is ignored.
In general the signal processing using the kernel is very robust, although slight systematic errors may arise for the combination of poor data and short action poten-tials. However, similar shifts will also occur for any other temporal filtering technique and manual inspection for the activation map analysis showed no visible shift for the detected upstroke compared to the true upstroke. Thus, this approach worked reliably for all data analysis purposes presented here.
4.3 Further Analysis
Equipped with the previous tools and results, it is now straight forward to calculate many of the interesting values describing the activation patterns of the heart. This includes activation map analysis and the analysis of cycle lengths. It is also used as a basis for the PS tracking described in Section 4.4.
4.3.1 Activation Map and Time Analysis for Quiescent Tissue
Activation maps describe how a shock, during the quiescent state of the heart, causes excitation that propagates and finally activates the whole surface. To visualize this activation it is customary to plot the the time until activation [4, 18, 20, 63]. Since this time changes with the applied shock voltage, a number of increasing shock voltages are always measured at a CL faster than the sinus rhythm5. Each shock voltage is also repeated multiple times for three reasons:
1. The heart is still in sinus rhythm, so it is not fully quiescent. Multiple shocks are necessary to “win” over the sinus rhythm, especially at low voltages.
2. When increasing the shock voltage a short transient can occur, so that the first shock may have a different activation time.
3. Multiple shocks allow to see variations and estimate errors.
Since the recording program runs both the shock protocol and the cameras simul-taneously, the exact time when a shock occurred in a video can be calculated. Using this information and the times when excitation occurred – as described in the previous section – the time until activation occurs is calculated for every pixel.
For the activation maps shown in this thesis, the time for each pixel is given as the median over the the shocks of the same voltage. The activation time is given as the time after the shock until 95% of the area is activated. Occasionally the sinus rhythm can disturb the measurement causing a large variability in the activation times. In rare cases also an arrhythmia occurred causing unusable measurements. Thus to filter out incorrect events or fluctuations, the following rules are applied:
5Generally 300 ms was used.
1. The result of the first shock is always ignored.
2. If the heart was largely activated within 100 ms before the shock the value for this shock is discarded. This is because the activation from the previous shock would have happened much earlier.
3. Shocks with an activation time outside a 1.5 inter quartile range compared to the other shocks of the same voltage are ignored.
4. If less than half the points remain, the measurements for that voltage are dis-carded.
These rules allow the analysis of a large amount of activation maps without manually inspecting where sinus rhythm disturbed the measurement.
In very rare cases a natural alternating pattern occurs for the activation times, these can sometimes be lost due to the filtering. However, typically the variability of the activation time measurements from individual shocks is within ±0.2ms, making the analysis used extremely robust.
4.3.2 Cycle Length
One interesting and commonly analyzed measure of a cardiac arrhythmia is its ac-tivation frequency. The cycle length (CL) is directly related to the frequency and thus can be analyzed analogously. To find the most typical CL as reliably as possible, all detected cycle lengths of a video, defined as the time between two upstrokes, are pooled. Then a kernel density estimator is used to find the dominant CL. The kernel density estimator used wasscipy.stats.gaussian_kde from the SciPy package [86].
Since different estimations give slightly different results, the Appendix A.4 (p. 150) includes a comparison of how a spatial average (over the average for each pixel) behaves compared to the dominant CL reported in this thesis. This appendix also compares the dominant CL to the period as detected from the ECG by fitting a sinus to a one second segment6.
4.3.3 Action Potential Duration
The action potential duration (APD) describes for how long the cardiac cell is depolar-ized or excitated. This depends on the exact level 𝑉mthresh of the membrane potential 𝑉m at which the APD is measured. A common value is for example the APD90 with the 90% denoting the duration for which the action potential is within 90% of its maximum value (compare also Figs. 1.2 and 4.3):
𝑉mthresh =min(𝑉m) + (max(𝑉m) −min(𝑉m.)) ⋅ (100 −90)/100 Two different methods for calculation are used:
6The approach of the fit was developed by Annette Witt and improved by me for the live data analysis task necessary in our defibrillation experiments.
4.3 Further Analysis 41 1. Based on the PseudoECG – the average fluorescent signal over a whole camera –
with the assumption that excitation is fast enough during sinus rhythm.
2. Based on “folding” and averaging action potentials during the arrhythmia or pacing protocols. This is done by aligning action potentials based on the excita-tion times found previously. Such folding approaches are more often used when the folding period is already known from a pacing frequency. This alignment then allows to take an average signal over all action potentials detected for each pixel. Then, the APD is directly estimated for each pixel giving a map. This method is used in Chapter 7 for pacing events. It is also used to calculate an estimated APD during the arrhythmias analyzed in Chapter 5. Thus, the APD values given for arrhythmic data should be seen as an APD of the averaged action potential rather than a true APD value. However, the definition of an APD during arrhythmia is otherwise difficult and this approach provides an es-timation. When reporting the APD for a VF episodes, the APD is here given as the spatial average over the APD map.
4.3.4 Triangularity Index
For the Pinacidil experiments shown in this thesis Daniel Hornung developed the triangularity index. This index aims to capture the changes in the action potential shape commonly associated with ischemia, i.e. the reduction of the plateau phase in the action potential towards a very narrow and pointy shape (compare Sec. 1.6).
While the APD captures such changes to some degree, multiple APD levels would be necessary to capture the change of the shape itself. Another definition of triangularity has been previously used by Hondeghem et al. [87] by using the difference between the APD30 and APD90. They have found it to be a good predictor of the pro-arrhythmic effects of drugs.
Here, the goal is to capture the shape in a way that is more independent of the APD.
Thus, the triangularity index is defined to quantify the deviation from a triangular action potential shape. Figure 4.3 shows three example traces of action potentials and their corresponding triangularity index at an 80% level (Δ80). The triangular shape indicated is given by the maximum point during the action potential and a threshold value defined in the same way as the APD level. The green area in the figure indicates the deviation of the action potential from the triangle. The triangularity index is then defined as the ratio of the integral over this deviation and the triangles area. A large value thus indicates a prominent plateau phase – associated with the healthy heart – and a value around or below zero translates to a narrow or pointy action potential associated with the ischemic condition.
The examples in Figure 4.3 are based on a single video containing multiple pacing events. For this analysis multiple action potentials are “folded” and averaged as ex-plained for the APD maps. For the overview plots, instead the PseudoECG is used as the basis for finding the triangularity index.
0.0 0.1 0.2 time [s]
0.0 0.2 0.4 0.6 0.8 1.0
RescaledIntensity ∆80= 0.24
0.0 0.1 0.2
time [s]
∆80= 0.12
0.0 0.1 0.2
time [s]
∆80=−0.09
Fig. 4.3Example of three action potentials and their triangularity index. All examples come from a recording paced at 300 ms on the 2017-10-05. The blue lines show the action potential scaled from zero to one. The horizontal dashed orange line shows the level corresponding to an APD80 or Δ80. An orange triangle extends from the maximum point in the action potential to the downstroke crossing the 80% level. The area of the triangle is indicated in orange. The deviation of the action potential from the triangular shape is indicated in green.
The Δ80is now given by the integral over the green area divided by the triangle area.