Acoustical fractal images applied to medical imaging

Architecture of human tissue can be investigated with an ultrasound beam. The broad objective of scattering-based tissue characterization studies employing ultrasound is to infer structure or architectural properties of tissue from measurement and analysis of ultrasonic data and images. Under certain conditions (for certain relationship among the tissue parameters), ultrasonic wave propagation in highly inhomogeneous human tissue can become chaotic, and can generate specific fractal image corresponding to this chaotic process. The inhomogeneous Helmholtz wave equation is represented by the nonlinear oscillator equation perturbed by an array of impulses. This is used as a mathematical model. Two approaches are used to obtain the algorithm to plot the fractal images. One is by stochastic approach to obtain the probability density function. The second approach is using mapping technique and the fractal image is obtained by iteration. As shapes of power spectrum of the scattering wave are affected by the distributions of scatterers, analyses of the shapes could be used for tissue characterization.