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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Physiol.</journal-id>
<journal-title>Frontiers in Physiology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Physiol.</abbrev-journal-title>
<issn pub-type="epub">1664-042X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1123190</article-id>
<article-id pub-id-type="doi">10.3389/fphys.2023.1123190</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physiology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>The three-dimensionality of the hiPSC-CM spheroid contributes to the variability of the field potential</article-title>
<alt-title alt-title-type="left-running-head">Hwang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphys.2023.1123190">10.3389/fphys.2023.1123190</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Hwang</surname>
<given-names>Minki</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1568197/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Lee</surname>
<given-names>Su-Jin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2152757/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Lim</surname>
<given-names>Chul-Hyun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2171648/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Shim</surname>
<given-names>Eun Bo</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/59713/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Lee</surname>
<given-names>Hyang-Ae</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/780604/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>AI Medic, Inc.</institution>, <addr-line>Seoul</addr-line>, <country>Republic of Korea</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Predictive Toxicology</institution>, <institution>Korea Institute of Toxicology</institution>, <addr-line>Daejeon</addr-line>, <country>Republic of Korea</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Mechanical and Biomedical Engineering</institution>, <institution>Kangwon National University</institution>, <addr-line>Chuncheon</addr-line>, <country>Republic of Korea</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/31493/overview">Yung E. Earm</ext-link>, Seoul National University, Republic of Korea</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/29782/overview">Bum-Rak Choi</ext-link>, Brown University, United States</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/460524/overview">Jae Boum Youm</ext-link>, Inje University, Republic of Korea</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Eun Bo Shim, <email>ebshim@kangwon.ac.kr</email>; Hyang-Ae Lee, <email>vanessa@kitox.re.kr</email>
</corresp>
<fn fn-type="equal" id="fn1">
<label>
<sup>&#x2020;</sup>
</label>
<p>These authors have contributed equally to this work</p>
</fn>
<fn fn-type="other">
<p>This article was submitted to Computational Physiology and Medicine, a section of the journal Frontiers in Physiology</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>21</day>
<month>03</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>14</volume>
<elocation-id>1123190</elocation-id>
<history>
<date date-type="received">
<day>13</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>10</day>
<month>03</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Hwang, Lee, Lim, Shim and Lee.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Hwang, Lee, Lim, Shim and Lee</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>
<bold>Background:</bold> 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 <italic>in silico</italic> three-dimensional (3-D) models of hiPSC-CM spheroids for the simulation of field potential measurement. We compared our model simulation results against <italic>in vitro</italic> experimental data under the effect of drugs E-4031 and nifedipine.</p>
<p>
<bold>Methods:</bold> <italic>In silico</italic> 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 <italic>in vitro</italic> experimental data.</p>
<p>
<bold>Results:</bold> 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 IC<sub>50</sub> of E-4031 and nifedipine calculated by matching the simulated FP durations with <italic>in vitro</italic> experimental data were in line with the experimentally measured ones reported in the literature.</p>
<p>
<bold>Conclusion:</bold> The 3-D <italic>in silico</italic> models of hiPSC-CM spheroids generated highly variable FPs similar to those observed in <italic>in vitro</italic> experiments. The <italic>in silico</italic> model has the potential to complement the interpretation of the FP signals obtained from <italic>in vitro</italic> experiments.</p>
</abstract>
<kwd-group>
<kwd>hiPSC-CM</kwd>
<kwd>multi-electrode array</kwd>
<kwd>field potential</kwd>
<kwd>drug toxicity</kwd>
<kwd>simulation</kwd>
</kwd-group>
<contract-num rid="cn001">19172MFDS168</contract-num>
<contract-num rid="cn002">2022M3A9H1015784</contract-num>
