# Geometric Understanding of Local Fluctuation Distribution of Conduction Time in Lined-Up Cardiomyocyte Network in Agarose-Microfabrication Multi-Electrode Measurement Assay

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Embryonic Mouse Primary Cardiomyocytes

_{2}and 0.5 mM MgCl

_{2}to induce heart contraction and remove corpuscles cells. The hearts were then transferred to PBS without CaCl

_{2}, and MgCl

_{2}and the ventricles were separated from the atria, minced into 1 mm

^{3}pieces with scissors. After that, they were incubated at 37 °C for 30 min in PBS containing 0.2% collagenase (Wako Pure Chemical Industries, Osaka, Japan) to digest the ventricular tissue. After this digestion step was repeated twice, the cell suspension was transferred to primary cultivation buffer (Dulbecco’s modified Eagle’s medium (DMEM, Invitrogen, Carlsbad, CA, USA) supplemented with 10% heat-inactivated fetal bovine serum (FBS, Invitrogen, Carlsbad, CA, USA), 1% penicillin-streptomycin (Invitrogen, Carlsbad, CA, USA) at 37 °C. In the subsequent experiments, the above primary cultivation medium was used to handle embryonic mouse primary cardiomyocytes. The cells were filtered through a 40 μm-nylon mesh cell strainer (BD Bioscience, Franklin Lakes, NJ, USA) to remove debris that was not able to be digested and then centrifuged at 200 g for 5 min at room temperature. After the precipitation of the cells was resuspended gently in the primary cultivation buffer, the cells were cultivated.

#### 2.2. Human Embryonic Stem Cell-Derived Cardiomyocytes

#### 2.3. Agarose Microfabrication

#### 2.4. Cell Culture

^{5}cells/mL of cardiomyocyte suspensions were placed on the prepared collagen-coated 35-mm dishes for three days at 37 °C in 5% CO

_{2}. For cell collection, 1 mL of 0.25% trypsin-ethylenediaminetetraacetic acid (EDTA). were added to the dishes and incubated for 5 min at 37 °C in 5% CO

_{2}. Then, the solutions in the dishes were collected and centrifuged at 200 g for 5 min. After the aspiration of the supernatant, 3 mL of cultivation buffers were added as the stop solutions. After cell counting, the cells were centrifuged at 200 g for 5 min again, and the cultivation buffers were added to 3 × 10

^{6}cells/mL. Ten microliters of the cell suspensions were placed to each microstructure on the MEA chips as the droplets, and the MEA chips were incubated at 37 °C for 3 h. Then, 1 mL of the cultivation buffers were added mildly and exchanged after incubating for one day. The cells were cultivated for 5–7 days, while changing the medium once every two days.

#### 2.5. Measurement System

_{2}.

#### 2.6. Data Analysis

#### 2.7. Drug Administration

#### 2.8. Cell Staining

#### 2.9. Statistical Analysis

#### 2.10. Simulation

## 3. Results and Discussion

#### 3.1. Distribution of Conduction Time in Width Controlled Cardiomyocyte Networks

^{3}cells/mm

^{2}in 100 μm width, 3.5 ± 0.98 × 10

^{3}cells/mm

^{2}in 200 μm width, and 3.2 ± 0.76 × 10

^{3}cells/mm

^{2}in 300 μm width of primary network (Figure 2Ab–Cb), and 1.1 ± 0.44 × 10

^{3}cells/mm

^{2}in 100 μm width, 1.2 ± 0.39 × 10

^{3}cells/mm

^{2}in 200 μm width, and 1.3 ± 0.34 × 10

^{3}cells/mm

^{2}in 300 μm width hES network (Figure 2Db–Fb). These concentrations mean the averaged cell sizes were 11 μm in diameter (3.0 × 10

^{3}cells/mm

^{2}) to 17 μm in diameter (1.3 × 10

^{3}cells/mm

^{2}) spread two-dimensionally in the rectangular microstructures on the MEA chips. Mean number of cells in the width direction (perpendicular to the propagation direction) were 6.24 ± 0.852 cells in 100 μm width, 13.8 ± 2.63 cells in 200 μm width, and 16.6 ± 1.18 cells in 300 μm width of primary network, and 4.51 ± 0.591 cells in 100 μm width, 6.68 ± 0.480 cells in 200 μm width, and 11.2 ± 1.64 cells in 300 μm width hES network (Figure 2Db–Fb), indicating that at least four to six cells in 100 μm width chamber were lined-up perpendicular to the propagation direction and competed for propagation as the faster firing regulation.

