Mathematical analysis of left ventricular elastance with respect to afterload change during ejection phase.

Since the left ventricle (LV) has pressure (Plv) and volume (Vlv), we can define LV elastance from the ratio between Plv and Vlv, termed as "instantaneous elastance." On the other hand, end-systolic elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic Plv-Vlv points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slope of isochronous Plv-Vlv points, that is Plv-Vlv points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous Plv-Vlv points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity-dependent force drops characteristics in instantaneous shortening. The other is the force-velocity relation of the cardiac cell. We also found that the linear isochronous pressure-volume relation is based on the approximately linear relation between the time derivative of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances.

Ionic Mechanisms of Propagated Repolarization in a One-Dimensional Strand of Human Ventricular Myocyte Model.

Although repolarization has been suggested to propagate in cardiac tissue both theoretically and experimentally, it has been challenging to estimate how and to what extent the propagation of repolarization contributes to relaxation because repolarization only occurs in the course of membrane excitation in normal hearts. We established a mathematical model of a 1D strand of 600 myocytes stabilized at an equilibrium potential near the plateau potential level by introducing a sustained component of the late sodium current (INaL). By applying a hyperpolarizing stimulus to a small part of the strand, we succeeded in inducing repolarization which propagated along the strand at a velocity of 1~2 cm/s. The ionic mechanisms responsible for repolarization at the myocyte level, i.e., the deactivation of both the INaL and the L-type calcium current (ICaL), and the activation of the rapid component of delayed rectifier potassium current (IKr) and the inward rectifier potassium channel (IK1), were found to be important for the propagation of repolarization in the myocyte strand. Using an analogy with progressive activation of the sodium current (INa) in the propagation of excitation, regenerative activation of the predominant magnitude of IK1 makes the myocytes at the wave front start repolarization in succession through the electrical coupling via gap junction channels.

Clarifying the composition of the ATP consumption factors required for maintaining ion homeostasis in mouse rod photoreceptors.

To date, no effective treatment has been established for photoreceptor loss due to energy imbalances, but numerous therapeutic approaches have reported some success in slowing photoreceptor degeneration by downregulating energy demand. However, the detailed mechanisms remain unclear. This study aimed to clarify the composition of ATP consumption factors in photoreceptors in darkness and in light. We introduced mathematical formulas for ionic current activities combined with a phototransduction model to form a new mathematical model for estimating the energy expenditure of each ionic current. The proposed model included various ionic currents identified in mouse rods using a gene expression database incorporating an available electrophysiological recording of each specific gene. ATP was mainly consumed by Na+/K+-ATPase and plasma membrane Ca2+-ATPase pumps to remove excess Na+ and Ca2+. The rod consumed 7 [Formula: see text] 107 molecules of ATP s-1, where 65% was used to remove ions from the cyclic nucleotide-gated channel and 20% from the hyperpolarization-activated current in darkness. Increased light intensity raised the energy requirements of the complex phototransduction cascade mechanisms. Nevertheless, the overall energy consumption was less than that in darkness due to the significant reduction in ATPase activities, where the hyperpolarization-activated current proportion increased to 83%. A better understanding of energy demand/supply may provide an effective tool for investigating retinal pathophysiological changes and analyzing novel therapeutic treatments related to the energy consumption of photoreceptors.

Theoretical prediction of early afterdepolarization-evoked triggered activity formation initiating ventricular reentrant arrhythmias.

BACKGROUND AND OBJECTIVE: Excessive prolongation of QT interval on ECGs in patients with congenital/acquired long QT syndrome and heart failure is a sign suggesting the development of early afterdepolarization (EAD), an abnormal repolarization in the action potential of ventricular cardiomyocytes. The development of EAD has been believed to be a trigger for fatal tachyarrhythmia, which can be a risk for sudden cardiac death. The role of EAD in triggering ventricular tachycardia (VT) remains unclear. The aim of this study was to elucidate the mechanism of EAD-induced triggered activity formation that leads to the VT such as Torsades de Pointes. METHODS: We investigated the relationship between EAD and tachyarrhythmia initiation by constructing homogeneous myocardial sheet models consisting of the mid-myocardial cell version of a human ventricular myocyte model and performing simulations of excitation propagation. RESULTS: A solitary island-like (clustering) occurrence of EADs in the homogeneous myocardial sheet could induce a focal excitation wave. However, reentrant excitation, an entity of tachyarrhythmia, was not able to be triggered regardless of the EAD cluster size when the focal excitation wave formed a repolarization potential difference boundary consisting of only a convex surface. The discontinuous distribution of multiple EAD clusters in the ventricular tissue formed a specific repolarization heterogeneity due to the repolarization potential difference, the shape of which depended on EAD cluster size and placed intervals. We found that the triggered activity was formed in such a manner that the repolarization potential difference boundary included a concave surface. CONCLUSIONS: The formation of triggered activity that led to tachyarrhythmia required not only the occurrence of EAD onset-mediated focal excitation wave but also a repolarization heterogeneity-based specific repolarization potential difference boundary shape formed within the tissue.