<contract-sponsor id="cn001">Ministry of Food and Drug Safety<named-content content-type="fundref-id">10.13039/501100003569</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">Ministry of Science and ICT, Republic of Korea<named-content content-type="fundref-id">10.13039/501100014188</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Drug toxicity screening is an important step in the development of new drugs. Especially, cardiotoxicity is related to arrhythmia which is often manifested by the prolongation of QT interval in the electrocardiogram (ECG) (<xref ref-type="bibr" rid="B36">Roden, 2016</xref>; <xref ref-type="bibr" rid="B3">Baracaldo-Santamaria et al., 2021</xref>). In the preclinical stage, the examination of cellular action potential (AP) under the effects of a drug using human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) provides a clue for the proarrhythmic risk of the drug (<xref ref-type="bibr" rid="B4">Blinova et al., 2017</xref>; <xref ref-type="bibr" rid="B46">Yu et al., 2019</xref>). The <italic>in vitro</italic> models are often limited to two-dimensional (2-D) monolayers and lack myocardial cell&#x2013;cell interactions, including heterotypic interactions between cardiomyocytes and cardiac fibroblasts (<xref ref-type="bibr" rid="B26">Kurokawa and George, 2016</xref>). With the recent advancements in bioengineering tools, three-dimensional (3-D) culture systems with varying degrees of complexity have gained significant traction in the field of drug testing and drug discovery (<xref ref-type="bibr" rid="B12">Fang and Eglen, 2017</xref>). Indeed, 3-D cultures of iPSC-CMs in the form of engineered myocardium have been shown to enhance physiological hypertrophy, improve maturity, and enhance drug response (<xref ref-type="bibr" rid="B23">Karbassi et al., 2020</xref>).</p>
<p>The comprehensive <italic>in vitro</italic> proarrhythmia assay (CiPA) (<xref ref-type="bibr" rid="B44">Vicente et al., 2018</xref>; <xref ref-type="bibr" rid="B45">Wallis et al., 2018</xref>), an international initiative for drug safety assessment includes the following three components in the preclinical stage: 1) <italic>in vitro</italic> assessment of drug effects on multiple cardiac ion channels, 2) <italic>in silico</italic> prediction of proarrhythmic risk using a computer model of human ventricular cardiomyocyte, and 3) <italic>in vitro</italic> assessment using hiPSC-CMs. For the <italic>in vitro</italic> assessment of drug effects on ion channels, patch clamp techniques are used to determine block potency such as half maximal inhibitory concentration (IC<sub>50</sub>) (<xref ref-type="bibr" rid="B8">Crumb et al., 2016</xref>; <xref ref-type="bibr" rid="B29">Mann et al., 2019</xref>). For the assessment using hiPSC-CMs, multi-electrode array (MEA) system is a platform that can characterize the electrical response of hiPSC-CMs under the effects of drugs (<xref ref-type="bibr" rid="B19">Harris, 2015</xref>; <xref ref-type="bibr" rid="B2">Andrysiak et al., 2021</xref>). While MEA measurements are high-throughput and less labor-intensive than patch clamp techniques, the output signal is field potential (FP) which is different from AP and requires working knowledge of the MEA measurement system to properly interpret the signal (<xref ref-type="bibr" rid="B41">Tertoolen et al., 2018</xref>; <xref ref-type="bibr" rid="B27">Kussauer et al., 2019</xref>). To detect electrical activities of tissues or organs <italic>in vitro</italic> and <italic>in vivo</italic>, the 3-D MEAs have emerged as a promising tool, but the 2-D MEAs are still widely used because there are many challenges to overcome (<xref ref-type="bibr" rid="B6">Choi et al., 2021</xref>; <xref ref-type="bibr" rid="B11">Demircan Yalcin and Luttge, 2021</xref>). Ideal 3-D MEA systems have to satisfy the requirements such as spatial coverage across the total volume of 3-D <italic>in vitro</italic> model, design flexibility according to types and sizes of models, a high spatial resolution to analyze the functional connectivity among cells in 3-D <italic>in vitro</italic> models, etc. (<xref ref-type="bibr" rid="B37">Shin et al., 2021</xref>). Moreover, the output signals from hiPSC-CMs on MEA system exhibit variability because there are different cell types in the population and the levels of differentiation are varied (<xref ref-type="bibr" rid="B1">Abbate et al., 2018</xref>). There have been a number of <italic>in silico</italic> studies that modeled and simulated MEA measurements on hiPSC-CMs with the purpose of complementing the interpretation of the <italic>in vitro</italic> signal (<xref ref-type="bibr" rid="B42">Tixier et al., 2017</xref>; <xref ref-type="bibr" rid="B1">Abbate et al., 2018</xref>; <xref ref-type="bibr" rid="B35">Raphel et al., 2018</xref>; <xref ref-type="bibr" rid="B41">Tertoolen et al., 2018</xref>). Most of those studies adopted 2-D model for the cells in the MEA well. Since many 3-D cardiac models are being developed as biomimetic models (<xref ref-type="bibr" rid="B14">Garzoni et al., 2009</xref>; <xref ref-type="bibr" rid="B30">Morrissette-McAlmon et al., 2020</xref>; <xref ref-type="bibr" rid="B40">Tani and Tohyama, 2022</xref>), the development and studies on the applicability of <italic>in silico</italic> 3-D models are needed to complement the interpretation of FP signals for these <italic>in vitro</italic> models. Because there are differences between 2-D and 3-D cultured hiPSC-CMs, the FP analysis from the 2-D model cannot be easily extrapolated to the 3-D model. Several studies report that 3-D cultured hiPSC-CMs have different physiological, contractile (<xref ref-type="bibr" rid="B47">Zhang et al., 2013</xref>; <xref ref-type="bibr" rid="B13">Gao et al., 2018</xref>; <xref ref-type="bibr" rid="B38">Silbernagel et al., 2020</xref>), and electrophysiological properties (<xref ref-type="bibr" rid="B32">Nunes et al., 2013</xref>; <xref ref-type="bibr" rid="B9">Daily et al., 2015</xref>; <xref ref-type="bibr" rid="B28">Lemoine et al., 2017</xref>; <xref ref-type="bibr" rid="B7">Correia et al., 2018</xref>) compared to 2-D cultured hiPSC-CMs.</p>
