The computational integrated myocyte: a view into the virtual heart

3D Imaging of vascular networks for biophysical modeling of perfusion distribution within the heart

One of the main determinants of perfusion distribution within an organ is the structure of its vascular network. Past studies were based on angiography or corrosion casting and lacked quantitative three dimensional, 3D, representation. Based on branching rules and other properties derived from such imaging, 3D vascular tree models were generated which were rather useful for generating and testing hypotheses on perfusion distribution in organs. Progress in advanced computational models for prediction of perfusion distribution has raised the need for more realistic representations of vascular trees with higher resolution. This paper presents an overview of the different methods developed over time for imaging and modeling the structure of vascular networks and perfusion distribution, with a focus on the heart. The strengths and limitations of these different techniques are discussed. Episcopic fluorescent imaging using a cryomicrotome is presently being developed in different laboratories. This technique is discussed in more detail, since it provides high-resolution 3D structural information that is important for the development and validation of biophysical models but also for studying the adaptations of vascular networks to diseases. An added advantage of this method being is the ability to measure local tissue perfusion. Clinically, indices for patient-specific coronary stenosis evaluation derived from vascular networks have been proposed and high-resolution noninvasive methods for perfusion distribution are in development. All these techniques depend on a proper representation of the relevant vascular network structures.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Cardiac cell: a biological laser?

We present a new concept of cardiac cells based on an analogy with lasers, practical implementations of quantum resonators. In this concept, each cardiac cell comprises a network of independent nodes, characterised by a set of discrete energy levels and certain transition probabilities between them. Interaction between the nodes is given by threshold-limited energy transfer, leading to quantum-like behaviour of the whole network. We propose that in cardiomyocytes, during each excitation-contraction coupling cycle, stochastic calcium release and the unitary properties of ionic channels constitute an analogue to laser active medium prone to "population inversion" and "spontaneous emission" phenomena. This medium, when powered by an incoming threshold-reaching voltage discharge in the form of an action potential, responds to the calcium influx through L-type calcium channels by stimulated emission of Ca2+ ions in a coherent, synchronised and amplified release process known as calcium-induced calcium release. In parallel, phosphorylation-stimulated molecular amplification in protein cascades adds tuneable features to the cells. In this framework, the heart can be viewed as a coherent network of synchronously firing cardiomyocytes behaving as pulsed laser-like amplifiers, coupled to pulse-generating pacemaker master-oscillators. The concept brings a new viewpoint on cardiac diseases as possible alterations of "cell lasing" properties.

Modelling the cardiac transverse-axial tubular system

The transverse-axial tubular system (TATS) of cardiac ventricular myocytes is a complex network of tubules that arises as invaginations of the surface membrane; it appears to form a specialised region of cell membrane that is particularly important for excitation-contraction coupling. However, much remains unknown about the structure and role of the TATS. In this brief review we use experimental data and computer modelling to address the following key questions: (i) What fraction of the cell membrane is within the TATS? (ii) Is the composition of the TATS membrane the same as the surface membrane? (iii) How good is electrical coupling between the surface and TATS membranes? (iv) What fraction of each current is within the TATS? (v) How important is the complex structure of the TATS network? (vi) What is the effect of current inhomogeneity on lumenal ion concentrations? (vii) Does the TATS contribute to the functional changes observed in heart failure? Although there are many areas in which experimental evidence is lacking, computer models provide a method to assess and predict the possible function of the TATS; such models suggest that although the surface and TATS membranes are electrically well coupled, concentration of ion flux pathways within the TATS, coupled to restricted diffusion, may result in the ionic composition in the TATS lumen being different from that in the bulk extracellular space, and varying with activity and in pathological conditions.

The challenge of cardiac modeling--interaction and integration

The goal of clinical cardiology is to obtain an integrated picture of the interacting parameters of muscle and vessel mechanics, blood circulation and myocardial perfusion, oxygen consumption and energy metabolism, and electrical activation and heart rate, thus relating to the true physiological and pathophysiological characteristics of the heart. Scientific insight into the cardiac physiology and performance is achieved by utilizing life sciences, for example, molecular biology, genetics and related intra- and intercellular phenomena, as well as the exact sciences, for example, mathematics, computer science, and related imaging and visualization techniques. The tools to achieve these goals are based on the intimate interactions between engineering science and medicine and the developments of modern, medically oriented technology. Most significant is the beneficiary effect of the globalization of science, the Internet, and the unprecedented international interaction and scientific cooperation in facing difficult multidisciplined challenges. This meeting aims to explore some important interactions in the cardiac system and relate to the integration of spatial and temporal interacting system parameters, so as to gain better insight into the structure and function of the cardiac system, thus leading to better therapeutic modalities.

