PPG Waveform Decomposition: Extracting Physiological Components from the Pulse Wave
The photoplethysmography waveform is not a simple cardiac pulse but a composite signal encoding information about cardiac function, vascular compliance, respiratory mechanics, autonomic nervous system activity, and peripheral hemodynamics. Decomposing this complex waveform into its constituent components unlocks clinical and physiological insights far beyond basic heart rate. This article examines the physiological origins of each PPG waveform component, the mathematical methods used to extract them, and the diagnostic potential of component-level analysis.
For background on how the PPG signal is generated and its basic characteristics, see our introduction to PPG technology.
Anatomy of the PPG Pulse Wave
A single PPG pulse cycle contains several morphological features, each carrying distinct physiological information. Understanding these features at the waveform level is the prerequisite for meaningful decomposition.
The Systolic Phase
The systolic phase begins at the foot of the pulse (the diastolic minimum) and rises to the systolic peak. This ascending limb represents the arrival of the arterial pressure wave at the measurement site, driven by left ventricular ejection. The slope of the systolic upstroke is determined by the rate of pressure rise in the arterial system, which depends on cardiac contractility, stroke volume, and proximal arterial compliance.
The maximum slope (maximum first derivative) of the systolic upstroke occurs approximately one-third of the way up the rising edge and correlates with the rate of pressure change (dP/dt) in the ascending aorta. Millasseau et al. (2002; DOI: 10.1161/01.HYP.0000016921.97657.A2) demonstrated significant correlation (r = 0.71, p < 0.001) between the maximum slope of the digital PPG pulse and invasively measured aortic dP/dt in 31 patients undergoing cardiac catheterization.
The Dicrotic Notch
The dicrotic notch is a small but physiologically significant dip that appears on the descending limb of the PPG pulse, separating the systolic and diastolic phases. It corresponds temporally to aortic valve closure and the subsequent brief retrograde flow in the aorta. In the peripheral PPG signal, the notch also encodes information about the reflected pressure wave returning from the lower body vasculature.
The visibility and timing of the dicrotic notch depend strongly on arterial compliance, peripheral vascular resistance, and measurement site. At the fingertip, where the signal amplitude is highest, the dicrotic notch is typically well-defined in healthy young adults but diminishes with age, hypertension, and atherosclerosis. Dawber et al. (1973) established that the dicrotic notch becomes progressively less distinct after age 40-50 in most individuals. At the wrist, the dicrotic notch is often attenuated or absent even in young subjects due to the lower signal quality in reflectance mode.
The Diastolic Phase
After the dicrotic notch, the diastolic phase represents the gradual runoff of blood from the arterial system through peripheral resistance vessels during cardiac relaxation. The diastolic decay rate follows an approximately exponential curve, with the time constant determined by the product of arterial compliance and peripheral resistance (the Windkessel time constant, tau = RC).
The diastolic time constant can be extracted from the PPG waveform by fitting an exponential function to the diastolic decay segment. Liu et al. (2013; DOI: 10.1088/0967-3334/34/3/359) showed that this time constant correlates with total peripheral resistance (r = 0.65, n = 42 subjects) and changes systematically with vasoactive interventions.
Multi-Component Signal Model
The total PPG signal can be conceptualized as the sum of several physiological components operating at different time scales. This multi-component model provides the framework for decomposition.
DC Component (Baseline)
The largest portion of the PPG signal (typically 95-99% of total light absorption) is the DC or non-pulsatile component. This represents steady-state light absorption by skin pigmentation (melanin), tissue matrix, non-pulsatile venous blood, and steady-state arterial blood volume. The DC component is not clinically uninteresting: changes in venous blood volume, tissue edema, and skin perfusion all modulate the DC level. However, because the DC component is dominated by non-vascular absorption and is sensitive to sensor placement and contact pressure, extracting reliable physiological information from it requires careful calibration.
