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Timetable (CPPW01)

The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart

Monday 20th July 2009 to Friday 24th July 2009

Monday 20th July 2009
08:15 to 09:00 Registration INI 1
09:00 to 09:15 Welcome - David Wallace INI 1
09:15 to 10:00 D Noble (University of Oxford)
The cardiac physiome: how it began and where should it go
10:00 to 10:45 R Vaughan-Jones (University of Oxford)
Connexins, buffers and mitochondria: novel pH/Ca2+ regulators in heart
10:45 to 11:00 C Soeller ([Auckland])
Quantitative fluorescence imaging with up to 30 nm resolution to provide 3D data for models of cardiac Ca2+ handling

Quantitative understanding of the Ca2+ handling in cardiac ventricular myocytes requires accurate knowledge of cardiac ultrastructure and protein distribution. We have therefore developed high-resolution imaging and analysis approaches to measure the three-dimensional distribution of immuno-labelled proteins with optical microscopy methods. Until recently optical imaging was thought to be limited to a resolution of ~250 nm set by the diffraction of light. We have overcome this limitation using a new technique that allows imaging of conventionally labelled fluorescent samples at much higher resolution.

Our technique, called reversible photobleaching microscopy (RPM), allows extension to multi-colour and full 3D localization and provides a new powerful method to study the nanostructure of cardiac muscle. We have used RPM and confocal microscopy to obtain new insight into the distribution of ryanodine receptors and related proteins such as the sodium calcium exchanger and caveolin.

To investigate potential effects of myocyte structure on Ca2+ wave propagation we determined the three-dimensional distribution of RyR clusters within an extended section of a single rat ventricular myocyte to construct a model of stochastic Ca2+ dynamics with a measured Ca2+ release unit (CRU) distribution. The model with a realistic CRU distribution supported Ca2+ waves that spread axially along the cell at velocities of ~50 µm/s. By contrast, in a simplified model with planar CRU distribution axial wave spread was slowed ~two-fold and wave propagation often nearly faltered.

These results demonstrate that features of the CRU distribution on multiple length scales may significantly affect intracellular Ca2+ dynamics and must be captured in detailed mechanistic models to achieve quantitative as well as qualitative insight.

11:00 to 11:30 Coffee
11:30 to 11:45 J Saucerman ([Virginia])
Modeling ß1-adrenergic receptor blockers and polymorphisms in cardiac myocytes

Modeling β1¬-adrenergic receptor blockers and polymorphisms in cardiac myocytes

Robert Amanfu, Ryan Connolly, Sean Meredith, and Jeff Saucerman

β-blockers are the one of the most effective medications for heart failure. But their success appears counterintuitive because they block the β1-adrenergic signaling pathway in cardiac myocytes, which enhances cardiac contractility. To evaluate mechanisms of β-blocker efficacy, we extended our cardiac myocyte β1-adrenergic signaling model using an extended ternary complex receptor model. This receptor model includes spontaneous switching between the active and inactive receptor conformations crucial for accurate representation of β-blockers and receptor polymorphisms. We determined parameters from the literature to model 11 agonists and 10 β-blockers and validated against a range of published experimental data. This new model predicts that at intermediate concentrations, β-blockers may protect the adrenergic pathway from chronic stress while paradoxically sensitizing the pathway to acute stress (like exercise). The Arg389 receptor polymorphism (prevalence ~50%) was predicted to constitutively stimulate calcium transients by 68%, which was restored to the activity of the wild type receptor by administration of 1 µM β-blocker (propranolol). Model predictions are being validated experimentally. These simulations are a first step towards evaluating personalized β-blocker therapies with computational models.

11:45 to 12:00 E Crampin ([Auckland])
Modelling Ca2+ and InsP3-dependent hypertrophic signalling pathways in the heart

Impairment of cellular metabolism in ischemic myocardium has a profound impact on cellular electrophysiology and contractility. Despite a wealth of available data, the multifactorial consequences of impaired metabolism are such that the sequence of events leading from coronary artery occlusion to life-threatening disturbances to the electrical rhythm and reduced pumping capacity remains poorly understood.

We are using integrative mathematical modelling to provide a framework within which to assess the quantitative contribution of different consequences of impaired metabolism to the overall deterioration of myocyte function during ischemia. This framework uses thermodynamically constrained models of energy consuming fluxes, including the Na-K pump (Prog Biophys Mol Biol 85 387 2004) and SERCA (Biophys J 96 2029 2009) and other metabolite-sensitive processes to couple cardiac cellular bioenergetics to electrophysiology and excitation-contraction coupling (Prog Biophys Mol Biol 97 348 2008; Tran et al. submitted).

We have applied this modelling framework to investigate the metabolic origins and functional consequences of several features of impaired myocyte physiology, including acidosis (Biophys J 90 3074 2006) and hyperkalemia (Am J Physiol 293 H3036 2007) arising over the first 15 minutes of zero flow ischemia, and subsequent calcium overload and calcium-dependent alternans (Terkildsen et al. in prep). These studies allow us to assess the quantitative contribution of changes to energy metabolism, pH regulation, ion homeostasis and electrophysiology to the development of ischemic heart disease.

12:00 to 12:15 J Jeneson ([TU, Eindhoven])
Development and testing of Cardiac Physiome cell model parts in skeletal muscle
In the living heart, the dynamic range of ATP turnover and associated oxygen consumption is relatively small - one order of magnitude - while metabolic homeostasis is highly robust (1). As a result, it has proven difficult to obtain in vivo dynamic data on ATP metabolism in the heart complicating parameterization and testing of computational models of cardiac energy metabolism. Typically, only steady-state data have been available to this aim (2, 3). In skeletal muscle, the situation is quite the opposite. The myofiber metabolic networks may undergo up to 500-fold changes in ATP turnover rate between rest and all-out sprint (4). These changes in ATP turnover rate are accompanied by very significant concentration changes in intermediairy metabolites such as the ATP hydrolysis products and glycolytic intermediates that can be tracked non-invasively using NMR spectroscopic techniques (4). Since the metabolic networks in cardiac and oxidative skeletal muscle fibers that supply the cell with ATP are to a large extend homologous (5), skeletal muscle provides a valuable experimental system to test and develop computational cell model parts for the Cardiac Physiome (6). Here, we report on the progress we have made in testing and development of computational models of mitochondrial oxidative metabolism and electrophysiology (Beard model) and glycogenolysis (Lambeth & Kushmerick model) and their integration in space and time.
12:15 to 12:30 D Beard (Medical College of Wisconsin)
Clinically observed phenomena on cardiac energetics in heart failure emerge from simulations of cardiac metabolism

The failing heart is hypothesized to suffer from energy supply inadequate for supporting normal cardiac function. We analyzed data from a canine left ventricular hypertrophy (LVH) model to determine how the energy state evolves due to changes in key metabolic pools. Our findings¡Xconfirmed by in vivo 31P-magnetic resonance spectroscopy (31P-MRS)¡Xindicate that the transition between the clinically observed early compensatory phase and heart failure and the critical point at which the transition occurs are emergent properties of cardiac energy metabolism. Specifically, analysis reveals a phenomenon in which low and moderate reductions in metabolite pools have no major negative impact on oxidative capacity while reductions beyond a critical tipping point lead to a severely compromised energy state.

Furthermore, our analysis reveals: (1.) the predicted metabolic tipping point coincides with the transition to severe cardiac dysfunction; (2.) the tipping point is associated with a ~30% reduction of TAN reduction corresponds to the reduction observed in humans in heart failure [Circ Res 95:135-145]; (3.), the predicted cytoplasmic AMP at the tipping point is approximately 1.6 mM and equal to the apparent AMP concentration at half-maximal activation of cardiac AMP-activated protein kinase; (4.) oxidative stress in the myocardium is predicted to progressively increase as the metabolic pools are diminished; and (5.) at given values of TAN and TEP during hypertrophic remodeling, CRtot attains a value that is associated with optimal ƒ´GATPase. Thus, both increases and decreases to the creatine pool are predicted to result in diminished energetic state unless accompanied by appropriate simultaneous changes in the other pools.

