A pressure distribution imaging technique with a conductive membrane using electrical impedance tomography

Habib Ammari, Kyungkeun Kang, Kyounghun Lee, Jin Keun Seo

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper presents a mathematical framework for a flexible pressure sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface deformation results in a change in the conductivity distribution. This change can be detected in the current-voltage data (i.e., EIT data) measured on the boundary of the membrane patch. Hence, the corresponding inverse problem is to reconstruct the pressure distribution from the data. Assuming that the material's conductivity distribution is constant, we derive a two-dimensional (2D) apparent conductivity (in terms of EIT data) corresponding to the surface deformation. Since the 2D apparent conductivity is found to be anisotropic, we consider a constrained inverse problem by restricting the coefficient tensor to the range of the map from pressure to the 2D apparent conductivity. This paper provides theoretical grounds for mathematically modeling the inverse problem. We develop a reconstruction algorithm based on a careful sensitivity analysis. We demonstrate the performance of the reconstruction algorithm through numerical simulations to validate its feasibility for future experimental studies.

Original language English 1493-1512 20 SIAM Journal on Applied Mathematics 75 4 https://doi.org/10.1137/140984671 Published - 2015 Jan 1

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Electrical Impedance Tomography
Acoustic impedance
Pressure Distribution
Inverse problems
Pressure distribution
Conductivity
Tomography
Membrane
Imaging
Membranes
Imaging techniques
Inverse Problem
Reconstruction Algorithm
Pressure sensors
Patch
Sensitivity analysis
Tensors
Pressure Sensor
Computer simulation
Electric potential

All Science Journal Classification (ASJC) codes

• Applied Mathematics

Cite this

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title = "A pressure distribution imaging technique with a conductive membrane using electrical impedance tomography",
abstract = "This paper presents a mathematical framework for a flexible pressure sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface deformation results in a change in the conductivity distribution. This change can be detected in the current-voltage data (i.e., EIT data) measured on the boundary of the membrane patch. Hence, the corresponding inverse problem is to reconstruct the pressure distribution from the data. Assuming that the material's conductivity distribution is constant, we derive a two-dimensional (2D) apparent conductivity (in terms of EIT data) corresponding to the surface deformation. Since the 2D apparent conductivity is found to be anisotropic, we consider a constrained inverse problem by restricting the coefficient tensor to the range of the map from pressure to the 2D apparent conductivity. This paper provides theoretical grounds for mathematically modeling the inverse problem. We develop a reconstruction algorithm based on a careful sensitivity analysis. We demonstrate the performance of the reconstruction algorithm through numerical simulations to validate its feasibility for future experimental studies.",
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In: SIAM Journal on Applied Mathematics, Vol. 75, No. 4, 01.01.2015, p. 1493-1512.

Research output: Contribution to journalArticle

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AU - Ammari, Habib

AU - Kang, Kyungkeun

AU - Lee, Kyounghun

AU - Seo, Jin Keun

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N2 - This paper presents a mathematical framework for a flexible pressure sensor model using electrical impedance tomography (EIT). When pressure is applied to a conductive membrane patch with clamped boundary, the pressure-induced surface deformation results in a change in the conductivity distribution. This change can be detected in the current-voltage data (i.e., EIT data) measured on the boundary of the membrane patch. Hence, the corresponding inverse problem is to reconstruct the pressure distribution from the data. Assuming that the material's conductivity distribution is constant, we derive a two-dimensional (2D) apparent conductivity (in terms of EIT data) corresponding to the surface deformation. Since the 2D apparent conductivity is found to be anisotropic, we consider a constrained inverse problem by restricting the coefficient tensor to the range of the map from pressure to the 2D apparent conductivity. This paper provides theoretical grounds for mathematically modeling the inverse problem. We develop a reconstruction algorithm based on a careful sensitivity analysis. We demonstrate the performance of the reconstruction algorithm through numerical simulations to validate its feasibility for future experimental studies.

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