Home
Search
Collections
Journals
About
Contact us
My IOPscience
Bladder volume estimation from electrical impedance tomography
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Physiol. Meas. 35 1813 (http://iopscience.iop.org/0967-3334/35/9/1813) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 139.184.14.159 This content was downloaded on 18/01/2015 at 18:39
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Physiol. Meas. 35 (2014) 1813–1823
Physiological Measurement doi:10.1088/0967-3334/35/9/1813
Bladder volume estimation from electrical impedance tomography T Schlebusch, S Nienke, S Leonhardt and M Walter Chair for Medical Information Technology, Helmholtz Institute for Biomedical Engineering, RWTH Aachen University, Pauwelsstr. 20, 52074 Aachen, Germany E-mail: [email protected] Received 11 March 2014, revised 28 May 2014 Accepted for publication 16 June 2014 Published 20 August 2014 Abstract
Non-invasive estimation of bladder volume is required to progress from scheduled voiding to a demand-driven emptying scheme for patients with impaired bladder volume sensation. Electrical impedance tomography (EIT) is a promising candidate for the non-invasive monitoring of bladder volume. This article focuses on four estimation algorithms used to map recorded EIT data to a volume estimate. Two different approaches are presented: the tomographic algorithms (one based on global impedance, the other on equivalent circular diameter) rely on the reconstruction of a tomographic image and then extract a volume estimate, whereas the parametric algorithms (one based on neural networks, the other on the singular value difference method) directly map the raw data to a volume estimate. The four algorithms presented here are evaluated for volume estimation error, noise tolerance and suppression of varying urine conductivity based on finite element simulation data. Keywords: electrical impedance tomography, cystovolumetry, bladder volume, volume estimation (Some figures may appear in colour only in the online journal) 1. Introduction Some patient groups (for example, paraplegics) have an impaired bladder volume sensation due to damaged neural structures, often associated with the inability to urinate properly. A common therapy is regular intermittent self-catheterisation following a fixed time schedule. However, the emptying interval has to be chosen properly: a too short interval will unnecessarily interfere with quality of life and increase the risk of urethral damage or urinary infections, whereas a too long interval will increase the risk of complications due to an overfull bladder, e.g. over-distension of the bladder wall, reflux, hydronephrosis or autonomic dysreflexia. These latter complications are the main instigators of most of the urology-related emergencies 0967-3334/14/091813+11$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK
1813
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Figure 1. Electrical impedance tomography (EIT) set-up for cystovolumetry.
among paraplegics. Therefore, a demand-driven emptying scheme would be preferable for some patients. To achieve this, a promising concept is non-invasive continuous impedancebased volume monitoring to estimate the appropriate moment for catheterisation. Impedance-based cystovolumetry systems exploit the difference in conductivity between urine and the tissue surrounding the bladder. Urine conductivity is mainly influenced by its saline concentration (Gazinski 2004) and is usually in the impedance range of 5–26 mS cm − 1. In contrast, the tissues surrounding the bladder (muscles, connective tissue and fat) are in the impedance range of 0.2–4 mS cm − 1 (Martinsen and Grimnes 2008). There is a relatively linear decrease in abdominal impedance with increasing bladder volume (Denniston and Baker 1975). Early experiments on non-invasive impedance-based bladder volume measurements were performed by Denniston and Baker in anaesthetised dogs in 1975 (Denniston and Baker 1975). For these measurements, the authors used a relatively unspecific electrode set-up by placing band electrodes around the abdomen. Later on, comparable set-ups using two-electrode (Liao and Jaw 2011) and four-electrode (Kim et al 1998) electrical impedance measurements reproduced their results in humans. To maximise the sensitivity to bladder volume while reducing artefacts, Hua et al (1988) applied a 2D-multi-electrode array to the ventral body surface, while still performing regular impedance measurements. Recently, both our group (Leonhardt et al 2011) and He et al (2012) demonstrated the application of electrical impedance tomography (EIT) for estimation of bladder volume. The measurement set-up is shown in figure 1: an EIT electrode belt embedded in the underwear at the level of the human bladder is connected to a portable EIT device, providing wireless volume estimates to a patient interface. This paper continues the approach of using EIT for bladder volume estimation, by focusing on the estimation algorithms used to map recorded EIT raw data to a volume estimate. Four algorithms based on two different approaches are presented: the two tomographic algorithms rely on the reconstruction of a tomographic image and extract a volume estimate in a second step, whereas the two parametric algorithms directly map the EIT raw data to a volume estimate. Finally, all four algorithms are compared with respect to volume estimation error, noise tolerance and the influence of varying urine conductivity. The paper is structured as follows: section 2.1 presents a brief introduction to EIT, section 2.2 outlines the simulated environment used to generate reproducible data for this experiment, and sections 2.3 and 2.4 describe the two tomographic and two parametric algorithms, respectively. Results concerning estimation error are presented in section 3.1, on noise tolerance in section 3.2 and concerning the influence of varying urine conductivity in section 3.3. Finally, section 4 presents the discussion and conclusions. 1814
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2. Tomograms of eight-step image analysis based ECD algorithm. (a) Reconstructed EIT image (b) threshold operation retains only negative impedance changes (c) Gaussian blurring filter removes artificial edges from FEM mesh cells (d) Canny edge detection to separate impedance regions (e) identify closed regions from edge image (f ) enumerate regions and calculate their area and mid-point coordinates.