<p>The current study is an extension of those studies and we have developed an <italic>in silico</italic> 3-D model for the simulation of FP measurement of <italic>in vitro</italic> 3-D hiPSC-CM spheroids. Excitation wave propagation can occur toward or away from the recording electrode in the 3-D model which is simulated in this study by changing the initial locations of the excitation wave. We compared the simulation results with <italic>in vitro</italic> data under the effects of drugs E-4031 and nifedipine. The <italic>in silico</italic> 3-D model provides insights into the role of three-dimensionality in the variability of the FPs from hiPSC-CM spheroid, and has the potential to be used in the interpretation of <italic>in vitro</italic> data under the effects of drugs.</p>
</sec>
<sec sec-type="methods" id="s2">
<title>2 Methods</title>
<sec id="s2-1">
<title>2.1 Formation of hiPSC-CMs spherical and discoidal models</title>
<p>Commercially available human iPSC-derived cardiomyocytes (Cardiosight&#xae;-S) were obtained from NEXEL Co., Ltd. (Seoul, Republic of Korea). Four differentiation batches for hiPSC-CMs (Lot&#x23; 12VAEZL, 12VVEZL, C2-6I1, C2-6U1) were used in this study. According to the COA (Certificate of Analysis) provided by the cell provider with the cell, all hiPSC-CM batches satisfied the provider&#x2019;s QC criteria which are purity (&#x3e;90% cTnT), MEA functionality, and drug reactivity for the reference drugs including E-4031 and nifedipine. The cells were cultured according to the instructions of the manufacturer. In brief, the cryopreserved hiPSC-CMs are thawed and seeded on the cell culture plate and then placed in an incubator at 37&#xb0;C supplemented with 5% CO<sub>2</sub>. The cells were maintained for 1 week to induce time-dependent maturation and electrophysiological stabilization. After then, the monolayered hiPSC-CMs were dissociated and harvested with the STEMdiff&#x2122; Cardiomyocyte Dissociation Kit (Stemcell Technologies, Vancouver, Canada) and replated to a 3-D culture microwell (SpheroFilm, 500&#xa0;&#x3bc;m inner diameter, INCYTO, Republic of Korea). The media in the microwell were changed daily, and the spheroids were cultured for 3&#xa0;days. After 3&#xa0;days, the hiPSC-CM spheroids were collected for MEA experiments. In the case of the discoidal models of hiPSC-CMs, the detached cells from culture plates on day 7 were directly plated onto the fibronectin pre-coated MEA plates to create a dome shape at a density of &#x223c;70,000 plated cells per well.</p>
</sec>
<sec id="s2-2">
<title>2.2 MEA experiments</title>
<p>Before the sample plating on MEA plates, the recording areas of the 12-well MEA plate (Axion Biosystems, Atlanta, GA) were coated with human fibronectin (Sigma-Aldrich, St. Louis, MO) at 5&#xa0;&#x3bc;L of 50&#xa0;&#x3bc;g/mL in phosphate-buffered saline (PBS). Then, the plate was incubated at 37&#xb0;C for 30&#xa0;min. Then, the prepared hiPSC-CM spheroids were plated on the fibronectin pre-coated area of MEA plates. As previously mentioned, the dissociated and harvested cells from culture plates were directly plated on the MEA plates. Next, the MEA plates containing the hiPSC-CM spherical and discoidal models were incubated in a 37&#xb0;C, CO<sub>2</sub> incubator for 1&#xa0;h to attach the sample to the multi-electrodes on each well. After 1&#xa0;h, each well was filled with 1&#xa0;mL of the culture medium. The medium was changed every 2&#xa0;days thereafter for 3&#x2013;7&#xa0;days to obtain the spherical and discoidal models of hiPSC-CMs with spontaneous and synchronous electrical activity on the MEA plates.</p>
<p>To evaluate the drug responses of the hiPSC-CM spheroids for ion channel-specific blockers, the effects of E-4031 (for a blocker of the hERG channel currents) and nifedipine (for a blocker of the calcium channel currents) on cardiac FPs of the hiPSC-CM spheroids were studied. The full of media on the plates was changed at least 4&#xa0;h before recordings. FPs were recorded from spontaneously beating hiPSC-CM spheroids. For the FP recording, the MEA plate was placed on the Maestro MEA system (Axion Biosystems, GA, USA) keeping 37&#xb0;C and 5% CO<sub>2</sub> conditions. Data were filtered with a Butterworth 0.1&#x2013;2&#xa0;kHz band-pass filter. The drugs were prepared with 1000X in dimethyl sulfoxide (DMSO) of the final target concentration and treated in each well as a cumulative method from the lowest concentration to the highest concentration every 20&#xa0;min. The FP waveforms of the last 1&#xa0;min of each dose were recorded and analyzed for data analysis. The beat per minute (BPM), FP amplitude (FPA), and FPD<sub>cF</sub> (FP duration (FPD) corrected with Fridericia&#x2019;s formula: FPD<sub>cF</sub> &#x3d; FPD/Beat Period<sup>0.33</sup>) were analyzed with the AxIS program (Axion Biosystems, ver. 2.3.2). Experimental procedures for forming the models and field potential recording are shown in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Experimental procedures of MEA assay. Experimental procedures are shown for the formation of spherical and discoidal hiPSC-CM models and MEA assay.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g001.tif"/>
