# Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface

^{*}

## Abstract

**:**

## 1. Introduction

## 2. EIT Principle

## 3. Thoracic Structures

## 4. Simulation Interface

#### 4.1. F.E.M. to RLC Equivalent Circuit Transformation

#### 4.2. EIT SPICE Circuitry

#### 4.3. Sampling and Digital Signal Processing

## 5. Reconstruction and Evaluation Method

#### 5.1. Image Reconstruction

#### 5.2. Image Evaluation Method

## 6. Results and Discussion

#### 6.1. Simulation Cases

#### 6.2. Simulation Results

#### 6.3. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Basic EIT hardware concept. The SUT, current injecting front-end (FE), voltage recording FE, and the finite state machine (FSM) are included.

**Figure 2.**(

**a**) Cross-section of the F.E. thoracic model boundaries and tissues simulated for the deflated and inflated states. (The deflated state is based on an adult male CT image.) (

**b**) Fine thoracic F.E. model for the deflated case (the lungs are not visible since their conductivity is similar to the background’s one). (

**c**) Fine thoracic F.E. model for the inflated case. The lungs’ conductivity is significantly lower than the background’s one. In both (

**b**,

**c**) cases, the skin has been included.

**Figure 3.**

**Left**: Relative conductivity per thoracic tissue in the frequency range between 1 kHz and 1 MHz.

**Right**: Relative permittivity per thoracic tissue in the frequency range between 1 kHz and 1 MHz.

**Figure 4.**LT SPICE analogue circuitry configurations for (

**a**) passive electrodes (cables and switches between the readout front-end circuit and the electrode) and (

**b**) partially active electrodes (the first stage of the readout circuit is implemented directly on each particular electrode). Blue-coloured components indicate the parasitic capacitors and channel resistors added to simulate their effect.

**Figure 6.**(

**a**) 2D reconstruction thoracic domain (Ω). (

**b**) Shape mismatch between the “true” cross-section model and Ω.

**Figure 7.**(

**a**) Visualization of the process to obtain the Ω domain reference image. (

**b**) The Ω domain reference image (15 kHz case).

**Figure 8.**Transient plus noise simulations and ADC sampling process for some particular voltage channel measurements, when at deflated state, acting at 15 kHz, 2mA

_{p−p}current signal, and considering 0.05 radius passive electrodes without position deviation. Sampling and quantization is performed for 2 sine periods, as shown in each right part. Current is injected from the 1st and the 2nd electrodes (adjacent current protocol). The ADC resolution is considered at 12-bit (10-bit ENOB) with a 3.3 V reference voltage. (

**a**) Adjacent voltage measuring between the 3rd and the 4th electrodes. (

**b**) Adjacent voltage measuring between the 4th and the 5th electrodes. (

**c**) Adjacent voltage measuring between the 5th and the 6th electrodes. (

**d**) Adjacent voltage measuring between the 6th and the 7th electrodes. As the voltage measuring electrode pair becomes far from the current injecting pair, the noise effect becomes more significant, due to the signal’s amplitude decrease.

**Figure 9.**Simulation results for 15 kHz input signal and passive electrode configuration. All further hardware configurations, as well as the corresponding $CC$s and $RRE$s, are noted in the figure.

**Figure 10.**Simulation results for 100 kHz input signal and passive electrode configuration. All further hardware configurations, as well as the corresponding $CC$s and $RRE$s, are noted in the Figure.

**Figure 11.**Simulation results for 100 kHz input signal and active electrode configuration. All further hardware configurations, as well as the corresponding $CC$s and $RRE$s, are noted in the Figure.

**Table 1.**Assigned conductivity and permittivity values to the thoracic models’ tissues for $f=15$ kHz and $f=100$ kHz. The admittance is estimated as $\gamma =\sigma +j\omega \u03f5{\u03f5}_{o}$. For the skin and fat case, the average values of wet skin and breast fat admittances (see Figure 3) were used.

