Evaluation of reconstruction parameters of electrical impedance tomography on aorta detection during saline bolus injection

Florian Thürk; Andreas D. Waldmann; Karin H. Wodack; Constantin J. Trepte; Daniel Reuter; Stefan Kampusch; Eugenijus Kaniusas

doi:10.1515/cdbme-2016-0113

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Evaluation of reconstruction parameters of electrical impedance tomography on aorta detection during saline bolus injection

Florian Thürk , Andreas D. Waldmann , Karin H. Wodack , Constantin J. Trepte , Daniel Reuter , Stefan Kampusch and Eugenijus Kaniusas

Published/Copyright: September 30, 2016

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From the journal Current Directions in Biomedical Engineering Volume 2 Issue 1

Abstract

An accurate detection of anatomical structures in electrical impedance tomography (EIT) is still at an early stage. Aorta detection in EIT is of special interest, since it would favor non-invasive assessment of hemodynamic processes in the body. Here, diverse EIT reconstruction parameters of the GREIT algorithm were systematically evaluated to detect the aorta after saline bolus injection in apnea. True aorta position and size were taken from computed tomography (CT). A comparison with CT showed that the smallest error for aorta displacement was attained for noise figure nf = 0.7, weighting radius rw = 0.15, and target size ts = 0.01. The spatial extension of the aorta was most precise for nf = 0.7, rw = 0.25, and ts = 0.07. Detection accuracy (F1-score) was highest with nf = 0.6, rw = 0.15, and ts = 0.04. This work provides algorithm-related evidence for potentially accurate aorta detection in EIT after injection of a saline bolus.

Keywords: aorta; electrical impedance tomography; GREIT; hemodynamics; saline bolus

1 Introduction

Electrical impedance tomography (EIT) is an imaging technique to investigate and monitor regional lung function and heart activity. Here 32 electrodes are placed around the thorax while weak alternating currents (1–5 mA, 50–200 kHz) are applied from one electrode to another and the resulting voltages are measured across the other electrodes [1]. Numerous temporal sequences of measured voltages result which serve as input for an algorithm to reconstruct the 2-D spatial distribution of electrical conductivity within the body at the level of the applied electrodes. Such algorithms (e.g. GREIT algorithm [2]) show high temporal but low spatial resolution so that EIT reflects rather dynamics of organ functions (typical resolution of about 20 ms) rather than their structure (typical resolution of about 5 mm²).

Recent works have shown the potential of EIT for the assessment of haemodynamic [3] and, in particular, for the calculation of cardiac related parameters like the pulse transit time. In this context, the detection of the aorta in EIT as the biggest blood vessel in the imaging space is of crucial importance. However, due to the ill-posed nature of EIT and inverse reconstruction algorithm, proper analysis methods in the aorta detection are still unknown. Uncertainties include the current injection pattern and electrode configuration as well as image reconstruction and processing techniques. Especially the reconstruction of images is crucial as it represents the interface between raw voltage data and analysis algorithms for hemodynamic assessment.

Theoretical evaluations and numerical simulations of different reconstruction algorithms and parameters for aorta detection are laid down in [4]. Complementary, we focus on experimental evaluation of the GREIT algorithm and its parameters for the subsequent aorta detection during saline bolus injection based on our algorithm [5].

2 Method

2.1 Study protocol

EIT data was acquired (Swisstom BB², Landquart, Switzerland) from anesthetized and mechanically ventilated pigs (n = 3) at T 9/10 (Ethics approval No.53/11). In addition, computed tomography (CT) images were recorded prior to the EIT measurements. During ceased ventilation, a saline bolus (10 ml, 20%) with higher conductivity than blood (by a factor of about 3) was injected into the ascending aorta.

2.2 Reconstruction

EIT images were reconstructed using the linearized differential reconstruction algorithm GREIT. Based on a finite element method model (FEM), a reconstruction matrix (RM) is calculated in order to map measured voltages to EIT impedance images Z=R⁢M⁢(U−Ur), with U and U_r (U_r∈U) as experimental voltage measurement and voltage reference, respectively. Since all images are reconstructed (and interpolated) to the same dimension Z ∈ ℝ^64×64, the resulting pixel size varies with thorax dimension (see Table 1). For each animal, CT images were segmented at the electrode plane to extract the thoracic circumference and to create an individual FEM as basis of the forward solution, shown in Figure 1. For the final creation of RM, the GREIT algorithm offers several adjustment parameters, such as noise figure nf, target size ts and weighting radius rw, all influencing characteristics of the reconstruction as described below.

Table 1

Evaluation metrics over all evaluated GREIT models (n = 400) for each pig.

Metric	Pig 1	Pig 2	Pig 3
Distance (mm)	7.6 ± 4.3	10.5 ± 14.5	14.9 ± 17
Area Error (%)	63 ± 54	107 ± 134	30 ± 24
F1-score (au)	0.5 ± 0.1	0.47 ± 0.1	0.3 ± 0.1
Pixel Size (mm)	2.8	3.06	3.28

Values are mean ± standard deviation.

Figure 1

Extruded 3D finite element model with lungs, aorta and electrode positions acquired from CT image.

Using least square method, GREIT tries to find a RM based on numerical simulation of FEM and defined image characteristics. To calculate the simulated voltages, known disturbances are introduced into the FEM. The relative diameter of these disturbances is controlled by ts and was varied from 0.01 to 0.08, whereas 0.06 approximately corresponds to the aorta diameter of ∼4 pixels in EIT. Another characteristic of the desired image, the point spread function, i.e. the size of the reconstructed target, is defined by rw (ranging from 0.05 to 0.25).

