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Detecting onsets of cardiovascular pulse wave signals is an important prerequisite for successfully conducting various analysis tasks involving the concept of pulse wave velocity. However, pulse onsets are frequently influenced by inherent noise and artifacts in signals continuously acquired in a clinical environment. The present work proposed and validated a neighbor pulse-based signal enhancement algorithm for reducing error in the detected pulse onset locations from noise-contaminated pulsatile signals. Pulse onset was proposed to be detected using the first principal component extracted from three adjacent pulses. This algorithm was evaluated using test signals constructed by mixing arterial blood pressure, cerebral blood flow velocity and intracranial pressure pulses recorded from neurosurgical patients with white noise of various levels. The results showed that the proposed pulse enhancement algorithm improved (p < 0.05) pulse onset detection according to all three different onset definitions and for all three types of pulsatile signals as compared to results without using the pulse enhancement. These results suggested that the proposed algorithm could help achieve robustness in pulse onset detection and facilitate pulse wave analysis using clinical recordings.
Intracranial pressure (ICP), arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) etc are popularly observed to monitor head injured patients in intensive care units. Those waveforms contain rich information about the cardiovascular system . Pulse onset is an important landmark for automated analysis of pulsatile cardiovascular signals because calculation of various useful parameters critically depends on its identification [2-4].. These parameters, including diastolic value, pulse wave velocity (PWV), and critical closing pressure etc, are widely used in many patient care areas involving cardiovascular and cerebrovascular diseases. Especially, PWV, the quotient of the pulse transmit distance divided by pulse transmit time (PTT) to denote how quickly a pulse travels from one point to another in the human body, is mostly used as a valid and reproducible index to assess stiffness of the arterial vessel wall, and one necessary parameter included for PWV calculation is PTT, which is usually referred to as the time interval between Q point of ECG and pulse onset . Accordingly, precise determination of PWV needs to locate the onset position precisely.
In existing literatures, pulse onset is usually regarded as the starting point of an incident pulse wave and hence relatively free, as compared to other landmarks of a pulse waveform, from influences from wave reflections. However, pulse onsets can be easily blurred by noise and artifacts due to their intrinsically small amplitude, therefore robust detection of pulse onset is challenging and meaningful [4, 6].
Several definitions of pulse onset for its computerized detection exist [3, 7, 8]. One definition is to select the point with the minimal diastolic value. A different choice is to select point at the maximal second derivative. Yet another definition involves finding the intersection of the line tangent to the initial systolic upstroke of a pulse and the horizontal line through its diastolic point. Essential to any of the above definitions are the accuracy and reproducibility of calculation results [3, 7, 9, 10].
Similarity of pulse morphology exists among adjacent pulses. This indicates that it could be beneficial to incorporate its adjacent pulses in the process of determining the onset of any pulse. The objectives of the present work are to introduce a computational approach that implements the idea of utilizing neighboring pulses to enhance signal quality for the purpose of onset detection and to demonstrate its efficacy. This approach is described in Section Methods and then the algorithm for calculating onset according to each of the above definitions will be introduced. In Section 3, we introduce the protocol of validating the proposed approach. In Section 4, we describe how the data set used in the validation was obtained. We then present the validation results in Section 5 and discuss these results in Section 6.
Consecutive physiological pulses resemble each other in most pathophysiological conditions if they are recorded without external disturbance. However, unavoidable noise corruptions cause dissimilarity in consecutive pulses  and consequently lead to errors in the detected pulse onset locations. Furthermore, noise and artifacts in signal recordings are likely to be time varying. This challenges the usage of traditional linear time invariant filters. We therefore argue that pulse onset detection errors due to noise influence could be reduced by performing onset detection after enhancing the signal component of each pulse from its temporally adjacent pulses. This is facilitated by using the principal component analysis (PCA) [12, 13] to a signal matrix composed of several consecutive pulses. This process is illustrated in Fig. 1 using ICP as an example.
