Towards real-time simulation of cardiac electrophysiology in a human heart at high resolution.

We have developed the capability to rapidly simulate cardiac electrophysiological phenomena in a human heart discretised at a resolution comparable with the length of a cardiac myocyte. Previous scientific investigation has generally invoked simplified geometries or coarse-resolution hearts, with simulation duration limited to 10s of heartbeats. Using state-of-the-art high-performance computing techniques coupled with one of the most powerful computers available (the 20 PFlop/s IBM BlueGene/Q at Lawrence Livermore National Laboratory), high-resolution simulation of the human heart can now be carried out over 1200 times faster compared with published results in the field. We demonstrate the utility of this capability by simulating, for the first time, the formation of transmural re-entrant waves in a 3D human heart. Such wave patterns are thought to underlie Torsades de Pointes, an arrhythmia that indicates a high risk of sudden cardiac death. Our new simulation capability has the potential to impact a multitude of applications in medicine, pharmaceuticals and implantable devices.

In silico cardiac risk assessment in patients with long QT syndrome: type 1: clinical predictability of cardiac models.

OBJECTIVES: The study was designed to assess the ability of computer-simulated electrocardiography parameters to predict clinical outcomes and to risk-stratify patients with long QT syndrome type 1 (LQT1). BACKGROUND: Although attempts have been made to correlate mutation-specific ion channel dysfunction with patient phenotype in long QT syndrome, these have been largely unsuccessful. Systems-level computational models can be used to predict consequences of complex changes in channel function to the overall heart rhythm. METHODS: A total of 633 LQT1-genotyped subjects with 34 mutations from multinational long QT syndrome registries were studied. Cellular electrophysiology function was determined for the mutations and introduced in a 1-dimensional transmural electrocardiography computer model. The mutation effect on transmural repolarization was determined for each mutation and related to the risk for cardiac events (syncope, aborted cardiac arrest, and sudden cardiac death) among patients. RESULTS: Multivariate analysis showed that mutation-specific transmural repolarization prolongation (TRP) was associated with an increased risk for cardiac events (35% per 10-ms increment [p < 0.0001]; ≥upper quartile hazard ratio: 2.80 [p < 0.0001]) and life-threatening events (aborted cardiac arrest/sudden cardiac death: 27% per 10-ms increment [p = 0.03]; ≥upper quartile hazard ratio: 2.24 [p = 0.002]) independently of patients' individual QT interval corrected for heart rate (QTc). Subgroup analysis showed that among patients with mild to moderate QTc duration (<500 ms), the risk associated with TRP was maintained (36% per 10 ms [p < 0.0001]), whereas the patient's individual QTc was not associated with a significant risk increase after adjustment for TRP. CONCLUSIONS: These findings suggest that simulated repolarization can be used to predict clinical outcomes and to improve risk stratification in patients with LQT1, with a more pronounced effect among patients with a lower-range QTc, in whom a patient's individual QTc may provide less incremental prognostic information.

Cardiac electromechanical models: from cell to organ.

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin-myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank-Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction-diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

Integrative modeling of the cardiac ventricular myocyte.

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

Computational modeling of cardiac disease: potential for personalized medicine.

Cardiovascular diseases are leading causes of death, reduce life quality and consume almost half a trillion dollars in healthcare expenses in the USA alone. Cardiac modeling and simulation technologies hold promise as important tools to improve cardiac care and are already in use to elucidate the fundamental mechanisms of cardiac physiology and pathophysiology. However, the emphasis has been on simulating average or exemplar cases. This report describes two classes of cardiac modeling efforts. First, electrophysiological models of channelopathies simulate the altered electrical activity that is thought to promote arrhythmias. Second, electromechanical models attempt to capture both the electrophysiological and mechanical aspects of heart function. One goal of the community is to develop models with sufficient patient customization to assist in personalized treatment planning. Some model aspects can be customized with existing data collection techniques to more closely represent individual patients while other model aspects will likely remain based on generic data. Despite important challenges, cardiac models hold promise to be important enablers of personalized medicine.

Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations.

We develop a point model of the cardiac myofilament (MF) to simulate a wide variety of experimental muscle characterizations including Force-Ca relations and twitches under isometric, isosarcometric, isotonic, and auxotonic conditions. Complex MF behaviors are difficult to model because spatial interactions cannot be directly implemented as ordinary differential equations. We therefore allow phenomenological approximations with careful consideration to the relationships with the underlying biophysical mechanisms. We describe new formulations that avoid mean-field approximations found in most existing MF models. To increase the scope and applicability of the model, we include length- and temperature-dependent effects that play important roles in MF responses. We have also included a representation of passive restoring forces to simulate isolated cell shortening protocols. Possessing both computational efficiency and the ability to simulate a wide variety of muscle responses, the MF representation is well suited for coupling to existing cardiac cell models of electrophysiology and Ca-handling mechanisms. To illustrate this suitability, the MF model is coupled to the Chicago rabbit cardiomyocyte model. The combined model generates realistic appearing action potentials, intracellular Ca transients, and cell shortening signals. The combined model also demonstrates that the feedback effects of force on Ca binding to troponin can modify the cytosolic Ca transient.