12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 A Garfinkel ([UCLA])
Mathematical concepts of cardiac arrhythmias
How can mathematics help us to understand cardiac arrhythmias? The best known approach is to take a mathematical model of cell electrophysiology, insert it into a more-or-less complex model of cardiac architecture, and then study the resulting waves of activation that propagate through the myocardium. The mathematical formalism is a reaction-diffusion partial differential equation (PDE), with the local cell model serving as the reaction and the (anisotropic) diffusion of current as the spatial component. Since these PDEs are highly nonlinear, the main strategic approach is to simulate them on supercomputers. This approach forms the basis of most work in the mathematics of cardiac arrhythmias. But there is another role for mathematics, which is to provide us with concepts with which to understand the qualitative phenomena that emerge from our equation models. Ventricular fibrillation, the leading cause of sudden cardiac death, offers some good examples of this role. Fibrillation, mathematically, is spatiotemporal chaos, a phenomenon known to arise in these PDEs. We will discuss two principal mechanisms of fibrillation: reentrant scroll waves and ectopic focal activity. Each has a mathematical formulation that gives us insight into the causes of the phenomenon, as well as suggesting potential therapeutic targets.
14:15 to 14:30 O Bernus ([Leeds])
Towards depth-resolved optical imaging of cardiac activity: insights from computational models

Optical imaging using voltage-sensitive dyes is a commonly applied technique to investigate cardiac activity in perfused tissue preparations or whole hearts. It offers superior spatiotemporal resolution, as well as the potential of obtaining simultaneous multi-modal recordings through the combination with various other indicators (e.g. calcium).

Conventional epi-fluorescence imaging was initially considered as a surface mapping technique, but careful interpretation of epi-fluorescence signals, taking photon absorption and scattering in to account, has shown that such recordings can yield information about sub-surface wave propagation. The use of detailed bio-photonics models combined with electrophysiological models of myocardium, so-called hybrid models, has been instrumental in understanding the synthesis of cardiac optical signals.

Wave propagation in cardiac tissue and ventricular myocardium in particular, is a three-dimensional phenomenon. Building on our earlier experimental and computational work, we are currently developing novel techniques for the 3D visualization of cardiac activity using optical methods. This requires the solution of the optical inverse problem, i.e. obtaining 3D information from a limited set of optical measurements, which is, as is often the case in bio-medical imaging, ill-posed and therefore requires regularization. Hybrid models of cardiac optical signals play here too an important role as they allow to assess the accuracy of the regularization scheme, and estimate the optimal spatiotemporal resolution of the reconstruction. We present results from a recent study that showed the feasibility of 3D reconstruction of paced activity in isolated rat hearts using an optical technique called Laminar Optical Tomography. Finally, we report on recent work which has focused on increasing depth penetration to achieve 3D reconstructions in larger hearts and developing a fast acquisition system for the imaging of arrhythmias during which activity is non-repetitive.

14:30 to 14:45 M Boyett ([Manchester])
Development of a virtual heart - Part l

Development of a virtual heart requires detailed anatomical models together with a family of action potential models for the different heart regions. In this and the following presentation, we will review progress to develop a virtual rabbit heart at the University of Manchester.

This presentation focuses on the cardiac conduction system, an essential element of a virtual heart. Based on serial sectioning, histology and immunolabelling of marker proteins, we have constructed 3D anatomical models of the rabbit sinoatrial node1 (SAN; pacemaker of heart) and the rabbit atrioventricular node2 (AVN; responsible for action potential conduction from atria to ventricles) as mathematical arrays. The model of the SAN includes both the centre and periphery of the SAN, whereas the model of the AVN includes the transitional zone (fast pathway), the inferior nodal extension (slow pathway) and the penetrating bundle.

Most recently, we have constructed a 3D anatomical model (mathematical array) of the right atrium of the rabbit heart based on high resolution MRI. The model of the right atrium includes 18 segmented objects, including the SAN and AVN and the major atrial muscle bundles, such as the crista terminalis. In 2000 we developed biophysically-detailed models of the action potentials in the centre and periphery of the rabbit SAN.3 More recently, we have developed biophysically-detailed models of the AN, N and NH action potentials (found predominantly in transitional zone, inferior nodal extension and penetrating bundle, respectively) of the rabbit AVN.4 We are using the 3D anatomical models together with the cellular automaton model, the Fitzhugh-Nagumo equations or biophysically-detailed action potential models to compute action potential conduction through the tissue during normal and abnormal activity (such as AVN reentry).

As an alternative strategy, we are using the biophysically-detailed action potential models together with an idealised 1D anatomical model of the AVN to explore the complex electrophysiology of the AVN (such as control of AVN conduction by parasympathetic nervous system).

References (1) H. Dobrzynski et al. Circulation 2005;111:846-54. (2) J. Li et al. Circ Res 2008;102:975-85. (3) H. Zhang et al. Am J Physiol 2000;279:H397-H421. (4) S. Inada et al. Biophys J 2009 (under revision).

14:45 to 15:00 H Zhang ([Manchester])
Development of a virtual heart - Part ll

Virtual tissue engineering of cardiac electrical activity requires detailed descriptions of local cell properties – their action potential (AP) mechanisms, local intercellular coupling, spatial heterogeneities, and their spatial and geometric relations. Over the last decade, we have developed a new family of single cell AP models for all distinctive regions of the rabbit heart. These single cell models include the centre and periphery of the sinoatrial node (SAN) (1), the right atrium (RA) and left atrium (LA) (2), crista terminalis and pectinate muscles (3), Bachmann’s bundle, pulmonary vein and coronary sinus (4), fast and slow pathways of the atrioventricular node (AN and N of the AVN) and His bundle (NH) (5), Purkinje fibers (PF), endocardial (Endo), middle (M) and epicardial (Epi) layers of the left ventricle (LV) (6). These single cell models were based on and validated against experimental data.

Using these single cell models, we have developed a 1D model for the whole heart conduction system that incorporates regional differences in both cellular electrical properties and intercellular electrical coupling among major distinctive regions of the rabbit heart, including the SAN, atrium muscle, AVN, PF and ventricle. The model reproduces the normal activation sequence of the heart with an endogenous SAN driven rate of ~180 beats/min. The activation is first initiated in the centre of the SAN. Once initiated, it propagates towards the periphery of the atrium and then to the AVN via the rapid conduction pathway of the crista terminalis. The AVN then transmits the excitation to the PF and then to the ventricle. The AP conduction velocities ranging from ~0.1 m/s in the SAN to 1.5 m/s in the PF, which are consistent with experimental data. The whole heart model also produces a pseudo-ECG with intervals (R-R=333 ms, Q-T=214 ms, P-R=85 ms) that fall in the range seen in isolated Langendorff perfused rabbit heart. Simulated effect of acetylcholine (ACh), a neurotransmitter released from vagal nerves upon stimulation, is also consistent with the measurement from Langendorff perfused rabbit heart.

15:00 to 15:30 Tea
15:30 to 15:45 S Panfilov ([Utrecht])
Electrophysiological metric and geometry of the heart

We develop an alternative view of the heart based on this fact, by considering the heart as a non-Euclidean manifold with a electrophysiological el- metric based on wave velocity. This metric is more natural than the Euclidean metric for studying the electrophysiology of the heart, because el-distances directly encode wave propagation.

We characterize this metric for a particular case of rotational orthotropic anisotropy of cardiac tissue on a small and a large scale. We show that although this metric is locally highly curved and non-Euclidean, its global geometry is close to that of an isotropic metric on the heart. That is, wave arrival times in anisotropic cardiac tissue with principal velocities v_f>v_s>v_n are well-approximated by arrival times in isotropic tissue with velocity v_f in all directions. We illustrate this with numerical simulations of a slab of cardiac tissue and of a model of the ventricles based on DTMRI scans of the canine heart.

