Non-Invasive Cardiac Output Estimation from PPG Waveform Morphology

Cardiac output -- the volume of blood the heart pumps per minute -- is the fundamental measure of cardiovascular performance, yet its non-invasive measurement remains one of the most technically challenging problems in physiological monitoring. The peripheral PPG waveform carries information about cardiac output encoded in its amplitude, shape, and timing, but extracting quantitative flow estimates from this volumetric signal requires bridging the complex transfer function between central cardiac pump performance and peripheral vascular pulsations.

Cardiac output (CO) monitoring is the cornerstone of hemodynamic management in critical care, anesthesia, and cardiology. The gold standard -- thermodilution via pulmonary artery catheterization -- is invasive, expensive, and carries procedural risk. Semi-invasive alternatives like arterial line pulse contour analysis (PiCCO, FloTrac) require arterial catheterization. Echocardiography provides non-invasive CO measurement but requires skilled operators and is intermittent. A continuous, non-invasive CO monitor based on PPG technology -- sensors already embedded in pulse oximeters and wearable devices -- could democratize hemodynamic monitoring from the ICU to the general ward to the home.

Physiological Foundations

From Cardiac Output to the Peripheral PPG Pulse

Understanding why PPG can potentially estimate cardiac output requires tracing the path from left ventricular ejection to the peripheral pulse waveform.

During each heartbeat, the left ventricle ejects a stroke volume (SV, typically 60-100 mL at rest) into the aorta. This bolus of blood generates a pressure pulse that propagates through the arterial tree at a velocity (pulse wave velocity, PWV) of 5-15 m/s, much faster than the actual blood flow velocity (0.3-0.5 m/s). As the pressure wave traverses the arterial system, it encounters impedance changes at branch points and arterioles, generating reflected waves that travel back toward the heart and interact with the forward-traveling wave.

The PPG sensor at the periphery (finger, wrist, earlobe) detects the net result of this wave propagation process: the volumetric blood pulse in the local microvascular bed. The amplitude, shape, and timing of this pulse carry information about the upstream hemodynamics:

• Pulse amplitude reflects pulse pressure (SBP - DBP), which is related to stroke volume and arterial compliance by the relationship: PP approximately equals SV / C_a, where C_a is total arterial compliance.
• Systolic upstroke slope reflects the rate of aortic pressure rise (dP/dt), which correlates with left ventricular contractility and aortic impedance.
• Diastolic decay reflects the arterial time constant (tau = R x C), the product of systemic vascular resistance (R) and arterial compliance (C).
• Dicrotic notch characteristics reflect aortic valve closure timing, wave reflection magnitude, and the balance between forward and reflected waves.

The central challenge is that the PPG signal is a peripheral volumetric measurement, not a central pressure measurement. The transfer function between aortic pressure/flow and peripheral PPG volume is complex, nonlinear, and modulated by factors independent of cardiac output (peripheral vascular resistance, autonomic vasomotor tone, skin temperature, venous return dynamics).

The Windkessel Model Framework

The Windkessel model provides the standard theoretical framework for relating arterial pressure waveform morphology to cardiac output. The model represents the arterial system as an electrical circuit analog:

Two-Element Windkessel:

• Compliance (C): Elastic energy storage in the arterial walls, primarily the aorta. Analogous to a capacitor.
• Resistance (R): Peripheral vascular resistance from arterioles. Analogous to a resistor.
• The time constant tau = RC governs the diastolic pressure decay: P(t) = P_d * exp(-t/RC), where P_d is the pressure at the beginning of diastole.

Three-Element Windkessel: Adds characteristic impedance (Z_c) of the aorta in series, improving the systolic pressure peak fit:

• Z_c captures the impedance to pulsatile flow in the proximal aorta.
• This addition separates the effects of aortic impedance (affecting systolic peak shape) from peripheral resistance (affecting diastolic decay).

Four-Element Windkessel: Adds arterial inertance (L) representing blood mass inertia:

• Inertance affects the high-frequency components of the pressure waveform.
• Generally provides marginal improvement over the three-element model for CO estimation.

