Organisers: Dr RH Clayton (Sheffield), Professor P Hunter (Auckland), Professor N Smith (Oxford) and Dr S Waters (OCIAM)

Programme Theme

Predicting physiological behaviour from experimental data combined with environmental influences is a compelling, but unfulfilled, goal of post-genomic biology. This undeniably ambitious goal is the aim of the Physiome Project and its subset the Cardiome Project which is an international effort to build a biophysically based multi-scale mathematical model of the heart. To achieve this goal requires further development of the current generation of advanced cardiac models which span an already diverse set of mathematical representations from stochastic sub-cellular regulation models to whole-organ-based sets of coupled partial differential equations. The focus of this programme will be on the development and application of the mathematical techniques which underpin the ongoing extension of this approach, and specifically to:

• integrate data from disparate sources into a common quantitative framework;
• examine the complex cause and effect relationships which exist across many temporal and spatial orders of magnitude in physiology;
• determine the appropriate level of detail to capture observable phenomena and the closely related issue of parameter identifiability;
• examine issues of model inheritance and multi-scale coupling for combining existing models together to create extended frameworks;
• define standards for the constituent electrical, mechanical and vascular classes of cardiac models.

The aim of this programme will be to debate and provide contributions from state of the art mathematical techniques for galvanising the wider research community into focused action on the emerging issues of applying mathematics and computational science to develop multi-scale computational models of physiological systems.

The theme for each week is:

Week 1:	Myocyte Cell Function
Week 2:	Excitation and Contraction
Week 3:	Coronary Vascular Fluid Dynamics
Week 4:	Integrated Cardiac Function, with a one week conference on The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart

Week 1 Sub-cellular Modelling

Focus: To review the characterisation of subcelluar measurement with biophysically based models of subcellular components including: channel and exchanger functions, signalling and transduction pathways.

Goal: The develop a position paper which review classes of subcellular models in terms of both structure (ODE/PDE, markov etc) and physiological function and then outlines a discussion based on:

• Which mathematical tools are most appropriate to quantify stability and parameter sensitivity in increasingly complex models of physiological systems?
• How much complexity is required at a given level (e.g. cell) for integrating into simulations of function at higher level (e.g. tissue), and what sort of analysis can be used to establish the level of complexity required for a specific simulation?
• What are the mathematical and computational criteria that models or sub-groups of model should conform to for different functions? How can these be promoted and enabled within the community?

This will be prepared for publication in a special issue of Progress in Molecular Biology and Biophysics

Program Outline

Monday Morning: Introduction (10:30-12:30)

Two slides for each participants to (1) introduce what they are working on and (2) significant challenge in their work.

Monday Afternoon: Review of the Field (4:30 - 5:30)

Kevin Burrage: Coupling fluctuations in channel behaviour at the cellular level to tissue : multiscale simulation of stochastic and deterministic processes in the heart

Followed by Welcome drinks reception at the Newton Institute and dinner in Cambridge

Tuesday Afternoon: Challenges ahead (2:00-5:00)

2:00-2:30 Dan Beard: Merging Cellular Biochemical Models Using Physicochemically Rigorous Rules

2:30-3:00 Martin Fink: Model Development and parameter estimation: the relationship between model structure, model parameter and available data.

3:00-3:20 Steven Niederer: A Meta Analysis of Cardiac Cell Models

3:20-3:40 Hans Dierckx: TBC

Discussion

Wednesday Social Event: Guided Walking Tour in Cambridge

Friday Afternoon: Bridging between scales and Physics (3:00-5:00)

3:00-4:00 Elizabeth Cherry: Tale of two dogs and implications for cardiac electrophysiology

4:00-5:00 Discussion chaired by Nic Smith

Week 2 Excitation and Contraction

Focus: To investigate frameworks and methods used to couple excitation and mechanics at both cell (ODE) and tissue scales (PDE). The influence and interdependence of these two phenomena will be discussed along with mathematical and computational tools.

