**Annabelle Ballesta, University of Warwick, UK**

**Title**: A multi-scale systems pharmacology approach for anticancer chemotherapy personalisation.

**Abstract**: Anticancer chemotherapy personalisation needs to reliably account for the activation of molecular pathways triggered by drug administration in each individual patient. Indeed, underlying gene and protein intracellular networks ultimately drive treatment antitumor efficacy and side effects in cancer and healthy tissues respectively, and they highly depend on patient- and tumour-specific genetic mutations or epigenetic alterations. However, clinical molecular data is usually minimally available in individual patients so that physiologically-based models designed through multi-scale approaches integrating preclinical and clinical investigations appears as an adapted solution. The models are based on ordinary differential equations (ODEs), and represent the relevant intracellular protein networks together with the pharmacokinetics-pharmacodynamics (PK-PD) of drugs of interest in both the tumour and the healthy tissues for which chemotherapy is critically toxic. While PK quantifies the transport and metabolism of the drug and its metabolites that are driving exposure concentration over time, PD quantifies drug interactions with cellular targets and subsequent cytotoxicity.

Basing mathematical models on physiology allows the use of in vitro studies to design whole-body preclinical rodent models, to be further scaled to patient population data. Partial re-calibration of the resulting human model for a given cancer patient according to individual biomarker recordings, genetic background and therapeutic history further allow for chemotherapy personalisation. The patient-specific models would then initiate a novel kind of clinical trial in which each individual patient would receive personalised drug combinations/scheduling computed via mathematical models informed with a continuous flow of multidimensional information obtained and tele-transmitted from patients.

I will first present how this multi-scale approach is currently undertaken for designing clinically-relevant models of the PK-PD of temozolomide, the cornerstone of treatments against brain tumours, and how they can be used to personalize combination chemotherapies [1]. Next, I will discuss the promises of personalized cancer chronotherapeutics, that is administering anticancer drugs according to the patient’s biological rhythms over the 24h span. The project focuses on individualizing the circadian delivery of the anticancer drug irinotecan, one of the three drugs of the current gold standard protocols against digestive cancers [2-4] .

**References**: (1) Ballesta, A., et al., *Multiscale design of cell-type-specific pharmacokinetic/pharmacodynamic models for personalized medicine: application to temozolomide in brain tumors.* CPT Pharmacometrics Syst Pharmacol, 2014. **3**: p. e112. (2) Dulong, S., et al., *Identification of Circadian Determinants of Cancer Chronotherapy through In Vitro Chronopharmacology and Mathematical Modeling.* Mol Cancer Ther, 2015.(3) Ballesta, A., et al., *A systems biomedicine approach for chronotherapeutics optimization: focus on the anticancer drug irinotecan*, in *New Challenges for Cancer Systems Biomedicine*. 2012, Springer.(4)Ballesta, A., et al., *A combined experimental and mathematical approach for molecular-based optimization of irinotecan circadian delivery.* PLoS Comput Biol, 2011. **7**(9): p. e1002143.

**Etienne Boileau, Swansea University, UK**

**Title**: Human cardiac systems electrophysiology for safety pharmacology and disease modelling

**Authors**: Etienne Boileau, Perumal Nithiarasu

**Abstract**: Traditional approaches in safety pharmacology are largely based on a pharmacoki- netic-pharmacodynamic (PK/PD) analysis of drug-induced effects on cardiovascu- lar (CV) function. Preclinical safety studies with CV endpoints include off-target activity assessed in vitro on molecular targets, in silico and quantitative structure- activity relationships (QSAR) models, and in vitro functional assessments using tissue-based studies. When considering replacements for current animal models, which only approximate human (patho-)physiology, human stem cell-derived car- diomyocytes (hSC-CMs) offer new perspectives, satisfying the need for physiologi- cal relevance [1]. However, study of hSC-CMs is confounded by the heterogeneity of these cells in culture, which recapitulate the developing myocardium, and reveal substantial differences between their electrophysiological, contractile properties, and their calcium handling capacity, and those of adult CMs.

