Reconstructing the aortic pressure waveform using a hybrid model of variational mode decomposition improved by particle swarm optimization and gated recurrent units

<i>Objective.</i>The aortic pressure waveform (APW) is relevant to diagnosing and treating cardiovascular diseases. While various non-invasive methods for APW estimation exist, more accurate and practical monitoring methods are required. This study introduces a hybrid model combining variational mode decomposition improved by particle swarm optimization (PSO-VMD) and gated recurrent unit (GRU) networks (PSO-VMD-GRU) to reconstruct the APW from the brachial pressure waveform (BPW).<i>Approach.</i>The model was verified using invasive APWs and BPWs. Data synthesis generated additional samples. The synthetic BPWs were decomposed into multiple intrinsic mode functions (IMFs) using PSO-VMD. A GRU was trained to map the relationship between the IMFs and synthetic APWs. The proposed model was evaluated by comparing the mean absolute errors and Spearman's correlation coefficients (SCCs) of reconstructed total waveform (TW) and key hemodynamic indices including systolic, diastolic and pulse pressures (SP, DP and PP, respectively) against those from generalized transfer function (GTF) and other neural network-based methods, including temporal convolutional network (TCN), and bi-directional long short-term memory and self-attention mechanism (CBi-SAN).<i>Main results.</i>Among the four methods, PSO-VMD-GRU achieved the highest SCCs for TW (0.9912) and DP (0.9676), while TCN performed the best for SP (0.9850) and PP (0.9875). In MAE comparisons, PSO-VMD-GRU matched CBi-SAN across TW, SP, DP, and PP, while surpassing GTF in TW (2.44 versus 2.66 mmHg) and DP (1.61 versus 1.94 mmHg), and outperforming TCN in DP (1.61 versus 1.93 mmHg).<i>Significance.</i>Experiment results have shown that integrating PSO-VMD with GRU improves the accuracy of APW reconstruction effectively.