Automated quantification study of human cardiomyocyte synchronization using holographic imaging

This paper investigates the rhythm strip and parameters of synchronization of human induced pluripotent stem cell (iPS) derived cardiomyocytes. The synchronization is evaluated from quantitative phase images of beating cardiomyocytes which are obtained using the time-lapse digital holographic imaging method. By quantitatively monitoring the dry mass redistribution, digital holography provides the physical contraction-relaxation signal caused by autonomous cardiac action potential. In order to analyze the synchronicity at the cell-to-cell level, we extracted single cardiac muscle cells, which contain the nuclei, from the phase images of cardiomyocytes containing multiple cells resulting from the fusion of kmeans clustering and watershed segmentation algorithms. We demonstrate that mature cardiomyocyte cell synchronization can be automatically evaluated by time-lapse microscopic holographic imaging. Our proposed method can be applied for studies on cardiomyocyte disorders and drug safety testing systems. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Recent advantages in the human induced pluripotent stem cells (hiPSCs) cardiomyocyte derivation methods [1,2] have provided the opportunity for utilizing these cells as a platform for disease modeling, regenerative approaches toward precision medicine, and toxicity screening.The atria (chambers in which the blood enters) and the ventricles (chambers in which the blood is collected and pumped out) of the heart are composed of cardiac muscle cells or cardiomyocytes (CM).For proper functioning of the heart, cells should be capable of shortening and lengthening their fibers as required, and these fibers must be flexible enough to stretch (for contraction-relaxation).The alternating action of contraction-relaxation is due to electrical stimulation created by ion fluxes in a well-sequenced order, in a process called cardiac excitation-contraction coupling.Each and every cell rapidly changes its 3D shape with the meaningful intermediate events (contraction period, relaxation period, and resting period) which occur at harmonic millisecond intervals.For perfect functioning of the cardiomyocyte system, all single cells should respond to the physical contraction command.This is achieved by the electro-chemical linkage between cells through structures known as gap junctions, which facilitates the action potential to travel to the adjoining cells, resulting in all cells contracting and relaxing simultaneously in a synchronized manner.
Several methods are proposed to study the electrophysiology and biomechanics of the CM.Common methods include patch clamping [3,4], calcium imaging [5,6], and imagebased contraction-relaxation studies [7,8].Mechanical transduction with microposts and traction force microscopy [9,10] are other useful techniques to study the mechanical aspects of CM force microscopy.Also, several techniques have been applied to detect structural changes of CM during the synchronized beating.In order to respond to environmental changes and receiving sign cell communi specific signa cell communi calcium chan allows screen is used to coo and strategies is used to stud beating [19]. of the whole automated m toxicity and c Fig. 1 inset i quanti Label-free Among the configuration related abnorm cells storage reconstructing bio-volume o environments [26], studying muscle cell ac coordination nals by a speci ication through al according to ication is essen nge in [15] ind ning of cell bea ordinate beatin s for cell synch dy cardiomyoc Indeed, the bea e image and n eans to evalu ardiovascular h .(a) shows the sc is the magnified se itative phase imag e imaging has label-free ima (DHM) is a p malities [20], lesion and m g the hologram of the motile [25].Indeed, g stem-derived ctivities at the of the beating ific receptor in h chemical sig the intensity o ntial for cell gr dicates that ca ating-related pa ng activity in [ hronization eva ytes and monit ating signal ex no single-cell ate synchroniz health care. of studying s ues available, .This techniqu croorganism id changes in blo ganism by in-li nd assessmen is used to exa iac muscle cel vel [28].The st communicate scular wall.Stu mentioned that signal.In [13, rdination of be in harmony w ectrical stimula n [17,18] over titative hologra cell shape and method presen iscussed.Acco great importanc ng, (b) shows a re yellow line is 500µ samples using digital holog ue can help to dentification [2 ood bank stor ine holography nt of cancer c amine fluctuati lls [27] and st tudy presented e through sen udies in [11,12 the cell respo ,14] it is menti ating cycle.M with cell beatin ation of cardiom rview different aphic imaging structure chang nted in [19] is ordingly, prov ce for evaluat ecorded hologram; µm), and (c) is the non-invasive a graphy in mic o study red blo 21], studying r rage [22], ima y [23], estimati cells migratio ions of red bl tudying human d in [27]  methods in order to quantify the beating at the whole-cell level.Therefore, it does not address the single-cell level quantification study.The study in [28] proposes a method to segment CMs and extract single cells to shows the quantification for individual cells.DHM is capable of imaging cells by recording the phase retardation of a coherent or semicoherent light wave transmitted through the transparent sample, wherein the transparent specimens shift the phase of light instead of intensity alternations.Consequently, DHM quantitatively visualizes the 3D shape of biological samples and monitors the dry mass redistribution.DHM can directly readout the cell morphological movement which monitors the physical contraction-relaxation when applied to study CMs.
The current study analyzes the quantitative beating profile of cardiomyocytes using phase images obtained by digital holographic imaging at the single cell level for synchronization purposes.In the first section, we introduce a technique to extract the best section of the cell in the phase image using image segmentation methods.The segmented single-cell mostly consists of the nucleus of the cell, since it is the best part of the cardiac cell which can be perfectly segmented by the thresholding.On visual investigation, we observed that all components of the cell get redistributed during dry mass redistribution.Several individual cells from different parts of the phase image are extracted, and multiple parameters related to the contraction and relaxation of each individual cell are investigated to reveal the synchronization through numerical and visual analysis.

