Computational and Mathematical Methods in Medicine
Volume 8 (2007), Issue 4, Pages 245-261
Original Article

Solutions of Inverse Problems with Potential Application for Breast Tumour Detection Using Microwave Measurements

1Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand
2Keam Holdem Associates Ltd, P. O. Box 408, Shortland Street, Auckland, New Zealand

Received 20 April 2007; Revised 14 September 2007; Accepted 9 October 2007

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents one-dimensional and two-dimensional microwave inverse computing methods to detect an internal object using measurements based on a signal applied from the surface of the host material. The modelling of our application system has been aimed towards the in vivo detection of a breast tumour, in particular, and to enable the calculation of the tumour size and its distance from the surface of the breast. However, our approach is also applicable for more general foreign object identification. Complex backscattered electromagnetic waves characterise the relations of the internal properties of the host material. Forward and backscattered signals are used to calculate the impedance and reflection coefficients as a function of the applied microwave frequency. In the study of one-dimensional modelling, we discuss the approach to identifying a foreign object hidden inside the host material and we present a method for computing the distance to the object from the surface of the host. Subsequently, a cylindrical coordinate system is used for two-dimensional modelling. A method to compute the size of the object (up to one millimetre in radius) is discussed. Computation of unknown electrical and non-electrical parameters using front-end microwave application is challenging but it is feasible.