Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes.

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD90, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in ICaL, INCX, and IKr, and decreases in IK1, Ib,Cl, IKur, ISERCA, and Ito are correlated with higher Smax values. The LIME algorithm determined that INaK plays a significant role in determining Smax as well as Ito and IKur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in INaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of INaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

Pro-Arrhythmogenic Effects of Heterogeneous Tissue Curvature　- A Suggestion for Role of Left Atrial Appendage in Atrial Fibrillation.

BACKGROUND: The arrhythmogenic role of complex atrial morphology has not yet been clearly elucidated. We hypothesized that bumpy tissue geometry can induce action potential duration (APD) dispersion and wavebreak in atrial fibrillation (AF). Methods and Results: We simulated a 2D-bumpy atrial model by varying the degree of bumpiness, and 3D-left atrial (LA) models integrated by LA computed tomographic (CT) images taken from 14 patients with persistent AF. We also analyzed wave-dynamic parameters with bipolar electrograms during AF and compared them with LA-CT geometry in 30 patients with persistent AF. In the 2D-bumpy model, APD dispersion increased (P<0.001) and wavebreak occurred spontaneously when the surface bumpiness was greater, showing phase transition-like behavior (P<0.001). The bumpiness gradient 2D-model showed that spiral wave drifted in the direction of higher bumpiness, and phase singularity (PS) points were mostly located in areas with higher bumpiness. In the 3D-LA model, PS density was higher in the LA appendage (LAA) compared with other parts of the LA (P<0.05). In 30 persistent-AF patients, the surface bumpiness of LAA was 5.8-fold that of other LA parts (P<0.001), and exceeded critical bumpiness to induce wavebreak. Wave dynamics complexity parameters were consistently dominant in the LAA (P<0.001). CONCLUSIONS: Bumpy tissue geometry promoted APD dispersion, wavebreak, and spiral wave drift in in-silico human atrial tissue, and corresponded to clinical electroanatomical maps.

Spatial reproducibility of complex fractionated atrial electrogram depending on the direction and configuration of bipolar electrodes: an in-silico modeling study.

Although 3D-complex fractionated atrial electrogram (CFAE) mapping is useful in radiofrequency catheter ablation for persistent atrial fibrillation (AF), the directions and configuration of the bipolar electrodes may affect the electrogram. This study aimed to compare the spatial reproducibility of CFAE by changing the catheter orientations and electrode distance in an in-silico left atrium (LA). We conducted this study by importing the heart CT image of a patient with AF into a 3D-homogeneous human LA model. Electrogram morphology, CFAE-cycle lengths (CLs) were compared for 16 different orientations of a virtual bipolar conventional catheter (conv-cath: size 3.5 mm, inter-electrode distance 4.75 mm). Additionally, the spatial correlations of CFAE-CLs and the percentage of consistent sites with CFAE-CL<120 ms were analyzed. The results from the conv-cath were compared with that obtained using a mini catheter (mini-cath: size 1 mm, inter-electrode distance 2.5 mm). Depending on the catheter orientation, the electrogram morphology and CFAE-CLs varied (conv-cath: 11.5±0.7% variation, mini-cath: 7.1±1.2% variation), however the mini-cath produced less variation of CFAE-CL than conv-cath (p<0.001). There were moderate spatial correlations among CFAE-CL measured at 16 orientations (conv-cath: r=0.3055±0.2194 vs. mini-cath: 0.6074±0.0733, p<0.001). Additionally, the ratio of consistent CFAE sites was higher for mini catheter than conventional one (38.3±4.6% vs. 22.3±1.4%, p<0.05). Electrograms and CFAE distribution are affected by catheter orientation and electrode configuration in the in-silico LA model. However, there was moderate spatial consistency of CFAE areas, and narrowly spaced bipolar catheters were less influenced by catheter direction than conventional catheters.

Isolation of human antigen-specific regulatory T cells with high suppressive function.