Label-free off-axis digital holographic imaging
The general layout of the off-axis digital holographic microscopic technique based on Mach-Zender interferometer is depicted in Fig. 1.The coherent laser source is split into an object (O) and reference beam (R) (See Fig. 1(a)).The object beam illuminates the specimen and a microscope objective (MO) collects and magnifies the object wavefront.The object and reference wavefronts are joined by a beam collector to create the hologram with a small tilt angle between them to provide the "Off-axis" geometry.At the end point, interferograms (Fig. 1(b)) are recorded by a CCD camera and transmitted to a personal computer for numerical reconstruction [29,30].The recorded hologram I H is the interference between object wave O and reference wave R, and is equated as follows: where R* and O* denote the complex conjugates of the reference and object beams, respectively.The small tilt angle between O and R enables us to eliminate the parasitic orders and isolate the real image from twin images and zero-order noise.To do so, we implement a spatial filter with properly defined size in order to cover only the bandwidth of the real image.By Fourier transforming the off-axis hologram and then multiplying it in frequency-domain by the filter and applying inverse Fourier transform, only the real image information is preserved by the formula: where FFT is the fast Fourier transform and IFFT is the inverse of the fast Fourier transform.
To reconstruct the phase image, the filtered hologram (I H F ) is multiplied by the digital reference wave, and the phase image is reconstructed by the Fresnel approximation: , ) e xp , where k, l, m, and n are integers (-N/2< = k, l, m, n< = N/2, N × N is the number of pixels in the CCD camera), and ( , ) m n Φ is the digital phase mask for the phase aberrations correction calculated by: ( ) Moreover, , ξ η Δ Δ are the sampling intervals in the observation plane expressed by: where d denotes the distance between the camera plane (hologram plane) and observation plane.A fine adjustment of k x , k y, and D can be performed in the absence of fringes by removal of residual gradients or curvature of the reconstructed phase distribution in some areas of the image where a constant phase is presumed [30].The digital phase mask resolves the phase aberrations caused by inserting microscopic objectives in the object wave arm, as shown in Fig. 1(a).Eventually, phase image (Fig. 1(c)) is obtained by the argument of:

Phase unwrapping
Since the numerically reconstructed phase value is limited between -π and + π and the result is given modulo 2π, discontinuities arise with values approximating 2π.The phase unwrapping procedure converts the undesired phase values to the desired ones by adding or subtracting 2π from the pixel value, thereby resolving the issue.Different approaches can be used for performing phase unwrapping; in this study, we followed the method explained in reference [31].This is a two-step technique, which first finds a reliable value for each pixel.For a pixel in an image, the values of its orthogonal and diagonal neighbors in a 3 × 3 window are required.These values are fed into a function, and reliability of the pixel is calculated according to gradients or differences between a pixel and its neighbors.The values are then used by another function to determine the unwrapping path.In conventional unwrapping algorithms, since the unwrapping path is simply calculated column-wise or row-wise, they are unable to resolve errors that occur due to variables such as discontinuity in the phase wraps, under-sampling in local areas, etc.Nevertheless, finding an unwrapping path with the use of reliable values can address these errors.The unwrapping path resolves the edges with a higher reliability prior to those with the less reliable edges.Since the unwrapping path is discrete, the unwrapping operation is therefore considered to be localized [31].The definition of phase retardation recoding is difficult to be addressed in biological applications.The more understandable concept is the optical path difference (OPD) which is related to the physical properties of a sample [32].The optical path difference (OPD) and phase values can be exchangeable, and are obtained by the following equation:

Phase im
Once we obt image proces noise of the im image in the t method and m cell-to-cell sy single still im for the mar segmentation CM [28].A cardiomyocyt  ) were procur for 14  The extrac OPD value of is imperative portion of the

Contract
During the ex their fibers, t holographic m during the phy useful periods of cells, we u OPD image v where opd i an standard devia   The total numbe minute.
The average tim during one minu

Standard deviat
The total numbe minute.
The average tim during one minu As shown in Fig. 3, the cardiomyocyte beating cycle includes two phases: the first is contraction, in which cell regions become denser and rise, and the entire cell changes its 3D shape; the second is the relaxation, in which the cell initiates resting.Figure 3(a) demonstrates the contraction and relaxation points of the beating curve of the cardiac cell; accordingly, the detected positive peaks for contraction and relaxation points are represented in Fig. 3(b).In order to numerically explore synchronization between single cardiac cells, we measured several parameters related to contraction and relaxation points.Table 1 summarizes the measured parameters and their corresponding description.In order to measure the abovedescribed parameters, positive peaks are detected by applying the first derivative technique to the original data curve.

