Filtering the photoplethysmography (PPG) signal from noise is an important pre-processing step. The aim of this work was to evaluate the effectiveness of finite impulse response (FIR) filters in suppressing electromagnetic noise of the PPG signal. We recorded raw finger PPG signals from 20 healthy subjects (40 signals in total) and processed them by different FIR filters, such as the windowed (Hanning) filter, equiripple filter and Savitzky-Golay filter. During the study, the filtering order varied from 20 to 100 for the windowed and equiripple filters and from 3 to 7 for the Savitsky-Golay filter. To evaluate the performance of the filters, we used the signal-to-noise ratio, which was calculated based on the spectral decomposition of a PPG signal, and root mean square error (RMSE) reflecting phase distortions of the pulse waveform. The best noise suppression efficiency was obtained for the windowed filter with an order of $40(17.03 \mathrm{~dB})$ and the Savitzky-Golay filter with a polynomial order of 3 and a moving window length of $0.253-0.316 \mathrm{~s}(18.13 \mathrm{~dB})$. However, the Savitzky-Golay filter showed the smallest RMSE compared to the windowed filter ($12.8 \%$ versus $52.9 \%$).

The paper is devoted to the study of physical mechanisms of photoplethysmography (PPG) signal formation using Monte Carlo simulations of light transport in biological tissue. The problem of estimating the contribution of absorption and scattering variations to the registered PPG signal is solved. Based on a three-layer skin model, changes in the optical properties of the dermal layer (absorption and scattering) were sequentially simulated and their contributions to the total signal were estimated. Calculations were carried out for two wavelengths, 525 nm and 810 nm. It was found that for green light the main contribution to the signal formation is made by absorption (88 % versus 12 % scattering, respectively). While for the near infrared light, scattering predominates over absorption. In this case, the contributions of absorption and scattering are 28 % and 72 %. Thus, for the green wavelength range the classical volumetric model of signal formation is valid. Whereas for the near-infrared range, the predominant factor in signal formation is scattering of the medium, which can change due to processes such as changes in orientation, aggregation and deformation of red blood cells, their concentration in the diagnostic volume of tissue, etc.

The effect of red blood cell (RBC) aggregation on the photoplethysmography (PPG) signal at a wavelength of 810 nm was investigated using the Monte Carlo method. It was found that the main contribution to the formation of the PPG signal is made by scattering variations due to changes in the rouleaux size ($84 \%$ versus $16 \%$ absorption, respectively).

Pre-processing of the photoplethysmography (PPG) signal plays an important role in the analysis of the pulse wave signal. The task of pre-processing is to remove noise from the PPG signal, as well as to transmit the signal without any distortions for further analysis. The integrity of the pulse waveform is essential since many cardiovascular parameters are calculated from it using morphological analysis. Digital filters with infinite impulse response (IIR) are widely used in the processing of PPG signals. However, such filters tend to change the pulse waveform. The aim of this work is to quantify the PPG signal distortions that occur during IIR filtering in order to select a most suitable filter and its parameters. To do this, we collected raw finger PPG signals from 20 healthy volunteers and processed them by 5 main digital IIR filters (Butterworth, Bessel, Elliptic, Chebyshev type I and type II) with varying parameters. The upper cutoff frequency varied from 2 to 10 Hz and the filter order—from 2nd to 6th. To assess distortions of the pulse waveform, we used the following indices: skewness signal quality index (SSQI), reflection index (RI) and ejection time compensated (ETc). It was found that a decrease in the upper cutoff frequency leads to damping of the dicrotic notch and a phase shift of the pulse wave signal. The minimal distortions of a PPG signal are observed when using Butterworth, Bessel and Elliptic filters of the 2nd order. Therefore, we can recommend these filters for use in applications aimed at morphological analysis of finger PPG waveforms of healthy subjects.

