Phenomenological analysis of simple ion channel block in large populations of uncoupled cardiomyocytes.

Current understanding of arrhythmia mechanisms and design of anti-arrhythmic drug therapies hinges on the assumption that myocytes from the same region of a single heart have similar, if not identical, action potential waveforms and drug responses. On the contrary, recent experiments reveal significant heterogeneity in uncoupled healthy myocytes both from different hearts as well as from identical regions within a single heart. In this work, a methodology is developed for quantifying the individual electrophysiological properties of large numbers of uncoupled cardiomyocytes under ion channel block in terms of the parameters values of a conceptual fast-slow model of electrical excitability. The approach is applied to a population of nearly 500 rabbit ventricular myocytes for which action potential duration (APD) before and after the application of the drug nifedipine was experimentally measured (Lachaud et al., 2022, Cardiovasc. Res.). To this end, drug action is represented by a multiplicative factor to an effective ion conductance, a closed form asymptotic expression for APD is derived and inverted to determine model parameters as functions of APD and $\varDelta $APD (drug-induced change in APD) for each myocyte. Two free protocol-related quantities are calibrated to experiment using an adaptive-domain procedure based on an original assumption of optimal excitability. The explicit APD expression and the resulting set of model parameter values allow (a) direct evaluation of conditions necessary to maintain fixed APD or $\varDelta $APD, (b) predictions of the proportion of cells remaining excitable after drug application, (c) predictions of stimulus period dependency and (d) predictions of dose-response curves, the latter being in agreement with additional experimental data.

Optimal heat transport induced by magnetic nanoparticle delivery in vascularised tumours.

We describe a novel mathematical model for blood flow, delivery of nanoparticles, and heat transport in vascularised tumour tissue. The model, which is derived via the asymptotic homogenisation technique, provides a link between the macroscale behaviour of the system and its underlying, tortuous micro-structure, as parametrised in Penta and Ambrosi (2015). It consists of a double Darcy's law, coupled with a double advection-diffusion-reaction system describing heat transport, and an advection-diffusion-reaction equation for transport and adhesion of particles. Particles are assumed sufficiently large and do not extravasate to the tumour interstitial space but blood and heat can be exchanged between the two compartments. Numerical simulations of the model are performed using a finite element method to investigate cancer hyperthermia induced by the application of magnetic field applied to injected iron oxide nanoparticles. Since tumour microvasculature is more tortuous than that of healthy tissue and thus suboptimal in terms of fluid and drug transport, we study the influence of the vessels' geometry on tumour temperature. Effective and safe hyperthermia treatment requires tumour temperature within certain target range, generally estimated between 42 °C and 46 °C, for a certain target duration, typically 0.5h to 2h. As temperature is difficult to measure in situ, we use our model to determine the ranges of tortuosity of the microvessels, magnetic intensity, injection time, wall shear stress rate, and concentration of nanoparticles required to achieve given target conditions.

Electrophysiological heterogeneity in large populations of rabbit ventricular cardiomyocytes.

AIMS: Cardiac electrophysiological heterogeneity includes: (i) regional differences in action potential (AP) waveform, (ii) AP waveform differences in cells isolated from a single region, (iii) variability of the contribution of individual ion currents in cells with similar AP durations (APDs). The aim of this study is to assess intra-regional AP waveform differences, to quantify the contribution of specific ion channels to the APD via drug responses and to generate a population of mathematical models to investigate the mechanisms underlying heterogeneity in rabbit ventricular cells. METHODS AND RESULTS: APD in ∼50 isolated cells from subregions of the LV free wall of rabbit hearts were measured using a voltage-sensitive dye. When stimulated at 2 Hz, average APD90 value in cells from the basal epicardial region was 254 ± 25 ms (mean ± standard deviation) in 17 hearts with a mean interquartile range (IQR) of 53 ± 17 ms. Endo-epicardial and apical-basal APD90 differences accounted for ∼10% of the IQR value. Highly variable changes in APD occurred after IK(r) or ICa(L) block that included a sub-population of cells (HR) with an exaggerated (hyper) response to IK(r) inhibition. A set of 4471 AP models matching the experimental APD90 distribution was generated from a larger population of models created by random variation of the maximum conductances (Gmax) of 8 key ion channels/exchangers/pumps. This set reproduced the pattern of cell-specific responses to ICa(L) and IK(r) block, including the HR sub-population. The models exhibited a wide range of Gmax values with constrained relationships linking ICa(L) with IK(r), ICl, INCX, and INaK. CONCLUSION: Modelling the measured range of inter-cell APDs required a larger range of key Gmax values indicating that ventricular tissue has considerable inter-cell variation in channel/pump/exchanger activity. AP morphology is retained by relationships linking specific ionic conductances. These interrelationships are necessary for stable repolarization despite large inter-cell variation of individual conductances and this explains the variable sensitivity to ion channel block.

Conventional rigid 2D substrates cause complex contractile signals in monolayers of human induced pluripotent stem cell-derived cardiomyocytes.

