Inferring Optical Tissue Properties from Photoplethysmography using Hybrid Amortized Inference

TL;DR

This work addresses the interpretability gap in PPG-based tissue-property inference by introducing PPGen, a biophysically grounded forward model that maps static and dynamic biophysical parameters to optical tissue properties and then to PPG signals via a differentiable light-transport surrogate. Building on PPGen, Hybrid Amortized Inference (HAI) couples neural posterior estimation of $p(\theta|\mathbf{x}_s)$ with a learned misspecification model $p(\mathbf{x}_s|\mathbf{x}_o)$, enabling fast, robust estimation of physiologically interpretable parameters from real PPG data even under misspecification. In extensive in-silico experiments, HAI demonstrates accurate recovery of biophysical parameters across multiple wavelength configurations and noise conditions, and shows robustness to forward-model misspecifications, with wide-spectrum sensors enhancing identifiability. The framework offers a path toward DL-informed yet physiology-grounded PPG features, supporting clinical interpretation and informed hardware design, while enabling scalable, population-level analyses. Overall, PPGen+HAI provide a principled, scalable approach to extract meaningful cardiovascular and tissue-properties from wearables, potentially bridging the gap between mechanistic modeling and data-driven prediction in photoplethysmography.

Abstract

Smart wearables enable continuous tracking of established biomarkers such as heart rate, heart rate variability, and blood oxygen saturation via photoplethysmography (PPG). Beyond these metrics, PPG waveforms contain richer physiological information, as recent deep learning (DL) studies demonstrate. However, DL models often rely on features with unclear physiological meaning, creating a tension between predictive power, clinical interpretability, and sensor design. We address this gap by introducing PPGen, a biophysical model that relates PPG signals to interpretable physiological and optical parameters. Building on PPGen, we propose hybrid amortized inference (HAI), enabling fast, robust, and scalable estimation of relevant physiological parameters from PPG signals while correcting for model misspecification. In extensive in-silico experiments, we show that HAI can accurately infer physiological parameters under diverse noise and sensor conditions. Our results illustrate a path toward PPG models that retain the fidelity needed for DL-based features while supporting clinical interpretation and informed hardware design.

Figures (10)

• Figure 1: Overview of PPGen, our biophysical forward model for generating synthetic PPG signals. 1. The process starts by sampling a set of biophysical parameters $\theta$ from a prior distribution $\pi(\theta)$. This prior combines dynamic parameters ($\theta_d$), such as blood volume waveforms from a hemodynamics simulator, with static parameters ($\theta_s$), such as melanin fraction and vessel diameters, sampled from literature-informed ranges. 2. These parameters, along with a specific light wavelength ($\lambda$), are given as inputs to a biophysical mapping function, $f_b$, which calculates the optical absorption ($\mu_a$) and scattering ($\mu_s$) coefficients for each skin layer. 3. Subsequently, a light transport model, $\hat{f}_{LT}$ (a neural network surrogate for Monte Carlo simulations), uses these optical coefficients and a given sensor architecture to predict the clean, noiseless PPG signal, $\hat{\mathbf{x}}_s)$. 4. In the final step, a realistic noise model, $p(\mathbf{x}_s \mid \hat{\mathbf{x}}_s)$, adds shot and electronic noise to produce the final synthetic raw sensor reading, $\mathbf{x}_s$. \ref{['alg:PPGen']} in \ref{['app:PPGen']} describes sampling and density evaluation. Appendix \ref{['app:PPGen']} further details each building block of PPGen.
• Figure 2: Identifiability analysis of biophysical parameters under varying noise levels and wavelength configurations. We report the Pearson correlation coefficient between the groundtruths and the values inferred from $\mathbf{x}_s$. For dynamic properties, we report averages of across-time correlation coefficients. We use three random seeds to estimate the variation across different training runs.
• Figure 3: Inferences of blood volume waveforms with a four-wavelength PPG sensor without misspecification at medium noise level. Histograms show the distribution of across-time correlation coefficients between groundtruths and predictions, and the right hand side shows an example waveform pair.
• Figure 4: On the left, Windkessel model relating the arterial pressure wave at the radial artery $P(t)$ to blood volumes in the two layers of the skin $q_2(t)$ and $q_3(t)$. On the right, solution of the Windkessel equations for three different virtual subjects over three cardiac cycles. The shaded area represents the last cardiac cycle, which would be used to extract the blood volumes to use in our model.
• Figure 5: Vizualization of the six noise levels considered in our experiments for a randomly selected four-wavelength measurement. The effect of the noise is mostly noticeable on the normalized AC component of PPG measurements. Nevertheless, it challenges parameter inference as shown in \ref{['fig:clean_results']}.