</fig>
</sec>
<sec id="s2-3">
<title>2.3 Scanning electron microscope (SEM) image acquisition</title>
<p>SEM imaging and analysis for hiPSC-CMs spherical and discoidal models was conducted at Korea Research Institute of Bioscience and Biotechnology (KRIBB) according to the internal protocol. In brief, the samples were fixed in a 2.5% paraformaldehyde-glutaraldehyde mixture buffered with 0.1&#xa0;M phosphate (pH 7.2) for 2&#xa0;h, postfixed in 1% osmium tetroxide in the same buffer for 1&#xa0;h, dehydrated in graded ethanol, and substituted by isoamyl acetate. Then they were dried at the critical point in CO<sub>2</sub>. Finally, the samples were sputtered with gold in a sputter coater (SC502, POLARON) and observed using the scanning electron microscope, FEI Quanta 250 FEG (FEI, USA) installed in KRIBB.</p>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> shows optical micrographs of the discoidal and spherical models of hiPSC-CMs. The discoidal model has a diameter of approximately 1876.29 &#xb1; 64.59&#xa0;&#xb5;m (<italic>n</italic> &#x3d; 3 from two batches) and is attached flatly to the bottom surface with a slightly thicker dome-like shape in the middle. In the case of the spherical models, it has a three-dimensional round shape and a diameter of 318.34 &#xb1; 10.25&#xa0;&#xb5;m (<italic>n</italic> &#x3d; 15 from two batches). In both models, adjacent cells are overlapped and tightly attached to conduct electrical signals (<xref ref-type="fig" rid="F2">Figure 2</xref>).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Morphology of discoidal and spherical hiPSC-CM models. Bright field and SEM images of hiPSC-CM models in discoidal and spherical shapes are shown. Scale bar in discoidal images, 500&#xa0;&#x3bc;m; scale bar in spherical images, 200&#xa0;&#x3bc;m.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g002.tif"/>
</fig>
</sec>
<sec id="s2-4">
<title>2.4 <italic>In silico</italic> 3-D models of hiPSC-CM spheroids</title>
<p>
<italic>In silico</italic> 3-D models of hiPSC-CM spheroids were constructed in spherical and discoidal shapes (<xref ref-type="fig" rid="F2">Figure 2</xref>). For the spherical model, it was slightly deformed such that a flat surface was generated, which was in contact with the bottom surface of the well of the MEA device. The diameters of the models were set to 1 and 2&#xa0;mm for spherical and discoidal models, respectively, which were consistent with experimental observation. Tetrahedral meshes were generated inside the models for the computation of AP propagation. The number of meshes was increased until the simulation results converged. The propagation of the AP in the model was obtained by numerically solving the following monodomain equation:<disp-formula id="equ1">
<mml:math id="m1">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2202;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">V</mml:mi>
<mml:mi mathvariant="bold-italic">m</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2202;</mml:mo>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2207;</mml:mo>
<mml:mo>&#x2219;</mml:mo>
<mml:mi mathvariant="bold-italic">D</mml:mi>
<mml:mo>&#x2207;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">V</mml:mi>
<mml:mi mathvariant="bold-italic">m</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mi mathvariant="bold-italic">o</mml:mi>
<mml:mi mathvariant="bold-italic">n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mi mathvariant="bold-italic">m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">C</mml:mi>
<mml:mi mathvariant="bold-italic">m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>where <italic>V</italic>
<sub>m</sub> is the membrane potential, <italic>t</italic> is time, <italic>D</italic> is the diffusion coefficient, <italic>I</italic>
<sub>ion</sub> and <italic>I</italic>
<sub>stim</sub> are ionic and stimulation currents, respectively, and <italic>C</italic>
<sub>m</sub> is the membrane capacitance. The diffusion coefficient was set to 0.0072&#xa0;mm<sup>2</sup>/s which resulted in the experimentally observed conduction velocity of 0.12 &#xb1; 0.0028&#xa0;mm/ms. The equation was numerically solved by using finite element method (<xref ref-type="bibr" rid="B22">Im et al., 2008</xref>). For the calculation of <italic>I</italic>