In the final step of the RM generation, GREIT calculates an inverse of a bad conditioned matrix. A more stable solution can be achieved by regularization. The regularization term is automatically adjusted by EIDORS [6] implementation of GREIT and is controlled by nf. In other words, the value of nf regulates the noise sensitivity of the resulting RM. Lower nf leads to a RM which is less sensitive to noise, but also has a lower spatial resolution. In this work, nf was varied from 0.2 to 0.9. In total, 400 combinations of nf, ts and rw, were used for each pig to reconstruct EIT images to assess the displacement and size of the aorta in EIT with respect to CT.

2.3 Evaluation

The prominence of the temporal bolus peak amplitude was detected for each pixel in EIT and the aorta pixel were identified according to the maximum prominence as described in our work [5]. The total aortic area A_EIT was obtained by unification of surrounding pixels with prominence of at least 70% of the maximum (see Figure 2). The ground truth of the aortic region A_CT was taken from CT images. Quality metrics were defined as (i) Euclidian distance, εd of A_EIT center to A_CT center, (ii) error of A_EIT area εa=|AEIT− ACT|/ACT and (iii) the F1-score as measure of accuracy since most pixels inside the thorax are classified non-aorta.

Figure 2

(A) Exemplary prominence image of the bolus application with superimposed anatomical structures from CT. (B) Zoomed area around CT aorta and threshold based detection of aorta in EIT and (C) temporal characteristics of a bolus injection for selected pixels.

3 Results

Average ε_d for all models over all pigs was 10.4 mm, average εa amounted to 70% while average F1-score was 0.4. Individual metrics of each pig over all models are shown in Table 1, indicating huge variations for different parameter combinations and thus highlighting the importance of optimal selection. Minimal error for εd (5.36 mm) and εa (7%) was observed with the following model parameters nf = 0.7, rw = 0.15, ts = 0.01 and nf = 0.7, rw = 0.25, ts = 0.07, respectively. Detection accuracy was highest (0.53) with nf = 0.6, rw = 0.15 ts = 0.04 (compare Figure 3C and Figure 4). Interestingly, ts had only little influence on εa and accuracy. Only some combinations with ts 0.01 (e.g. with rw 0.1 and 0.05) showed higher εa and less accuracy. In general, εd was lower for higher values of ts. The effect of nf was mainly visible for εa with a decrease (averaged over all models of one fixed nf) of 200% (nf = 0.2) to 12% (nf = 0.7). For higher nf, εa increased again to 35%. In addition, nf of 0.2 also showed high εD and low accuracy compared to higher nf levels. Values of rw below 0.1 showed high ε_D.

Figure 3

(A) Distance error, (B) size error and (C) accuracy for each generated model with parameters noise figure, target size and weighting radius. Encircled regions show models with lowest errors and highest accuracy. Note that for error functions in (A) and (B), low (blue) values are favorable, whereas for the accuracy function in (C), large values (red) are strived for.

Figure 4

Pooled accuracy values over selected parameters. Noise figure (left), target size (middle) and weighting radius (right).

Optimal clusters of low εd were identified at nf = 0.4 and 0.2, ts = 0.02–0.7 and rw = 0.2 (Figure 3A), clusters of low εa at nf = 0.5–0.7, ts = 0.02–0.8 and rw = 0.2–0.25 (Figure 3B) and clusters of high accuracy at nf = 0.5–0.7, ts = 0.03–0.8 and rw = 0.15–0.2 (Figure 3C). Pooled accuracy values for selected parameters are shown in Figure 4.

4 Discussion

The influence of various parameters of the GREIT algorithm on the reconstruction of EIT images was investigated. Subsequently, we identified model parameters for aorta detection in EIT which yield small errors for spatial localization and extension as well as high accuracy with respect to CT. The study suggests a nf between 0.5 and 0.7, rw of 0.2 and ts between 0.04 and 0.08.

Since nf regulates noise smoothing, lower values (i.e. more smoothing) directly changes the spatial extension of the bolus event in the EIT image. Consequently, the threshold based calculations of the aorta dimensions – as used in this work – will include larger areas with lower nf. It should be noted, that values of nf higher than 0.7 introduced larger errors due to insufficient noise attenuation. Instead of a fixed threshold, the number of pixels of A_CT could be used as a reference for the number of pixels in A_EIT.

The value of ts seems to have a negative effect on the specific reconstruction when dropping below the pixel size (i.e. ts smaller than 1/64 = 0.0156). We could not identify the exact cause of this phenomenon. Although similar results were obtained for ts in the range of 0.02 and 0.08, we believe that a value of ts close to the aortic dimension should be preferred.

One of the limitation of this study was that CT and EIT recordings were performed at different times. Anatomical structures might have gotten slightly displaced during relocation and transfer of pigs.

Even though the same analysis algorithm was used on all reconstructions, there was a significant variation in the localization quality of the aorta in EIT (compare Table 1). This highlights the importance of appropriately selected reconstruction parameters not only for simulation but also for experimental studies. Further investigations of the influence of reconstruction modalities on functional analysis (e.g. stroke volume or lung aeration) are crucial to establish standardized clinical applications of EIT.

Author’s Statement

Research funding: The study was supported by departmental funds of the Department of Anaesthesiology, University Medical Center Hamburg-Eppendorf, Germany. Conflict of interest: Andreas Waldmann is employee and research support engineer of Swisstom AG. Informed consent: Informed consent is not applicable. Ethical approval: The research related to animals use complies with all the relevant national regulations and institutional policies for the care and use of animals (Ethics approval No.53/11).

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Published Online: 2016-9-30

Published in Print: 2016-9-1

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Articles in the same Issue

https://doi.org/10.1515/cdbme-2016-0113

Keywords for this article

aorta; electrical impedance tomography; GREIT; hemodynamics; saline bolus

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