Integrating Nonlinear Analysis and Machine Learning for Human Induced Pluripotent Stem Cell-Based Drug Cardiotoxicity Testing

Abstract

Utilizing recent advances in human induced pluripotent stem cell (hiPSC) technology, nonlinear analysis and machine learning we can create novel tools to evaluate drug-induced cardiotoxicity on human cardiomyocytes. With cardiovascular disease remaining the leading cause of death globally it has become imperative to create effective and modern tools to test the efficacy and toxicity of drugs to combat heart disease. The calcium transient signals recorded from hiPSC-derived cardiomyocytes (hiPSC-CMs) are highly complex and dynamic with great degrees of response characteristics to various drug treatments. However, traditional linear methods often fail to capture the subtle variation in these signals generated by hiPSC-CMs. In this work, we integrated nonlinear analysis, dimensionality reduction techniques and machine learning algorithms for better classifying the contractile signals from hiPSC-CMs in response to different drug exposure. By utilizing extracted parameters from a commercially available high-throughput testing platform, we were able to distinguish the groups with drug treatment from baseline controls, determine the drug exposure relative to IC50 values, and classify the drugs by its unique cardiac responses. By incorporating nonlinear parameters computed by phase space reconstruction, we were able to improve our machine learning algorithm’s ability to predict cardiotoxic levels and drug classifications. We also visualized the effects of drug treatment and dosages with dimensionality reduction techniques, t-distributed stochastic neighbor embedding (t-SNE). We have shown that integration of nonlinear analysis and artificial intelligence has proven to be a powerful tool for analyzing cardiotoxicity and classifying toxic compounds through their mechanistic action.

Introduction

With the advancement of human induced pluripotent stem cells (hiPSCs) technology, cardiomyocytes derived from hiPSCs (hiPSC-CMs) have enabled the drug cardiotoxicity screening under human biological background(Bruyneel et al. 2018; Li et al. 2020; Mathur et al. 2016). A variety of techniques have been utilized for quantitative assessment of drug and chemical effects on hiPSC-CMs(Burnett et al. 2021b). For example, hiPSC-CM contractility can be quantified through video recording of conventional phase-contrast microscopy using edge detection and block-matching optical flow algorithms(Lee et al. 2015). Using commercially available calcium sensitive dyes or genetically encoded fluorescent calcium indicators (e.g., GCaMP6f), intracellular calcium transient can be measured through fluorescent microscopy to represent the contractile functionality of hiPSC-CMs under drug exposure(Sirenko et al. 2013). Recently, automated algorithms and in-depth statistical analyses have gathered more attention to effectively differentiate the cardiotoxicity types for drug candidates(Kofron et al. 2021). For example, a semi-automatic data analysis software was developed to improve the accuracy, reliability, and throughput of measurements of hiPSC-CMs’ field potentials. This software was coupled to correlation analysis and ensemble averaging techniques that successfully distinguished between normal field potentials and arrhythmogenic complexes from microelectrode array (MEA) recordings(Pradhapan et al. 2013). Concurrently, nonlinear analytical techniques have been shown to improve the sensitivity of hiPSC-based assays by detecting subtle abnormal aberrations from contractile function readouts in response to drug exposure(Hoang et al. 2018, 2019).

Integration of computational tools with machine learning techniques has been introduced to develop in vitro drug screening assays with high reproducibility and accuracy. By pairing optical flow method with machine learning algorithm, Support Vector Machine (SVM) model could effectively detect dose-dependent drug effects on hiPSC-CMs based on a contractile motion analysis(Lee et al. 2015). Furthermore, a more comprehensive SVM model trained by three cardioactive drugs showed the capability of predicting the mechanistic action of unknown compounds by evaluating the force readouts from hiPSC-derived cardiac microtissues(Lee et al. 2017). Using a voltage sensitive dye for electrophysiological measurements in hiPSC-CMs, the Random Forest (RF) classifiers could distinguish control group, isoproterenol-treated group, and propranolol-treated group with 75% accuracy(Heylman et al. 2015). In a recent study of calcium transient analysis for hiPSC-based cardiotoxicity testing, initial SVM training was performed to detect abnormal calcium signals with total 14 quantifiable parameters, and these first classification results were then fed forward to a second SVM classification to achieve 87% accuracy for the testing groups(Hwang et al. 2020). Nonlinear dimensionality reduction techniques have also been utilized to classify abnormal signals when fed into an SVM with 89% accuracy(Orita et al. 2020).

