Search

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

The physiological importance of NCX in human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) is not well characterized but may depend on the relative strength of the current, compared to adult cardiomyocytes, and on the exact spatial arrangement of proteins involved in Ca

Human induced pluripotent stem cell‐derived cardiomyocytes (hiPSC‐CMs) are becoming instrumental in cardiac research, human‐based cell level cardiotoxicity tests, and developing patient‐specific care. As one of the principal functional readouts is contractility, we propose a novel electromechanical hiPSC‐CM computational model named the hiPSC‐CM‐CE. This model comprises a reparametrized version of contractile element (CE) by Rice et al., 2008, with a new passive force formulation, integrated into a hiPSC‐CM electrophysiology formalism by Paci et al. in 2020. Our simulated results were validated against in vitro data reported for hiPSC‐CMs at matching conditions from different labs. Specifically, key action potential (AP) and calcium transient (CaT) biomarkers simulated by the hiPSC‐CM‐CE model were within the experimental ranges. On the mechanical side, simulated cell shortening, contraction–relaxation kinetic indices (RT50 and RT25), and the amplitude of tension fell within the experimental intervals. Markedly, as an inter‐scale analysis, correct classification of the inotropic effects due to non‐cardiomyocytes in hiPSC‐CM tissues was predicted on account of the passive force expression introduced to the CE. Finally, the physiological inotropic effects caused by Verapamil and Bay‐K 8644 and the aftercontractions due to the early afterdepolarizations (EADs) were simulated and validated against experimental data. In the future, the presented model can be readily expanded to take in pharmacological trials and genetic mutations, such as those involved in hypertrophic cardiomyopathy, and study arrhythmia trigger mechanisms., We present the first hiPSC‐CM computational model that accounts for essential AP, CaT, and mechanical biomarkers incorporating experimental variability. The introduced passive force handling enables the model to capture the inotropic effect of non‐cardiomyocytes in hiPSC‐CM tissues. Simulated cell shortening and contraction–relaxation indices fall within experimental ranges, and EAD‐based aftercontractions predicted by the model are in accord with experimental observations. Predicted Verapamil and Bay‐K 8644 inotropic effects agree with in vitro data.

Hypertrophic cardiomyopathy (HCM) is a cardiac genetic disease accompanied by structural and contractile alterations. We identified a rare c.740C>T (p.T247M) mutation in ACTN2, encoding α‐actinin 2 in a HCM patient, who presented with left ventricular hypertrophy, outflow tract obstruction, and atrial fibrillation. We generated patient‐derived human‐induced pluripotent stem cells (hiPSCs) and show that hiPSC‐derived cardiomyocytes and engineered heart tissues recapitulated several hallmarks of HCM, such as hypertrophy, myofibrillar disarray, hypercontractility, impaired relaxation, and higher myofilament Ca2+ sensitivity, and also prolonged action potential duration and enhanced L‐type Ca2+ current. The L‐type Ca2+ channel blocker diltiazem reduced force amplitude, relaxation, and action potential duration to a greater extent in HCM than in isogenic control. We translated our findings to patient care and showed that diltiazem application ameliorated the prolonged QTc interval in HCM‐affected son and sister of the index patient. These data provide evidence for this ACTN2 mutation to be disease‐causing in cardiomyocytes, guiding clinical therapy in this HCM family. This study may serve as a proof‐of‐principle for the use of hiPSC for personalized treatment of cardiomyopathies., Disease modeling of a rare ACTN2 mutation in iPSC‐derived cardiomyocytes & heart tissues engineering revealed typical features of hypertrophic cardiomyopathy & electrophysiological anomalies. Diltiazem reversed the in vitro phenotypes & guided clinical therapy in the family, reducing QTc intervals.