As shown in Fig. 1, both Electrocardiogram (ECG) and a pulsatile signal are used in finding the pulse onset. Locating the QRS peak of ECG beats is a mature biomedical signal processing technique and facilitates the processing of pulsatile cardiovascular signals. Particularly, only the portion of each pulse that lies between the QRS peak and the peak of each pulse needs to be enhanced for the purpose of onset detection. This reduces the computational cost. Let denote the i-th sample of the k-th pulse, the following signal matrix ( S ), constructed from taking two adjacent pulses of the k-th one, is formed for the k-th pulse for enhancing its signal component.
where L is the minimal length of the intervals from QRS peak to the peaks of three pulses. In practice, we found that one can simply set L to be the half length of the shortest pulse among these three pulses. Then the principal component analysis is applied to S using the numerically robust singular value decomposition (SVD). The first (or principal) component, corresponding to the large singular value, contains the fundamental pulse information, and is used in subsequent onset detection.
Three different pulse onset definitions can be found in literature [1, 3, 8, 14]. They include defining the pulse onset using the diastolic point, the maximal second derivative, and the tangent intersection. The algorithm to incorporate the aforementioned neighbor pulse-based signal enhancement into the calculation of each of these definitions will be described in the following three sections.
Using this approach, pulse onset location can be determined by searching for the minimum point within the interval between the QRS peak and the pulse upstroke. A pictorial illustration of this definition is shown in Fig. 2. Finding the minimum point directly on the raw pulse waveform would be erroneous. A modified version of an existing noise reduction method proposed in  for locating diastolic point was therefore incorporated into the baseline implementation of diastolic point detection. The method can be described as follows.
The portion of a pulse that is within the searching interval is first separated into consecutive small fractions. Let n be the total number of such segments and k be the number of the points of each segment. Each segment is then fitted with a smooth spline curve to obtain the minimum of the segment. Therefore, a total of n local minimums are obtained. These points are fitted again using a spline curve whose minimum is then taken as the diastolic point. The aim of separating the waveforms into small fractions is to lower the noise effect and find the local minimum values as robust as possible. In current work, each small segment contains 8 samples for signals sampled at 400 Hz. It is expected this choice should be sampling-rate dependent. The approach can be schematically described in Fig.3 where we can see that the pulse waveform is well delineated by the spline fitting.
Applying the neighbor-based pulse reconstruction to the detection of diastolic point, we obtain the following pulse onset detection algorithm.
BEGINDetect all M QRS peaks in an ECG recordingfor i=1:MConstruct the neighboring pulse matrix S for i-th pulse using Equation 1);Use PCA to decompose S into P1, P2, and P3 with descending eigen values;Select the principal component P1 for onset detection;Separate P1 into K small fraction segments;for k=1:KFit the kth fraction segment with cubic spline smooth curve;Find the minimum value and the corresponding position on the kth fitted curve;endEstimate the cubic spline curve using the K local minimum values as spline control points;Find the diastolic point with minimum value on the fitted curveendEND
At the beginning of this procedure, we used the robust QRS complex detection algorithm [15, 16] to detect the R peaks prior to the onset detection. An implicit assumption used in formulating neighborhood of pulses for PCA analysis is that the neighborhood should be formed from adjacent beats. In practice, this assumption cannot be satisfied for the boundary beats and for beats with missed adjacent QRS detections, where the adjacent QRS pulses refer to those close enough subsequent pulses with interval<3.0 times of subject's mean heart RR interval. In such cases, the principal component analysis of the pulse neighborhood is neglected and the proposed algorithm is simplified to have only the spline fitting for noise reduction.
The location of the maximal second derivative (MSD), to be found in the same interval between QRS peak and pulse upstroke, can be also used as pulse onset location. This definition is illustrated in Fig.2 where the second derivative was calculated using a 5-point central difference formula.
Similar to the algorithm of locating the diastolic point on a pulse signal, we propose the following algorithm for finding the MSD point.
BEGINDetect all M QRS peaks in an ECG recordingfor i=1:MConstruct the neighboring pulse matrix S for i-th pulse using Equation 1);Use PCA to decompose S into P1, P2, and P3 with descending eigen values;Select the principal component P1 for onset detection;Use a 5-point central difference formula to calculate the 2nd order derivative;Find the point with maximum 2nd order derivative on the derivative curve.endEND
Similar to the detection of diastolic point, when the neighboring pulses are lost, this approach is simplified to the original MSD detection method without PCA enhancement.