15:45 to 16:00 E Cherry ([Cornell])
Restitution curve splitting as a mechanism for the bifurcation to alternans
Cardiac tissue displays a bifurcation in electrical response at rapid pacing rates. Traditionally, this bifurcation has been explained in terms of the slope of the restitution curve, a function that relates the response duration to the duration of the interval preceding it. However, we have recently observed that this curve is not a single-valued function under a wide range of physiological conditions. We will show examples of this restitution curve splitting and discuss the implications.
16:00 to 16:15 D Holm (Imperial College London)
Optimal paths in cardiology
Mathematical concepts will be discussed that are shared by certain approaches for modelling cardiac waves of electrical activity potential with those that are used in the modelling of other types of waves and also with the methods of imaging science using template matching. The main concept to be discussed is the derivation of optimal path dynamics obtained by applying reduction by symmetry to Hamilton's principle for evolution on the tangent space of smooth invertible maps possessing smooth inverses (diffeomorphisms). This concept is shared by cardiac waves, fluid dynamics, shape dynamics, shallow water waves, imaging science and solitons. Several applications will also be discussed.
16:15 to 16:30 F Sachse ([Utah])
A novel approach to multidomain modeling of electrical conduction in cardiac tissue

Various types of models have been developed in the past to study electrical conduction in cardiac tissue. Model types include macroscopic approaches e.g. cellular automata and reaction-diffusion systems. In general, macroscopic approaches are based on the assumption that myocytes are the exclusive cell type in cardiac muscle. However, cardiac tissue is known to be a composite material composed of various cell types including - in addition to myocytes - fibroblasts, myofibroblasts, endothelial, vascular smooth muscle, and neuronal cells. We hypothesize that heterogeneity of cell type affects electrical conduction. We tested this hypothesis by developing a novel approach for macroscopic multidomain modeling, applying the model in computational simulations, and analyzing the simulation results.

Our multidomain model represents cardiac tissue as a mixture of various cell types. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added spatial and physical domains associated with other cell types. Cells in these domains can be electrically coupled with each other and with cells from other domains. We implemented the model equations based on finite differences and finite element methods applying the PETSc toolkit for scientific computation. We applied the model in exemplary computational simulations of electrical conduction in cardiac tissue composed of myocytes and fibroblasts. In these simulations, volume ratios of cells and their inter- and intracellular electrical coupling were varied.

In support of our hypothesis, the simulations showed that cellular heterogeneity, electrical coupling between myocytes and fibroblasts, and inter-fibroblast coupling have distinct effects on tissue conduction. For example, myocyte-fibroblast coupling reduced anisotropy of conduction velocity only for significant inter-fibroblast coupling. We suggest that these effects can be tested in experimental studies with engineered tissue. Furthermore, we believe that the presented modeling approach provides novel means to understand mechanisms of conduction in diseased and engineered cardiac tissue.

16:30 to 16:45 G Plank (Medizinische Universität Graz)
Using multiscale in-silico models of the heart for optimisation of anti-arrhythmia therapies

Several multi-center clinical trials have provided consistent evidence that implantable defibrillation therapy prolongs patient life. This convincing demonstration of efficacy has led to a nearly exponential growth, over the last decade, in the number of patients receiving implantable devices. Currently, around 0.2 million implantable cardioverter defibrillators (ICDs) are implanted every year throughout the world.

Despite the importance and wide-spread use of this therapy, understanding of mechanisms by which electric shocks halt life-threatening arrhythmias remains incomplete. Further, ICD therapy is clearly suboptimal: to reliably restore sinus rhythm high shock strengths are required which are perceived as extremely painful by most patients, leading to traumatization with a significant impact on quality of life; the high current densities close to the electrode damage adjacent tissue; ICDs sometimes deliver inadequate shocks which may even trigger lethal arrhythmias instead of preventing them.

Recent experimental advances allow a better characterization of the shock-tissue interaction which have led to new mechanistic insights. Nonetheless, current experimental techniques cannot resolve, with sufficient accuracy, electrical events confined to the depth of the myocardial walls which limits observations to the surfaces of the heart. In-silico computer models are a powerful complementary approach to bridge this gap by providing a mechanistic link between elecrical activity observed at endocardial and epicardial surfaces.

The overall objective of this research is, by employing anatomically and functionally realistic in-silico computer simulations of the defibrillation process and the physics of experimental mapping techniques, to shed light on basic mechanisms underlying shock-tissue interactions and to test new hypotheses which may, eventually, pave the road to reliable defibrillation at a fraction of the energy requirements of current ICDs.

16:45 to 17:45 Welcome Wine Reception
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Tuesday 21st July 2009
09:15 to 10:00 A Popel ([Johns Hopkins])
Systems biology of angiogenesis in ischemic diseases
Angiogenesis is the formation of new blood vessels from pre-existing microvasculature. Angiogenesis is important under physiological and pathological conditions (e.g., exercise, ischemic heart and peripheral vascular diseases). Over 70 diseases have been identified as angiogenesis dependent. Angiogenesis involves numerous processes such as: cell sensing of oxygen levels during hypoxia; upregulation of vascular endothelial growth factor (VEGF) by parenchymal and stromal cells, and of matrix metalloproteinases (MMPs) by endothelial cells; extracellular matrix (ECM) proteolysis and release of matrix-bound growth factors; endothelial cell migration, proliferation and differentiation; tubulogenesis or formation of capillary tubes; network morphogenesis; and vessel maturation and remodeling. We use computational approaches to explore the mechanisms and quantitative features of these processes. We use post-genomic bioinformatic approaches as an aid to model development. We have developed a series of molecular-level computational models that serve as modules in multiscale integrative models. These include a model of Hypoxia-Inducible Factor HIF1á regulation; models of interactions of several VEGF isoforms with their receptors VEGFR1, VEGFR2, co-receptor Neuropilin-1 and heparan sulfate proteoglycans; and a model of ECM proteolysis by MMPs, specifically MMP2, MMP9 and membrane-type MT1-MMP, in the presence of tissue inhibitors of metalloproteinases (TIMPs). In addition to these biochemically and biophysically detailed molecular-level models, we have developed a compartmental pharmacokinetic model that allows us to predict distribution of VEGF isoforms and intermediate products upon administration of pro-angiogenic factors, e.g. via gene delivery. The models will lead to a better understanding of therapeutic interventions in disease conditions including pro-angiogenic approaches to ischemic heart disease and peripheral vascular disease.
10:00 to 10:15 PF Davies ([Pennsylvania])
Haemodynamics and endothelial phenotype heterogeneity

Endothelial phenotype defines the multi-functional capabilities of the tissue (endothelial monolayer). Within coronary arteries and heart valves, as elsewhere in the arterial circulation, the endothelial phenotype is spatially heterogeneous. Endothelial heterogeneity in general can be considered at different length scales from vascular beds to specialized vascular structures such as heart valves to single cells and it arises from a combination of 'intrinsic' genetic programming and functional changes modified by epigenetic, including important environmental, influences.

A prominent environmental influence is haemodynamics, the usually complex blood flow characteristics that arise from a combination of pulsatile flow, the composition of blood elements, and the geometry of the vessels. Local changes of haemodynamics characteristics, including the flow velocity, direction, frequency and oscillatory behaviour, create two broad consequences in modifying endothelial structure and function. First the transport characteristics of (i) molecules derived from the cells themselves (e.g. short-lived regulatory molecules such as vasoregulators) and (ii) blood molecules that are modified or degraded at the endothelial surface. The kinetics of these solutes is greatly influenced by changes in their transport characteristics in the boundary layer near the cell surface. Second, haemodynamic forces generated by flow, particularly shear stress, greatly influence endothelial biology (and pathophysiology); consequently the steady state phenotype of endothelial cells is sensitive to the temporal-spatial distribution of the forces.

Together, the complex environment defines regions (and perhaps cellular foci) of endothelial phenotypes, with consequences for the underlying artery wall. These mechanisms and their heterogeneous distribution are relevant to the incorporation of vascular biology contributions to the cardiac physiome. I will discuss some of the flow-related mechanisms responsible for endothelial heterogeneity in coronary arteries and valves gathered from genomics, molecular biochemistry and fluid dynamic experimentation, and interpret their pathological implications.

