Impedance Ratio Method for Urine Conductivity-Invariant Estimation of Bladder Volume

To the knowledge of the authors, the first application of EIT for cystovolumetry has been reported by our group in 2011 [7]. In this study, nine male paraplegic patients have been monitored by EIT during regular urodynamic examination. A total volume of 99–585 ml contrast agent (conductivity of 13.35 mS/cm) has been instilled. An elastic electrode belt of 16 conductive silicone electrodes has been attached to the lower torso of the patient and an experimental EIT System (EEK2, Dr¨ager Medical, Lübeck, Germany) was connected for impedance measurement. The device uses adjacent injection and measurement patterns, which means that neighbouring electrodes are used for current injection as well as voltage measurement. This pattern results in a total of 208 readings per measurement (so called frame, for further details on the EIT measurement method, the interested reader is referred to the literature [9]). For image reconstruction, a reference measurement at empty bladder has been used. By summation of the pixel values of the reconstructed impedance-change image, the global impedance is obtained which was correlated with infused bladder volume. The results show excellent linearity of global impedance with bladder volume, with Pearson’s correlation coefficients of up to -0.97958.

A different EIT-based approach was presented and evaluated in an in-vitro agar phantom by He et al. [8] in 2012. They used a planar 8×8 array of metal electrodes for ventral placement with a dorsal ground electrode. Current was injected between one of the ventral array electrodes and the dorsal common ground electrode, voltage measurements are taken from the remaining 63 electrodes, therefore implying a tripolar measurement. A total of 64 · 63 = 4032 readings was recorded per measurement. Bladder volume calculation was performed in terms of boundary detection in the reconstructed images in 3D and volume of the extracted closed surface is calculated. For evaluation, an agar phantom with a cylindrical cavity filled with sodium chloride solution has been designed. In-vitro evaluation showed excellent estimation accuracy of up to 1 ml.

When thinking of an impedance-based bladder volume monitor it is evident that electrical impedance is not only influenced by volume but also by urine conductivity. In the human body, the kidneys are in charge of maintaining constant blood osmolarity, mainly by regulation of its sodium concentration [10]. In consequence, urine conductivity is highly dependent on renal activity and can not be assumed constant. Early experiments identified the influence of different urine conductivities on bladder volume estimation from impedance measurements [11, 12] and suggested further research in this field.

To quantify intra- and inter-individual variability of urine conductivity, we collected 81 urine samples from nine hospitalized patients (five female, four male, age 47.5 ± 17.9 years). All patients have sensorimotor defects (paraplegia) of different severity (ASIA A to ASIA D, cervical to lumbal). Subject 2 had antidiuretic medication which affects urine concentration, all other subjects had medication without known impact on urine concentration. Urine samples were taken at three consecutive days, each day at 8:00, 12:00 and 16:00. Urine conductivity has been measured using an HI 8733 (Hanna Instruments, Woonsocket, USA) conductivity meter. Results are shown in Figure 1, grouped for each patient as a box plot. The box contains 50% of all measurements with a horizontal bar indicating the mean value. The whiskers to the top and bottom of the box representthe 1.5 interquartile range, while the plus signs indicate outliers. There was no obvious information from the time series data so that this data representation emphasizing the conductivity variation Δσ has been chosen. From Figure 1, high inter-individual variation of urine conductivity in the range of 5.9. . .32.2 mS/cm is apparent, although intra-individual variation is lower. Intra-individual variation ranged from Δσ = 4.8 mS/cm (subject 6) to Δσ = 17.1 mS/cm (subject 7). From this results we can conclude that even for hospitalized patients with comparable daily routine and meals, urine conductivity can not be assumed constant and its influence on impedance-based volume estimation has to be taken into account.

Fig. 1

To evaluate the influence of urine conductivity on EIT global impedance, experiments comparable to an urodynamic examination have been performed in a freshly euthanized pig (≤ 30 min). For EIT measurement, the set-up has been kept close to the human experiment performed in 2007 [7] incorporating an EEK1 (Dräger Medical, Lübeck, Germany) EIT device with adjacent injection and measurement pattern as well as an elastic belt with 16 conductive rubber electrodes. Solutions of demineralized water with sodium chloride concentrations of 0%, 0.9% and 1.8% accoding to conductivities of ∼0 mS/cm, ∼15 mS/cm and ∼28 mS/cm have been prepared. As shown in Figure 2, a 50 ml syringe and two three-way taps have been used to perform urodynamic examination-like filling and emptying of the bladder through an intravesical catheter. The electrode belt has been attached as caudal as possible while maintaining stable electrode contact, resulting in the electrode belt placed cranial of the iliac crest.

