Metrics of high cofluctuation and entropy to describe control of cardiac function in the stellate ganglion

Figures

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  Figure 1.. Event rate (E⁢R) and entropy results between control and heart failure (HF) animals (horizontal axes). White triangles indicate data points. (A, B) HF group animals show higher ERMEAN and ERSTD compared to control group (p<0.05). (C, D) HF group animals show higher entropy variability (EntropySTD, Equation 2, p=0.008, in (D)), and no difference in EntropyMEAN (Equation 2, p=0.08, in (C)). For E⁢R, p values are from two-sample t-test or Wilcoxon rank-sum tests, depending on normality. For entropy, p-values are from linear mixed effects (LMEs, Equation 2) detailed in Materials and methods.

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  Figure 2.. Cofluctuation histograms (calculated from mean or standard deviation of sliding spike rate, referred as CofluctuationMEAN and CofluctuationSTD, respectively) and log-normal fits for each animal group. μF⁢I⁢T and σF⁢I⁢T are the respective mean and standard deviation (STD) of fitted distribution, used for 68% confidence interval bounds. (A, B) Control animals have narrower bounds and represent a better fit to log-normal distribution. (C, D) Heart failure (HF) animals display more heavily skewed distributions that indicate heavy tails.

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  Figure 3.. Cofluctuations time series at convergent C values for each animal. (A) Cofluctuations from coactivity calculation from mean of sliding spike rate for control animals. (B) Cofluctuations from coactivity calculation from mean of sliding spike rate for heart failure (HF) animals. (C) Cofluctuations from coactivity calculation from standard deviation of sliding spike rate for control animals. (D) Cofluctuations from coactivity calculation from standard deviation of sliding spike rate for HF animals.

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  Figure 4.. Events time series at convergent (C,T) pairs for each animal. (A) Events from coactivity calculation from mean of sliding spike rate for control animals. (B) Events from coactivity calculation from mean of sliding spike rate for heart failure (HF) animals. (C) Events from coactivity calculation from standard deviation of sliding spike rate for control animals. (D) Events from coactivity calculation from standard deviation of sliding spike rate for HF animals.

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  Figure 5.. Event entropy Equation 2 investigation involved consideration of entropy values inside and outside of event regions. (A) There is significant difference between in EntropyMEAN,EVENT and EntropySTD,EVENT across all animals (p=0.0006). (B) There is no significant difference in EntropyMEAN,EVENT between animal groups (p=0.07). (C) There is significant difference in EntropySTD,EVENT between events and non-events across all animals (p<0.0001). (D) There is significant difference in EntropySTD,EVENT between animal groups (p<0.012).

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  Figure 6.. Experimental workflow and overall concept. (A) A linear microelectrode array (LMA) was inserted to the left stellate ganglion (SG) for each animal. A total of 16 channels of neural activity were collected along with simultaneous left ventricular pressure (LVP). Representative spike trains are displayed for each animal group. (B) Specifications of the LMA. (C) Conceptual representation of this work. SG receives efferent and afferent information from the spinal cord’s intermediolateral complex (IML) and dorsal root ganglion, respectively, and transmits efferent information to the heart. In this work, we investigate neural activity and its relationship to cardiac function as represented by a control target such as LVP. (D) Among 17 Yorkshire pigs, 11 had heart failure induced by ventricular pacing, and 6 were in control group. SG recordings were collected at terminal experiments for both groups. (E) Experimental flow descripting the surgical preparation for the recordings. DH, dorsal horn.

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  Figure 7.. Signal processing block diagram.

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  Figure 8.. Coactivity matrix and event rate (E⁢R) computation pipeline illustrated for four channels. (A) Pearson’s cross-correlation coefficients (R) of pairwise sliding spike rate windows for four channels. (B) R values for cross-correlation of ‘i’ and ‘j’ channels are stored in the ‘i’ and ‘j’ positions of a 4×4 matrix at each timestamp. (C) Coactivity matrix super-diagonals at each timestamp are vertically stacked. At each timestamp t, n⁢(n-1)/2=6 unique cross-correlations are possible corresponding to super-diagonals with 3, 2, and 1 members. The y-axis begins at the bottom with the three members of the first super-diagonal followed by subsequent super-diagonals. Colors represent the R value. (D) Cofluctuation time series are the percentage of Pearson’s R values at each timestamp that exceed a cofluctuation threshold (C). (E) Discrete events correspond to time intervals when cofluctuations show an up/down crossing through an event threshold (T).

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  Appendix 1—figure 1.. Cofluctuation bootstrapping pipeline for individualized event rate (ER) for each animal—Part I. (A) Coactivity matrix and cofluctuation time series for a cofluctuation threshold and event threshold pair (C,T). (B) Cofluctuation time series with depicted events (red triangles are up-crossing timestamps) for a range of (C,T) pairs. Panel A is further explained in Appendix 1—figure 5.

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  Appendix 1—figure 2.. Cofluctuation bootstrapping pipeline for individualized event rate (ER) for each animal—Part II. (A) Bootstrapped histogram of ERs for a single (C,T) pair with 95% confidence interval (C⁢I) width. (B) Threshold pair (C,T) is chosen for an animal given non-zero E⁢R and E⁢R convergence. Depicted C⁢I widths are found at all of the depicted 18(C,T) pairs available on the axes grid. (C) List of (C,T) pairs that show E⁢R convergence with C⁢I widths for each animal.

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  Appendix 1—figure 3.. Neural specificity and entropy computation—Part I. (A) Neural specificity sample showing left ventricular pressure (LVP) and neural spikes. Spiking activity is more specific or biased (yellow), over random sampling, to LVP just below systolic pressures. (B) Normalized histograms of random and neurally sampled LVP. (C) Bars show subtracted histograms and colors indicate the specificity thresholded with α=0.5: specificity exceeding α is yellow, below -α is blue, and between the bounds (-α,α) is teal.

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  Appendix 1—figure 4.. Neural specificity and entropy computation—Part II. (A) Sliding neural specificity time series (top) for a selected sliding window width Δ⁢t. Entropy of neural specificity, computed from red highlighted window of width, Δ⁢t absolute difference (shown for a sample at bottom). (B) Entropy time series corresponding to the overall experiment, entropy sample computed from steps in (D). An animated version is in Appendix 1—Animation 1.Appendix 1—Animation 1