Extensi´on a isotrop´ıa transversal

Compared to the currently available EIT systems (primarily targeted for ventilation monitoring in the lungs), we hypothesize that there is a measurement setup better suited for EIT-based SV monitoring. In the following, besides addressing the abovementioned limitations, we also justify theimprovedmeasurement setup used in the experimental study presented later on in Chapter 12.

First, concerning the electrode positions, one can imagine that having a higher density of electrodes in the left ventral region (i.e. a patch of electrodes on the chest close to the heart as illustrated in Figure 10.1a) could lead to an improved sensitivity in the heart region. However, given the same total amount of electrodes, this also results in less electrodes on the sides and the back which in turn could be very sensitive to errors of this specific electrodes (detachment, contact impedance issues). In addition, if one further wants to analyze pulsatile information in the lungs, it is of advantage to have a setup not only targeted for measuring the heart. Therefore, for theimprovedmeasurement setup (see Chapter 12) the electrodes were placed on two transversal planes of 2×16 electrodes. This placement enables 3D EIT and is assumed to at least partly overcome the abovementioned undesired influences such as out-of-EIT-plane heart displacement.

10.2. Finding a Setup Better Suited for EIT-Based SV Monitoring Ch romo so mes e1 e2 e3 e4 e5 e6 e32 e7 c1 c2 c3 c4 c5 c6 c32 c7 z-Score in Heart ... ... Genetic Algorithm 0 100 200 300 400 500 generation 0 50 100 150 200 250

position of the best

genomes of the population

50 100 150 200 250 5 10 15 20 25 30 0 50 100 150 200 250 300 subject 0.014 0.015 0.016 0.017 0.018 0.019 0.02 0.021 0.022 0.023 current performance

Figure 10.2 – (Left) Block diagram of the genetic algorithm (GA) [158] used to find a better stimulation and measurement pattern. The human thorax model (presented in Chapter 4) with belts TL and TH and the 2×16 electrode placement shown in Figure 10.1b, was used to evaluate the sensitivity in the heart region by means of the z-score (distinguishability [8]). For each of theni=500 iterations of the GA, a population ofnp=256 chromosomes

was evaluated. These arenp vectors (with a fixed length of 32 each) representing possible

connections between the electrodeei and the EIT device cableci(withi∈{1, 32}). At the end

of each iteration, the chromosome were ranked (i.e. highestzfirst, lowestzlast), the highest ranked one was kept and the rest of the population was evolved in four steps: (1) 64 new chromosomes were generated by exchanging two randomly chosen alleles in the 25 % highest ranked chromosomes; (2) 64 new chromosomes were generated by randomly swapping all alleles in the 25 % highest ranked chromosomes; (3) 64 new chromosomes were generated by crossing over of two randomly chosen chromosomes; (4) The remaining 63 chromosomes were generated randomly. (Right) The temporal evolution of the best solution found via the GA ( blue) compared to skip 0 ( red), skip 4 ( black), and skip 6 ( gray).

finding the most suitable stimulation and measurement pattern, i.e. finding the particular sequence and combination of the electrodes injecting currents and those measuring the resulting voltages. Even worse, if one wanted to find the optimal solution, one would need to simultaneously optimize the electrode positions and the stimulation and measurement pattern while preferably considering real-live constraints from the EIT device used. Although this is a fascinating subject, it is out of the scope of the present thesis.

Nonetheless, if one is limited to one of the commercially available EIT systems with bipolar measurements and a fixed skip, this challenge gets simplified. When further considering the aforementioned two-plane (2×16) electrode placement shown in Figure 10.1b, there is one sole remaining degree of freedom influencing the stimulation and measurement pattern. This is the way on how the 32 electrodes (e1toe32) are connected to the 32 cables of the EIT device

(c1toc32), also illustrated in Figure 10.1b. This issue is similar to the well-knowntraveling

salesman problem1. Therefore, in an attempt to solve it, a genetic algorithm (GA) was applied which is very briefly presented and described in Figure 10.2. For more information regarding GA one is referred to the book by Weise [158]. Even though this approach does not lead to

theoptimal solution, it finds the best possible one within a reasonable amount of time. As shown in Figure 10.2, the performance of the GA-based solution does not outperform a skip

1_{In thetraveling salesman problemone is given a list of cities which the salesman has to visit. The goal is then to} find the shortest possible route that visits each city only once and returns back to the city of departure. Analogously we have to find the best possible order (e.g. in terms of sensitivity in the heart region) on how to connect the 32 cables of our EIT device (c1toc32) to the 32 available electrodes (e1toe32).

coronal y=1.50e-02

(a) Best stimulation and measurement pattern obtained via the GA

coronal y=1.50e-02

(b) Skip 4 pattern

coronal y=1.50e-02

(c) Skip 0 pattern

Figure 10.3 – Forward sensitivities [66] for the human thorax model (presented in Chapter 4) with belts TL and TH and the 2×16 electrode placement shown in Figure 10.1b for three different stimulation and measurement patterns: (a) the best possible obtained via the genetic algorithm approach, (c) skip 4, (b) skip 0. Columns from left to right show: sagittal plane (x=30 cm), coronal plane (y=10 cm), transverse plane (z=40 cm, i.e. in between the two electrode planes). All images use the same color scale.

4 pattern by more than 15 % (in terms ofz-score). This is further shown in Figure 10.3 by means of forward sensitivities [66]. The best solution found via the GA (Figure 10.3a) does not significantly outperform a skip 4 pattern (Figure 10.3b). However, the latter two are clearly more sensitive than a skip 0 pattern (Figure 10.3c). For the above reasons, and for the fact that in practice complex cabling could decrease the performance of thebestsolution, the skip 4 pattern was chosen for theimprovedmeasurement setup and applied in the experimental study (see Chapter 12).

Finally, a remark concerning the frequency of the injected EIT current. It would be of advantage to use a stimulation frequency in the range of 100 kHz as this represents a trade-off between the signal-to-noise ratio [2] and cardiosynchronous signal strength [30]. Yet, being restricted to a specific EIT device (Swisstom BB2) a fixed stimulation frequency of 195 kHz was used for theimprovedmeasurement setup.