Recently, we formulated a novel mathematical model of hSC-CM with the objec- tive of complementing the information obtained from temporal patterning of intra- and intercellular calcium signals in spontaneously contractile syncitia of hSC-CMs. The mathematical formulation for the different currents uses the Hodgkin-Huxley formalism, and is based on experimental observations from a wide survey of the existing literature on hSC-CMs. The formulation is used to create a population of models by selecting relevant parameter sets (conductances, parameters governing calcium cycling, etc.). Each model in the population is then calibrated based on selected biomarkers. Preliminary statistical analysis shows how intrinsic variability within the model parameters modulate action potential morphology, and how these changes represent natural, genetic or drug-induced alterations in ionic currents or in calcium cycling capacity which can affect preclinical biomarkers of arrhythmic risk.

References: [1] Lewis, K.J., Silvester, N.C., Barberini-Jammaers, S., Mason, S.A., Marsh, S.A., et al. 2015 J. Biomol. Screen. 20 330–340

**Sara Brueningk, Institute of Cancer Research, London, UK**

**Title**: A high performance multiscale model to simulate *in vitro*experiments of focused ultrasound mediated heating combined with irradiation

**Abstract**: Combination treatments of radiotherapy and heat offer great potential for the successfully treatment of radiation-resistant tumours by overcoming their resistance through thermo- sensitisation. Focused ultrasound (FUS) provides a potential method for locally applying hyperthermia at temperatures ranging from 45 to 50̊C. We present a multiscale simulation framework that models the cellular response to *in vitro* experiments of combination treatments of radiation and FUS mediated heating. The framework comprises a cellular automaton model to simulate treatment response of cell populations to combinations of FUS and radiation, together with an iterative solver to model FUS beams and corresponding heat distributions.

The talk will cover the underlying mathematical and biological concepts of radiation and heat induced cell killing, as well as the computational aspects of the simulation which includes a high performance implementation of the cellular automaton and diffusion models. Finally, a number of biological and physical experiments which point out the importance of model calibration and validation against relevant experimental data are presented.

**Helen Byrne, University of Oxford, UK**

**Title: **Understanding the Impact of Heterogeneity on Tumour Responses to Radiotherapy

**Abstract:** There are multiple sources of heterogeneity within solid tumours and each of these can affect the response to radiotherapy. For example, an irregular distribution of blood vessels may create tumour regions with low oxygen concentrations and decreased radio sensitivity. Alternatively, the tumour may comprise distinct cellular populations, each with different intrinsic radiosensitivity.

In this talk, I will present recent results from several complementary mathematical and computational models that we are developing in order to understand the impact of cellular and vascular heterogeneity on tumour responses to radiotherapy.

**Igor Chernyavsky, University of Manchester, UK**

**Title**: Image-based modelling of blood flow and oxygen transfer in feto-placental capillaries (**Poster)**

**Authors**: Philip Pearce, Paul Brownbill, Jiří Janáček, Marie Jirkovská, Lucie Kubínová,Igor L Chernyavsky, Oliver E Jensen

**Abstract**: During pregnancy, oxygen diffuses from maternal to fetal blood through villous trees in the placenta. In this paper, we simulate blood flow and oxygen transfer in feto-placental capillaries by converting three-dimensional representations of villous and capillary surfaces, reconstructed from confocal laser scanning microscopy, to finite-element meshes, and calculating values of vascular flow resistance and total oxygen transfer. The relationship between the total oxygen transfer rate and the pressure drop through the capillary is shown to be captured across a wide range of pressure drops by physical scaling laws and an upper bound on the oxygen transfer rate. A regression equation is introduced that can be used to estimate the oxygen transfer in a capillary using the vascular resistance. Two techniques for quantifying the effects of statistical variability, experimental uncertainty and pathological placental structure on the calculated properties are then introduced. First, scaling arguments are used to quantify the sensitivity of the model to uncertainties in the geometry and the parameters. Second, the effects of localized dilations in fetal capillaries are investigated using an idealized axisymmetric model, to quantify the possible effect of pathological placental structure on oxygen transfer. The model predicts how, for a fixed pressure drop through a capillary, oxygen transfer is maximized by an optimal width of the dilation. The results could explain the prevalence of fetal hypoxia in cases of delayed villous maturation, a pathology characterized by a lack of the vasculo-syncytial membranes often seen in conjunction with localized capillary dilations. This study has been supported by EPSRC grants EP/L504877/1 & EP/K037145/1 and MRC NIRG grant MR/N011538/1 (dx.doi.org/10.1371/journal.pone.0165369).

