Probing deep lung regions using a new 6-electrode tetrapolar impedance method

The electrical impedance measured across the thorax at any specific measurement frequency changes significantly with the breathing cycle due to filling up of spaces within the lung by low conductivity air to varying degrees. Therefore, measurement of electrical impedance of lungs has a potential application in pulmonary medicine, particularly for the low and medium income countries (LMIC), for its technological simplicity resulting in low cost devices that are easy to apply and maintain.

The basic method for measuring bioelectrical impedance is the age old Tetrapolar Impedance Measurement (TPIM) technique, which uses four electrodes and can eliminate electrode contact impedance. This technique was introduced by William Thomson, popularly known as Lord Kelvin in 1861, to measure low resistances where the lead wire resistance and the contact resistance created problems [1]. Later, this technique was applied by Nyboer for bio-electrical measurements where the contact impedance is a major problem [2]. Since then it has been the standard measurement method in the measurement of biological tissues including the human body. Different derived techniques based on TPIM, such as Electrical Impedance Tomography (EIT) (originally named as Applied Potential Tomography, APT) [3] and Focused Impedance Method (FIM) [4,5] have evolved over time to provide better localisation of the measurement regions. All these methods were applied to study lung parameters during the breathing cycle by many researchers [6, 7, 8, 9] showing reasonable outcomes. EIT gives an image of the impedance distribution but is a rather complex technique which would be potentially expensive when commercially produced. On the other hand, TPIM and FIM are simple techniques which would result in potentially low cost devices and would be more appropriate for the LMICs. Recently, another simple technique, a 6-electrode TPIM was proposed by one of the authors [9], which was particularly aimed at getting improved sensitivity in the deeper regions of a volume conductor using surface electrodes employing the same electrical measurement setup of the simple TPIM.

The new 6-electrode TPIM is described here with the help of figure 1, reproduced from [9], which is particularly targeted to one lung. In this method, two current electrodes are fixed at the two sides (lateral points) of the thorax while two pairs of potential measuring electrodes are affixed on the front and back symmetrically over the region of interest (figure 1a), in the same horizontal plane. The corresponding potential measuring electrodes on the front and back are connected together. This was expected to give better sensitivity in the deep regions compared to a similar configuration of conventional 4-electrode TPIM having only one pair of potential electrodes on the front or at the back (figure 1b). Qualitative visualisations of the sensitivities of the two configurations are represented in these figures through shades of dark red. The idea is similar to that of a Helmholtz coil for producing a uniform magnetic field between two coils [10].

Fig.1

The above proposal for a 6-electrode TPIM was made based on concepts of physics, from qualitative visualisations based on concepts of equipotentials and sensitivity [11]. Subsequently, Roy et al. [12] studied this new 6-electrode TPIM on a cylindrical phantom, both through numerical simulation using a software package named COMSOL Multiphysics [13], which utilises the Finite Element Method (FEM), and through experimental measurements, and found improvement in the deep region sensitivity compared to that for the conventional 4-electrode TPIM configuration (figure 1b). However, this work was targeted to any volume conductor in general, not necessarily to any particular organ.

The present work particularly focused on the lungs which required changes in the shape and the design of the volume conductor.

For an initial understanding of the point sensitivity pattern, a simple rectangular volume conductor with rounded edges (phantom) was simulated in COMSOL with electrodes for a 6-electrode TPIM targeting one side of the volume, over the region of a lung, as shown in figure 2. The dimensions of the volume were 33 cm × 26 cm × 12 cm corresponding to assumed x, y and z directions respectively as shown. Here the electrodes were long electrodes, current electrodes covering the full height while the potential electrodes were 3 cm long placed at vertical mid-level. All the electrodes had a width of 3 mm. The separation between the potential measuring electrodes, both in the front and the back, was 15 cm. For simulation of a 6-electrode TPIM and for a 4 electrode TPIM, electrical connections as shown in figure 1 were used. The volume conductor was supposed to be filled with a fluid with uniform a conductivity of 0.081 S/m.

Fig.2

Since the current drive and potential measuring electrodes are not the same in a TPIM, the measured impedance, given by Z=V/I, is usually called a ‘transfer impedance’ [14] to distinguish it from the simple bipolar impedance measurement based on Ohm’s Law.