This study aimed to examine the mechanisms of the photoplethysmography (PPG) signal formation using Monte Carlo simulations of light transport in biological tissues and experimental observations. Based on a three-layer skin model in backscattering geometry, we sequentially simulated volumetric blood changes and the aggregation/disaggregation of erythrocytes in the dermal layer and estimated their contribution to the registered PPG signal. The calculations were conducted for two wavelengths: 525 nm and 810 nm. For green light, absorption predominates over scattering in the formation of a PPG signal, whereas, for near-infrared light, scattering prevails over absorption. This theoretical result was verified using the Modified Beer–Lambert law and clinical in vivo PPG data of seven healthy subjects. Changes in the size of the scatterers during erythrocyte aggregation and disaggregation can significantly contribute to the PPG signal at near-infrared light. Thus, for the green waveband, the classical volumetric model can be considered dominant in the PPG signal formation. In contrast, for the near-infrared range, both volumetric and aggregation effects must be considered as being approximately equal.

This paper is devoted to the study of mechanisms of photoplethysmography (PPG) signal formation using Monte Carlo simulations of light transport in biological tissue. Specifically, one problem is being solved: what is the contribution of absorption and scattering variations to the total PPG signal? Based on a three-layer skin model in backscattering geometry, we sequentially simulated changes in the optical properties of the dermal layer and estimated their contribution to the registered PPG signal. Calculations were carried out for two wavelengths, 525 nm and 810 nm. It was found that for green light, absorption predominates over scattering in the formation of a PPG signal. In particular, contributions of absorption and scattering to the total signal are 88 ± 6% and 12 ± 5%, respectively. Whereas for near-infrared light, scattering prevails over absorption. In this case, proportions of absorption and scattering are 28 ± 5% and 72 ± 4%. Thus, for the green wavelength range the classical volumetric model of signal formation is valid, while for the near-infrared range scattering processes due to, e.g., aggregation, orientation and deformation of erythrocytes or changes in their concentration in the diagnostic volume of tissue are predominant.

In this paper, we propose a method for measuring a pulse wave velocity (PWV) along the entire body of the patient with the use of a standard tonometer cuff and a photoplethysmography (PPG) sensor attached to a toe. This approach makes it possible to calculate PWV simultaneously with the measurement of a blood pressure (BP), which takes several minutes. To test the developed method, 2 contrasting groups of subjects were recruited: group 1 (n=15) - healthy volunteers; group 2 (n=14) - patients with diabetes mellitus (DM). Healthy volunteers had the lowest median PWV value: 5.055 [4.427; 5.295] m/s, whereas in the group 2, the median PWV was significantly higher than in the group 1: 5.905 [5.612; 6.215] m/s, p<0.001. The proposed method for measuring PWV correlates with clinical data and allows a rapid integral assessment of vascular stiffness in both the trunk and lower extremities.

ЦЕЛЬ: исследовать информативность комбинации разных неинвазивных оптических подходов в диа- гностике заболеваний артерий нижних конечностей (ЗАНК) у пациентов с сахарным диабетом (СД). МАТЕРИАЛЫ И МЕТОДЫ: проведено обсервационное исследование на 54 пациентах с СД 2 типа (39 конечностей со стенозами/окклюзией, 69 – без стенозов). Наличие гемодинамически значимых стено- зов магистральных артерий нижних конечностей (более 50%) оценивали по результатам ультразвукового дуплексного сканирования (УЗДС) как референтного метода. Всем пациентам оценивали показатели гемо- динамики при помощи комплексной технологии, реализующей методы некогерентной оптической флук- туационной флоуметрии (НОФФ), фотоплетизмографии и тонометрической осциллометрии. Технология позволяет одновременно оценивать перфузию тканей стопы в ходе теплового теста, перфузию тканей руки, скорость пульсовой волны, форму пульсовой волны. Дополнительно пациентам оценивали лодыжечно- плечевой индекс (ЛПИ) как стандартный скрининговый метод выявления ЗАНК. РЕЗУЛЬТАТЫ: применение показателей перфузии на стопе в ходе теплового теста, измеренных методом НОФФ, позволяет с чувствительностью 79,5% и специфичностью 88,4% выявлять конечности с гемоди- намически значимыми стенозами (AUROC 0,884, CI: 0,817-0,953). При комбинации показателей перфузии на руке и ноге, формы пульсовой волны и скорости пульсовой волны при помощи модели множественной логистической регрессии, чувствительность модели в выявлении конечностей со стенозами значимо воз- растает до 88,6%, а специфичность – до 92,8 % (AUROC 0.928, CI: 0.8742-0.9809). При этом чувствительность и специфичность ЛПИ, как стандартного метода выявления ЗАНК значимо ниже, и составляет 48,7% и 87,0 % соответственно. ВЫВОДЫ: комбинация нескольких параметров гемодинамики, оцениваемых одномоментно при помо- щи комплексной оптической технологии, позволяет добиться высокой чувствительности и специфичности в выявлении ЗАНК у пациентов с СД (88,6% и 92,8% соответственно). Техническая простота измерения (10 минутное измерение с низкой оператор-зависимостью) позволяет рассматривать подход как перспектив- ный для скринингового выявления ЗАНК.

