A deep neural network for a hemiarray EIT system

Mason Manning; Nicholas Wharff; Shelby Horth; Jacob Roarty; Rosalind J. Sadleir; Malena I. Español

doi:10.3934/ammc.2023004

Article Contents

2023, Volume 1, Issue 1: 39-60. Doi: 10.3934/ammc.2023004

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A deep neural network for a hemiarray EIT system

1.
School of Human Evolution and Social Change, Arizona State University, Tempe, AZ, United States
2.
Department of Mathematics and Computer Science, Drake University, Des Moines, IA, United States
3.
Department of Applied Mathematics and Computer Science, Wake Forest University, Winston-Salem, NC, United States
4.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, United States
5.
School of Biological and Health System Engineering, Arizona State University, Tempe, AZ, United States

^*Corresponding author: Malena I. Español
^*Corresponding author: Malena I. Español

Received: May 2023

Revised: August 2023

Early access: September 2023

Published: September 2023

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Abstract

Electrical Impedance Tomography (EIT) can map electrical property distributions within the body using a surface electrode array. EIT systems using a circumferential array applied to the abdomen can be used to monitor acute intra-abdominal hemorrhages in trauma patients. Nevertheless, these patients may also have suffered spinal injuries that might be exacerbated by lifting the patient to place the array. Thus, a half array ('hemiarray') applied only to the anterior abdomen may be more practical. However, severe reconstruction artifacts result in posterior regions using standard EIT reconstruction methods. This study proposes a novel machine learning-based approach for standard full and hemiarray EIT reconstructions, demonstrating superior reconstruction characteristics compared to conventional methods. Notably, our method mitigates the challenges of reconstructing anomalies in posterior regions. This performance advantage was consistently observed across reconstructions from simulated and real tank data. Based on our findings, we conclude that the machine learning-based hemiarray reconstruction method holds significant promise for challenging imaging scenarios, particularly when access to the anterior or posterior abdomen is restricted.

Keywords:

Mathematics Subject Classification: Primary: 92C55, 68T07, 65N21; Secondary: 65R32.

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Figure 1. The electrode layout for the fullarray and hemiarray configurations and the EIDORS "c2C" mesh with 576 triangular elements used for the training. Notice that in this particular hemiarray arrangement, the electrodes cover less than half of the circumference

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Figure 2. (a) Voltage gathering process of the fullarray EIT system by injecting adjacent electrodes with current, producing 208 boundary voltage measurements. (b) FA-DNN architecture that uses boundary voltage measurements to reconstruct a discretized internal conductivity distribution

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Figure 3. (a) Voltage gathering process of the hemiarray EIT system. The boundary voltage measurements are collected using the adjacent current injection pattern; in the hemiarray, electrodes 1 and 8 are adjacent, producing 40 boundary voltage measurements. (b) The HA-DNN architecture, except for its input layer, shared the same architecture as the FA-DNN. The hemiarray input layer was not a perfect subset of the fullarray, as it contained the connection between electrodes 1 and 8 that was not present in the fullarray. The diagram highlights some of the unique connections of the hemiarray in green

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Figure 4. Results of full- and hemiarray reconstructions of simulated data. The first column shows the true internal conductivity. The second, third, and fourth columns show the reconstructions produced by Tikhonov (TK), TSVD, and the FA-DNN, respectively, using the fullarray configuration. Further, the fifth, sixth, and seventh columns show reconstructions produced by TK, TSVD, and the HA-DNN, respectively, using the hemiarray configuration

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Figure 5. Average values of each figure of merit for reconstructing small conductive anomalies. Bold lines indicate the mean value of each figure of merit for all radial positions at a given angle. Shaded regions show two standard errors (one-fifth standard deviation) above and below the mean value, indicating the models' robustness to changes in anomaly radial positions. QI subplots have a black dashed line representing the normalized true QI at each angle. QI values are averages over the entire mesh in units of S/m

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Figure 6. HA-DNN reconstructions of internal conductivity based on actual voltage measurements from a hemiarray EIT system, with the true placement of cylindrical anomalies superimposed. The graphic also includes a picture of the "phantom tank, " i.e., the EIT device utilized to collect the data, and a depiction of anomaly placement within the elliptical domain (major/minor axis ratio of 30 cm/26 cm). The top two rows depict metal anomalies, and the lower two rows depict plastic anomalies

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Figure 7. GREIT figure of merit metrics for DNN reconstructions from real tank data on a disk. The left figure corresponds to metal anomaly measures, and the right-hand side shows plastic anomaly values. QI values are averages over entire mesh in S/m

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Figure 8. Results of full- and hemiarray reconstructions of simulated data using an elliptical domain. The first column shows the true internal conductivity. The second, third, and fourth columns show the reconstructions produced by Tikhonov (TK), TSVD, and the FA-DNN, respectively, using the fullarray configuration. Further, the fifth, sixth, and seventh columns show reconstructions produced by TK, TSVD, and the HA-DNN, respectively, using the hemiarray configuration

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Figure 9. Hemiarray reconstructions of internal conductivity based on phantom data, with the true placement of cylindrical anomalies superimposed. The graphic also includes a picture of the "phantom tank, " i.e., the EIT device utilized to collect the data, and a depiction of anomaly placement within the elliptical boundary (major/minor axis ratio of 30 cm/26 cm). The top two rows of the figure depict metal anomalies, while the bottom two rows depict plastic anomalies

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Figure 10. QI expressed as average conductivity over mesh for reconstructions on an elliptical domain for each anomaly type

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