**Igor Chernyavsky, University of Manchester, UK**

**Title**: A theoretical model for bronchial thermoplasty therapy in asthma (**Poster**)

**Authors**: Igor L Chernyavsky, Ruth M Saunders, Gavin E Morris, Felicity RAJ Rose,

Oliver E Jensen, Christopher E Brightling, Bindi S Brook

**Abstract**: Bronchial thermoplasty (BT) is a recently introduced non-pharmacological therapy that selectively heats conductive airways with low-power electric current delivered into the airway wall via a bronchoscope-inserted catheter. In severe asthma this procedure improves quality of life and reduces exacerbation frequency beyond the peri-procedure period. Although BT is believed to induce the loss of functional airway smooth muscle (ASM), there are very limited theoretical and experimental studies that assess the effect of heat on ASM cells survival and function. To address this, we employed a finite element-based Joule heating and bioheat transfer model that implemented the BT protocol and predicted heat distribution in a bronchial wall, and we also subjected ASM cells cultured in isolation to a range of temperatures 37–70ºC for 10 seconds. The *in-vitro *heated ASM cells undergo necrosis at temperatures above 65ºC, but the heat has relatively low impact on the cells at lower temperatures. The simulations show a high degree of heterogeneity in thermal variations over an airway wall, with only a small fraction of the wall heated to 65ºC. The heterogeneity is intrinsic to the BT design and is amplified in larger airways. The combined *in vitro* and *in silico* approach thus suggests that the acute loss of ASM mass is likely not to dominate the effect of BT, and alternative mechanisms, by which asthma conditions could be relieved post-BT, should be investigated. This study has been supported by EU grant #270194 within AirPROM project (www.airprom.eu).

**Gianne Derks, University of Surrey, UK**

**Title**: Dimer dynamics and degenerate transversally intersecting manifolds

**Abstract**: We consider a pharmacological model of dimerisation, i.e., a receptor binding two ligand (drug) molecules. This model is an extension of thewell studied target mediated drug disposition model (TMDD) in which the receptor binds to one ligand molecule. It is assumed that the binding is the fastest process. This gives a separation of time scales, which allows us to use geometric singular perturbation theory to analyse these models. In both models, the slow manifold consists of two components, which intersect transversely in the origin. The dimerisation model leads to a degenerate intersection. To analyse such intersection, we consider a general two parameter slow-fast system in which the critical set consists of a one dimensional manifold and a two dimensional manifold, intersecting at the origin. Using geometric desingularisation, we determine the fate of the incoming one dimensional manifold and show that for a subset of the parameter set there is a jump away from the intersection at the origin and away from the critical set. For most of the remaining parameter set, there is an exchange of stability between the attracting components of the critical set and the direction of the continuation can be expressed in terms of the parameters. The parameters for the dimerisation model fit into the latter category and we will give an approximation of the dynamics in the dimerisation model.

This is joint work with Philip Aston and Christine Gavin

**Sara Hamis, Swansea University, UK**

**Title**: Simulating tumour growth with a cellular automaton using high performance computing methods

**Abstract**: Cellular automata (CA) are popular for modelling discrete tumour cell proliferation, however CA for biological systems may yield computationally heavy simulations when working with complex and/or large systems. Thus conventional serial programming may prove insufficient to produce in silico experiments that execute in a feasible time frame. In quest for reduced execution times high-performance computing methods are explored, one such method is parallelisation by spatial decomposition. The premise is that a speed-up can be achieved by distributing the CA grid and thus the workload across multiple physical hardware resources (processing units). Parallelisation by spatial decomposition is implemented using the Message Passing Interface (MPI) in C++.

Here tumour growth is modelled with a CA incorporating both intracellular and extracellular regulations. Whilst the intracellular regulations are explicitly parallelisable the extracellular regulations are not due to read and write neighbour dependencies, therefore parallel algorithms that correctly handle neighbour dependencies are devised.

**Benoit Huard, Northumbria University, UK**

**Title**: Ultradian rhythms in glucose regulation and diabetic deficiencies

**Abstract**:The mathematical theory of periodic solutions in systems of functional-differential equations has found applications in mathematical biology as it provides an invaluable tool for characterising cyclic regulatory patterns in negative feedback loops. It is well known that physiological delays can often be sufficient for explaining the presence of a cyclic regulation without relying on an internal clock mechanism.