Adoptive transfer of regulatory T (Treg) cells could be an alternative to chronic immunosuppression for prevention of allogeneic graft rejection. While polyspecific Treg cells can prevent immune responses under lymphopenic conditions, Ag-specific Treg cells are needed to treat autoimmunity and graft rejection. Yet, reliable markers for Ag-specific Treg cells are missing. We report that latency-associated peptide (LAP) and glycoprotein A repetitions predominant (GARP) can identify human Ag-specific Treg cells. In addition, we show that the depletion of CD154(+) cells from LAP(+) or GARP(+) Treg cells increases the Treg-cell purity to over 90%, as assessed by epigenetic analysis. These Ag-specific Treg cells can be isolated magnetically and might contribute to the development of GMP-based protocols. In addition, Ag-specific Treg cells are functionally far superior to CD4(+) CD25(high) or CD4(+) CD25(high) CD127(low) Treg cells in vitro and in preventing strong alloreactions in humanized mice. They could, therefore, have a high therapeutic potential for the control of alloimmune, autoimmune, and allergic immune responses in patients.

Parameter sensitivity analysis of stochastic models provides insights into cardiac calcium sparks.

We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca(2+) release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca(2+) spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca(2+) spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca(2+) spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca(2+) sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca(2+) release unit structures, and the regression model both accurately predicts changes in Ca(2+) spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.

Decoding myocardial Ca²âº signals across multiple spatial scales: a role for sensitivity analysis.

Numerous studies have employed mathematical modeling to quantitatively understand release of Ca(2+) from the sarcoplasmic reticulum (SR) in the heart. Models have been used to investigate physiologically important phenomena such as triggering of SR Ca(2+) release by Ca(2+) entry across the cell membrane and spontaneous leak of Ca(2+) from the SR in quiescent heart cells. In this review we summarize studies that have modeled myocardial Ca(2+) at different spatial scales: the sub-cellular level, the cellular level, and the multicellular level. We discuss each category of models from the standpoint of parameter sensitivity analysis, a common simulation procedure that can generate quantitative, comprehensive predictions about how changes in conditions influence model output. We propose that this is a useful perspective for conceptualizing models, in part because a sensitivity analysis requires the investigator to define the relevant parameters and model outputs. This procedure therefore helps to illustrate the capabilities and limitations of each model. We further suggest that in future studies, sensitivity analyses will aid in simplifying complex models and in suggesting experiments to differentiate between competing models built with different assumptions. We conclude with a discussion of unresolved questions that are likely to be addressed over the next several years.

EPMA quantification on the chemical composition of retained austenite in a Fe-Mn-Si-C-based multi-phase steel.

An electron probe X-ray microanalyzer (EPMA) is an essential tool for studying chemical composition distribution in the microstructure. Quantifying chemical composition using standard specimens is commonly used to determine the composition of individual phases. However, the local difference in chemical composition in the standard specimens brings the deviation of the quantified composition from the actual one. This study introduces how to overcome the error of quantification in EPMA in the practical aspect. The obtained results are applied to evaluate the chemical composition of retained austenite in multi-phase steel. Film-type austenite shows higher carbon content than blocky-type one. The measured carbon contents of the retained austenite show good coherency with the calculated value from the X-ray diffraction.

Complex and rate-dependent beat-to-beat variations in Ca2+ transients of canine Purkinje cells.

Purkinje fibers play an essential role in transmitting electrical impulses through the heart, but they may also serve as triggers for arrhythmias linked to defective intracellular calcium (Ca(2+)) regulation. Although prior studies have extensively characterized spontaneous Ca(2+) release in nondriven Purkinje cells, little attention has been paid to rate-dependent changes in Ca(2+) transients. Therefore we explored the behaviors of Ca(2+) transients at pacing rates ranging from 0.125 to 3 Hz in single canine Purkinje cells loaded with fluo3 and imaged with a confocal microscope. The experiments uncovered the following novel aspects of Ca(2+) regulation in Purkinje cells: 1) the cells exhibit a negative Ca(2+)-frequency relationship (at 2.5 Hz, Ca(2+) transient amplitude was 66 ± 6% smaller than that at 0.125 Hz); 2) sarcoplasmic reticulum (SR) Ca(2+) release occurs as a propagating wave at very low rates but is localized near the cell membrane at higher rates; 3) SR Ca(2+) load declines modestly (10 ± 5%) with an increase in pacing rate from 0.125 Hz to 2.5 Hz; 4) Ca(2+) transients show considerable beat-to-beat variability, with greater variability occurring at higher pacing rates. Analysis of beat-to-beat variability suggests that it can be accounted for by stochastic triggering of local Ca(2+) release events. Consistent with this hypothesis, an increase in triggering probability caused a decrease in the relative variability. These results offer new insight into how Ca(2+) release is normally regulated in Purkinje cells and provide clues regarding how disruptions in this regulation may lead to deleterious consequences such as arrhythmias.

