Genetic algorithm

We used the GA to optimize the conductance of each current so that the AP model reproduced the experimental values in previous studies24,29. We executed the GA optimization using a program implemented in C# with reference to the method of Bot et al.55, and its type was a real-coded GA. We evaluated the degree of adaptation of each model in the population using the score calculated using Eq.(1). We calculated the AP for each model 60s after the initial state. We performed numerical integration to compute APs using the forward Euler method with a time step of 0.01ms. The initial values of ion concentration inside and outside the cell, and temperature were equivalent to the conditions of the experiments. We fixed the intracellular potassium and sarcoplasmic reticulum calcium concentrations to accelerate convergence. We estimated the cell volume from the cell surface area data24,56. We used the same value as that in the Paci model for the ratio of the sarcoplasmic reticulum volume to the cytoplasmic volume23. We used a model population with random values assigned to each conductance as the starting generation. The upper and lower scaling limits were 0.010.0 for GNa, GCaL, and Gf in the ventricular-type model and 0.05.0 for all others. We describe the details of the GA optimization of AP models in the Supplementary Methods.

To estimate magnetic signals from iPS-CMs, we simulated the 2D electrical activity of the cell population. We set the intracellular ion concentrations using adult mouse cardiac AP model values57. We determined the extracellular ion concentrations from the composition of the culture medium and set the temperature to room temperature (RT: 24C). The temperature coefficients (Q10) used in the AP models referred to values from the published literature58. We computed the solution to the partial differential Eq.(2) using the CrankNicolson method, with the spatial step set to x=y=60m and the time step set to t=0.01ms. We determined the averaged cellular resistivity to reproduce the conduction velocity measured in neonatal rat cardiac cell sheets40 (Supplementary Methods and Supplementary Fig. S7). The list of parameters used in the simulation is summarized in Supplementary Table S3. We calculated the magnetic field using BiotSavart's law from the currents flowing in the cells at each time point. We estimated the observed waveforms using integration in the area of each pickup coil. We assumed that the cancellation component of the magnetic field caused by the extracellular return current was negligibly small because the volume of the medium was sufficiently large relative to the spreading of cultured cells. We also checked how much the observed waveforms were affected when the cell position was shifted from directly under the sensor. As a result, we confirmed that a displacement of2mm in the x-axis or y-axis directions had almost no effect on the measurements (Supplementary Fig. S8).

The procedure for dataset preparation is as follows: A peak region (250ms) was cut from the magnetic signals estimated using simulation and subjected to random stretching and scaling. Non-peak regions between peak regions were linearly interpolated to make data of 120s each. For the background noise, four data of the x component of the magnetic field with no current applied (for artificial signal experiments) or eight data of the y component with no cell sample placed (for cell experiments) were used in equal proportions within each dataset. Random time shifts were performed in the superposition of these magnetic signals and noise data. Even when the cycle length and amplitude were fixed, this shift brought diversity to the dataset. Finally, datasets (n=160 for artificial signal experiments or 640 for cell experiments) were generated, including three data types in a 1:1:2 ratio: positive peak direction, negative peak direction, and background noise only. Representative waveforms are shown in Supplementary Fig. S9.

The window used in the spectral calculation with the FSST33 was the Kaiser window, with a size of 512 points. The sidelobe attenuation was 13.6dB. The real and imaginary parts of the spectral were input as separate features. The input values were pre-standardized by subtracting the mean and dividing by the standard deviation. Training was iterated for up to 60 epochs (one epoch means one round of data). The network was validated using the validation data for each epoch. If the validation loss exceeded the previous minimum value more than ten times, it was decided that there was no further improvement and training was stopped. The initial learning rate was set to 0.001 and the learning rate was dropped by a factor of 0.1 every 20 epochs. The training data were divided into segments of 10s lengths and the mini-batch size (a subset of the training data used in one step to evaluate the gradient of the loss function and update the weights) was set to 16.

We calculated the AUROC36 to evaluate network classification performance. The AUROC is the area under the curve plotted with the false positive rate on the horizontal axis and the true positive rate on the vertical axis. The AUROC is 1.0 when separation performance is best and 0.5 when classification is performed randomly. In this study, we defined each data point as positive if it was peak (P) or negative if it was non-peak (N).

From the output label data, we plotted a histogram of the lengths of segments labeled as class P (Fig.4f). Using this histogram as a reference, we estimated the appropriate distribution of peak region lengths, set a lower limit, and identified segments longer than this threshold as peak regions (Fig.1c). We used the average count number for the analysis of samples measured multiple times. We obtained the average waveform by superimposing magnetic signals of 175ms before and after the center position of each peak region and averaging their amplitudes. Then, we repeated the adaptive correlation filter59 ten times to correct for positional fluctuations.

