Design of a drop-in EBI sensor probe for abnormal tissue detection in minimally invasive surgery

As shown in Fig. 1, the proposed drop-in probe aims to assist the surgeon in detecting abnormal tissue areas during a laparoscopic surgery. The surgeon can grasp it with a laparoscopic forceps and slightly press on the surface of the suspicious tissue area for examination. An EBI meter is connected to the probe for providing excitation signals and measuring corresponding EBI values. The measured EBI values are then sent to the connected laptop for data processing. With the constructed training dataset, a tissue identification algorithm is developed to distinguish the normal and abnormal tissue.

Fig.1

In order to satisfy the objectives mentioned above, the following criteria are considered in the design phase as listed below:

The size of the designed probe should be smaller than 12 mm so that it can enter the abdominal cavity through a trocar;

The electrical bioimpedance of the measured value can be modelled as shown in Fig. 2(A). The overall electrical impedance value consists of the tissue impedance and the electrode polarization impedance Z_epi. The tissue impedance is commonly described using the Cole model [28]. This model imitates biological structure constructed by a resistor R_int simulating the intra-cellular component, a resistor R_ext simulating the extra-cellular component and a capacitor C_m simulating the cell membrane as shown in Fig. 2(A). In order to extrapolate the tissue's electric property, signals of multi-frequencies in the range from 1 kHz to 2 MHz, known as the β dispersion, are used for excitation. Within this range, high frequency signal is more capable to pass through the cell membrane and the measured impedance value involves more portions of the intra-cellular resistance, while low frequency current mainly passes the extra-cellular region and reflects the electrical impedance of this region.

Fig.2

In addition, the electrode polarization effect can influence the measured value significantly. The electrode polarization impedance is generated due to the double layer phenomenon in the contacting layer between the electrode and the tissue, which is known as the Gouy-Chapman effect [29]. The value of Z_epi is found to be affected by several factors such as temperature, electrode materials, electrode geometry, tissue types, environmental pH, applied pressure, excitation waveform and excitation frequencies [30]. Thus, the electrode polarization effect is commonly considered as a main reason of variate in the measured EBI value.

Cross-finger electrodes configuration is often exploited for EBI sensing [15]. In a two-electrodes configuration, the excitation current is injected through the electrode pair, and the reciprocal current is measured through the same electrodes. Although the measured signal mixes both biological impedance and the electrode impedance when bipolar electrode configuration is used, this configuration enables compact design and simple circuit connection to an LCR meter. In this study, the electrodes are designed as a plate with a popularly used pattern of bipolar electrode as shown in Fig. 3. With this electrode configuration, the injected excitation current can be distributed evenly on the target tissue area. The size of the electrode is designed to be 7×9 mm, allowing it to enter the trocar and to facilitate the measurement on a relatively big area with good contact. It is necessary to mention that the key parameters of this pattern consists of the number of the fingers, and the electrode's width w_e to the gap width w_g. According to the study of Stulik et al. [31], having more fingers on the electrodes can not only increase the signal value but also the background noise, thus leading to no changes in signal-noise ratio. Meanwhile, wider electrode fingers provide more electrode surface area, but lose some of the radial diffusion pattern. Therefore, while the overall signal increases, nonspecific surface reactions (background signals) increase with a slightly faster rate, and further decreasing the signal-noise ratio. With fully consideration of the above-mentioned analysis, the electrodes plate is made with three fingers, the electrode width w_e is set to be 24 mil and the gap width w_g is set to be 48 mil.

Fig.3

The measurement sensitivity using the designed electrode is analyzed as follows. We assume that the tissue material is homogeneous. According to previous studies [32], the impedance of tissue is calculated as an integration of the sensitivity density distribution S, the tissue's electrical conductivity σ and the tissue's relative permittivity ɛ over the measured tissue volume Ω: (1) Z=∫Ω1σ−jωεSdΩ Z = \int_{\it \Omega } {{1 \over {\sigma - j\omega \varepsilon }}Sd{\it \Omega }} where the sensitivity S for a bipolar configuration is equal to the square of the current density J:S=|J→|2 J:S = {\left| {\vec J} \right|^2} .