#### 3.2. Effect of Fast Inward-Sodium-Current Blocking on the Distribution of Conduction Time

#### 3.3. Correlation of Beating Intervals and Conduction Time

#### 3.4. Correlation of Conduction Time and Its Fluctuation between Neighboring Units

#### 3.5. Influence of Cell Density for Conduction Velocity in Unit Length

^{3}–3 × 10

^{3}cells/mm

^{2}to form the homogeneous monolayered two-dimensional (2D) sheet of cells in the rectangular microchambers. Figure 4 shows the cell concentration dependence of unit length conduction velocity in 100 μm, 200 μm, and 300 μm width primary (A) and hES (B) networks. Both plots showed weak correlations between cell density and conduction velocity in primary and hES cardiomyocytes (correlation coefficient = 0.39 in primary and 0.31 in hES). In both cell types, the fluctuation (S.D.) of conduction velocity was large when conduction velocity was large. In addition, when cell density and conduction velocity was lower, the conduction velocity was stable. However, in primary cardiomyocytes, the fluctuation was large when conduction velocity was small in low cell density.

#### 3.6. Can the Faster Firing Regulation Explain These Conduction Characteristics?

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Conduction time measurement system setup and method. (

**A**) Schematic drawing of multi-electrode array measurement system. Cardiomyocyte networks were cultivated in the rectangular-shaped agarose microstructures on the multi-electrode array (MEA) chip. The external field potentials (FPs) of cardiomyocytes on microelectrodes were amplified and digitally recorded to calculate the conduction time. (

**B**) Setup of optical light pathways of the system. For the preparation of linearly craved MEA chip with collagen coating, a 1480-nm infrared laser beam was focused on the agarose layer of the MEA chip with x10 objective lens for spot heating of a portion of agarose layer for forming the microstructures. Phase-contrast images of cells in the microchambers were also recorded by the charge-coupled device (CCD) camera. (

**C**) Time-course of drug administration. FP waveforms were recorded during 5 min of drug exposure in control medium (Ct), low concentration Quinidine (a1), and high concentration of Quinidine (a2).

**Figure 2.**Propagation manner of linear mouse primary cardiomyocyte network and human embryonic stem cell-derived (hES) cardiomyocyte network. (

**A**–

**C**) Mouse primary network in 100 μm width (D), 200 μm width (E), 300 μm width (F). (a) Phase-contrast micrograph of mouse primary cardiomyocytes network with 2100 μm in length. Microelectrodes for measuring the external field potential were set 300 μm interval. The left numbers represent the associated microelectrodes. (b) Fluorescent micrograph of mouse primary cardiomyocytes in the network. The nuclei of each cell were stained by 4’,6-Diamidino-2-phenylindole dihydrochloride (DAPI). (c) Examples of Extracellular field potential signals of microelectrodes. The red numbers represent microelectrodes shown in (a). (d) Histograms of propagation time between specific two electrodes. (

**D**–

**F**) hES cardiomyocyte network in 100 μm width (A), 200 μm width (B), 300 μm width (C). (a) Phase contrast micrograph of hES cardiomyocyte network with 2100 μm in length. Microelectrodes for measurering the external field potential were set 300 μm interval. The left numbers represent the associated microelectrodes. (b) Fluorecent microgragh of hES cardiomyocytes in the network. The nuclei of each cells were stained by DAPI. (c) Examples of extracellular field potential signals of microelectrodes. The red numbers represent microelectrodes shown in (a). (d–f) Histgrams of propagation time between specific two electrodes; 0 μM Quinidine (Control) (d), M 3 μM Quinidine (e), and 9 μM Quinidine (f), respectively. N represents beating number. Bars, 100 μm.

**Figure 3.**Characteristics of conduction time distribution in cardiomyocyte networks. (

**A**) Comparison of fluctuations of conduction time in cardiomyocyte networks. (a)–(l) Unit length dependence of mean time (blue circles) and S.D. (orange circles) in 100 μm width (a,d,g,j), 200 μm width (b,e,h,k), and 300 μm width (c,f,i,l). Mouse primary (a–c), 0 μM Quinidine (Control) (d–f), 3 μM Quinidine (g–i), and 9 μM Quinidine (j–l). (m) The short-term variability (STV) are indicated between the neighboring electrodes from both ends of conducting section in 100 μm width (blue open circles and lines), 200 μm width (orange open squares and lines), and 300 μm width (gray open triangles and lines) were plotted. (