A vector-type SQUID magnetometer12,15 was applied to measure magnetic fields. The vector-type SQUID magnetometer had an axial-type first-order gradiometric pickup coil with a diameter of 15.5mm and two planar-type first-order gradiometric squared pickup coils of 915.5 mm2 and 1115.5 mm2. The baseline length of each gradiometric pickup coil was 50mm. The three gradiometric pickup coils were oriented perpendicular to each other and assembled on a cylindrical bobbin. Three Ketchen-type low-temperature SQUIDs were individually coupled to each pickup coil and simultaneously detected the three independent components of the magnetic field: Bx, By, and Bz. The SQUID readouts were connected to double-integrator type flux-locked loop (FLL) circuits for output linearization and dynamic range improvement. The total noise level, including environmental noise, was 1020 fT/Hz at 10Hz. The SQUID magnetometer was installed in a glass-fiber reinforced plastic (GFRP) cryostat with an MSB. The MSB comprised two 1mm thick mu-metal layers with double front doors. The shielding factor of the MSB was more than 40dB at 10Hz. The GFRP cryostat consisted of a cylindrical main body that stored 6-L liquid helium and a narrow GFRP tube that dropped from the bottom of the main body. The main body was installed in the ceiling of the MSB and only the GFRP tube penetrated the MSB through a hole in its top. The SQUID magnetometer was installed at the bottom end of the GFRP tube and placed at the center of the MSB.

The cell sample was placed on a height-adjustable stage made of non-magnetic materials and adjusted to 3mm from the bottom edge of the pickup coil. Measurements were taken at room temperature, and the FLL readout signals were digitally recorded at the sampling rate of 1kHz with HPF at 3Hz, LPF at 100Hz, and notch filters at 60Hz.

We kept the resistance fixed and varied the output voltage of the function generator to adjust the current that generated magnetic signals. With no filtering, we increased the voltage until the peak of the magnetic signal could be identified by visual inspection and recorded the peak amplitude at that point. Based on that value, we adjusted the voltage to generate the desired magnetic signals. We enhanced the artificial signal (2.74) so that the signal-to-noise ratio was equivalent to that in the cell sample experiment. To confirm the validity of this procedure, we compared the amplitude spectrum densities of the background noise between the artificial signal experiment and the cell sample experiment (Supplementary Fig. S4). Although differences in amplitude existed, the spectral distribution had the same trend within the range of 3.540Hz used to train the LSTM networks.

We implemented the scaled template technique following previous research22. We slid the template (the event waveform of interest to detect) along the time series data and scaled it to fit the data at each position. Then, we divided the template scaling factor by the standard error of the time series data, which was the detection criterion, and we considered the event waveform of interest to be detected when this criterion exceeded a threshold value. The template was a peak waveform of 250ms in length cut from the magnetic signal estimated using numerical simulation, which we also used as the training data in deep learning. To compare the two methods without bias, we set the threshold so that the number of detected peaks from background noise was equal to that of deep learning.

The mouse iPS cell line iPS-MEF-Ng-20D-17 (Expressing GFP by Nanog promoter)44, established by the Center for iPS Cell Research and Application, Kyoto University, was provided by the RIKEN BRC through the National BioResource Project of the Ministry of Education, Culture, Sports, Science, and Technology, Japan. For the culture method, we referred to previous studies44,60,61. To maintain the undifferentiated state of iPS cells, MEFs (EmbryoMax Primary Mouse Embryonic Fibroblasts, PMEF-NL, Neo Resistant, Strain FVB; purchased from Sigma-Aldrich, St Louis, MO, USA), in which cell proliferation was arrested by mitomycin C (Nacalai Tesque, Kyoto, Japan) treatment, were cocultured as feeder cells. The maintenance medium was composed of Dulbecco's modified Eagle's medium (Sigma-Aldrich) with 15% fetal bovine serum (Equitech-Bio Inc., Kerrville, TX, USA), 50 U/ml penicillin, 50g/ml streptomycin (Sigma-Aldrich), 2mM L-glutamine (Sigma-Aldrich), nonessential amino acids (100) (Sigma-Aldrich), 0.1mM 2-mercaptoethanol (FUJIFILM Wako Chemicals, Osaka, Japan), and 0.1% human leukemia inhibitory factor (FUJIFILM Wako Chemicals). The medium was refreshed daily and iPS cells were passaged every two days. Colonies were detached with 0.25% trypsin/1mM EDTA (FUJIFILM Wako Chemicals), dispersed in cell suspension, counted, and 1.0106 cells were seeded into MEFs on 60mm plates.