Furthermore, the inverse problem based on the designed electrode pattern is analyzed as follows. The inverse problem in the EBI measurement is the procedure to derive the material's impedance given the injected current value and the measured voltage. Here, we simplify the electrode pattern as a dipole model, in which the electric current flows into the tissue via the electrode pair. Assuming that the tissue does not generate induced current flow, the current density J is approximated to be proportional to the electric field strength E: (2) J→=(σ−jωε0εr)⋅E→ \vec J = \left( {\sigma - j\omega {\varepsilon _0}{\varepsilon _r}} \right) \cdot \vec E

As shown in Fig. 3(B), the electric field of a random point P in the region caused by applied excitation current, can be calculated according to Coulomb's law as (3) Ep→=∫S1dq14π(σ−jωε)r12+∫S2dq24π(σ−jωε)r22 \overrightarrow {{E_p}} = \int_{{S_1}} {{{d{q_1}} \over {4\pi \left( {\sigma - j\omega \varepsilon } \right)r_1^2}} + } \int_{{S_2}} {{{d{q_2}} \over {4\pi \left( {\sigma - j\omega \varepsilon } \right)r_2^2}}} where S₁ and S₂ are the area of two electrodes, respectively. r_i (i = 1,2) represents the distance from an element on electrode i to point P, and dq_i is the charge on this element.

Considering the complexity of the inverse problem, the Finite Element Method is utilized for the simulation based on COMSOL Multiphysics^® software. Through the simulation results of the current density distribution, the depth of the tissue to which the excitation current flows, can be estimated. The model is simplified by using direct current in the simulation. As shown in Fig. 3(C), the electrode pattern is placed on the top surface of the material, and a direct current is injected between the electrodes. The simulation results indicate that 80% of the energy is contained within the depth of 4.5 mm.

A prototype is fabricated as shown in Fig.4, which is made as a piece of PCB, which potentially can be bio-compatible [35]. Gold plated electrodes are used in order to minimize the electrode polarization effect [38]. The casing is made by 3D printing due to the low-cost consideration.

Fig.4

A small extrusion structure is added to the casing to allow the force grasping it in different angles and manipulation. The width, the length and the height of the probe are 8 mm, 11 mm, and 16 mm, respectively, allowing it to pass through the trocar used for MIS to insert surgical tools such as laparoscopy. In addition, all the corners of the probe are rounded so as not to scratch the tissue during the manipulation.

In order to judge the measurement for distinguishing between healthy tissue and pathological tissue, supervised machine learning algorithm is used. Then new sensing data can be estimated from the training dataset.

Discrimination Analysis is a supervised algorithm using information of classes to find new features in order to maximize its separability. Based on different feature assumptions, this classification method includes 2 main applied methods: Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA). LDA assumes the feature covariance matrices of both classes are the same, which results in a linear decision boundary. In contrast, QDA is less strict and allows different feature covariance matrices for different classes, which leads to a quadratic decision boundary.

Both LDA and QDA works under the assumption that the data are normally distributed. Given an input x₀, the response as in a Bayes classifier is predicted: (4) y^0=argmaxyP^(Y=y|X=x0) {\hat y_0} = {{\bf argmax}_y}\,\hat P(Y = y|X = {x_0})

For a binary group classification, a data set can be defined as (xi,yi)in \left( {{x_i},{y_i}} \right)_i^n where x_i ∈ ℝ^d is the input, y_i is the output, and n is the number of the data points. In this case, the input x_i is a vector of measurements of different excitation frequencies [R₁, C₁, R₂, C₂, ... , R_d/2, C_d/2], of which R is the resistance and C is the capacitance. The output y_i has 2 values, 0 and 1, representing normal tissue and pathological tissue respectively.

Here, we use the Bayes rule to obtain the estimate: (5) P^(Y=k|X=x)=P^(X=x|Y=k)P^(Y=k)P^(X=x) \hat P(Y = k|X = x) = {{\hat P(X = x|Y = k)\hat P(Y = k)} \over {\hat P(X = x)}}