Mathematical analysis of phototransduction reaction parameters in rods and cones.

Retinal photoreceptor cells, rods and cones, convert photons of light into chemical and electrical signals as the first step of the visual transduction cascade. Although the chemical processes in the phototransduction system are very similar to each other in these photoreceptors, the light sensitivity and time resolution of the photoresponse in rods are functionally different than those in the photoresponses of cones. To systematically investigate how photoresponses are divergently regulated in rods and cones, we have developed a detailed mathematical model on the basis of the Hamer model. The current model successfully reconstructed light intensity-, ATP- and GTP-dependent changes in concentrations of phosphorylated visual pigments (VPs), activated transducins (Tr*s) and phosphodiesterases (PDEs) in rods and cones. In comparison to rods, the lower light sensitivity of cones was attributed not only to the lower affinity of activated VPs for Trs but also to the faster desensitization of the VPs. The assumption of an intermediate inactive state, MIIi, in the thermal decay of activated VPs was essential for inducing faster inactivation of VPs in rods, and possibly also in cones.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes.

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (Gx) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of Gxs of the baseline model. Gxs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-Gx relationship during optimization revealed progressive convergence of the randomized population of Gxs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing Gxs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Specific decreasing of Na+ channel expression on the lateral membrane of cardiomyocytes causes fatal arrhythmias in Brugada syndrome.

Reduced cardiac sodium (Na+) channel current (INa) resulting from the loss-of-function of Na+ channel is a major cause of lethal arrhythmias in Brugada syndrome (BrS). Inspired by previous experimental studies which showed that in heart diseases INa was reduced along with expression changes in Na+ channel within myocytes, we hypothesized that the local decrease in INa caused by the alteration in Na+ channel expression in myocytes leads to the occurrence of phase-2 reentry, the major triggering mechanism of lethal arrhythmias in BrS. We constructed in silico human ventricular myocardial strand and ring models, and examined whether the Na+ channel expression changes in each myocyte cause the phase-2 reentry in BrS. Reducing Na+ channel expression in the lateral membrane of each myocyte caused not only the notch-and-dome but also loss-of-dome type action potentials and slowed conduction, both of which are typically observed in BrS patients. Furthermore, the selective reduction in Na+ channels on the lateral membrane of each myocyte together with spatial tissue heterogeneity of Na+ channel expression caused the phase-2 reentry and phase-2 reentry-mediated reentrant arrhythmias. Our data suggest that the BrS phenotype is strongly influenced by expression abnormalities as well as genetic abnormalities of Na+ channels.

Mechanisms Underlying Spontaneous Action Potential Generation Induced by Catecholamine in Pulmonary Vein Cardiomyocytes: A Simulation Study.

Cardiomyocytes and myocardial sleeves dissociated from pulmonary veins (PVs) potentially generate ectopic automaticity in response to noradrenaline (NA), and thereby trigger atrial fibrillation. We developed a mathematical model of rat PV cardiomyocytes (PVC) based on experimental data that incorporates the microscopic framework of the local control theory of Ca2+ release from the sarcoplasmic reticulum (SR), which can generate rhythmic Ca2+ release (limit cycle revealed by the bifurcation analysis) when total Ca2+ within the cell increased. Ca2+ overload in SR increased resting Ca2+ efflux through the type II inositol 1,4,5-trisphosphate (IP3) receptors (InsP3R) as well as ryanodine receptors (RyRs), which finally triggered massive Ca2+ release through activation of RyRs via local Ca2+ accumulation in the vicinity of RyRs. The new PVC model exhibited a resting potential of -68 mV. Under NA effects, repetitive Ca2+ release from SR triggered spontaneous action potentials (APs) by evoking transient depolarizations (TDs) through Na+/Ca2+ exchanger (APTDs). Marked and variable latencies initiating APTDs could be explained by the time courses of the α1- and ß1-adrenergic influence on the regulation of intracellular Ca2+ content and random occurrences of spontaneous TD activating the first APTD. Positive and negative feedback relations were clarified under APTD generation.

Evaluation of critical flicker-fusion frequency measurement methods using a touchscreen-based visual temporal discrimination task in the behaving mouse.

