Analyzing blood cell concentration as a stochastic process

The hemogram is a prime index of evolution and prognosis of a variety of severe pathological disorders. The concentration of circulating blood elements, taken as a parameter of the system dynamics, displays a remarkable temporal variability. This variability can be considered as the integrated result of all the multiple interactions involved in controlling processes of generation, lifetime, and remotion of circulating cells. Designing a model able to satisfactorily predict the evolution (i.e., range of future values) of a hemogram series would be of high medical relevance. This article reports on basic characteristics of normal hemogram variability, analyzed as a stochastic process, within the framework of a mathematically defined theoretical model, the fractional Brownian motion. These results are compared with those obtained by standard spectral analysis: the autocorrelation function and its Fourier transform. Time series corresponding to day-to-day records of the circulating blood cells concentration obtained from two healthy sheep over a period of 1024 days were used.