<sub>ion</sub>, the O&#x2019;Hara-Rudy dynamic (ORd) human ventricular cell model was used (<xref ref-type="bibr" rid="B33">O&#x27;Hara et al., 2011</xref>). At the locations of the electrodes, the extracellular potential was calculated as described in a study (<xref ref-type="bibr" rid="B43">Ugarte et al., 2014</xref>). The method uses the ratio of the extracellular to intracellular conductivities which we set to three following the value used by <xref ref-type="bibr" rid="B1">Abbate et al. (2018)</xref>. The FP measurement system was modeled as an equivalent circuit with an electrode capacitance, an electrode resistance, and the internal resistance of the measurement device as described in previous studies (<xref ref-type="bibr" rid="B31">Moulin et al., 2008</xref>; <xref ref-type="bibr" rid="B35">Raphel et al., 2018</xref>). The FP was calculated as the electric current through the equivalent circuit due to the extracellular potential, multiplied by the internal resistance of the measurement device (<xref ref-type="bibr" rid="B35">Raphel et al., 2018</xref>).</p>
</sec>
<sec id="s2-5">
<title>2.5 Simulation of the effect of drug</title>
<p>The effects of drugs E-4031 and nifedipine were incorporated by partly blocking <italic>I</italic>
<sub>Kr</sub> and <italic>I</italic>
<sub>CaL</sub> channels, respectively, more with increasing drug concentration. The percentages of each channel blockade were determined such that the simulated FPD were matched with experimentally measured data. Using the percentages of each channel blockade at multiple drug concentrations, the IC<sub>50</sub> and Hill Coefficient were calculated by applying the Hill equation (<xref ref-type="bibr" rid="B17">Goutelle et al., 2008</xref>).</p>
</sec>
<sec id="s2-6">
<title>2.6 Statistical analysis</title>
<p>All experimental results were statistically processed using GraphPad Prism (GraphPad, San Diego, United States), AxIS program (Axion Biosystems, ver. 2.3.2), and Excel (Microsoft, Redmond, WA, United States). All values are represented as mean &#xb1; Standard error of mean (SEM) and n represents the number of experimental replicates with individual samples. Statistical significance was determined using the Student&#x2019;s <italic>t</italic>-test; <italic>p</italic> &#x3c; 0.05 was considered to indicate statistical significance.</p>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Analysis of field potentials from discoidal and spherical models of hiPSC-CMs</title>
<p>Field potentials were recorded in the hiPSC-CMs-based discoidal and spherical models using the MEA system. To check the quality of the hiPSC-CMs used in model production, we confirmed that cardiac troponin T (<italic>cTnT</italic>) and &#x3b1;-cardiac actin (<italic>&#x3b1;-actinin</italic>) were expressed in &#x3e;90% of hiPSC-CMs. Also, it was confirmed that the human ether-&#xe0;-go-go-related gene (<italic>hERG</italic>) and cardiac L-type calcium channel (<italic>Cav1.2</italic>), which contribute to ventricular repolarization and are the leading causes of drug-induced cardiac arrhythmia in drug development, were also expressing in the cell membrane (<xref ref-type="fig" rid="F3">Figure 3A</xref>). The field potential parameters were recorded and analyzed by attaching discoidal or spherically shaped multi-cellular hiPSC-CMs on the MEA plates. The average BPM was significantly higher in the discoidal model than the spherical model [52.8 (<italic>n</italic> &#x3d; 15) vs. 39.3&#xa0;bpm (<italic>n</italic> &#x3d; 9), <italic>p</italic> &#x3d; 0.0141]. The field potential amplitudes were 0.99 and 1.1&#xa0;mV for the discoidal and spherical models, respectively, and there was no statistical difference between the two groups. In the case of the FPD<sub>cF</sub> as well, there was no statistical difference between the two groups with the values of 436.4 and 459.2&#xa0;ms for the discoidal and spherical models, respectively (<xref ref-type="fig" rid="F3">Figure 3B</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Characterization of spherical and discoidal hiPSC-CM models. <bold>(A)</bold> Immunocytochemistry images for cardiac myogenic markers (cTnT, a-actinin) and ion channels (Nav1.5, Cav1.2). <bold>(B)</bold> Comparison of field potential parameters for spherical and discoidal hiPSC-CM models. &#x2a;<italic>p</italic> &#x3c; 0.05 by one-way ANOVA with Student&#x2019;s <italic>t</italic>-test (<italic>n</italic> &#x3d; 15 for the discoidal models, <italic>n</italic> &#x3d; 9 for the spherical models, each from two differentiation batches). n.s., not significant; BPM, beats per minute; FPA, field potential amplitude; FPD<sub>cF</sub>, FP duration (FPD) corrected with Fridericia&#x2019;s formula to correct the FPD dependence on beating rate.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g003.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Simulated field potentials from 3-D spheroid models</title>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> shows simulated FPs obtained from the spherical model of hiPSC-CM spheroid. The electrical stimulations were applied at four different sites on the model surface from the bottom to the top of the model (<xref ref-type="fig" rid="F4">Figure 4A</xref>). The simulated FPs obtained at four different electrode locations at the bottom surface (a, b, c, and d in <xref ref-type="fig" rid="F4">Figure 4A</xref>) are shown in <xref ref-type="fig" rid="F4">Figure 4B</xref>. The shape of the signal exhibits a large variation similar to the observation reported by Abbate et al. (<xref ref-type="bibr" rid="B1">Abbate et al., 2018</xref>). The signals showed inverted shape between the electrode locations a and c for the stimulation sites 1 (blue color). The amplitudes of the signals were relatively small at the electrode location d compared to the other locations. The positive deflection corresponding to the repolarization was relatively more noticeable for the stimulation sites near the top of the model. <xref ref-type="fig" rid="F4">Figure 4C</xref> shows the AP propagation on the surface of the model for each stimulation site.