A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte

An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca2+, and Na+ concentrations in the myoplasmic and mitochondrial matrix compartments. The pseudo steady-state relationship between force and oxygen consumption at various stimulus frequencies and external Ca2+ concentrations is reproduced in both model simulations and direct experiments in cardiac trabeculae under normoxic conditions, recapitulating the linearity between cardiac work and respiration in the heart. Importantly, the model can also reproduce the rapid time-dependent changes in mitochondrial NADH and Ca2+ in response to abrupt changes in workload. The steady-state and dynamic responses of the model were conferred by ADP-dependent stimulation of mitochondrial oxidative phosphorylation and Ca2+ -dependent regulation of Krebs cycle dehydrogenases, illustrating how the model can be used as a tool for investigating mechanisms underlying metabolic control in the heart.     

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic-based damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits.     

Intracellular calcium handling in ventricular myocytes from mdx mice

Duchenne muscular dystrophy (DMD) is a lethal degenerative disease of skeletal muscle, characterized by the absence of the cytoskeletal protein dystrophin. Some DMD patients show a dilated cardiomyopathy leading to heart failure. This study explores the possibility that dystrophin is involved in the regulation of a stretch-activated channel (SAC), which in the absence of dystrophin has increased activity and allows greater Ca(2+) into cardiomyocytes. Because cardiac failure only appears late in the progression of DMD, we examined age-related effects in the mdx mouse, an animal model of DMD. Ca(2+) measurements using a fluorescent Ca(2+)-sensitive dye fluo-4 were performed on single ventricular myocytes from mdx and wild-type mice. Immunoblotting and immunohistochemistry were performed on whole hearts to determine expression levels of key proteins involved in excitation-contraction coupling. Old mdx mice had raised resting intracellular Ca(2+) concentration ([Ca(2+)](i)). Isolated ventricular myocytes from young and old mdx mice displayed abnormal Ca(2+) transients, increased protein expression of the ryanodine receptor, and decreased protein expression of serine-16-phosphorylated phospholamban. Caffeine-induced Ca(2+) transients showed that the Na(+)/Ca(2+) exchanger function was increased in old mdx mice. Two SAC inhibitors streptomycin and GsMTx-4 both reduced resting [Ca(2+)](i) in old mdx mice, suggesting that SACs may be involved in the Ca(2+)-handling abnormalities in these animals. This finding was supported by immunoblotting data, which demonstrated that old mdx mice had increased protein expression of canonical transient receptor potential channel 1, a likely candidate protein for SACs. SACs may play a role in the pathogenesis of the heart failure associated with DMD. Early in the disease process and before the onset of clinical symptoms increased, SAC activity may underlie the abnormal Ca(2+) handling in young mdx mice.     

A computational model of the human thyroid

The thyroid, the largest gland in the endocrine system, secretes hormones that help promote bodily growth and development. This gland regulates hormonal secretion rate in spite of changes in dietary iodine which is a key ingredient in the hormone's biosynthesis. The thyroid relies on several feedback mechanisms for this regulation, and in this paper we use recent molecular-level and clinical observations to engineer a computational thyroid model. We use simulation and analysis to show that this models captures known aspects of thyroid physiology. We identify features in the model that are responsible for hormonal regulation, and use the model to identify and evaluate competing hypotheses associated with Wolff-Chaikoff escape.     

Effect of thymol on calcium handling in mammalian ventricular myocardium

Concentration-dependent effects of thymol on calcium handling were studied in canine and guinea pig cardiac preparations (Langendorff-perfused guinea pig hearts, canine ventricular trabeculae, canine sarcoplasmic reticular vesicles and single ryanodine receptors). Thymol induced a concentration-dependent negative inotropic action in both canine and guinea pig preparations (EC(50) = 297 +/- 12 microM in dog). However, low concentrations of thymol reduced intracellular calcium transients in guinea pig hearts without decreasing contractility. At higher concentrations both calcium transients and contractions were suppressed. In canine sarcoplasmic reticular vesicles thymol induced rapid release of calcium (V(max) = 0.47 +/- 0.04 nmol s(-1), EC(50) = 258 +/- 21 microM, Hill coefficient = 3.0 +/- 0.54), and decreased the activity of the calcium pump (EC(50) = 253 +/- 4.7 microM, Hill coefficient = 1.62 +/- 0.05). Due to the less sharp concentration-dependence of the ATPase inhibition, this effect was significant from 50 microM, whereas the thymol-induced calcium release only from 100 microM. In single ryanodine receptors incorporated into artificial lipid bilayer thymol induced long lasting openings, having mean open times increased with 3 orders of magnitude, however, the specific conductance of the channel remained unaltered. This effect of thymol was not voltage-dependent and failed to prevent the binding of ryanodine. In conclusion, the negative inotropic action of thymol can be explained by reduction in calcium content of the sarcoplasmic reticulum due to the combination of the thymol-induced calcium release and inhibition of the calcium pump. The calcium-sensitizer effect, observed at lower thymol concentrations, indicates that thymol is likely to interact with the contractile machinery also.     

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

     

A model for human ventricular tissue

The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.     