Background References: Davies PF. Flow-mediated endothelial mechanotransduction. Physiol. Rev. 1995, 75:519-560. Davies PF. Polacek, D.C., Shi, C., Helmke, B.P. The Convergence of Hemodynamics, Genomics, and Endothelial Structure, in Studies of the Focal Origin of Atherosclerosis. Biorheology 2002, 39: 299-306. Simmons, C.A, Manduchi, E., Grant, G., Davies, P.F. 2005. Spatial heterogeneity of endothelial phenotypes correlates with side-specific vulnerability to calcification in normal porcine aortic valves. Circ. Research 96:792-799. Davies, P.F. Hemodynamic Shear Stress and the Endothelium in Cardiovascular Pathophysiology. Nature Clinical Practice Cardiovasc. Medicine 2009, 6:16-26.

10:15 to 10:30 A Pries ([Freie, Berlin])
Modeling adaptive processes: vascular remodeling

Dynamic biological systems adapt to changes in internal or external conditions. A typical example is the response of the vascular system to changes in body size or local tissue function. Also during development, adaptive responses are used widely to determine the design of body systems. Such reactions entail functional or structural feedback signals which are typical for the system considered. In the case of the vascular system, the most relevant signals are generated by hemodynamics (local blood pressure and wall shear stress) and the metabolic situation determined by the relation between supply and demand (e.g. of oxygen).

According to the usual approach, reactions to such signals are established in experimental conditions aiming at a single stimulus at a time and interrupting the involved feedback loop. Such experiments showed an increase of vessel diameter with increasing flow or metabolic demand and a decrease with increasing pressure. Such reactions seem to be reasonable and the described reactions may be congruent with observed system responses under certain conditions (e.g. lower resistance for higher perfusion). Thus they are frequently used as the basis for concepts of vascular adaptation or design. However, the isolated appreciation of individual reaction patterns can not support an ‘understanding’ of system properties in several aspects: The quantitative relation of the different reactions is not addressed, it is not possible to determine whether the observed reactions are necessary and sufficient to explain system behavior and the stability of the assumed feedback regulation can not be assessed.

To answer such questions, a mathematical description or modeling of the assumed responses in a functional context is needed. Obviously, the prerequisite for such modeling is a gross simplification of the biological situation raising questions as to the validity of the obtained results. However, by not pertaining to specific biological properties lost in the simplification, the modeling analysis should represent general characteristics of systems which fit into the assumptions made in the model. With respect to vascular adaptation, mathematical models were, e.g., able to demonstrate that a directed information transfer along the vessel wall is necessary to prevent maldistribution of the blood flow within the tissue and the generation of functional shunting. Such a finding should be independent of the biological implementation of the information transfer but should stimulate respective experimental investigations. Based on the respective findings intuitive assumptions on systems behavior can then be tested by more detailed and more realistic models.

10:30 to 10:45 T Secomb ([Arizona])
Theoretical models for regulation of blood flow in the microcirculation

Local control of blood flow is achieved by contraction and dilation of smooth muscle cells in microvessel walls, particularly in arterioles, allowing rapid local responses to changing conditions. Several types of vessel response are involved. In the myogenic response, increased wall tension causes contraction. In the shear-dependent response, increased wall shear stress causes dilation. In the metabolic response, arteriolar diameters change according to the metabolic status sensed at downstream locations (capillaries and venules) after oxygen has been extracted from the blood. Information is transferred upstream along vessel walls by conducted responses, which involve electrical coupling of the cells.

We have developed theoretical models for flow regulation based on a mechanism for the metabolic response in which decreased oxygen levels in venules cause increased release of ATP, which acts on vessel walls to initiate upstream conducted responses leading to vasodilation. This model is used to explore the roles of the various vessel responses in autoregulation, in which flow is almost constant independent of changes in blood pressure, and in metabolic regulation, in which flow is modulated in response to changing metabolic demands. It is shown that autoregulation is achieved by the combined action of myogenic and metabolic responses, which overcome the opposing effect of shear-dependent responses. Metabolic responses are primarily responsible for metabolic flow regulation, but are opposed by the effects of shear-dependent and myogenic responses. The model is based on an explicit description of vascular network structure, and has potential application to the simulation of coronary flow regulation.

10:45 to 11:00 T Passerini ([Emory])
3D/1D geometrical multiscale modeling of vascular networks

Geometrical multiscale modeling is a strategy advocated in computational hemodynamics for representing in a single numerical model dynamics that involve different space scales. This approach is particularly useful to describe complex vascular networks and has been applied to the study of cerebral vasculature, where a one-dimensional (1D) description of the circle of Willis, relying on the one-dimensional Euler equations, has been coupled to a fully three-dimensional (3D) model of a carotid artery, based on the solution of the incompressible Navier-Stokes equations.

Even if vascular compliance is often not relevant to the meaningfulness of 3D results (e.g. in large arteries), it is crucial in the multiscale model, since it is the driving mechanism of pressure wave propagation. Unfortunately, 3D simulations in compliant domains still demand computational costs significantly higher than the rigid case. Appropriate matching conditions between the two models have been devised to gather the effects of the compliance at the interfaces and to obtain reliable results still solving a 3D problem on rigid vessels.

More precisely, we introduce a lumped parameter model at the interface, in the form of a RCL network, giving a simplified representation of the compliance of the 3D vessel in the multiscale model. For simple cases, e.g. a cylindrical pipe, numerical results are promising, showing that the multiscale model can both capture the correct wave propagation (in comparison with a fully 1D model) and compute the local 3D flow. In more complex situations, like the circle of Willis, results compare well with a fully 1D model, however a mathematically sound fine tuning of the parameters is required.

We point out that this approach can be easily extended, for instance to the analysis of the coronary artery bypass, the 3D model representing the grafted and the host arteries, and the coronary circulation being described by 1D models.

11:00 to 11:30 Coffee
11:30 to 12:30 Commented Poster Session 1
Commented Posters at the The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart conference.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 A McCulloch ([UC, San Diego])
Multi-scale modeling of cardiac excitation-contraction coupling in the normal and failing heart

The excitation-contraction coupling properties of cardiac myocytes isolated from different regions of the mammalian left ventricular wall have been shown to vary considerably, with uncertain effects on ventricular function. We developed a detailed model of excitation-contraction coupling model with region-dependent parameters for epicardial, mid-myocardial and endocardial myocytes, and then embedded it within a fully coupled finite element model of ventricular electromechanics coupled to a lumped parameter model of the circulation. Comparing this model with one in which heterogeneous myocyte parameters were assigned randomly throughout the mesh while preserving the total amount of each cell subtype, we observed similar transmural patterns of fiber and cross-fiber strains at end systole, but clear differences in fiber strain distributions at earlier times during systole. Hemodynamic function, including peak left ventricular pressure, maximum rate of left ventricular pressure development, and stroke volume were essentially identical in the two models.

We also modeled ventricular electromechanics in the dyssynchronous failing dog heart and examined the relative roles of dilation, negative inotropy, negative lusitropy and electrical dyssynchrony on global and regional function. The analysis suggested that there is significant interactions between dilation and dyssynchrony especially on regional mechanics.

Finally, we present initial findings on a preliminary clinical study to test the ability of such multi-scale models of electromechanics in the failing heart to predict clinical outcomes of cardiac resynchronization therapy.

Supported by : NIH, NSF, UC Discovery, Medtronic

14:15 to 14:30 S Tavener ([Colorado State])
A posteriori error estimation and adaptivity for operator decomposition methods

Operator decomposition methods are commonly used to solve multiscale and multiphysics models since they decompose complex systems into individual components with relatively simple physics and with behaviors that occur on a relatively narrow range of scales. In some scientific communities, operator decomposition is referred to as a "segregated" as opposed to a "monolithic" approach. Obtaining an approximation of the full problem typically requires iteration of the solutions of the individual components, introducing transfer and projection errors as well as errors due to iteration.

These new errors compound the discretization errors of individual components in a complicated fashion that is typically poorly understood. The ability to identify and estimate each of these new error contributions is essential when designing adaptive strategies. We have developed adjoint-based a posteriori analyses for a number of common operator decomposition techniques. These analyses address the global effects of operator decomposition as well as the accuracy with which individual components are solved. We present illustrative examples of the application of these analyses to multi-rate differential equations, coupled elliptic and parabolic problems and discuss the challenges (and some ideas) for large scale implementation.

