Peripheral Artery Disease Diagnosis Based on Deep Learning-Enabled Analysis of Non-Invasive Arterial Pulse Waveforms

Abstract

This paper intends to investigate the feasibility of peripheral artery disease (PAD) diagnosis based on the analysis of non-invasive arterial pulse waveforms. We generated realistic synthetic arterial blood pressure (BP) and pulse volume recording (PVR) waveform signals pertaining to PAD present at the abdominal aorta with a wide range of severity levels using a mathematical model that simulates arterial blood circulation and arterial BP-PVR relationships. We developed a deep learning (DL)-enabled algorithm that can diagnose PAD by analyzing brachial and tibial PVR waveforms, and evaluated its efficacy in comparison with the same DL-enabled algorithm based on brachial and tibial arterial BP waveforms as well as the ankle-brachial index (ABI). The results suggested that it is possible to detect PAD based on DL-enabled PVR waveform analysis with adequate accuracy, and its detection efficacy is close to when arterial BP is used (positive and negative predictive values at 40% abdominal aorta occlusion: 0.78 vs 0.89 and 0.85 vs 0.94; area under the ROC curve (AUC): 0.90 vs 0.97). On the other hand, its efficacy in estimating PAD severity level is not as good as when arterial BP is used (r value: 0.77 vs 0.93; Bland-Altman limits of agreement: −32%-+32% vs −20%-+19%). In addition, DL-enabled PVR waveform analysis significantly outperformed ABI in both detection and severity estimation. In sum, the findings from this paper suggest the potential of DL-enabled non-invasive arterial pulse waveform analysis as an affordable and non-invasive means for PAD diagnosis.

1. Introduction

Peripheral artery disease (PAD) is highly prevalent in the United States with 12.4% average prevalence between 2003–2012 [1], afflicting 8–10 million patients [2] which is predicted to increase to 19 million by 2050 [3]. PAD is associated with deteriorated quality of life, hospitalization and amputation risks, and mortality risk with >30% mortality rate within 5 years of diagnosis [4]. Screening and early diagnosis can reduce morbidity and mortality risks [5]. However, PAD is underdiagnosed due to the lack of awareness [6] as well as knowledge of symptoms and complications.

Conventional gold standard methods for PAD diagnosis are imaging-based techniques [7]–[9], which can provide definitive detection of the presence of atherosclerosis (including its location and severity). However, imaging-based diagnosis is often invasive as well as requires trained experts and expensive imaging equipment. The most widely used non-invasive and imaging-free diagnosis is ankle-brachial index (ABI). In clinical practice, ABI=<0.9 is commonly used as threshold to diagnose PAD [10], [11]. In some work, ABI appears to be used to define the PAD severity level: borderline (0.90–0.99), low-normal (1.0–1.09), and normal (1.10–1.29) [11]. PAD may also be diagnosed by symptoms, such as leg pain [10] and impaired walking endurance [12]–[14] (which may be attributed to the deteriorated blood perfusion in the extremity muscles). Notably, lower ABI values are associated with an increase in leg pain [10]. However, leg pain is not sensitive nor specific to PAD [10]. Hence, the trustworthiness of the ABI technique remains controversial [15]. In summary, there is an urgent need for convenient and accurate alternatives for PAD diagnosis.

Recently, there is an increasing interest in PAD diagnosis by exploiting arterial pulse waveform analysis. PAD forms occlusions in the arteries, which in turn alters pulse wave propagation and reflection characteristics in the arteries subject to PAD, thereby resulting in the alterations in the morphology of arterial BP and blood flow waveforms [16]. Prior works include a support vector machine (SVM) classifier based on frequency response functions [17], various machine learning (ML) classifiers based on Fourier series coefficients of arterial blood pressure (BP) and blood flow waveforms [18], [19], and deep learning (DL) analysis of arterial BP waveforms [20], [21]. All these prior investigations clearly suggest the promise of ML-enabled arterial pulse waveform analysis for PAD diagnosis. However, these prior efforts have a common shortcoming: that they used arterial BP and blood flow waveforms, which cannot be measured affordably and conveniently. Indeed, gold standard reference method to measure arterial BP is invasive, expensive, and risky catheterization. Existing non-invasive methods to measure arterial BP and blood flow include artery tonometry [22], volume clamping method [23], and ultrasound, all of which require trained experts and expensive equipment. To widely deploy PAD diagnosis based on arterial pulse waveform analysis, a technological leap must be made to realize arterial pulse waveform analysis with affordable, convenient, and non-invasive measurement modalities.