The distribution of the EBI values in either group is considered as a Multivariate Normal Distribution: P^(X=x|Y=k)=f^k(x) \hat P(X = x|Y = k) = {\hat f_k}(x) . In this case, the density function for class k satisfies (6) fk(x)=1(2π)p/2|Σk|1/2e−12(x−μk)TΣk−1(x−μk) {f_k}(x) = {1 \over {{{(2 \pi)}^{p/2}}{{\left| {{{\it \Sigma }_k}} \right|}^{1/2}}}}{e^{ - {1 \over 2}{{(x - {\mu _k})}^T}{\it \Sigma }_k^{ - 1}(x - {\mu _k})}} where μ_k and Σ_k is the mean and the covariance matrix of the input for class k. In addition, we assume the initial degree of beliefs in either classes are equal, and thus P^(Y=0)=P^(Y=1)=Πk \hat P(Y = 0) = \hat P(Y = 1) = {{\it \Pi }_k} . Furthermore, Eq. (5) can be also written as: (7) P(Y=k|X=x)=fk(x)ΠkP(X=x)=CΠk|Σk|−1/2e−12(x−μk)TΣ−1(x−μk) P(Y = k|X = x) = {{{f_k}(x){{\it \Pi }_k}} \over {P(X = x)}} = C{{\it \Pi }_k}|{{\it \Sigma }_k}{|^{ - 1/2}}{e^{ - {1 \over 2}{{(x - {\mu _k})}^T}{{\it \Sigma }^{ - 1}}(x - {\mu _k})}} where C = ((2π)^p/2P(X = x))⁻¹ is constant and keeps the same for both classes. Furthermore, we take the logarithm of both sides and we have: (8) logP(Y=k|X=x)=logC+logΠk−12log|Σk|−12μkTΣk−1μk+xTΣk−1μk−12xTΣk−1x {\it log}P(Y = k|X = x) = {\it log}C + {\it log}{{\it \Pi }_k} - {1 \over 2}{\it log}|{{\it \Sigma }_k}| - {1 \over 2}\mu _k^T{\it \Sigma }_k^{ - 1}{\mu _k} + {x^T}{\it \Sigma }_k^{ - 1}{\mu _k} - {1 \over 2}{x^T}{\it \Sigma }_k^{ - 1}x

In QDA, since the covariance matrix for both classes are different, the classifier ℱ_QDA can be obtained as: (9) ℱQDA=logΠk−12log|Σk|−12μkTΣk−1μk+xTΣk−1μk−12xTΣk−1x {{\cal F}_{QDA}} = {\it log}{{\it \Pi }_k} - {1 \over 2}{\it log}\left| {{{\it \Sigma }_k}} \right| - {1 \over 2}\mu _k^T{\it \Sigma }_k^{ - 1}{\mu _k} + {x^T}{\it \Sigma }_k^{ - 1}{\mu _k} - {1 \over 2}{x^T}{\it \Sigma }_k^{ - 1}x

While the covariance matrices of both classes are the same for LDA, namely Σ₁ = Σ₂, the classifier ℱ_LDA can be simplified as: (10) ℱLDA=logΠk−12μkTΣk−1μk+xTΣk−1μk {{\cal F}_{LDA}} = {\it log}{{\it \Pi }_k} - {1 \over 2}\mu _k^T{\it \Sigma }_k^{ - 1}{\mu _k} + {x^T}{\it \Sigma }_k^{ - 1}{\mu _k}

The experimental setup is shown in Fig. 5; the setup consists of the designed EBI probe, an LRC meter (Keysight E4980A, Keysight Technologies Inc., U.S.), material for test, and a laptop for data collection and processing.

Fig.5

For the safety consideration, the electric level of the LCR meter is set to be 10 mV. In the following study, the maximum current at this voltage in all the frequencies is found not to be more than 0.1 mA, which does not cause any tissue damage according to international standards IEC6060-1. In addition, 200 different frequencies from 1 kHz to 2 MHz were applied for each measurement. The frequencies within this range are corresponding to the β-dispersion of biological tissues [40], which can provide rich information about the tissues’ dielectric properties.

Two experiments were performed in this study, to characterize and evaluate the designed sensor probe.

The first experiment was designed to characterize the electrode sensing capability with saline solutions of different concentrations. Five saline solutions in different concentrations, namely 0.1%, 0.2%, 0.3%, 0.4%, and 0.5% were made and used for the first experiment. During the experiment, the electrode was immersed into the solutions. After waiting for about 5 s, we measured the impedance values 10 times for each saline solution. Then, the collected data were analyzed and compared with the theoretical electrical properties of the saline solutions.