Based on calcium transient analysis, hiPSC-CMs with RyR2 mutations were used to test drug-induced arrhythmias in cells with inherited arrhythmogenic disorders. A total of 12 parameters were processed with Z-normalization and two machine learning algorithms of SVM and k-Nearest Neighbor (kNN) with RF classifiers. The calcium transient data resulted in the accuracy of 87% for distinguishing between healthy and diseased cells(Juhola et al. 2019). The algorithm was able to classify each drug’s response(Juhola et al. 2021). To identify diseased hiPSC-CMs based on the calcium transients, hiPSC-CMs with hypertrophic cardiomyopathy were identified with accuracies of up to 89%, and hiPSC-CMs with long QT syndrome were classified with accuracy of up to 100%, showing considerable promise for separating these two disease states through computational analysis(Joutsijoki et al. 2020). To distinguish the contractile profiles between healthy wild-type and diseased hiPSC-CMs with Timothy Syndrome, machine learning algorithms, including decision trees, quadratic discriminant analysis, SVM, kNN, and naive Bayes, were used to analyze the quantitative measurements derived from the pixel intensity of hiPSC-CM contractile profiles. Specifically, decision trees and quadratic discriminant analysis achieved 92% accuracy, somewhat outperforming SVM and kNN at 91% accuracy(Teles et al. 2021). In addition to the functional analyses based upon contractile motion or calcium transients, deep learning models trained with microscopic images of hiPSC-CMs have also been proven to be effective at detecting adverse effects of cardiotoxic drugs(Grafton et al. 2021; Maddah et al. 2020; Orita et al. 2019).

In this study, we demonstrated the feasibility of integrating machine learning algorithms and nonlinear analytical techniques in conjunction with data from a high-throughput testing assay to successfully quantify and classify cardiotoxicity using hiPSC-CMs. Particularly, our integrated analytical tool was able to predict the toxicity and classify the adverse effect type of three drugs (isoproterenol, verapamil, and cisapride), free of user bias. This methodology can be potentially applied to future large-scale datasets with other drugs and chemicals with potential cardiotoxic effects. We have found that our analytical techniques combined with nonlinear analysis boosted the accuracy of machine learning classifiers. IC50 toxicity threshold and Drug classification in particular proved to be reliably boosted with the addition of nonlinear parameters. The addition of t-distributed stochastic neighbor embedding (t-SNE) also proved to be instrumental in interpreting the results of our machine learning classification algorithms. The overall workflow of this study is depicted in Figure 1.

Figure 1. Experimental workflow for hiPSC-CM recording, analysis, and machine learning pipeline.

(a) High-throughput assay using a 384 well plate for hiPSC-CMs drug testing. (b) Parametric feature extraction of the fluorescent calcium transient signals comprising of both linear and nonlinear parameters. Examples of reconstructed phase spaces for a regular signal and an irregular signal. (c) Half maximal inhibitory concentration (IC50) analysis of utilized parameters. (d) Supervised machine learning classification with a neural network to detect drug treatment (e) Exploratory data analysis of the parametric signals using t-SNE data visualization.

Materials and Methods

Experimental and Technical Design

The experiment was designed as a high throughput drug testing platform for hiPSC-CM cardiotoxicity. Cultured cells were plated and maintained before drug testing and imaging. All collected data was then analyzed utilizing the standard linear analysis, nonlinear analysis and utilized to train machine learning algorithms. Each step is carefully detailed in the following sections.

hiPSC-CMs Plating and Cell Culture

iCell cardiomyocytes² (cat. no: CMC-100–012-001, lot #CMC485222) were purchased from FujiFilm Cellular Dynamics (Madison, WI). Cells were thawed and cultured following the manufacturer’s iCell Cardiomyocytes² User’s guide. Briefly, 384-well microplates (Cat# 353962, Corning Life Sciences, Corning, NY) were coated with 0.1% gelatin in water for 1 hour at 37°C, then rinsed 1x with PBS. During this incubation, cardiomyocytes were thawed for 3 minutes in a 37°C water bath, then the suspension was transferred to a 50 mL conical tube and diluted with 2 mL of Plating media (Cat# M1001, FujiFilm-CDI) over 2 minutes (dropwise), and an additional 7 mL of plating media over ~30 seconds to minimize osmotic shock. Live cell counts were confirmed using trypan blue exclusion, and cells were plated at 10,000 cells/well in 50 μL plating media (200,000 cells/mL density) in the gelatin-coated plates. Cells were incubated at 37°C and 5% CO₂ for 24 hours. The plating medium was then exchanged with 50 μL of maintenance medium (Cat# M1003, FujiFilm-CDI) containing 0.2% penicillin/streptomycin. Maintenance medium was replaced 48 hours later (day 3 post-plating).