2. Materials and methods 2.1. Electrical impedance tomography
EIT (also called applied potential tomography, APT), is a medical imaging technique, which estimates an impedance distribution in the body volume by non-invasive measurements using electrodes attached to the skin. Similar techniques are also used in geophysics (electrical resistivity tomography, ERT, or electrical resistivity imaging, ERI) and industrial process monitoring (electrical capacitance tomography, ECT). For medical EIT measurements, usually a small fixed current (e.g. 5 mA at 50 kHz in accordance with IEC 60601-1, patient auxiliary current) is applied to the body and the resulting voltage potential distribution is recorded. To generate one EIT frame, successive measurements with varying injecting electrodes are required. For each injection, the voltage potentials of all remaining electrodes are recorded. Several injection and measurement patterns can be used to describe the spatial relation of the electrode pairs. One well-established pattern uses adjacent measurements with neighbouring electrode pairs for current injection and voltage measurement. In this case, N current injections are done for each EIT frame using an N-electrode EIT system. When omitting injecting electrodes due to unknown contact impedances from the voltage measurements, N − 3 pairwise, differential voltage measurements are performed, resulting in a total of N · (N − 3) = 208 voltages for one EIT frame (see figure 3). However, due to reciprocity, only 104 voltages are linearly independent. To estimate the unknown impedance distribution using 208 marginal potentials, different inverse solution methods can be applied. Medical applications of EIT cover a wide field, including ventilation monitoring (Leonhardt and Lachmann 1815
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
2012), assessment of cranial haemorrhage (Romsauerova et al 2006), gastric function monitoring (Smallwood et al 1994), quantification of abdominal fluid accumulations (Sadleir and Fox 2001), cancer monitoring (Kerner et al 2002) and bladder volume monitoring (Leonhardt et al 2011, He et al 2012). 2.2. Finite element simulation
In this work, EIT measurement data are created artificially by means of finite element simulation. Considerable simplification of the abdominal geometry has been accepted to keep the computational cost low: i.e. the abdomen is assumed to be a circular cylinder of 30 cm diameter and 30 cm height. The bladder is modelled as a ball located at the bottom of the cylinder, at the cylinder wall. With increasing volume, the bladder ball extends upwards to the middle of the cylinder. To ensure that the influence of a changing mesh structure with increasing ball size remains low, a fine mesh of 1 259 150 elements is used. A ring of 16 evenly distributed electrodes is placed around the cylinder at half the total height. Adjacent patterns are used for both the injection and the measurements. The EIDORS framework (Adler and Lionheart 2006) with NetGen (Schöberl 1997) was used to create and simulate the mesh. Unity background conductivity was assigned to the cylinder volume, while bladder conductivity was kept variable to account for the different urine conductivities. To identify the quality of an algorithm for real-life applications, its robustness has to be evaluated. In our case, two influence classes were identified: uncorrelated measurement noise and correlated artefacts by body movement, organ shift or internal organ impedance changes (e.g. intestine content). In the scope of this article, we focused on measurement noise susceptibility as well as the effect of urine conductivity on the estimation accuracy of all four algorithms. An analysis of body movement on estimation accuracy will be addressed in future work, when a FEM model representing body movement is available. To find reasonable measurement noise SNR levels, several EIT recordings from a Goe MF II EIT device (Abimek, Friedland, Germany) in patients and a passive electrical network dummy have been analysed for their temporal variations. We found noise levels from 42 dB SNR to 156 dB SNR, so this paper focuses on noisy test data with levels of 40 dB, 80 dB and 120 dB SNR. To model noisy voltage vectors, white uncorrelated noise was superimposed on the simulated EIT raw data, ui: noise signal η(1) = · ui,noise = ui + η noise SNR
Here, SNR defines the desired signal-to-noise ratio, ui the measured EIT raw data and noise the generated noise. Noisy EIT raw data ui,noise are calculated by superimposing the scaled noise η on the noise-free measurements ui. 2.3. Tomographic approaches
In the two tomographic approaches, an image is reconstructed from the EIT raw data using a linear reconstruction matrix (Adler et al 2009). In a subsequent step, a parameter is extracted from the image and used for volume estimation. 2.3.1. Global impedance. In the case of short-term processes, like urodynamics or micturition, an EIT image of a (partially) filled bladder referenced to an empty-bladder measurement mainly shows changes in impedance related to bladder volume. By summing the 1816
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
impedance changes for every pixel ΔZi, j in the reconstructed image, the global impedance (GI) is obtained: GI = ∑ ΔZ i, j (2) i, j
From two reference measurements with known volume, e.g. empty and maximally full bladder, a linear calibration curve mapping GI to volume is calculated in the noise-free case and is taken for all successive volume estimations. Since the image reconstruction using a matrix multiplication is a linear operation, the zero-mean noise is directly mapped on the impedance image data and the noisy GI data varies around the noise-free result. Image artefacts, such as ringing (impedance oscillations in the image) can cause volume errors, whereas some shape deformation and blurring can be tolerated. 2.3.2. Equivalent circular diameter algorithm. Instead of simply summing the impedance
changes in an image, which basically results in a general impedance measurement, the spatial information in the tomogram can be exploited by means of image analysis. Instead of correlating the GI change with bladder volume, the area of bladder pixels in the tomogram is used for estimation of the volume. The algorithm is based on the equivalent circular diameter (ECD) and works as follows: (a) reconstruction of a tomographic image at unknown volume referenced to an empty bladder using a GREIT reconstruction matrix (figure 2(a)) (b) application of a threshold to cut away positive inclusions (potential artefacts). Only negative impedance changes are retained, since urine has a lower impedance than surrounding tissue (figure 2(b)) (c) conversion to a black and white colour scale and applying Gaussian blurring filter to remove edges from pixels or finite element mesh cells in the tomogram (figure 2(c)) (d) application of the Canny algorithm (Canny 1986) for edge detection; this algorithm was chosen due to its high sensitivity to weak edges in blurred images (figure 2(d)) (e) application of imdilate and imfill from Matlab Image Processing Toolbox to create closed, filled areas (figure 2(e)) (f) for each numbered region (figure 2(f)), area and mid-point coordinates are calculated (g) the region closest to the expected bladder position is selected as the bladder (h) the ECD is calculated and mapped to a volume estimate using calibration data: 4 · Area ECD = (3) π 2.4. Parametric approaches
The basic concept of the following two parametric approaches for volume estimation from EIT measurements is to avoid the ill-conditioned reconstruction process. Instead of mapping 208 EIT raw data to 1024 image pixels and extracting one volume estimate, a direct mapping of 208 EIT raw data to one volume estimate is proposed. This procedure was expected to reduce the influence of noise and numerical instabilities, which usually require regularisation in image reconstruction. 2.4.1. Neural networks. To learn a mapping from input to output values, f eed-forward neural networks (NN) can be used. In our case, 208 input nodes and one single output 1817
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
V
V
V V
V
V
V
V
V
V
V
V
V
V
V
V
u18
u205
V
u19
u16
u17
u204
V
u20
u206
u198 u199
V
u21
u15
16th injection i16 , measurements u196 –u208
V
u4
u207
V
V V
u6
u22
u14
V
V
u7
u3
Second injection i2 , measurements u14 –u26
V
V
V
u8
u5
u23
V
V
u9
u2
u197
u208 V
V
u10
First injection i1 , measurements u1 –u13
u196
V
V
u24
V
u11
i16
i2
V
V
V
u12
u26
u25
u1
V
i1 u13
u203 u202
u200
u201
Figure 3. Numbering of the recorded EIT raw data.
