Methodological Advances on Pulse Measurement through Functional Imaging

Abstract

The blood pressure and velocity rise rapidly as a result of the opening of the aortic valve in early systole. This spike in blood pressure and momentum travels the length of the aorta and is passed on to peripheral arteries such as the brachial, the carotid, and beyond. The thus formed pulse is an example of a traveling wave in a fluid medium that involves transport of mass and heat. The alteration of the electric field that moves the heart’s muscle and the thermo-mechanical effects of pulse propagation in the vascular network creates opportunities for measurement across different modalities. The method that is considered to be the gold standard for pulse measurement is electrocardiography (ECG) [12]. It produces crisp results because it focuses on the source (heart). Other commonly used methods, such as piezoelectric probing [4], photoplethysmography [13] and Doppler ultrasound [9], focus on the vascular periphery. One main characteristic of all these methods is that they require contact with the subject. There are clinical applications, however, where a contact-free method is desirable. Such applications usually involve sustained physiological monitoring of patients who are in delicate state or form; examples range from sleep studies to neonatal monitoring.

Appendix

Description of the ALMModel: Here follows a brief description of the Along the Vessel Model:

• In step one, within the MROI, the operator selects manually or automatically a straight segment of 7–10 pixels (depending on the vessel selected) along the center line of the superficial blood vessel. The algorithm expands symmetrically into an elongated rectangle the width of which can be from 1 to 13 pixels (as opposed to 3–7 pixels used before). The width of this rectangle depends on the width of the vessel on the thermal imagery.

• In step two, we record the time evolution of the pixel matrix delineated by rectangle R for 2^N frames, where N ∈ [7, 11] (only the use of N = 9 or 512 frames was reported in our previous studies. In this paper, we investigated all values of N). Thus, we produce a 3-D matrix A(x, y, t), where x and y is the spatial extent of rectangle R and t is the timeline.

• In step three and in order to reduce the noise, we average the pixel temperatures along the x dimension.

• In step four, for each effective pixel on the measurement line, we obtain the time evolution signal of its temperature. We apply the FFT on each of these signals.

• In step five, we average all the power spectra computed in the previous step into a composite power spectrum.

Description of the ACM Model: Here follows a brief description of the Across the Vessel Model:

• In step one, the operator draws manually or automatically a line that traverses the cross section of the thermal imprint of the vessel (e.g., FSTA). The section spans between 1 and 15 pixels (as opposed to 3–7 pixels used before). The spatial resolution of the measurement line is increased by applying quadratic interpolation once (as opposed to 5 times used before) to minimize the computational complexity while achieving good performance. We model the cross section temperature function using the first five (5) cosine functions of the Fourier series.

• In step two, we compute the ridge and the boundary points at each frame. The first corresponds to the middle of the vessel’s cross section, where the blood flow speed is maximal, while the second is recorded at the vessel’s boundary where the minimum blood flow speed occurs. The time evolution of these points form the ridge and boundary temperature functions (R _TF and B _TF ) respectively.

• In step three, we compute the static mean pulse frequency (SMPF). We apply the FFT on both R _TF and B _TF 1D signals and obtain their power spectrum (P _r and P _b). We model both power spectrum as a multi-normal distribution by applying a Parzen window method [8] and get the multi-normal distributions P _r ^′ and P _b ^′. We multiply P _r ^′ and P _b ^′ to obtain the combined model spectrum P _rb ^′. Then, we find the frequency f _n for which P _rb ^′ assumes its maximum amplitude. The f _n frequency is considered the SMPF of the subject during the time period of the first T ≥ 30 s or ≈ 1, 024 frames and it is represented as the normal distribution N(μ_p,$\bar{{\sigma }_{\mathrm{p}}^{2}}$) with mean μ_p=f _p and variance $\bar{{\sigma }_{\mathrm{p}}^{2}}$.

• In this paper, we go a step further and compute the dynamic MPF (DMPF). This is performed by updating the MPF for every 64 frames after the first 1,024 frames. We have also optimized the value of the variance to achieve better performance results.

• In step four, we compute the instantaneous pulse frequency (IPF). We apply exactly the same procedure that we described in step 3 for long observation periods (T ≥ 30 s). Then, we can use either the SMPF or the DMPF computed to localize our attention in the IPF spectrum by multiplying P _rb ′ with N(μ_p,$\bar{{\sigma }_{\mathrm{p}}^{2}}$) that is denoted as P _rb ′′. The tentative IPF is the frequency f _i for which the amplitude of the spectrum P _rb ′′ is maximum.

Adaptive Estimation Filter and Pulse Recovery: The instantaneous computation described by both ALM and ACM suffers by occasional thermo-regulatory vasodilation and noise despite the effective mechanisms built into both models. This problem has been addressed by building an estimation function that takes into account the current measurement as well as a series of past measurements. This idea is based on the adaptive line enhancement method reported in [3]. In our previous studies, we reported that the current power spectrum of the temperature signal is being computed over the previous 2⁹=512 frames by applying the ALM or ACM models. Now, we investigate a frame range from 128 and up to 2,048 frames (2^N frames for N ∈ [7, 11]).

To compute the pulse frequency, first we convolve the current power spectrum computed by either model with a weighted average of the power spectra computed during the previous 60 frames. This is because at the average speed of 30 fps sustained by our system, there is at least one full pulse cycle contained within 60 frames even in extreme physiological scenarios. Then, we compute the historical frequency response (HFR) at a particular frequency. HFR is given as the summation of all the corresponding frequency responses for the spectra, normalized over the total sum of all the frequency responses for all the historical spectra. Finally, we convolve the HFR with the current power spectrum and we then designate as pulse the frequency that corresponds to the highest energy value of the filtered spectrum within the operational frequency band.