Deliverables: We would invite everyone to contribute to a position paper establishing the level of detail that is appropriate for different types of numerical experiment. This paper might cover the following areas and include specific numerical examples:

• Review of physiology: Calcium handing (storage, sequestration, release and uptake), force transduction, electrical and mechanical coupling in tissue, mechano-electric feedback.
• Modelling: Models of excitation (cell and tissue), force development, and tissue deformation. Examples of tight and weak time coupling, distributed and lumped models of force generation, constitutive law identification. Influence of mechanics on activation during normal beats and arrhythmias. Potential for patient specific models.
• Mathematics and computation: Parameter identification and parameter sensitivity in models of excitation and contraction. Relative merits of different numerical schemes

This will be prepared for publication in a special issue of Progress in Molecular Biology and Biophysics

Program Outline

Monday Morning: Introduction (10:30-12:30)

• Two slides for each participants to (1) introduce what they are working on and (2) significant challenge in their work.
• Issues board - identify foci for further work during the week.
• Set initial directions and loose group formation

Monday Afternoon: Review of the Field (4:30 - 5:30)

Sasha Panfilov: TBC

Followed by Welcome drinks reception at the Newton Institute and dinner in Cambridge

Tuesday Afternoon: Challenges ahead (2:00-5:00)

2:00-2:30 Olivier Bernus

2:30-3:00 Flavio Fenton: TBC

3:00-3:20 Steve Niederer Coupling cardiac excition and contraction

3:20-3:40 Early Career Participant TBC

Discussion

Wednesday Social Event: Visit to Trinity College Library

Friday Morning: Open poster session

Friday Afternoon: Bridging between scales and Physics (3:00-5:00)

3:00-4:00 Martyn Nash (TBC)

4:00-5:00 Discussion chaired by Richard Clayton

Week 3 Coronary Vascular Fluid Dynamics

Focus: To investigate frameworks and methods to describe the flow and transport properties of the coronary vasculature, and to consider how these models link to the cell and tissue models considered in weeks 1 and 2.

Deliverables: To develop a position paper that reviews the current state of play in coronary vascular fluid mechanics, and outlines discussions that have taken place during week 3. This paper might cover the following areas:

• Physiology: Large vessel and microvascular haemodynmics, circulatory control, vessel topology
• Modelling: Simplified haemodynamical modelling, ontological representation of vascular networks, fluid mechanical interactions in the coronary system, non-Newtonian flows
• Mathematics and computation: network and graph representations, ordering schemes, spectral methods, visco-elastic deformation, parameter extraction, homogenisation (continuum compared to discrete spatial models)

This will be prepared for publication in a special issue of Progress in Molecular Biology and Biophysics.Program Outline

Monday Morning: Introduction (10:30-12:30)

• Two slides for each participants to (1) introduce what they are working on and (2) significant challenge in their work.
• Issues board - identify foci for further work during the week.
• Set initial directions and loose group formation

Monday Afternoon: Review of the Field (4:30 - 5:30)

Spencer Sherwin: Large scale vascular flow modelling

Followed by Welcome drinks reception at the Newton Institute and dinner in Cambridge

Tuesday Afternoon: Challenges ahead (2:00-5:00)

2:00-3:00 Tim Secomb: Determinants of coronary structure and flow

3:00-4:00 Peter Davies: Title TBC

4:20-4:40 Rebecca Shipley Homogenization of the Vasculature in Tissues

4:40-5:00 David Nordsletten Blood flow and Cardiac Mechanics in the Left Ventricle

Discussion

Wednesday Social Event: Punting

Friday Afternoon: Bridging between scales and Physics (3:00-5:00)

3:00-4:00 Nic Smith Integrating fluid mechanical models into global heart function,/p>

4:00-5:00 Discussion chaired by Sarah Waters

Week 4: The Cardiac Physiome Workshop:

Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart

Supported by BBSRC, the Wellcome Trust and the Newton Institute

See: http://www.newton.ac.uk/programmes/CPP/cppw01p.html

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