Drug Testing Procedure

To achieve high-throughput drug cardiotoxicity testing, the cardiomyocytes were treated with a calcium transient dye (Early Cardiotoxicity Kit, Cat# R8210, Molecular Devices, San Jose, CA). Briefly, on day 4 post-seeding, Ca2+ dye was prepared following manufacturer’s instructions, and equilibrated to 37°C. 25 μL of maintenance media was removed from each well in the cell-seeded 384-well plate and replaced with 25 μL of 2x Ca2+ dye solution (bringing the total volume back to 50 μL). This solution was incubated at 37°C, 5% CO₂ for 2 hours. Following the 2-hour incubation, baseline intracellular Ca2+ flux was recorded using the FLIPR-Tetra Cellular Screening System (Molecular Devices) to achieve simultaneous screening and uniform capture. Ca2+ flux was recorded every 0.125 s over 100 s (n = 800 total reads) at 37°C with ex/em = 494/520 nm, gain = 2000, and an exposure time of 0.05 s. After collection of the “baseline” reads, 12.5 μL of 5X chemical solution was added to each well, bringing the final volume to 62.5 μL. Cells were treated with either vehicle (0.5% DMSO), or chemical (cisapride, verapamil, or isoproterenol [all fromSigma-Aldrich, St Louis, MO] at a final concentration of 1, 10, 100, 1000, or 10000 nM) for 30 minutes. After incubation, calcium flux was recorded again with seven replicates per concentration for each compound. The fluorescent signal of calcium transient was analyzed using ScreenWorks PeakPro software (Molecular Devices). Data from each timepoint was analyzed as detailed in previously published work(Burnett et al. 2019, 2021a; Sirenko et al. 2017). Here, we used “baseline” as a quantifying metric to ensure even beating from the samples in all the wells and across the plates prior to chemical treatment. We normalized each parameter to a DMSO control set to correct the spontaneous beating variations at the same timepoint post treatment. We applied all these normalization in our analysis utilizing machine learning algorithms and EC50 calculations, so we think additional normalization to beating rate is less important.

Data Collection and Analysis

After acquiring the calcium transient fluorescent signals from each well of hiPSC-CMs, standard linear parameters were calculated as the averages of peak frequency, decay to rise ratio, decay time, peak width, peak spacing, rise time, peak amplitude as well as averages from the nonlinear embedding and fractal dimensions (Figure 2a and Supporting Information Figure 1). All the measurements were normalized to the baseline for all drug groups. The IC50 (EC50) analysis was conducted in R-studio with algorithm of the drc: dose response package(Ritz et al. 2015). For all the parameters, the IC50 (EC50) values were calculated from the dose response curves that were fitted to the standard four-parameter log-logistic model function. The IC50 (EC50) values were then utilized as the toxicity threshold for our machine learning models, which allowed us to train the models to detect cytotoxic effects of each drug.

Figure 2. Extracted parameters for heatmap comparisons.

(a) All the parameters used in the heatmaps, machine learning models and exploratory data analysis. (b) Hierarchical heatmap to show the data relationship among different drug exposure. (c) Hierarchical heatmap to show the data relationship between baseline controls and drug treatment groups.

Nonlinear Analysis Based on Phase Space Reconstruction

Nonlinear parameters were calculated using an open-source algorithm based on phase space reconstruction (Hoang et al. 2018, 2019). Briefly, one-dimensional time-series data can be reconstructed into a multidimensional phase space that consists of a set of typical trajectories of the system, in which each point corresponds to one system state. The dimensionality of the phase space can be quantified by determining the fractal properties of the attractors in a dynamic system. The fractal is a subset of points at a small scale that can resemble the whole object. Analyzing the fractal properties of a waveform represents a useful tool for identifying the number of independent parameters necessary for generating a corresponding process or state. Specifically, to this study, we were able to reconstruct the calcium transient data into phase space and derived two nonlinear parameters, embedding dimension and fractal dimension, which measure the signal’s complexity and regularity. This gives us the ability to quantify the regularity and complexity of a signal in a quantifiable way. The embedding dimension is sensitive to the changes in the beat rhythm. The changes in the periodic regularity of the overall signal will increase the average embedding dimension. In contrast, the fractal dimension is sensitive to smaller noise-like aberrations within the signal. More irregular and sporadic variations within the signal will increase the overall complexity seen in the signal waveform and can be observed in supporting information figure 3h.

