Wave propagation enhances extracellular signal strength in small excitable tissues

Figures

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  Fig. 1. A: Default model geometry. hiPSC-CMs are arranged in a dogbone-like geometry in a single well (see Chip C1 in ref. 18). Each cell has a length of 25 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m and a width of 8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m. The location of one stimulation electrode and six measuring electrodes are indicated. Note that hiPSC-CMs are also located at the location of the electrodes. B: Stimulation protocols. We consider four different stimulation protocols: (i) no stimulation (spontaneous action potential firing), (ii) weak global optical stimulation applied in the entire cell collection, (iii) same as (ii) but stronger stimulation, and (iv) localized extracellular stimulation through an electrode.

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  Fig. 2. Circular MEA geometry used in some simulations. hiPSC-CMs are arranged in a circular geometry with radius 1.56 mm. Each cell has a length of 25 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m and a width of 8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m. The location of one stimulation electrode and 15 measuring electrodes are indicated. The electrode width is 50 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}m and the distance between electrodes is 350 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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  Fig. 3. Identical cells. Simulation of a collection identical hiPSC-CMs for four different stimulation protocols. The upper panel displays the extracellular potential measured in the main measurement electrode illustrated in Fig. 1A. The extracellular potential is zero in all cases except for localized stimulation. The next panel shows the membrane potential recorded at the location of the same electrode. All stimulation protocols display clear and similar action potential (AP) firing. In the lower panel, snapshots of the membrane potential are displayed for three points in time during AP firing. For the localized stimulation, an excitation wave is generated with a conduction velocity of 1.0 cm/s, whereas for the remaining stimulation protocols, the cells fire uniformly across the cell collection.

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  Fig. 4. Varying cell properties. Simulations like in Fig. 3, except that cell-to-cell variation is introduced in the conductances of the membrane currents (20% standard deviation). In this case, there are spatial gradients in the membrane potential for all stimulation protocols. Consequently, EPs are present in all cases, but wave initiation continues to yield the strongest signal.

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  Fig. 5. Improved gap junction coupling. Simulations like in Fig. 3 except that the gap junction coupling strength is increased by a factor of 100, to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_g = 170$$\end{document} nS, and that there is 20% cell-to-cell variation in ion channel conductances. The increased gap junction coupling greatly enhances the EP signal strength for a localized stimulation.

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  Fig. 6. Identical cells in a circular MEA geometry. Simulations like in Fig. 3, except that we use a circular MEA geometry, as illustrated in Fig. 2. The upper panel shows the extracellular potential (EP) recorded in each measuring electrode and the insets show the location of the individual EP traces in the MEA setup. The second panel shows the membrane potential recorded in the measuring electrodes. All stimulation protocols display clear and similar action potential (AP) firing. In the lower panel, snapshots of the membrane potential are displayed for two points in time during AP firing. Like in Fig. 3, the cells fire uniformly across the collection for all stimulation protocols except for the localized stimulation.

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  Fig. 7. Varying cell properties in a circular MEA geometry. Simulations like in Fig. 6, except that cell-to-cell variation is introduced in the conductances of the membrane currents (20% standard deviation). Again, the EP signals are strongest for localized or no stimulation, weaker for a weak global stimulation, and weakest for a strong global stimulation.

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  Fig. 8. Improved gap junction coupling in a circular MEA geometry. Simulations like in Fig. 6, except that the gap junction coupling strength is increased by a factor of 100, to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_g = 170$$\end{document} nS, and that there is 20% cell-to-cell variation in ion channel conductances. The improved gap junction coupling greatly enhances the EP signal strength for the no stimulation and localized stimulation cases.