AC Cardiac Component (0.5-4 Hz)
The pulsatile cardiac component, oscillating at the heart rate frequency and its harmonics, represents the primary signal of interest in most PPG applications. This component has a typical amplitude of 1-2% of the DC level at the fingertip and 0.1-0.5% at the wrist. The cardiac AC component contains the morphological features described above: systolic upstroke, peak, dicrotic notch, and diastolic decay.
The harmonic content of the cardiac component is itself informative. A fundamental-only pulse (pure sinusoid) would indicate a highly damped vascular system, while a pulse rich in harmonics indicates sharp waveform features associated with wave reflections and preserved vascular compliance. Fourier analysis of individual pulses typically reveals 4-8 significant harmonics, with the relative harmonic amplitudes changing with arterial stiffness and age (Millasseau et al., 2002).
Respiratory Component (0.15-0.5 Hz)
Respiration modulates the PPG signal through three distinct mechanisms, each contributing to a respiratory component in the 0.15-0.5 Hz band.
First, respiratory-induced intrathoracic pressure changes modulate venous return, which in turn affects stroke volume through the Frank-Starling mechanism. This produces beat-to-beat amplitude modulation of the PPG pulse. During inspiration, reduced intrathoracic pressure increases venous return, which (after a 1-2 beat delay) increases stroke volume and PPG pulse amplitude. Lázaro et al. (2013; DOI: 10.1016/j.medengphy.2013.02.004) extracted respiratory rate from the PPG amplitude envelope with mean absolute error of 1.2 breaths per minute compared to chest impedance in 35 subjects.
Second, respiration modulates heart rate through respiratory sinus arrhythmia (RSA), producing baseline frequency modulation of the pulse intervals. This component can be extracted from the IBI time series as described in our guide to PPG inter-beat interval measurement.
Third, changes in intrathoracic pressure directly affect peripheral arterial pressure, causing baseline wander in the PPG signal. This mechanism is most apparent during deep breathing or mechanical ventilation, where the baseline modulation can approach 5-10% of the AC amplitude.
Sympathetic/Vasomotor Component (0.04-0.15 Hz)
Low-frequency oscillations in vascular smooth muscle tone, known as Mayer waves or vasomotor waves, produce oscillations in the PPG baseline and amplitude at approximately 0.1 Hz (roughly a 10-second cycle). These oscillations reflect baroreflex-mediated sympathetic nervous system modulation of peripheral vascular resistance and are of interest in autonomic function assessment.
Nitzan et al. (1994; DOI: 10.1007/BF02348079) characterized these low-frequency PPG oscillations and showed their correlation with sympathetic nerve activity measured by microneurography. The amplitude of the vasomotor component in the PPG signal increases during sympathetic activation (e.g., cold pressor test, orthostatic stress) and decreases with sympathetic blockade, confirming its autonomic origin.
Thermoregulatory and Very Low Frequency Components (< 0.04 Hz)
Very slow oscillations in the PPG baseline reflect thermoregulatory vasoconstriction-vasodilation cycles, which operate on time scales of minutes. These components are relevant for long-duration PPG recordings but are typically filtered out in standard cardiac monitoring applications.
Mathematical Decomposition Methods
Several mathematical frameworks have been applied to separate PPG waveform components, each with distinct strengths and physiological interpretability.
Gaussian Decomposition
The PPG pulse can be modeled as a sum of Gaussian functions, where each Gaussian represents a physiological sub-wave. The forward-traveling systolic wave is modeled as a primary Gaussian centered near the systolic peak. Reflected waves from major arterial bifurcation sites (renal, iliac, aortic) are modeled as additional Gaussians arriving at later times.
Rubins (2008; DOI: 10.1007/978-3-540-89208-3_328) demonstrated that 3-5 Gaussian components are typically sufficient to reconstruct a PPG pulse with residual errors below 2% of peak amplitude. The timing and amplitude parameters of each Gaussian carry physiological meaning: the delay between the primary and reflected wave Gaussians relates to pulse wave velocity and arterial path length, while the amplitude ratio encodes the reflection coefficient of the peripheral vasculature.