Machine Learning Algorithms

An ensemble approach was utilized to investigate the practical feasibility of supervised machine learning algorithms as an integrated tool for analyzing cardiac contractile functions and drug responses. All measurements were standardized by Z-normalization, which ensures that all analyzed parameters can be equally weighted for training the machine learning models. We performed exploratory data analysis (EDA) utilizing t-distributed stochastic neighbor embedding (t-SNE) method to visualize high-dimensional dataset and investigate the relationships within different parameters(Van Der Maaten and Hinton 2008). t-SNE is a nonlinear dimensionality reduction technique based upon Stochastic Neighbor Embedding that embeds higher dimensional data into a lower-dimensional space, which allows us to easily visualize the relationships of many parameters. The algorithm can group higher dimensional pairs along a probability distribution, as the higher probability is assigned to the pairs with higher similarity. Then, a similar probability distribution is defined for the lower dimensional map by minimizing the divergence between the two distributions via multiple iterations. t-SNE graphs were created using a Barnes-Hut implementation with the R package Rtsne(Krijthe 2015) with a max perplexity of 10.

Support Vector Machines (SVM) model is a popular and powerful non-probabilistic classifier that maps boundaries, called hyperplanes, to maximize the distance between two or more classes in a supervised training dataset. Hyperplanes are a subspace that comprises n-1 dimensions from the n-dimensional space of the data. The dataset can be fitted with nonlinear kernels and transformed into a higher dimensional space by creating the hyperplanes between unique classes with a set of linear equations. We trained our SVM model with a Gaussian radial basis kernel, the cost of constraints violation equal to 5 and a 3-fold cross validation using the kernlab package(Karatzoglou et al. 2004).

Random Forests (RF) model is an ensemble of decision trees that can be grouped together into a forest to create a powerful learning algorithm for classification. RF algorithm enables the random selection of features and training sets to prevent overfitting for the initial trees. Once the training is completed, the classification decision is ultimately made by assigning the class with the most trees within the forest. Our RF models were trained with a maximum of 500 trees with 3 parameters tried at each split using the randomforest package(Liaw and Wiener 2002).

Artificial neural networks (ANN) model is a collection of neurons that form an interconnected neural network to transmit information via synapses. The ANN models are trainable by assigning weights to each neuron during the learning process. The final output layer of the ANN can be trained to predict the specific outputs to meet the training objective of the network. After comparing multiple network sizes, we utilized sigmoidal, or logistic, activation functions between 5 layers of 5 neurons in our classifier ANN, which provided the most generalizable performance across our classification models utilizing the neuralnet package (Stefan Fritsch, Frauke Guenther, and Marvin N. Wright 2019).

Statistical Analysis

To quantify the predictive performance of each machine learning model, we used a confusion matrix (Table 1) by plotting the predicted and actual labels of testing and training dataset.

Table 1.

Confusion Matrix

	Predicted Positive	Predicted Negative
Actual Positive	True Positive (TP)	False Negative (FN)
Actual Negative	False Positive (FP)	True Negative (TN)

The accuracy of the algorithm is defined as the ratio of correct predictions vs total predictions, giving insight into the general performance of the tested algorithm.

$$Accuracy=\frac{TP+TN}{AllCases(TP+TN+FP+FN)}$$ (1)

The precision of the algorithm is defined as the ratio of true positives to total predicted positives, showing how accurately the algorithm can ascertain the true labels.

$$Precision=\frac{TP}{TP+FP}$$ (2)

Recall of the algorithm is defined as the ratio of true positives compared to true positives and false negatives, giving insight into how many true instances the algorithm fails to detect. Recall is especially important to the cases where false negatives, such as mislabeling cardiotoxic effects, must be minimized.

$$Recall=\frac{TP}{TP+FN}$$ (3)

The precision and recall can be considered simultaneously with the F₁ score, which combines these two scores into a single metric. F₁ score can give a general measure of the performance of the tested algorithm.

$$F1Score=\frac{2\times TP}{2\times TP+FP+FN}$$ (4)

Results

Classic parametric analysis of drug responses

For proof-of-concept of integrating nonlinear analysis and machine learning models into hiPSC-based drug screening workflow (Figure 1), we tested three drugs with known cardio-active effects: verapamil, a calcium channel blocker considered class-IV antiarrhythmic agents, isoproterenol, a beta-adrenergic agonist primarily used for the treatment of bradycardia, and cisapride, a serotonin receptor agonist as a gastroprokinetic agent with known cardiotoxic effects of QT prolongation(Burnett et al. 2021b; Sirenko et al. 2013). The drug concentrations ranged from 1 nM to 10 μM with a logarithmic interval of base 10 increasing by 10x for each subsequent concentration. Calcium transient signals were collected and analyzed to derive the linear parameters, meanwhile 1D time-series signals were inputted into the phase space reconstruction algorithm to derive nonlinear parameters (Figure 1b and Supporting Information Figure 1). Data was imported, organized, scaled, visualized in R using the tidyverse library of packages(Wickham et al. 2019), and used for the following IC50/EC50 calculations, statistical comparisons, machine learning and exploratory data analysis.

