Estimating pulse wave velocity from the radial pressure wave using machine learning algorithms

Abstract

One of the European gold standard measurement of vascular ageing, a risk factor for cardiovascular disease, is the carotid-femoral pulse wave velocity (cfPWV), which requires an experienced operator to measure pulse waves at two sites. In this work, two machine learning pipelines were proposed to estimate cfPWV from the peripheral pulse wave measured at a single site, the radial pressure wave measured by applanation tonometry. The study populations were the Twins UK cohort containing 3,082 subjects aged from 18 to 110 years, and a database containing 4,374 virtual subjects aged from 25 to 75 years. The first pipeline uses Gaussian process regression to estimate cfPWV from features extracted from the radial pressure wave using pulse wave analysis. The mean difference and upper and lower limits of agreement (LOA) of the estimation on the 924 hold-out test subjects from the Twins UK cohort were 0.2 m/s, and 3.75 m/s & -3.34 m/s, respectively. The second pipeline uses a recurrent neural network (RNN) to estimate cfPWV from the entire radial pressure wave. The mean difference and upper and lower LOA of the estimation on the 924 hold-out test subjects from the Twins UK cohort were 0.05 m/s, and 3.21 m/s & -3.11m/s, respectively. The percentage error of the RNN estimates on the virtual subjects increased by less than 2% when adding 20% of random noise to the pressure waveform. These results show the possibility of assessing the vascular ageing using a single peripheral pulse wave (e.g. the radial pressure wave), instead of cfPWV. The proposed code for the machine learning pipelines is available from the following online depository (https://github.com/WeiweiJin/Estimate-Cardiovascular-Risk-from-Pulse-Wave-Signal).

Fig 1. Data pre-processing for pulse wave velocity estimation from the features extracted from the radial pressure wave.

(a) The fiducial points containing key features identified by the LASSO regression. (b) Identified outliers in the database using principal component analysis (PCA). Red, blue and green dots represent subject groups with pulse wave velocity (PWV) less than 7 m/s, 7–9 m/s, and greater than 9 m/s, respectively.

Fig 2. Estimation of pulse wave velocity (PWV) on a hold-out test set containing 924 subjects using Gaussian process regression and recurrent neural network with long short-term memory.

Panels (a) and (b) show estimated PWV against measured PWV with the linear regression line in red, the coefficient of determination, r², and the p-value. Panels (c) and (d) show the Bland-Altman plots comparing the estimated and measured PWV. Panels (e) and (f) show Pearson correlation coefficients (r) between the biological characteristics of the cohort and the “Difference” values shown on panels (c) and (d), respectively. BMI: body mass index; DBP: diastolic blood pressure; SBP: systolic blood pressure; MAP: mean arterial pressure.

Fig 3. Schematic illustration of the recurrent neural network structure used to estimate pulse wave velocity from the entire radial pressure wave.

P_t−1, P_t and P_t+1 are the radial pressure values at the discrete time points t − 1, t, and t+1, cfPWV is the carotid-femoral pulse wave velocity.

Fig 4. An example of an original signal, and the same signal with added white noise, with signal to noise ratios (SNR) of 20, 10 and 5.

Fig 5. Estimation of PWV on a hold-out test set containing 1312 virtual subjects using the recurrent neural network, with different levels of added white noise.

Estimated against measured PWV with the linear regression line in red, the coefficient of determination, r², and the p-value (top). Corresponding Bland-Altman plots (bottom). SNR: signal to noise ratio.