The point sensitivity values were calculated using the following equation [11] which was based on lead fields introduced by Geselowitz [15]:

where J 1 and J 2$J_1 \text { and } J_2$are the current density vectors at a point within the volume conductor due to injection of the same current I through the exciting (current drive) and sensing (potential measuring) electrode pairs, respectively. This analysis draws its justification from the well-known reciprocity theorem [16] which essentially says that if the current and the potential electrode pairs are interchanged in any system, the measured values of transfer impedance remain unchanged.

The transfer impedance Z of the volume conductor is then given by,

where ρ is the point impedivity and the integral is carried out over the full volume V. (Impedivity is the specific impedance, an equivalent to resistivity, which is the specific resistance.)

In order to visualise the point sensitivity distribution of the uniform volume conductor (phantom), colour contours in specific 2D planes were displayed while variations of numerical values were plotted along two lines ab and cd as indicated in figure 2, which lie centrally in the respective geometries.

Next, the efficacy of the 6-electrode TPIM technique in targeting deep regions of one lung was simulated using a near to real life 3D model of the thorax, as developed by one of the authors [17] and shown in figure 3. The dimensions of the thorax were estimated from typical CT images of an adult human male of height 170 cm. The overall depth and height of the modelled thorax were 21.4 cm and 31 cm respectively. This assumes a person standing. The width was 33 cm on the back and 32 cm on the front. The model incorporated skin, transcutaneous fat, ribs, muscle, heart filled with blood and lungs as indicated in figure 4. To build the overall model and to give it a realistic shape, various geometry operations of COMSOL Multiphysics were performed. The appropriate impedances for the different tissue types incorporated in the model were taken from a publication of the Italian Institute for Applied Physics [18].

Fig.3

Fig.4

The simulations were performed at full inspiration and full expiration of the lungs at a measuring frequency of 10 kHz. The conductivity and permittivity of the lung tissue at this frequency were obtained from the above publication which were 0.2429 S/m and 34044 respectively at full expiration and 0.093172 S/m and 17174 respectively at full inspiration.

Normally, the lung volume changes significantly with the breathing cycle, but for simplicity, in this modelled thorax, it was assumed constant. Similarly, the volumes of other organs around the lungs were assumed constant. Both the left and right lungs modelled were similar in shape and size and the volume of each lung was 2030 cm³. The details are available in the original work [17].

For simplicity, the thorax model was considered as piecewise homogeneous and isotropic. This means that any domain within the model was assumed to be homogeneous and isotropic, but the electrical properties of different domains are different. Boundary conditions were set so that the current density on the outer boundary of the thorax is zero whereas the boundaries between internal domains satisfy continuity.

Circular stainless steel electrodes of 0.3 cm diameter were taken to touch the outer skin surface for all the electrodes (Figure 3). The electrode plane was taken at a height of 6 cm from the bottom of the thorax (in the vertical direction of the thorax, for a standing posture) for the present study. The current electrodes were fixed on the sides at about the midpoint of the depth of the thorax. The potential electrodes, on both the front and back surfaces, were positioned as shown in figure 3, with a 7 cm separation for the initial study. The potential electrode nearest to the side of the body was at a distance of 6.5 cm from the front edge of the thorax. The outcome of this study showed the presence of negative sensitivity regions at the corners of the horizontal cross section of the lungs (showed in the results section, figure 8). With a view to reduce this negative sensitivity region, a second study was taken up for which the potential electrode nearest to the side of the body was moved laterally to a new position at a distance of 3.5 cm from the front edge of the thorax. The inner electrode was kept fixed in position. This created an electrode separation of 10 cm (measured on the surface of the thorax) between the potential electrodes on both the front and back.

Fig.5

Fig.6

Fig.7

Fig.8

Equation 2 gives the total transfer impedance for the whole volume of the thorax in which the respective impedivity of each point is considered according to the assumed thorax model. For convenience, ‘transfer impedance’ is shortened to simply ‘impedance’ henceforth. Since the total impedance will change during respiration, the total impedance change (TIC), expressed in the form of a percentage, was defined for this study as,

Obviously, one would like to have a configuration giving a maximum value of the above parameter.

Since the lung is the target organ in this present study, the contribution of the target lung to the total impedance, CLTI, is an interesting and useful parameter. Any measurement targeting the lung should try to maximise CLTI. Depending on the target lung region, either both or anyone, CLTI may be adapted to consider the appropriate lung volume.