From hierarchical clustering in the heatmaps(Gu, Eils, and Schlesner 2016) (Figures 2b & 2c), we observed a close relationship among the parameters associated with calcium transient duration and decay (decay time, peak width, peak spacing and decay-rise ratio). For these four parameters, verapamil showed no significant changes across the exposures, except for a reduction in peak spacing at 100 nM and 1 μM drug concentrations (Supporting Information Figure 2b). Isoproterenol showed a decrease trend of these parameters with the increase of concentration, indicating an enhancement of cardiac outputs, while cisapride showed an increase trend of these parameters with the increase in concentration, indicating the prolongation of QT intervals. For the parameters of rise time, peak amplitude and frequency, verapamil showed slightly higher values only at the low concentrations. Both isoproterenol and cisapride showed a significant increase of peak amplitude and frequency, while these two drugs had opposite effect on rise time, shown as prolongation of rise time with cisapride but reduction of rise time with isoproterenol (Supporting Information Figure 2f).

Next, we reconstructed the linear signals into the phase spaces to derive the nonlinear parameters. Showing as examples, we can observe that regular beating of the hiPSCs in culture can result in a repeating loop in the phase space (Supporting Information Figure 3a) and adding DMSO did not make a significant change on the looping features (Supporting Information Figure 3b). Similarly, we can convert the calcium transient signals generated from the hiPSCs under different drug treatment into complex looping structures based on phase space reconstruction. The increase of complexity and decrease in repeatability of the loops would be associated with the changes in beat rhythms and aberrations due to the drug exposure (Supporting Information Figure 3c–h). For the nonlinear parameters, increase of concentration of both verapamil and isoproterenol induced an increase in the fractal dimension (Supporting Information Figure 2i) and a decrease in the embedding dimension (Supporting Information Figure 2h). Specifically, for verapamil at the high concentrations (1 μM and 10 μM), significant changes were only observed from the nonlinear parameters but not from the linear parameters. These nonlinear parameters captured the toxic effects on hiPSC-CMs that linear parameters failed to perform, which highlighted the importance of incorporating nonlinear analysis in drug toxicity testing. For cisapride, significant drug effects could be observed at concentrations as low as 1 nM, but higher concentrations resulted in little response from hiPSC-CMs manifested from most parameters, including nonlinear parameters. This indicated that integrated data analytical approaches would be needed to further determine the drug toxic responses from cisapride.

The IC50 based on nonlinear parameters were calculated for all three drugs. The predicted IC50 values were 285.14 nM for isoproterenol, 142.97 nM for verapamil, and 1130.33 nM for cisapride (Figure 3a). Our IC50 values for isopropanol and verapamil were within the same range as previous studies(Heylman et al. 2015; Orvos et al. 2019), however our IC50 for cisapride was at the higher end of the wide range of reported values(Burnett et al. 2021b; Dempsey et al. 2016; Gilchrist et al. 2015; Sirenko et al. 2013). Embedding dimension proved to be an extremely effective and sensitive measure for calculating the inhibitory concentration necessary as it’s average measure was more sensitive than the benchmark beat frequency calculation. For isoproterenol, the IC50 of beat frequency is 294.72 nM, while IC50 of embedding dimension is 142.01 nM. The IC50 values from verapamil and isoproterenol were comparable between linear variables and nonlinear variables. However, for cisapride, the average calculation of nonlinear variables (355.45 nM) was far more sensitive in regard to the linear variables (1521.99 nM). Most parameters did not have any dose response within the administered dosages, indicating that hiPSC-CMs were not very responsive to this specific drug in traditional analysis. The fractal dimension was able to quantitatively detect aberrations within the signals that linear parameters failed to capture. This led to a pronounced shift in the dose-response curve, which allowed us to calculate a response missed from linear parameters.

Figure 3. Calculated IC50 Values.

(a) The IC50 values were calculated for all the parameters for three drugs. The average values were used in the machine learning models as the IC50 threshold. Example plots of IC50 curves for (b) embedding dimension and (c) fractal dimension for all three drugs.

Machine learning models for drug toxicity prediction

For the machine learning models, we randomly split our dataset by assigning two-thirds of all data as the training group and the other one-third as the testing group. We used three machine learning models, SVM, RF and ANN, to perform three classification tasks: (1) treatment determination to simply classify baseline control group or drug treatment group, (2) IC50 thresholding to classify the drug exposures below or above IC50 values, and (3) drug classification to classify three different drugs (verapamil, isoproterenol or cisapride). Furthermore, we determined the level of improvement for three classification tasks of three machine learning models based on the addition of nonlinear parameters.