14:30 to 14:45 M Nash ([Auckland])
Re-entry and fibrillation in an electro-mechanical model of the human ventricles
We present an integrative 3D electro-mechanical model of the human heart ventricles (RVLV), constructed from diffusion tensor magnetic resonance imaging data provided by Drs Helm, Winslow and McVeigh (Johns Hopkins University and NIH). Mathematical models of electrical activity (TNNP) and contractile tension (NHS) of cardiac myocytes are coupled within a transversely isotropic passive mechanical (Guccione) constitutive framework embedded within the RVLV model. Excitation-contraction coupling is achieved via the intracellular calcium concentration of the biophysical myocyte models. Mechano-electrical feedback is represented by stretch-activated channels, which carry currents that are modulated by local deformation. Numerical model integration combines an explicit finite differences scheme for the electrophysiology with a non-linear finite element method for the mechanics. The model was tuned and verified by simulating a normal ventricular cycle and comparing the resulting myocardial strain distributions with experimental recordings. This human RVLV model was used to investigate the effects of mechano-electrical feedback on re-entrant wave dynamics. We examine factors that cause wavebreak and the degeneration of stable re-entry into fibrillatory activity. We identify the mechanisms of this transition to VF, and study the 3D organisation of mechanically induced VF in the human heart.
14:45 to 15:00 P Kohl (University of Oxford)
An attempt for dialectics: what can we learn from interdigitating wet and dry research into structure and function underlying elec/mech activity of the heart
This lecture will briefly review key principles of the dialectic research method, and explore how this may be productive in the context of integrating cardiac electro-mechanics, using a combination of wet and dry research techniques to explore cardiac structure and function. Core concepts of dialectics include the notion (i) that there is a ‘unity of contradictions’ (i.e. seemingly opposing aspects of a matter ‘require’ each other, like day and night, or like wet & dry, structure & function, electrics & mechanics of the heart), (ii) that quantitative change accumulates to give rise to a change in quality of a matter or behaviour (like adding energy to bring water to the boil, or like bringing membrane potential to threshold), and (iii) that development moves in 3D spirals, not 2D circles (like boom and bust economy that – while perceived as ‘cyclic’ – tends to still involve a forward component, or like rejection of a modelling prediction that – while sending us back to the drawing board – will eventually yield an improved model [one hopes…]). The topical focus of the lecture will be on aspects relevant to cardiac mechano-electric coupling.
15:00 to 15:30 Tea
15:30 to 15:45 Commented Posters 1
15:45 to 16:00 Poster
16:00 to 16:15 Poster
16:15 to 16:30 Poster
18:45 to 19:30 Dinner at Woflson Court (Residents Only)
Wednesday 22nd July 2009
09:15 to 10:00 N Trayanova ([Johns Hopkins])
Integrative models of heart function in health and disease
Simulating cardiac electromechanical function is one of the most striking examples of a successful integrative multi-scale modeling approach applied to a living system directly relevant to human disease. Today, thanks to nearly fifty years of research in the field and the rapid progress of high-performance computing, we stand at the threshold of a new era: anatomically-detailed tomographically-reconstructed models that integrate from the ion channel or sarcomere to the electromechanical interactions in the intact heart are being developed. Such models, while still in its infancy, hold high promise for interpretation of clinical and physiological measurements in terms of cellular mechanisms; for improving the basic understanding of the mechanisms of dysfunction in disease conditions, such as reentrant arrhythmias, myocardial ischemia, and heart failure; and for the development and performance optimization of medical devices, ultimately enabling manufacturers to predict device and procedure performance and outcome prior to clinical trials. Attempt is made to extend these models beyond electromechanics and include regulatory processes such as energy metabolism and signal transduction. Here we provides specific examples of the state-of-the-art in cardiac integrative modeling, including 1) uncovering the role of ventricular structure in defibrillation; 2) improving ventricular ablation procedure by using MRI reconstructed heart geometry and structure to investigate the reentrant circuits formed in the presence of an infarct scar; 3) employing an electromechanical model of the heart to determine the electromechanical delay in the heart; and 4) understanding the origin of mechanically-induced ventricular premature beats in acute regional ischemia.
10:00 to 10:15 B Rodriguez (University of Oxford)
Investigating drug-induced effects on cardiac electrophysiological function: from ion channels to the ECG
Many drugs fail to reach the market due to adverse side effects on the heart, and this translates into important socio-economic costs. A major concern for society, regulatory agencies and industry is that drug-induced alterations in cardiac function can increase the risk of development of potentially life threatening arrhythmias, such as Torsades de Pointes. Given the limitations of in vitro and in vivo testing in preclinical prediction of drug cardiotoxicity, there is increasing interest in in silico methods to supplement experimental methods. This presentation will describe how advanced computational techniques are developed and used in our group to investigate the mechanisms of drug action on cardiac electrophysiological function, from the ionic to the ECG level. Our main aim is to unravel the mechanisms of drug-induced arrhythmic risk in the context of high inter-subject electrophysiological variability, and to propose novel arrhythmic risk biomarkers based on this research.
10:15 to 10:30 I Efimov ([Washington, St. Louis])
Physiology of the human heart: Do we really know it?
10:30 to 10:45 F Fenton ([Cornell])
Termination of atrial fibrillation using pulsed low-energy far-field stimulation; a computational and optical mapping study
Electrical therapies for termination of atrial fibrillation fall into two categories, anti-tachycardia pacing (ATP), which is effective in terminating only slow tachycardias, and cardioversion, which uses high-energy shocks that can produce tissue damage and patient pain. We propose a new method that is effective for slow and fast tachycardia and fibrillation and requires very low energies. We demonstrate theoretically and experimentally that low-intensity field stimulation can create wave emission (“virtual” electrodes that can act as control sites) from tissue bordering natural anatomical heterogeneities within cardiac tissue and that the number of these activation sites depends on the sizes of the heterogeneities and the electric field strength applied. Using high-resolution magnetic resonance imaging (MRI) of canine cardiac structure and computer simulations of the bidomain model with canine ionic models, we quantify the recruitment of activation sites from heterogeneites as a function of low applied electric field strengths and their ability to terminate reentrant arrhythmias. Then, using optical mapping in isolated perfused canine cardiac preparations, we show that a series of pulses at low field strength (0.9-1.4 V/cm) recruits a sufficient number of activation sites to entrain and subsequently extinguish AF with a success rate of 93 percent (69/74 trials in 8 preparations). Thus, AF can be terminated by FF-AFP using on average only 13% of the energy required for cardioversion. This marked reduction in energy can be expected to increase the effectiveness and safety of terminating atrial tachyarrhythmias clinically.
10:45 to 11:00 V Grau (University of Oxford)
Building detailed cardiac electrophysiological models from high-resolution images
Computational models of the heart using simplified geometries have been used successfully in a number of applications. At the same time, the effect of microstructure has been shown to be relevant in studies of fundamental mechanisms of cardiac function. Our goal is to investigate the effect of the level of detail of cardiac electrophysiological models when applied to the study of specific problems. We have developed a semi-automated pipeline to build highly-detailed model geometries from high resolution MRI and histological images. The methods include segmentation of MRI images, co-registration of MRI volumes with histology slices, delineation of important structures such as papillary muscles or valves, mesh generation and electrophysiological simulation. Preferential orientation of myocytes is estimated and added to the model using either diffusion tensor MRI (DTMRI) or a parametric description. A quantitative comparison between these two techniques shows a general agreement between the estimated orientations, with localised differences for which specific modifications of the mathematical rules can be postulated. We have also developed methods to build simplified models (lacking macro- and microstructural elements such as papillary muscles, endocardial trabeculations or coronary vessels) from the same images. We apply these methods to build detailed and simplified models of rabbit and rat hearts. Simulations of electrical activation after stimulation at different anatomical locations highlight important local differences between different levels of detail, and allow us to investigate separately the effects of relevant macro- and microstructure.
11:00 to 11:30 Coffee
11:30 to 12:30 Commented Poster Session 2
Commented Posters at the The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart conference.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 13:45 R Hose ([Sheffield])
Fluid solid interaction for vascular applications
Classical fluid solid interaction calculations require specification of boundary conditions for both fluid and solid phases. For vascular applications the structural support conditions are provided by other tissue and organs, the stiffness and constraints on which are generally unknown. It is suggested that the the gross motion (as opposed to the local dilation) of large arteries such as the aorta should be constrained by information from 4D medical images. In this paper we focus on the computation of aortic pulse wave velocity from 4D image data. Our hypothesis is that this parameter can be measured using displacement fields obtained by registration of time-series images. We will present a method in which a form of the one-dimensional wave equation is used as a regularisation term in a linear least squares registration process. It is demonstrated that the method can capture the pulse wave velocity from numerical phantom images, even when noise is added to these images. The sensitivity of the method to a number of numerical and image parameters will be discussed. It will further demonstrated that the method yields plausible results when operated on a real 4D image dataset.
13:45 to 14:00 S Sherwin (Imperial College London)
Computational modelling to investigate the role of aging and species on arterial branch lesion patterns