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Spherical model of hiPSC-CM spheroid. <bold>(A)</bold> Geometry of the spherical model of hiPSC-CM spheroid with stimulation (1, 2, 3, and 4) and measurement (a, b, c, and d) locations. <bold>(B)</bold> Simulated field potentials and action potentials for different stimulation and measurement locations. The difference between FPD (314 &#xb1; 92&#xa0;ms, mean &#xb1; SD, <italic>n</italic> &#x3d; 16, SD &#x3d; Standard Deviation) and APD (427 &#xb1; 4&#xa0;ms, mean &#xb1; SD, <italic>n</italic> &#x3d; 16) is 113&#xa0;ms based on mean values. <bold>(C)</bold> Simulated action potential propagations for different stimulation sites.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g004.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F5">Figure 5</xref> shows simulated FPs obtained from the discoidal model of hiPSC-CM spheroid. The shape of the signal showed a large variation as in the case of the spherical model. The positive deflection corresponding to the repolarization was relatively more noticeable at the electrode location c for the stimulation sites 1 and 2 (<xref ref-type="fig" rid="F5">Figures 5A, B</xref>). <xref ref-type="fig" rid="F5">Figure 5C</xref> shows the AP propagation on the surface of the model for each stimulation site.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Discoidal model of hiPSC-CM spheroid. <bold>(A)</bold> Geometry of the discoidal model of hiPSC-CM spheroid with stimulation (1, 2, and 3) and measurement (a, b, c, and d) locations. <bold>(B)</bold> Simulated field potentials and action potentials for different stimulation and measurement locations. The difference between FPD (292 &#xb1; 46&#xa0;ms, mean &#xb1; SD, <italic>n</italic> &#x3d; 12) and APD (426 &#xb1; 4&#xa0;ms, mean &#xb1; SD, <italic>n</italic> &#x3d; 12) is 134&#xa0;ms based on mean values. <bold>(C)</bold> Simulated action potential propagations for different stimulation sites.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g005.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>3.3 The effect of drug simulated using the 3-D spheroid model</title>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> shows experimentally measured and simulated FPs under the effect of E-4031 from the spherical model of hiPSC-CM spheroid. The use of the mid-myocardial cell model, for which the action potential duration (APD) is longer than endocardial or epicardial cell, resulted in similar FPD as the experimentally observed one before the drug was applied. The simulated APs are shown in <xref ref-type="sec" rid="s10">Supplementary Figure S1</xref>. To match the experimentally observed FPD increase with increasing E-4031 concentration, the percentage of the <italic>I</italic>
<sub>Kr</sub> blockade was searched for each E-4031 concentration used in the <italic>in vitro</italic> experiment because E-4031 is an hERG channel blocker. The <italic>I</italic>
<sub>Kr</sub> had to be blocked 95% when E-4031 concentration was 0.1 &#x3bc;M, for which the FPD<sub>cF</sub> increased by 80% (<xref ref-type="fig" rid="F6">Figure 6</xref>). The IC<sub>50</sub> calculated using the percentages of the <italic>I</italic>
<sub>Kr</sub> blockade at each E-4031 concentration was 8&#xa0;nM which is close to the experimentally determined value of 7.7&#xa0;nM with a Hill coefficient of 1.0 reported in the literature (<xref ref-type="bibr" rid="B48">Zhou et al., 1998</xref>). The simulated positive deflection corresponding to the repolarization tended to be flattened with increasing drug concentration which was also observed in the study of Tertoolen et al. (<xref ref-type="bibr" rid="B41">Tertoolen et al., 2018</xref>) although the flattening was not observed in our <italic>in vitro</italic> experiment. The simulated FPA change with increasing drug concentration was negligible, which qualitatively agreed with experimental data (<xref ref-type="fig" rid="F6">Figure 6</xref>).</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Comparison of field potentials between <italic>in vitro</italic> experiment and <italic>in silico</italic> simulation for E-4031. <bold>(A)</bold> Effect of E-4031 on the FPs in the experimental model (<italic>n</italic> &#x3d; 12 from two differentiation batches). <bold>(B)</bold> Effect of E-4031 on the FPs in the simulation model. The APDs at 0.03 and 0.1&#xa0;&#x3bc;M are not available due to the failure of AP repolarization (<xref ref-type="sec" rid="s10">Supplementary Figure S1</xref>). The shapes, amplitude, and heart rate corrected duration of field potentials are compared. BPM, beats per minute; FPA, field potential amplitude; FPD<sub>cF</sub>, FP duration corrected with Fridericia&#x2019;s formula. FPD<sub>cF</sub> &#x3d; FPD/(beat period)<sup>0.33</sup>.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g006.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> shows experimentally measured and simulated FPs under the effect of nifedipine for the spherical model of hiPSC-CM spheroid. The simulated APs are shown in <xref ref-type="sec" rid="s10">Supplementary Figure S2</xref>. Because nifedipine is a Ca<sup>2&#x2b;</sup> channel blocker, the percentage of the <italic>I</italic>
