# Quantification of Cardiomyocyte Beating Frequency Using Fourier Transform Analysis

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

^{−4}mM β-mercaptoethanol, 1X antibiotics/antimyoctic and 1000 U/mL LIF). Clonal lines were established and were checked to ensure that the MHCα::GFP is expressed in all cardiac cells and only in cardiac cells [19]. For differentiation studies, ES cells were passaged off of MEFs and were differentiated as embryoid bodies (EBs) using the hanging drop method, as previously described [19]. Single EBs, consisting of approximately 300 cells each, were plated in each well of a 48-well plate and were allowed to differentiate for 17–21 days prior to imaging.

- $R\left(t\right)=\frac{F\left(t\right)-{F}_{0}\left(t\right)}{{F}_{0}\left(t\right)}$where F is intensity and t is time. F
_{0}, the local minimum intensity, is found by - ${F}_{0}\left(t\right)=\left\{\mathrm{min}(\overline{F\left(x\right)})|(t+\frac{{\tau}_{1}}{2}\le x\le t+{\tau}_{2},x=t+\frac{{\tau}_{1}}{2}+0.01n\right\}$where n = 0, 1, 2,… etc.
- $\overline{F\left(x\right)}\approx \frac{1}{{\tau}_{1}}{{\displaystyle \int}}_{x-\frac{{\tau}_{1}}{2}}^{x+\frac{{\tau}_{1}}{2}}F\left(z\right)dz$where $\overline{F\left(x\right)}=\frac{1}{{\tau}_{1}}\left\{\frac{{\tau}_{1}}{n}\left[F\left({z}_{1}\right)+2F\left({z}_{2}\right)+2F\left({z}_{3}\right)+\cdots +2F\left({z}_{n-2}\right)+2F\left({z}_{n-1}\right)+F\left({z}_{n}\right)\right]\right\}$And ${z}_{n}={z}_{1}+0.01n$ and ${z}_{1}=x-\frac{{\tau}_{1}}{2}$
- $\left\{t=\frac{{\tau}_{1}}{2}+{\tau}_{0}n|0<t<a-{\tau}_{2}\right\}$where n = 0, 1, 2, … etc. and a = max(t)

_{0}, τ

_{1}, and τ

_{2}are spacing parameters and can be adjusted for different methods of imaging. The parameter τ

_{0}can be adjusted for different frequency images using the following equation:

## 3. Results and Discussion

_{0}= 0.1) satisfied the Nyquist sampling criteria to detect fast, SAN-like beating (<300 bpm at room temperature), with values of τ

_{1}= 0.75 and τ

_{2}= 2 found empirically to be optimal. However, the algorithm can easily be adapted for other time parameters and, therefore, is not limited to use with a single sampling frequency, time length, or type of imaging. Figure 2 shows how the normalization process eliminates low frequency noise from the data.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Time-lapse series of beating cardiomyocytes with ROIs (region of interest) placed to extract motion. (

**A**) Phase-contrast image of beating areas within an EB (embryoid bodies), and corresponding MHCα::GFP image confirming cardiomyocyte identity. ROIs (5 × 5 pixels) are placed at the edges of the beating areas (purple, green and orange squares) and a non-beating control area (cyan square). Scale bare = 100 µm; (

**B**) Plot showing changes in the mean pixel intensities within ROIs over time, which correspond to beating motion.

**Figure 2.**Normalization of time series data and FFT (fast Fourier transform) power spectrum analysis to beating frequency. (

**A**) Raw time series data showing high frequency changes in mean intensity combined with slow, sinusoidal changes due to secondary motion imaging artifact. (

**B**) FFT plot of the raw time series data attributes dominant beating frequency (6 bpm) to motion caused by imaging artifact. (

**C**) Normalization of time series data eliminates changes due to secondary imaging artifacts. (

**D**) FFT plot of normalized time series data correctly identifies fast beating (166 bpm) as the dominant frequency.

**Figure 3.**FFT analysis correctly identifies dominant frequencies despite pauses in beating. (

**A**) Time series plot showing intermittent pauses (red bracket) in fast beating. (

**B**) FFT plot reveals a single dominant beating frequency (145 bpm) that is approximately double the value calculated manually by averaging the number of spikes over time (~84 bpm).

**Figure 4.**Comparison of cardiomyocyte contraction and calcium transients using FFT analysis. (

**A**) Time series plot of cardiomyocyte contractions measured by phase-contrast intensity fluctuations and (

**B**) corresponding FFT plot that identifies the dominant beating frequency (58 bpm). (

**C**) Time series plot of cardiomyocyte calcium transients that were measured by Fluo-4 fluorescence intensity fluctuations in the same beating area as (

**A**). Video S2 shows Fluo-4 imaging with the ROI (green square) used to measure intensity fluctuations. (

**D**) FFT plot of Fluo-4 data identifies a dominant beating frequency (65 bpm) based on calcium transients that is similar to the contraction frequency that is based on phase-contrast imaging. Sampling frequency was 18 Hz for both imaging modalities.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Reno, A.; Hunter, A.W.; Li, Y.; Ye, T.; Foley, A.C.
Quantification of Cardiomyocyte Beating Frequency Using Fourier Transform Analysis. *Photonics* **2018**, *5*, 39.
https://doi.org/10.3390/photonics5040039

**AMA Style**

Reno A, Hunter AW, Li Y, Ye T, Foley AC.
Quantification of Cardiomyocyte Beating Frequency Using Fourier Transform Analysis. *Photonics*. 2018; 5(4):39.
https://doi.org/10.3390/photonics5040039

**Chicago/Turabian Style**

Reno, Allison, Andrew W. Hunter, Yang Li, Tong Ye, and Ann C. Foley.
2018. "Quantification of Cardiomyocyte Beating Frequency Using Fourier Transform Analysis" *Photonics* 5, no. 4: 39.
https://doi.org/10.3390/photonics5040039