The critical flicker-fusion frequency (CFF), defined as the frequency at which a flickering light is indistinguishable from a continuous light, is a useful measure of visual temporal resolution. The mouse CFF has been studied by electrophysiological approaches such as recordings of the electroretinogram (ERG) and the visually evoked potential (VEP), but it has not been measured behaviorally. Here we estimated the mouse CFF by using a touchscreen based operant system. The test with ascending series of frequencies and that with randomized frequencies resulted in about 17 and 14 Hz, respectively, as the frequency which could not be distinguished from steady lights. Since the ascending method of limits tend to overestimate the threshold than the descending method, we estimated the mouse CFF to be about 14 Hz. Our results highlight usefulness of the operant conditioning method in measurement of the mouse visual temporal resolution.

The novel primers for mammal species identification-based mitochondrial cytochrome b sequence: implication for reserved wild animals in Thailand and endangered mammal species in Southeast Asia.

We presented the powerful techniques for species identification using the short amplicon of mitochondrial cytochrome b gene sequence. Two faecal samples and one single hair sample of the Asian tapir were tested using the new cytochrome b primers. The results showed a high sequence similarity with the mainland Asian tapir group. The comparative sequence analysis of the reserved wild mammals in Thailand and the other endangered mammal species from Southeast Asia comprehensibly verified the potential of our novel primers. The forward and reverse primers were 94.2 and 93.2%, respectively, by the average value of the sequence identity among 77 species sequences, and the overall mean distance was 35.9%. This development technique could provide rapid, simple, and reliable tools for species confirmation. Especially, it could recognize the problematic biological specimens contained less DNA material from illegal products and assist with wildlife crime investigation of threatened species and related forensic casework.

A new myofilament contraction model with ATP consumption for ventricular cell model.

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca2+-crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca2+ activation and force (F b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F b activation by transient Ca2+ ([Ca2+]-F b), [Ca2+]-ATP hydrolysis relations, sarcomere length-F b, and F b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load-velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

Regulation of the glucose supply from capillary to tissue examined by developing a capillary model.

A new glucose transport model relying upon diffusion and convection across the capillary membrane was developed, and supplemented with tissue space and lymph flow. The rate of glucose utilization (J util) in the tissue space was described as a saturation function of glucose concentration in the interstitial fluid (C glu,isf), and was varied by applying a scaling factor f to J max. With f = 0, the glucose diffusion ceased within ~20 min. While, with increasing f, the diffusion was accelerated through a decrease in C glu,isf, but the convective flux remained close to resting level. When the glucose supplying capacity of the capillary was measured with a criterion of J util /J max = 0.5, the capacity increased in proportion to the number of perfused capillaries. A consistent profile of declining C glu,isf along the capillary axis was observed at the criterion of 0.5 irrespective of the capillary number. Increasing blood flow scarcely improved the supplying capacity.

Genetic diversity of the captive Asian tapir population in Thailand, based on mitochondrial control region sequence data and the comparison of its nucleotide structure with Brazilian tapir.

The Asian tapir (Tapirus indicus) has been classified as Endangered on the IUCN Red List of Threatened Species (2008). Genetic diversity data provide important information for the management of captive breeding and conservation of this species. We analyzed mitochondrial control region (CR) sequences from 37 captive Asian tapirs in Thailand. Multiple alignments of the full-length CR sequences sized 1268 bp comprised three domains as described in other mammal species. Analysis of 16 parsimony-informative variable sites revealed 11 haplotypes. Furthermore, the phylogenetic analysis using median-joining network clearly showed three clades correlated with our earlier cytochrome b gene study in this endangered species. The repetitive motif is located between first and second conserved sequence blocks, similar to the Brazilian tapir. The highest polymorphic site was located in the extended termination associated sequences domain. The results could be applied for future genetic management based in captivity and wild that shows stable populations.

Mechanisms underlying the volume regulation of interstitial fluid by capillaries: a simulation study.

BACKGROUND: Control of the extracellular fluid volume is one of the most indispensable issues for homeostasis of the internal milieu. However, complex interdependence of the pressures involved in determination of fluid exchange makes it difficult to predict a steady-state tissue volume under various physiological conditions without mathematical approaches. METHODS: Here, we developed a capillary model based on the Starling's principle, which allowed us to clarify the mechanisms of the interstitial-fluid volume regulation. Three well known safety factors against edema: (1) low tissue compliance in negative pressure ranges; (2) lymphatic flow driven by the tissue pressure; and (3) protein washout by the lymph, were incorporated into the model in sequence. RESULTS: An increase in blood pressure at the venous end of the capillary induced an interstitial-fluid volume increase, which, in turn, reduced negative tissue pressure to prevent edema. The lymphatic flow alleviated the edema by both carrying fluid away from the tissue and decreasing the colloidal osmotic pressure. From the model incorporating all three factors, we found that the interstitial-fluid volume changed quickly after the blood pressure change, and that the protein movement towards a certain equilibrium point followed the volume change. CONCLUSION: Mathematical analyses revealed that the system of the capillary is stable near the equilibrium point at steady state and normal physiological capillary pressure. The time course of the tissue-volume change was determined by two kinetic mechanisms: rapid fluid exchange and slow protein fluxes.