Cardiac cell synchronization analysis
For the optimal functionality of the cardiac muscle system, cells have to respond to the commands of mechanical contraction.signal will propagate amongst whole cells, resulting in the myocardium pumping the blood out of the ventricle chamber.This requires synchronization between cells; i.e., the contraction and relaxation times need to be well tuned with no time-lag between the signals of two cells of the same sample.In the following sections, we present the same visually and by analyzing the cross-correlation between two signals.

Cell-to-cell synchronization analysis: visualization and cross-correlation analysis
After segmentation and extracting several cells, we compared the contraction and relaxation points of cells labelled in Fig. 2(c), and evaluated the data collected to reveal synchronization.2).We observed common characteristics between measured parameters, including beating rate and beating period, and also relaxation and contraction period.In addition, two other individual cells were analyzed to check for the beatrate synchronization.ing at the g a highly

Cross-correlation analysis between cells
Another analysis evaluated the cross-correlation to check the similarity and synchronization between two signals (two cells).This approach can be extended to other cells, thereby obtaining general synchronization results.To obtain cross-correlation between two signals, we used the following equation:   With the help of induced pluripotent stem cell derived cardiomyocytes model the chance of performing cardiac drug-treatment tests, the cardiac-toxicity during the drug discovery process and synchronization studies are made possible.To the best of our knowledge, this is

Cross-correlation value
the first research wherein a numerical analysis has been performed in a label-free manner for detecting cardiomyocyte beat-rate synchronization.Our results demonstrate the effectiveness of the proposed method for detecting cell-to-cell synchronization in the cardiovascular system.We propose that this method can be utilized for all kinds of cell synchronization detections in a given cell population.We believe that these numerical tools can also be useful for analyzing various fast dynamic behaviors in other cellular investigations.

Conclusions
Our results show that OPD variance analyzed at the single cell level along with different parameters can be used to evaluate cell-to-cell synchronization.The idea can further be generalized for cluster-to-cluster synchronization analysis.The presented work shows potential techniques for automatic synchronization investigation of mature human cardiac cells by visual and numerical parameters.Our study demonstrates that the proposed system can quantitatively detect synchronization for beating dynamics in the individual cardiac cells at the single cell level.The proposed method offers automatic ways of detecting the synchronization of isolated cardiac cells by quantification of critical parameters related to the beating profile, and demonstrates improvements in synchronization detection both by numerical and visual means.The proposed method can also be helpful to detect other abnormalities in the cardiovascular system, and in drug toxicity probes.

Fig. 4 .
Fig. 4. (a-b) Contraction and relaxation points for cell numbers 7 and 8, and (c) comparison of rhythm strips to detect and visualize synchronization.

Figures 4
Figures 4(a) and (b) show the detected positive peaks for contraction and relaxation points of two single cardiac cells.Figure 4(c) represents the rhythm strip comparison of isolated extracted cells for visual demonstration of synchronization during the time.As shown in Fig. 4(c), individual cells are fully synchronized for more than one cycle, considering both the rising and falling time of contraction and relaxation points.We investigated the synchronization in terms of comparing the measured parameters for isolated cells to reveal cardiomyocyte synchronization (Table2).We observed common characteristics between measured parameters, including beating rate and beating period, and also relaxation and contraction period.In addition, two other individual cells were analyzed to check for the beatrate synchronization.

Fig. 5 .
Fig. 5. (a-b) Detected contraction and relaxations points for cell numbers 3 and 4, and (c) comparison of rhythm strips to detect and visualize synchronization.The beating activity profile of two extracted individual cardiac cells is shown in Fig.5(cell numbers 3 and 4).Positive peaks for contraction and relaxation are marked by the automated detection method.To obtain the peaks, the larger value among two adjacent values 9) where * f denotes conjugate of f (first signal), g is the second signal, and n is the time lag between the two signals in the time domain (m).Cross-correlation has different applications in signal processing fields.In terms of investigating signal synchronization, it is a useful tool for determining the time delay between two heart beat signals.Maximum cross-correlation of functions indicates the time where the signals are best aligned.

Figure 7
Figure 7 shows the cross-correlation between the beating signal of two cells.According to this figure, we can see that two signals have the maximal value when the time lag is zero, indicating that the two signals are perfectly synched in time (similar figures were found for other cells, but are not shown here).With the help of induced pluripotent stem cell derived cardiomyocytes model the chance of performing cardiac drug-treatment tests, the cardiac-toxicity during the drug discovery process and synchronization studies are made possible.To the best of our knowledge, this is