This paper intends to investigate the feasibility of PAD diagnosis based on the analysis of non-invasive arterial pulse waveforms called pulse volume recording (PVR) signals, which are non-invasive arterial volume pulse waveform signals that can be easily measured using low-cost BP cuff devices [24]. To achieve our goal, we generated realistic synthetic arterial BP and PVR waveform signals pertaining to PAD at the abdominal aorta with a wide range of severity levels using a mathematical model that simulates arterial blood circulation and arterial BP-PVR relationships. We developed a DL-enabled algorithm that can diagnose PAD by analyzing brachial and tibial PVR waveforms, and evaluated its efficacy in comparison with the same DL-enabled algorithm based on invasive brachial and tibial arterial BP waveforms as well as the ABI.

This paper is organized as follows. Section 2 describes the mathematical model used and the details of synthetic data generation as well as the DL-enabled PVR waveform analysis algorithm for PAD diagnosis. Section 3 presents key results, which are discussed in Section 4. Section 5 concludes the paper.

2. Methods

2.1. Data Generation

As a basis to develop and evaluate a deep learning (DL)-enabled non-invasive arterial pulse waveform analysis algorithm for peripheral artery disease (PAD) diagnosis, we generated a large number of physiologically plausible synthetic arterial pulse waveform signals (including arterial blood pressure (BP) and pulse volume recording (PVR)) pertaining to a wide range of PAD severity levels. For this purpose, we used a multi-branch transmission line (TL) model of arterial blood circulation and viscoelastic models relating arterial BP to PVR at brachial and tibial arteries (Fig. 1).

Fig. 1:

Mathematical model for generation of physiologically plausible arterial BP waveform and pulse volume recording (PVR) signals. The mathematical model is composed of a multi-branch transmission line (TL) model of arterial blood circulation and viscoelastic models relating arterial BP to PVR at brachial and tibial arteries.

2.1.1. Generation of Arterial BP Waveform Signals

We generated a large number of synthetic arterial BP waveform signals using a multi-branch TL model of arterial blood circulation developed and validated in a prior work [25], [26] (Fig. 1), by randomly perturbing arterial anatomical and biomechanical parameters therein from their nominal values. The TL model is composed of 55 TL segments, each representing an artery segment characterized by segment-specific viscous, elastic, and inertial properties. The TL model was previously validated with physiological measurements and the results of other studies, and was successfully employed in prior investigations related to arterial viscoelasticity, arterial stenosis, and PAD diagnosis [17], [20], [21], [25], [27].

First, we generated synthetic patients by simulating inter-individual variability (IIV) in arterial geometry and stiffness. We perturbed the length, stiffness, diameter, and thickness of all the arteries as well as resistances associated with terminal arteries. Existing literature suggests that no persistent dependency among these parameters exists. Hence, we perturbed these parameters randomly and independently. We perturbed arterial length so that the overall arterial length is compatible with 162–198cm in height (+/−10% perturbation with respect to a nominal height of 180cm). We perturbed arterial diameter, thickness, and terminal load resistance parameters up to +/−20% of their nominal values. Then, we perturbed arterial stiffness so that the range of pulse wave velocity (PWV) observed in hypertensive adults of 50–60 years in age (systolic BP>160mmHg and diastolic BP>100mmHg; PWV 4.8–15.1m/s) [28] can be replicated by the multi-branch TL model. Using the multi-branch TL model, PWV can be calculated by dividing the difference between the aorto-femoral arterial length and the aorto-carotid arterial length by the foot-to-foot time delay between carotid and femoral arterial BP waveforms [29]. Combined with the IIV associated with arterial diameter, thickness, and peripheral load resistances, perturbing arterial stiffness in the range of −60%-+350% around its nominal value resulted in PWV in the range of 4.4–15.8m/s.

Second, in each synthetic patient, we generated random variability in arterial anatomical and biomechanical characteristics by simulating intra-individual uncertainty (IIU). Specifically, we modeled IIU pertaining to the above 5 arterial anatomical and biomechanical parameters as lognormal distributions with subject-specific (i.e., nominal plus IIV) values as mean values and coefficient of variation of 0.01. Then, we generated random samples from these subject-specific distributions to simulate IIU.

Third, in each synthetic patient subject to IIU, we simulated PAD by including occlusion at the abdominal aorta (proximal PAD). To increase PAD severity level, we decreased the diameter of the abdominal aorta from its nominal value. We defined the PAD severity level as the degree of area occlusion: 0% when normal, and 100% when fully occluded.

Then, we assigned these IIV, IIU, and PAD severity parameters to the multi-branch TL model and simulated it to generate a wide range of synthetic arterial BP waveform signals (including those at brachial and tibial arteries).

2.1.2. Generation of Brachial and Tibial Pulse Volume Recording Signals

We generated synthetic brachial and tibial PVR waveform signals using the synthetic brachial and tibial arterial BP waveform signals (see Section 2.1.1) and viscoelastic models relating arterial BP to PVR at brachial and tibial arteries developed in a prior work [24] (Fig. 1). From the viscoelastic model parameters associated with real patients analyzed in [24], we inferred probability density functions describing the multi-dimensional distributions of these parameters, generated random samples from these probability density functions, and generated synthetic PVR waveform signals by inputting the synthetic arterial BP waveform signals (see Section 2.1.1) into the viscoelastic models parameterized with these samples.