Atherosclerotic lesions are non-uniformly distributed at arterial bends and branch sites suggesting haemodynamic factors, particularly wall shear stress (WSS), are important factors in their development. The pattern of lesions at aortic branch sites depends on age and species [1]. To investigate this observation we have applied computational modelling around idealised intercostal arteries in the descending aorta (fig a) [2], where in-vivo lesion patterns are also available (fig b) [3,4]. In this model we have two parameters, the flow rate and the flow split between the aorta and intercostal branch. Some, but not all, of the in-vivo features can be associated with variations in flow split and flow rate. In a complementary study we have therefore considered alternative convection-diffusion continuum based models and in particular a micro-scale concentration polarisation of low density lipoproteins accumulation [5] to see if this can provide alternative insight into the pattern discrepancies.

1. Weinberg, P. D. 2002 Disease patterns at arterial branches and their relation to flow.Biorheology 39, 533-537. 2. Kazakidi, A, Sherwin, S.J, Weinberg, P.D , Effect of Reynolds number and flow division on patterns of haemodynamic wall shear stress near branch points in the descending thoracic aorta, J. R. Soc, Interface, , 2008 3. McGillicuddy, C. J., Carrier, M. J. & Weinberg, P. D. 2001 Distribution of lipid deposits around aortic branches of mice lacking LDL receptors and apolipoprotein E. Arterioscler. Thromb. Vasc. Biol. 21, 1220-1225. 4. Barnes, S. E. & Weinberg, P. D. 1999 Two patterns of lipid deposition in the cholesterol-fed rabbit. Arterioscler. Thromb. Vasc. Biol. 19, 2376-2386. 5. Vincent, P.E, Sherwin, S.J, Weinberg, P.D , The Effect of a Spatially Heterogeneous Transmural Water Flux on Concentration Polarisation of Low Density Lipoprotein in Arteries, Biophysical Journal, Accepted for publication, 2009

14:00 to 14:15 G Salama (University of Pittsburgh)
Ion Channel Regulation by Estrogen
Due to the mutual interaction between cardiac contraction and variations in pre- and after-load, experimental validation studies of mathematical modeling of the heart and the coronary circulation seem to be restricted to in-vivo animal- or patient-studies and hereby are hampered by ethical regulations as well as by the complexity of the in-tact in-vivo system. We aim to partly overcome these limitations by developing phantom and ex-vivo experimental platforms that mimic the cardiovascular system as close as possible and provide good accessibility to imaging- and sensor-based measurement equipment. The phantom circulation-loop features a control mechanism based on a heart model defined by a Hill-type muscle contraction and is capable of adapting its contractile behavior as a function of time, ventricular volume and ejection rate. The heart rate is controlled by a baroreflex model that describes the heart rate as a function of systemic blood pressure and time. By real-time monitoring of systemic blood-pressure in an extended windkessel-type mock-loop and control of heart rate and stroke volume a pressure-volume loop that physiologically responds to external variations can be realized. A specially designed module for coronary flow dependent on systemic and ventricular pressure completes the system. In the ex-vivo platform, slaughterhouse pig hearts (420 ± 30 g) were isolated, arrested and transported according to human transplantation protocols. After preparation the isolated hearts were connected to a special circulatory system, that has been engineered to enable physiological cardiac performance using physical and medical principles while coronary flow was reinstated. The platform allows to either choosing a Langendorff mode, a 2- or 4 chamber working heart mode or a heart-lung mode. Hemodynamic function in terms of cardiac output, aortic pressures, ventricle pressures, dP/dt, heart rate, and coronary flow can be monitored and controlled and allows not only to achieve physiological cardiac electromechanical and hemodynamic responses but also to vary cardiac/hemodynamic performance for at least 3 hours, while surgical and interventional procedures can be carried out.
14:15 to 14:30 B Griffith ([New York])
Simulating cardiac fluid-structure interaction using the immersed boundary method
The immersed boundary (IB) method is a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. Over the last several years, we have developed an adaptive version of the IB method which uses Cartesian grid adaptive mesh refinement (AMR), thereby allowing us to deploy locally high spatial resolution where it is most needed (e.g., in the vicinity of the heart valve leaflets and the vorticies shed from those leaflets), and to use comparatively coarse resolution where it suffices. In this talk, we shall describe our adaptive version of the IB method, along with recent extensions of this method which enable the specification of physical boundary conditions for the fluid, thereby allowing us to connect three-dimensional immersed boundary models to reduced flow models (e.g., Windkessel models) via fluid boundary conditions. (Earlier versions of the IB method generally imposed periodic boundary conditions on the fluid, and for such methods, connections to reduced flow models were mediated by internal fluid sources and sinks.) Three-dimensional computational results will be presented to demonstrate the application of this methodology to simulating the fluid mechanics of isolated models of heart valves, as well as a new whole heart model derived from cardiac computed tomography (CT) data from a healthy human heart.
14:30 to 14:45 X Luo ([Glasgow])
Dynamic modelling of chorded mitral valve
The dynamic behaviour of a novel chorded mitral prosthesis is studied using an immersed boundary model. To investigate the mechanical behaviour of the mitral design under physiological flow conditions without having to model the left ventricle, we make use of in vivo magnetic resonance images of the left ventricle. The relative motion of the mitral annulus and motion of the ventricle determined from these MRI images is then used as a prescribed boundary condition for the chorded mitral valve in a dynamic cycle. This model allows us to investigate the influences of the flow vortex generated by the ventricle motion on the valve dynamics, as well as the effect of the motion of the chordae attachment points. Results are compared with two other cases: (i) a ventricle model with no prescribed motion of the chordae attachment points, (ii) a tube model in which the ventricle is replaced by a tube, although the motion of the chordae is incorporated. It is found that the vortex flow helps to reduce the cross valve pressure gradient; however, it can significantly increase the chordae and the valve stretch in the commissural region and make the flow field strongly asymmetric. Surprisingly, we observe that the presence of the flow vortex does not necessarily aid the valve closure.
14:45 to 15:00 M Alber ([North Dame])
Study of blood flow impact on growth of blood clot using a multi-scale model
