Mathematical Modeling of Arterial Blood Pressure Using Photo-Plethysmography Signal in Breath-hold Maneuver

Recent research has shown that each apnea episode results in a significant rise in the beat-to-beat blood pressure and by a drop to the pre-episode levels when patient resumes normal breathing. While the physiological implications of these repetitive and significant oscillations are still unknown, it is of interest to quantify them. Since current array of instruments deployed for polysomnography studies does not include beat-to-beat measurement of blood pressure, but includes oximetry, it is both of clinical interest to estimate the magnitude of BP oscillations from the photoplethysmography (PPG) signal that is readily available from sleep lab oximeters. We have investigated a new method for continuous estimation of systolic (SBP), diastolic (DBP), and mean (MBP) blood pressure waveforms from PPG. Peaks and troughs of PPG waveform are used as input to a 5th order autoregressive moving average model to construct estimates of SBP, DBP, and MBP waveforms. Since breath hold maneuvers are shown to simulate apnea episodes faithfully, we evaluated the performance of the proposed method in 7 subjects (4 F; 32+-4 yrs., BMI 24.57+-3.87 kg/m2) in supine position doing 5 breath maneuvers with 90s of normal breathing between them. The modeling error ranges were (all units are in mmHg) -0.88+-4.87 to -2.19+-5.73 (SBP); 0.29+-2.39 to -0.97+-3.83 (DBP); and -0.42+-2.64 to -1.17+-3.82 (MBP). The cross validation error ranges were 0.28+-6.45 to -1.74+-6.55 (SBP); 0.09+-3.37 to -0.97+-3.67 (DBP); and 0.33+-4.34 to -0.87+-4.42 (MBP). The level of estimation error in, as measured by the root mean squared of the model residuals, was less than 7 mmHg

💡 Research Summary

The manuscript presents a novel, non‑invasive method for estimating beat‑to‑beat arterial blood pressure (BP) during simulated apnea events using only the photoplethysmography (PPG) signal that is routinely recorded in sleep laboratories. Recognizing that polysomnography (PSG) setups typically lack continuous BP monitoring, the authors propose to extract the peaks (systolic surrogates) and troughs (diastolic surrogates) of the PPG waveform and feed them into a fifth‑order autoregressive moving‑average (ARMA) model. The model is trained to predict systolic blood pressure (SBP), diastolic blood pressure (DBP), and mean arterial pressure (MBP) on a beat‑to‑beat basis.

Study Design
Seven healthy volunteers (four females, mean age 32 ± 4 years, BMI 24.6 ± 3.9 kg/m²) participated in a supine breath‑hold protocol designed to mimic obstructive sleep apnea (OSA) episodes. Each subject performed five breath‑holds (BH) of self‑limited duration, separated by 90‑second normal breathing (NB) intervals. Continuous BP was recorded with a Finapres device (gold‑standard beat‑to‑beat measurement) while PPG was captured using a Nellcor OxiMax N‑600x monitor. Both signals were originally sampled at 1000 Hz and down‑sampled to 100 Hz for computational efficiency while preserving physiological dynamics.

Model Development
The authors constructed a single‑input (PPG peak or trough) – single‑output (SBP or DBP) ARMA model of order (na = 5, nb = 5) with a pure time‑delay of k = 5 samples. Model parameters were estimated via ordinary least squares in MATLAB, and the order/delay were selected by minimizing the mean‑squared error (MSE) across all possible combinations, guided by the principle of parsimony. For each BH interval a separate SBP and DBP model was derived, yielding ten subject‑specific models (five for SBP, five for DBP). Estimated MBP was then calculated from the estimated SBP and DBP using the conventional formula MBP = DBP + 1/3(SBP − DBP).

Performance Evaluation
Two error metrics were reported: (1) “model errors” – the difference between measured and estimated BP within the same BH interval, and (2) “cross‑validation errors” – the error when a model trained on one BH interval is applied to a different BH interval. The model errors showed mean ± SD values of approximately –0.9 ± 4.9 mmHg for SBP, 0.3 ± 2.4 mmHg for DBP, and –0.5 ± 2.6 mmHg for MBP across the five BHs. Cross‑validation errors were larger, as expected, but still modest: SBP ranged from 0.28 ± 6.45 to –1.74 ± 6.55 mmHg, DBP from 0.09 ± 3.37 to –0.97 ± 3.67 mmHg, and MBP from 0.33 ± 4.34 to –0.87 ± 4.42 mmHg. The root‑mean‑square errors (rMSE) for model errors were 3.9 mmHg (SBP), 2.4 mmHg (DBP), and 2.4 mmHg (MBP). For cross‑validation, the worst‑case rMSE did not exceed 7 mmHg, a threshold commonly regarded as acceptable for cuff‑less BP estimation.

Interpretation and Context
The results demonstrate that a relatively simple linear time‑invariant ARMA framework can capture both the slow trend (rise and fall of BP during breath‑holds) and the higher‑frequency beat‑to‑beat fluctuations inherent in arterial pressure. Compared with prior pulse‑transit‑time (PTT) approaches, which typically report correlation coefficients around 0.8, the ARMA method yields comparable or slightly superior absolute error performance while requiring only the PPG waveform, without the need for an additional ECG reference. The authors acknowledge that inter‑individual variability in autonomic regulation, vascular compliance, and fluid dynamics may limit the generalizability of a single universal model; thus, subject‑specific calibration appears necessary for optimal accuracy.

Limitations
Key limitations include the small sample size (n = 7), the exclusive use of healthy subjects, and the artificial nature of breath‑holds versus spontaneous obstructive events. Moreover, the duration of each breath‑hold varied across participants, potentially introducing heterogeneity in the training data. The linear ARMA assumption may also be insufficient to capture complex nonlinear cardiovascular dynamics that could become more pronounced in pathological OSA populations.

Future Directions
The authors propose extending the methodology to larger, more diverse cohorts, including patients with diagnosed OSA, and to longer overnight recordings. They also suggest exploring nonlinear modeling techniques (e.g., recurrent neural networks or hybrid ARMA‑machine‑learning models) to improve robustness across subjects and to reduce the need for per‑subject calibration.

Conclusion
In summary, the study provides proof‑of‑concept evidence that beat‑to‑beat systolic, diastolic, and mean arterial pressures can be reliably estimated from the PPG signal alone using a fifth‑order ARMA model during simulated apnea. With an overall error below 7 mmHg, the approach holds promise for augmenting standard PSG with continuous, non‑invasive BP monitoring, potentially enhancing the clinical assessment of cardiovascular risk in sleep‑disordered breathing without additional hardware costs.