Tissue | $\mathit{\sigma}$ at 15 kHz (S/m) | $\mathit{\omega}\mathit{\u03f5}{\mathit{\u03f5}}_{\mathit{o}}$ at 15 kHz (F·Hz/m) | $\mathit{\sigma}$ at 100 kHz (S/m) | $\mathit{\omega}\mathit{\u03f5}{\mathit{\u03f5}}_{\mathit{o}}$ at 100 kHz (F·Hz/m) |
---|---|---|---|---|

Heart | $0.164\pm 0.003$ | $0.041\pm 0.001$ | $0.215\pm 0.004$ | $0.0548\pm 0.001$ |

Inflated Lung | $0.095\pm 0.003$ | $0.010\pm 0.000$ | $0.107\pm 0.002$ | $0.014\pm 0.000$ |

Deflated Lung | $0.247\pm 0.007$ | $0.020\pm 0.001$ | $0.272\pm 0.003$ | $0.029\pm 0.001$ |

Bones | $0.021\pm 0.000$ | $0.000\pm 0.000$ | $0.021\pm 0.000$ | $0.001\pm 0.000$ |

Skin and Fat | $0.015\pm 0.000$ | $0.012\pm 0.000$ | $0.045\pm 0.000$ | $0.043\pm 0.000$ |

Muscle and Plasma | $0.350\pm 0.007$ | $0.017\pm 0.001$ | $0.380\pm 0.008$ | $0.024\pm 0.001$ |

Model | No of Elements (${\mathit{L}}_{\mathit{e}}$) | No of Nodes (${\mathit{n}}_{\mathit{e}}$) |
---|---|---|

Inflated, Uniform Electrodes, ${R}_{el}=0.05$ | 145,900 | 29,507 |

Inflated, Uniform Electrodes, ${R}_{el}=0.03$ | 133,756 | 26,861 |

Inflated, Non-Uniform Electrodes, ${R}_{el}=0.05$ | 146,000 | 29,542 |

Inflated, Non-Uniform Electrodes, ${R}_{el}=0.03$ | 135,330 | 27,120 |

Deflated, Uniform Electrodes, ${R}_{el}=0.05$ | 134,200 | 27,460 |

Deflated, Uniform Electrodes, ${R}_{el}=0.03$ | 133,756 | 24,849 |

Deflated, Non-Uniform Electrodes, ${R}_{el}=0.05$ | 133,529 | 27,328 |

Deflated, Non-Uniform Electrodes, ${R}_{el}=0.03$ | 119,654 | 23,965 |

**Table 3.**Calculated mean SNR values (dB) for each measuring parameter case, according to (19).

f (kHz) | ${\mathit{L}}_{\mathit{ADC}}$ (bits) | ${\mathit{f}}_{\mathit{s}}$ | ${\mathit{N}}_{\mathit{T}}$ | $\mathit{SNR}$ (dB) |
---|---|---|---|---|

15 | 12 | $4f$ | 2 | $27.5$ |

15 | 12 | $4f$ | 4 | $30.5$ |

15 | 12 | $16f$ | 2 | $33.5$ |

15 | 12 | $16f$ | 4 | $36.5$ |

15 | 16 | $4f$ | 2 | $27.5$ |

15 | 16 | $4f$ | 4 | $30.5$ |

15 | 16 | $16f$ | 2 | $33.5$ |

15 | 16 | $16f$ | 4 | $36.6$ |

100 | 12 | $4f$ | 2 | $20.8$ |

100 | 12 | $4f$ | 4 | $23.8$ |

100 | 12 | $16f$ | 2 | $26.8$ |

100 | 12 | $16f$ | 4 | $29.8$ |

100 | 16 | $4f$ | 2 | $20.8$ |

100 | 16 | $4f$ | 4 | $23.8$ |

100 | 16 | $16f$ | 2 | $26.8$ |

100 | 16 | $16f$ | 4 | $29.9$ |

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**MDPI and ACS Style**

Dimas, C.; Alimisis, V.; Georgakopoulos, I.; Voudoukis, N.; Uzunoglu, N.; Sotiriadis, P.P.
Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface. *Technologies* **2021**, *9*, 58.
https://doi.org/10.3390/technologies9030058

**AMA Style**

Dimas C, Alimisis V, Georgakopoulos I, Voudoukis N, Uzunoglu N, Sotiriadis PP.
Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface. *Technologies*. 2021; 9(3):58.
https://doi.org/10.3390/technologies9030058

**Chicago/Turabian Style**

Dimas, Christos, Vassilis Alimisis, Ioannis Georgakopoulos, Nikolaos Voudoukis, Nikolaos Uzunoglu, and Paul P. Sotiriadis.
2021. "Evaluation of Thoracic Equivalent Multiport Circuits Using an Electrical Impedance Tomography Hardware Simulation Interface" *Technologies* 9, no. 3: 58.
https://doi.org/10.3390/technologies9030058