node are used to represent the mapping from EIT raw data to the volume estimate. In addition, three hidden layers are used. The number of hidden layers was determined empirically. Matlab Neural Network Toolbox was used for backpropagation training of the NN. As is usual for NN, a huge training dataset providing raw data to volume tuples is required. For simulated work, this is relatively easy, but also for real measurements the training data can be collected by continuous EIT and drained urine volume measurements during micturition (uroflowmetry). In our case, noise-free simulation data are used to train the network. The data are randomly partitioned into three parts using Matlab’s divideParam routine: 70% for training, 15% for validation and 15% for testing. Since the NN is directly trained on the link between EIT raw data and volume, no further calibration or conversion of the output is necessary. 2.4.2. Singular value difference method. EIT raw data from an adjacent measurement of
an empty saline tank phantom generally shows a regular comb pattern of padded U-shapes. When introducing inhomogeneity into the tank phantom, the comb pattern changes slightly in both amplitude and shape. The general idea of the proposed Singular Value Difference Method is to quantify these changes and correlate them with bladder volume. To apply our ^ . The matrix is filled columnmethod, we re-order all 208 raw values in a 13 × 16 matrix M wise, holding all raw data recordings belonging to a single injection position per column. The rows are filled clockwise with adjacent measurements, starting from the injecting electrode pair (as shown in figure 3): ⎛ u ref,1 u1 u14 ⋯ u196 ⎞ ⎜ u ref,2 u2 u15 u197 ⎟ M=⎜ ⋮ ⋮ ⋮ ⎟⎟ (4) ⎜ ⋮ ⎝ u ref,13 u13 u26 ⋯ u208 ⎠ ^ , this results in aligned U-shaped EIT raw data curves When plotting the columns of M which differ, in our case, only due to noise or volume change. Since we aim to analyse deformation of the EIT raw data vectors due to changes in bladder volume, a reference measurement ^ . Then, singular value decomposition is with empty bladder is added as the first column of M applied to this 13 × 17 matrix M. By applying singular value decomposition, a m × n matrix M can be decomposed into a m × m matrix U holding the left singular vectors, a n × n matrix VT holding the right singular 1818
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
λ =1
Original
λ =0.1
1
1
2
0.04
0.16
0.9
0.03 0.14
0.8
0.6
0.01
0.1
0.5
0
0.08
0.4
−0.01
0.06 0.3 0.2 0.1 0
0
5
10
(a)
0.04
−0.02
0.02
−0.03
0
3
λ =1, λ =λ =0.1 1
0.2
0.025
0.18
0.02
0.16
0.015
0.14
0.01
0.12
0.005
0.1
0
0.08
−0.005
0.06
−0.01
0.04
−0.015
0.02
2
3
0.02
0.12
0.7
λ =0.1 0.03
0
5
10
−0.04
0
5
(b)
(c)
10
−0.02
0
5
10
(d)
0
0
5
10
(e)
Figure 4. Interpretation of singular vectors and singular values: (a) original matrix,
(b)–(d) visualizations of the effects of λ1–λ3, (e) oversubscribed shape change represented by the first three singular values.
vectors and a sparse m × n matrix Σ with its only non-zero elements on its main diagonal, called singular values λi. (5) M = U ΣV T In our case, where m 1000
0.00 0.00 805.57 > 1000
0.81 0.81 1.94 193.38
0.00 0.01 2.37 213.21
4.70 4.70 4.71 87.68
0.00 0.00 0.15 85.09
GI, global impedance; ECD, equivalent circular diameter; NN, neural networks; SVDM, singular value difference method.