The mean of fasting, 1-h, and 2-h plasma glucose levels is superior to each separate index in predicting diabetes.

AIMS: The fasting, 1-h, and 2-h plasma glucose (PG) levels during oral glucose tolerance test represent different glucose metabolic functions. We examined whether averaging these PG indices (GLUM0.60.120) results in a better predictor of future type 2 diabetes (T2DM). METHODS: 7533 participants were followed up biannually for 12 years. Hazard ratios (HRs), area under the curve (AUC) of the receiver-operating characteristic, and the net reclassification index (NRI) for T2DM were calculated to compare the discriminative ability of GLUM0.60.120 versus other PG indices. RESULTS: The adjusted HRs and 95% confidence intervals for an increase in SD of GLUM0.60.120 was 2.50 (2.36-2.65) and 1.88 (1.73-2.04) in T2DM-free and normal glucose tolerance (NGT) participants, respectively. The AUC of GLUM0.60.120 was higher than that of fasting PG, 1-h, and 2-h PG values for T2DM-free (0.79 versus 0.67, 0.77, and 0.73) and NGT (0.73 versus 0.65, 0.72, and 0.61). The model using GLUM0.60.120 improved the classification of the models with fasting PG, 1-h, and 2-h PG values (NRI: 0.369, 0.272, and 0.282 for T2DM-free and 0.249, 0.131, and 0.351 for NGT participants with all p < 0.001). CONCLUSIONS: The mean of fasting, 1-h, and 2-h PG levels predicts future T2DM better than each index.

A reanalysis of competing hypotheses for the spread of the California sea otter.

From 1938 to 1972, the range of California sea otters (Enhydra lutris nereis) expanded with the northern and southern fronts spreading at rates of approximately 1.4 km/yr and 3.1 km/yr, respectively. J. A. Lubina and S. A. Levin proposed the following three factors to explain the large disparity in spread rates: (1) regional differences in dispersal; (2) regional differences in population growth; and (3) advection due to the known presence of a southerly flowing offshore current. While Lubina and Levin used a reaction-diffusion framework to argue for large differences in dispersal, our approach uses a stage-structured integrodifference matrix model to show that relatively minor differences in survival provide a more parsimonious explanation for the disparity in spread rates; especially if the survival rates between the northern and southern groups differ in more than one life stage. The argument is made that many of the present estimates for otter survival rates span intervals wide enough to explain the different spread rates--even more so in the likely case that advection plays at least a minor role in otter movement.

Development and evaluation of ICNP-based Electronic Nursing Record System.

This study was conducted to cross-map nursing statements with International Classification of Nursing Practice (ICNP) Version 1 and to develop and evaluate ICNP-based Electronic Nursing Record System. Among the 7,631 nursing statements which were cross-mapped, 5,970(78.2%) nursing statements were completely expressed and 1,520(19.9%) statements were partially expressed. ICNP-based Electronic Nursing Record System was developed for the Asan Medical Center in Korea. Most nursing statements (6,671 of 7,931, 87.0%) and Most cross-mapped ICNP terms (965 of 1,015, 94.9%) were documented by user in all the units from July, 2007 to August, 2008.

A clinical-decision support system for the nursing process in the ENR.