For the task of treatment determination, all three models were trained on the same dataset with each set of measurements labeled as Baseline or Treated. All three models resulted in a high degree of accuracy (greater than 92%) when predicting whether the hiPSC-CMs were exposed to a drug or not, even for low exposure concentrations. Incorporation of nonlinear analysis boosted the accuracy of SVM and ANN models from 92.7% (linear parameters only) to 94.2% (combined parameters) but did not influence the accuracy of the RF model (Figure 4a and Supporting Information Figure 4a).

Figure 4. Machine learning classification and t-SNE comparison.

For all three classification tasks, including (a) treatment determination to simply classify baseline control group or drug treatment group, (b) IC50 thresholding to classify the drug concentrations below or above IC50 values, and (c) drug classification to classify three different drugs (verapamil, isoproterenol or cisapride), summary tables for three machine learning models were generated to compare the model prediction accuracy for linear parameters only and combined with nonlinear parameters. Accordingly, t-SNE plots were generated for linear parameters only (left) and combined with nonlinear parameters (right).

For the task of IC50 thresholding, we used the machine learning models to detect whether drug dose exposed to the hiPSC-CMs was above IC50 (toxic) or below IC50 (nontoxic). With only linear parameters, we had an impressive ability to predict toxicity with 97.14% accuracy for SVM model and 91.42% accuracy for RF and ANN models. Impressively, all three models obtained 100% precision for their IC50 thresholding prediction. More importantly, the addition of nonlinear parameters could boost all three algorithms to 100% accuracy for the data using combined parameters (Figure 4b and Supporting Information Figure 4b), which showcased the capability of nonlinear analysis to detect the complex dynamics present in the arrhythmia caused by toxic drug exposure.

For the task of drug classification, the addition of nonlinear parameters greatly improved the performance of machine learning models. The classification accuracy of the SMV model improved over 10% from 54.3% to 65.7% with the addition of nonlinear parameters. This improvement lifted the algorithm’s performance from negligible guesswork to the possibility of being a generalizable model for drug classification. The RF model had a statistically relevant accuracy of 62.9% on drug classifications, but the addition of nonlinear parameters had no benefit to its classifier’s accuracy. The ANN model outperformed both RF and SVM models with an initial accuracy of 71.4%, which was boosted to 80% accuracy with the addition of nonlinear parameters. From these three drugs, cisapride which was the most difficult drug to be classified, had a 90% recall with combined parameters, compared to 63.6% with only linear parameters. Most summary statistics were significantly improved for our ANN model with the addition of nonlinear parameters, which made a strong case for nonlinear analysis to detect subtle changes related to the unique mechanism of each drug (Figure 4c and Supporting Information Figure 4c).

Dimension reduction technique for integrated data analysis and visualization

Additional data analysis was performed with t-SNE data clustering to project data into 2D plots. Previous studies have demonstrated that dimensionality reduction techniques were a useful visualization of data relationships that machine learning techniques may be capturing(Hoyt and Owen 2021). We used these t-SNE plots aiming to help us visualize how the addition of nonlinear parameters can benefit to the separation of drug cardiotoxic effects and why machine learning algorithms can detect such subtle variations among drugs and dosages. By generating unsupervised learning t-SNE plots for linear parameters with and without nonlinear parameters, we were able to compare the clustering benefits of nonlinear parameters and approximate the potential benefits of those parameters in the machine learning algorithms. The t-SNE data points for each plot were then labeled with the true label classifications with color coded for drug name, IC50 thresholding, and treated vs non-treated groups. This allowed us to visualize the enhancement in data grouping with the addition of nonlinear parameters for the classification tasks (Figure 4). By not including any information for the drug category, dosage level or treatment group, we can therefore utilize this technique to directly compare our linear-only parameters versus combined parameters without any user bias, in order to determine the usefulness of including nonlinear parameters for future analysis.

Each point’s proximity is based on the combination of all investigated parameters in the plot. Increased clustering indicated the similarity among the parameters, while spacing indicated dissimilarity, enabling the visualization of possible trends within the data that our trained machine learning models may have also observed. For our classification between baseline and treated groups, we see minimal grouping benefits for our labeled data from t-SNE plots. Similarly, classification with machine learning models between baseline and treated groups received the least benefit from the addition of nonlinear parameters (Figure 4a). In the plot we observed an enhanced separation for higher exposures of each drug (larger dots) in comparison to the lower concentrations (smaller dots) in the t-SNE plot. Meanwhile, the addition of nonlinear parameters improved the separation and spacing for lower concentrations, which might indicate its ability to capture the more subtle and nuanced effects of each drug at lower treatment concentrations (Figure. 4c). The largest benefit from the addition of nonlinear parameters can be visualized in the t-SNE plot for labeling above and below the IC50 threshold for toxicity determination (Figure 4b). Enhanced separation of more subtle effects of toxicity was captured due to the addition of nonlinear parameters similar to what was observed in our machine learning classifications that were all boosted to 100% accuracy.

