Design Automation of a Dynamic Thorax-Like Mesh Phantom for Evaluating the Performance of Electrical Impedance Tomography System

Phantoms are used to evaluate, calibrate, and compare the performance of electrical impedance tomography (EIT) systems. This paper presents a dynamic thorax-like mesh phantom, which mimics the changes in electrical conductivity distribution within a human thorax at different time frames. Furthermore, element merging and contour smoothing, electrode placement techniques, and PCB design automation methods are proposed to simplify, optimize the mesh phantom, and reduce the hardware implementation cost. To verify the accuracy of the mesh phantom and its PCB, SPICE simulations and experimental testings are performed to obtain the conductance of the mesh phantom and reconstruct the images through the EIDORS software. These images achieve an image correlation coefficient (ICC) of 0.680 (model versus SPICE simulation) and 0.9098 (SPICE simulation versus measurement result), respectively. This demonstrates the validity of our proposed dynamic thorax-like mesh phantom.

(ii) Mesh phantom consists of a network of resistors soldered onto the printed circuit board (PCB), where the topology of interconnection creates the corresponding shape, size, and conductivity distribution [29], [30], [36], [37]. Thus, the mesh phantom allows a more predictable, stable, and reproducible method to evaluate the performance of EIT systems. To date, there are six different designs of mesh phantoms: the Cardiff phantom [30], the wheel phantom [31], the first Göttingen phantom [33], the second Göttingen phantom [34], the FEM phantom [35], and the thorax-like mesh phantom [38]. Unlike our prior work [38], the conductivity distributions of these mesh phantoms [30], [31], [33], [34], [35] are either in a circular or octagon shape, which does not mimic the real human thorax. Furthermore, none of these works are able to mimic the dynamic changes within the human thorax [39], [40]. Thus, this motivates us to further explore the opportunity to develop a realistic dynamic mesh phantom, where the distribution of human-like conductivity changes in different states.
The contributions of our work are summarized ( Figure 2) as follows: 1) Optimizations of Mesh Phantom: For the ease of soldering and cost of hardware implementation, it is important to optimize the number of resistors on a given size of PCB board without compromising the image's quality. Therefore, we propose elements merging and contour smoothing techniques to reduce the number of resistors. As a result, the number of resistors and resistor density has reduced from 4,616 to 313 and from 33 to 3 per cm 2 . We also optimize the electrode placement to improve the reconstructed image quality.  achieves an image correlation coefficient (ICC) of 0.9098 compared to the SPICE simulation result. The rest of this paper is organized as follows. Section II provides a background understanding of developing a mesh phantom and using SPICE simulation and EIDORS program to reconstruct the image. Section III provides the details of our proposed dynamic thorax-like mesh phantom design method with PCB automation. Section IV presents the experimental results and discusses the effectiveness of each proposed technique. Finally, the conclusion is drawn in Section V.

A. MESH PHANTOM
A basic mesh phantom is created by translating the finite element method (FEM) modeling into a solvable matrix, which represents the electrical connectivity of the mesh [35]. The FEM modeling computes and decomposes any arbitrary shape (Figure 3(b)) into triangle elements (Figure 3(a)). The coordinates of a triangular element (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), the admittance between each node are derived as follows [35]: and σ e is the conductivity inside the triangle elements.

B. SIMULATION VERIFICATION OF MESH PHANTOM
To ensure the proper functionality and accuracy of the mesh phantom before fabricating the design onto the printed circuit board (PCB), its circuit netlist is verified through a Simulation Program with Integrated Circuit Emphasis (SPICE) circuit simulator. A differential current is injected through a pair of terminals and measures the potential differences across the remaining pairs of terminals. These actions are repeated for all N terminals through successive rotations to obtain an N×N-3 matrix for creating one frame of the image. As compared to other reconstruction algorithms [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], we have chosen the Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS) [41] software as it can be directly used to reconstruct the images of a thorax-like mesh phantom based on the potential difference matrix. As shown in Figure 3, the reconstructed image is composed of multiple triangle elements. The conductivity within a triangle element remains the same, and different colors represent different conductivity. The blue area indicates the conductivity value of the region is smaller than the average. The verification method allows us to optimize the number of resistors, interconnect topology, and electrode placement, which will be discussed in Section III.

