seen in many situations, for example: after the administration of certain anesthetics, following deep binocular pressure, and shortly after the ingestion of drugs such as LSD and Marijuana. Since the seminal work of Ermentrout and Cowan in the 1970s an understanding of the latter has come about through studies of spontaneous pattern formation in neural field models. However, visual hallucinations may also arise in response to sensory input, such as flickering lights. This poster extends the analysis of pattern formation in neural field models to incorporate retinal drive. This will then be used to test the hypothesis that flicker-induced hallucinations are biased by the presentation of adjacent geometrical stimuli.

Bakhtier Vasiev (Liverpool) - Chemotactic mechanisms of cellular migration in biological tissues

In developmental biology patterns formed by morphogens are often affected by movement of cells producing the morphogens. The mutual effects of cell movement and dynamics of concentration patterns are enhanced when the movement is due to chemotactic response to the morphogens. Here we present a set of cell movement patterns with associated patterns formed in concentration fields of chemotactic agents obtained analytically in continuous model and numerically in individual-cell based model. We have found that group of cells can push itself to move, provided that it produces a chemical which acts as a chemorepellent to its constituent cells. Also, the group of cells can be pulled to move by the chemoattractor produced by the surrounding cells in a tissue. Many other chemotactic scenarios are in play when the group of cells is inhomogeneous, i.e. when only part of cells is reacting chemotactically to the morphogen produced by the other part or in the surrounding tissue. We demonstrate these scenarios on the models of primitive streak extension and regression in the chick embryo.




En suite accommodation will be provided on Jubilee Campus (Newark Hall). This will include bed & breakfast, lunch and dinner, for the nights of 3-4 September 2012. Additional nights may be available on request, at a cost of £57.60 per night.


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How to get here...


Directions to and from Jubilee Campus

 Between campuses

The University operates a free Hopper Bus service between Jubilee Campus, University Park and Sutton Bonington Campus.  You can view the Hopper Bus timetables online. They are also available on the buses.

All our campuses have cycle parking facilities and those within the City have links to numerous cycle paths.

 From Nottingham (approximately 4 miles)

By bus:

  • Nottingham City Transport, service 28  ( City - Ilkeston Road - Jubilee Campus - Beechdale Baths - Bilborough )
  • Nottingham City Transport, service 30  ( City - Ilkeston Road - Jubilee Campus - Wollaton Village - Wollaton Vale )
  • Nottingham City Transport, service Unilink 31  ( City - Ilkeston Road - Jubilee Campus *term-time only )
  • Nottingham City Transport, service L10 ( City - Ilkeston Road - Jubilee Campus - Wollaton - Bramcote - Beeston )
  • Nottingham City Transport, service L12 ( City Hospital - Basford - Hyson Green - Jubilee Campus - QMC - Nottingham University )
  • Nottingham City Transport, service L53 ( Arnold, City Hospital, Jubilee, QMC, Clifton Boulevard, Clifton )

By taxi:

There are taxi ranks throughout the City Centre and immediately adjacent to the main railway and bus stations. The journey to the campus takes about 15 minutes.

From East Midlands Airport (Approximately 10 miles)

From East Midlands Airport you can take the Skylink  service to the City Centre to connect with Nottingham City Transport buses, or the Indigo service, operated by Trent Barton Buses, for which the nearest stop to Jubilee Campus is the Queens Medical Centre.  Buses leave from outside the Airport Arrivals hall.

You can also walk to the taxi rank on the terminal forecourt and take a direct taxi to the University. The cost of a single/one way journey is approximately £20. Taxis are normally available 24 hours.

From M1 Motorway

By car:

Leave the M1 motorway at Junction 25 to join the A52 to Nottingham. After five miles turn left onto the A6514, Middleton Boulevard. Turn right at the next roundabout onto the A609 Wollaton Road. The main entrance to Jubilee Campus is clearly signposted on the right

Car Parking on campus:

Visitors to the University will be required to use the pay and display facilities.

Parking charges for 2013/14 are:

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Restrictions will apply in some locations.

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Campus contact details

Jubilee Campus
Wollaton Road
telephone : +44 (0) 115 951 5151





For further details, please contact Markus Owen.


CMMB and MBI are grateful for the support of the following.

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Centre for Mathematical Medicine and Biology

School of Mathematical Sciences
University of Nottingham
Nottingham, NG7 2RD

telephone: +44 (0) 115 846 7214
fax: +44 (0) 115 951 4951
email: markus.owen@nottingham.ac.uk