A.5 Alternative analysis of the Spatial Organiza-tion
Here the alternative analysis of the spatial organization similar to the one performed in Section 7.2.1 is shown. The Analysis is here varied in the use of the APD and the transform:
• Figure A.13: the same analysis based on−Δ80 without the additional transform.
(Additional smoothing is applied.)
• Figure A.13: the same analysis, but based on the APD80.
• Figure A.15: the same analysis based on the APD80 and without the additional transform. (Additional smoothing is applied.)
Fig. A.13 The same as Figure 7.4 but based on −Δ80 after additional spatial smoothing with a Gaussian function with𝜎 = 5for similarity. a)The strength of the structuring seen in the PS density plotted against the expected structuring strength. Circles indicate time spans with many VF episodes while stars indicate a single long VF episode. Colours indicate the experiment day, and the legend also applies to the stars. b)The spatial correlation coefficient between the PS density and the expected structure. The two boxplots show the result of the time spans containing multiple VF episodes and the single long VF episodes.
0 1 2 3 4 std(Expected Structure) 0.2
0.4 0.6 0.8 1.0 1.2
std(PSDensity)/mean(PSDensity)
09-21 09-28 10-05 10-12 10-17 11-16 11-23 11-30
time spans single
−0.3
−0.2
−0.1 0.0 0.1 0.2 0.3 0.4
CorrelationPSDensityandExpectation
N = 15
N= 15
a) b)
Fig. A.14The same as Figure 7.4 but based on APD80. a)The strength of the structuring seen in the PS density plotted against the expected structuring strength. Circles indicate time spans with many VF episodes while stars indicate a single long VF episode. Colours indicate the experiment day, and the legend also applies to the stars. b) The spatial cor-relation coefficient between the PS density and the expected structure. The two boxplots show the result of the time spans containing multiple VF episodes and the single long VF episodes.
A.5 Alternative analysis of the Spatial Organization 155
0.00 0.05 0.10 0.15 0.20 CV(Expected Structure) 0.2
0.4 0.6 0.8 1.0 1.2
CV(PSDensity)
09-21 09-28 10-05 10-12 10-17 11-16 11-23 11-30
time spans single
−0.4
−0.2 0.0 0.2 0.4 0.6
CorrelationPSDensityandExpectation
N = 15
N = 15
a) b)
Fig. A.15 The same as Figure 7.4 but based on−APD80after additional spatial smoothing with a Gaussian function with𝜎 = 5for similarity. a)The strength of the structuring seen in the PS density plotted against the expected structuring strength. Circles indicate time spans with many VF episodes while stars indicate a single long VF episode. Colours indicate the experiment day, and the legend also applies to the stars. b)The spatial correlation coefficient between the PS density and the expected structure. The two boxplots show the result of the time spans containing multiple VF episodes and the single long VF episodes.
Appendix B
Code Sample
B.1 Windowing Function for Upstroke Detection
The below python snippet defines the exact kernel used to find the excitation times (upstrokes). The default parameters are the ones used for the analysis of arrhythmia,
more details can be found in Section 4.2.
import operator import numpy as np
from scipy . signal import tukey
def upstroke_kernel ( apd_dur=15 , upstroke_dur=5, tukey_alpha=0.75):
"""
Returns the kernel function used for upstroke / activation detection .
Parameters ---apd_dur : int
A measure for the total length of the kernel , a time approximately related to the action potential duration as measured in camera frames .
upstroke_dur : int
How strongly the step should be smoothed .
"""
# Slightly adjust input parameters , to avoid issues
# e.g. with 0 duration
# operator . index makes sure the input is an integer . apd_dur = operator . index ( apd_dur ) + 2
upstroke_dur = operator . index ( upstroke_dur ) + 1
# Use Tukey and Hanning windows as basis :
before_w = tukey ( apd_dur * 2, alpha=tukey_alpha )[:apd_dur]
after_w = tukey ( apd_dur * 2, alpha=tukey_alpha )[apd_dur:]
center_w = np. hanning ( upstroke_dur * 2)
# We assume a linear increase weighted by the window
# to smoothen out the step.
times = np.linspace(-1, 1, upstroke_dur * 2) ramp = times * center_w
ramp += np.sign( times ) * (1 - center_w ) kernel = np.ones(2 * apd_dur )
kernel[:apd_dur] = -1
kernel[apd_dur-upstroke_dur:apd_dur+upstroke_dur] = ramp kernel[:apd_dur] *= before_w
kernel[-apd_dur:] *= after_w
# Normalize kernel
kernel /= abs( kernel ).sum() kernel -= kernel .mean() return kernel
Appendix C
Additional Information or Details
C.1 Experimental Recommendations
Experimental work can become tricky and sometimes based on experience we find a certain way of doing things is successful. Some of these tips may thus not hold up to thorough scientific analysis. However, such tips may be helpful to scientists new in the fields. Thus, in this appending I provide a list of experiences gathered or taught to me when conducting experiments.
• Especially when using drugs it can sometimes happen that even the strongest shock protocols cannot defibrillate a heart or the arrhythmia self induces again very quickly. Especially if the second observation is the case a good option to try is many shocks with a fast sinus period and an amplitude such that a single shock should be able to defibrillate. In some cases this will work to defibrillate the arrhythmia.
• Pacing protocols can sometimes induce arrhythmia accidentally, at least unless timed carefully. While not always an option, especially if this occurs and is unwanted, care should be taken to reduce the amplitude as much as possible.
This will make the vulnerable window smaller and can solve or at least limit the issue. An other solution should of course be to synchronize the pacing (or first shock) to the natural heart rhythm.
• Inducing arrhythmia is often conveniently done using 50 Hz or 60 Hz local or far field pacing protocols. These typically reliably induce fibrillation. As taught to me, one thing to keep an eye on is again the camera traces. If the camera traces start to look irregular there is a very high chance of arrhythmia induction. If this does not work, increasing the pacing duration or simply repeating the procedure is a good idea. If however the traces are not irregular, increasing the pacing strength or repositioning the electrode may help. Additional one can try to lower the pacing frequency since 50 Hz is much higher than any arrhythmia and the overall pacing strength at this high frequency might require larger energies.
While lowering the frequency too much may fail to induce arrhythmia as well, trying out a few lower frequencies can be helpful.
• It is a good habit for the experimenter to keep an eye on the camera traces of the heart during the experiment. This allows to observe possible changes already during the experiment. This trace observations will also show if there is still movement in the heart, although the same can be achieved using a bandpass filter as implemented into our experimental software. For example, sometimes resonance with the pump can cause small movements and once found these movements can be easily avoided by increasing the pumping speed.
• Additionally observing a single pixel or small trace will provide the experimenter with an idea of whether or not the data is good enough for the purpose of analysis.
And whether restaining should be considered. A single pixel trace should show a very clear action potential during sinus: with good quality, the single pixel noise amplitude will be well below the sinus rhythm amplitude. If this is not the case, even with strong filtering the data will be very hard or impossible to analyze in depth during fibrillation.
• The perfusion is sometimes better at the start of the experiment. Likely because of this, staining the heart very early on in the experiment sometimes seemed to provide for a better image quality.