This study was conducted to develop the clinical-decision support system for the nursing process in the Electronic nursing record system. Nursing diagnoses were linked to 4 components of the nursing process (except for diagnoses) and applied to ENR in 2007.

A calcium-induced calcium release mechanism mediated by calsequestrin.

Calcium (Ca(2+))-induced Ca(2+) release (CICR) is widely accepted as the principal mechanism linking electrical excitation and mechanical contraction in cardiac cells. The CICR mechanism has been understood mainly based on binding of cytosolic Ca(2+) with ryanodine receptors (RyRs) and inducing Ca(2+) release from the sarcoplasmic reticulum (SR). However, recent experiments suggest that SR lumenal Ca(2+) may also participate in regulating RyR gating through calsequestrin (CSQ), the SR lumenal Ca(2+) buffer. We investigate how SR Ca(2+) release via RyR is regulated by Ca(2+) and calsequestrin (CSQ). First, a mathematical model of RyR kinetics is derived based on experimental evidence. We assume that the RyR has three binding sites, two cytosolic sites for Ca(2+) activation and inactivation, and one SR lumenal site for CSQ binding. The open probability (P(o)) of the RyR is found by simulation under controlled cytosolic and SR lumenal Ca(2+). Both peak and steady-state P(o) effectively increase as SR lumenal Ca(2+) increases. Second, we incorporate the RyR model into a CICR model that has both a diadic space and the junctional SR (jSR). At low jSR Ca(2+) loads, CSQs are more likely to bind with the RyR and act to inhibit jSR Ca(2+) release, while at high SR loads CSQs are more likely to detach from the RyR, thereby increasing jSR Ca(2+) release. Furthermore, this CICR model produces a nonlinear relationship between fractional jSR Ca(2+) release and jSR load. These findings agree with experimental observations in lipid bilayers and cardiac myocytes.

In vitro and in vivo assessment of biomedical Mg-Ca alloys for bone implant applications.

BACKGROUND: Magnesium (Mg)-based alloys are considered to be promising materials for implant application due to their excellent biocompatibility, biodegradability, and mechanical properties close to bone. However, low corrosion resistance and fast degradation are limiting their application. Mg-Ca alloys have huge potential owing to a similar density to bone, good corrosion resistance, and as Mg is essential for Ca incorporation into bone. The objective of the present work is to determine the in vitro degradation and in vivo performance of binary Mg- xCa alloy ( x = 0.5 or 5.0 wt%) to assess its usability for degradable implant applications. METHODS: Microstructural evolutions for Mg- xCa alloys were characterized by optical, SEM, EDX, and XRD. In vitro degradation tests were conducted via immersion test in phosphate buffer saline solution. In vivo performance in terms of interface, biocompatibility, and biodegradability of Mg- xCa alloys was examined by implanting samples into rabbit femoral condyle for 2 and 4 weeks. RESULTS: Microstructural results showed the enhancement in intermetallic Mg2Ca phase with increase in Ca content. Immersion tests revealed that the dissolution rate varies linearly, with Ca content exhibiting more hydrogen gas evolution, increased pH, and higher degradation for Mg-5.0Ca alloy. In vivo studies showed good biocompatibility with enhanced bone formation for Mg-0.5Ca after 4 weeks of implantation compared with Mg-5.0Ca alloy. Higher initial corrosion rate with prolonged inflammation and rapid degradation was noticed in Mg-5.0Ca compared with Mg-0.5Ca alloy. CONCLUSIONS: The results suggest that Mg-0.5Ca alloy could be used as a temporary biodegradable implant material for clinical applications owing to its controlled in vivo degradation, reduced inflammation, and high bone-formation capability.

Ganglionated plexi stimulation induces pulmonary vein triggers and promotes atrial arrhythmogenecity: In silico modeling study.

