Mathematical model of biological tissue surface based on one dimensional stochastic process of fractional Brownian motion

Abstract

In this work the model for the profiling of biological tissue surfaces is introduced. The surface was considered as the realization of the stochastic process of the fractional Brownian motion (fBm) with the scale parameter σ and Hurst index H. The contour of the epidermal surface of the normal cut banana peel was studied. The magnified digital photos of the investigated specimens were made using the microscope (spatial resolution 1 μm) with the built-in camera. The function that linearly interpolated the surface contour was derived. The dispersion law of the differences between the values of the interpolating function in the adjacent knots was in good agreement with that one of the fBm stochastic process. The values of σ=0.1 and H=0.806 were obtained.