Thus if Z_T is the total impedance as given by equation 2, integrated over the whole thorax volume, and Z_L is the impedance of the target lung region, obtained through an integration of equation 2 only for the respective target lung volume, then CLTI is given by,

Here, Z_T includes Z_L. CLTI was expressed in percentage.

In this work, two versions of CLTI were used. In one, named CLTI(1), the integration for Z_L was performed over only the target lung volume, around which the electrodes are placed. For the second, named CLTI(2), the integration was performed over both the lung volumes even though the electrodes were positioned to target one lung only. A comparison of CLTI(1) with CLTI(2) will give an idea of the degree of localization achieved through the electrode configurations as described above.

The overestimations in CLTI of a target lung due to the other lung (OCLTI) was obtained as,

OCLTI was expressed in percentage and would indicate the success of the electrode placement in focusing the target lung. A low value of OCLTI is desired which would indicate a small contribution from the other lung outside the potential electrode configuration.

This work presents a quantitative evaluation of a new technique of 6-electrode TPIM introduced by one of the authors [9], and this work particularly targeted the lungs, using finite element simulation, employing the COMSOL software package.

Firstly, the sensitivity distribution within a rectangular volume for a particular separation between the potential electrodes was studied and the results shown in figure 5 clearly shows the improvement produced. The sensitivity of the one sided 4-electrode TPIM remains limited to one side of the volume while for the 6-electrode TPIM the sensitivity extends through the whole depth. The normalised sensitivity distributions along the depth of the volume at the midpoint of the potential electrode configuration were shown in figure 6. This also shows clearly that the variation of sensitivity along the depth for 6-electrode TPIM (by a factor of about 1.7) is much reduced compared to that (about 8.3) for 4-electrode TPIM. The main point to note is that the 4-electrode TPIM is only good for organs at shallow depths near the potential electrodes, while for organs like the lungs, extending almost through the depth, 6-electrode TPIM is a better choice.

Figure 7 shows the normalised sensitivity along the width of the rectangular volume, where both the 6-electrode TPIM and the 4-electrode TPIM have exactly the same pattern, which is expected. The sensitivity has a very low value on the left edge (since the potential electrodes in this case were placed on the right hand side of the volume as shown in figure 2) and it goes through a maximum at the midpoint of the potential electrode configuration, which is also expected.

It may be anticipated that the uniformity with depth would improve through increasing the separation between the potential electrodes on each side, however, depending on the geometry of the target organ one may have to make a trade off. Looking at Figure 1, the electrodes were placed to target one lung only. However, if one intends to cover both the lungs, the two potential electrodes may be positioned near the two edges of the thorax when the uniformity with depth would be better. This was also indicated by Rabbani [9] and reproduced in Figure 9. Of course, in this case the heart with low impedivity blood will take a good share of the current distribution. However, for any measurement on lungs, one usually looks for changes during respiration and the contribution of the heart may be separated since the rates of the two changes are normally different and they are not synchronised.

Fig.9

The life like thorax model developed by one of the authors [17] adds a new dimension to this work. It has modelled the main tissues and organs within the thorax including the heart filled with blood. However, the volume of lung is assumed to be constant during respiration, for simplicity, which is a limitation. This approximation will have a bearing on the outcome of the present work as well. In future, if the lung volume is changed appropriately in the model, the simulation quality will improve. Again, the heart volume is also assumed to be constant, which needs appropriate changes in the future. However, since the beating of the heart and respiration have different rates and are not synchronous, as mentioned above, the assumed fixed heart will not affect the outcome of the present work significantly.

The improvement in depth sensitivity using the new 6-electrode TPIM over a conventional 4-electrode TPIM is adequately demonstrated through the sensitivity distributions obtained using the above mentioned life like thorax model as presented in Figure 8. The 1^st row and the last row show how the whole depth of the lung contributes to the measurements. On the other hand, the 4-electrode TPIM either on the front or on the back only covers the respective regions down to a certain depth. However, it is apparent that 4-electrode TPIM placed at the back covers a greater volume of the target lung because of the anatomy and geometry of the lung itself.