Strategies and Tactics in Multiscale Modeling of Cell-to-Organ Systems

Modeling is essential to integrating knowledge of human physiology. Comprehensive self-consistent descriptions expressed in quantitative mathematical form define working hypotheses in testable and reproducible form, and though such models are always "wrong" in the sense of being incomplete or partly incorrect, they provide a means of understanding a system and improving that understanding. Physiological systems, and models of them, encompass different levels of complexity. The lowest levels concern gene signaling and the regulation of transcription and translation, then biophysical and biochemical events at the protein level, and extend through the levels of cells, tissues and organs all the way to descriptions of integrated systems behavior. The highest levels of organization represent the dynamically varying interactions of billions of cells. Models of such systems are necessarily simplified to minimize computation and to emphasize the key factors defining system behavior; different model forms are thus often used to represent a system in different ways. Each simplification of lower level complicated function reduces the range of accurate operability at the higher level model, reducing robustness, the ability to respond correctly to dynamic changes in conditions. When conditions change so that the complexity reduction has resulted in the solution departing from the range of validity, detecting the deviation is critical, and requires special methods to enforce adapting the model formulation to alternative reduced-form modules or decomposing the reduced-form aggregates to the more detailed lower level modules to maintain appropriate behavior. The processes of error recognition, and of mapping between different levels of model complexity and shifting the levels of complexity of models in response to changing conditions, are essential for adaptive modeling and computer simulation of large-scale systems in reasonable time.

A strategy for integrative computational physiology

Organ function (the heart beat for example) can only be understood through knowledge of molecular and cellular processes within the constraints of structure-function relations at the tissue level. A quantitative modeling framework that can deal with these multiscale issues is described here under the banner of the International Union of Physiological Sciences Physiome Project.

Multiscale modeling of cardiac cellular energetics

Multiscale modeling is essential to integrating knowledge of human physiology starting from genomics, molecular biology, and the environment through the levels of cells, tissues, and organs all the way to integrated systems behavior. The lowest levels concern biophysical and biochemical events. The higher levels of organization in tissues, organs, and organism are complex, representing the dynamically varying behavior of billions of cells interacting together. Models integrating cellular events into tissue and organ behavior are forced to resort to simplifications to minimize computational complexity, thus reducing the model's ability to respond correctly to dynamic changes in external conditions. Adjustments at protein and gene regulatory levels shortchange the simplified higher-level representations. Our cell primitive is composed of a set of subcellular modules, each defining an intracellular function (action potential, tricarboxylic acid cycle, oxidative phosphorylation, glycolysis, calcium cycling, contraction, etc.), composing what we call the "eternal cell," which assumes that there is neither proteolysis nor protein synthesis. Within the modules are elements describing each particular component (i.e., enzymatic reactions of assorted types, transporters, ionic channels, binding sites, etc.). Cell subregions are stirred tanks, linked by diffusional or transporter-mediated exchange. The modeling uses ordinary differential equations rather than stochastic or partial differential equations. This basic model is regarded as a primitive upon which to build models encompassing gene regulation, signaling, and long-term adaptations in structure and function. During simulation, simpler forms of the model are used, when possible, to reduce computation. However, when this results in error, the more complex and detailed modules and elements need to be employed to improve model realism. The processes of error recognition and of mapping between different levels of model form complexity are challenging but are essential for successful modeling of large-scale systems in reasonable time. Currently there is to this end no established methodology from computational sciences.

Systems modeling: a pathway to drug discovery

Systems modeling is emerging as a valuable tool in therapeutics. This is seen by the increasing use of clinically relevant computational models and a rise in systems biology companies working with the pharmaceutical industry. Systems models have helped understand the effects of pharmacological intervention at receptor, intracellular and intercellular communication stages of cell signaling. For instance, angiogenesis models at the ligand-receptor interaction level have suggested explanations for the failure of therapies for cardiovascular disease. Intracellular models of myeloma signaling have been used to explore alternative drug targets and treatment schedules. Finally, modeling has suggested novel approaches to treating disorders of intercellular communication, such as diabetes. Systems modeling can thus fill an important niche in therapeutics by making drug discovery a faster and more systematic process.

Systems biology in drug discovery

The hope of the rapid translation of 'genes to drugs' has foundered on the reality that disease biology is complex, and that drug development must be driven by insights into biological responses. Systems biology aims to describe and to understand the operation of complex biological systems and ultimately to develop predictive models of human disease. Although meaningful molecular level models of human cell and tissue function are a distant goal, systems biology efforts are already influencing drug discovery. Large-scale gene, protein and metabolite measurements ('omics') dramatically accelerate hypothesis generation and testing in disease models. Computer simulations integrating knowledge of organ and system-level responses help prioritize targets and design clinical trials. Automation of complex primary human cell-based assay systems designed to capture emergent properties can now integrate a broad range of disease-relevant human biology into the drug discovery process, informing target and compound validation, lead optimization, and clinical indication selection. These systems biology approaches promise to improve decision making in pharmaceutical development.