Fig. 2

Before starting the experiment, the bladder was drained completely and EIT reference baseline was recorded. Then, the bladder was filled successively by 50 ml syringe fillings with 0.9% sodium chloride solution until a total volume of 200 ml was reached and successive emptying in 50 ml syringe fillings followed. The whole procedure was then repeated for 1.8% and 0% sodium chloride solutions.

The resulting global impedance from the experiment is shown in Figure 3. For each solution concentration, global impedance decreases with increasing volume which confirms the negative correlation of volume and extracorporal impedance reported earlier [12, 5]. Additionally, the experiment reveals great dependence of the slope of impedance change on solution conductivity. The higher the conductivity the steeper the negative slope of global impedance with volume.

Fig. 3

From this results we conclude that varying urine conductivity has to be taken into account for accurate, impedance-based bladder volume estimation.

The general idea of the Impedance Ratio Method is to correlate volume with a ratio of three different impedances measured at bladder level around the abdomen to reduce the influence of unknown urine conductivity on the volume estimate. The sensitivity of a bioimpedance measurement system is normally highest nearby the electrodes due to

higher current densities [13]. With increasing volume, the bladder extends and displaces surrounding tissue. To exploit the spatial change, three spatially distributed impedance measurements have been chosen, which are shown in Fig. 4. The first measurement (U_f /I_f , front) is located ventrally in front of the bladder, the second measurement (U_b/I_b, back) is located dorsally and a third measurement (U_s/I_s, side) is located at the patient’s side. To justify the chosen electrode placements, sensitivity simulations inspired by the work of Kauppinen et al. [14] have been calculated. As Fig. 5 visualizes, the front measurement is very sensitive to bladder impedance changes, while the back measurement has only low sensitivity in the bladder region and is used as a baseline impedance reference. The sensitivity of the side measurement is dependent on bladder size and therefore bladder volume: the influence of the bladder to the side impedance measurement increases with increasing bladder size.

Fig. 4

Fig. 5

The Impedance Ratio is defined as

where Z_s is the measured impedance at side position, Z_f at front position and Z_b at back position, respectively.

It can be understood as a measure to quantify the influence of the bladder on abdominal impedance inhomogeneity, which correlates with its volume.

Especially for low bladder volumes, the impedance differences are very small and the division by a small difference amplifies measurement errors. Therefore, we define a trust factor (TF) to quantify the amount of impedance difference in the pelvis:

Below a certain threshold of TF, IR is assumed to be susceptible to measurement errors.

Three different versions of the Impedance Ratio Method have been taken into account in this work:

While tissue shows a complex, frequency dependent impedance, urine can be assumed purely resistive in the bioimpedance measurement range below 1 MHz. Therefore, a decreased imaginary part or decreased frequency differential impedance indicates increased bladder volume.

During an initial calibration measurement, a mapping of IR values to bladder volume has to be found, which is used for volume calculation in all subsequent measurements.

For the simulative analysis, the EIDORS toolkit for Matlab [15] has been used. A cylinder of 30 cm diameter and 3.9 cm height modelling our in-vitro tank phantom has been defined with a cylindrical cavity located eccentrically to model the bladder. The frequency dependent impedance of muscle based on the Gabriel database [16] has been assigned to the material surrounding the cavity, resulting in 3.492mS/cm + i0.235mS/cm at 37.5 kHz and 3.825mS/cm+i0.695mS/cm at 193 kHz, respectively. Conductivities of 4 mS/cm, 12 mS/cm, 20 mS/cm and 28 mS/cm have been assigned to the material inside the cylindrical cavity to represent varying urine conductivity. The measurement at 20 mS/cm has been selected for calibration of the IR to volume mapping.

To test the noise tolerance of the algorithm variants, white uncorrelated noise was added to the simulated EIT impedance measurements in the following manner:

Here, SNR defines the desired signal-to-noise ratio, Z_i the measured impedance raw data vector and noise the generated noise. Noisy impedance raw data Z_i,noise are calculated by superimposing the noise-free measurements Z_i with the scaled noise η. Considering that patient impedance recordings and dummy test measurements using a Goe MF II EIT device (Abimek, Friedland, Germany) showed noise levels between 42 dB SNR and 156 dB SNR, this paper focuses on noisy test data with levels of 40, 50, 60 and σ dB SNR.