For the 1^st to 3^rd row of Figure 8, the separation between the potential electrodes on each side was 7 cm, as shown in Figure 3. This shows presence of small regions of negative sensitivity within the target lung, on the left side of the figure, which would underestimate the contribution from the lung in the impedance measurement. Negative sensitivity regions occur in between the current and voltage electrodes in a TPIM measurement. Intuitively, shifting the electrodes near the edges further towards the edge may reduce the negative sensitivity region. Based on this intuition, these electrodes were shifted by 3 cm over the surface of the thorax as a trial, increasing the separation between the potential electrodes to 10 cm. The 4^th row in Figure 8 gives a visual indication, only for the 6-electrode TPIM, of the improvement thus obtained. Table-3 shows this improvement numerically, comparing the corresponding values presented in Tables 1 and 2. For 6-electrode TPIM, the improvement in %CLTI(1) was small at expiration, a mere 2%, but at inspiration, the improvement was higher at 9%. The figures for the 4-electrode TPIMs were between 5% and 7%. However, the improvement in overestimation error due to the presence of the other lung is substantial, particularly for expiration. This shows that the intuitive logic behind shifting the electrodes near the edges worked. However, further studies are required to get an optimum separation.

A point worth noting from Figure 8 is that at inspiration, the overall sensitivity in the target lung region is much less than that at expiration. This is due to higher impedivity of lungs at inspiration when the current lines divert away to outer tissues in the thorax, while at expiration, more current lines converge into the lungs increasing its contribution. An assessment of the magnitudes involved is presented by the numerical values presented in Tables 1 and 2. From Table 2, for 10 cm separation between the potential electrodes, CLTI(1) of the target lung at inspiration stood at 26.3% for 6-electrode TPIM, 21.9% for 4-electrode TPIM at front, and 29.8% for 4-electrode TPIM at back. The corresponding figures at expiration were, 36.4%, 33.4% and 42.8% respectively. The reduction of the corresponding values at inspiration with respect to that at expiration stood at 27.6%, 34.4% and 20.5% respectively. These are significant changes and it is important that one considers this effect when using electrical impedance for diagnosis of the lungs.

Another point studied was the overestimations in CLTI of a target lung due to the other lung, given by OCLTI. The idea is that when one lung is targeted through a particular electrode configuration, it is desirable that no contribution should come from the other lung that is not targeted. In any lung disorder the two lungs may have different physiological conditions when the contribution from the other lung may lead to erroneous inferences. This parameter is shown numerically in Tables 1 and 2 for 7 cm and 10 cm separation of potential electrodes respectively. For 6-electrode TPIM, this overestimation stood at 3.6% and 6.8% respectively at inspiration and expiration for 7 cm electrode separation, and the corresponding values were 3.2% and 4.6% respectively for 10 cm electrode separation. The values are similar for the other TPIM configurations. These figures are very low, indicating that there is a very low contribution from the other lung in both these configurations, which is a success of this arrangement.

Again, to assess the improvement obtained using potential electrode separation of 10 cm over that for 7 cm, Table 3 shows the ratios of the values for %CLTI(1) and %OCLTI both for inspiration and expiration. For %CLTI(1) the ratios varied between by 2% to 9%, which indicate only small improvements. However, there was a considerable reduction in %OCLTI ratio, particularly for expiration, which were between 0.68 and 0.79 for the different TPIM configurations indicating a marked improvement with 10 cm separation over 7 cm separation. At inspiration, the corresponding ratios were not that low, about 0.9 for both 6-electrode TPIM, and 4-electrode TPIM (frontal), indicating a small improvement. However, for the 4-electrode TPIM at back, the overestimation at inspiration changed signs and so the ratio was not shown. For this case, it can be seen from Tables 1 and 2 that for 7 cm separation, the other lung contributed negatively by 0.3% while for 10 cm separation there was a positive contribution of 0.2%. Both these values are very small and negligible. However, the negative value suggests the presence of a very small negative sensitivity region in the other lung.

Looking at the OCLTI values in Tables 1 and 2, 4-electrode TPIM applied at the front gives high overestimation, but that the back gives very low values, even lower than that for 6-electrode TPIM, indicating low contributions from the other lung. From this viewpoint 4-electrode TPIM applied at the back may give the best performance, however, going back to the sensitivities shown in figure 8, 4-electrode TPIM does not cover the whole depth of the lungs, which is covered by the 6-electrode TPIM configuration. Therefore, if only the back side of the lungs is of interest, 4-electrode TPIM may be chosen, but if the whole depth of the lungs is of interest, which is normally the case in any diagnosis, 6-electrode TPIM would be the better choice.

The present work establishes the recently proposed 6-electrode TPIM on a stringer footing for application in real life.