The pathophysiology of atrial fibrillation (AF) is broad, with components related to the unique and diverse cellular electrophysiology of atrial myocytes, structural complexity, and heterogeneity of atrial tissue, and pronounced disease-associated remodeling of both cells and tissue. A major challenge for rational design of AF therapy, particularly pharmacotherapy, is integrating these multiscale characteristics to identify approaches that are both efficacious and independent of ventricular contraindications. Computational modeling has long been touted as a basis for achieving such integration in a rapid, economical, and scalable manner. However, computational pipelines for AF-specific drug screening are in their infancy, and while the field is progressing quite rapidly, major challenges remain before computational approaches can fill the role of workhorse in rational design of AF pharmacotherapies. In this review, we briefly detail the unique aspects of AF pathophysiology that determine requirements for compounds targeting AF rhythm control, with emphasis on delimiting mechanisms that promote AF triggers from those providing substrate or supporting reentry. We then describe modeling approaches that have been used to assess the outcomes of drugs acting on established AF targets, as well as on novel promising targets including the ultra-rapidly activating delayed rectifier potassium current, the acetylcholine-activated potassium current and the small conductance calcium-activated potassium channel. Finally, we describe how heterogeneity and variability are being incorporated into AF-specific models, and how these approaches are yielding novel insights into the basic physiology of disease, as well as aiding identification of the important molecular players in the complex AF etiology.

Inherited ion channelopathies and electrical remodeling in heart disease alter the cardiac action potential with important consequences for excitation-contraction coupling. Potassium channel-interacting protein 2 (KChIP2) is reduced in heart failure and interacts under physiological conditions with both Kv4 to conduct the fast-recovering transient outward K+ current ( Ito,f) and with CaV1.2 to mediate the inward L-type Ca2+ current ( ICa,L). Anesthetized KChIP2−/− mice have normal cardiac contraction despite the lower ICa,L, and we hypothesized that the delayed repolarization could contribute to the preservation of contractile function. Detailed analysis of current kinetics shows that only ICa,L density is reduced, and immunoblots demonstrate unaltered CaV1.2 and CaVβ2 protein levels. Computer modeling suggests that delayed repolarization would prolong the period of Ca2+ entry into the cell, thereby augmenting Ca2+-induced Ca2+ release. Ca2+ transients in disaggregated KChIP2−/− cardiomyocytes are indeed comparable to wild-type transients, corroborating the preserved contractile function and suggesting that the compensatory mechanism lies in the Ca2+-induced Ca2+ release event. We next functionally probed dyad structure, ryanodine receptor Ca2+ sensitivity, and sarcoplasmic reticulum Ca2+ load and found that increased temporal synchronicity of the Ca2+ release in KChIP2−/− cardiomyocytes may reflect improved dyad structure aiding the compensatory mechanisms in preserving cardiac contractile force. Thus the bimodal effect of KChIP2 on Ito,f and ICa,L constitutes an important regulatory effect of KChIP2 on cardiac contractility, and we conclude that delayed repolarization and improved dyad structure function together to preserve cardiac contraction in KChIP2−/− mice.

Although t-tubules have traditionally been thought to be absent in atrial cardiomyocytes, recent studies have suggested that t-tubules exist in the atria of large mammals. However, it is unclear whether regional differences in t-tubule organization exist that define cardiomyocyte function across the atria. We sought to investigate regional t-tubule density in pig and rat atria and the consequences for cardiomyocyte Ca2+ homeostasis. We observed t-tubules in approximately one-third of rat atrial cardiomyocytes, in both tissue cryosections and isolated cardiomyocytes. In a minority (≈10%) of atrial cardiomyocytes, the t-tubular network was well organized, with a transverse structure resembling that of ventricular cardiomyocytes. In both rat and pig atrial tissue, we observed higher t-tubule density in the epicardium than in the endocardium. Consistent with high variability in the distribution of t-tubules and Ca2+ channels among cells, L-type Ca2+ current amplitude was also highly variable and steeply dependent on capacitance and t-tubule density. Accordingly, Ca2+ transients showed great variability in Ca2+ release synchrony. Simultaneous imaging of the cell membrane and Ca2+ transients confirmed t-tubule functionality. Results from mathematical modeling indicated that a transmural gradient in t-tubule organization and Ca2+ release kinetics supports synchronization of contraction across the atrial wall and may underlie transmural differences in the refractory period. In conclusion, our results indicate that t-tubule density is highly variable across the atria. We propose that higher t-tubule density in cells localized in the epicardium may promote synchronization of contraction across the atrial wall.