A 30 cm diameter perspex tank phantom with sixteen equally spaced stainless steel screws as electrodes (of which eight have been used in this work) has been used for in-vitro measurements. A dispersive agar-sodium-chloride filling has been used to model frequency-dependent tissue impedance. Although neither exact muscle impedance nor a Cole-like dispersion curve can be modelled using agar, the set-up provides a dispersive surrounding around the cavity representing the bladder, thus allowing to evaluate the suitability of the Impedance Ratio Method.

A commercial precision LCR meter (E4980, Agilent Technologies, Santa Clara, CA, United States) connected to a custom-built multiplexer intended for 8-electrode multifrequency electrical impedance tomography has been used for all measurements. A schematic drawing of the measurement set-up is shown in Fig. 6. Although the E4980 does not provide a tetrapolar measurement eliminating the influence of varying contact impedances, the resulting error can at least be assumed to be constant for measurements at one frequency.

Fig. 6

To model the bladder, a cylindrical cavity has been cut into the agar filling, as shown in Fig. 7. De-mineralized water, 0.9% and 1.8% sodium-chloride solution have been used to represent urine of varying conductivity in the cylindrical cavity, thus resulting in a smaller fluid filled cylinder inside the agar cylinder (see upper left sketch in Fig. 7). Themeasurements were started with a small cylindrical cavity, then measurements for all three conductivities were recorded before the cavity was enlarged with greater radius as shown in the upper right sketch of Fig. 7. Then, measurements of all three conductivities started over again for the next volume. Between all measurements, the fluid has been drained completely from the cavity. For each cavity size, the volume was measured once by instilling fluid using a syringe. The measurement with 0.9% sodium-chloride solution has been used to calibrate the IR to volume mapping.

Fig. 7

For all three algorithm variants, four plots presenting simulation results are shown in the Figures 8, 9, 10, respectively. The top plot shows the estimated to instilled volume for all four conductivities, while the lower three plots show the volume error over instilled volume, the error mean (blue line) and 1.96 standard deviation of the error (red lines).

Fig. 8

Fig. 9

Fig. 10

Common to all three variants is a high volume error at very low bladder volumes. At low volumes, the measured differential voltages are very small and noise as well as numerical effects get amplified by the division, which is also represented by the trust factor value.

The single frequency variant using absolute values shows high errors for low urine conductivities in the range of surrounding tissue impedances (σ = 4 mS/cm), as shown in Fig. 8. For higher conductivities, the method works as expected: the volume estimation result is independent of the urine conductivity to a great extend.

If using a complex impedance measurement device, the error at low urine conductivities can be reduced by using the imaginary parts of the impedances, as shown in Fig. 9. This is because surrounding tissue shows dispersive effects while urine can be assumed purely resistive in our measurement frequency range and a displacement of dispersive tissue in favour of more purely resistive urine introduces a phase change in the measured impedance.

The frequency differential variant using absolute values in Fig. 10 shows comparable results to the single frequency variant with imaginary parts. The reason for comparable performance is the same for both methods: tissue shows a frequency-dependent impedance while the conductivity of urine can be assumed constant in our frequency range. The higher the bladder volume, the less impedance changes between both frequencies can be measured.

Fig. 11 visualizes the influence of noise on volume estimation by all three variants. Both single frequency variants show acceptable noise influence, while the frequency differential variant shows much higher noise susceptibility. This results from the drastically reduced amplitude of the impedance difference vector compared to a single frequency vector.

Fig. 11

However, since diuresis is a very slow process compared to impedance measurement time, temporal filtering can be applied for further noise reduction, which has not been taken into account in this work.

The measurement results for our Agar tank phantom measurements are shown in figure 12 (single frequency, absolute values), figure 13 (single frequency, imaginary parts), and figure 14 (multi-frequency, absolute values). Common to all variants is a higher variation in estimated volume compared to the results from simulated measurements. The narrowest band of variation shows the single frequency variant using imaginary parts in Fig. 13, followed by the single frequency variant using absolute values. The high variation in the multifrequency measurement may result from varying electrode contact impedances, which are affecting the measured impedance in our set up. For greater impedance changes (0.9% and 1.8% saline solution), all methods show acceptable estimation errors below 50 ml.

Fig. 12

Fig. 13

Fig. 14