First, we inferred the probability density functions pertaining to the viscoelastic model parameters using the viscoelastic model parameters associated with the real patients derived from their arterial BP and PVR data based on system identification trials in our prior work [24]. We used the parameter values determined for (i) the standard linear solid (SLS) model at the brachial artery (N=124) and (ii) the Voigt model at the tibial artery (N=99):

$$Y_B(s)=\frac{E_{B2}+{\eta }_{B}s}{E_{B1}{E}_{B2}+\left(E_{B1}+E_{B2}\right){\eta }_{B}s}{P}_B(s),Y_T(s)=\frac{1}{E_T+{\eta }_{T}s}{P}_T(s)$$ (1)

where Y_B and Y_T are brachial and tibial PVR signals, respectively, P_B and P_T are brachial and tibial arterial BP signals, respectively, and s is the Laplace variable. For each PVR location, we transformed the viscoelastic model parameter data into orthogonal components using the principal component analysis (PCA). Then, we approximated each of the orthogonalized viscoelastic model parameter data into probability density functions. This process resulted in two univariate Gaussian density functions and one univariate Rayleigh density function pertaining to the SLS model parameters at the brachial artery (E_B1, E_B2, and η_B) and two univariate Gaussian density functions pertaining to the Voigt model parameters at the tibial artery (E_T and η_T).

Second, we generated synthetic viscoelastic models to replicate the viscoelastic arterial BP-PVR relationships in a synthetic patient by (i) generating a random sample (which includes 3 brachial SLS model parameters and 2 tibial Voigt model parameters) from the orthogonalized univariate probability density functions and (ii) transforming the sample back to the original viscoelastic parameter space.

Third, we generated random variability in the viscoelastic model pertaining to a synthetic patient by simulating IIU. Specifically, we modeled IIU pertaining to the viscoelastic model parameters as lognormal distributions with subject-specific (i.e., the sampled parameters in the above step) values as mean values and coefficient of variation of 0.01. Then, we generated random samples from these subject-specific distributions to simulate IIU.

Then, we assigned the parameters thus sampled to the viscoelastic models pertaining to each synthetic patient subject to IIU and then simulated them (by inputting the corresponding synthetic arterial BP waveform signals) to generate synthetic brachial and tibial PVR waveform signals.

2.1.3. Data Summary

We generated synthetic arterial BP and PVR waveform signals to train and test the DL-enabled PAD diagnosis algorithm as follows. First, we generated training data by (i) randomly sampling 70 synthetic patients based on the aforementioned IIV, (ii) randomly choosing a PAD severity level (within the range of 0%−80%) and viscoelastic model parameters individually for all the synthetic patients, (iii) randomly sampling 100 IIUs in each synthetic patient (including viscoelastic model parameters) based on the aforementioned IIU, and (v) simulating the multi-branch TL-viscoelastic model repeatedly 7,000 (=70×100) times to generate synthetic arterial BP and PVR waveform signals pertaining to all the synthetic patients subject to all the IIUs. The resulting 7,000 arterial BP and PVR waveform signals along with the corresponding PAD severity levels and arterial anatomical and biomechanical parameters formed the training data to develop the DL-enabled PVR waveform analysis algorithm for PAD diagnosis.

Second, we generated validation data in the same way as described above. The resulting 7,000 (=70×100) arterial BP and PVR waveform signals along with the corresponding PAD severity levels and arterial anatomical and biomechanical parameters formed the validation data. We used the validation data to tune the hyperparameters in the DL algorithm.

Third, we generated test data by sampling synthetic patients associated with a large number of IIV and IIU as well as PAD severity levels. 1) We generated nominal synthetic patients characterized by a wide range of arterial anatomical and biomechanical parameters (IIV): 5 lengths (−10%, −5%, 0%, +5%, +10% perturbations from nominal lengths) × 5 diameters (−20%, −10%, 0, +10%, +20% perturbations from nominal diameters) × 5 thicknesses (−20%, −10%, 0, +10%, +20% perturbations from nominal thicknesses) × 5 terminal load resistances (−20%, −10%, 0, +10%, +20% perturbations from nominal terminal resistances) × 32 stiffnesses (−60%, −50%, … +340%, +350% perturbations from nominal stiffnesses) = 20,000 nominal synthetic patients, each combined with randomly sampled viscoelastic model parameters from the probability density functions in Section 2.1.2 and 17 PAD severity levels (0%, 5%, … 80%). 2) For each synthetic patient, we generated 10 random samples based on the lognormal distributions representing IIU. Then, we simulated the multi-branch TL-viscoelastic model repeatedly 3,400,000 (=5×5×5×5×32×17×10) times to generate synthetic arterial BP and PVR waveform signals pertaining to all the synthetic patients subject to all the IIUs. The resulting 3,400,000 arterial BP and PVR waveform signals along with the corresponding PAD severity levels and arterial anatomical and biomechanical parameters formed the test data. The rationale behind generating a large-size test data was to extensively evaluate the feasibility of DL-enabled PAD diagnosis based on PVR waveform signals relative to arterial BP waveform signals.