Recent studies have demonstrated that changes in the activity of calcium-calmodulin-dependent protein kinase II (CaMKII) induce a unique cardiomyocyte phenotype through the regulation of specific genes involved in excitation-contraction (E-C)-coupling. To explain the transcriptional effects of CaMKII we identified a novel CaMKII-dependent pathway for controlling the expression of the pore-forming α-subunit (Cav1.2) of the L-type calcium channel (LTCC) in cardiac myocytes. We show that overexpression of either cytosolic (δC) or nuclear (δB) CaMKII isoforms selectively downregulate the expression of the Cav1.2. Pharmacological inhibition of CaMKII activity induced measurable changes in LTCC current density and subsequent changes in cardiomyocyte calcium signalling in less than 24 h. The effect of CaMKII on the α1C-subunit gene (Cacna1c) promoter was abolished by deletion of the downstream regulatory element (DRE), which binds transcriptional repressor DREAM/calsenilin/KChIP3. Imaging DREAM-GFP (green fluorescent protein)-expressing cardiomyocytes showed that CaMKII potentiates the calcium-induced nuclear translocation of DREAM. Thereby CaMKII increases DREAM binding to the DRE consensus sequence of the endogenous Cacna1c gene. By mathematical modelling we demonstrate that the LTCC downregulation through the Ca2+-CaMKII-DREAM cascade constitutes a physiological feedback mechanism enabling cardiomyocytes to adjust the calcium intrusion through LTCCs to the amount of intracellular calcium detected by CaMKII.

The ability to generate homogeneous intracellular Ca2+ oscillations at high frequency is the basis of the rhythmic contractions of mammalian cardiac myocytes. While the specific mechanisms and structures enabling homogeneous high-frequency Ca2+ signals in adult cardiomyocytes are well characterized, it is not known how these kind of Ca2+ signals are produced in developing cardiomyocytes. Here we investigated the mechanisms reducing spatial and temporal heterogeneity of cytosolic Ca2+ signals in mouse embryonic ventricular cardiomyocytes. We show that in developing cardiomyocytes the propagating Ca2+ signals are amplified in cytosol by local Ca2+ releases. Local releases are based on regular 3-D sarcoplasmic reticulum (SR) structures containing SR Ca2+ uptake ATPases (SERCA) and Ca2+ release channels (ryanodine receptors, RyRs) at regular intervals throughout the cytosol. By evoking [Ca2+]i-induced Ca2+ sparks, the local release sites promote a 3-fold increase in the cytosolic Ca2+ propagation speed. We further demonstrate by mathematical modelling that without these local release sites the developing cardiomyocytes lose their ability to generate homogeneous global Ca2+ signals at a sufficiently high frequency. The mechanism described here is robust and indispensable for normal mammalian cardiomyocyte function from the first heartbeats during the early embryonic phase till terminal differentiation after birth. These results suggest that local cytosolic Ca2+ releases are indispensable for normal cardiomyocyte development and function of developing heart.

AIMS The study investigates how increased Ito, as mediated by the activator NS5806, affects excitation-contraction coupling in chronic heart failure (HF). We hypothesized that restoring spike-and-dome morphology of the action potential (AP) to a healthy phenotype would be insufficient to restore the intracellular Ca(2) (+) transient (CaT), due to HF-induced remodelling of Ca(2+) handling. METHODS AND RESULTS An existing mathematical model of the canine ventricular myocyte was modified to incorporate recent experimental data from healthy and failing myocytes, resulting in models of both healthy and HF epicardial, midmyocardial, and endocardial cell variants. Affects of NS5806 were also included in HF models through its direct interaction with Kv4.3 and Kv1.4. Single-cell simulations performed in all models (control, HF, and HF + drug) and variants (epi, mid, and endo) assessed AP morphology and underlying ionic processes with a focus on calcium transients (CaT), how these were altered in HF across the ventricular wall, and the subsequent effects of varying compound concentration in HF. Heart failure model variants recapitulated a characteristic increase in AP duration (APD) in the disease. The qualitative effects of application of half-maximal effective concentration (EC50) of NS5806 on APs and CaT are heterogeneous and non-linear. Deepening in the AP notch with drug is a direct effect of the activation of Ito; both Ito and consequent alteration of IK1 kinetics cause decrease in AP plateau potential. Decreased APD50 and APD90 are both due to altered IK1. Analysis revealed that drug effects depend on transmurality. Ca(2+) transient morphology changes-increased amplitude and shorter time to peak-are due to direct increase in ICa,L and indirect larger SR Ca(2+) release subsequent to Ito activation. CONCLUSIONS Downstream effects of a compound acting exclusively on sarcolemmal ion channels are difficult to predict. Remediation of APD to pre-failing state does not ameliorate dysfunction in CaT; however, restoration of notch depth appears to impart modest benefit and a likelihood of therapeutic value in modulating early repolarization.