Discussion

By integrating hiPSC-CM technology, a high-throughput screening platform, nonlinear analysis, and artificial intelligence techniques, it is possible to streamline data collection and automate data analysis to minimize the potential human biases in toxicity screening. Using 9 parametric quantities derived from the calcium transient signals, including 7 linear parameters and 2 nonlinear parameters, we were able to train accurate and reproducible machine learning models that were generalized well to our randomized datasets. Although we were not blinded to any drug treatments, we refrained from attempting to group or classify calcium transient signals or phase space reconstructions. This allowed us to take advantage of artificial intelligence to classify the signals and phase space reconstructions free of human bias. It is also probable that combing phase space reconstruction with artificial intelligence is able to detect calcium transient irregularity more accurately and sooner than a human observer. By incorporating nonlinear analysis into machine learning algorithms, we were able to create a sensitive and novel method for determining the cardiotoxicity level of investigated drugs. Nonlinear analysis based on phase space reconstruction has proven to be more sensitive to the signal aberrations from hiPSC-CMs and boosted the unbiased performance of multiple machine learning algorithms in the detection of cardiotoxic effects.

In the training of our models, we found NN models proved to be the most generalizable algorithm for all three classification attempts showing the highest degree of accuracy for treatment classification and drug classification. The addition of nonlinear parameters boosted NN classification ability for both IC50 thresholding and drug classification, which outperformed RF and SVMs by over 17% and 14% increase in accuracy, respectively. SVM received the most benefit from the addition of nonlinear parameters, which improved the SVM’s accuracy for all three tasks. In contrast, RF received the least benefit from the additional nonlinear parameters, as it only boosted the classification accuracy for IC50 thresholding. Interestingly, the addition of nonlinear parameters boosted all three investigated algorithms to 100% classification accuracy for detecting whether the analyzed signal passed the calculated IC50 threshold. Nonlinear parameters proved to be the key to distinguishing the toxic effects of each drug to a high degree of certainty, bolstering the consideration of nonlinear analytical techniques for analyzing the toxic effects of drugs.

In this work, we integrated EDA-based data visualization techniques into our analytical workflow for drug toxicity screening and classification to increase the interpretability of machine learning algorithms. Utilizing dimensionality reduction techniques to interpret machine learning algorithms such as recurrent NNs has been proven to be an effective strategy for improving the interpretability of such “black box” models. Recent studies showed the correlation of t-SNE outputs between successive layers of a NN model and the increasingly organized arrangement of data points of each NN layer, highlighting that t-SNEs could be a useful lower dimensional projection coordinate system for probing the underlying mechanics of black box NNs(Hoyt and Owen 2021). In our work, the resulting t-SNE graphs appeared to pair well with the results of machine learning classification models, possibly giving insight into the key features and relationships within the datasets captured by these models. By including the effects of drugs and dosages on all the parameters in a single t-SNE plot, we were able to visualize how the addition of nonlinear parameters benefited the separation of drug cardiotoxic effects. The clearest example would be the task of IC50 classification. The performance of all three supervised machine learning algorithms for detecting drug exposure above IC50 threshold was boosted by the addition of nonlinear parameters. This can be visualized with improved t-SNE performance separating out the signals above the IC50 threshold (Figure 4). We can build upon this intuitive analysis by investigating the separation of drugs at high dosages, especially for verapamil and isoproterenol. The separation was not as clear at lower dosages due weaker drug effects, while the addition of nonlinear parameters helped separate out more subtle effects for the lower dosages of isoproterenol from verapamil and cisapride. We believe that this technique can be potentially used to separate the drugs with different mechanism of action with a larger dataset of many more drugs at different dosages, which can be a continuous study to be explored in future.

Machine learning techniques have also been employed in a series of successful studies of clinical electrocardiogram (ECG) data. Particular focus has been given to detecting the occurrence of cardiac arrhythmia with novel algorithms such as VF15(Guvenir et al. 1997), which boosted arrhythmia classification to 62% accuracy. However, modern deep learning techniques with embedded autoencoders were able to predict arrhythmia with the near-perfect accuracy (>99%)(Ebrahimi et al. 2020). Deep learning enables detecting and labeling abnormalities in ECG signals with high accuracy but still requires additional development to test them upon real-time signals in the clinical setting. A plethora of widely available and well-documented datasets along with the advancement in accessible computing resources made it possible for further development of deep learning techniques for arrhythmia detection from ECG. In addition, nonlinear analysis based on the Takens method(Fojt and Holcik 1998) for phase space reconstruction has been proposed as a tool for ECG signal processing alongside machine learning classification. Similar to our work, the combination of linear and nonlinear features of the ECG signals has been shown to increase the overall accuracy of machine learning algorithms for arrhythmia detection(Elhaj et al. 2016).