In order to evaluate the overall performance of the designed probe for distinguishing the normal and abnormal states of the same tissue type, the second experiment was designed and conducted with real phantoms based on fresh porcine liver, given that the porcine liver has similar electrical properties as human [12]. Liver tissue is coated with a 40 to 70 μm thick serosal layer [41] which is within the 20% sensitivity range according to Fig. 3. Also, blood or body fluid may contaminate the tissue surface in practice. This effect can be minimized by slightly pressing the probe on the tissue. These factors can be the source of measurement variation and methods to minimize their impact will be a focus in our future study.

To avoid that the EBI data collected on individual liver samples, be affected during each experiment, stabs of cold stored porcine liver was cut into 18 pieces of block with the dimension of 30×30×20 mm. 9 pieces of liver samples remained fresh and the other 9 pieces were soaked in pure water for 5 min to modify the cell architecture of the liver tissue. Normally, the healthy status of tissue can be reflected by its extracellular component and intracellular component. By soaking the liver sample into water, water could be injected into the tissue due to passive transport phenomena [33] and thus change these parameters.

During the second experiment, we first cleaned the liver surface to ensure its dryness. Then the probe was placed on the surface of a liver sample and we slight pressed the probe. According to study [39], the applied force between the probe and the tissue can cause change of electrical property of the tissue. Thus, the experimenter controlled the pressing force based on visual inspection to ensure that the electrodes was contacting the tissue sample well but not causing too much deformation of the tissue. Then the EBI values were measured by the LCR meter. For each sample, the measurements were repeated 10 times, and the data were collected to the laptop for processing. As mentioned in Section Algorithms for tissue classification, this study tested and compared the two constructed classifiers, ℱ_LDA and ℱ_QDA modelling the probability of a class y given sample x_i. The collected input-output pairs {x_t, y_t} were accumulated as one training dataset 𝒫tA {\cal P}_t^A for establishing the classifiers and the other one as testing dataset 𝒫tB {\cal P}_t^B for evaluating the performance of the classifiers. Here, 25% cross validation was used for verification. The experimental results were compared and presented in Section Ex vivo tissue results.

The conducted research is not related to either human or animal use.

Fig. 6 shows the measurement results of different saline solutions using the designed probe. Each curve represents the mean values measured in one saline solution. The x axis is the excitation frequency in logarithmic scale and the y axis represent the corresponding capacitance values and resistance values, respectively.

Fig.6

The experimental results show that the capacitance values for different saline solutions have little variance (relative standard deviation <4.4%), and this value decreases from 638 nF to 4.4 nF when the excitation frequency increased from 1 kHz to 2 MHz. In contrast, the resistance values were less dependent to the applied frequency. In the low frequency range from 1 kHz to 10 kHz, the resistance values showed a relatively bigger change due to the electrode polarization effect. When higher excitation frequencies (10 kHz to 2 MHz) were applied, the polarization impedance Z_epi became small and contributed less to the resistance value.

The capacitance and resistance values of ex vivo tissues measured by the designed probe at different excitation frequencies are shown in Fig. 7. Here, we use ‘Normal tissue’ to denote fresh liver samples, and ‘Abnormal tissue’ to denote water soaked tissues. The results of normal tissue samples are plotted in blue lines with a semi-transparent shading representing the standard deviation, while the results of abnormal tissue samples are shown in red.

Fig.7

Then the data analysis was proceeded. First, the Kolmogorov-Smirnov method [34] was used to test whether the collected results are normally distributed. The test results indicate that the p-values of both classes were >0.05. Therefore, the null hypothesis can be rejected for both classes, and the discriminant analysis method is legit for the data classification. In total, 160 data were collected, and 1 data was rejected due to unexpected big noise. Among the collected data samples, 119 data were randomly selected as a training dataset, and 40 data were used as a testing dataset. After the training procedure, the LDA classifier was found to achieve around 100% accuracy and the QDA classifier achieved a 79% accuracy with the training dataset.

Subsequently, the testing dataset were used for evaluating both classifiers. The classification accuracy was 100% for the LDA classifier, and 80% for the QDA classifier. Therefore, a further investigation of the QDA method was carried out and the confusion matrix of the QDA classification results is shown in Tab. 1. According to the classification results, 8 false positive cases were found in the test dataset.