This definition of pulse onset location, was based on methods analogous to those described by Chiu et al  for the detection of arterial pulse wave signals. A tangential line was determined by a straight-line fitting of the pulse rising edge. This line fitting process takes two steps. The pulse sample having the maximal first derivative was first identified on the rising edge of pulse. Then centering at this pulse sample, additional neighboring pulse samples were added in the line fitting process until the fitted line failed to correlate with the original rising edge at a threshold above 0.999. A second line was defined by the horizontal line passing the minimum of the pulse. Pulse onset was then defined as the intersection of these two lines. Similar to the algorithm of locating the diastolic point on a pulse signal, we propose the following algorithm for finding the tangent intersection point (TIP).
BEGINDetect all M QRS peaks in an ECG recordingfor i=1:MConstruct the neighboring pulse matrix S for i-th pulse using Equation 1);Use PCA to decompose S into P1, P2, P3 with descending eigen values;Select the principal component P1 for onset detection;Form the tangent line and robustly determine the diastolic point on this recovered pulse;Calculate the intersection point of the tangent line and the horizontal line passing through the diastolic point.endEND
Similar to the detection of diastolic point and the MSD point, this approach is simplified to the original TIP detection method without PCA enhancement when the neighboring pulses matrix cannot be formulated.
A typical algorithm validation strategy as used in many studies [3, 7, 8,] was to establish ground truth of the locations of the landmarks of interest by taking the results from human observers. True detection by the automated method is granted if its results are within certain distance to the ground truth. In our previous work, we showed that a significant variance existed between the results from two observers  when asked to mark the diastolic points for intracranial pressure signals. It will become even more infeasible to manually tag the MSD and the TIP points. We therefore chose a different strategy for validating the proposed method. First, a set of reference signals from various pulse signals including arterial blood pressure (ABP), intracranial pressure (ICP), and cerebral blood flow velocity signals (CBFV) were constructed. Simulated noise signals at different power levels were then added to the reference signals. For different pulse onset definitions, the corresponding approaches with/without neighbor pulse-based enhancement were then applied to both the reference signals and their noisy versions.
We aim to evaluate the proposed algorithm by comparing the onset locations identified from noise-corrupted signals with those identified using its original signal. The error between the locations identified from the original and its noisy version can be calculated as
where ti is the location of a landmark of interest identified using the original signal and i is the location identified from its noisy version. Assuming there are N beats in the whole data set, the mean and the standard derivation variance of ei can be calculated as
where ē is the mean error and σ is the standard derivation variance of error. Therefore, our hypothesis to be tested in the validation study is that the proposed neighbor based approach would achieve a smaller ē as compared to those without using the neighbor pulse-based enhancement.
Our validation data set contained three pulsatile signal recorded from 16 patients including eight subarachnoid hemorrhage patients and eight normal pressure hydrocephalus patients. The three signals include arterial blood pressure, intracranial pressure and cerebral blood flow velocity that were recorded during 15~25 minutes of passive monitoring of patients. The monitoring protocol was approved by the local internal review board and was conducted with informed consents from either the patients or their next of kin. For the SAH patients, invasive ABP, ECG, and ICP were collected from the bedside monitors. CBFV was collected from the Transcranial Doppler ultrasound device (Viasys, Madison). For the NPH patients, ABP was recorded at bedside using a noninvasive ABP device (Collin Biomedical, Japan) and ICP was monitored using Codman intraparenchymal microsensors (Codman and Schurtleff, Raynaud, MA) situated in the right frontal lobe. All signals were digitalized at 400 Hz by using a PowerLab TM SP-16 data acquisition system (ADInstruments, Colorado Springs, CO). One recording for one patient was selected for algorithm validation. Therefore, there were 16 data sets used in the validation that contained 16842 beats.
These signals were low-pass filtered using a fourth-order zero-phase Elliptic filter with a cutoff frequency at 5 Hz to obtain the baseline reference signals. Different realizations of white noise sequence were added to each signal. Variance of noise was scaled relative to the variance of corresponding reference signal at four different levels: 5%, 10%, 15%, and 20%.