Quantitative comparison of cardiac ventricular myocyte electrophysiology and response to drugs in human and nonhuman species

Explanations for arrhythmia mechanisms at the cellular level are usually based on experiments in nonhuman myocytes. However, subtle electrophysiological differences between species may lead to different rhythmic or arrhythmic cellular behaviors and drug response given the nonlinear and highly interactive cellular system. Using detailed and quantitatively accurate mathematical models for human, dog, and guinea pig ventricular action potentials (APs), we simulated and compared cell electrophysiology mechanisms and response to drugs. Under basal conditions (absence of β-adrenergic stimulation), Na(+)/K(+)-ATPase changes secondary to Na(+) accumulation determined AP rate dependence for human and dog but not for guinea pig where slow delayed rectifier current (I(Ks)) was the major rate-dependent current. AP prolongation with reduction of rapid delayed rectifier current (I(Kr)) and I(Ks) (due to mutations or drugs) showed strong species dependence in simulations, as in experiments. For humans, AP prolongation was 80% following I(Kr) block. It was 30% for dog and 20% for guinea pig. Under basal conditions, I(Ks) block was of no consequence for human and dog, but for guinea pig, AP prolongation after I(Ks) block was severe. However, with β-adrenergic stimulation, I(Ks) played an important role in all species, particularly in AP shortening at fast rate. Quantitative comparison of AP repolarization, rate-dependence mechanisms, and drug response in human, dog, and guinea pig revealed major species differences (e.g., susceptibility to arrhythmogenic early afterdepolarizations). Extrapolation from animal to human electrophysiology and drug response requires great caution.     

A computational model of the human left-ventricular epicardial myocyte

A computational model of the human left-ventricular epicardial myocyte is presented. Models of each of the major ionic currents present in these cells are formulated and validated using experimental data obtained from studies of recombinant human ion channels and/or whole-cell recording from single myocytes isolated from human left-ventricular subepicardium. Continuous-time Markov chain models for the gating of the fast Na(+) current, transient outward current, rapid component of the delayed rectifier current, and the L-type calcium current are modified to represent human data at physiological temperature. A new model for the gating of the slow component of the delayed rectifier current is formulated and validated against experimental data. Properties of calcium handling and exchanger currents are altered to appropriately represent the dynamics of intracellular ion concentrations. The model is able to both reproduce and predict a wide range of behaviors observed experimentally including action potential morphology, ionic currents, intracellular calcium transients, frequency dependence of action-potential duration, Ca(2+)-frequency relations, and extrasystolic restitution/post-extrasystolic potentiation. The model therefore serves as a useful tool for investigating mechanisms of arrhythmia and consequences of drug-channel interactions in the human left-ventricular myocyte.     

The ex-vivo effects of thyroid status and extracellular calcium concentration on rat atrial and ventricular electrophysiology

The purpose of this study was to explore the relationship between the thyroid status and both ventricular and atrial electrophysiology in the rat. The study was extended to consider the effects of altering the extracellular calcium concentration. The work was performed in two sections. First, hypothyroid animals were compared with euthyroid (untreated animals); second, hypothyroid animals were compared with hyperthyroid animals. Rats were rendered hypothyroid by pretreatment with the goitrogen methimazole and hyperthyroid by additional treatment with triiodothyronine. Action potential recordings were obtained using standard microelectrode techniques. Action potential measurements were made initially in a Krebs solution to which had been added 2.55 mM calcium (higher Ca Krebs solution) and at the end of each experiment after stabilization with Krebs solution to which had been added 1.28 mM calcium (lower Ca Krebs solution). Assessment of the change in action potential duration on transition from higher to lower Ca Krebs solution revealed that the euthyroid preparations demonstrated less prolongation of action potential duration than the hypothyroid group, and the hyperthyroid group showed hardly any response to reduction in calcium concentration.     

A second-generation computational modeling of cardiac electrophysiology: response of action potential to ionic concentration changes and metabolic inhibition

Background

Cardiac arrhythmias are becoming one of the major health care problem in the world, causing numerous serious disease conditions including stroke and sudden cardiac death. Furthermore, cardiac arrhythmias are intimately related to the signaling ability of cardiac cells, and are caused by signaling defects. Consequently, modeling the electrical activity of the heart, and the complex signaling models that subtend dangerous arrhythmias such as tachycardia and fibrillation, necessitates a quantitative model of action potential (AP) propagation. Yet, many electrophysiological models, which accurately reproduce dynamical characteristic of the action potential in cells, have been introduced. However, these models are very complex and are very time consuming computationally. Consequently, a large amount of research is consecrated to design models with less computational complexity.

Results

This paper is presenting a new model for analyzing the propagation of ionic concentrations and electrical potential in space and time. In this model, the transport of ions is governed by Nernst-Planck flux equation (NP), and the electrical interaction of the species is described by a new cable equation. These set of equations form a system of coupled partial nonlinear differential equations that is solved numerically. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm.