BACKGROUND: The role of the autonomic nervous system (ANS) on atrial fibrillation (AF) is difficult to demonstrate in the intact human left atrium (LA) due to technical limitations of the current electrophysiological mapping technique. We examined the effects of the ANS on the initiation and maintenance of AF by employing a realistic in silico human left atrium (LA) model integrated with a model of ganglionated plexi (GPs). METHODS: We incorporated the morphology of the GP and parasympathetic nerves in a three-dimensional (3D) realistic LA model. For the model of ionic currents, we used a human atrial model. GPs were stimulated by increasing the IK[ACh], and sympathetic nerve stimulation was conducted through a homogeneous increase in the ICa-L. ANS-induced wave-dynamics changes were evaluated in a model that integrated a patient's LA geometry, and we repeated simulation studies using LA geometries from 10 different patients. RESULTS: The two-dimensional model of pulmonary vein (PV) cells exhibited late phase 3 early afterdepolarization-like activity under 0.05µM acetylcholine (ACh) stimulation. In the 3D simulation model, PV tachycardia was induced, which degenerated to AF via GP (0.05µM ACh) and sympathetic (7.0×ICa-L) stimulations. Under sustained AF, local reentries were observed at the LA-PV junction. We also observed that GP stimulation reduced the complex fractionated atrial electrogram (CFAE)-cycle length (CL, p<0.01) and the life span of phase singularities (p<0.01). GP stimulation also increased the overlap area of the GP and CFAE areas (CFAE-CL≤120ms, p<0.01). When 3 patterns of virtual ablations were applied to the 3D AF models, circumferential PV isolation including the GP was the most effective in terminating AF. CONCLUSION: Cardiac ANS stimulations demonstrated triggered activity, automaticity, and local reentries at the LA-PV junction, as well as co-localized GP and CFAE areas in the 3D in silico GP model of the LA.

The Spatiotemporal Stability of Dominant Frequency Sites in In-Silico Modeling of 3-Dimensional Left Atrial Mapping of Atrial Fibrillation.

BACKGROUND: We previously reported that stable rotors were observed in in-silico human atrial fibrillation (AF) models, and were well represented by dominant frequency (DF). We explored the spatiotemporal stability of DF sites in 3D-AF models imported from patient CT images of the left atrium (LA). METHODS: We integrated 3-D CT images of the LA obtained from ten patients with persistent AF (male 80%, 61.8 ± 13.5 years old) into an in-silico AF model. After induction, we obtained 6 seconds of AF simulation data for DF analyses in 30 second intervals (T1-T9). The LA was divided into ten sections. Spatiotemporal changes and variations in the temporal consistency of DF were evaluated at each section of the LA. The high DF area was defined as the area with the highest 10% DF. RESULTS: 1. There was no spatial consistency in the high DF distribution at each LA section during T1-T9 except in one patient (p = 0.027). 2. Coefficients of variation for the high DF area were highly different among the ten LA sections (p < 0.001), and they were significantly higher in the four pulmonary vein (PV) areas, the LA appendage, and the peri-mitral area than in the other LA sections (p < 0.001). 3. When we conducted virtual ablation of 10%, 15%, and 20% of the highest DF areas (n = 270 cases), AF was changed to atrial tachycardia (AT) or terminated at a rate of 40%, 57%, and 76%, respectively. CONCLUSIONS: Spatiotemporal consistency of the DF area was observed in 10% of AF patients, and high DF areas were temporally variable. Virtual ablation of DF is moderately effective in AF termination and AF changing into AT.

Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity.

BACKGROUND: Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation. METHODS: Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed. RESULTS: 1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area. CONCLUSION: Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF.

A New Efficient Method for Detecting Phase Singularity in Cardiac Fibrillation.