Wang et al. (2013; DOI: 10.1088/0967-3334/34/11/1541) extended this approach with a multi-Gaussian model using 4 components and validated it against invasive aortic pressure measurements, finding that the model parameters could predict central systolic blood pressure with mean error of 3.2 mmHg (n = 58 patients). This relates directly to emerging approaches in cuffless blood pressure estimation.
Empirical Mode Decomposition (EMD)
EMD adaptively decomposes the PPG signal into a set of intrinsic mode functions (IMFs) without requiring predefined basis functions. Each IMF represents an oscillatory component at a characteristic time scale, extracted through an iterative sifting process.
For PPG signals, EMD typically produces the following hierarchy of IMFs. IMF1 captures high-frequency noise and sensor artifacts. IMF2-3 contain the cardiac pulse waveform details. IMF4-5 capture the respiratory modulation. IMF6-7 represent the sympathetic/vasomotor oscillations. Higher-order IMFs and the residual represent very slow trends and the DC component.
Garde et al. (2013; DOI: 10.1109/TBME.2013.2246160) applied EMD to PPG signals from 29 children during anesthesia and extracted respiratory rate from IMF4-5 with mean absolute error of 2.1 breaths per minute. The advantage of EMD over fixed-frequency filtering is its ability to track non-stationary respiratory patterns where the breathing rate varies over time.
The limitation of EMD is mode mixing, where components from different physiological sources contaminate the same IMF. Ensemble EMD (EEMD), which averages multiple EMD decompositions with added white noise, partially addresses this problem (Wu & Huang, 2009; DOI: 10.1142/S1793536909000047).
Wavelet Decomposition
The discrete wavelet transform (DWT) decomposes the PPG signal into approximation and detail coefficients at multiple resolution levels. Each level corresponds to a specific frequency band, allowing separation of cardiac, respiratory, and vasomotor components based on their characteristic frequencies.
For a PPG signal sampled at 125 Hz, the typical wavelet decomposition levels align as follows. Level 1-2 details (31-62 Hz) capture high-frequency noise. Level 3-4 details (8-31 Hz) contain cardiac harmonic content. Level 5 details (2-4 Hz) capture the fundamental cardiac component. Level 6 details (1-2 Hz) overlap cardiac and respiratory bands. Level 7-8 details (0.24-1 Hz) contain respiratory modulation. Level 9-10 details (0.06-0.24 Hz) capture sympathetic oscillations.
Addison (2005; DOI: 10.1088/0967-3334/26/5/R01) provided a comprehensive review of wavelet methods for physiological signal analysis, including specific applications to PPG decomposition. The choice of mother wavelet affects the decomposition quality, with the Daubechies-4 (db4) and symlet-4 (sym4) wavelets commonly used for PPG due to their morphological similarity to the pulse waveform.
Second Derivative Analysis (SDPPG)
The second derivative of the PPG waveform, known as the acceleration plethysmogram (APG) or SDPPG, provides an alternative decomposition into characteristic wave components labeled a, b, c, d, and e. The a-wave represents initial systolic positive acceleration. The b-wave represents systolic negative acceleration (early systolic deceleration). The c-wave is a mid-systolic re-acceleration related to the reflected wave. The d-wave is a late systolic deceleration. The e-wave represents early diastolic acceleration after the dicrotic notch.
Takazawa et al. (1998; DOI: 10.1038/hr.1998.82) demonstrated that the ratios b/a, c/a, d/a, and e/a change systematically with age and correlate with arterial stiffness indices. In a study of 600 subjects aged 20-79, the b/a ratio increased progressively with age (r = 0.72, p < 0.001), reflecting the age-related increase in arterial stiffness and earlier arrival of reflected waves. The composite aging index (b-c-d-e)/a showed even stronger age correlation (r = 0.81) and has been proposed as a non-invasive vascular aging biomarker.
For more on how waveform analysis algorithms are implemented in PPG processing pipelines, see our algorithms documentation.