In this contribution, we provide an investigation of the effect of Type I and Type II diabetic deficiencies on the production of an ultradian oscillatory regime in the glucose-insulin regulation using a system which incorporates two biological delays. The system, adapted from [1,2], also includes parameters which modulate efficiency in the secretion insulin secretion and the glucose utilisation.

Using the production of an oscillatory regime in a physiologically acceptable range as an indicator of healthy regulation, we investigate the contribution of current strategies for restoring it. The presence of a curve of Hopf bifurcations in the space of delays allows us to provide explicit conditions on the diabetic and therapeutic parameters ensuring the generation of a periodic orbit.

This is joint work with A. Bridgewater and M. Angelova.

[1] Li, J., Kuang, Y., Mason, C. C. (2006) Journal of Theoretical Biology, 242(3), 722-735 [2] Huard, B., Easton, J. F., Angelova, M. (2015) Communications in Nonlinear Science and Numerical Simulation, 26(1), 211-222.

**Dante Kalise, Radon Institute for Computational and Applied Mathematics, Austria**

**Title:** A computational approach to multiscale optimal control of collective behaviour phenomena

**Abstract**: Multi-agent dynamics are often represented as particle systems where the different states (agents) interact with each other under simple rules such as attraction, repulsion, and alignment. For a large number of agents, the mean field approximation describes the state of the system through the evolution of an agent density function. This idea has played a crucial role in the study of control and games for multi-agent systems in the context of mean field games and mean field type control. In this talk, we present a multiscale model where the agents admit a mean field approximation, whereas the controller remains finite-dimensional. Such a setting translates into a coupled ODE/PDE system, where the coupling is via a nonlocal operator in the mean field PDE. We will address the development of a computational approach for the synthesis of controllers via dynamic programming in conjunction with binary interaction algorithms, and the approximation of the optimality systems arising in multiscale optimal control.

**Meta Kallista, Institut Teknologi Bandung, Indonesia**

**Title**: Blood Flow Model for Dengue Infection Consider the Dependence of Viscosity Value Due to the Hematocrit Changes (**Poster**)

**Abstract:** The phenomenon of dengue infection within host is shown here. In this paper, we construct the dynamics of healthy cells, infected cells, immune response and virus; which can affect the dynamics of hematocrit. Hematocrit value is the one of parameters that can detect the stage of fatality dengue infection. By using the relation between hematocrit and viscosity, we implement the viscosity changes due to Dengue infection to the blood flow model. We use Stokes equation as a description of the blood flow in the small vessels. The weak formulation using appropriate boundary conditions for normal and leakage condition is proposed here. Numerically, we obtain the different volume flux because of viscosity changes due to dengue infection and the normal condition.

**John King, University of Nottingham, UK**

**Title:** Organization of vascular pattern in plant roots

**Authors**: Nathan Mellor, Anthony Bishopp, Britta Kuempers and John King.

**Abstract**: In higher plants the root vascular tissue or stele contains the xylem vessels, which transport water and nutrients from root to shoot, and the phloem, which transport photosynthetic products (sugars) from shoot to root. In Arabidopsis there are exactly two xylem vessels and two phloem vessels in every root, arranged in a diarch pattern, and regulated and organised by the two plant hormones, auxin and cytokinin. Mathematical modelling has shown that an embryonic asymmetry in auxin, originating from the two cotyledons, may establish the vascular pattern prior to germination, and that once established this pattern is robust to perturbations in hormone concentrations. However, the models have not yet been able to explain how the patterning of the vascular bundles of monocots, such as cereals that may have ten or more xylem poles, can originate from a single cotyledon auxin source. Furthermore, it can be shown that vascular pattern may be altered in growing roots via experimental manipulation, suggesting some post-embryonic patterning mechanism is present. A variety of modelling approaches to investigate how such de-novo patterning with multiple xylem and phloem vessels may occur in plant roots will be outlined.

**Fiona Macfarlane, Mathematics and Statistics, University of St Andrews**

**Title**: Multiscale Mathematical Modelling of the Immune Response to a Solid Tumour

**Abstract**: The recent developments in immunotherapy have highlighted the need to understand the mechanisms underpinning the immune response to cancer. Mathematical modelling of these systems allows for key aspects to be recognised in a cheap and timely manner. The aim of my research is to create a spatio-temporal multi-scale mathematical model describing the interactions between the immune system and a solid tumour. Dendritic cells can act as antigen presenting cells towards Cytotoxic T Lymphocytes, once activated these CTLs can then interact with tumour cells and potentially cause cell death. Initial numerical simulations highlight the importance of antigen presentation in removal of tumour cells but also that a large number of Dendritic cells present can lead to an overcrowding effect and block the CTLs from reaching the solid tumour mass. Once validated this model could be extended and aid in the development of new immunotherapy techniques.