generated from noise-free data and noisy measurements were only used for actual volume estimation. For each volume estimate (4 algorithms · 4 noise levels · 17 volumes · 100 simulations), the relative error was computed. Table 1 shows the arithmetic mean value of the relative error for each algorithm and noise level, calculated for all simulations of bladder volumes ranging from 60 ml to 360 ml. In addition, the mean value of the standard deviation (SD) at bladder volumes ranging from 60 ml to 360 ml is shown. Note that the first two volumes (10 ml and 35 ml), and the last two volumes (385 ml and 410 ml) were omitted for error calculation. In particular, the NN algorithm has poor capability for extrapolation outside or near the training region borders; this precludes a plausible comparison of the overall performance of the four algorithms. 3.3. Influence of urine conductivity
Urine conductivity is mainly influenced by its ion concentration and can vary throughout the week depending on, for example, the amount of salt and water intake. Ideally, the calculation of bladder volume should be independent of urine conductivity. To assess the influence of varying urine conductivity on the estimated volume, the finite element simulation was repeated with a fixed bladder volume of 185 ml, fixed background conductivity of 1 unit, but varying urine conductivity from 1.5 to 5 units. All algorithms were calibrated at a reference conductivity of 2 units. 1821
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Figure 6 shows the estimated volume for all simulated urine conductivities. The ideal result is a horizontal line (represented by the dashed line in figure 6). The ECD algorithm is the only one that is independent of urine conductivity, although it presents a high static offset to the correct value. All other algorithms show a significant dependence of volume estimate on urine conductivity. With increasing EIT image contrast (ratio of urine conductivity to background conductivity), the influence of urine conductivity on volume calculation decreases (shallower slope of the curve). 4. Discussion and conclusion In these simulations, the GI and NN algorithms show the lowest estimation error in the noisefree case and acceptable estimation errors for medium noise levels. For high noise levels the SVDM has some advantages but, even in the noise-free case, shows a volume error of 4.7% . The ECD algorithm shows unacceptable volume errors. In its current implementation, no amplitude information is used from the reconstructed image; however, in the future this could be included to enhance volume estimation. When assessing the dependence on variation in urine conductivity, ECD seems to be completely independent; however, this might be due to the generally low sensitivity of this approach. When extending the algorithm to include amplitude information, this advantage will probably be lost. Of the other algorithms, the SVDM shows the best performance, followed by the GI and NN algorithms. Further research is needed to identify influences with high impact on the EIT measurement when using the system in a patient’s real life. One aspect is to compare algorithm performance for inter- and intra-individual variations in reconstruction model geometries, like a patient’s physique as well as movement or posture changes. Particularly for the tomographic approaches, a good approximation of the true geometry is needed for the reconstruction model. In conclusion, the GI, NN and SVDM algorithms are well suited for volume estimation; however, these results are preliminary and additional simulative research as well as patient measurements are required before a final judgement can be made regarding the algorithms. In addition, extending the ECD algorithm to include amplitude information from the tomogram seems to be a promising option. Acknowledgments This work was supported by the German Federal Ministry of Education and Research (BMBF) in the scope of the research programme ‘Innovative Hilfen in der Rehabilitation und für Behinderte’, grant number 13EZ1128A. References Adler A et al 2009 GREIT: a unified approach to 2D linear EIT reconstruction of lung images Physiol. Meas. 30 S35 Adler A and Lionheart W R B 2006 Uses and abuses of EIDORS: an extensible software base for EIT Physiol. Meas. 27 S25 Canny J 1986 A computational approach to edge detection IEEE Trans. Pattern Anal. Mach. Intell. 8 679–98 Denniston J C and Baker L E 1975 Measurement of urinary bladder emptying using electrical impedance Med. Biol. Eng. Comput. 13 305–6 1822
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Gazinski E 2004 Die elektrische Leitfähigkeit als Maß für die Konzentriertheit des menschlichen Urins PhD Thesis Bayerische Julius-Maximilians-Universität zu Würzburg He W, Ran P, Xu Z, Li B and Li S N 2012 A 3D visualization method for bladder filling examination based on EIT Comput. Math. Methods Med. 2012 528096 Hua P, Woo E J, Webster J G and Tompkins W J 1988 Bladder fullness detection using multiple electrodes Proc. of the Annual Int. Conf. of the IEEE Engineering in Medicine, Biology Society (New York: IEEE) pp 290–1 Kerner T E, Paulsen K D, Hartov A, Soho S K and Poplack S P 2002 Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects IEEE Trans. Med. Imag. 21 638–45 Kim C T, Linsenmeyer T A, Kim H and Yoon H 1998 Bladder volume measurement with electrical impedance analysis in spinal cord-injured patients Am. J. Phys. Med. Rehabil. 77 498–502 Leonhardt S, Cordes A, Plewa H, Pikkemaat R, Soljanik I, Moehring K, Gerner H J and Rupp R 2011 Electric impedance tomography for monitoring volume and size of the urinary bladder Biomed. Tech./Biomed. Eng. 56 301–7 Leonhardt S and Lachmann B 2012 Electrical impedance tomography: the holy grail of ventilation and perfusion monitoring? Inten. Care Med. 38 1917–29 Liao W C and Jaw F S 2011 Noninvasive electrical impedance analysis to measure human urinary bladder volume J. Obstet. Gynaecol. Res. 37 1071–5 Martinsen O G and Grimnes S 2008 Bioimpedance and Bioelectricity Basics (London: Academic) Romsauerova A, McEwan A, Horesh L, Yerworth R, Bayford R H and Holder D S 2006 Multi-frequency electrical impedance tomography (EIT) of the adult human head: initial findings in brain tumours, arteriovenous malformations and chronic stroke, development of an analysis method and calibration Physiol. Meas. 27 147–61 Sadleir R J and Fox R A 2001 Detection and quantification of intraperitoneal fluid using electrical impedance tomography IEEE Trans. Biomed. Eng. 48 484–91 Schöberl J 1997 NETGEN an advancing front 2D/3D-mesh generator based on abstract rules Comput. Vis. Sci. 1 41–52 Smallwood R H, Mangnall Y F and Leathard A D 1994 Transport of gastric contents (electric impedance imaging) Physiol. Meas. 15 A175–88