AIM Activity of early embryonic cardiomyocytes relies on spontaneous Ca(2+) oscillations that are induced by interplay between sarcoplasmic reticulum (SR) - Ca(2+) release and ion currents of the plasma membrane. In a variety of cell types, Ca(2+) -activated K(+) current (IK(Ca) ) serves as a link between Ca(2+) signals and membrane voltage. This study aimed to determine the role of IK (Ca) in developing cardiomyocytes. METHODS Ion currents and membrane voltage of embryonic (E9-11) mouse cardiomyocytes were measured by patch clamp; [Ca(2+) ]i signals by confocal microscopy. Transcription of specific genes was measured with RT-qPCR and Ca(2+) -dependent transcriptional activity using NFAT-luciferase assay. Myocyte structure was assessed with antibody labelling and confocal microscopy. RESULTS E9-11 cardiomyocytes express small conductance (SK) channel subunits SK2 and SK3 and have a functional apamin-sensitive K(+) current, which is also sensitive to changes in cytosolic [Ca(2+) ]i . In spontaneously active cardiomyocytes, inhibition of IK (Ca) changed action and resting potentials, reduced SR Ca(2+) load and suppressed the amplitude and the frequency of spontaneously evoked Ca(2+) oscillations. Apamin caused dose-dependent suppression of NFAT-luciferase reporter activity, induced downregulation of a pattern of genes vital for cardiomyocyte development and triggered changes in the myocyte morphology. CONCLUSION The results show that apamin-sensitive IK (Ca) is required for maintaining excitability and activity of the developing cardiomyocytes as well as having a fundamental role in promoting Ca(2+) - dependent gene expression.

Brugada syndrome (BrS) is a rare inherited disease that can give rise to ventricular arrhythmia and ultimately sudden cardiac death. Numerous loss-of-function mutations in the cardiac sodium channel Nav1.5 have been associated with BrS. However, few mutations in the auxiliary Navβ1–4 subunits have been linked to this disease. Here we investigated differences in expression and function between Navβ1 and Navβ1b and whether the H162P/Navβ1b mutation found in a BrS patient is likely to be the underlying cause of disease. The impact of Navβ subunits was investigated by patch-clamp electrophysiology, and the obtained in vitro values were used for subsequent in silico modeling. We found that Navβ1b transcripts were expressed at higher levels than Navβ1 transcripts in the human heart. Navβ1 and Navβ1b coexpressed with Nav1.5 induced a negative shift on steady state of activation and inactivation compared with Nav1.5 alone. Furthermore, Navβ1b was found to increase the current level when coexpressed with Nav1.5, Navβ1b/H162P mutated subunit peak current density was reduced by 48% (−645 ± 151 vs. −334 ± 71 pA/pF), V1/2 steady-state inactivation shifted by −6.7 mV (−70.3 ± 1.5 vs. −77.0 ± 2.8 mV), and time-dependent recovery from inactivation slowed by >50% compared with coexpression with Navβ1b wild type. Computer simulations revealed that these electrophysiological changes resulted in a reduction in both action potential amplitude and maximum upstroke velocity. The experimental data thereby indicate that Navβ1b/H162P results in reduced sodium channel activity functionally affecting the ventricular action potential. This result is an important replication to support the notion that BrS can be linked to the function of Navβ1b and is associated with loss-of-function of the cardiac sodium channel.

Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation (AF). In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential (AP) alternans. To assess the models' ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation (cAF) was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate AP and restitution properties, as well as the initiation of reentrant circuits.