Spatially-compressed cardiac myofilament models generate hysteresis that is not found in real muscle.

In the field of cardiac modeling, calcium- (Ca-) based activation is often described by sets of ordinary differential equations that do not explicitly represent spatial interactions of regulatory proteins or crossbridge attachment. These spatially compressed models are most often mean-field representations as opposed to methods that explicitly compute the surrounding field (or equivalently, the surrounding environment) of individual regulatory units and crossbridges. Instead, a mean value is used to represent the whole population. Almost universally, the mean-field approach assumes developed force produces positive feedback to globally increase the mean binding affinity of the regulatory proteins. We show that this approach produces hysteresis in the steady-state Force-Ca responses when developed force increases Ca-affinity troponin to the degree that is observed in real muscle. Specifically, multiple stable solutions exist as a function of Ca level that could be alternatively reached depending on stimulus history. The resulting hysteresis is quite pronounced and disagrees with experimental characterizations in cardiac muscle that generally show little if any hysteresis. Moreover, we provide data showing that hysteresis does not occur in carefully controlled myofibril preparations. Hence, we suggest that the most widely used methods to produce multiscale models of cardiac force generation show bistability and hysteresis effects that are not seen in real muscle responses

A plausible model for the digital response of p53 to DNA damage.

Recent observations show that the single-cell response of p53 to ionizing radiation (IR) is "digital" in that it is the number of oscillations rather than the amplitude of p53 that shows dependence on the radiation dose. We present a model of this phenomenon. In our model, double-strand break (DSB) sites induced by IR interact with a limiting pool of DNA repair proteins, forming DSB-protein complexes at DNA damage foci. The persisting complexes are sensed by ataxia telangiectasia mutated (ATM), a protein kinase that activates p53 once it is phosphorylated by DNA damage. The ATM-sensing module switches on or off the downstream p53 oscillator, consisting of a feedback loop formed by p53 and its negative regulator, Mdm2. In agreement with experiments, our simulations show that by assuming stochasticity in the initial number of DSBs and the DNA repair process, p53 and Mdm2 exhibit a coordinated oscillatory dynamics upon IR stimulation in single cells, with a stochastic number of oscillations whose mean increases with IR dose. The damped oscillations previously observed in cell populations can be explained as the aggregate behavior of single cells.

Reconstructing biological networks using conditional correlation analysis.

MOTIVATION: One of the present challenges in biological research is the organization of the data originating from high-throughput technologies. One way in which this information can be organized is in the form of networks of influences, physical or statistical, between cellular components. We propose an experimental method for probing biological networks, analyzing the resulting data and reconstructing the network architecture. METHODS: We use networks of known topology consisting of nodes (genes), directed edges (gene-gene interactions) and a dynamics for the genes' mRNA concentrations in terms of the gene-gene interactions. We proposed a network reconstruction algorithm based on the conditional correlation of the mRNA equilibrium concentration between two genes given that one of them was knocked down. Using simulated gene expression data on networks of known connectivity, we investigated how the reconstruction error is affected by noise, network topology, size, sparseness and dynamic parameters. RESULTS: Errors arise from correlation between nodes connected through intermediate nodes (false positives) and when the correlation between two directly connected nodes is obscured by noise, non-linearity or multiple inputs to the target node (false negatives). Two critical components of the method are as follows: (1) the choice of an optimal correlation threshold for predicting connections and (2) the reduction of errors arising from indirect connections (for which a novel algorithm is proposed). With these improvements, we can reconstruct networks with the topology of the transcriptional regulatory network in Escherichia coli with a reasonably low error rate.

Approaches to modeling crossbridges and calcium-dependent activation in cardiac muscle.

While the primary function of the heart is a pump, ironically, the development of myofilament models that predict developed force have generally lagged behind the modeling of the electrophysiological and Ca2+-handling aspects of heart cells. A major impediment is that the basic events in force generating actin-myosin interactions are still not well understood and quantified despite advanced techniques that can probe molecular levels events and identify numerous energetic states. As a result, the modeler must decide how to best abstract the many identified states into useful models with an essential tradeoff in the level of complexity. Namely, complex models map more directly to biophysical states but experimental data does not yet exist to well constrain the rate constants and parameters. In contrast, parameters can be better constrained in simpler, lumped models, but the simplicity may preclude versatility and extensibility to other applications. Other controversies exist as to why the activation of the actin-myosin is so steeply dependent on activator Ca2+. More specifically steady-state force-[Ca2+] (F-Ca) relationships are similar to Hill functions, presumably as the result of cooperative interactions between neighboring crossbridges and/or regulatory proteins. We postulate that mathematical models must contain explicit representation of nearest-neighbor cooperative interactions to reproduce F-Ca relationships similar to experimental measures, whereas spatially compressing, mean-field approximation used in most models cannot. Finally, a related controversy is why F-Ca relationships show increased Ca2+ sensitivity as sarcomere length (SL) increases. We propose a model that suggests that the length-dependent effects can result from an interaction of explicit nearest-neighbor cooperative mechanisms and the number of recruitable crossbridges as a function of SL.

Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions.

We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca(50)) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca(50), and becomes uncooperative again at higher [Ca]. The steepness near Ca(50) mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca(50), high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.