DataSheet1_The three-dimensionality of the hiPSC-CM spheroid contributes to the variability of the field potential.PDF

Background: Field potential (FP) signals from human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM) spheroid which are used for drug safety tests in the preclinical stage are different from action potential (AP) signals and require working knowledge of the multi-electrode array (MEA) system. In this study, we developed in silico three-dimensional (3-D) models of hiPSC-CM spheroids for the simulation of field potential measurement. We compared our model simulation results against in vitro experimental data under the effect of drugs E-4031 and nifedipine.Methods:In silico 3-D models of hiPSC-CM spheroids were constructed in spherical and discoidal shapes. Tetrahedral meshes were generated inside the models, and the propagation of the action potential in the model was obtained by numerically solving the monodomain reaction-diffusion equation. An electrical model of electrode was constructed and FPs were calculated using the extracellular potentials from the AP propagations. The effects of drugs were simulated by matching the simulation results with in vitro experimental data.Results: The simulated FPs from the 3-D models of hiPSC-CM spheroids exhibited highly variable shapes depending on the stimulation and measurement locations. The values of the IC50 of E-4031 and nifedipine calculated by matching the simulated FP durations with in vitro experimental data were in line with the experimentally measured ones reported in the literature.Conclusion: The 3-D in silico models of hiPSC-CM spheroids generated highly variable FPs similar to those observed in in vitro experiments. The in silico model has the potential to complement the interpretation of the FP signals obtained from in vitro experiments.</p

A New Efficient Method for Detecting Phase Singularity in Cardiac Fibrillation

<div><p>Background</p><p>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.</p><p>Methods</p><p>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.</p><p>Results</p><p>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 × I_CaL), 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.</p><p>Conclusion</p><p>We propose a new location-centric method for calculating PS, which is robust and more efficient compared with the conventionally used method.</p></div

Predicted Intimal Growth for Low and High Flow Conditions.

<p>The shear stresses corresponding to low (<b>A</b>) and high (<b>B</b>) flow conditions are 1.8 and 14 dynes/cm², respectively. The simulation curves are the averages of 10⁴ simulations. Experimental data of intimal area are shown for comparison.</p

Rule-Based Model of Vein Graft Remodeling

<div><p>When vein segments are implanted into the arterial system for use in arterial bypass grafting, adaptation to the higher pressure and flow of the arterial system is accomplished thorough wall thickening and expansion. These early remodeling events have been found to be closely coupled to the local hemodynamic forces, such as shear stress and wall tension, and are believed to be the foundation for later vein graft failure. To further our mechanistic understanding of the cellular and extracellular interactions that lead to global changes in tissue architecture, a rule-based modeling method is developed through the application of basic rules of behaviors for these molecular and cellular activities. In the current method, smooth muscle cell (SMC), extracellular matrix (ECM), and monocytes are selected as the three components that occupy the elements of a grid system that comprise the developing vein graft intima. The probabilities of the cellular behaviors are developed based on data extracted from in vivo experiments. At each time step, the various probabilities are computed and applied to the SMC and ECM elements to determine their next physical state and behavior. One- and two-dimensional models are developed to test and validate the computational approach. The importance of monocyte infiltration, and the associated effect in augmenting extracellular matrix deposition, was evaluated and found to be an important component in model development. Final model validation is performed using an independent set of experiments, where model predictions of intimal growth are evaluated against experimental data obtained from the complex geometry and shear stress patterns offered by a mid-graft focal stenosis, where simulation results show good agreements with the experimental data.</p> </div

Model coefficients derived through regression analysis of primary experimental data.

<p>Model coefficients derived through regression analysis of primary experimental data.</p

Secondary variables used in model development.

<p>Secondary variables used in model development.</p

Three-dimensional maps of wave dynamics parameters.

<p>Maps of voltage, PS, DF, ShEn, and CFAE are shown for the case in which mother rotor was observed. The PS, DF, ShEn, and CFAE were mapped for 6 s.</p

Cardiac wave dynamics around the mother rotor.

<p>Maps of voltage, PS, DF, ShEn, and CFAE under the control condition (A), at which ion current conductance values are the Courtemanche et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149695#pone.0149695.ref017" target="_blank">17</a>] model values, and under AF condition (B), at which ion current conductance values are adjusted as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149695#pone.0149695.t001" target="_blank">Table 1</a>. In the DF map of the AF condition, the two highest DF areas are circled. Action potential curves are also shown for both control and AF conditions (C). D. DF areas (blue) are completely covered by the rotor tip trajectories (red). E. The trajectory of the mother rotor tip (black) is overlaid on the DF map. F. The trajectory of the mother rotor tip (black) is overlaid on the ShEn map. G. The trajectory of the mother rotor (black) tip is overlaid on the CFAE map.</p

Schematics comparison of the Iyer-Gray and location-centric method.

<p>A. The Iyer-Gray method calculates phases that range from –π to π and calculates the line integral of the phases at a candidate point with its eight neighbor points. B. The location-centric method searches for a singularity point at a candidate point, subject only to one condition, θ_n+1—θ_n < M.</p

Quantitative comparison of spatial distributions in terms of the Hausdorff distance.

<p>Hausdorff distances between the results obtained by the location-centric method and the Iyer-Gray method were measured for different thresholds (M). (A) Hausdorff distances calculated for the control condition. (B) Hausdorff distances calculated for the 0.3 × I_CaL condition.</p