It is noted that we sampled the arterial geometry and stiffness parameters (Section 2.1.1) and the viscoelastic model parameters (Section 2.1.2) independently. However, the viscoelasticity associated with the BP-PVR relationships may be governed by both arterial viscoelasticity and tissue viscoelasticity. Hence, arterial geometry and stiffness parameters and viscoelastic model parameters may be correlated with each other, especially if arterial viscoelasticity is the dominating factor of the viscoelastic model parameters. Regardless, we did not consider such correlations in our sampling of these parameters, which implies that our sampling may have been conservative (i.e., a subset of samples may represent physiologically unrealistic model parameter combinations). To prevent any adverse impact of our conservative sampling, we examined all the synthetic data we generated and ascertained that all the synthetic data used in our analysis appear to be at least visually sensical.

2.2. Peripheral Artery Disease Diagnosis Algorithm

To enable PAD diagnosis based on non-invasive arterial pulse waveforms, we extended our prior work on PAD diagnosis based on DL-enabled arterial BP waveform analysis. In the algorithm, PAD is diagnosed by analyzing brachial and tibial PVR waveforms using a convolutional neural network (CNN) trained with the continuous property-adversarial regularization (CPAR) method developed in our prior work [21].

We adopted the AlexNet [30], which includes 5 convolutional layers for feature extraction and 3 fully connected layers for label prediction (Fig. 2). We formed input to the CNN by concatenating brachial and tibial PVR waveform signals into a single channel. We set the kernel size of the 5 convolutional layers to 96×1×5, 256×1×3, 384×1×3, 384×1×3, and 256×1×3, respectively. In this way, the 2-dimensional structure of the input (i.e., brachial and tibial PVR waveform signals) could be maintained while features could be extracted separately from the two PVR signals efficiently using shared kernels. We included 64, 64, and 1 neuron(s) in the fully connected layers so as to reduce the complexity of the AlexNet considering the simplicity of our classification task based on two 1-dimensional signals.

Fig. 2:

Convolutional neural network (CNN) architecture and its training based on the continuous property-adversarial regularization (CPAR) method.

The resulting AlexNet still included approximately 3 million parameters to be trained in its feature extraction and label prediction layers, making it vulnerable to overfitting. Hence, we enforced two regularization measures. First, we included batch normalization layers after each convolutional layer (except after the first convolutional layer). Second, we regularized feature extraction using the CPAR method developed in our prior work [21], which discourages the extraction of features influenced by confounding disturbances influencing the morphology of PVR waveform signals. In this way, the CPAR method promotes the extraction of features influenced only by PAD severity level. As was done in our prior work [21], we regularized feature extraction against arterial length and arterial stiffness (which exert large influences on the morphology of arterial pulse waveforms among all the disturbances due to arterial anatomical and biomechanical characteristics [31]) using subject height and PWV as surrogate measures. Based on the CPAR method, we trained the CNN using the following cost functions (Fig. 2):

$$\begin{gathered} {\theta }_l^{\ast }=\text{arg}\underset{{\theta }_l}{\text{min}}{L}_L\left({\theta }_f,{\theta }_l\right) \\ {\theta }_{\eta ,H}^{\ast }=\text{arg}\underset{{\theta }_{\eta ,H}}{\text{min}}{L}_{D,H}\left({\theta }_f,{\theta }_{\eta ,H}\mid H\right) \\ {\theta }_{\eta ,V}^{\ast }=\text{arg}\underset{{\theta }_{\eta ,V}}{\text{min}}{L}_{D,V}\left({\theta }_f,{\theta }_{\eta ,V}\mid V\right) \\ {\theta }_f^{\ast }=\text{arg}\underset{{\theta }_f}{\text{min}}{L}_L\left({\theta }_f,{\theta }_l\right)+\lambda \frac{1}{L_{D,H}\left({\theta }_f,{\theta }_{\eta ,H}\mid H\right)+L_{D,V}\left({\theta }_f,{\theta }_{\eta ,V}\mid V\right)} \end{gathered}$$ (2)

where θ_l, θ_η,H, θ_η,V, and θ_f are the trainable parameters in the label prediction layer, disturbance domain regression layer associated with height (H) and PWV (V), and feature extraction layer, respectively; L_L(θ_f, θ_l), L_D,H(θ_f, θ_η,H|H), and L_D,V (θ_f, θ_η,v|V) are the loss functions pertaining to label prediction as well as disturbance domain regression associated with height (H) and PWV (V), respectively; and λ is the regularization weight that modulates the strength of CPAR relative to label prediction. We defined the loss functions as follows:

