A narrow-band level set method applied to EIT in brain for cryosurgery monitoring

In this paper, we investigate the feasibility of applying a novel level set reconstruction technique to electrical imaging of the human brain. We focus particularly on the potential application of electrical impedance tomography (EIT) to cryosurgery monitoring. In this application, cancerous tissue is treated by a local freezing technique using a small needle-like cryosurgery probe. The interface between frozen and nonfrozen tissue can be expected to have a relatively high contrast in conductivity and we treat the inverse problem of locating and monitoring this interface during the treatment. A level set method is used as a powerful and flexible tool for tracking the propagating interfaces during the monitoring process. For calculating sensitivities and the Jacobian when deforming the interfaces we employ an adjoint formula rather than a direct differentiation technique. In particular, we are using a narrow-band technique for this procedure. This combination of an adjoint technique and a narrow-band technique for calculating Jacobians results in a computationally efficient and extremely fast method for solving the inverse problem. Moreover, due to the reduced number of unknowns in each step of the narrow-band approach compared to a pixel- or voxel-based technique, our reconstruction scheme tends to be much more stable. We demonstrate that our new method also outperforms its pixel-/voxel-based counterparts in terms of image quality in this application.