The hemostatic system has evolved to prevent the loss of blood at the site of vascular injury. The response is rapid to limit bleeding and is regulated to prevent excessive clotting that can limit flow. The processes that are involved in the assembly of a thrombus (blood clot) include complex interactions among multiple molecular and cellular components in the blood and vessel wall occurring under fluid flow. Formation of a thrombus (thrombogenesis) involves the close interplay between many processes that occur at different scales (subcellular, cellular and multicellular). In the past, these processes have been studied separately. In this talk an extended multi-scale model will be described for studying the formation of platelet thrombi in blood vessels. The model describes the interplay between viscous, incompressible blood plasma, activated and non-activated platelets, as well as other blood cells, activating chemicals, fibrinogen and vessel walls. The macroscale dynamics of the blood flow is represented by the continuous submodel in the form of the Navier-Stokes equations. The microscale cell-cell interactions are described by extended stochastic lattice and off-lattice models. Simulations indicate that increase in flow rates leads to greater structural heterogeneity of the clot. As heterogeneous structural domains within the clot affect thrombus stability, understanding the factors influencing thrombus structure is of significant biomedical importance. Xu, Z., Chen, N., , Kamocka, M.M., Rosen, E.D., and M.S. Alber [2008], Multiscale Model of Thrombus Development, Journal of the Royal Society Interface 5 705-722. Xu, Z., Chen, N., Shadden, S., Marsden, J.E., Kamocka, M.M., Rosen, E.D., and M.S. Alber, Study of Blood Flow Impact on Growth of Thrombi Using a Multiscale Model, Soft Matter DOI:10.1039/b300001a (to appear).
15:00 to 15:30 Tea
15:30 to 15:45 Commented Posters
15:45 to 16:00 Poster
16:15 to 16:30 Poster
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
Thursday 23rd July 2009
09:30 to 10:15 N Ayache ([INRIA])
Towards personalization of cardiac models from medical images and signals
I will present some recent advances made at INRIA in collaboration with partners on the personalization of the electrical and mechanical components of computational models of the heart from the analysis of images and electrophysiological data of a specific patient. The presentation will describe the models and the personalization methods, current results and remaining challenges for clinical applications.
10:15 to 10:30 A Frangi ([Pompeu Fabra])
Overview of statistical shape models for cardiac image analysis and modeling
This talk will overview the cardiac image analysis and statistical modeling work at Universitat Pompeu Fabra. In particular, we will cover in some detail and point to to key references of our work concerning spatio-temporal statistical cardiac models and application of these models to the analysis of MR, SPECT, 3DUS and CARTO data. The use of registration-based strategies for automatically constructing point distribution models from large databases together with methods for generating automatically the appearance in multimodal data allow us to efficiently construct model-based approaches to image analysis and populational modeling. We show that it is possible to use these methods for consistently handling multimodal data and, hence, allow for consistently mapping information coming from multiple sources in the same coordinate system.
10:30 to 10:45 I LeGrice ([Auckland])
Multi-scale volume imaging in animal models of disease
To model electrical or mechanical function in a normal or diseased heart, or to use models to interpret complex experimental data, it is necessary to incorporate an appropriate description of myocardial structure for the relevant state. Myocardial function, both normal and abnormal, is dependent on myocardial structure at different levels of scaling, from whole organ to subcellular. Furthermore, both normal function and pathological change vary regionally. When considering models of cardiac structure and function, it is therefore necessary to develop appropriately detailed descriptions of myocardial structure and function with these criteria in mind. We are investigating several animal models of cardiac pathology, and have developed techniques to describe both structure and function throughout appropriate regions of the heart, and at a scales matched to the particular functional analysis required.
10:45 to 11:00 B Smaill ([Auckland])
Tissue-specific models of electrical activity in the heart: Multi-scale and Multi-dimensional approaches
There is strong experimental and theoretical evidence that structural discontinuity and the material orthotropy that results from it affect the 3D spread of electrical activity in the heart. This behaviour should be accounted for accurately in cardiac activation models. However, in order to do so, it is necessary to incorporate 3D structural detail at a scale that imposes considerable computational overheads. As a result, the use of detailed, tissue-specific 3D models can prove to be intractable in studies of reentrant arrhythmia where it is necessary to model repeated cycles of electrical activation. Alternative approaches here include the development of realistic higher order descriptions of 3D electrical properties or the use of 2D models that capture key features of 3D structure and electrical behaviour. The use of these approaches to investigate the contributions of structural discontinuity to normal electrical propagation and to reentrant activation in the right atrium and in the border zone surrounding a myocardial infarct will be outlined. The extent to which structural discontinuities provides a substrate for inactivation across the excitable gap when defibrillation strength shocks are applied during reentrant arrhythmia will also be considered.
11:00 to 11:30 Coffee INI 1
11:30 to 11:45 A Young ([Auckland])
The Cardiac Atlas Project, Progress Report July 2009
The Cardiac Atlas Project is a multinational initiative to establish a database of cardiac magnetic resonance imaging studies, together with derived information, in healthy and disease populations. This database will facilitate computational atlases of cardiac function and structure. Probabilistic statistical descriptions of regional wall motion will enable the creation of classifiers and descriptors for different patient groups. Open source software will be provided for the analysis and visualization of the images and derived models of heart shape and function. This talk will report on the current progress and status of the Cardiac Atlas Project, including mechanisms for participation.
11:45 to 12:00 JAE Spaan (Academic Medical Center Amsterdam)
Intramural structure of coronary arteries and transmural distribution of coronary blood flow
Coronary arteries distribute flow over the epicardium and branch into transmural arteries, which over about 10 orders of branching nodes connect to the capillary bed for exchange of nutrients between blood and tissue. Understanding of the 3-dimensional structure of the intramural vascular system is needed to understand local mis-balance between supply and demand that especially may occur at the subendocardium. This mis-balance is the explanation for the observation that infarctions most often start at the subendocardium. The intramural vascular structure of larger animals and humans can now be studied by a novel imaging cryomicrotome (slicing at 40 microns, in plane pixels of cutting plane images: 4000*4000) by studying the distribution of fluorescently labeled elastomer by which the arterial system is filled. Flow distributions are then measured from fluorescently labeled microsphere distributions (5 colors) injected at different physiological conditions with the heart still in situ. Since microsphere distribution and arterial structure are measured in the same heart, for the first time intramural vascular structure and flow distribution can be studied concomitantly.
12:00 to 12:15 PC Shi ([RIT])
Integrative System Framework for Noninvasive Understanding of Myocardial Tissue Electrophysiology