There are a number of limitations to this study. First, in this study, hiPSC-CMs were used as an in vitro model. There are a number of options for replacing animal studies in cardiotoxicity testing, but hiPSC-CMs offer many advantages(Burnett et al. 2021b). Not only these cells are commercially available, they are also not associated with ethical concerns, are available from multiple donors and yield highly reproducible data(Grimm et al. 2018). It has been also shown that hiPSC-CMs are comparable to hESC-CMs in phenotype and structure(Lundy, S. et al. 2018) as well as, if not better, in regards to drug response(Zhao et al. 2017). Overall, hiPSC-CMs are an invaluable cell-based model to increase the accuracy, precision, and efficiency of cardiotoxicity hazard identification for both drugs and non-pharmaceuticals. Second limitation is a lack of comparison on sex-specific drug responses of hiPSC-CMs. In current study, the hiPSC-CMs were used from tone donor (donor 1434, male). The hiPSC-CMs from this donor have been well characterized in a number of publications (Blanchette et al. 2019; Burnett et al. 2021a; Martewicz, Magnussen, and Elvassore 2020), showing the ability to generate clinically-relevant data. hiPSC-CMs derived from female donors were shown to be more sensitive to hERG blockers, based on qualitative assessments(Zeng et al. 2019) and were more sensitive to drug-induced QT prolongation(Huo et al. 2019). However, in a large-scale study of 134 chemicals (pharmaceuticals, industrial and environmental chemicals and food constituents) in iPSC-derived cardiomyocytes from 43 individuals, comprising both sexes and diverse ancestry(Burnett et al. 2019), the relative contribution of sex was low for most chemicals tested. Third limitation of this study is that we only used one phenotyping method based on calcium transient, instead of using a multiplexed approach. Calcium transient and contractility testing has been favored in the studies utilizing machine learning techniques for their high-throughput capabilities to generate the datasets large enough to train machine learning algorithms. While traditional patch-clamp technique is a powerful and critical tool for electrophysical measurements of hiPSC-CMs, its disadvantages of time consuming and technical demanding preclude its utilization in the high-throughput applications (Fang et al. 2021). In our analytical flow, brightfield videos were also recorded to analyze the contractile motions of the hiPSC-CMs, but these analyses presented too much noise to effectively generate contractile motion vectors for machine learning applications. Due to this technical limitation, we focused our high-throughput analysis based on calcium transients signals due to excellent signal-to-noise ratio for drug responses. Lastly, hiPSC-CMs were spontaneously beating without any external electrical pacing in this study, which is the limitation of our drug-screening platform. We understand the importance to ensure consistent contractile activities of hiPSC-CMs to reduce well-to-well variability using electrical pacing system, but such system is still difficult to be integrated with high-throughput platform for drug screening(Fang et al. 2021).

Overall, our work demonstrated a proof-of-concept analysis pipeline with significant potential for studying new pharmacological agents and their mechanisms of action. In the future, a larger dataset can be created for high throughput analysis with an ever-expanding library that may lead to potential success in classifying unknown drugs based on their cardiotoxic effects. Additional advanced nonlinear signal analyses can be applied to the workflow to bolster machine learning algorithms and create improved classification models for cardiotoxicity studies. Ultimately, a deep learning model trained upon the raw calcium transient signals of hiPSC-CMs may prove to be the most successful model for cardiotoxicity studies. While such a model can be trained with the least amount of data lost, there would be an overall decline in interpretability without traditional quantitative peak analysis. Therefore, a model trained with nonlinear signal analysis will retain the nonlinear interactions captured by deep learning methods while still providing quantifiable parameters for general understanding.

Conclusion

In this study, a high-throughput drug assay based on calcium transients enabled an automated process to increase the speed and decrease the potential human biases in cardiotoxicity screening. The machine learning algorithms were able to distinguish the utilized drug with 80% accuracy, suggesting great promise in training future models for drug classifications. Furthermore, nonlinear analysis based on phase space reconstruction has proven to be sensitive to aberrations within the transient signals of hiPSC-CMs and boosted the unbiased performance of multiple machine learning algorithms in the detection of cardiotoxic effects. With unbiased yet sensitive quantification of cardiac physiology, we believe that this proof-of-concept work demonstrated great potential as a valid, animal free, and ethical drug testing platform.