By fitting a Windkessel model to the arterial pressure or PPG waveform, the model parameters (R, C, Z_c) can be estimated. Cardiac output is then derived from:

CO = MAP / R

where MAP is mean arterial pressure and R is peripheral resistance estimated from the model fit. Alternatively, stroke volume can be estimated from the systolic area of the waveform and the compliance parameter.

Pulse Contour Methods for CO Estimation

The Systolic Area Method

The foundational pulse contour method for stroke volume estimation was proposed by Wesseling et al. (1983), who showed that stroke volume is proportional to the area under the systolic portion of the arterial pressure waveform, corrected for aortic impedance (DOI: 10.1007/BF02450538):

SV = k * A_sys / Z_ao

where A_sys is the systolic area (from pulse onset to the dicrotic notch), Z_ao is aortic impedance (estimated from patient demographics -- age, sex, height, weight -- or from the pulse waveform itself), and k is a calibration constant.

This principle underlies the commercial PiCCO (Pulsion Medical Systems) and FloTrac (Edwards Lifesciences) systems, which use invasive arterial line pressure waveforms. Adapting this to non-invasive PPG requires addressing two additional challenges: (1) the PPG waveform measures volume, not pressure, so the area relationship must account for the pressure-volume compliance curve; and (2) the PPG measurement site (finger, wrist) is far from the aorta, so wave transmission effects must be considered.

PPG Pulse Contour Analysis

Wang et al. (2009) demonstrated that PPG-derived pulse contour features correlate with echocardiographic stroke volume in 36 healthy volunteers during passive leg raising (a preload challenge). The systolic area of the finger PPG pulse correlated with echo-derived SV with r = 0.72 (DOI: 10.1088/0967-3334/30/12/003). The correlation improved to r = 0.81 when the PPG systolic area was normalized by the diastolic decay time constant, which accounts for changes in peripheral resistance.

Reisner et al. (2008) provided a comprehensive review of pulse contour CO methods applied to non-invasive signals, noting that uncalibrated PPG-based methods typically achieve percentage errors of 30-50% for absolute CO values, but perform better for tracking relative changes (percentage error 15-25% for delta-CO) (DOI: 10.1097/ALN.0b013e3181a96a8e). The distinction between absolute accuracy and trending ability is clinically important: many hemodynamic management decisions require knowing the direction and magnitude of CO changes in response to interventions (fluid bolus, vasopressor titration) rather than the absolute CO value.

Modified Liljestrand-Zander Method

Liljestrand and Zander (1928) proposed estimating pulse pressure from the ratio of systolic to diastolic areas of the arterial waveform. Adapting this to PPG, the stroke volume index can be estimated as:

SVI proportional to (A_sys - A_dia) / (A_sys + A_dia)

where A_sys and A_dia are the areas above and below the mean level of the PPG pulse. This ratio is less sensitive to absolute signal amplitude calibration because it normalizes by the total pulse area. Mukkamala et al. (2006) evaluated this approach with finger PPG, finding correlation of r = 0.68 with thermodilution-derived SV in 15 cardiac surgery patients (DOI: 10.1109/TBME.2006.883792).

Machine Learning Approaches

Feature-Based Models

Classical ML approaches extract hand-crafted features from the PPG waveform and train regression models to predict stroke volume or cardiac output.

Saugel et al. (2020) catalogued the PPG features most relevant to CO estimation (DOI: 10.1007/s10877-019-00386-4). Key features include:

• Systolic upstroke time and slope: Reflects rate of ventricular ejection and aortic impedance.
• Pulse width at various amplitude levels (25%, 50%, 75%): Captures the overall pulse shape, which changes with stroke volume and vascular tone.
• Diastolic decay time constant: Estimated by fitting an exponential to the diastolic portion; reflects the RC time constant of the arterial system.
• Augmentation index (AI): The ratio of the reflected wave amplitude to the forward wave amplitude; reflects wave reflection magnitude and arterial stiffness.
• Pulse area ratios: Systolic area, diastolic area, and their ratio.
• First and second derivative features: Peak values and timing of the first derivative (dPPG) and second derivative (ddPPG/acceleration plethysmogram) provide information about cardiac contractility and arterial stiffness.

