Enhancing coronary Wave Intensity Analysis robustness by high order central finite differences

Abstract

BackgroundCoronary Wave Intensity Analysis (cWIA) is a technique capable of separating the effects of proximal arterial haemodynamics from cardiac mechanics. Studies have identified WIA-derived indices that are closely correlated with several disease processes and predictive of functional recovery following myocardial infarction. The cWIA clinical application has, however, been limited by technical challenges including a lack of standardization across different studies and the derived indices' sensitivity to the processing parameters. Specifically, a critical step in WIA is the noise removal for evaluation of derivatives of the acquired signals, typically performed by applying a Savitzky–Golay filter, to reduce the high frequency acquisition noise.MethodsThe impact of the filter parameter selection on cWIA output, and on the derived clinical metrics (integral areas and peaks of the major waves), is first analysed. The sensitivity analysis is performed either by using the filter as a differentiator to calculate the signals' time derivative or by applying the filter to smooth the ensemble-averaged waveforms.Furthermore, the power-spectrum of the ensemble-averaged waveforms contains little high-frequency components, which motivated us to propose an alternative approach to compute the time derivatives of the acquired waveforms using a central finite difference scheme.Results and ConclusionThe cWIA output and consequently the derived clinical metrics are significantly affected by the filter parameters, irrespective of its use as a smoothing filter or a differentiator. The proposed approach is parameter-free and, when applied to the 10 in-vivo human datasets and the 50 in-vivo animal datasets, enhances the cWIA robustness by significantly reducing the outcome variability (by 60%).

Automatic selection of optimal Savitzky-Golay filter parameters for Coronary Wave Intensity Analysis

“…Briefly, the beats of interest are selected and then pressure p and velocity v waveforms are ensemble-averaged in order to remove high frequency noise. The signals' time derivatives (dp, dv), input to the WIA, are computed using a 4 th order central finite difference scheme, since it has been shown to be optimal in reducing the outcome variability [7]. After computing the signals time derivative, the simultaneous forward and backward travelling waves can be separated, as it follows:…”

“…The awS-G and the apS-G algorithm, both for the SURE and rSURE estimators, are then applied on the single trace as well as pre or post ensemble-averaging over the 5 noisy beats. Based on [7], we chose a window width range where the awS-G algorithm can automatically choose the optimal M of [7 − 35], and a polynomial range of [1 − 5] for the apS-G algorithm. The suitable pre-selected polynomial degree and window width, for the awS-G and apS-G respectevely, are chosen based on an extensive sensitivity analysis.…”

“…Beatwise processing has never been considered due to the strong impact that noise has on the velocity signal over a single cardiac cycle. Recently, Rivolo et al [7] showed, using in vivo human and animal data, that the pressure and velocity time derivatives are strongly sensitive to the S-G parameters choice (polynomial degree N and window width M), significantly affecting, in turn, the cWIA-derived metrics (areas and peaks of the main waves). They suggested that the common practice of ensemble-averaging over few cardiac beats combined with a central finite difference scheme enhances the robustness of the cWIA.…”

“…The algorithm has been developed for automatically smoothing the ECG signals and tested on simulated and real ECG data, showing promising results. Furthermore, in Rivolo et al [7] solely the variability could be assessed since to evaluate accuracy a cWIA gold standard is required. Recently, Lee et al [8] developed an integrative framework aimed at enabling an in silico cWIA.…”

Changes in Non:Invasive Wave Intensity Parameters with Variations of Savitzky:Golay Filter Settings

“…The original formulation required invasive simultaneous measurements of blood pressure and flow velocity (U), but the parallel development of ultrasound systems enabled performing WIA through ultrasound-measured diameter (D) and U instead [3,4]. D and U are commonly filtered (smoothed) to eliminate high-frequency noise; however the filter settings affect WIA parameters, calculated not directly from D and U, but from their time derivatives (dD, dU) [5]. One of the most common smoothing algorithmsfor these signals is the Savitzky-Golay (SG) filter [6], which fits a sub-set of data points of the signal, contained in a window of specific length (w), with a polynomial of a specific degree (p), via the least-squares method.…”