2D intravascular E.I.T. using a non-iterative, non-linear reconstruction algorithm

Abstract

We developed an Intravascular Impedance Catheter (2D-IIC) together with a non-iterative, non-linear reconstruction algorithm, capable of assessing a series of 2D discretized images of the impedance distribution of the arterial wall.

The 2D-IIC uses a differential measurement technique based on our early version of the IIC [1], but features two new elements: asymetrically placed electrodes and a rotational motion of the catheter around its longitudinal axis. This transforms the original 1D technique into a tomographic 2D imaging device. Because of these extensions however, the Finite Element or Boundary Element calculations that solve the forward problem in Newton-like reconstruction algorithms would be prohibitively timeconsuming.

In this paper we first decribe the 2D-IIC, and subsequently formulate a new, non-linear, algorithm solving the inverse problem non-iteratively. This algorithm exploits the algorithmic possibilities offered by the differential measurement technique and combines the Clausius-Mosotti approximation for field distortion with a modified Boundary Element method. Furthermore we provide a mathematical foundation for the validity of this method when applied to the 2D-IIC, and describe more generally its applicability to E.I.T.-techniques that involve a differential measurement.