**Carmel Mothersill, Department of Medical Physics and Applied Radiation Sciences, McMaster University, Canada**

**Title**: Modelling low dose effects of ionising radiation: How do we deal with non-targeted effects?

**Authors**: Carmel Mothersill and Colin Seymour

**Abstract**: Ionising radiation is a known carcinogen and is conventionally thought to cause cancer by causing mutations in DNA at critical sites. Radiation protection models assume a linear relationship between dose (i.e. energy deposition) and effect (in this case probability of an adverse DNA interaction leading to a mutation). This model does not consider non-targeted effects (NTE) such as bystander effects or delayed effects which occur in cells not directly receiving energy deposition from the dose. There is huge controversy concerning the role of NTE with some saying they reflect “biology” and that repair and homeostatic mechanisms sort out the apparent damage while others consider them to be a class of damage which increases the size of the target. One thing which has recently become apparent is that NTE may be very critical for modelling long-term effects at the level of the population rather than the individual. The issue is that NTE resulting from an acute high dose such as occurred after the A-bomb or Chernobyl occur in parallel with chronic effects induced by the continuing residual effects due to radiation dose decay. This means that if ambient radiation doses are measured for example 25 years after the Chernobyl accident, they only represent a portion of the dose effect because the contribution of NTE is not included. Current attempts in our laboratiory to calculate separate contributions of actual residual dose and contribution of NTE to effects will be presented for discussion.

**Perumal Nithiarasu, Swansea University, UK**

**Title:** Interaction between calcium dynamics, intercellular communication and vasomotion.

**Authors:** Alberto Coccarelli, Dimitris Parthimos, David Edwards and P. Nithiarasu

**Abstract:** The objective of this work is to predict vasomotion, triggered by calcium dynamics, in a controlled environment. The first step towards this objective is to understand the interrelationships between cellular Ca2+ and intercellular communication. This is carried out through coupled ordinary differential equations and parameters determined through experimental and theoretical observations. The intercellular communication is then translated into wall motion through appropriate constitutive relationship for arterial wall material.

**Angelique Stephanou, Universités Grenoble Alpes, France**

**Title: **Design of a virtual tumour

**Abstract:** The design of a patient-specific virtual tumour is an important step towards personalized medicine since the virtual tumour can be used to define the most adapted and efficient treatment protocol. However this requires to capture the description of many key events of tumour development, including angiogenesis, matrix remodelling, hypoxia, cell heterogeneity that will all influence the tumour growth kinetics and degree of tumour invasiveness. To that end, an integrated hybrid and multiscale approach has been developed based on data acquired on a preclinical mouse model as a proof of concept. Fluorescence imaging is exploited to build case-specific virtual tumours and to validate their spatiotemporal evolution. The validity of the model will be discussed as well as its potential to identify the best therapeutic strategy for each individual tumour case.

**Heni Widayani, Institut Teknologi Bandung, Indonesia**

**Title**: Model Reaction-Diffusion In Host Vector Model (**Poster**)

**Abstract:** Dengue is one of virus that spread through Aedes aegypti bites [3]. The spread of dengue has been modeled by [2] using host vector compartment model. The host population was divided into three subpopulation, susceptible, infected, and recovered host. While the vector population was divided into two subpopulations, namely susceptible and infected vector. The model is a system of ordinary differential with 5 equations in which the solution is a function of time. In here, we developed that model by adding diffusion parameter in mosquitoes population, since we assumed model only applied to a small area and no mobility in host population. Further, total population of both host and

vector are also assumed to be constant, so Neumann boundary conditions are used in the model. The temporal equilibrium of the model which incorporated diffusion parameter is obtained, i.e spatial independent spatial and spatial dependent. Formula for the basic reproduction ratio (R0) for the diffusion model is also obtained. When R0 < 1 solution will lead to DFE state, while when R0> 1 solution will lead to END state. Finally, numerical simulation using a combination of Runge Kutta order 4 and finite difference schemes is also presented to illustrate the results.