Temporal Cardiovascular Dynamics for Improved PPG-Based Heart Rate Estimation

TL;DR

This work addresses the challenge of estimating heart rate from PPG signals under real-world noise by recognizing non-linear, chaotic cardiovascular dynamics. It introduces a framework that conditionally models HR from volumetric blood signals while incorporating past HR variations, guided by mutual information concepts and a conditional information-flow objective. The proposed encoder–decoder architecture combines LSTM-based temporal encoding of HR with CNN-based processing of the current signal and uses HR-augmentation to improve generalization. Across four diverse real-world datasets, the method achieves up to 30–45% MAE reduction over prior learning-based approaches while using fewer sensing modalities, demonstrating robust, real-time applicability for wearable-based cardiovascular monitoring.

Abstract

The oscillations of the human heart rate are inherently complex and non-linear -- they are best described by mathematical chaos, and they present a challenge when applied to the practical domain of cardiovascular health monitoring in everyday life. In this work, we study the non-linear chaotic behavior of heart rate through mutual information and introduce a novel approach for enhancing heart rate estimation in real-life conditions. Our proposed approach not only explains and handles the non-linear temporal complexity from a mathematical perspective but also improves the deep learning solutions when combined with them. We validate our proposed method on four established datasets from real-life scenarios and compare its performance with existing algorithms thoroughly with extensive ablation experiments. Our results demonstrate a substantial improvement, up to 40\%, of the proposed approach in estimating heart rate compared to traditional methods and existing machine-learning techniques while reducing the reliance on multiple sensing modalities and eliminating the need for post-processing steps.

Figures (4)

• Figure 1: The heatmap of estimated mutual information between random variables $\boldsymbol{\xi}$ (previous heart rate values) and $Y$ (the current heart rate). We investigated the effect of time (y-axis) and noise (x-axis) for $\boldsymbol{\xi}$ with $\boldsymbol{\xi} = \xi + \sigma \odot \epsilon$ where $\epsilon \sim \mathcal{N}(0, I)$. And, $\boldsymbol{\xi}^N = [y_{t-1},y_{t-2}, \dots, y_{t-N}]$.
• Figure 2: The heatmap of calculated Pearson correlation between random variables $\boldsymbol{\xi}$ (previous heart rate values) and $Y$ (the current heart rate). We investigated the effect of time (y-axis) and noise (x-axis) for $\boldsymbol{\xi}$ with $\boldsymbol{\xi} = \xi + \sigma \odot \epsilon$ where $\epsilon \sim \mathcal{N}(0, I)$. And, $\boldsymbol{\xi}^N = [y_{t}, y_{t-1},y_{t-2}, \dots, y_{t-N}]$.
• Figure 3: Modified encoder-decoder architecture. The encoder part incorporates the HR variations into the model. The decoder outputs the HR by using both the current signal and encoded HR. Black arrows represent the input-output flow while double arrows show the content of a block.
• Figure 4: Bland-Altman and correlation plots. Top row: SPC15-22, bottom row: Dalia. Left column: without learning the heart rate variations, right column: learning variations with $\boldsymbol{\xi}$ vector for the HR estimation. Colors represent subjects.