1823
Search
Collections
Journals
About
Contact us
My IOPscience
Bladder volume estimation from electrical impedance tomography
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Physiol. Meas. 35 1813 (http://iopscience.iop.org/0967-3334/35/9/1813) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 139.184.14.159 This content was downloaded on 18/01/2015 at 18:39
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Physiol. Meas. 35 (2014) 1813–1823
Physiological Measurement doi:10.1088/0967-3334/35/9/1813
Bladder volume estimation from electrical impedance tomography T Schlebusch, S Nienke, S Leonhardt and M Walter Chair for Medical Information Technology, Helmholtz Institute for Biomedical Engineering, RWTH Aachen University, Pauwelsstr. 20, 52074 Aachen, Germany E-mail: [email protected] Received 11 March 2014, revised 28 May 2014 Accepted for publication 16 June 2014 Published 20 August 2014 Abstract
Non-invasive estimation of bladder volume is required to progress from scheduled voiding to a demand-driven emptying scheme for patients with impaired bladder volume sensation. Electrical impedance tomography (EIT) is a promising candidate for the non-invasive monitoring of bladder volume. This article focuses on four estimation algorithms used to map recorded EIT data to a volume estimate. Two different approaches are presented: the tomographic algorithms (one based on global impedance, the other on equivalent circular diameter) rely on the reconstruction of a tomographic image and then extract a volume estimate, whereas the parametric algorithms (one based on neural networks, the other on the singular value difference method) directly map the raw data to a volume estimate. The four algorithms presented here are evaluated for volume estimation error, noise tolerance and suppression of varying urine conductivity based on finite element simulation data. Keywords: electrical impedance tomography, cystovolumetry, bladder volume, volume estimation (Some figures may appear in colour only in the online journal) 1. Introduction Some patient groups (for example, paraplegics) have an impaired bladder volume sensation due to damaged neural structures, often associated with the inability to urinate properly. A common therapy is regular intermittent self-catheterisation following a fixed time schedule. However, the emptying interval has to be chosen properly: a too short interval will unnecessarily interfere with quality of life and increase the risk of urethral damage or urinary infections, whereas a too long interval will increase the risk of complications due to an overfull bladder, e.g. over-distension of the bladder wall, reflux, hydronephrosis or autonomic dysreflexia. These latter complications are the main instigators of most of the urology-related emergencies 0967-3334/14/091813+11$33.00 © 2014 Institute of Physics and Engineering in Medicine Printed in the UK
1813
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Figure 1. Electrical impedance tomography (EIT) set-up for cystovolumetry.
among paraplegics. Therefore, a demand-driven emptying scheme would be preferable for some patients. To achieve this, a promising concept is non-invasive continuous impedancebased volume monitoring to estimate the appropriate moment for catheterisation. Impedance-based cystovolumetry systems exploit the difference in conductivity between urine and the tissue surrounding the bladder. Urine conductivity is mainly influenced by its saline concentration (Gazinski 2004) and is usually in the impedance range of 5–26 mS cm − 1. In contrast, the tissues surrounding the bladder (muscles, connective tissue and fat) are in the impedance range of 0.2–4 mS cm − 1 (Martinsen and Grimnes 2008). There is a relatively linear decrease in abdominal impedance with increasing bladder volume (Denniston and Baker 1975). Early experiments on non-invasive impedance-based bladder volume measurements were performed by Denniston and Baker in anaesthetised dogs in 1975 (Denniston and Baker 1975). For these measurements, the authors used a relatively unspecific electrode set-up by placing band electrodes around the abdomen. Later on, comparable set-ups using two-electrode (Liao and Jaw 2011) and four-electrode (Kim et al 1998) electrical impedance measurements reproduced their results in humans. To maximise the sensitivity to bladder volume while reducing artefacts, Hua et al (1988) applied a 2D-multi-electrode array to the ventral body surface, while still performing regular impedance measurements. Recently, both our group (Leonhardt et al 2011) and He et al (2012) demonstrated the application of electrical impedance tomography (EIT) for estimation of bladder volume. The measurement set-up is shown in figure 1: an EIT electrode belt embedded in the underwear at the level of the human bladder is connected to a portable EIT device, providing wireless volume estimates to a patient interface. This paper continues the approach of using EIT for bladder volume estimation, by focusing on the estimation algorithms used to map recorded EIT raw data to a volume estimate. Four algorithms based on two different approaches are presented: the two tomographic algorithms rely on the reconstruction of a tomographic image and extract a volume estimate in a second step, whereas the two parametric algorithms directly map the EIT raw data to a volume estimate. Finally, all four algorithms are compared with respect to volume estimation error, noise tolerance and the influence of varying urine conductivity. The paper is structured as follows: section 2.1 presents a brief introduction to EIT, section 2.2 outlines the simulated environment used to generate reproducible data for this experiment, and sections 2.3 and 2.4 describe the two tomographic and two parametric algorithms, respectively. Results concerning estimation error are presented in section 3.1, on noise tolerance in section 3.2 and concerning the influence of varying urine conductivity in section 3.3. Finally, section 4 presents the discussion and conclusions. 1814
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
(a)
(b)
(c)
(d)
(e)
(f)
Figure 2. Tomograms of eight-step image analysis based ECD algorithm. (a) Reconstructed EIT image (b) threshold operation retains only negative impedance changes (c) Gaussian blurring filter removes artificial edges from FEM mesh cells (d) Canny edge detection to separate impedance regions (e) identify closed regions from edge image (f ) enumerate regions and calculate their area and mid-point coordinates.
