Echoscan : Electrical Impedance Tomography by Elastic Perturbation
Résumé
There has been a lot of effort to develop electrical impedance tomography (EIT) as an imaging technique for cancer detection. However, it has been shown that this problem is seriously ill-posed, which in practice hampers any attempt of reconstruction with the required level of resolution (of the order of the mm in the case of breast cancer detection). Perturbing EIT measurements by focused ultrasound waves has been proposed as a method to obtain additional information for the reconstruction of the conductivity. Assuming that the local variation of the conductivity is proportional to the amplitude of the elastic perturbation, one asymptotically recovers the pointwise values of the energy density at the center of the perturbation. The inverse problem becomes then one of reconstructing the conductivity from internal measurements. We will discuss how knowledge of internal data greatly helps in the resolution of this inverse problem and how mathematical modeling could be pertinent in the design of new imaging modalities and devices, where one may combine several types of waves to probe a medium with high resolution.