C. EVALUATION OF IMAGE QUALITY
To evaluate the quality of reconstructed EIT images, we have adopted the image correlation coefficient (ICC) analysis method to understand the similarity between two images [52], [53], [54]. The formula of ICC is as follows: are the expected and the real outputs of the conductivity value, respectively. A larger ICC value indicates better imaging quality and modeling accuracy of the mesh phantom.

III. PROPOSED DYNAMIC MESH PHANTOM METHOD
In this work, the design methodology of the basic mesh phantom has been further extended to a thorax-like mesh phantom. Our work is based on the human model provided by Netgen's shape library [55]. The contours of a human's thorax and lungs are extracted from computed tomography (CT) of the healthy human being. However, this library does not clearly present the contours of a heart, so we have simply used a round shape as a substitute for FEM modeling. The conductance value of the lungs and heart is defined as 0.392 and 0.637, respectively [56]. For the conductance value for the remaining parts of the human model, we took an average value of different types of tissues and defined it as 0.5. To mimic the changes in electrical conductivity distribution within a human thorax, we propose a dynamic thorax-like mesh phantom with the optimization of resistor number and electrode placement to further reduce the complexity of PCB fabrication, and an automated PCB design flow to implement this phantom. Figure 3(b), the original thorax-like mesh provided by the Netgen shape library has a total of 4,626 edges in the FEM model. Each edge represents a resistor component. To fabricate the mesh design onto an A4 paper size PCB board (21cm×29.7cm), similar to the size of our body thorax, it is important to optimize the number of resistors on a given size of PCB board without compromising the image's quality. This will also simplify the soldering problem and reduce the cost of hardware implementation. For the convenience of soldering and to make use of surface mount technology (SMT), we have restricted the number of resistors per cm 2 to no more than 3. Therefore, we propose a method to reduce the number of resistors, which consists of two steps: (i) elements merging and (ii) contour smoothing.

Method 1 -Resistors Reduction Technique: As shown in
(i) Elements Merging Technique: refers to the merging of triangle elements into larger triangle elements by averaging the adjacent nodes into one node. The detail of elements merging is presented in Algorithm . The algorithm traverses all nodes on the contour (Line 5). If there are any M adjacent nodes where the angle between the M points is greater than D, these nodes are merged into one node (Line 6-9). For the nodes that are not on the contour, the algorithm merges 1: Set N m as the collection of output FEM's nodes; 2: Set C t , C l , C h as the collection of points on the contour of the chest, lungs and heart, respectively; 3: Set E as the collection of elements; 4: Set ∠N is the angle between n i n i−1 and n i n i+1 ; 5: for each node ∈ C t , C l , C h do 6: if ∠N > 170 then 7: Add n i = (n i + n i−1 + n i+1 )/3 to N m 8: delete n i+1 from C t , C l , C h 9: end if 10: Add n i to N m 11: end for 12: for i = 1 to 3 do 13: Initialize a set T; 14: for each element in E do 15: Set n 1 , n 2 , n 3 as the three vertices of the element 16: Add (n 1 + n 2 + n 3 )/3 to T 17: end for 18: E ← T s corresponding set of elements 19: end for 20: Add E s nodes to N m ; each triangle element's M nodes into one node (Line 14-17) and iterates T times (Line 12). Based on our preliminary experiments to achieve a good trade-off between the quality of reconstructed image quality and the number of resistor components, M and T have been determined to be 3 and degree to be 170 • . Figure 3(c) presents the reduced version of thorax-like mesh phantom using the "elements merging" technique.
(ii) Contour Smoothing Technique: removes the sharp contour of the lungs' shape by reducing the number of clustered nodes within a defined distance. As shown in Figure 3(c), the sharp contours with corners that are less than 90 • are circled in red. As shown in Figure 3(d), the number of resistors near these corners has been reduced using the element merging technique to fit the resistors in the PCB.