We applied the signal enhancement method to original signals without adding noise and then conducted onset detection under the three definitions. The resultant mean errors between the onsets detected on the original and those on the enhanced signals are listed in Table 1 for ICP, ABP, and CBFV, respectively. Table 1 shows that the onset difference between the onsets with the same definition detected on the reference signals when PCA approach is considered or not actually existed. These results provide a baseline to evaluate whether the adoption of signal enhancement to process noisy signals could be beneficial. The mean onset error is calculated one by one for 16 patients, and then the following comparison is implemented on the averaged 16 patient samples. Tables 2 through 4 show the basic statistics of the error between the onsets identified from the reference signals and their corresponding noise-contaminated versions for the three kinds of onset definitions, respectively. For each noise level, the paired t test was used to test the null hypothesis that the error as assessed using equation 2) is not significantly different between the approach that incorporated the neighbor pulse-based enhancement and the approach that did not. An asterisk is used in tables to indicate that the null hypothesis can be rejected at a significance level of 0.05. It can be seen from the results that the mean error was significantly reduced after adopting the neighbor pulse-based enhancement across all noise levels, all types of signals, and all types of onset definitions. In addition, by comparing to the results in Table 1, it can be seen that the mean error from processing the 5%-noise case without using signal enhancement is already significantly greater than the error introduced by using the signal enhancement to process the original signal. This observation would support the adoption of the neighbor pulse-based signal enhancement.
To further analyze results in Tables 2 through through4,4, a two-way analysis of variance was conducted taking different signal types and different onset definitions as two factors. This analysis shows that different definitions of onset have significant influence on the mean error. This was true for the result from not using the signal enhancement (F = 18.52, p<0.0000) and results from using the signal enhancement (F = 13.64, p=0.0001). On the other hand, different signal types did not have such significant influence (p > 0.05) and the interaction of these two factors was not significant. The two-way analysis of variance was also used to analyze the amount of reduced mean error due to the adoption of signal enhancement. In addition to the similar finding that different onset definitions have significant effect on the amount of mean error reduction, the interaction between these two factors became significant (F= 3.35, p = 0.0238).
Fig.4 shows one representative example of detecting pulse onset for ABP, CBFV, and ICP corrupted with a 15% noise. For each signal, the onset detection results under the three onset definitions are all presented. These results convey the same message that incorporating the neighbor pulse information improved the detection of pulse onsets irrespective of which definition was adopted.
Pulse onset is an important landmark for pulsatile signals frequently encountered in clinical monitoring. Robustness of any pulse onset detection methods is hence highly desirable for processing these signals that usually are collected in an active clinical environment where noise and artifacts are inevitable. As shown in Table 1, certain bias exists within those onsets defined in the same sense when they are detected with/without PCA enhancement. Whatever the filters are used to filter signal, the noise still cannot be totally removed, i.e., compared to the actual pure physiological signal, this reference signal still contains noise with certain power. The PCA approach can further eliminate those existed artifacts and simultaneously we cannot exclude the possibility that PCA will induce some other artifacts. Moreover, for the physiological signals we cannot exactly know where the true onset is localized, i.e., no gold standard for onset position. Therefore, it is possible that some bias exists between the onsets with same definition when they are detected with/without PCA approach even for the reference signals, and it is part reason why we evaluate the localization methods in view of stability. The method proposed in the present work offers a viable solution to increase the robustness of onset detection in terms of a smaller mean error, which is an important indicator of the quality of a robust pulse detection approach.
Frequency domain digital filters are usually used for enhancing signal quality. One challenge of using a linear time invariant filter to process a continuously acquired biomedical signal is to tailor the design of the filter to the ever-changing property of signals. Hence, optimal filter design may be different for different types of signals and for different patient conditions. On the other hand, the neighbor-pulse based signal enhancement is intrinsically data-driven with a reasonable assumption that adjacent pulses resemble each other. Therefore, it is adaptive to the local signal condition of a small time-interval (three beats in the present work) without the need of a globally optimal solution. This feature makes it very desirable to be adopted in practice as also shown by other similar data driven filtering approaches [18-21] .
Our results also showed that different onset definitions might show different levels of noise-resistance irrespective of whether a signal enhancement was used. Particularly, we demonstrated that the diastolic point definition is the most robust to noise. This is probably because that the other two approaches require the computation of signal derivatives, which acts like a high-pass filter that boosts the noise influence on the onset detection. It should also be pointed out that the proposed approach should be taken as a component of a comprehensive solution to robust onset detection because other aspects like legitimate pulse recognition and detection of spurious ECG beats are not addressed by this algorithm but are important to achieve overall robustness of the pulse onset detection.
The present work is partially supported by NINDS R21 awards (NS055998, NS055045 and NS059797) to X.H. and a R01 award (NS054881) to M.B.