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CM) in monolayers interact mechanically via cell-cell and cell-substrate adhesion. Spatiotemporal features of contraction were analysed in hiPSC-CM monolayers (1) attached to glass or plastic (Young's modulus (E) >1 GPa), (2) detached (substrate-free) and (3) attached to a flexible collagen hydrogel (E = 22 kPa). The effects of isoprenaline on contraction were compared between rigid and flexible substrates. To clarify the underlying mechanisms, further gene expression and computational studies were performed. HiPSC-CM monolayers exhibited multiphasic contractile profiles on rigid surfaces in contrast to hydrogels, substrate-free cultures or single cells where only simple twitch-like time-courses were observed. Isoprenaline did not change the contraction profile on either surface, but its lusitropic and chronotropic effects were greater in hydrogel compared with glass. There was no significant difference between stiff and flexible substrates in regard to expression of the stress-activated genes NPPA and NPPB. A computational model of cell clusters demonstrated similar complex contractile interactions on stiff substrates as a consequence of cell-to-cell functional heterogeneity. Rigid biomaterial surfaces give rise to unphysiological, multiphasic contractions in hiPSC-CM monolayers. Flexible substrates are necessary for normal twitch-like contractility kinetics and interpretation of inotropic interventions. KEY POINTS: Spatiotemporal contractility analysis of human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM) monolayers seeded on conventional, rigid surfaces (glass or plastic) revealed the presence of multiphasic contraction patterns across the monolayer with a high variability, despite action potentials recorded in the same areas being identical. These multiphasic patterns are not present in single cells, in detached monolayers or in monolayers seeded on soft substrates such as a hydrogel, where only 'twitch'-like transients are observed. HiPSC-CM monolayers that display a high percentage of regions with multiphasic contraction have significantly increased contractile duration and a decreased lusotropic drug response. There is no indication that the multiphasic contraction patterns are associated with significant activation of the stress-activated NPPA or NPPB signalling pathways. A computational model of cell clusters supports the biological findings that the rigid surface and the differential cell-substrate adhesion underly multiphasic contractile behaviour of hiPSC-CMs.

Electrophysiology of hiPSC-Cardiomyocytes Co-Cultured with HEK Cells Expressing the Inward Rectifier Channel.

The immature electrophysiology of human-induced pluripotent stem cell-derived cardiomyocytes (hiCMs) complicates their use for therapeutic and pharmacological purposes. An insufficient inward rectifying current (IK1) and the presence of a funny current (if) cause spontaneous electrical activity. This study tests the hypothesis that the co-culturing of hiCMs with a human embryonic kidney (HEK) cell-line expressing the Kir2.1 channel (HEK-IK1) can generate an electrical syncytium with an adult-like cardiac electrophysiology. The mechanical activity of co-cultures using different HEK-IK1:hiCM ratios was compared with co-cultures using wildtype (HEK-WT:hiCM) or hiCM alone on days 3-8 after plating. Only ratios of 1:3 and 1:1 showed a significant reduction in spontaneous rate at days 4 and 6, suggesting that IK1 was influencing the electrophysiology. Detailed analysis at day 4 revealed an increased incidence of quiescent wells or sub-areas. Electrical activity showed a decreased action potential duration (APD) at 20% and 50%, but not at 90%, alongside a reduced amplitude of the aggregate AP signal. A computational model of the 1:1 co-culture replicates the electrophysiological effects of HEK-WT. The addition of the IK1 conductance reduced the spontaneous rate and APD20, 50 and 90, and minor variation in the intercellular conductance caused quiescence. In conclusion, a 1:1 co-culture HEK-IK1:hiCM caused changes in electrophysiology and spontaneous activity consistent with the integration of IK1 into the electrical syncytium. However, the additional electrical effects of the HEK cell at 1:1 increased the possibility of electrical quiescence before sufficient IK1 was integrated into the syncytium.

Addendum: Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling.

The analytical theory of our earlier study (Mortensen et al., 2021, Math. Med. Biol., 38, 106-131) is extended to address the outstanding cases of fibroblast barrier distribution and myocyte strait distribution. In particular, closed-form approximations to the resting membrane potential and to the critical parameter values for propagation are derived for these two non-uniform fibroblast distributions and are in good agreement with numerical estimates.

Action potential propagation and block in a model of atrial tissue with myocyte-fibroblast coupling.

The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias, but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte-fibroblast coupling. In particular, three idealized fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait-all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealized fibroblast distribution, and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte-fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.

Conditions for propagation and block of excitation in an asymptotic model of atrial tissue.

Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction of the models. Earlier results have shown that the asymptotics of cardiac equations are nonstandard. Here we apply such a novel asymptotic method to an ionic model of human atrial tissue to obtain a reduced but accurate model for the description of excitation fronts. Numerical simulations of spiral waves in atrial tissue show that wave fronts of propagating action potentials break up and self-terminate. Our model, in particular, yields a simple analytical criterion of propagation block, which is similar in purpose but completely different in nature to the "Maxwell rule" in the FitzHugh-Nagumo type models. Our new criterion agrees with direct numerical simulations of breakup of reentrant waves.