2. Materials and methods 2.1. Electrical impedance tomography
EIT (also called applied potential tomography, APT), is a medical imaging technique, which estimates an impedance distribution in the body volume by non-invasive measurements using electrodes attached to the skin. Similar techniques are also used in geophysics (electrical resistivity tomography, ERT, or electrical resistivity imaging, ERI) and industrial process monitoring (electrical capacitance tomography, ECT). For medical EIT measurements, usually a small fixed current (e.g. 5 mA at 50 kHz in accordance with IEC 60601-1, patient auxiliary current) is applied to the body and the resulting voltage potential distribution is recorded. To generate one EIT frame, successive measurements with varying injecting electrodes are required. For each injection, the voltage potentials of all remaining electrodes are recorded. Several injection and measurement patterns can be used to describe the spatial relation of the electrode pairs. One well-established pattern uses adjacent measurements with neighbouring electrode pairs for current injection and voltage measurement. In this case, N current injections are done for each EIT frame using an N-electrode EIT system. When omitting injecting electrodes due to unknown contact impedances from the voltage measurements, N − 3 pairwise, differential voltage measurements are performed, resulting in a total of N · (N − 3) = 208 voltages for one EIT frame (see figure 3). However, due to reciprocity, only 104 voltages are linearly independent. To estimate the unknown impedance distribution using 208 marginal potentials, different inverse solution methods can be applied. Medical applications of EIT cover a wide field, including ventilation monitoring (Leonhardt and Lachmann 1815
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
2012), assessment of cranial haemorrhage (Romsauerova et al 2006), gastric function monitoring (Smallwood et al 1994), quantification of abdominal fluid accumulations (Sadleir and Fox 2001), cancer monitoring (Kerner et al 2002) and bladder volume monitoring (Leonhardt et al 2011, He et al 2012). 2.2. Finite element simulation
In this work, EIT measurement data are created artificially by means of finite element simulation. Considerable simplification of the abdominal geometry has been accepted to keep the computational cost low: i.e. the abdomen is assumed to be a circular cylinder of 30 cm diameter and 30 cm height. The bladder is modelled as a ball located at the bottom of the cylinder, at the cylinder wall. With increasing volume, the bladder ball extends upwards to the middle of the cylinder. To ensure that the influence of a changing mesh structure with increasing ball size remains low, a fine mesh of 1 259 150 elements is used. A ring of 16 evenly distributed electrodes is placed around the cylinder at half the total height. Adjacent patterns are used for both the injection and the measurements. The EIDORS framework (Adler and Lionheart 2006) with NetGen (Schöberl 1997) was used to create and simulate the mesh. Unity background conductivity was assigned to the cylinder volume, while bladder conductivity was kept variable to account for the different urine conductivities. To identify the quality of an algorithm for real-life applications, its robustness has to be evaluated. In our case, two influence classes were identified: uncorrelated measurement noise and correlated artefacts by body movement, organ shift or internal organ impedance changes (e.g. intestine content). In the scope of this article, we focused on measurement noise susceptibility as well as the effect of urine conductivity on the estimation accuracy of all four algorithms. An analysis of body movement on estimation accuracy will be addressed in future work, when a FEM model representing body movement is available. To find reasonable measurement noise SNR levels, several EIT recordings from a Goe MF II EIT device (Abimek, Friedland, Germany) in patients and a passive electrical network dummy have been analysed for their temporal variations. We found noise levels from 42 dB SNR to 156 dB SNR, so this paper focuses on noisy test data with levels of 40 dB, 80 dB and 120 dB SNR. To model noisy voltage vectors, white uncorrelated noise was superimposed on the simulated EIT raw data, ui: noise signal η(1) = · ui,noise = ui + η noise SNR
Here, SNR defines the desired signal-to-noise ratio, ui the measured EIT raw data and noise the generated noise. Noisy EIT raw data ui,noise are calculated by superimposing the scaled noise η on the noise-free measurements ui. 2.3. Tomographic approaches
In the two tomographic approaches, an image is reconstructed from the EIT raw data using a linear reconstruction matrix (Adler et al 2009). In a subsequent step, a parameter is extracted from the image and used for volume estimation. 2.3.1. Global impedance. In the case of short-term processes, like urodynamics or micturition, an EIT image of a (partially) filled bladder referenced to an empty-bladder measurement mainly shows changes in impedance related to bladder volume. By summing the 1816
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
impedance changes for every pixel ΔZi, j in the reconstructed image, the global impedance (GI) is obtained: GI = ∑ ΔZ i, j (2) i, j
From two reference measurements with known volume, e.g. empty and maximally full bladder, a linear calibration curve mapping GI to volume is calculated in the noise-free case and is taken for all successive volume estimations. Since the image reconstruction using a matrix multiplication is a linear operation, the zero-mean noise is directly mapped on the impedance image data and the noisy GI data varies around the noise-free result. Image artefacts, such as ringing (impedance oscillations in the image) can cause volume errors, whereas some shape deformation and blurring can be tolerated. 2.3.2. Equivalent circular diameter algorithm. Instead of simply summing the impedance
changes in an image, which basically results in a general impedance measurement, the spatial information in the tomogram can be exploited by means of image analysis. Instead of correlating the GI change with bladder volume, the area of bladder pixels in the tomogram is used for estimation of the volume. The algorithm is based on the equivalent circular diameter (ECD) and works as follows: (a) reconstruction of a tomographic image at unknown volume referenced to an empty bladder using a GREIT reconstruction matrix (figure 2(a)) (b) application of a threshold to cut away positive inclusions (potential artefacts). Only negative impedance changes are retained, since urine has a lower impedance than surrounding tissue (figure 2(b)) (c) conversion to a black and white colour scale and applying Gaussian blurring filter to remove edges from pixels or finite element mesh cells in the tomogram (figure 2(c)) (d) application of the Canny algorithm (Canny 1986) for edge detection; this algorithm was chosen due to its high sensitivity to weak edges in blurred images (figure 2(d)) (e) application of imdilate and imfill from Matlab Image Processing Toolbox to create closed, filled areas (figure 2(e)) (f) for each numbered region (figure 2(f)), area and mid-point coordinates are calculated (g) the region closest to the expected bladder position is selected as the bladder (h) the ECD is calculated and mapped to a volume estimate using calibration data: 4 · Area ECD = (3) π 2.4. Parametric approaches
The basic concept of the following two parametric approaches for volume estimation from EIT measurements is to avoid the ill-conditioned reconstruction process. Instead of mapping 208 EIT raw data to 1024 image pixels and extracting one volume estimate, a direct mapping of 208 EIT raw data to one volume estimate is proposed. This procedure was expected to reduce the influence of noise and numerical instabilities, which usually require regularisation in image reconstruction. 2.4.1. Neural networks. To learn a mapping from input to output values, f eed-forward neural networks (NN) can be used. In our case, 208 input nodes and one single output 1817
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
V
V
V V
V
V
V
V
V
V
V
V
V
V
V
V
u18
u205
V
u19
u16
u17
u204
V
u20
u206
u198 u199
V
u21
u15
16th injection i16 , measurements u196 –u208
V
u4
u207
V
V V
u6
u22
u14
V
V
u7
u3
Second injection i2 , measurements u14 –u26
V
V
V
u8
u5
u23
V
V
u9
u2
u197
u208 V
V
u10
First injection i1 , measurements u1 –u13
u196
V
V
u24
V
u11
i16
i2
V
V
V
u12
u26
u25
u1
V
i1 u13
u203 u202
u200
u201
Figure 3. Numbering of the recorded EIT raw data.
