Estimación de errores

CAI(x) was generated and denoted as CAIA, CAIHand CAIL, respectively. These were calculated

by the pixel-wise standard deviation in the time domain. In order to reveal those pixels with highest contribution from the aorta, an aortic signal-to-noise ratio SNRAwas defined as:

SNRA(x)=

CAIA(x)

CAIA(x)+CAIL(x)+CAIH(x)∈

[0, 1]. (A.6)

Hence, the pixels of interest are those with a high SNRAand thus with a predominant contri-

bution of aortic signal – compared to pulmonary and cardiac influences. Therefore, the final figure of merit SNRAwas chosen – similar to the first experiment – as the average of those four

neighbouring pixels (2×2 pixel region) having highest SNRAvalues inside the aortic region

ROIAorta. This region of interest, to which the selection of the four best pixels is restricted, was

defined as these connected pixels where CAIA(x) is larger than 10 % of its maximal value.

A.3 Results

The dependence of both figures of merit²rel(first experiment) and SNRA(second experiment)

on the noise figure (NF) for three different reconstruction algorithm configurations are shown in Figure A.6. Over the entire range GN shows a lower relative error²relcompared to the two

GREIT configurations. Starting from a NF of 0.5 (TH and TM) or 0.75 (TL),²relof GN lies below

4.5 % and stabilizes for higher NFs. Regarding the aortic signal contribution, the TH and TM belt placements in combination with GN show highest SNRAvalues, especially for a NF in the

range between 0.5 and 1.25.

The two specific GREIT weighting radiiRWused in Figure A.6 (RW=0.09 andRW=0.03) were

selected based on Figure A.7 which shows the dependence of²reland SNRAonRW. For certain

belt placements (SNRAfor TL and TH, or²relfor TH) anRWof 0.09 shows best performance

whereas for TM in terms of timing anRWof 0.03 is favourable.

A.4 Discussion

Two simulation experiments were performed with the aim to 1) quantify the error in EIT- derived PAT estimation and 2) measure the aortic signal contribution at different pixels of the aortic region in EIT image sequences. The goal of these experiments was to investigate the influence of different belt placements and reconstruction algorithms when aiming for an EIT-based monitor of aorta pulsatility.

The first experiment shows the feasibility to estimate the aortic PAT with a minimal error²rel

of below 3.6 % or 4.3 %, for measurements performed with a TM or TH belt placement and reconstructed with GN, starting from an NF of 0.5 upwards. These errors in terms of EIT-based blood pressure estimation would translate to±1.4 mmHg or±1.7 mmHg, when conservatively assuming a relationship of 1 mmHg/ms [138]. The TL belt placement follows from a NF of 0.75 upwards with an error lower than 4.3 %. In comparison, for images reconstructed with

Figure A.6 – (Top row) Relative error²rel(the lower the better) and (Bottom row) aortic con-

tribution SNRA (the larger the better) as a function of the noise figure (NF) for the three

belt placements (TH, TM, TL) and three different algorithm configurations (Left column) Gauss-Newton, (Middle column) GREIT withRW=0.03 and (Right column)RW=0.09.

(a) GREIT NF=1 (b) GREIT NF=1

Figure A.7 – (a) Relative error²rel(the lower the better) and (b) aortic contribution SNRA(the

larger the better) as a function of GREIT weighting radiusRWfor the three belt placements

A.4. Discussion

GREIT and all three belt placements investigated, the error never falls below 7.6 %, which would correspond to±3.0 mmHg. However, this is the case for high NFs. At lower NFs, in a range of NF between 0.5 and 1 – which is favourable in order to be more robust to noise –

²relof GREIT is nearly three-fold higher compared to GN. As these comparisons are made for

the two algorithms having identical NFs and image size, the significant differences observed are assumed to be due to a higher spatial smoothing of the GREIT algorithm. As alluded to earlier in Section A.1, even a small influence of the much stronger lung or heart signals can lead to a quasi-elimination of the aortic signal. To summarize, in terms of PAT error²rel, we

recommend the use of GN reconstruction and a NF of at least 0.5.

The second experiment reveals that images reconstructed with GN allow best to isolate the aortic signal from the interfering ones (pulmonary and cardiac). This applies in particular to the TM or TH belt placements where aortic signal contributions SNRAof up to 71 % or 68 % are

present (for NFs in the range of 0.5 to 1.0). In contrast, using GREIT, for all three belts analysed, the SNRAstays below 50 % – or for NFs limited to 1.0 even below 43 %. These findings suggest

the use of GN reconstruction with a TM or TH belt placement.

Based on two different simulation experiments showing comparable results, a GN recon- struction (with NF≥0.5) is suggested for measuring aortic PAT. The few discrepancies between SNRA and²rel probably stem from the lower specificity of the PAT experiment. Since the

cardiac-related activity is not changing between the forty different PAT states of the first expe- riment, the timing error²relcan be small in pixels where an accurate aortic PAT estimation

is obtained despite a high cardiac contribution. The same applies for pixels having high pulmonary signal influence and located close to the pulmonary valve, where the disturbing PWVL-dependent variations are negligibly small. This could be improved by simulating diffe-

rent cardiac volume conditions and pulmonary pressure morphologies. However, the current simulations are very time-consuming; the PAT experiment took nearly four days to compute. This is also the reason why the present analysis was limited to a single stimulation pattern. Thus, before performing further investigations, a more efficient implementation of the forward solver is required.

Regarding the performance of GREIT, it needs to be emphasized that an appropriate adjus- tment of the algorithm parameters (increased image size, modified point spread function) might lead to improved results. This was, however, out of the scope of the present investiga- tions and should be investigated in the future. Moreover, the current analysis did not take into account any noise, which could alter the outcome when comparing the two algorithms. Therefore, we suggest the development of an appropriate noise model and a subsequent noise analysis for future work.

The results for GN suggest that a TM or TH belt placement is preferred over TL. This is somewhat counter-intuitive as one would expect the lowest pulmonary activity for the TL belt (see Figure A.1a). Nevertheless, the larger radial distension of the aorta and increased sensitivity of changes originating from the aortic arch at higher belt levels are arguments in

favour of a high belt placement. This might explain our observations from a signal strength perspective as studied in the second experiment. Nevertheless, the rationale for the lower timing errors at higher belt levels (as observed for GN from the first experiment), might be biased by the aforementioned fact that belts placed closer to the pulmonary valve (PV) could show lower timing errors.

As none of the results shows an aortic contribution SNRA of more than 71 %, we have to

expect pulmonary or cardiac influence in every pixel. A plausible explanation is the low spatial resolution of EIT which leads to an overlap of different signal sources. This in turn might be exaggerated for the pulmonary influence due to the simplistic model used for the lungs which propagates a worst-case conductivity change of 10 % homogeneously throughout the entire lung region. Therefore, improvements towards a more realistic lung model are suggested in order to examine this in more detail.

In conclusion, the confirmation of the current findings by validating against real EIT-based aortic PAT recordings should bring cardiovascular EIT another step closer towards clinical practice.