Lyapunov Exponents of Laser Doppler Flowmetry Signals in Healthy and Type 1 Diabetic Subjects

Abstract

The skin of diabetic subjects presents abnormalities in capillary blood flow and its regulation, often leading to the generation of plantar ulcers. In order to gain insight into this pathology for type 1 diabetic patients, Lyapunov exponents (LEs) of signals reflecting microvascular perfusion--laser Doppler flowmetry (LDF) signals--are calculated. The algorithm to compute LEs is first validated on simulated data and LDF surrogates. Then, LDF signals recorded at rest and during the application of local and progressive pressure of 11.1 Pa/s are processed. The exponents appear in pairs and are different for healthy and type 1 diabetic subjects at rest; P = 0.0556 for the 7th, 8th, and 9th LEs. Furthermore, progressive pressure has also a distinct effect on LEs. The difference is more pronounced for diabetic patients, for whom P = 0.0625 for the four LEs of highest absolute value. Because these differences arise from abnormalities in microvascular blood flow, they may help to explain the high prevalence of type 1 diabetic patients developing foot ulcers.