Conclusions

We give numerical simulations obtained for different input scenarios in the case of suicide substrate reaction which were compared to those obtained in literature. These input scenarios have been chosen so as to provide an intuitive understanding of dynamics of the model. By accessing time and space domains, it is shown that interpreting the electrical potential of cell membrane at steady state is incorrect. This model is general and applies to ions of any charge in space and time domains. The results obtained show a complete agreement with literature findings and also with the physical interpretation of the phenomenon. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is second-order accurate in space.

     

Simultaneous assessment of calcium handling and contractility dynamics in isolated ventricular myocytes of a rat model of post-acute isoproterenol-induced cardiomyopathy

Stress-induced cardiomyopathy (SIC) results from a profound catecholaminergic surge during strong emotional or physical stress. SIC is characterized by acute left ventricular apex hypokinesia, in the absence of coronary arteries occlusion, and can lead to arrhythmias and acute heart failure. Although, most SIC patients recover, the process could be slow, and recurrence or death may occur. Despite that the SIC common denominator is a large catecholamine discharge, the pathophysiological mechanism is incompletely understood. It is thought that catecholamines have direct cytotoxicity on apical ventricular myocytes (VM), which have the highest β-adrenergic receptors density, and whose overstimulation might cause acute Ca²⁺ overload and oxidative stress, causing death in some VM and stunning others. Rodents receiving acute isoproterenol (ISO) overdose (OV) mimic SIC development, however, they have not been used to simultaneously assess Ca²⁺ handling and contractility status in isolated VM, which might explain ventricular hypokinesia. Therefore, treating rats with a single ISO-OV (67 mg/kg body weight), we sought out to characterize, with confocal imaging, Ca²⁺ and shortening dynamics in Fluo-4-loaded VM, during the early (1–5 days) and late post-acute phases (15 days). We found that ISO-OV VM showed contractile dysfunction; blunted shortening with slower force development and relaxation. These correlated with Ca²⁺ mishandling; blunted Ca²⁺ transient, with slower time to peak and SR Ca²⁺ recovery. SR Ca²⁺ content was low, nevertheless, diastolic Ca²⁺ sparks were more frequent, and their duration increased. Contractility and Ca²⁺ dysfunction aggravated or remained altered over time, explaining slow recovery. We conclude that diminished VM contractility is the main determinant of ISO-OV hypokinesia and is mostly related to Ca²⁺ mishandling.     

Defective calcium handling in cardiomyocytes isolated from hearts subjected to ischemia-reperfusion

Although ischemia-reperfusion (I/R) has been shown to affect subcellular organelles that regulate the intracellular Ca2+ concentration ([Ca2+]i), very little information regarding the Ca2+ handling ability of cardiomyocytes obtained from I/R hearts is available. To investigate changes in [Ca2+]i due to I/R, rat hearts in vitro were subjected to 10-30 min of ischemia followed by 5-30 min of reperfusion. Cardiomyocytes from these hearts were isolated and purified; [Ca2+]i was measured by employing fura-2 microfluorometry. Reperfusion for 30 min of the 20-min ischemic hearts showed attenuated cardiac performance, whereas basal [Ca2+]i as well as the KCl-induced increase in [Ca2+]i and isoproterenol (Iso)-induced increase in [Ca2+]i in cardiomyocytes remained unaltered. On the other hand, reperfusion of the 30-min ischemic hearts for different periods revealed marked changes in cardiac function, basal [Ca2+]i, and Iso-induced increase in [Ca2+]i without any alterations in the KCl-induced increase in [Ca2+]i or S(-)-BAY K 8644-induced increase in [Ca2+]i. The I/R-induced alterations in cardiac function, basal [Ca2+]i, and Iso-induced increase in [Ca2+]i in cardiomyocytes were attenuated by an antioxidant mixture containing superoxide dismutase and catalase as well as by ischemic preconditioning. The observed changes due to I/R were simulated in hearts perfused with H2O2 for 30 min. These results suggest that abnormalities in basal [Ca2+]i as well as mobilization of [Ca2+]i upon beta-adrenoceptor stimulation in cardiomyocytes are dependent on the duration of ischemic injury to the myocardium. Furthermore, Ca2+ handling defects in cardiomyocytes appear to be mediated through oxidative stress in I/R hearts.     

A computational model for dynamic analysis of the human gait

Biomechanical models are important tools in the study of human motion. This work proposes a computational model to analyse the dynamics of lower limb motion using a kinematic chain to represent the body segments and rotational joints linked by viscoelastic elements. The model uses anthropometric parameters, ground reaction forces and joint Cardan angles from subjects to analyse lower limb motion during the gait. The model allows evaluating these data in each body plane. Six healthy subjects walked on a treadmill to record the kinematic and kinetic data. In addition, anthropometric parameters were recorded to construct the model. The viscoelastic parameter values were fitted for the model joints (hip, knee and ankle). The proposed model demonstrated that manipulating the viscoelastic parameters between the body segments could fit the amplitudes and frequencies of motion. The data collected in this work have viscoelastic parameter values that follow a normal distribution, indicating that these values are directly related to the gait pattern. To validate the model, we used the values of the joint angles to perform a comparison between the model results and previously published data. The model results show a same pattern and range of values found in the literature for the human gait motion.