Photoplethysmography (PPG) is an optical technique for detection of blood volume changes in the microvascular bed of a biological tissue. Many aspects of the PPG signal formation are still unclear. In particular, it is not known how the shape of a registered PPG signal depends on the geometry of tissue illumination. The aim of this study is to model the PPG waveform using the Monte Carlo (MC) method. For this, we developed a three-layer optical model of the skin in a reflectance geometry and verified it experimentally for different wavelengths (660, 810, and 940 nm) and source-detector distances (from 4 to 10 mm). The MC simulation results showed that the PPG waveform depends on the source-detector distance. The most pronounced diastolic wave is observed at the distance of 6 mm for the wavelength of 810 nm. The results obtained can be used for the development of reflectance PPG sensors.

Incoherent Optical Fluctuation Flowmetry (IOFF) is an optical technique for assessing tissue blood flow (BF). This technique is based on the spectral analysis of low-frequency fluctuations in the registered optical signal caused by blood volume changes inside a tissue. The technique can be realized using an optical probe with LEDs. The aim of this study was to evaluate the signal-to-noise ratio (SNR) in IOFF as a function of the distance between a LED and a detector. For this, we developed an experimental setup with a variable source-detector separation. The measurements were carried out on 5 healthy volunteers at the wavelength of 810 and at distances of 4, 6, 8 and 10 mm. To obtain a useful signal, we used the spectral approach to remove noise. The best signals were obtained at a distance of 10 mm (SNR median is 63). Good quality signals were also obtained at distances of 6 and 8 mm (SNR medians are 49 and 55, respectively). It was found that calculated BF is directly proportional to the source-detector separation. As one of the options for standardization of measurements, it was proposed to normalize the output value of BF to a distance.

The photoplethysmographic waveform was modeled for different source-detector distances using the Monte Carlo technique. For this, a three-layer optical model of the skin for reflection was developed. It was found that the pulse wave is most pronounced for the distance of 6 mm.

The aim of this study was to investigate the ratio of baseline perfusion levels in the skin of the palmar surfaces of the fingers and plantar surfaces of the big toe in healthy volunteers and patients with diabetes mellitus. Three study groups were included: healthy volunteers (group 1, n = 29), patients with type 2 diabetes mellitus (DM2) without diabetic foot syndrome (group 2, n = 27), and patients with diabetic foot syndrome (group 3, n = 27). All subjects were measured for the level of perfusion in the skin of the upper and lower extremities using the method of incoherent optical fluctuation flowmetry (IOFF). Perfusion was assessed in perfusion units (p.u.). The measurement was carried out sequentially, first on the left side of the body, then on the right. The baseline perfusion values from the index finger of the hand (BPh) and from the big toe of the foot (BPf) in perfusion units (p.u.) were assessed at rest. The BPh value in group 1 was 11.5 [5.4; 16.8] p.u.; in group 2, 17.4 [13.2; 24.8] p.u.; in group 3, 18.4 [13.2; 23.6] p.u. The BPh level was statistically significantly lower in group 1 than in groups 2 (p1–2 < 0.001) and 3 (p1–3 < 0.001). There was no statistically significant difference in finger perfusion between groups 2 and 3 (p2–3 = 1). The BPf values in groups 1, 2, and 3 were 4.4 [2.3; 8.8], 7.9 [5.4; 14.6], and 3.9 [1; 9.9] p.u., respectively. The BPf level in group 2 was higher than in group 1 (p1–2 = 0.006), but the parameter in group 3 was comparable to the values from group 1 (p1–3 = 0.73) and different from group 2 (p2–3 < 0.001). Thus, in group 3, there was a pseudonormalization of this index due to abnormally low BPf values in the extremities with hemodynamically significant stenoses. The baseline perfusion ratio (BPh/BPf) in groups 1, 2, and 3 was 2.11 [1.22; 3.03], 1.91 [1.18; 3.92], and 4.29 [1.8; 12.84], respectively. The BPh/BPf ratio in group 3 was significantly higher than in groups 1 (p1–3 < 0.001) and 2 (p2–3 < 0.001). The ability to detect the presence of hemodynamically significant lower limb arterial stenoses was analyzed by the BPf and BPh/BPf indices; the area under the ROC curve for BPf was 0.808 (0.729; 0.887); for BPh/BPf, 0.855 (0.782; 0.928). It was shown that an increase in the BPh/BPf ratio to exceed 3.7 with a sensitivity of 75.7

In this paper, the original design of a remote optical cerebral sensor is proposed. An approach is suggested for theoretical justification of distances between light emitters and a photodetector based on the data of multispiral computed tomography and Monte Carlo simulation of light propagation in human head tissues. On the basis of the formulated criteria, the optimal distances between emitters and a photodetector were obtained, the usage of which in the sensor design has a potential to reduce the noise contribution of extracerebral tissues in the assessment of oxyhemoglobin saturation in brain tissues.

Photoplethysmography (PPG) is an optical method for recording pulse wave (PW) propagating in the tissue microvasculature. As a rule, filters with infinite impulse response (Butterworth, Bessel, etc.) often used in PPG signal processing introduce distortions in the PW signal. At the same time, the filtering parameters for a more accurate reproduction of PW have not yet been substantiated. The aim of this work is to study the influence of digital filtering parameters, such as bandwidth and filter order, on the pulse waveform. In the study, a digital bandpass Butterworth filter was used. The lower cutoff frequency of the filter varied from 0.1 to 1 Hz, the upper cutoff frequency varied from 2 to 10 Hz and the filter order – from 2nd to 6th. It was found that an increase in the lower cutoff frequency of the bandpass filtering leads to a decrease in the amplitude of the reflected diastolic wave and distortion of the front of the direct systolic wave. A decrease in the upper cutoff frequency leads to damping of the dicrotic notch and a phase shift of the PW. Increasing the filter order decreases the reflected wave amplitude. The minimal distortions of the PPG signal were observed at the lower cutoff frequency of 0.1 Hz, the upper one at 10 Hz and the filter order equal to 2. Thus, these parameters of a bandpass filtering can be recommended for processing PPG signals for a more accurate morphological analysis of PW. The obtained results make it possible to create devices for PW analysis with substantiated medical and technical requirements for filtration parameters.

The sensitivity of the laser Doppler flowmetry (LDF) and incoherent optical flowmetry (IOF) to blood flow oscillations was studied experimentally. IOF is a method of measuring the perfusion index from a raw photoplethysmographic signal. It was shown that the IOF is approximately 2-10 times more sensitive than LDF.

The model for estimation of the amplitude modulation depth of photoplethysmographic (PPG) signal based on the modified Beer-Lambert law was developed. It was analytically confirmed that the modulation depth of PPG signal depends on the wavelength and illumination geometry. The modulation depth is directly proportional to the distance between the light source and the detector. The sensitivity of green light (525 nm) to blood volume changes is approximately 6-9 times greater than that for red (640 nm) and IR (805 nm) light. It was found that in case of green light, the main contribution to the modulation of PPG signal is made by absorption coefficient changes while in case of red and IR light, the modulation is mainly caused by scattering coefficient changes.

The dc component of the laser Doppler signal was studied experimentally during arterial occlusion. It was shown that the dc component strongly depends on the tissue blood volume. It can be used for evaluation of the tissue ischemia.