BACKGROUND: The point of phase singularity (PS) is considered to represent a spiral wave core or a rotor in cardiac fibrillation. Computational efficiency is important for detection of PS in clinical electrophysiology. We developed a novel algorithm for highly efficient and robust detection of PS. METHODS: In contrast to the conventional method, which calculates PS based on the line integral of the phase around a PS point equal to ±2π (the Iyer-Gray method), the proposed algorithm (the location-centric method) looks for the phase discontinuity point at which PS actually occurs. We tested the efficiency and robustness of these two methods in a two-dimensional mathematical model of atrial fibrillation (AF), with and without remodeling of ionic currents. RESULTS: 1. There was a significant association, in terms of the Hausdorff distance (3.30 ± 0.0 mm), between the PS points measured using the Iyer-Gray and location-centric methods, with almost identical PS trajectories generated by the two methods. 2. For the condition of electrical remodeling of AF (0.3 × ICaL), the PS points calculated by the two methods were satisfactorily co-localized (with the Hausdorff distance of 1.64 ± 0.09 mm). 3. The proposed location-centric method was substantially more efficient than the Iyer-Gray method, with a 28.6-fold and 28.2-fold shorter run times for the control and remodeling scenarios, respectively. CONCLUSION: We propose a new location-centric method for calculating PS, which is robust and more efficient compared with the conventionally used method.

The Contribution of Ionic Currents to Rate-Dependent Action Potential Duration and Pattern of Reentry in a Mathematical Model of Human Atrial Fibrillation.

Persistent atrial fibrillation (PeAF) in humans is characterized by shortening of action potential duration (APD) and attenuation of APD rate-adaptation. However, the quantitative influences of particular ionic current alterations on rate-dependent APD changes, and effects on patterns of reentry in atrial tissue, have not been systematically investigated. Using mathematical models of human atrial cells and tissue and performing parameter sensitivity analysis, we evaluated the quantitative contributions to action potential (AP) shortening and APD rate-adaptation of ionic current remodeling seen with PeAF. Ionic remodeling in PeAF was simulated by reducing L-type Ca2+ channel current (ICaL), increasing inward rectifier K+ current (IK1) and modulating five other ionic currents. Parameter sensitivity analysis, which quantified how each ionic current influenced APD in control and PeAF conditions, identified interesting results, including a negative effect of Na+/Ca2+ exchange on APD only in the PeAF condition. At high pacing rate (2 Hz), electrical remodeling in IK1 alone accounts for the APD reduction of PeAF, but at slow pacing rate (0.5 Hz) both electrical remodeling in ICaL alone (-70%) and IK1 alone (+100%) contribute equally to the APD reduction. Furthermore, AP rate-adaptation was affected by IKur in control and by INaCa in the PeAF condition. In a 2D tissue model, a large reduction (-70%) of ICaL becomes a dominant factor leading to a stable spiral wave in PeAF. Our study provides a quantitative and unifying understanding of the roles of ionic current remodeling in determining rate-dependent APD changes at the cellular level and spatial reentry patterns in tissue.

Fibrillation number based on wavelength and critical mass in patients who underwent radiofrequency catheter ablation for atrial fibrillation.

The heart characteristic length, the inverse of conduction velocity (CV), and the inverse of the refractory period are known to determine vulnerability to cardiac fibrillation (fibrillation number, FibN) in in silico or ex vivo models. The purpose of this study was to validate the accuracy of FibN through in silico atrial modeling and to evaluate its clinical application in patients with atrial fibrillation (AF) who had undergone radiofrequency catheter ablation. We compared the maintenance duration of AF at various FibNAF values using in silico bidomain atrial modeling. Among 60 patients (72% male, 54±13 years old, 82% with paroxysmal AF) who underwent circumferential pulmonary vein isolation (CPVI) for AF rhythm control, we examined the relationship between FibN AF and postprocedural AF inducibility or induction pacing cycle length (iPCL). Clinical FibNAF was calculated using left atrium (LA) dimension (echocardiogram), the inverse of CV, and the inverse of the atrial effective refractory periods measured at proximal and distal coronary sinus. In silico simulation found a positive correlation between AF maintenance duration and FibNAF ( R = 0.90, ). After clinical CPVI, FibNAF ( 0.296±0.038 versus 0.192±0.028, ) was significantly higher in patients with postprocedural AF inducibility ( n = 41) than in those without ( n = 19 ). Among 41 patients with postprocedural AF inducibility, FibNAF ( P = 0.935, ) had excellent correlations with induction pacing cycle length. FibNAF, based on LA mass and wavelength, correlates well with AF maintenance in computational modeling and clinical AF inducibility after CPVI.