Forward and Reflected Wave Separation
A particularly informative decomposition separates the PPG pulse into its forward-traveling (incident) wave and backward-traveling (reflected) wave components. The forward wave originates from cardiac ejection, while the reflected wave returns from peripheral impedance mismatches, primarily at major arterial bifurcations.
Wave Separation Analysis
Westerhof et al. (2006; DOI: 10.1097/01.hjh.0000199108.29331.5c) developed wave separation analysis (WSA) for arterial pressure waveforms, which has been adapted for PPG. The method assumes that the measured PPG waveform is the superposition of a forward wave Pf and a reflected wave Pb:
The forward and reflected components can be estimated using the characteristic impedance of the arterial segment and the flow waveform. For PPG, where direct flow measurement is not available, the forward-reflected separation is approximated using waveform modeling approaches that fit the measured pulse as a sum of sub-waves with constrained temporal relationships.
Augmentation Index
The augmentation index (AIx) quantifies the contribution of the reflected wave to the systolic peak. It is defined as the difference between the second and first systolic peaks (or the systolic peak and the inflection point) divided by the pulse pressure. Higher AIx values indicate greater wave reflection and are associated with arterial stiffness, increased cardiovascular risk, and aging.
Millasseau et al. (2006; DOI: 10.1161/01.HYP.0000239206.64989.e0) validated finger PPG-derived AIx against carotid tonometry in 50 subjects and found moderate correlation (r = 0.61, p < 0.001), though the absolute values differed due to peripheral amplification effects. The PPG-derived reflection index (RI), calculated as the diastolic peak amplitude divided by the systolic peak amplitude, provides a simpler alternative that is less sensitive to waveform calibration.
Clinical Applications of Waveform Decomposition
PPG waveform decomposition has enabled several clinical applications beyond basic heart rate and SpO2 monitoring. These applications represent the cutting edge of non-invasive cardiovascular assessment.
Respiratory Rate Estimation
Extracting the respiratory component from decomposed PPG signals enables continuous, contactless respiratory rate monitoring. This is particularly valuable in clinical settings where dedicated respiratory monitoring equipment is not available. Charlton et al. (2018; DOI: 10.1088/1361-6579/aa670e) systematically evaluated 314 respiratory rate algorithms applied to PPG signals and found that the best-performing methods achieved mean absolute errors of 1.0-2.5 breaths per minute under controlled conditions.
Arterial Stiffness Assessment
The timing and amplitude of the reflected wave component provide non-invasive indices of arterial stiffness. The stiffness index (SI), calculated as body height divided by the time delay between systolic and diastolic peaks, estimates pulse wave velocity in the lower body. Millasseau et al. (2002) validated SI against carotid-femoral PWV with correlation r = 0.65 in 87 subjects. While not replacing clinical PWV measurement, PPG-derived stiffness indices enable longitudinal tracking and screening.
Cardiac Output Estimation
The amplitude and area of the systolic component of the decomposed PPG waveform correlate with stroke volume. Mukkamala et al. (2015; DOI: 10.1146/annurev-bioeng-071813-105544) reviewed PPG-based cardiac output estimation methods and found that pulse contour analysis of the PPG waveform can estimate cardiac output changes with correlation coefficients of r = 0.7-0.85 compared to thermodilution, though absolute accuracy remains insufficient for clinical decision-making.
Conclusion
PPG waveform decomposition transforms a seemingly simple pulse signal into a rich source of cardiovascular and autonomic information. The mathematical methods available, from Gaussian fitting to wavelet analysis to SDPPG, offer complementary perspectives on the underlying physiology. The key challenge remains ensuring that decomposition results are robust to the signal quality limitations of real-world PPG measurement, including motion artifacts, sensor contact variability, and inter-individual morphological differences. As computational methods improve and multi-wavelength PPG sensors become standard, the clinical utility of waveform-level analysis will continue to expand.
For deeper exploration of PPG signal processing and analysis methods, visit our algorithms reference and PPG learning center.