Fractal nature of arterial blood oxygen saturation data

The subject matter of this study was the processing of arterial blood oxygen saturation data (SaO2). The aim was to investigate the downsampling procedure of the SaO2 records on a broad range of scales. The object of study was a small data set (20 subjects, about 164 seconds duration, sampling rate 300 Hz) borrowed from the well-known portal of medical databases Physionet. The tasks to be solved are a test of the dataset heterogeneity, downsampling of the SaO2 series and its increments in a broad range of possible, checking the randomness of SaO2 series increments, argumentation in favor of applying the theory of Levy-type processes to the SaO2 increments and proving of their self-similarity, the definition of the geometrical fractal and its Hausdorff dimension. The methods used are the Levy-type processes theory, statistical methods, boxes-covering method for fractal structures, the autocorrelation function, and programming within MAPLE 2020. The authors obtained the following results: the dataset comprises three subsets with different variability; the records and their increments remain scale-invariant if the switching frequencies remain lower than the reduced sample rate; the increments of SaO2 records are a Levy-type and self-similar random process; the fractal is the set of positions of the non-zero increments (switch-overs) from a geometrical viewpoint. Conclusions. The scientific novelty of the results obtained is as follows: 1) the fractal nature and the self-similarity of SaO2 records and their increments were proved for the first time; 2) authors found the fractal Hausdorff dimensions for the subsets in the range (0.48…0.73) in dependence on variability; 3) authors found the principal possibility of the SaO2 data sizes essential reducing without losses of vital information.