<sub>CaL</sub> blockade was searched for each nifedipine concentration used in the experiment to match the experimentally observed FPD change with increasing nifedipine concentration. The IC<sub>50</sub> calculated using the percentages of the <italic>I</italic>
<sub>CaL</sub> blockade at each drug concentration were 0.018&#xa0;&#x3bc;M which is close to the experimentally measured value of 0.012&#xa0;&#x3bc;M with a Hill coefficient of 1.02 reported in the literature (<xref ref-type="bibr" rid="B25">Kramer et al., 2013</xref>). The simulated FPA change with increasing drug concentration was negligible, although experimental data showed slightly increasing FPA with increasing drug concentration (<xref ref-type="fig" rid="F7">Figure 7</xref>).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Comparison of field potentials between <italic>in vitro</italic> experiment and <italic>in silico</italic> simulation for nifedipine. <bold>(A)</bold> Effect of nifedipine on the FPs in the experimental model (<italic>n</italic> &#x3d; 11 from two differentiation batches). <bold>(B)</bold> Effect of nifedipine on the FPs in the simulation model. The shapes, amplitude, and heart rate corrected duration of field potentials are compared. BPM, beats per minute; FPA, field potential amplitude; FPD<sub>cF</sub>, FP duration corrected with Fridericia&#x2019;s formula. FPD<sub>cF</sub> &#x3d; FPD/(beat period)<sup>0.33</sup>.</p>
</caption>
<graphic xlink:href="fphys-14-1123190-g007.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussion</title>
<p>For the safety assessment of new drugs in the preclinical stage, utilization of hiPSC-CMs on MEA system is a relatively new platform and was adopted in the CiPA initiative. While MEA system has technical advantages over patch clamp measurement, the output signals from hiPSC-CMs on MEA system are highly variable and specific knowledge of the MEA system is needed for proper interpretation of the signal. In this study, we developed 3-D <italic>in silico</italic> models of hiPSC-CM spheroid on MEA system and validated the model using experimentally measured FP signals under the effect of drugs. The discoidal model has a 2.5-D dome-like shape with a diameter of approximately 1.8&#xa0;mm and the spherical models has a 3-D round shape and a diameter of approximately 300&#xa0;&#xb5;m (<xref ref-type="fig" rid="F2">Figure 2</xref>). Recent studies have shown that large 3-D spheroids (&#x3e;500&#xa0;&#xb5;m) have a large necrotic core compared to small spheroids (&#x3c;350&#xa0;&#xb5;m) and low drug effect and dye uptake (<xref ref-type="bibr" rid="B15">Gaze et al., 1992</xref>; <xref ref-type="bibr" rid="B5">Buffa et al., 2001</xref>; <xref ref-type="bibr" rid="B20">Horas et al., 2005</xref>; <xref ref-type="bibr" rid="B16">Gong et al., 2015</xref>; <xref ref-type="bibr" rid="B10">Daster et al., 2017</xref>; <xref ref-type="bibr" rid="B39">Singh et al., 2020</xref>; <xref ref-type="bibr" rid="B18">Han et al., 2021</xref>).</p>
<p>There have been <italic>in silico</italic> studies in which the variability of the FP signals was modeled using various approaches. <xref ref-type="bibr" rid="B1">Abbate et al. (2018)</xref> modeled the variability of the FP by introducing different cell phenotypes in the model and rescaling the amplitudes of the AP after observing that their two-dimensional model generated relatively homogeneous signals. They also tested different distributions of the cell types in the model and reported that the clustered configuration produced a higher level of variability in the FP shapes. <xref ref-type="bibr" rid="B42">Tixier et al. (2017)</xref> applied a probabilistic approach in distributing different cell types in the model. They assumed that the transition states between the two cell types were determined by a random process parameter and the cells in transition states were distributed using a correlation function. In our 3-D study, the variability of the FPs was observed depending on the stimulation sites and electrode locations even when a single cell type was present in the model. This implies that the three-dimensionality of the spheroid on MEA system contributes to the variability of the FPs although other factors such as different cell types and the level of differentiation are definite sources of the heterogeneity. Examining the effects of the heterogeneity in action potentials among the cells is the next step of this study. The variation of the AP traces was less noticeable than that of FP as observed in the 2-D study by <xref ref-type="bibr" rid="B1">Abbate et al. (2018)</xref>. The small difference in the voltage distribution in the spheroid caused by different initial activation site may contribute to the large variation in FP shapes. More study seems to be needed to clarify the role of three-dimensionality in the variability of the FPs from hiPSC-CM spheroid.</p>