node are used to represent the mapping from EIT raw data to the volume estimate. In addition, three hidden layers are used. The number of hidden layers was determined empirically. Matlab Neural Network Toolbox was used for backpropagation training of the NN. As is usual for NN, a huge training dataset providing raw data to volume tuples is required. For simulated work, this is relatively easy, but also for real measurements the training data can be collected by continuous EIT and drained urine volume measurements during micturition (uroflowmetry). In our case, noise-free simulation data are used to train the network. The data are randomly partitioned into three parts using Matlab’s divideParam routine: 70% for training, 15% for validation and 15% for testing. Since the NN is directly trained on the link between EIT raw data and volume, no further calibration or conversion of the output is necessary. 2.4.2. Singular value difference method. EIT raw data from an adjacent measurement of
an empty saline tank phantom generally shows a regular comb pattern of padded U-shapes. When introducing inhomogeneity into the tank phantom, the comb pattern changes slightly in both amplitude and shape. The general idea of the proposed Singular Value Difference Method is to quantify these changes and correlate them with bladder volume. To apply our ^ . The matrix is filled columnmethod, we re-order all 208 raw values in a 13 × 16 matrix M wise, holding all raw data recordings belonging to a single injection position per column. The rows are filled clockwise with adjacent measurements, starting from the injecting electrode pair (as shown in figure 3): ⎛ u ref,1 u1 u14 ⋯ u196 ⎞ ⎜ u ref,2 u2 u15 u197 ⎟ M=⎜ ⋮ ⋮ ⋮ ⎟⎟ (4) ⎜ ⋮ ⎝ u ref,13 u13 u26 ⋯ u208 ⎠ ^ , this results in aligned U-shaped EIT raw data curves When plotting the columns of M which differ, in our case, only due to noise or volume change. Since we aim to analyse deformation of the EIT raw data vectors due to changes in bladder volume, a reference measurement ^ . Then, singular value decomposition is with empty bladder is added as the first column of M applied to this 13 × 17 matrix M. By applying singular value decomposition, a m × n matrix M can be decomposed into a m × m matrix U holding the left singular vectors, a n × n matrix VT holding the right singular 1818
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
λ =1
Original
λ =0.1
1
1
2
0.04
0.16
0.9
0.03 0.14
0.8
0.6
0.01
0.1
0.5
0
0.08
0.4
−0.01
0.06 0.3 0.2 0.1 0
0
5
10
(a)
0.04
−0.02
0.02
−0.03
0
3
λ =1, λ =λ =0.1 1
0.2
0.025
0.18
0.02
0.16
0.015
0.14
0.01
0.12
0.005
0.1
0
0.08
−0.005
0.06
−0.01
0.04
−0.015
0.02
2
3
0.02
0.12
0.7
λ =0.1 0.03
0
5
10
−0.04
0
5
(b)
(c)
10
−0.02
0
5
10
(d)
0
0
5
10
(e)
Figure 4. Interpretation of singular vectors and singular values: (a) original matrix,
(b)–(d) visualizations of the effects of λ1–λ3, (e) oversubscribed shape change represented by the first three singular values.
vectors and a sparse m × n matrix Σ with its only non-zero elements on its main diagonal, called singular values λi. (5) M = U ΣV T In our case, where m 1000
0.00 0.00 805.57 > 1000
0.81 0.81 1.94 193.38
0.00 0.01 2.37 213.21
4.70 4.70 4.71 87.68
0.00 0.00 0.15 85.09
GI, global impedance; ECD, equivalent circular diameter; NN, neural networks; SVDM, singular value difference method.