Shin et al. (2020) trained a random forest model using 42 PPG morphological features to estimate stroke volume index (SVI, stroke volume normalized by body surface area), achieving r = 0.78 and MAE of 7.3 mL/m^2 against echocardiographic reference in 62 subjects during graded exercise (DOI: 10.1016/j.bspc.2020.101911). When combined with PPG-derived heart rate for CO calculation, the estimated CO correlated with reference CO at r = 0.82 with a mean percentage error of 28%.

Deep Learning on Raw PPG

Deep learning models can learn to extract CO-relevant features directly from raw PPG waveforms. This approach may capture subtle waveform characteristics that are not captured by traditional hand-crafted features.

Gonzalez-Landaeta et al. (2023) applied a 1D ResNet to 10-second PPG segments for stroke volume estimation, achieving r = 0.76 and mean percentage error of 32% against echocardiographic reference in 85 subjects from a multi-center study. The model was trained with data augmentation (amplitude scaling, temporal stretching, additive noise) to improve robustness to PPG signal variability.

Lee et al. (2022) developed a CNN-LSTM architecture that processes 30-second PPG windows, capturing both intra-beat morphological features (via CNN) and inter-beat temporal patterns (via LSTM). The temporal component captures respiratory-induced stroke volume variation and other slow hemodynamic oscillations. The model achieved CO estimation with r = 0.81 and mean percentage error of 26% in 48 cardiac surgery patients, using pulse contour (FloTrac) as reference.

Transfer Learning and Domain Adaptation

A key challenge for deep learning CO estimation is the limited availability of paired PPG-cardiac output training data. Most reference CO measurements (thermodilution, echocardiography) are obtained in hospital settings with different PPG hardware than consumer wearables.

Cano et al. (2022) proposed a transfer learning approach where a model is first pre-trained on the large MIMIC-III dataset for blood pressure estimation (which shares many relevant waveform features with CO estimation) and then fine-tuned on a smaller dataset with CO reference values. The pre-training step improved CO estimation accuracy by 15% compared to training from scratch, demonstrating that learned PPG representations transfer across hemodynamic estimation tasks.

Validation Against Reference Methods

Thermodilution (Gold Standard)

Pulmonary artery catheter thermodilution provides intermittent CO measurements with a precision of approximately 10-15% (coefficient of variation of repeated measurements). The Bland-Altman framework is the standard for evaluating agreement between a new method and thermodilution:

• Bias: Mean difference between methods. Acceptable bias is typically less than 0.5 L/min.
• Limits of agreement (LOA): Mean +/- 1.96 SD of differences. Should be within +/- 1.5 L/min for clinical acceptability.
• Percentage error: LOA / mean reference CO. Critchley and Critchley (1999) proposed that a percentage error below 30% indicates clinical equivalence with thermodilution, accounting for the reference method's own imprecision (DOI: 10.1046/j.1365-2044.1999.00684.x).

No published PPG-based CO estimation method has consistently achieved the 30% percentage error threshold in diverse clinical populations. The best results (25-30% percentage error) have been obtained in controlled settings with calibrated systems and homogeneous patient populations.

Echocardiography

Transthoracic echocardiography (TTE) provides non-invasive CO measurement via Doppler velocity-time integral (VTI) across the aortic valve. While less precise than thermodilution (typical coefficient of variation 8-15%), TTE is widely available and non-invasive, making it a practical reference for ambulatory PPG validation studies.

Studies comparing PPG-based CO estimates to echocardiographic reference typically report correlations of r = 0.65-0.85 and percentage errors of 25-45%, with better performance for trending ability than absolute accuracy.