Application of the Kalman Filter for Faster Strong Coupling of Cardiovascular Simulations.

In this paper, we propose a method for reducing the computational cost of strong coupling for multiscale cardiovascular simulation models. In such a model, individual model modules of myocardial cell, left ventricular structural dynamics, and circulatory hemodynamics are coupled. The strong coupling method enables stable and accurate calculation, but requires iterative calculations which are computationally expensive. The iterative calculations can be reduced, if accurate initial approximations are made available by predictors. The proposed method uses the Kalman filter to estimate accurate predictions by filtering out noise included in past values. The performance of the proposed method was assessed with an application to a previously published multiscale cardiovascular model. The proposed method reduced the number of iterations by 90% and 62% compared with no prediction and Lagrange extrapolation, respectively. Even when the parameters were varied and number of elements of the left ventricular finite-element model increased, the number of iterations required by the proposed method was significantly lower than that without prediction. These results indicate the robustness, scalability, and validity of the proposed method.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling.

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology.

A human ventricular myocyte model with a refined representation of excitation-contraction coupling.

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 µM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Quantitative Decomposition of Dynamics of Mathematical Cell Models: Method and Application to Ventricular Myocyte Models.

Mathematical cell models are effective tools to understand cellular physiological functions precisely. For detailed analysis of model dynamics in order to investigate how much each component affects cellular behaviour, mathematical approaches are essential. This article presents a numerical analysis technique, which is applicable to any complicated cell model formulated as a system of ordinary differential equations, to quantitatively evaluate contributions of respective model components to the model dynamics in the intact situation. The present technique employs a novel mathematical index for decomposed dynamics with respect to each differential variable, along with a concept named instantaneous equilibrium point, which represents the trend of a model variable at some instant. This article also illustrates applications of the method to comprehensive myocardial cell models for analysing insights into the mechanisms of action potential generation and calcium transient. The analysis results exhibit quantitative contributions of individual channel gating mechanisms and ion exchanger activities to membrane repolarization and of calcium fluxes and buffers to raising and descending of the cytosolic calcium level. These analyses quantitatively explicate principle of the model, which leads to a better understanding of cellular dynamics.

A motion tracking method that applies a spread spectrum communication technique to tagging MR imaging.

PURPOSE: We propose a new motion tracking method that encodes an object's position information using tagging magnetic resonance (MR) images as digital codes, and we assess the method's feasibility in stationary and moving phantoms. The encoding and decoding of tag patterns employ principles of spread spectrum communication. METHODS: We used a segmented fast low angle shot cine sequence (FLASH) with spatial modulation of magnetization (SPAMM) preparation pulses to encode position information as 7-bit code words and used this spread code to decode the position information. To make 7-bit code words using tag images, we adjusted the flip angle and phase of the 4 composite radiofrequency (RF) pulses and the gradient magnetic field strength in the SPAMM pulse to generate 7 types of tag patterns. The proposed method required 7 acquisitions with 7 types of tag patterns. We compared results with images obtained by conventional tagging in stationary and moving phantom experiments. RESULTS: In a stationary phantom, the proposed method showed the same ability to identify pixel position as conventional tagging method using improved SNR images with the average of 7 acquisitions. In a moving phantom, pixel position was successfully decoded by the proposed method on a pixel-by-pixel basis. In this method, the motion of the phantom was detected by the simple calculation of the correlation coefficient of the code words. CONCLUSION: We introduced a spread spectrum communication technique to tagging MR imaging that regards tag patterns as digital codes, and we demonstrated the method's potential to detect pixel position in sub-pixel resolution.

Reproducing retinal rod bipolar cell light response by mathematical model including neurotransmitter receptors.

Detailed mathematical model of retinal cells is useful for the quantitative understanding of the subcellular processes of the visual system. Retinal bipolar cells receive information from photoreceptor cells, horizontal cells and amacrine cells, thus it can be considered as information integration system. Despite its importance, bipolar cell model including inputs and outputs has not been proposed. In this paper, we propose a rod bipolar cell model which can reproduce voltage response of light. The model includes TRPM1 channel which receives signal from photoreceptor cells, GABA channel which receives signal from surrounding amacrine cells, and cell body model which is based on the model proposed by Ishihara et al. The model was evaluated with several light signals, where experimentally obtained photoreceptor cell responses were used as TRPM1 channel input. Resulting bipolar cell membrane potential showed good agreement with the reported experimental results.