Deep Learning-Enabled Diagnosis of Abdominal Aortic Aneurysm Using Pulse Volume Recording Waveforms: An In Silico Study

Figures

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  Figure 1. Mathematical model for the generation of physiologically plausible arterial blood pressure (BP) waveform and pulse volume recording (PVR) signals. The mathematical model is composed of a multi-branch transmission line (TL) model of systemic arterial circulation and viscoelastic models relating arterial BP to PVR at brachial and tibial arteries. HR: heart rate. SV: stroke volume. l: length of a TL. r: radius of a TL. h: thickness of a TL. RT: terminal resistance of a peripheral load. CT: terminal compliance of a peripheral load. E: Young’s modulus of a TL. AAA: abdominal aortic aneurysm. lAAA: ratio of AAA length to the length of TL31. TL31: TL pertaining to the abdominal aorta between right renal artery and inferior mesenteric artery. ASL: relative increase in maximum luminal area. KE: scaling coefficient for Young’s modulus pertaining to AAA wall. PB: brachial BP. PT: tibial BP. YB: brachial PVR. YT: Tibial PVR. IIV: inter-individual variability. N: normal distribution.

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  Figure 2. Convolutional neural network (CNN) architecture and its training based on the continuous property-adversarial regularization (CPAR) method, described in Equations (4) and (5). The network processes vertically concatenated brachial and tibial arterial blood pressure (BP) or pulse volume recording (PVR) waveforms through five convolutional layers with a skip connection, two attention modules (CBAM), and a compression phase, yielding latent features of size (32 × 2 × 64). These features are passed to three regressor heads: one for abdominal aortic aneurysm (AAA) volumetric severity index (VSI) estimation and two adversarial regressors for continuous property-adversarial regularization, enforcing invariance to subject height and age. Blue and red arrows show the flow of the input data and gradients in training, respectively.

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  Figure 3. Illustration of the three waveform-derived features evaluated in this study. (a) Carotid upstroke index (CUI): the foot-to-peak interval of the carotid arterial blood pressure (BP) waveform is divided at the optimized intersection point (filled dot), least-squares lines are fitted to the two upstroke regions, and CUI is calculated as the ratio of the peak-to-intersection amplitude to the pulse pressure. (b) Carotid area ratio (CAR): the systolic (dotted) and diastolic (hatched) areas under the carotid arterial BP waveform are calculated, and CAR is calculated as the diastolic area divided by the systolic area. (c) Carotid oscillatory ratio (COR): the carotid arterial BP waveform is transformed into the frequency domain after mean subtraction, and COR is calculated as the ratio of spectral energy in the high-frequency band (defined as 3–8 times the fundamental frequency = HR/60) to that in the low-frequency band (defined as 0–3 times the fundamental frequency).

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  Figure 4. Age-related changes in key hemodynamic parameters. (a) Synthetic results from the age-adjusted arterial circulation model, where arterial geometry (length and radius), stiffness, peripheral resistance and compliance, and stroke volume were made age-dependent using the empirical equations reported in a prior work [25]. (b) Corresponding age-related trends from in vivo measurements reported in a prior work [25]. Solid lines represent mean values across patients, while the filled areas indicate ±1 standard deviation. SBP: systolic blood pressure. PP: pulse pressure. PWV: carotid–femoral pulse wave velocity. PP amplification is measured between aorta and brachial artery.

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  Figure 5. Effect of abdominal aortic aneurysm (AAA) on simulated pulse volume recording (PVR) and arterial blood pressure (BP) waveforms pertaining to a 70-year-old subject with nominal physiological parameters: (1st row) carotid arterial BP, (2nd row) brachial PVR, (3rd row) femoral arterial BP, and (4th row) tibial PVR. Each column corresponds to a different arterial tree stiffness (E): reduced stiffness ((a), 0.8 × E), nominal stiffness ((b), E), and elevated stiffness ((c), 1.6 × E). In each plot, three waveforms are shown: healthy (solid blue), 50% expansion in maximum TL31 diameter (dashed orange), and 100% expansion in maximum TL31 diameter (dash-dotted red). Key waveform features are annotated in carotid and femoral arterial BP panels: carotid upstroke index (CUI), carotid area ratio (CAR), and carotid–femoral pulse wave velocity (PWV). The results demonstrate how AAA changes upstream and downstream arterial BP and PVR waveforms.

