Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

Figures

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  FIGURE 1. Fourier analysis in a high-frequency entrained canine heart. (A,B) show the epicardium of a canine heart that is paced from the top (RV anterior) entrained with f p = 3.2 Hz (no alternans) and f p = 8.0 Hz (2:2 DA), respectively. Shown is the Fourier space (phase and amplitude) of frequencies f and f 1/2. The white arrows indicate the direction of the propagation wave. Two AP rhythms measured at two independent locations (P1 and P2, 6 × 6 pixel FOV) and their respective Fourier spectra are shown exemplarily. (B) shows a typical example where nodal lines are visible at f 1/2. Every second AP time course is shown in red to facilitate visualization of the 2:2 AP rhythm. The second peak 2f p in the Fourier space of the upper AP rhythms is a typical higher-order frequency mode. The positions P1 and P2 are highlighted by pink and cyan squares in (A) and (B). Three waves are marked by the wave numbers, as n − 1, n, and n + 1.

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  FIGURE 2. Simultaneous DA of different AP rhythms in a high-frequency entrained epicardium of a canine heart. (A) shows two AP rhythms (P1 and P2, 6 × 6 pixel FOV) of 2:2 and 4:4 alternans and their Fourier spectra, respectively. The stimulation site is on the bottom (base) of the heart with f p = 8.50 Hz. f indicates the entrainment frequency, and f 3/4 indicates the presence of a 4:4 AP rhythm with its two corresponding peaks, f1/21 and f1/22 around f p/2. The peak at f 1/4 corresponds to a wavelet of four APs that is fully expressed by f p. Every second or fourth AP is shown in red to facilitate visualization of the 2:2 or 4:4 AP rhythms. (B) shows the corresponding spatial phase and amplitude information of the five frequency peaks. The Fourier data shown at f 3/4 indicate a 4:4 AP rhythm on the right side (RV anterior) of the heart only. The respective counter phase is illustrated at f1/21 . f1/22 shows the typical 2:2 phase of a 2:2 AP rhythm, similarly to that illustrated in Figure 1B. The positions P1 and P2 are highlighted by pink and cyan squares. (C) shows the direction of the respective phase information indicated by red arrows that are shown in (B). Nodal lines are outlined by…

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  FIGURE 3. Pacing-site–dependent frequency maps. (A) shows frequency maps obtained from the top (base, left panels) and left (RV posterior, right panels) paced canine ventricles, respectively. The top and bottom panels show data recorded at the epicardium (EPI) and endocardium (ENDO). 2:2 AP rhythms (f 1/2) are observed from about 4.5 Hz. 4:4 AP rhythms (f 3/4) are observed only in base paced canine recordings at a pacing of about 9.2 Hz. (B) shows a guide of the eye for (A) with the main frequencies (solid lines), secondary peaks (dashed lines), and higher-ordered peaks (dotted lines). (C) shows a comparison of the normalized amplitudes for 4:4 alternans (9.2 Hz, red line) and fibrillation (10.7 Hz, black line) that is observed at the ENDO paced from the RV posterior.

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  FIGURE 4. Stabilization of nodal line formation at higher entrainment frequencies. (A) shows the evolution of alternans from lower to higher pacing frequencies. The Fourier space, phase and amplitude at f 1/2 and ΔAPD, is shown from f p = 2 Hz to 7.2 Hz. (B) shows the concordant alternans evolution of the frequency maps shown in Figures 3A,B. The top (base, left panels) and left (RV posterior, right panels) paced canine hearts are shown on the left and right sides, and the respective epicardium (EPI) and endocardium (ENDO) are shown at the bottom and top. The regimes of no alternans, concordant alternans (CA), and discordant alternans (DA) are indicated on the top and bottom of the figures. Red arrows indicate the position of the electrode.

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  FIGURE 5. Optical ultrastructure extracted from the low-frequency regime of the epicardium (EPI). (A) shows the Fourier space—phase and amplitude—at f = 0.5 Hz for f p = 3 Hz frequency entrained tissues that are paced on the endocardium from four different directions, as indicated by the white arrows. (B) shows the amplitudes of the Fourier space at f = 0.5 Hz for different entrainment frequencies f p that are stimulated at the base. The white arrows in (A,B) indicate the respective direction of wave propagation. Below the amplitude images are indicated the regimes of no alternans and discordant 2:2 alternans (DA).

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  FIGURE 6. Data assimilation procedure and cardiac alternans maps for stimulation at the base of the ventricle. (A) Spatial map of the Fourier spectrum at f = 0.5 Hz and tissue boundary. (B) Computed heterogeneity maps from the tissue ultrastructure (see the text) for both diffusivity, H 1 (x, y), and time constants regulating the APD, H 2 (x, y). Black dashed lines represent one-dimensional cuts of the heterogeneity maps (top panels). (C) Modeled alternans maps: homogeneous case, heterogeneity in diffusivity (H1 model), and heterogeneity in APD (H2 model). (D) Comparison between the modeled alternans map, with combined heterogeneities in APD-regulating time constants and diffusivity (H3 model), and experimental alternans. Top row: ΔAPD maps. Bottom row: FFI phase maps at f = f p /2 (f 1/2). Alternans maps are obtained at a pacing frequency f p = 6.2 ± 0.4 Hz.

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  FIGURE 7. Data assimilation and cardiac alternans maps for right ventricle anterior stimulation. (A) Heterogeneity maps for both diffusivity, H 1 (x, y), and time constants regulating the APD, H 2 (x, y). (B) Modeled alternans maps at pacing frequencies f p = 4.0 Hz and 5.6 Hz and corresponding FFI phase maps at f = f p /2 (f 1/2). (C) Experimental alternans corresponding to modeled maps shown in panel (B) and corresponding experimental FFI phase maps at f 1/2.