A mathematical liver model and its application to system optimization and texture analysis.

Abstract

This dissertation presents realistic mathematical models of normal and diseased livers and a nuclear medicine camera. The mathematical model of a normal liver is developed by creating a data set of points on the surface of the liver and fitting it to a truncated set of spherical harmonics. We model the depth-dependent MTF of a scintillation camera taking into account the effects of Compton scatter, linear attenuation, intrinsic detector resolution, collimator resolution, and Poisson noise. The differential diagnosis on a liver scan includes normal, focal disease, and diffuse disease. Object classes of normal livers are created by randomly perturbing the spherical harmonic coefficients. Object classes of livers with focal disease are created by introducing cold ellipsoids within the liver volume. Cirrhotic livers are created by modelling the gross morphological changes, heterogenous uptake, and decreased overall uptake. Simulated nuclear medicine images are made by projecting livers through nuclear imaging systems. The combination of object classes of simulated livers and models of different imaging systems is applied to imaging-system design optimization in a psycho-physical study. Human observer performance on simulated liver images made on nine different systems is compared to the Hotelling trace criterion (HTC). The system with the best observer performance is judged to be the best system. The correlation between the human performance metric dₐ and the HTC for this study was 0.829, suggesting that the HTC may have value as a predictor of observer performance. Texture in a liver scan is related to the three-dimensional distribution of functional acini, which changes with disease. One measure of texture is the fractal dimension, related to the Fourier power spectrum. We measured the average radial power spectra of 70 liver scans. All of these scans yield straight lines when plotted on a log-log scale, a characteristic of fractal objects. The slope of the line is related to the fractal dimension of the acini. The slopes are significantly higher for normal than abnormal livers (t = 4.04, df = 29, p = 0.005). On 32 liver scans with confirmed diagnoses, receiver operating characteristics (ROC) analysis was performed using power spectral slope as a feature. Analysis of the ROC curve yielded an area under the curve of 85, suggesting that power spectral slope may be a useful classifier of disease.