Method 2 -Electrodes Optimization Technique:
The number of electrodes and their placement affects the quality of the reconstructed EIT image [57], [58], [59], [60]. Due to the irregular shape of the human's thorax, it is impossible to evenly place all electrodes on the mesh phantom, unlike the circular phantom. Thus, we explore different types of electrode placement based on symmetry (mound or flat or asymmetrical), skew (right or left), spread (narrow spread or wide spread), and the number of peaks (unimodal, bimodal, or multiple peaks) and compare the quality of the reconstructed image, hoping to identify an optimal electrode placement without compromising the image quality. The result of different placements is discussed in Section IV-B.

B. DYNAMIC THORAX-LIKE MESH PHANTOM USING DCS TECHNIQUES
To create a perturbation in the resistive network (mesh phantom) (Figure 4(a)) without causing errors in the image reconstruction at different time frames [58], [59], we have to identify the number of resistors at the correct locations for discretization (Figure 4(b)), which replaces the resistor with the equivalent resistance of two resistors connected in series (RX = R1 + R2) ( Figure 5(a)). In particular, the discretization ratio (DR) refers to the ratio between the discretized resistor and the original one as follows: It is important to identify this ratio to ensure good image quality, which will be discussed in Section IV. This technique is termed Discretization Component Selection (DCS-I). As illustrated in Figure 4(c), controllable voltage-control relays (switches) are used to short one of the two resistors to create a change in the resistance path. These switches are turned either "ON" or "OFF" using a microcontroller at different time frames to create gradual changes in the resistive network (Figure 4(d)). These resistors and switches are soldered onto a separate PCB plug board ( Figure 5(b)), which can be connected to the original location. This technique is termed Dynamic Component Switching (DCS-II).

C. DESIGN AUTOMATION OF THE MESH PHANTOM ON PRINTED CIRCUIT BOARD (PCB)
The implementation of the mesh phantoms [16], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38] requires a meticulous handcrafting design of the PCB layout. Thus, we propose the following PCB design automation for the mesh phantom: (i) contour construction of the mesh phantom, (ii) placement and routing of resistors, and (iii) implementation of dynamic mesh phantom. We use the MATLAB programming language to create the entire design automation flow and generate the PCB file according to the Protel PCB 2.8 ASCII format.

Contour Construction of the Mesh Phantom:
A coordinate transformation is applied to each node of the mesh phantom to allow its contour to be uniformly distributed over the PCB board (Figure 6(a)). Solder pads are automatically added to each node in the resistive network for the ease of measuring the resistance during the testing phase (Figure 6(c)).  Snap buttons are automatically placed onto the PCB based on the electrode optimization technique. Resistor-capacitor (RC) circuit networks are added between the mesh phantom and the electrodes to mimic the impedance behavior of Ag/AgCl electrodes [35] (Figure 6(b)).
Placement and Routing of Resistance Components: Resistors are placed in between the nodes with wires connecting to them and the values of these resistors are rounded off to the nearest available resistance values (Figure 7(a)).
Implementation of Dynamic Mesh Phantom: Based on the DCS techniques, the selective resistors are replaced with 100-mil PCB connector headers so that the plug boards can be inserted to mimic the gradual changes in the mesh phantom (Figure 7(b)).
PCB components: Beside generating the PCB file for fabrication on FR4 substrate, we have used the following discrete components for the PCB fabrication of the proposed mesh phantom as presented in Table 1.

IV. RESULTS AND DISCUSSION
As discussed in Section II-C, the image correlation coefficients (ICC) are used to evaluate the imaging quality of mesh phantoms for each optimization step.