generated from noise-free data and noisy measurements were only used for actual volume estimation. For each volume estimate (4 algorithms · 4 noise levels · 17 volumes · 100 simulations), the relative error was computed. Table 1 shows the arithmetic mean value of the relative error for each algorithm and noise level, calculated for all simulations of bladder volumes ranging from 60 ml to 360 ml. In addition, the mean value of the standard deviation (SD) at bladder volumes ranging from 60 ml to 360 ml is shown. Note that the first two volumes (10 ml and 35 ml), and the last two volumes (385 ml and 410 ml) were omitted for error calculation. In particular, the NN algorithm has poor capability for extrapolation outside or near the training region borders; this precludes a plausible comparison of the overall performance of the four algorithms. 3.3. Influence of urine conductivity
Urine conductivity is mainly influenced by its ion concentration and can vary throughout the week depending on, for example, the amount of salt and water intake. Ideally, the calculation of bladder volume should be independent of urine conductivity. To assess the influence of varying urine conductivity on the estimated volume, the finite element simulation was repeated with a fixed bladder volume of 185 ml, fixed background conductivity of 1 unit, but varying urine conductivity from 1.5 to 5 units. All algorithms were calibrated at a reference conductivity of 2 units. 1821
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Figure 6 shows the estimated volume for all simulated urine conductivities. The ideal result is a horizontal line (represented by the dashed line in figure 6). The ECD algorithm is the only one that is independent of urine conductivity, although it presents a high static offset to the correct value. All other algorithms show a significant dependence of volume estimate on urine conductivity. With increasing EIT image contrast (ratio of urine conductivity to background conductivity), the influence of urine conductivity on volume calculation decreases (shallower slope of the curve). 4. Discussion and conclusion In these simulations, the GI and NN algorithms show the lowest estimation error in the noisefree case and acceptable estimation errors for medium noise levels. For high noise levels the SVDM has some advantages but, even in the noise-free case, shows a volume error of 4.7% . The ECD algorithm shows unacceptable volume errors. In its current implementation, no amplitude information is used from the reconstructed image; however, in the future this could be included to enhance volume estimation. When assessing the dependence on variation in urine conductivity, ECD seems to be completely independent; however, this might be due to the generally low sensitivity of this approach. When extending the algorithm to include amplitude information, this advantage will probably be lost. Of the other algorithms, the SVDM shows the best performance, followed by the GI and NN algorithms. Further research is needed to identify influences with high impact on the EIT measurement when using the system in a patient’s real life. One aspect is to compare algorithm performance for inter- and intra-individual variations in reconstruction model geometries, like a patient’s physique as well as movement or posture changes. Particularly for the tomographic approaches, a good approximation of the true geometry is needed for the reconstruction model. In conclusion, the GI, NN and SVDM algorithms are well suited for volume estimation; however, these results are preliminary and additional simulative research as well as patient measurements are required before a final judgement can be made regarding the algorithms. In addition, extending the ECD algorithm to include amplitude information from the tomogram seems to be a promising option. Acknowledgments This work was supported by the German Federal Ministry of Education and Research (BMBF) in the scope of the research programme ‘Innovative Hilfen in der Rehabilitation und für Behinderte’, grant number 13EZ1128A. References Adler A et al 2009 GREIT: a unified approach to 2D linear EIT reconstruction of lung images Physiol. Meas. 30 S35 Adler A and Lionheart W R B 2006 Uses and abuses of EIDORS: an extensible software base for EIT Physiol. Meas. 27 S25 Canny J 1986 A computational approach to edge detection IEEE Trans. Pattern Anal. Mach. Intell. 8 679–98 Denniston J C and Baker L E 1975 Measurement of urinary bladder emptying using electrical impedance Med. Biol. Eng. Comput. 13 305–6 1822
T Schlebusch et al
Physiol. Meas. 35 (2014) 1813
Gazinski E 2004 Die elektrische Leitfähigkeit als Maß für die Konzentriertheit des menschlichen Urins PhD Thesis Bayerische Julius-Maximilians-Universität zu Würzburg He W, Ran P, Xu Z, Li B and Li S N 2012 A 3D visualization method for bladder filling examination based on EIT Comput. Math. Methods Med. 2012 528096 Hua P, Woo E J, Webster J G and Tompkins W J 1988 Bladder fullness detection using multiple electrodes Proc. of the Annual Int. Conf. of the IEEE Engineering in Medicine, Biology Society (New York: IEEE) pp 290–1 Kerner T E, Paulsen K D, Hartov A, Soho S K and Poplack S P 2002 Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects IEEE Trans. Med. Imag. 21 638–45 Kim C T, Linsenmeyer T A, Kim H and Yoon H 1998 Bladder volume measurement with electrical impedance analysis in spinal cord-injured patients Am. J. Phys. Med. Rehabil. 77 498–502 Leonhardt S, Cordes A, Plewa H, Pikkemaat R, Soljanik I, Moehring K, Gerner H J and Rupp R 2011 Electric impedance tomography for monitoring volume and size of the urinary bladder Biomed. Tech./Biomed. Eng. 56 301–7 Leonhardt S and Lachmann B 2012 Electrical impedance tomography: the holy grail of ventilation and perfusion monitoring? Inten. Care Med. 38 1917–29 Liao W C and Jaw F S 2011 Noninvasive electrical impedance analysis to measure human urinary bladder volume J. Obstet. Gynaecol. Res. 37 1071–5 Martinsen O G and Grimnes S 2008 Bioimpedance and Bioelectricity Basics (London: Academic) Romsauerova A, McEwan A, Horesh L, Yerworth R, Bayford R H and Holder D S 2006 Multi-frequency electrical impedance tomography (EIT) of the adult human head: initial findings in brain tumours, arteriovenous malformations and chronic stroke, development of an analysis method and calibration Physiol. Meas. 27 147–61 Sadleir R J and Fox R A 2001 Detection and quantification of intraperitoneal fluid using electrical impedance tomography IEEE Trans. Biomed. Eng. 48 484–91 Schöberl J 1997 NETGEN an advancing front 2D/3D-mesh generator based on abstract rules Comput. Vis. Sci. 1 41–52 Smallwood R H, Mangnall Y F and Leathard A D 1994 Transport of gastric contents (electric impedance imaging) Physiol. Meas. 15 A175–88
1823
