In Vivo and In Silico Investigation Into Mechanisms of Frequency Dependence of Repolarization Alternans in Human Ventricular Cardiomyocytes

Supplemental Digital Content is available in the text.


CHOICE OF MODEL OF HUMAN VENTRICULAR ELECTROPHYSIOLOGY
In silico investigations into the network of mechanisms underlying the generation of the two types of repolarization alternans in human ventricular cardiomyocytes were based on the O'Hara et al. model 1 (ORd). Even though several human ventricular models have been published in the past, the ORd model is now the gold standard for human studies of pro-arrhythmia, the only one extensively constructed and validated based on recordings over 140 human hearts, and the only model dimmed suitable for regulatory used by the USA Food and Drug Administration (see CiPA initiative). Importantly, the ORd model is the only one to include detailed formulations for the Ca 2+ subsystem and Ca 2+ extrusion dynamics based on human electrophysiology data. This is supported by the comparison to other models of the human ventricular action potential published prior to the ORd model, and specifically the well-known Grandi-Bers (GB) and Ten Tusccher-Panfilov (TP) models. 2,3

BIOMARKER CALCULATION OF SIMULATED ACTION POTENTIALS
The stimulation protocol in the simulations mimicked the one applied in vivo. In silico models were stimulated for 1000 beats at each of the CLs in a step protocol from 600ms to 350ms to reach their steady states. For each of the human models, the following biomarkers were calculated at steady state for each of the 6 considered CLs: APD (at three repolarization levels: APD 30 , APD 80 , APD 90 ), APD tri (triangulation), CaTD (calcium transient duration), UPD (upstroke duration), V max (peak upstroke voltage), RMP (resting membrane potential), APA (action potential amplitude), CaT max (systolic Ca 2+ level) and CaT min (diastolic Ca 2+ level). See Supplemental Table II for a detailed description of biomarkers calculation. Peak current and flux magnitudes were calculated as the maximum absolute value of their current densities during the AP. We also calculated two additional property referred to as sarcoplasmic reticulum calcium balance (SRCB) and sarcolemmal calcium balance (SCB), defined as the overall Ca 2+ flow through the SR and cell membrane, respectively (Supplemental Table II).
The occurrence of APD (or CaTD) alternans was defined as a difference greater than 5ms between APD 80 (or CaTD 80 ) in the last two APs of the pacing train.

CALIBRATION OF THE HUMAN IN SILICO MODELS POPULATION
With our methodology, we specifically propose the investigation of variability in in vivo human ventricular rate dependence using in silico investigations with the population of human ventricular models. The in vivo recordings were analysed and the histograms shown in Supplemental Figure I show the distribution of ARI values for each of the CLs from 600 to 350ms. A rigorous analysis of the data was conducted, as described in Supplemental Figure II, to obtain physiological ranges of ARI variability in vivo for each CL while avoiding including possible outliers. This was done by fitting the aggregated ARIs at each CLs to a skewed normal distribution, and the cumulative distribution function was used to obtain 95% physiological ARI ranges to exclude the effects of extreme values but to still consider the variability in the data, as one of the key goals of our study.
The initial 10000 models in the human population were then filtered to only retain the models yielding APD values within the 95% in vivo ARI ranges for each of the CLs (Filter 1). In addition, we also ensured that each of the APD restitution curves was monotonically decreasing until the eventual occurrence of alternans (Filter 2). This calibration for rate dependence based on the in vivo data was crucial as it allowed retaining critical information on in vivo human rate dependence in the in silico study, an aspect that is key for the study of repolarization alternans.
In addition to calibrating the in silico population with the human in vivo rate dependence data (Filters 1 and 2), we also considered the following filters based on well-known properties of undiseased human ventricular cardiomyocytes reported in the literature: It is also important to stress that our approach does not aim to find a 1:1 match between the in silico and in vivo data, but rather to provide a tool to explore variability in human electrophysiology. This means that for example, a same model could indeed be representative of the rate dependent behavior of several sites in vivo. With the calibration with ensure that the human models in the population are representative of physiology variability in the in vivo data and cover a wide range of possible underlying combinations of ionic properties as illustrated Supplemental Figure III and analysed in the main body of the Manuscript. Supplemental Figure IV shows the effect of each of the Filters in constraining the distribution of each of the ionic properties. The consideration of a wide range of variability adds two advantages to the study. Firstly, we evaluate the consistency of the mechanisms of different alternans types when variability in ionic currents is considered within the population. Secondly, the calibrated population supports the model independency of the findings with respect to the parameter values, which is often compromised in studies using a single action potential model. Indeed in our study, we use over 2000 models to investigate the consistency in the mechanisms of alternans in human, all of them displaying physiological human electrophysiology consistent with the in vivo recordings too.

CALCULATION OF IN VIVO ALTERNANS AND IN VIVO RESTITUTION CURVES
The ventricles were stimulated from the apex of the left ventricle. The pattern of activation was consistent for different cycle lengths, being the correlation between the activation sequences for different S1 very high. In unipolar electrograms recorded in vivo, restitution curves illustrating Eye or Fork-type alternans are constructed as follows: Definition of alternans: APD alternans was identified as being present whenever the beat-to-beat variation of ARI, ΔARI = ARI i -ARI i-1 , exhibited an alternating pattern (long, short, long, short, etc) for at least 7 consecutive beats. Alternans magnitude was then calculated as median (|ΔARI k |) where k represents the heart beats exhibiting an alternating pattern. The first 7 beats of each train of steady state S1 paced beats are discarded in order not to include alternans due to fast rate adaptation. If at a given cycle length alternans occur then two points are plotted. These 2 points correspond to ARI m ±ALT/2, where ARI m is the median ARI calculated over the ARI that are actually alternating, and ALT is the alternans magnitude. The span between the 2 points is equal to the alternans magnitude.

Classification of
Initial alternans CL for in vivo Eye/Fork alternans: the longest pacing cycle length when alternans occur at a site.

ACTION POTENTIAL CLAMP SIMULATION
For each single model, two protocols were generated from its steady state: two consecutive long beats (L+L) or two consecutive short beats (S+S). The simulation started from the end of the 1000 th beat, and then either the L+L protocol or the S+S protocol were applied.

ICAL KINETICS VARIATION ANALYSIS
I CaL activation time constant τd, inactivation time constant τf and recovery from Ca 2+ dependent inactivation time constant τj were decreased (×50% or 75%) or increased (×125% or 150%), and models were still paced for 1000 beats to reach steady states. Coupling from CaT alternans to APD alternans is determined by the relative balance between I NaCa and I CaL . Under control condition, I NaCa is the major coupling link.  The distribution of several ionic parameters tended to be asymmetric, such as those for G CaL , G NaCa , G NaK and P Jup , whereas the distribution of G Kr was bell-shaped. Small values in G Na were completely rejected after the calibration, which indicated the irreplaceable role of this Na + current in the action potential upstroke.