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  Figure 6. Frequency-domain analysis of arterial blood pressure waveforms in the presence of abdominal aortic aneurysm (AAA) for a 70-year-old subject with nominal physiological parameters. (top) Amplitude spectra of mean-subtracted carotid arterial blood pressure. (bottom) Amplitude spectra of mean-subtracted femoral arterial blood pressure. Each column corresponds to a different arterial stiffness: reduced stiffness ((a), 0.8 × E), nominal stiffness ((b), E), and elevated stiffness ((c), 1.6 × E). In each plot, three waveforms are shown: healthy (solid blue), 50% expansion in maximum TL31 diameter (dashed orange), and 100% expansion in maximum TL31 diameter (dash-dotted red). The carotid oscillatory ratio (COR) is annotated in the upper row. Frequency is normalized to the heart rate fundamental (f0 = HR/60 Hz). The results demonstrate how AAA alters harmonic content and energy distribution in upstream and downstream arterial blood pressure waveforms.

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  Figure 7. Correlation between abdominal aortic aneurysm (AAA) volumetric severity index and four representative arterial BP waveform features in the test data: (a) carotid–femoral pulse wave velocity (PWV), (b) carotid upstroke index, (c) carotid area ratio, and (d) carotid oscillatory ratio. Pearson correlation coefficients (ρ) are shown in each panel. The results highlight how morphological features in the arterial blood pressure waveforms are influenced by AAA severity. All reported correlations are statistically significant (p < 0.05).

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  Figure 8. Comparison of abdominal aortic aneurysm (AAA) severity estimation performance of the deep learning-enabled AAA diagnosis algorithm using arterial blood pressure waveforms (DL-ABP) versus pulse volume recording waveforms (DL-PVR). Solid lines show the mean predicted value across the 10 independently trained CNNs for each true-severity bin (5–15%, 15–25%, …, 85–95%), shaded areas indicate their ±1 standard deviation, and the dashed diagonals denote the ideal response (y = x). Pearson correlation coefficient (ρ), mean absolute error (MAE), and root-mean-squared error (RMSE) are computed per CNN on the test data and then summarized as mean ± standard deviation (MAE and RMSE reported in %VSI).

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  Figure 9. Accuracy, F1 score, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) values associated with DL-enabled arterial BP waveform analysis (DL-ABP) vs. DL-enabled PVR waveform analysis (DL-PVR) at 20–80% AAA severity levels as the labeling threshold. The metrics were computed with the classifier threshold set equal to the labeling threshold. Note that the labeling threshold controls how positive and negative classes are defined in the dataset (a case is labeled positive if VSI exceeds the labeling threshold and negative otherwise).

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  Figure 10. Receiver operating characteristic plots (ROCs) and precision–recall curves (PRCs) associated with DL-enabled arterial BP waveform analysis (DL-ABP) vs. DL-enabled PVR waveform analysis (DL-PVR) at 30%, 50%, and 70% AAA severity levels as the labeling threshold (i.e., the VSI thresholds used to define positive versus negative cases). The area under the curve (AUC) value is annotated in each plot. Solid lines represent the average, while shaded areas represent the standard deviation across 10 tests. The gray dashed line in the ROC plots represents a classifier with no discriminative ability, and in the PRC plots it marks the baseline precision expected from random guessing (equal to the prevalence of positives). Note that the labeling threshold sets the ground truth (a case is labeled positive if VSI exceeds the labeling threshold and negative otherwise). Once this ground truth is fixed, we compute ROC and PRC by sweeping the classifier’s decision threshold over the algorithm’s predicted VSI values and, at each decision threshold, we record both true positive rate and false positive rate for ROC and both precision and recall for PRC. In other words, the labeling threshold controls…