Based on previous studies37,62, cardiomyocyte differentiation was induced by forming EB. The differentiation medium was Iscove's modified Dulbecco's medium (Sigma-Aldrich) containing 20% fetal bovine serum, 50 U/ml penicillin, 50g/ml streptomycin, 2mM L-glutamine, nonessential amino acids (100), and 0.1mM 2-mercaptoethanol. Mouse iPS cells were suspended at 1.5104 cells/ml in the differentiation medium and seeded 0.2ml into each well of a 96-well U-shaped-bottom microplate (Nunclon Sphera; Thermo Fisher Scientific, Waltham, MA, USA). The plates had a cell-nonadherent surface treatment, which allowed uniform and stable EBs to form. For further differentiation, the culture was switched from floating to adherent on day 5. Plastic dishes of 100mm diameter and MEA (Alpha MED Scientific, Osaka, Japan) were used for magnetic measurement, and glass bottom dishes (AGC Techno Glass, Shizuoka, Japan) were used for fluorescence microscopy. These dishes were coated with 0.1 w/v% gelatin solution (FUJIFILM Wako Chemicals) and one EB was transplanted at the center of each dish. Beating areas began to appear on day 7. Magnetic measurement was performed during days 1921 when the area of differentiated cells was extensive and synchronized beating was observed. Fluorescence microscopy was also performed at this time. To ensure that one peak corresponded to the electrical activity of the entire cell population, samples with a single beating area larger than 3mm square were selected for measurement. To bring the cells closer to the sensor, the cylinder of the MEA was excised to a height of 1mm. For comparison with iPS-CMs, MEFs were also cultured in cloning rings with an inner diameter of 5mm. In the experiment to detect the drug's chronotropic effects from magnetic signals, the medium was replaced with a medium supplemented with isoproterenol at a final concentration of 10M, and magnetic signals were measured from iPS-CMs after incubation for 30min.

Cardiomyocytes were immunostained on day 19 of differentiation, and the expression of cardiomyocyte marker cardiac troponin T and connexin 43 that forms gap junctions was confirmed. iPS-CMs were fixed in 4% paraformaldehyde for 20min at 4C, followed by blocking with 5% goat serum (Nichirei, Tokyo, Japan) and 0.1% Triton-X diluted in Dulbecco's phosphate buffered saline (DPBS) for 20min at RT. The cells were washed three times for 5min with DPBS and incubated with a primary antibody diluted in DPBS containing 1% goat serum for 1h at RT and then overnight at 4C. The primary antibodies were rabbit polyclonal IgG anti cardiac troponin T antibody (1.4g/mL; Proteintech, Rosemont, IL, USA) and rabbit polyclonal IgG anti connexin 43 antibody (10g/mL; Thermo Fisher Scientific). The cells were washed three times for 5min with DPBS with shaking and further incubated with the secondary antibody Alexa fluor 546 goat anti rabbit IgG (Invitrogen, Carlsbad, CA, USA; 1:1000 dilution in DPBS/0.05% Triton X-100) for 30min at RT. The cells incubated with connexin 43 antibody were also treated with Alexa fluor 488 Phalloidin (Thermo Fisher Scientific; 1:50 dilution in DPBS/0.05% Triton X-100) and stained for actin filaments. The cells were washed three times with tris buffered saline for 5min and once with DPBS for 5min, and immersed in 4',6-diamidino-2-phenylindole (DAPI)-added anti-fading agent (Nacalai Tesque). Observation and imaging were performed with an IX71 fluorescence microscope (Olympus, Tokyo, Japan).

We measured FPs using MEA38. We selected the electrode near the center of the beating area and recorded the potential difference between it and a reference electrode not in contact with the cells. To avoid noise when measuring simultaneously with magnetic signals, we output the electrical signals from the probe externally through an IC clip and did not use the attached connector. When measuring FP only, we used it. We performed the measurement at room temperature and recorded data at the sampling rate of 1kHz with HPF at 0.16Hz, LPF at 160Hz, and notch filters at 60Hz.

Deep learning network training and data classification were performed in MATLAB (Mathworks Inc., Natick, MA, USA). The GA for parameter optimization of the AP model and the numerical simulation of the electrical activity of cardiomyocytes were performed using our programs implemented in C#.

Data are presented as meanstandard error of the mean (SEM). Comparisons between two groups were analyzed using the unpaired t-test unless otherwise indicated. For comparisons of three or more groups, when equal variances could be assumed, one-way ANOVA was used, followed by Tukey's test as a post hoc test. When equal variances could not be accepted, the BrownForsythe correction was performed, followed by the GamesHowell test as a post hoc test. Differences between data were considered statistically significant at p<0.05.

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