It is well established that skin temperature oscillations in fingertips coexist with blood flow oscillations and there is a certain correlation between them. At the same time, the reasons for differences in waveform and the delay between the blood flow and temperature oscillations are far from being fully understood. In this study we determine the relationships between spectral components of the blood flow and temperature oscillations in fingertips, and we ascertain the frequency dependences of amplitude attenuation and delay time for the temperature oscillations. The blood flow oscillations were considered as a source of thermal waves propagating from micro-vessels towards the skin surface and manifesting as temperature oscillations. The finger temperature was measured by infrared thermography and blood flow was assessed by photoplethysmography for ten healthy subjects. The time-frequency analysis of oscillations was based on the Morlet wavelet transform. The frequency dependences of delay time and amplitude attenuation in temperature compared with blood flow oscillations have been determined in endothelial (0.005-0.02 Hz) and neurogenic (0.02-0.05 Hz) frequency bands using the wavelet spectra. We approximated the experimental frequency dependences by equations describing thermal wave propagation through the medium and taking into account the thermal properties and thickness of a tissue. Results of analysis show that with the increase of frequency f the delay time of temperature oscillations decreases inversely proportional to f(1/2), and the attenuation of the amplitude increases directly proportional to exp f(1/2). Using these relationships allows us to increase correlation between the processed temperature oscillations and blood flow oscillations from 0.2 to 0.7 within the frequency interval 0.005-0.05 Hz. The established experimental and theoretical relationships clarify an understanding of interrelation between the dynamics of blood flow and skin temperature, and define possibilities and limitations of temperature measurements as a method of blood flow assessment in extremities.

The determination of the relationship between skin blood flow and skin temperature dynamics is the main problem in thermography-based blood flow imaging. Oscillations in skin blood flow are the source of thermal waves propagating from micro-vessels toward the skin's surface, as assumed in this study. This hypothesis allows us to use equations for the attenuation and dispersion of thermal waves for converting the temperature signal into the blood flow signal, and vice versa. We developed a spectral filtering approach (SFA), which is a new technique for thermography-based blood flow imaging. In contrast to other processing techniques, the SFA implies calculations in the spectral domain rather than in the time domain. Therefore, it eliminates the need to solve differential equations. The developed technique was verified within 0.005-0.1 Hz, including the endothelial, neurogenic and myogenic frequency bands of blood flow oscillations. The algorithm for an inverse conversion of the blood flow signal into the skin temperature signal is addressed. The examples of blood flow imaging of hands during cuff occlusion and feet during heating of the back are illustrated. The processing of infrared (IR) thermograms using the SFA allowed us to restore the blood flow signals and achieve correlations of about 0.8 with a waveform of a photoplethysmographic signal. The prospective applications of the thermography-based blood flow imaging technique include non-contact monitoring of the blood supply during engraftment of skin flaps and burns healing, as well the use of contact temperature sensors to monitor low-frequency oscillations of peripheral blood flow.

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