$$\begin{gathered} L_L\left({\theta }_f,{\theta }_l\right)=\frac{1}{N}\sum _{i=1}^N{\left(y_i-G_l\left(G_f\left(x_i\right)\right)\right)}^2 \\ {L}_{D,H}\left({\theta }_f,{\theta }_{\eta ,H}\mid H\right)=\frac{1}{N}\sum _{i=1}^N\text{log}\left(\frac{1}{1-\text{tanh}\left|H_i-G_{\eta ,H}\left(G_f\left(x_i\right)\right)\right|}\right) \\ {L}_{D,V}\left({\theta }_f,{\theta }_{\eta ,V}\mid V\right)=\frac{1}{N}\sum _{i=1}^N\text{log}\left(\frac{1}{1-\text{tanh}\left|V_i-G_{\eta ,V}\left(G_f\left(x_i\right)\right)\right|}\right) \end{gathered}$$ (3)

where G_l(∙), G_η,H(∙), G_η,V(∙), and G_f(∙) are the mappings pertaining to the label prediction layer (to predict label from features), disturbance domain regression layers associated with height (H) and PWV (V) (to regress features to disturbances), and feature extraction layer (to extract features from input), respectively.

We trained the CNN using the ADAM algorithm and the training data and validation data described in Section 2.1. We used a hyperparameter optimization method called Optuna [32] to optimize the hyperparameters associated with (2)-(3), which include the parameters in the ADAM algorithm, the CPAR regularization weight λ, and the batch size. To obtain robust results, we repeated the data generation and training procedures 10 times to derive 10 CNNs, which were subsequently used to test the efficacy of the PAD diagnosis algorithm based on PVR waveform analysis (see Section 2.3).

To compare the efficacy of PVR-based PAD diagnosis with arterial BP-based PAD diagnosis, we repeated the above training procedure using brachial and tibial arterial BP waveform signals. We adopted the identical AlexNet structure, while we used distinct hyperparameter values in training this benchmark algorithm to optimize its efficacy.

2.3. Data Analysis

To probe the feasibility of PAD diagnosis based on DL-enabled analysis of PVR waveform signals, we compared arterial BP and PVR waveform signals at brachial and tibial arteries. For direct comparison of the two signals, we calibrated PVR signals using mean and diastolic BP levels pertaining to the corresponding arterial BP signals. We used (i) systolic peak, (ii) pulse amplitude, (iii) crest time (time interval between diastolic trough and systolic peak), (iv) pulse width at half amplitude, and (v) the degree of diastolic oscillations measured in terms of the sum of absolute time derivative values of the signal in the diastole. It is well known in the literature that as far as arterial BP signal is concerned, (i) systolic peak and pulse amplitude decreases, (ii) crest time and pulse width at half amplitude increases, and (iii) diastolic oscillation decreases as PAD severity level increases [33]–[38]. Hence, we analyzed PVR signals to determine if these trends persist in them.

We evaluated the efficacy of our CPAR-trained, DL-enabled PVR waveform analysis-based PAD diagnosis algorithm in terms of its ability to detect PAD and assess PAD severity level using the test data described in Section 2.1. We repeatedly evaluated the efficacy of the algorithm using the 10 CNNs pertaining to PVR and arterial BP, respectively. Then, we reported the efficacy of the algorithm in terms of the aggregated (i.e., averaged) performance obtained from the 10 tests.

Our metrics to quantitatively assess the efficacy of the algorithm included (i) sensitivity, specificity, accuracy, positive predictive value (PPV), negative predictive value (NPV), F1 score, and area under the receiver operating characteristic (ROC) curve (AUC) as measures of PAD detection and (ii) correlation coefficient and Bland-Altman limits of agreement between actual vs CNN-predicted PAD severity level as measures of PAD severity level assessment. In evaluating the detection efficacy, we used 20%, 30%, 40%, 50%, and 60% PAD severity levels as the PAD labeling thresholds in order to analyze how the detection efficacy varies as the PAD labeling threshold increases. We computed these metrics pertaining to both PVR-based and arterial BP-based algorithms and compared their PAD detection and severity level assessment performance.

In addition to comparing DL-enabled PVR waveform analysis-based algorithm with its arterial BP-based counterpart, we also compared it with the conventional ABI technique. To ensure objective and fair comparison, we mapped ABI value to PAD severity level using a second-order polynomial regression model, which was pre-constructed using training data.

3. Results

Fig. 3 shows nominal arterial blood pressure (BP) waveforms at brachial and tibial arteries and the corresponding pulse volume recording (PVR) waveforms at 0% and 80% peripheral artery disease (PAD) severity levels. Table 1 compares morphological features in tibial arterial BP and PVR signals. As PAD severity level increases, tibial PVR signal exhibits (i) decreases in systolic peak and pulse amplitude, (ii) increases in crest time and pulse width at half amplitude, and (iii) a decrease in diastolic oscillation (Fig. 3 and Table 1), which all are generally anticipated PAD-induced changes in tibial arterial BP signal. However, the viscoelasticity associated with the arterial wall and the tissues had a large influence on the morphology of PVR signals relative to arterial BP signals (Fig. 3). For both 0% and 80% PAD severity levels, tibial arterial BP and PVR signals in particular show that (i) systolic peak and pulse amplitude decreased, (ii) crest time and pulse width at half amplitude increased (meaning that the signal became blunter), and (iii) the oscillations in the signals during diastole decreased (meaning that the signal became smoother) in tibial PVR signal compared to tibial arterial BP signal, owing perhaps to the dampening effect originating from the viscoelasticity (Table 1). In addition, crest time and pulse width at half amplitude exhibited larger variability in PVR signal relative to arterial BP signal (Table 1).

Fig. 3:

Nominal arterial BP waveforms at brachial and tibial arteries and the corresponding PVR waveforms at 0% and 80% severity levels. The shaded areas associated with the PVR signals represent the variability associated with the inter-individual variability of the viscoelastic model in Eq. (1).

Table 1:

Comparison of morphological features in tibial arterial BP and PVR signals with respect to the change in PAD severity level from 0% to 80%. PVR was calibrated using mean and diastolic BP at tibial artery. Ranges are expressed in [Q1, Q3] across all synthetic test data.

	Tibial arterial BP	Tibial PVR
Systolic Peak [mmHg]	[140, 174] → [133, 167]	[136, 169] → [131, 164]
Pulse Amplitude [mmHg]	[77, 102] → [67, 098]	[72, 98] → [65, 96]
Crest Time [ms]	[109, 125] → [125, 156]	[125, 156] → [141, 188]
Pulse Width at Half Amplitude [ms]	[230, 250] → [245, 258]	[241, 264] → [249, 273]
Diastolic Oscillation [mmHg/s]	[55, 69] → [44, 57]	[46, 61] → [38, 52]

Fig. 4 shows receiver operating characteristic (ROC) curves associated with deep learning (DL)-enabled PVR waveform analysis, DL-enabled arterial BP waveform analysis, and ABI at 20%, 40%, and 60% PAD severity level as the labeling threshold. Fig. 5 shows sensitivity, specificity, accuracy, positive predictive value (PPV), negative predictive value (NPV), and F1 score values associated with DL-enabled PVR waveform analysis, DL-enabled arterial BP waveform analysis, and ankle-brachial index (ABI) at 20%−60% PAD severity levels as the labeling threshold. The area under the ROC curve (AUC) value pertaining to DL-enabled PVR waveform analysis was consistently high (>=0.89) and comparable to DL-enabled arterial BP waveform analysis (>=0.96) while was much higher than ABI (<=0.59). The accuracy value remained consistently high (>0.8). However, the sensitivity exhibited degradation as PAD labeling threshold increased, whereas the specificity exhibited degradation as PAD labeling threshold decreased. PPV (>=0.78) and NPV (>=0.85) were both reasonably high and robust against PAD labeling threshold. The F1 value was adequate but showed a decreasing trend as PAD labeling threshold increased, due to the sensitivity.

Fig. 4:

ROC curves associated with DL-enabled PVR waveform analysis (“DL-PVR”), DL-enabled arterial BP waveform analysis (“DL-ABP”), and ankle-brachial index (“ABI”) at 20%, 40%, and 60% PAD severity level as the labeling threshold. Lines represent average, while shaded areas represent standard deviation across 10 tests.

Fig. 5:

Sensitivity, specificity, accuracy, PPV, NPV, and F1 score values associated with DL-enabled PVR waveform analysis (“DL-PVR”) and DL-enabled arterial BP waveform analysis (“DL-ABP”) at 20%−60% PAD severity levels as the labeling threshold.

Fig. 6 shows the PAD severity estimation accuracy of DL-enabled PVR waveform analysis, DL-enabled arterial BP waveform analysis, and ABI, in the form of (a) correlation plot and (b) Bland-Altman plot. The correlation coefficient (r) value pertaining to DL-enabled PVR waveform analysis was adequately high on the average (0.77). But, it was 16% lower on the average than its arterial BP waveform counterpart. In addition, the Bland-Altman limits of agreement were largely wider than its arterial BP waveform counterpart (>70%). On the other hand, the r value pertaining to DL-enabled PVR waveform analysis was much higher than its ABI counterpart. In addition, the Bland-Altman limits of agreement were likewise much narrower. Specifically, the PAD severity level estimated by ABI was practically random (r≈0) and suffered from large limits of agreement (60% larger than DL-enabled PVR waveform analysis).

Fig. 6:

PAD severity estimation accuracy of DL-enabled PVR waveform analysis, DL-enabled arterial BP waveform analysis, and ABI, in the form of (a) correlation plot and (b) Bland-Altman plot.

4. Discussion

Peripheral artery disease (PAD) is a highly prevalent disease in the United States with profound implications on the quality of life, hospitalization and amputation risks, and mortality risk. Regardless, it is underdiagnosed due to the lack of awareness and knowledge as well as affordable and convenient yet accurate methods for screening and diagnosis. Recent advances in PAD diagnosis based on arterial blood pressure (BP) and blood flow waveform signals show promise. However, these methods are not ideal because the measurement of arterial BP and blood flow waveform signals is invasive and/or costly. Hence, there is a need to enable PAD diagnosis using affordable, convenient, and non-invasive arterial pulse waveform signals. This paper intends to investigate the feasibility of PAD diagnosis based on the analysis of non-invasive arterial pulse waveforms called pulse volume recording (PVR) signals, which can be easily measured using low-cost BP cuff devices.

4.1. Feasibility of PAD Diagnosis via PVR Waveform Analysis

The investigation of PVR waveform signals relative to the corresponding arterial BP waveform signals revealed both challenges and feasibility associated with PAD diagnosis based on PVR waveform analysis. On the one hand, the alteration in the signal morphology (Fig. 3, Table 1) combined with larger variability (especially in crest time and pulse width at half amplitude) may present challenges in enabling PAD diagnosis based on the analysis of PVR waveform signals relative to the analysis of arterial BP waveform signals. On the other hand, the same investigation also showed promise in exploiting PVR waveform signals for PAD diagnosis. Indeed, all the anticipated morphological changes in tibial arterial BP signal due to PAD were also observed in tibial PVR signal (Fig. 3, Table 1). These observations imply that PAD diagnosis based on PVR waveform analysis may be feasible, although it may not be as effective as PAD diagnosis based on arterial BP waveform analysis.

4.2. Efficacy of DL-Enabled PVR Waveform Analysis-Based PAD Diagnosis

As we anticipated in Section 4.1, despite the challenges associated with the viscoelasticity-induced alteration of arterial BP waveforms to PVR waveforms, our results suggest that PAD may be detected reasonably well with deep learning (DL)-enabled analysis of PVR waveforms. In particular, the PAD diagnosis decisions made by DL-enabled PVR waveform analysis are highly correct (as indicated by positive predictive value (PPV) and negative predictive value (NPV); Fig. 5). In addition, its overall accuracy is high (as indicated by the accuracy values; Fig. 5) with adequate sensitivity-specificity trade-off across a wide range of PAD labeling threshold values (Fig. 4). Notably, these promising findings were robust against PAD labeling threshold. On the other hand, DL-enabled PVR waveform analysis showed a non-ideal trade-off between sensitivity and specificity: (i) it can miss PAD patients when PAD labeling threshold is high (sensitivity degraded as PAD labeling threshold increased), while (ii) it can incorrectly diagnose normal subjects (i.e., subjects not having PAD or those having PAD with severity lower than PAD labeling threshold) as PAD patients when PAD labeling threshold is low (specificity decreased as PAD detection labeling decreased). Due to its dependence on sensitivity, F1 score likewise showed degradation as PAD labeling threshold increased. On the one hand, the test data is balanced only at 40% PAD labeling threshold. Hence, the low values of sensitivity and specificity at the extreme PAD labeling threshold values may not be as concerning as they appear, because they are derived from relatively a small number of samples (e.g., sensitivity is assessed using only 24% of the test data samples when PAD labeling threshold is 60%, and as well, specificity is assessed using only 29% of the test data samples when PAD labeling threshold is 20%). On the other hand, the decreasing trend in F1 score (which is a commonly used classification performance metric when data are unbalanced) with respect to an increase in PAD labeling threshold value is clearly a weakness. Regardless, high F1 score at low PAD labeling thresholds as well as consistently high accuracy across a wide range of PAD labeling thresholds is still promising, considering that an ideal PAD labeling threshold required for real-world deployment of a PAD diagnosis algorithm must be low in order to enable early identification of PAD patients before PAD progresses to a severe level.

The performance of DL-enabled PVR waveform analysis was qualitatively comparable to DL-enabled arterial BP waveform analysis. But, the metrics pertaining to the former were lower than those pertaining to the latter (Fig. 5), which may not be surprising and may be attributed to the viscoelasticity associated with the arterial wall and the tissues altering the morphology of PVR waveform and increasing its variability relative to arterial BP waveform (Table 1). But, the degree of degradation in the metrics was not large. As an example, at 40% PAD labeling threshold, specificity, PPV, and F1 score were approximately 10% lower, while the other metrics showed even smaller degradation. In addition, DL-enabled PVR waveform analysis outperformed ankle-brachial index (ABI) by a large amount, whose metrics at 40% PAD labeling threhosld were only marginally higher than 50% on the average. Our analysis to better understand the relatively abysmal performance of the ABI showed that the ABI value showed noticeable decrease from its nominal value of 1.1 only when PAD severity level was high, reaching 1.0 at 80% PAD severity level and 0.9 at 90% PAD severity level (not shown). Hence, ABI may be effective in diagnosing PAD only when PAD severity is high. In fact, our finding is consistent with a previous report showing that the accuracy of ABI in PAD diagnosis is deteriorated at low PAD severity levels [39]. All in all, the results of this paper demonstrate the promise of PAD detection based on non-invasive arterial pulse waveform signals such as PVR signals.