Clinical Applications and Future Directions

Goal-Directed Fluid Therapy

One of the most impactful potential applications of non-invasive CO monitoring is goal-directed fluid therapy (GDFT) during surgery. GDFT uses real-time CO or SV monitoring to guide intravenous fluid administration, optimizing tissue perfusion while avoiding fluid overload. Meta-analyses show that GDFT reduces postoperative complications by 20-30% compared to standard fluid management (Pearse et al., 2014; DOI: 10.1001/jama.2014.5305).

Currently, GDFT requires an arterial line with pulse contour analysis or esophageal Doppler, limiting its use to high-risk surgeries in major medical centers. A PPG-based CO monitor integrated into a standard pulse oximeter could extend GDFT to a much broader surgical population, potentially improving outcomes for millions of patients annually.

Stroke Volume Variation for Fluid Responsiveness

Stroke volume variation (SVV) -- the percentage change in stroke volume across the respiratory cycle -- is a validated predictor of fluid responsiveness in mechanically ventilated patients. SVV above 12-15% predicts a positive CO response to fluid administration with sensitivity of 79-88% and specificity of 85-93% (Marik et al., 2009; DOI: 10.1097/CCM.0b013e3181a590da).

PPG-derived SVV can be estimated from the respiratory-induced amplitude variation (RIAV) of the pulse waveform. Cannesson et al. (2008) demonstrated that PPG-derived plethysmographic variability index (PVI, now commercially available in Masimo monitors) predicts fluid responsiveness with an area under the ROC curve of 0.85 in 25 mechanically ventilated patients (DOI: 10.1213/ane.0b013e31816c4682). This represents one of the most clinically mature applications of PPG-based hemodynamic estimation, as it requires only relative (not absolute) stroke volume measurement.

For more on how respiratory modulations of the PPG signal encode hemodynamic information, see our article on PPG respiratory rate estimation. Our algorithms reference provides foundational signal processing methods relevant to pulse contour analysis, and our overview of cardiovascular conditions provides clinical context for hemodynamic monitoring applications. For preprocessing requirements, our guide to PPG motion artifact removal covers the signal quality considerations essential for reliable waveform morphology analysis.

Wearable Hemodynamic Monitoring

Looking further ahead, continuous CO estimation from wrist PPG could enable longitudinal hemodynamic tracking for heart failure patients. Serial changes in resting CO, exercise CO response, and nocturnal hemodynamic patterns could provide early warning of decompensation, enabling preemptive medication adjustment and reducing hospital readmissions. This application requires only accurate trending (detecting changes from an individual baseline) rather than absolute CO measurement, which plays to the relative strengths of PPG-based methods.

The convergence of improved PPG sensor hardware (multi-wavelength arrays, improved skin coupling), advanced signal processing for motion artifact removal, and deep learning models trained on growing databases of paired PPG-hemodynamic data suggests that clinically useful non-invasive CO estimation from PPG is an achievable near-term goal, likely first in controlled clinical settings (operating room, ICU) and eventually in ambulatory and wearable applications.

References

• Cannesson, M. et al. (2008). Anesthesia & Analgesia. DOI: 10.1213/ane.0b013e31816c4682
• Critchley, L.A. and Critchley, J.A.J.H. (1999). Anaesthesia. DOI: 10.1046/j.1365-2044.1999.00684.x
• Marik, P.E. et al. (2009). Critical Care Medicine. DOI: 10.1097/CCM.0b013e3181a590da
• Mukkamala, R. et al. (2006). IEEE Transactions on Biomedical Engineering. DOI: 10.1109/TBME.2006.883792
• Pearse, R.M. et al. (2014). JAMA. DOI: 10.1001/jama.2014.5305
• Reisner, A. et al. (2008). Anesthesiology. DOI: 10.1097/ALN.0b013e3181a96a8e
• Saugel, B. et al. (2020). Journal of Clinical Monitoring and Computing. DOI: 10.1007/s10877-019-00386-4
• Wang, L. et al. (2009). Physiological Measurement. DOI: 10.1088/0967-3334/30/12/003
• Wesseling, K.H. et al. (1983). Intensive Care Medicine. DOI: 10.1007/BF02450538