A. EVALUATION OF THE RESISTOR REDUCTION OPTIMIZATION TECHNIQUE
The original thorax-like mesh phantom based on the Netgen shape library [41] has a total number of 4,626 edges (resistors). As shown in Figure 2(a), the maximum resistor density (number of resistors on the PCB board per cm 2 ) has reached up to 33 components per cm 2 , which is not practical to fabricate the PCB due to the physical size of the surface mounted technology (SMT) resistors. Note that the size of common surface mount technology (SMT) 0603, 0805 and 1206 resistors are 1.6mm×0.8mm, 2mm×1.25mm, and 3.2mm×1.6mm, respectively. SMTs with a footprint smaller than 0603 may not be suited since they have a smaller voltage break tolerance and a larger resistance tolerance of up to 10%.
As presented in Table 2, the use of merging and smoothing optimization techniques without compromising the ICC has reduced the number of resistors by 699 (6.91× reduction) and 313 (14.78× reduction), respectively. Similarly, the maximum resistor densities have reduced down to 11 and 3 components per cm 2 , respectively. The final area of the thorax-like mesh is 483.7cm 2 , which fits well onto the A4 size PCB with a dimension of 21cm×29.7cm.

B. EVALUATION OF ELECTRODE PLACEMENT
To determine the optimal placement of electrodes through SPICE simulation and evaluate the image quality with ICC, we have explored different types of electrode's placement based on symmetry (mound or flat) or asymmetrical, skew (up or bottom or right or left), spread (narrow spread or wide spread), and number of peak (unimodal, bimodal or multiple peaks). Thus, we have concluded to use 4 general electrode placement methods to understand the optimal placement of electrodes. We did not explore number of peaks as it is not easy to use in practical situation in EIT system. Figure 8 shows the four types of electrodes' placement and their corresponding reconstructed images: (i) mesh-A uses asymmetrical and skew left electrodes' placement strategy, (ii) mesh-B and mesh-C use asymmetrical and skew bottom and up electrodes' placement strategy, and (iv) mesh-D uses evenly spread placement strategy. The reconstructed images are divided into four regions to obtain the mean and variance of the ICC, and the results are presented in Table 3. It is observed that the density of electrodes affects the corresponding regional ICC. To obtain satisfying EIT imaging quality, the variation of ICC among the regions needs to be minimized and it must be at least 0.5 [52]. Thus, mesh-D is chosen as it achieves the highest ICC with acceptable regional variation (Figure 8(d)).

Selection of Discretization Ratio (DR):
To create a perturbation in the resistive network within the mesh phantom (Figure 4(a)) without causing errors in the image reconstruction at different time frames [58], [59], we need to identify the suitable discretization ratio (DR) for the DCS  techniques. The SPICE simulations are used to verify 100 different mesh phantom and identify the suitable DR value. As shown in Figure 10, when the DR decreases, the perturbation becomes more apparent in the reconstructed image along with the increase in ICC. The EIT image with a DR of 0.1 achieves the best ICC of 0.631, where the ICC value for the original mesh is 0.691.
Selection of Discretization Location: Upon determining the DR of 0.1, we applied DCS techniques to different parts of the lung region. Figure 11 illustrates 3 distinct discretization locations in the top, middle, and bottom of the right lung, respectively. The ICC of these reconstructed images is 0.642, 0.631, and 0.680, respectively. Clearly, our DCS technique is applicable to different parts of the lung area without compromising the image's quality. We have selected the 'middle' discretization location to clearly observe the perturbation of the dynamic mesh phantom. Figure 9 illustrates the fabricated PCB board using FR4 material and the outline of the board resembles the human thorax-like shape, which is 255.4×196.6 mm 2 . Resistors with 1% tolerance and a temperature coefficient of ±200ppm/ • C are assembled onto the PCB. Each plug board is fabricated on a 28.4×10.5 mm 2 rectangular board. To validate the accuracy of the fabricated PCB, we have tested it with our 16-electrode EIT system [11] and reconstructed the image using the measured result, and compared it with the SPICE simulation. Figure 12 presents the reconstructed image with an ICC of 0.9098.

V. CONCLUSION
A dynamic thorax-like mesh phantom is designed and fabricated on an A4 PCB board to evaluate the performance of EIT systems. This phantom mimics the changes in electrical conductivity distribution within a human thorax at 4 different time frames while achieving an average ICC of 0.651. Several optimization techniques have reduced the number of resistors and resistor density from 4,616 to 313 and from 33 to 3 per cm 2 . To verify the accuracy of the mesh phantom, SPICE simulation and experimental testing are performed on the fabricated PCB to obtain the conductance of the mesh phantom and reconstruct the images through