Recent studies have demonstrated that changes in the activity of calcium-calmodulin-dependent protein kinase II (CaMKII) induce a unique cardiomyocyte phenotype through the regulation of specific genes involved in excitation-contraction (E-C)-coupling. To explain the transcriptional effects of CaMKII we identified a novel CaMKII-dependent pathway for controlling the expression of the pore-forming α-subunit (Cav1.2) of the L-type calcium channel (LTCC) in cardiac myocytes. We show that overexpression of either cytosolic (δC) or nuclear (δB) CaMKII isoforms selectively downregulate the expression of the Cav1.2. Pharmacological inhibition of CaMKII activity induced measurable changes in LTCC current density and subsequent changes in cardiomyocyte calcium signalling in less than 24 h. The effect of CaMKII on the α1C-subunit gene (Cacna1c) promoter was abolished by deletion of the downstream regulatory element (DRE), which binds transcriptional repressor DREAM/calsenilin/KChIP3. Imaging DREAM-GFP (green fluorescent protein)-expressing cardiomyocytes showed that CaMKII potentiates the calcium-induced nuclear translocation of DREAM. Thereby CaMKII increases DREAM binding to the DRE consensus sequence of the endogenous Cacna1c gene. By mathematical modelling we demonstrate that the LTCC downregulation through the Ca2+-CaMKII-DREAM cascade constitutes a physiological feedback mechanism enabling cardiomyocytes to adjust the calcium intrusion through LTCCs to the amount of intracellular calcium detected by CaMKII.

Electrophysiological studies of the human heart face the fundamental challenge that experimental data can be acquired only from patients with underlying heart disease. Regarding human atria, there exist sizable gaps in the understanding of the functional role of cellular Ca2+ dynamics, which differ crucially from that of ventricular cells, in the modulation of excitation-contraction coupling. Accordingly, the objective of this study was to develop a mathematical model of the human atrial myocyte that, in addition to the sarcolemmal (SL) ion currents, accounts for the heterogeneity of intracellular Ca2+ dynamics emerging from a structurally detailed sarcoplasmic reticulum (SR). Based on the simulation results, our model convincingly reproduces the principal characteristics of Ca2+ dynamics: 1) the biphasic increment during the upstroke of the Ca2+ transient resulting from the delay between the peripheral and central SR Ca2+ release, and 2) the relative contribution of SL Ca2+ current and SR Ca2+ release to the Ca2+ transient. In line with experimental findings, the model also replicates the strong impact of intracellular Ca2+ dynamics on the shape of the action potential. The simulation results suggest that the peripheral SR Ca2+ release sites define the interface between Ca2+ and AP, whereas the central release sites are important for the fire-diffuse-fire propagation of Ca2+ diffusion. Furthermore, our analysis predicts that the modulation of the action potential duration due to increasing heart rate is largely mediated by changes in the intracellular Na+ concentration. Finally, the results indicate that the SR Ca2+ release is a strong modulator of AP duration and, consequently, myocyte refractoriness/excitability. We conclude that the developed model is robust and reproduces many fundamental aspects of the tight coupling between SL ion currents and intracellular Ca2+ signaling. Thus, the model provides a useful framework for future studies of excitation-contraction coupling in human atrial myocytes., Author Summary In the human heart, the contraction of atrial and ventricular muscle cells is based largely on common mechanisms. There is, however, a fundamental difference in the cellular calcium dynamics that underlie the contractile function. Here, we have developed a computational model of the human atrial cell that convincingly reproduces the experimentally observed characteristics of the electrical activity and the cyclic fluctuations of the intracellular calcium concentration. With the model, we evaluate the relative roles of the most important cellular calcium transport mechanisms and their impact on the electrical behavior of the cell. Our simulations predict that the amount of calcium released from the cellular stores during each electrical cycle crucially regulates the excitability of the human atrial cell. Furthermore, the results indicate that the cellular sodium accumulation related to faster heart rates is one of the main mechanisms driving the adaptation of cardiac electrical activity. Finally, we conclude that the presented model also provides a useful framework for future studies of human atrial cells.

The ability to generate homogeneous intracellular Ca(2+) oscillations at high frequency is the basis of the rhythmic contractions of mammalian cardiac myocytes. While the specific mechanisms and structures enabling homogeneous high-frequency Ca(2+) signals in adult cardiomyocytes are well characterized, it is not known how these kind of Ca(2+) signals are produced in developing cardiomyocytes. Here we investigated the mechanisms reducing spatial and temporal heterogeneity of cytosolic Ca(2+) signals in mouse embryonic ventricular cardiomyocytes. We show that in developing cardiomyocytes the propagating Ca(2+) signals are amplified in cytosol by local Ca(2+) releases. Local releases are based on regular 3-D sarcoplasmic reticulum (SR) structures containing SR Ca(2+) uptake ATPases (SERCA) and Ca(2+) release channels (ryanodine receptors, RyRs) at regular intervals throughout the cytosol. By evoking [Ca(2+)](i)-induced Ca(2+) sparks, the local release sites promote a 3-fold increase in the cytosolic Ca(2+) propagation speed. We further demonstrate by mathematical modelling that without these local release sites the developing cardiomyocytes lose their ability to generate homogeneous global Ca(2+) signals at a sufficiently high frequency. The mechanism described here is robust and indispensable for normal mammalian cardiomyocyte function from the first heartbeats during the early embryonic phase till terminal differentiation after birth. These results suggest that local cytosolic Ca(2+) releases are indispensable for normal cardiomyocyte development and function of developing heart.

