### 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 |
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Pages (from-to) | 1493-1512 |

Number of pages | 20 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 75 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2015 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*75*(4), 1493-1512. https://doi.org/10.1137/140984671

}

*SIAM Journal on Applied Mathematics*, vol. 75, no. 4, pp. 1493-1512. https://doi.org/10.1137/140984671

**A pressure distribution imaging technique with a conductive membrane using electrical impedance tomography.** / Ammari, Habib; Kang, Kyungkeun; Lee, Kyounghun; Seo, Jin Keun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A pressure distribution imaging technique with a conductive membrane using electrical impedance tomography

AU - Ammari, Habib

AU - Kang, Kyungkeun

AU - Lee, Kyounghun

AU - Seo, Jin Keun

PY - 2015/1/1

Y1 - 2015/1/1

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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84940707019&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940707019&partnerID=8YFLogxK

U2 - 10.1137/140984671

DO - 10.1137/140984671

M3 - Article

VL - 75

SP - 1493

EP - 1512

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -