A machine learning approach for computation of cardiovascular intrinsic frequencies

Figures

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  Fig 1. Illustration of the intrinsic frequency (IF) method. A) Reconstruction of a carotid pulse waveform using the IF method. The original raw waveform in arbitrary units (dashed black) is overlaid on a waveform (blue) that is reconstructed from the IF method. B) IF visualization during a cardiac cycle. The values ω1 and ω2 represent IFs during systole and diastole, respectively, and dθ/dt is the instantaneous frequency [20]. The location of the dicrotic notch is marked by the vertical green–dotted line. The values Rs and Rd are the envelopes of the IF reconstruction associated with ω1 and ω2, respectively (note that, in general, Rs ≠ Rd). The values φ1 and φ2 are the initial intrinsic phases associated with ω1 and ω2, respectively.

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  Fig 2. Structural schematic of the sequentially–reduced feedforward ANN model for predicting the IF method outputs from a single carotid waveform with a given dicrotic notch time (the decoupling time). Here, L is the number of hidden layers.

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  Fig 3. Flowchart diagram summarizing the standard optimization–based IF approach and the proposed ML–based IF approach.

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  Fig 4. Sensitivity of precision in terms of mean squared error (MSE) loss (for training and validation) versus the relative training data size. Here, 100% of the training size corresponds to N = 13,008 waveforms. MSE is in absolute units corresponding to its calculation from the normalized outputs.

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  Fig 5. Statistical analysis of the blind clinical tests in terms of regression plots (left column), Bland–Altman plots (middle column), and error histograms (right column) of the scaled IFs ω^1 (top row: a1, a2, and a3, respectively) and ω^2 (bottom row: b1, b2, and b3, respectively).

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  Fig 6. Statistical analysis of the blind clinical tests in terms of regression plots (left column), Bland–Altman plots (middle column), and error histograms (right column) of the scaled first intrinsic envelope (R^s; top row: a1, a2, and a3, respectively), the scaled first intrinsic phase (φ1^; middle row: b1, b2, and b3, respectively), and the scaled fitting constant (c^; bottom row: c1, c2, and c3, respectively).

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  Fig 7. Effects of the original sampling rate and measurement device on predictions of IFs from the ANN model. Scatter plots and box–whisker plots of the error for the scaled IFs ω^1 (top row: a1 and a2, respectively) and ω^2 (bottom row: b1 and b2, respectively). The measurement devices include Tonometry (shown by blue circles), Vivio (shown by red circles), and iPhone (shown by orange circles).

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  Fig 8. Effects of the original sampling rate and measurement device on predictions of related IF parameters from the ANN model. Scatter plots and box–whisker plots for the scaled first intrinsic envelope (R^s; top row: a1 and a2, respectively), the scaled first intrinsic phase (φ1^; middle row: b1 and b2, respectively), and the scaled fitting constant (c^; bottom row: c1 and c2, respectively). The measurement devices include Tonometry (shown by blue circles), Vivio (shown by red circles), and iPhone (shown by orange circles).