<p>For the simulation of the effect of drug using the present model of MEA system, the change of the FPD based on the repolarization wave was examined in this study, which was adopted in many <italic>in vitro</italic> and <italic>in silico</italic> studies (<xref ref-type="bibr" rid="B42">Tixier et al., 2017</xref>; <xref ref-type="bibr" rid="B35">Raphel et al., 2018</xref>; <xref ref-type="bibr" rid="B27">Kussauer et al., 2019</xref>). The repolarization wave of FP signal corresponds to the end of repolarization of the AP (<xref ref-type="bibr" rid="B41">Tertoolen et al., 2018</xref>), and the change of the APD correlates with that of QT interval in the ECG (<xref ref-type="bibr" rid="B21">Hwang et al., 2019</xref>). A drawback of the approach used in this study is that the percentage of ion channel block depending on the concentration of a drug cannot be known <italic>a priori</italic>, and it only can be determined by matching the change of FPD with experimental data. As a result, <italic>in vitro</italic> assessment of drug effects on ion channels should be performed first, which is the number one step of the CiPA initiative (<xref ref-type="bibr" rid="B44">Vicente et al., 2018</xref>). As <italic>in silico</italic> prediction of APD change under the effects of a drug is performed using <italic>in vitro</italic> data of ion channel block in the second component of the CiPA initiative, the <italic>in silico</italic> approach presented in this study also needs the <italic>in vitro</italic> data of ion channel block. However, the present <italic>in silico</italic> approach could be used in the interpretation of the experimental data of MEA measurement by comparing the data of ion channel block such as IC<sub>50</sub> and Hill coefficient. Also, the present approach could provide insight into the characteristics of the spheroid such as the composition and distribution of different cell types.</p>
<p>There are some limitations in the present study. Due to the large variability of the FP signal, it was not easy to establish a correlation between FPD and APD. The FP signal shape was dependent on the locations of stimulation and measurement. The FP signal also turned out to be sensitive to the change in the slope of AP in the 2D study by <xref ref-type="bibr" rid="B1">Abbate et al. (2018)</xref>. Accordingly, it seems that caution should be taken in identifying the repolarization peak in the FP signal. In the cases of higher concentrations of the two drugs tested in this study, the FP repolarization peaks did not mean AP repolarization (<xref ref-type="sec" rid="s10">Supplementary Figures S1, S2</xref>). In the cases of higher concentrations of E-4031, the FP repolarization may have resulted from more or less the same transmembrane potential (around 0&#xa0;mV) over the entire spheroid due to the failure of AP repolarization. In the cases of higher concentrations of nifedipine, the FP repolarization peaks were hardly recognizable, and the peaks appeared to be far from the AP repolarization. These suggest that FP signals should be interpreted with great caution, especially at higher concentrations of drugs, and further investigation is needed in this regard. The cellular electrophysiological model used is not hiPSC-CM model, and single cell type was implemented in the spheroid models. Incorporation of recently developed electrophysiological models of hiPSC-CM (<xref ref-type="bibr" rid="B34">Paci et al., 2013</xref>; <xref ref-type="bibr" rid="B24">Koivumaki et al., 2018</xref>) would provide simulation results closer to the <italic>in vitro</italic> data. Also, the spherical and discoidal shapes are simplified models of the 3-D spheroids. Nevertheless, the present 3-D models of hiPSC-CM spheroid provide insights into the role of three-dimensionality in the variability of the FPs from hiPSC-CM spheroid, and have potential to be used in the interpretation of <italic>in vitro</italic> data under the effects of drugs.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/<xref ref-type="sec" rid="s10">Supplementary Material</xref>, further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>H-AL and ES provided the main idea for this research. S-JL performed <italic>in vitro</italic> experiments. MH and C-HL performed <italic>in silico</italic> simulations. MH and S-JL wrote the initial draft of the manuscript. H-AL and ES edited the manuscript.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This work was supported by the Ministry of Food and Drug Safety of Korea (19172MFDS168) and the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT of Korea (2022M3A9H1015784).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>MH, C-HL, and ES were employed by AI Medic, Inc.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s10">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fphys.2023.1123190/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fphys.2023.1123190/full&#x23;supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet1.PDF" id="SM1" mimetype="application/PDF" xmlns:xlink="http://www.w3.org/1999/xlink"/>
</sec>
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