A GA based approach for boundary detection of left ventricle with echocardiographic image sequences

Abstract

In this paper automatic detection of the boundary of left ventricle (LV) in a sequence of cardiac images has been proposed. The contour detection algorithm is formulated as a constrained optimization problem based on active contour model. The optimization problem has been solved using Genetic Algorithm (GA). The result obtained by the proposed GA based approach is compared with conventional nonlinear programming methods. Validation of the computer-generated boundaries is done after comparing them with manually outlined contours by expert observers. The performance of the algorithm is comparable to inter-observer anomalies.

Introduction

Contour extraction is an important criterion for subjective evaluation of the cardiac function and has become an area of focus. Possible applications include calculation of stroke volume and ejection fraction. In addition, a quantitative interpretation of left ventricle (LV) motion dynamics from the sequential contours may become a powerful diagnostic aid for clinical pathology and appropriate surgical planning. Conventionally trained observers or radiologists detect the boundary of LV manually using different imaging modalities. With such an approach it becomes increasingly difficult and sometimes leads to error if the data size is huge. Such a situation may arise when the heart is to be characterized over entire cardiac cycle for a 3-D surface visualization rather than at the end systole (ES) and end diastolic (ED) positions.

A number of issues concerning the development of technique and algorithms for the computerized automation of the process using verity of imaging techniques are reported in Ref. [1], [2], [3], [4], [5], [6]. Suh et al. [3] presented a technique using the uncertainty reasoning within the Dempster–Shafer framework after combining the low-level image features. The methods suggested by Chu et al. [5] require mostly the gray level information along with some user defined initial contours to extract the boundary in the images.

Nastar et al. [7] have proposed a basic model for the contour as a set of mass linked by springs to track the motion in a sequence of 2-D images. However, method proposed by Staib et al. [8] implemented a probabilistic deformable model considering the boundary as two-dimensional deformable object using maximum posteriori estimate.

Recent work by Chalana et al. [9] reports an interesting approach to detect epicardial and endocardial boundary of short axis echocardiographic sequences using a multiple active contour model, an extension to the original model proposed by Kass et al. [10]. The multiple-active-contour model is a special case of active surface model where the surface is represented as a sequence of planar contours. The algorithm requires user defined initial approximation for epicardial boundary that detects the contour by computing gradients using Canny's edge detection method. The variance of the Gaussian kernel used to convolve the gradient image progressively decreases to intensify the convergence. The optimized contours of the epicardial boarders are used as initial approximation for endocardial boundary with empirically determined values of the snake model parameters. A similar automated contour extraction algorithm proposed by Ranganath [11] is applicable to spin and gradient echo MRI image sequences. It suggests a contour propagation technique to track the boundary in a sequence despite its poor temporal resolution. A recent work on segmentation of medical images has been reported using geometric active deformable models where the contour propagates with a velocity profile as a function of curvature [12]. The stopping criteria in geometric model are critical and smoothness parameters do not satisfy the physical characteristic of cardiac muscles surrounding the blood pull. Zhu et al. [13] address boundary extraction using a modified Holpfield's neural network for tumor boundary detection in MRI images. The method is computationally expensive to implement for cardiac image sequences where the data is huge and the contour needs to be optimized at a number of sample points in each frame.

In this paper we address the contour optimization functional based on an active contour model. The objective function i.e. snake energy is minimized in a constrained feasible solution space using Genetic Algorithm (GA). GA is computationally expensive in comparison to other non-linear optimization techniques. However, it shows promising results when the initial population of chromosomes (genotype or candidate solutions) is constrained in a search area. Finally the performance of the proposed algorithm is compared with constrained quasi-Newton method.

Section 2 describes a brief overview of an active contour model based on which the optimization function is evaluated. In Section 3 essential preprocessing techniques have been discussed to find out the rough boundary required for initial approximation. Section 4 describes the problem formulation. Section 5 describes implementation of GA in a constrained space. The results and discussion are presented in Section 6.