Nicolas Smith

An Anatomically Based Model of Transient Coronary Blood Flow in the Heart

An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier--Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax--Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton--Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy...

Computational physiology and the physiome project

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization – from proteins to cells, tissues, organs and organ systems – these methods have the potential to link patient‐specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web‐accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer‐intensive discipline.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Coupling multi-physics models to cardiac mechanics

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.

Cardiac cell modelling: observations from the heart of the cardiac physiome project.

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Length-dependent tension in the failing heart and the efficacy of cardiac resynchronization therapy

AIMS Cardiac resynchronization therapy (CRT) has emerged as one of the few effective and safe treatments for heart failure. However, identifying patients that will benefit from CRT remains controversial. The dependence of CRT efficacy on organ and cellular scale mechanisms was investigated in a patient-specific computer model to identify novel patient selection criteria. METHODS AND RESULTS A biophysically based patient-specific coupled electromechanics heart model has been developed which links the cellular and sub-cellular mechanisms which regulate cardiac function to the whole organ function observed clinically before and after CRT. A sensitivity analysis of the model identified lack of length dependence of tension regulation within the sarcomere as a significant contributor to the efficacy of CRT. Further simulation analysis demonstrated that in the whole heart, length-dependent tension development is key not only for the beat-to-beat regulation of stroke volume (Frank-Starling mechanism), but also the homogenization of tension development and strain. CONCLUSIONS In individuals with effective Frank-Starling mechanism, the length dependence of tension facilitates the homogenization of stress and strain. This can result in synchronous contraction despite asynchronous electrical activation. In these individuals, synchronizing electrical activation through CRT may have minimal benefit.

Integration from proteins to organs: the IUPS Physiome Project

The IUPS Physiome Project is an internationally collaborative open source project intended to provide a public domain framework for computational physiology, including the development of modeling standards, computational tools and web-accessible databases of models of structure and function at all spatial scales and across all organ systems. Here, we illustrate the application of this multi-scale modeling approach to three organ systems: the heart, the lungs and the musculo-skeletal system, and in each case we show how the organ level models incorporate tissue and cell-level physiology. Although the computational physiology framework presented here does not yet incorporate models of ageing processes, the model-based approach is certainly capable of describing ageing and disease-related processes both via parameter changes within the models of normal physiological processes and via models of additional processes added to the framework.

A meta‐analysis of cardiac electrophysiology computational models

Computational models of cardiac electrophysiology are exemplar demonstrations of the integration of multiple data sets into a consistent biophysical framework. These models encapsulate physiological understanding to provide quantitative predictions of function. The combination or extension of existing models within a common framework allows integrative phenomena in larger systems to be investigated. This methodology is now routinely applied, as demonstrated by the increasing number of studies which use or extend previously developed models. In this study, we present a meta‐analysis of this model re‐use for two leading models of cardiac electrophysiology in the form of parameter inheritance trees, a sensitivity analysis and a comparison of the functional significance of the sodium potassium pump for defining restitution curves. These results indicate that even though the models aim to represent the same physiological system, both the sources of parameter values and the function of equivalent components are significantly different.

Three-Dimensional Models of Individual Cardiac Histoanatomy: Tools and Challenges

Abstract:  There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high‐resolution cardiac structure–function models. The current article presents a step in this general direction: it illustrates how whole‐heart noninvasive imaging can be combined with whole‐heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 × 26.4 × 24.4 μm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.

Generation of an anatomically based geometric coronary model.

AbstractA discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh.