Temporal complexity in photoplethysmography and its influence on blood pressure

Abstract

Objective: The temporal complexity of photoplethysmography (PPG) provides valuable information about blood pressure (BP). In this study, we aim to interpret the stochastic PPG patterns with a model-based simulation, which may help optimize the BP estimation algorithms. Methods: The classic four-element Windkessel model is adapted in this study to incorporate BP-dependent compliance profiles. Simulations are performed to generate PPG responses to pulse and continuous stimuli at various timescales, aiming to mimic sudden or gradual hemodynamic changes observed in real-life scenarios. To quantify the temporal complexity of PPG, we utilize the Higuchi fractal dimension (HFD) and autocorrelation function (ACF). These measures provide insights into the intricate temporal patterns exhibited by PPG. To validate the simulation results, continuous recordings of BP, PPG, and stroke volume from 40 healthy subjects were used. Results: Pulse simulations showed that central vascular compliance variation during a cardiac cycle, peripheral resistance, and cardiac output (CO) collectively contributed to the time delay, amplitude overshoot, and phase shift of PPG responses. Continuous simulations showed that the PPG complexity could be generated by random stimuli, which were subsequently influenced by the autocorrelation patterns of the stimuli. Importantly, the relationship between complexity and hemodynamics as predicted by our model aligned well with the experimental analysis. HFD and ACF had significant contributions to BP, displaying stability even in the presence of high CO fluctuations. In contrast, morphological features exhibited reduced contribution in unstable hemodynamic conditions. Conclusion: Temporal complexity patterns are essential to single-site PPG-based BP estimation. Understanding the physiological implications of these patterns can aid in the development of algorithms with clear interpretability and optimal structures.

Keywords: Windkessel model; blood pressure; photoplethysmography; single-site; temporal patterns.

FIGURE 1

Schematics of the proposed simulation method, hypothesis, and experimental verifications. The modified Windkessel model is introduced in detail in Section 2.1, with a simplified assumption of the left ventricular ejection (q _in). Pulse and continuous simulations with different timescales were carried out to locate the origin of complexity patterns.

FIGURE 2

(A) The equivalent circuit of the modified WK4 model. q(t) represents blood flow. C ₁ is time-dependent and varies with central BP. (B) The elastic property of the aorta under different pressures (Langewouters et al., 1984). Aorta1: Am = 3.5 cm², P0 = 50.4 mmHg, P1 = 42.3 mmHg; Aorta2: Am = 6.18 cm², P0 = −2.3 mmHg, P1 = 21.6 mmHg.

FIGURE 3

(A) Continuous q _in fluctuation with SV variation. (B) Definition of an SV pulse stimulus that lasted a cardiac cycle. (C) The simulated PPG response and definition of half width (HW) and overshoot (OS). Simulation parameters were set as follows: A_m = 3.5 cm², P₀ = 50.4 mmHg, P₁ = 42.3 mmHg, T = 0.8 s, α = 1/3, T _s = 0.35 s, CO = 5.95 L/min, C ₂ = 0.1 mL/mmHg, R = 1.4 mmHg s/ml, L = 0.03 mmHg s²/ml. (D) The SV pulse-induced PPG changes. (E) q _in fluctuation within a cardiac cycle. (F) Definition of a “mini” pulse stimulus that lasted for 0.01 s. (G) The simulated PPG response to a “mini” pulse. (H) The “mini” pulse induced PPG changes.

FIGURE 4

(A, B) Random CO and R stimuli using baseline hemodynamic status from subject X1047. (C) Simulated peripheral BP. (D) PPG signals were obtained from personalized P-V translations.

FIGURE 5

(A) ACF of three experimental measurements as examples. M1-3 refers to measurements 1–3. ACF_HW refers to the time lag taken to reach 0.5. (B, C) ln(L) versus ln(1/k). The intercept of the cubic fitting is used for HFD_DC and HFD_AC calculation. (D) ln(L) versus ln(1/k) for HFD_wave calculation.

FIGURE 6

PPG recovery parameters versus hemodynamic status at different CO. (A–C) Half width (HW) of PPG response (D–F) Overshoot of PPG amplitude. The unit for R is “mmHg.s/ml”. The simulation data is presented as “mean ± SD” to accommodate the variations attributed to different C ₂ and L. Here, SD refers to the standard deviation of the data in each bin.

FIGURE 7

Comparison of continuous PPG simulation and experimental results. (A–D) Random stimuli caused complexities and their dependence on hemodynamic status. (E–H) Measured complexities and their dependence on hemodynamic status. The simulation and experimental data are binned and presented as “mean ± SD”.

FIGURE 8

Scaling factor-induced HFD and ACF changes (mean ± SD).

FIGURE 9

Experimental temporal complexity measure distributions and their sensitivity to CO, R, and C ₁. The size of the bubble represented the relative number of measurements. The color represented the complexity measure or gradient value. (A–D) HFD_DC distribution and its sensitivity to hemodynamic parameters. $\partial {HFD}_{DC}/\partial CO$ is locally positive in the 6–8 L/min subregion. (E–H) ACF_HW distribution and its sensitivity to hemodynamic parameters.

FIGURE 10

(A, B) The correlation of PPG features and BP (MAP and PP). “*” indicated a significant difference between groups. Temporal features are in the shaded area. (C, D) Correlation of BP (MAP and PP) estimation and reference with complexity features only, morphology features only, and combined features. “*” indicated a significant difference between low and high CO variation.