**B**) Correlation between inter beat interval (IBI) and conduction time (CT) in 100 μm width hES network (a,d,g), 200 μm width hES network (b,e,h), 300 μm width hES network (c,f,i). The numbers represent those shown in Figure 2D–Fd–f. Zero micrometers Quinidine (Control) (a–c), 3 μM Quinidine(d–f), and 9 μM Quinidine (g–i). R represents correlation coefficient. (

**C**) Cross-correlation of conduction time in 100 μm width hES network (a,d,g), 200 μm width hES network (b,e,h), 300 μm width hES network (c,f,i). The numbers represent those shown in Figure 2D–Fd–f. Zero micrometers Quinidine (Control) (a–c), 3 μM Quinidine (d–f), and 9 μM Quinidine (g–i). R represents correlation coefficient.

**Figure 4.**Cell concentration dependence of conduction velocity in unit lengths. Mean conduction velocities of mouse primary cells (

**A**) and hES cells (

**B**) in 300 μm unit length were plotted. Blue circles for 100 μm width, orange circles for 200 μm width, and green circles for 300 μm width, respectively. Error bars are S.D. of the mean conduction velocities.

**Figure 5.**Simulation results of conduction time distribution in the faster firing regulation model. Histogram (

**A**), mean value (

**B**), and S.D. (

**C**) of propagation time acquired from the one way random walk model ($n={10}^{3}$, mean propagation time $3.3$ μm/s, and S.D. $0.36$ μm/s). The distribution of conduction time dispersed, and both the mean time and S.D. increased as the firing signal propagated.

Conduction Time (Mean ± S.D.) [ms] | |||||||
---|---|---|---|---|---|---|---|

Propagation Distance [μm] | |||||||

Cell Type | Width [μm] | Sample | 300 | 600 | 900 | 1200 | 1500 |

Mouse primary | 100 | 1 | 8.11 ± 0.747 | 10.8 ± 0.576 | 13.6 ± 0.692 | ||

2 | 7.91 ± 0.599 | 16.7 ± 0.703 | 28.5 ± 0.780 | 39.2 ± 1.38 | |||

200 | 1 | 8.19 ± 1.77 | 13.8 ± 1.68 | 17.3 ± 1.75 | 22.6 ± 1.80 | ||

2 | 5.51 ± 0.409 | 9.00 ± 0.469 | 16.9 ± 0.603 | 29.4 ± 1.06 | |||

300 | 1 | 5.94 ± 0.256 | 10.4 ± 0.333 | 14.7 ± 0.457 | 19.9 ± 0.447 | 22.7 ± 0.473 | |

2 | 6.63 ± 0.296 | 12.6 ± 0.445 | 23.2 ± 0.915 | ||||

hES | 100 | 3.23 ± 0.210 | 6.55 ± 0.193 | 8.54 ± 0.212 | |||

200 | 5.80 ± 0.327 | 8.23 ± 0.361 | 13.6 ± 0.422 | 17.6 ± 0.298 | |||

300 | 2.14 ± 0.140 | 7.62 ± 0.189 | 12.2 ± 0.212 | 17.0 ± 0.155 | 19.2 ± 0.148 |

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**MDPI and ACS Style**

Sakamoto, K.; Aoki, S.; Tanaka, Y.; Shimoda, K.; Hondo, Y.; Yasuda, K.
Geometric Understanding of Local Fluctuation Distribution of Conduction Time in Lined-Up Cardiomyocyte Network in Agarose-Microfabrication Multi-Electrode Measurement Assay. *Micromachines* **2020**, *11*, 1105.
https://doi.org/10.3390/mi11121105

**AMA Style**

Sakamoto K, Aoki S, Tanaka Y, Shimoda K, Hondo Y, Yasuda K.
Geometric Understanding of Local Fluctuation Distribution of Conduction Time in Lined-Up Cardiomyocyte Network in Agarose-Microfabrication Multi-Electrode Measurement Assay. *Micromachines*. 2020; 11(12):1105.
https://doi.org/10.3390/mi11121105

**Chicago/Turabian Style**

Sakamoto, Kazufumi, Shota Aoki, Yuhei Tanaka, Kenji Shimoda, Yoshitsune Hondo, and Kenji Yasuda.
2020. "Geometric Understanding of Local Fluctuation Distribution of Conduction Time in Lined-Up Cardiomyocyte Network in Agarose-Microfabrication Multi-Electrode Measurement Assay" *Micromachines* 11, no. 12: 1105.
https://doi.org/10.3390/mi11121105