The presence of injured tissue after myocardial infarction (MI) creates substrate responsible for life-threatening ventricular arrhythmia, such as ventricular tachycardia and fibrillation, which often lead to cardiac arrest and sudden death. However, arrhythmogenic mechanism of such substrate is not well defined, because its investigation requires quantitative, complete and detailed knowledge on the correlation of local abnormality in phenomenal electrical function and inherent tissue property during normal sinus rhythm.

We have developed a physiological model-constrained framework which utilizes noninvasive body surface potential measurements and tomographic images for personalized imaging of volumetric cardiac electrophysiology, including electrical functioning, tissue property and arrhythmogenic substrate inside the heart.

Under the guidance of a prior knowledge of general cardiac electrical activity, this framework extracts subject-specific information from personal data to reconstruct transmembrane potential dynamics and tissue excitability inside the 3D myocardium. Abnormalities in these two different electrophysiological quantities are localized for identifying the latent arrhythmogenic substrate, investigating its possible mechanisms, and therefore assessing arrhythmia susceptibility of individual subject.

For four post-MI patients, quantitative evaluation of infarct extent and location is validated by gold standard provided by cardiologists, and exhibit notable improvements over existent results.

12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 R Razavi (King's College London)
Translating biophysical models to the heart of the clinic
14:15 to 14:30 P Kilner (Imperial College London)
The Whole Heart
The heart, great vessels and passing blood function as a dynamically interconnected whole. As a counterpart to more analytical approaches, this presentation includes images chosen to encourage an integrated and contextualized view of the heart. It begins with photographs of the Earth, where it has been deduced from fossil evidence that our vertebrate ancestors have been evolving for some 500 million years. It includes magnetic resonance cine images, photographs of endovascular casts, and illustrations of human, vertebrate and invertebrate hearts, and concludes with a simulation of flow through a healthy heart during exercise, prepared in collaboration with Michael Markl and colleagues in Freiburg. The images used for this were from a resting, 3-dimensional, time-resolved, 3-component magnetic resonance flow velocity acquisition in a healthy volunteer. To simulate a moderate (walking) state of exercise, the second half of diastole was removed and the remaining frames played back at 100 cycles/minute. The movie helps to make apparent the changes of momentum, and associated cyclic exchanges of force and counter-force, that must accompany the movements of blood through the curvatures of the heart and aorta on exercise.
14:30 to 14:45 F Weber ([Karlsruhe (TH)])
Towards patient-specific simulations of atrial fibrillation
Patient-specific cardiac simulations are approaching clinical applications. They could for example improve the treatment of atrial fibrillation (AF). Currently, many patients suffering from AF are treated with minimally-invasive catheter ablation. Using this technique, trigger sources for AF (mainly the pulmonary veins), are electrically isolated from the rest of the atrium. However, a large set of different ablation strategies is currently used in clinical practice. Therefore, the choice of a certain ablation strategy as well as the probability for successful and sustained AF termination are strongly dependent on the experience of the cardiologist. Atrial simulations could assist the cardiologist in the choice of a suitable method for an individual patient. For this, the atrial models have to be adapted to the patient. Besides anatomical modeling, several challenges must be faced in this process. First, an appropriate model of cellular electrophysiology and excitation conduction must be chosen. The model must provide the necessary accuracy and at the same time be fast enough for clinical applications. As a trade-off between accuracy and speed, we propose a minimal model adapted to atrial electrophysiology. Second, a main problem is the adaptation of physiological parameters in the patient-specific model as well as its validation. Therefore, an interface between clinical data and the model is needed. Data collected in standard clinical workflow are mainly intracardiac catheter ECGs. We therefore present techniques to model such catheter measurements. Signals from both circular mapping catheters (such as Lasso or Orbiter) as well as Coronary Sinus catheters can be simulated and compared to clinical signals. These are important steps towards clinical applications of atrial models. The long-term goal then is to assist the cardiologist in the choice of the best treatment for an individual patient.
14:45 to 15:00 H Delingette ([INRIA])
Adaptive Tetrahedral Meshing for Personalized Cardiac Simulations
15:00 to 15:15 K Rhode (King's College London)
Image and physiological data fusion for cardiac biophysical modelling
Personalisation of cardiac models can be achieved using a combination of imaging and physiologiocal data that is acquired from patients. This data is acquired using several imaging modalities including magnetic resonance imaging, computerised tomography, ultrasound, and x-ray fluoroscopy. This presentation will illustrate several of the methods that have been developed at King's College London to fuse this data with application to biophysical modelling.
15:15 to 15:45 Tea
15:45 to 16:00 M Sermesant
Personalised electromechanical model of the heart for the prediction of the acute effects of cardiac resynchronisation therapy
Cardiac resynchronisation therapy (CRT) has been shown to be an effective adjunctive treatment for patients with dyssynchronous ventricular contraction and symptoms of the heart failure. However, clinical trials have also demonstrated that up to 30% of patients may be classified as non-responders. In this article, we present how the personalisation of an electromechanical model of the myocardium could help the therapy planning for CRT. We describe the four main components of our myocardial model, namely the anatomy, the electrophysiology, the kinematics and the mechanics. For each of these components we combine prior knowledge and observable parameters in order to personalise these models to patient data. Then the acute effects of a pacemaker on the cardiac function are predicted with the in silico model on a clinical case. This is a proof of concept of the potential of virtual physiological models to better select and plan the therapy.
16:00 to 16:15 G Seemann ([Karlsruhe (TH)])
Modeling of cardiac Ischemia in human myocytes and tissue including spatiotemporal electrophysiological variations
Cardiac tissue exhibits spatially heterogeneous electrophysiological properties. In cardiac diseases, these properties change also in time. This study introduces a framework to investigate their role in cardiac ischemia using mathematical modeling and computational simulations at cellular and tissue level. Ischemia was incorporated by reproducing effects of hyperkalemia, acidosis, and hypoxia with a human electrophysiological model. In tissue, spatial heterogeneous ischemia was described by central ischemic (CIZ) and border zone. Anisotropic conduction was simulated with a bidomain approach in an anatomical ventricle model including realistic fiber orientation and transmural, apico-basal, and interventricular electrophysiological heterogeneities. A model of electrical conductivity in a human torso served for ECG calculations. Ischemia raised resting but reduced peak voltage, action potential duration and upstroke velocity. These effects were strongest in subepicardial cells. In tissue, conduction velocity decreased towards CIZ but effective refractory period increases. At 10 min of ischemia 19% of subepi- and 100% of subendocardial CIZ cells activated with a delay of 34.6±7.8 ms and 55.9±18.8 ms, respectively, compared to normal. Significant ST elevation and premature T wave end appeared only with the subepicardial CIZ. The model reproduced effects of ischemia at cellular and tissue level. The results suggest that the presented in-silico approach can complement experimental studies e.g. in understanding the role of ischemia or the onset of arrhythmia.
16:15 to 16:30 P Bovendeerd ([TU, Eindhoven])
Modeling cardiac growth and remodeling
19:00 to 23:00 Conference Dinner at Emmanuel College
Friday 24th July 2009
09:30 to 10:15 J Bassingthwaighte ([Washington])
Integrative multilevel modular approach to modeling the cardiac physiome
The “Physiome” is the quantitative description of the functional behavior of the physiological state of an individual of a species. Personalized medicine will depend on a combination of a generalized representation of a patient augmented by patient-specific information. Predictive medicine depends on knowing the quantitative relationships between variables and the effects of therapeutic interventions. Integrative models of genetic, cellular and physiological systems are necessarily multiscalar and hierarchical. Following the precepts of Claude Bernard, one uses an integrative viewpoint, or model, to reconcile contradictions and maximize descriptive and biophysical, biochemical accuracy. Practicality is facilitated by a modular approach to quantitative multiscale model construction, for it allows the coordination of expertise from different fields, encompassing the specific expertise in specific modules while bringing diverse modules together into an integrated system defining the whole. Individual modules can be simplified to gain computational speed and facilitating their use as mind expanders, but then their range of coverage of the physiological conditions is compromised and the robustness of the model system reduced. To retain predictability in the face of needs to simplify computation, it is important to design model systems to allow automated substitution of one module for another as the real system goes through changes of state in an intensive care unit or through long term responses to therapy, aging, or progressive disease. Such flexibility in integrative modeling is a difficult challenge, but is needed to bring physiomic understanding to practical utility from the current stage of being diagnostically helpful to a stage of providing therapeutic advice or control. Practical models and the JSim simulation analysis platform are available at (Supported by NIH grants RO1-HL73598 and T!5-HL088516 and NSF 0506477).
10:15 to 10:30 O Jensen ([Nottingham])
Building tissue mechanics into novel types of multi-scale models
10:30 to 10:45 S Omholt ([Norwegian Uni of Life Sciences])
Genetics meets multiscale modeling: the epistemic value of causally cohesive genotype-phenotype (cGP) models
Many challenges in personalized medicine reflect a lack of understanding of the genotype-phenotype map (GP map) of complex disease traits, i.e. the aggregated phenotypic effects across different length and time scales of different constellations of genetic variation (genotypes). A deep understanding of the GP map for a given complex trait requires mechanistic model descriptions of high-dimensional phenotypic effects of genetic variation, i.e. very advanced multiscale physiological models with an explicit link to genetic information in a population context ("cGP models", causally cohesive genotype-phenotype models). The Cardiac Physiome programme defines a very potent framework for developing this link. The talk will address important methodological challenges associated with incorporating genetics theory and methodology more tightly into the programme. It will also illustrate by specific examples the added epistemic value of accomplishing this.
10:45 to 11:00 P Nielsen ([Auckland])
CellML language and tools supporting the cardiac physiome
The CellML language is an established standard designed to encode lumped parameter mathematical models of biological processes. CellML supports the sharing of models by including information about model structure, mathematics, and metadata. It makes use of existing standards for encoding mathematics (Content MathML ) and representing metadata (Resource Description Framework ). Model reuse is facilitated by the element, enabling new models to be constructed by combining existing models to form model hierarchies. Almost 400 CellML models from peer-reviewed publications are currently available in the Physiome Model Repository . The repository contains models of biological processes ranging from gene regulation, ion channel electrophysiology, signal transduction, and metabolic pathways to bioengineering constitutive laws and larger scale systems physiology processes. A major focus of the CellML effort involves the development of tools to facilitate the curation and annotation of models within the repository. The aim of this effort is to link entities and processes described in CellML models to their corresponding definitions in, for example, biological and biophysical ontologies. Doing so enables richer searching, automatic rule checking, and the ability to produce biologically meaningful visual representations of models.
11:00 to 11:30 Coffee
11:30 to 11:45 P Hunter ([Auckland])
The cardiac physiome: next steps
11:45 to 12:00 N Smith (University of Oxford)
Closing comments
12:30 to 13:30 Lunch at Wolfson Court
18:45 to 19:30 Dinner at Wolfson Court (Residents Only)
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons