Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915474618449920 |
|---|---|
| author | Abdulla, Ugur G. Rodrigues, Jose H. |
| author_facet | Abdulla, Ugur G. Rodrigues, Jose H. |
| contents | We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial differential equations. Relying on the fact that the electrical conductivity of the cancerous tumor is significantly higher than the conductivity of the healthy tissue, we consider an inverse EIT problem on the identification of the conductivity map in the complete electrode model based on the $m$ current-to-voltage measurements on the boundary electrodes. A variational formulation as a PDE-constrained optimal control problem is introduced based on the novel idea of increasing the size of the input data by adding "voltage-to-current" measurements through various permutations of the single "current-to-voltage" measurement. The idea of permutation preserves the size of the unknown parameters on the expense of increase of the number of PDE constraints. We apply a gradient projection (GPM) method based on the Fréchet differentiability in Besov-Hilbert spaces. Numerical simulations of 2D and 3D model examples demonstrate the sharp increase of the resolution of the cancerous tumor by increasing the number of measurements from $m$ to $m^2$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs Abdulla, Ugur G. Rodrigues, Jose H. Optimization and Control Analysis of PDEs 49M41, 49K20, 65M30 We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial differential equations. Relying on the fact that the electrical conductivity of the cancerous tumor is significantly higher than the conductivity of the healthy tissue, we consider an inverse EIT problem on the identification of the conductivity map in the complete electrode model based on the $m$ current-to-voltage measurements on the boundary electrodes. A variational formulation as a PDE-constrained optimal control problem is introduced based on the novel idea of increasing the size of the input data by adding "voltage-to-current" measurements through various permutations of the single "current-to-voltage" measurement. The idea of permutation preserves the size of the unknown parameters on the expense of increase of the number of PDE constraints. We apply a gradient projection (GPM) method based on the Fréchet differentiability in Besov-Hilbert spaces. Numerical simulations of 2D and 3D model examples demonstrate the sharp increase of the resolution of the cancerous tumor by increasing the number of measurements from $m$ to $m^2$ |
| title | Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs |
| topic | Optimization and Control Analysis of PDEs 49M41, 49K20, 65M30 |
| url | https://arxiv.org/abs/2509.02050 |