Heart rate variability analysis during central hypovolemia using wavelet transformation

Abstract

Detection of hypovolemia prior to overt hemodynamic decompensation remains an elusive goal in the treatment of critically injured patients in both civilian and combat settings. Monitoring of heart rate variability has been advocated as a potential means to monitor the rapid changes in the physiological state of hemorrhaging patients, with the most popular methods involving calculation of the R–R interval signal’s power spectral density (PSD) or use of fractal dimensions (FD). However, the latter method poses technical challenges, while the former is best suited to stationary signals rather than the non-stationary R–R interval. Both approaches are also limited by high inter- and intra-individual variability, a serious issue when applying these indices to the clinical setting. We propose an approach which applies the discrete wavelet transform (DWT) to the R–R interval signal to extract information at both 500 and 125 Hz sampling rates. The utility of machine learning models based on these features were tested in assessing electrocardiogram signals from volunteers subjected to lower body negative pressure induced central hypovolemia as a surrogate of hemorrhage. These machine learning models based on DWT features were compared against those based on the traditional PSD and FD, at both sampling rates and their performance was evaluated based on leave-one-subject-out fold cross-validation. Results demonstrate that the proposed DWT-based model outperforms individual PSD and FD methods as well as the combination of these two traditional methods at both sample rates of 500 Hz (p value <0.0001) and 125 Hz (p value <0.0001) in detecting the degree of hypovolemia. These findings indicate the potential of the proposed DWT approach in monitoring the physiological changes caused by hemorrhage. The speed and relatively low computational costs in deriving these features may make it particularly suited for implementation in portable devices for remote monitoring.

Appendices

Appendix 1

This section explains the process of QRS detection performed prior to feature extraction. Construction of the RR signal using the RR intervals in the ECG signal first requires that the R-waves be identified, which is done via QRS detection. The most common technique is the Pan-Tompkins algorithm [49], which detects QRS complexes based on analysis of their slope, amplitude and width. This method consists of four stages: band-pass filtering, differentiation, squaring, and windowing. The first stage applies the same filter as described in Sect. 2.2. The signal is then passed through a differentiator which suppresses the low-frequency P and T wave components and emphasizes the steep slopes of the QRS complex. The QRS complex also displays high amplitude, which is emphasized by applying a squaring operator. The next stage uses a moving average window to smooth the signal and reduce noise. The final step is to select a threshold that detects the QRS peaks in the waveform.

This study applies a modified version of the Pan-Tompkins algorithm which incorporates an additional histogram analysis step after averaging is performed, to identify any unusual values which may cause errors in the QRS detection process. It also employs an adaptive threshold T to detect the QRS peaks, which offers more flexibility in dealing with individuals than a fixed threshold. This is calculated as $T = \mu (S) + \hbox{max} (S)*\alpha$, where S is the filtered ECG stage segment currently being analyzed and α is an empirically-chosen weight measure. This study found α = 0.4 to be a suitable value.

In calculating the RR intervals, any single interval is compared to those previously detected using a sliding window. This process is described as follows. Let $I_{i}$ be the estimate of the RR interval at sample i, n the total number of RR intervals detected so far, and $\omega_{0}$, $\omega_{1}$, and $\omega_{2}$be boundaries on the acceptable range of variation of the interval, chosen based on previous interval values. In order to find the new RR interval l, the following rules are followed:

$$ \begin{array}{*{20}c} {l = I_{i} ,} \hfill & {{\text{if}}\,\omega_{0} \le I_{i} \le \omega_{1} } \hfill \\ {{\text{insert}}\,{\text{one}}\,{\text{interval}},I_{i + 1} = I_{i} - l,} \hfill & {{\text{if}}\,\omega_{1} \le I_{i} \le \omega_{2} } \hfill \\ {{\text{insert}}\,{\text{two}}\,{\text{intervals}},I_{i + 2} = I_{i} - 2l,} \hfill & {\text{Otherwise}} \hfill \\ \end{array} $$

(3)

The boundaries are set as $\omega_{0} = 0.89m,\,\omega_{1} = 1.29m$ and $\omega_{2} = 2m$, where m is the median value of the previous eight RR intervals.

Appendix 2

This section briefly explains the two other HRV analysis methods used in this study. Power spectral density (PSD) describes the distribution of the power in a signal with frequency [22]. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The measures of interest in this study are the powers of the high frequency (HF; 0.15–0.4 Hz), low frequency (LF; 0.04–0.15 Hz) and very low frequency (VLF; 0.003–0.04 Hz) bands, the normalized powers of the LF and HF bands, and the ratios of LF to HF and HF to LF. These are calculated by integrating the spectrum for each band. Normalization is performed by calculating

$$ HF_{n} = \frac{HF}{(TAP - VLF)} $$

(4)

$$ LF_{n} = \frac{LF}{(TAP - VLF)} $$

(5)

where TAP is the total average power of the RR interval [7].

Fractal analysis monitors data via fractals: sets of points that can be divided into subsets which each resemble the whole. Calculating the FD of a signal quantifies both this self-similarity and the signal’s complexity. FD is commonly used in analyzing biosignals such as electrocardiogram (ECG) and electroencephalogram (EEG) to differentiate physiological states. This study applies Higuchi’s algorithm to calculate the FD of the ECG segments recorded over each LBNP stage. Consider a signal $X_{i} = x_{1} ,x_{2} , \ldots ,x_{n}$, consisting of n samples. This is first divided into smaller epochs, by constructing k new time series $x_{m}^{k}$such that

$$ x_{m}^{k} = \left\{ {x(m),x(m + k),x(m + 2k), \ldots ,x\left( {m + \left\lfloor {\frac{N - m}{k}} \right\rfloor } \right)k} \right\} $$

(6)

where $m = 1, \ldots ,k$ indicates the initial time value and k is the time interval between points. For each $x_{m}^{k}$, the average length $L_{m} (k)$ is calculated as

$$ L_{m} (k) = \frac{{\sum\nolimits_{i = 1}^{a} {|x(m + ik) - x(m + (i - 1)k)|(n - 1)} }}{\left\lfloor a \right\rfloor k} $$

(7)

where $a = \frac{N - m}{k}$. The average length $L(k)$for each delay k is calculated as the mean of the k lengths $L_{m} (k)$ for $m = 1,2, \ldots ,k$. This is repeated for each of the k time series. The Higuchi FD is estimated as the slope of the least-squares best fit line to the curve of $\ln [L(k)]$ versus $\ln \left( \frac{1}{k} \right)$ for $k = 1, \ldots ,k_{\hbox{max} }$ [23]. Calculation accuracy depends on the epoch length; this study tested lengths of 8 and 15.