Numerical simulation of an inverse method for tumour size and location estimation

Abstract

Manual breast exams are widely used for early detection of breast cancer. These exams rely heuristically on the significant stiffness (elastic modulus) difference between cancerous tissue and normal tissue. We wish to systematize this approach by developing an inverse technique which is capable of inferring the elastic modulus throughout the breast tissue based on the application of known surface forces. In this study, we proposed appropriate inverse computational algorithms and examined their performance on two-dimensional model problems. Finite element methods were used to model the tissue response for the forward problem - solving for the surface tissue displacements for a given forcing function. A variety of tumour locations were assumed, and 'measured results' were created with numerical noise added to simulate measurement errors. A genetic algorithm was then developed to solve the inverse problem - given the measured surface displacements, what is the distribution of tissue material properties within the breast? We developed an eigenvector expansion technique to create effective force test patterns for use in concert with the genetic algorithm. A series of test cases at various noise levels for a coarse and a fine mesh were examined. When a tumour was present, a tumour was always detected. When a tumour was absent, the algorithm always correctly reported no cancer. © 2010 Taylor & Francis.