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.

Background The cardiomyocyte is a prime example of inherently complex biological system with inter- and cross-connected feedback loops in signalling, forming the basic properties of intracellular homeostasis. Functional properties of cells and tissues have been studied e.g. with powerful tools of genetic engineering, combined with extensive experimentation. While this approach provides accurate information about the physiology at the endpoint, complementary methods, such as mathematical modelling, can provide more detailed information about the processes that have lead to the endpoint phenotype. Results In order to gain novel mechanistic information of the excitation-contraction coupling in normal myocytes and to analyze sophisticated genetically engineered heart models, we have built a mathematical model of a mouse ventricular myocyte. In addition to the fundamental components of membrane excitation, calcium signalling and contraction, our integrated model includes the calcium-calmodulin-dependent enzyme cascade and the regulation it imposes on the proteins involved in excitation-contraction coupling. With the model, we investigate the effects of three genetic modifications that interfere with calcium signalling: 1) ablation of phospholamban, 2) disruption of the regulation of L-type calcium channels by calcium-calmodulin-dependent kinase II (CaMK) and 3) overexpression of CaMK. We show that the key features of the experimental phenotypes involve physiological compensatory and autoregulatory mechanisms that bring the system to a state closer to the original wild-type phenotype in all transgenic models. A drastic phenotype was found when the genetic modification disrupts the regulatory signalling system itself, i.e. the CaMK overexpression model. Conclusion The novel features of the presented cardiomyocyte model enable accurate description of excitation-contraction coupling. The model is thus an applicable tool for further studies of both normal and defective cellular physiology. We propose that integrative modelling as in the present work is a valuable complement to experiments in understanding the causality within complex biological systems such as cardiac myocytes.

When developing large-scale mathematical models of physiology, some reduction in complexity is necessarily required to maintain computational efficiency. A prime example of such an intricate cell is the cardiac myocyte. For the predictive power of the cardiomyocyte models, it is vital to accurately describe the calcium transport mechanisms, since they essentially link the electrical activation to contractility. The removal of calcium from the cytoplasm takes place mainly by the Na + /Ca 2+ exchanger, and the sarcoplasmic reticulum Ca 2+ ATPase (SERCA). In the present study, we review the properties of SERCA, its frequency-dependent and β -adrenergic regulation, and the approaches of mathematical modelling that have been used to investigate its function. Furthermore, we present novel theoretical considerations that might prove useful for the elucidation of the role of SERCA in cardiac function, achieving a reduction in model complexity, but at the same time retaining the central aspects of its function. Our results indicate that to faithfully predict the physiological properties of SERCA, we should take into account the calcium-buffering effect and reversible function of the pump. This ‘uncomplicated’ modelling approach could be useful to other similar transport mechanisms as well.

At the cellular level, one of the most important regulators of myocardial relaxation is the sarcoplasmic reticulum calcium ATPase (SERCA), which is controlled by phosphorylation both directly and indirectly through the endogenous inhibitor phospholamban. According to experimental observations, this regulation is interplay of protein kinase A (PKA), and calcium/calmodulin dependent kinase II (CaMK). Despite the physiological importance of this modulation, the significance of the crosstalk in this dual regulation has not been thoroughly described, and the exact quantitative roles of these two enzymes have remained partly elusive. We use the approach of mathematical modeling to dissect the different aspects of the regulation of SERCA in cardiomyocytes. We present a novel model of SERCA that includes phosphorylation targets for both PKA and CaMK. To study the physiological impact of these regulatory mechanisms, we implement the SERCA model into a mathematical model of a mouse ventricular myocyte. We validate the model by comparing the simulated results to the corresponding in vivo observations, both in physiological phenomena and transgenic test cases. Our results show that under varying levels of beta-adrenergic stimulation, and thus at varying PKA activities, the frequency-dependent changes in the calcium dynamics show a clear dose-dependence. Furthermore, the in silico experiments indicate that these changes are drastically blocked with CaMK inhibitors. The results also point out the diverging time windows of regulation for PKA (∼ tens of seconds) and CaMK (∼ few minutes). Based on the results, we conclude that despite the prominent role of PKA in the beta-adrenergic modulation of calcium dynamics in a cardiac myocyte, both the direct and the indirect effects mediated by CaMK phosphorylation appear to more important for the regulation of SERCA, though the time scale of observation has a significant impact on the quantitative roles of these two enzymes.