In contrast to its efficacy in PAD detection, DL-enabled PVR waveform analysis modestly underperformed its arterial BP waveform analysis counterpart in PAD severity estimation (Fig. 6). Most notably, DL-enabled PVR waveform analysis exhibited the tendency to overestimate the severity at low PAD severity levels and underestimate the severity at high PAD severity levels. This tendency was responsible for the degradation of sensitivity and F1 score at high PAD labeling threshold as well as the degradation of specificity at low PAD labeling threshold mentioned earlier in this section (Fig. 5). The same tendency was observed in DL-enabled arterial BP waveform analysis, but to a lesser degree. However, DL-enabled PVR waveform analysis largely outperformed ABI. ABI, even with the aid of the pre-constructed ABI-PAD severity mapping, could not estimate PAD severity due to its limited sensitivity to PAD with low severity levels. DL-enabled PVR waveform analysis could estimate PAD severity more accurately than ABI at all the PAD severity levels considered in this work (i.e., 20%−60%).

All in all, the results of this paper suggest that DL-enabled analysis of non-invasive arterial pulse waveform signals may have value in detecting PAD as well as relatively modest value in assessing its severity level. Noting that being able to confidently detect PAD, especially when its severity level is relatively low, is an advantage (since patients can be referred to more definitive imaging-based tests to confirm the presence and quantify the severity level of PAD while its severity is still low), DL-enabled non-invasive arterial pulse waveform analysis may find a role in affordable and convenient PAD diagnosis.

4.3. Study Limitations

An important limitation of our work is that the investigation was conducted using synthetic in silico data created using a mathematical model. The validity and utility of the mathematical model used in this work, especially in the context of PAD, was shown in prior work [17], [20], [21], [25], [27]. In addition, considering that it is costly and time-consuming to collect and analyze clinical data to validate disease diagnosis algorithms, it is reasonable to conduct preliminary investigation using credible synthetic data. However, DL-enabled PVR waveform analysis algorithm must ultimately be validated using clinical data. In this regard, this work must be regarded as an initial proof-of-concept study that strongly supports follow-up in vivo investigations. Another limitation of our work is that DL-enabled PVR waveform analysis was not as good as its arterial BP waveform counterpart in PAD severity estimation. Although DL-enabled PVR waveform analysis (and more generally, DL-enabled non-invasive arterial pulse waveform analysis) may still be valuable in early and preliminary diagnosis of PAD for more definitive tests, future work to improve its ability to estimate PAD severity will be undoubtedly rewarding. Many potential solutions may exist. However, given that the modest degradation in PAD severity estimation associated with DL-enabled PVR waveform analysis may be due to the distortion of arterial BP waveform caused by the arterial and tissue viscoelasticity, one promising approach may be to infer brachial and tibial arterial BP waveforms from PVS signals at the corresponding locations, e.g., via novel system identification methods [40]. In addition to mitigating the adverse influence of viscoelasticity-induced artifacts in PAD diagnosis, inferring arterial BP waveforms has an added potential advantage: it may also open up a new pathway to provide DL-enabled PVR waveform analysis with interpretability, e.g., by presenting the inferred arterial BP waveforms and the key signatures used by DL therein to clinician users. It may be worthwhile to pursue these opportunities to advance DL-enabled non-invasive arterial pulse waveform analysis in general.

5. Conclusion

This paper demonstrated the preliminary proof-of-concept of deep learning (DL)-enabled pulse volume recording (PVR) waveform analysis for peripheral artery disease (PAD) diagnosis. We illustrated that PVR signals exhibit alterations from arterial blood pressure (BP) signals, but they qualitatively share common morphological changes caused by PAD. Then, we extended our prior work to develop and analyze a DL-enabled PVR waveform analysis algorithm for PAD diagnosis. We demonstrated that PVR may be effective in detecting PAD, and to a lesser extent, in estimating its severity level. Future work must conduct the development and analysis of the proposed algorithm using in vivo clinical data, as well as the application of DL-enabled non-invasive arterial pulse waveform analysis for diagnosis of various cardiovascular diseases.

Highlights.

1. We developed a deep learning-based peripheral artery disease (PAD) diagnosis method.

2. PAD is diagnosed via deep learning analysis of non-invasive arterial pulse waveforms.

3. Our diagnosis algorithm is regularized against adversarial continuous properties.