In cardiac myocytes, the calcium flux through the release channels (Ryanodine Receptors; RyRs) defines the transient changes of intracellular calcium corresponding to the trigger, i.e., the transmembrane calcium current, and therefore determines the dynamics of the contractile function of myocytes on a beat-to-beat basis. A controversy exists related to the exact mechanisms responsible for the activation and termination of calcium release, as well as to the increased leakiness of RyR, which has been reported in association with various heart failure conditions. Our aim was to develop, based on previously published models, a mathematical model of RyR that would describe both the calcium-dependent dynamics and the regulation of the calcium release by calcium/ calmodulin dependent kinase II (CaMK). We validate the model by comparing the simulated results to in vivo observations, both under normal and CaMK hyperphosphorylation conditions. Results show that the model describes, in a quantitative way, the functional connection between the calcium trigger and release, the dynamic enzymatic regulation, as well as the role of RyR as a component of the whole myocyte. Our results also suggest that CaMK is an important downstream effector in β-adrenergic regulation. We conclude that the presented model is a solid component that can be employed in further modeling studies, e.g., to explore the double-edged role of CaMK in various heart failure conditions.

Background and Aim: Given higher abundance in atria vs. ventricles, and a suggested important role in atrial fibrillation (AF), small-conductance Ca2+-activated K+ channels (SKs) are a promising atrial-selective pharmacological target for AF. As their role in atrial physiology and arrhythmia is not yet fully understood, this study aims to investigate the role of the SK current (IK,Ca) in human atrial myocytes during both sinus rhythm and rapid pacing.Methods and Results: A new mathematical formulation of IK,Ca, replicating characteristic Ca2+-dependent activation and mild voltage rectification, was developed using a broad set of experimental observations in rodent and human myocytes, and incorporated into our human atrial cell model.We validated our updated model by assessing the consequences of IK,Ca inhibition on action potential (AP) properties. When paced at 1 Hz, IK,Ca block prolongs simulated AP by ∼18% (enhancing Ca2+ influx, and consequently intracellular Ca2+ load), increases the effective refractory period (ERP) by ∼16%, depolarizes the resting membrane potential by ∼1.5 mV, and decreases maximum upstroke velocity by ∼15%, all in agreement with ranges observed in human atrial experiments.Next, we used this comprehensive model to investigate the effect of hyper-activation/block of IK,Ca in several arrhythmia-provoking scenarios. Our analysis suggests that IK,Ca is protective against focal arrhythmia (phase-2 and phase-3 early afterdepolarizations, delayed-afterdepolarizations, and triggered activity), but contributes to a reentrant substrate (ERP shortening and alternans).Future directions: We will study the effect of administration of IK,Ca modulators to determine if a therapeutic window for SKs in AF exists. We will also evaluate the synergistic consequences of IK,Ca modulation and (atrial-selective) Na+ current inhibition, to test the hypothesis that a combination of low dose drugs may have higher efficacy than monotherapy.

The progress in the field of human-computer interaction with hand held electronic devices, such as, personal digital assistants (PDAs) and mobile phones searches for new interaction techniques. Proximity sensing extends the concept of computer-human interaction beyond actual physical contact with a device. In this paper, a virtual keyboard implementation is presented and keystroke recognition experiments with the keyboard utilizing proximity measurements are described. An infrared (IR) transceiver array is used for detecting the proximity of a finger. Keystroke recognition accuracy is examined with k-nearest neighbor (k-NN) classifier while a multilayer perceptron (MLP) classifier is designed for online implementation. Experiments and results of keystroke classification are presented for both classifiers. The recognition accuracy, which is between 78% and 99% for k-NN classifier and between 69% and 96% for MLP classifier, depends mainly on the location of a specific key on the keyboard area.