Waveform descriptor for pulse onset detection of intracranial pressure signal

Medical Engineering & Physics 34 (2012) 179–186

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Waveform descriptor for pulse onset detection of intracranial pressure signal Li Yang a,∗ , Mingxi Zhao a , Chenglin Peng a , Xiao Hu b , Hua Feng c , Zhong Ji a a

111 Project Laboratory of Biomechanics and Tissue Repair, Bioengineering College, Chongqing University, Chongqing 400030, China Neural Systems and Dynamics Laboratory, Department of Neurosurgery, the David Geffen School of Medicine, University of California, Los Angeles 900095, USA c Department of Neurosurgery, Southwest Hospital, Third Military Medical University, Chongqing 400038, China b

a r t i c l e

i n f o

Article history: Received 16 January 2011 Received in revised form 4 July 2011 Accepted 11 July 2011 Keywords: Intracranial pressure Onset identification Waveform descriptor Detector comparison

a b s t r a c t We present an algorithm to identify the onset of intracranial pressure (ICP) pulses. The algorithm creates a waveform descriptor to extract the feature of each local minimum of the waveform and then identifies the onset by comparing the feature with a customized template. The waveform descriptor is derived by transforming the vectors connecting a given point and the local waveform samples around it into log-polar coordinates and ranking them into uniform bins. Using an ICP dataset consisting of 40933 normal beats and 306 segments of artifacts and noise, we investigated the performance of our algorithm (waveform descriptor, WD), global minimum within a sliding window (GM) and two other algorithms originally proposed for arterial blood pressure (ABP) signal (slope sum function, SSF and pulse waveform delineator, PUD). As a result, all the four algorithms showed good performance and WD showed overall better one. At a tolerance level of 30 ms (i.e., the predicted onset and ground truth were considered as correctly matched if the distance between the two was equal or less than 30 ms), WD achieved a sensitivity of 0.9723 and PPV of 0.9475, GM achieved a sensitivity of 0.9226 and PPV of 0.8968, PUD achieved a sensitivity of 0.9599 and PPV of 0.9327 and SSF, a sensitivity of 0.9720 and PPV of 0.9136. The evaluation indicates that the algorithms are effective for identifying the onset of ICP pulses. © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

1. Introduction Continuous intracranial pressure (ICP) monitoring is common practice in diagnosing and managing neurosurgical conditions, such as traumatic brain injury, subarachnoid hemorrhage and hydrocephalus. The fluctuation of ICP associates with physiological factors, such as, cerebral blood flow (CBF), arterial blood pressure (ABP) and cardiac cycle. Corresponding to rhythmic heart beating, ICP signal propagates in a beat-by-beat way and exhibits quasiperiodic dynamics. During a heartbeat, the pulsatile component of ICP can provide important information [1]. Beat-level analysis has been performed in various applications of ICP waveform analysis [1–8]. Onset identification is a fundamental stage of ICP pulse analysis such as three characteristic peaks identification [9,10], slope [8], pulse amplitude [5] and latency [11]. Robust and automatic detection can be time-saving and can minimize subjective influence on extracting useful information. Pulse onset denotes the arrival of ICP pulse. There are several pulse onset definitions [12–14], such as the point of minimum diastolic pressure [13] and the maximum point of the second derivative [14]. Several methods have been developed for automatic ICP pulse onset identification. Eide proposed a method to detect the valley

with lowest pressure value, i.e., the point of minimum diastolic pressure, using a sliding window [15]. It may be inaccurate to treat the valley in the sliding window as the onset when ICP pulse exhibits an oscillating tail that is contributed by wave reflections [16]. In this case, the onset may not be the global minimum point in the window. In addition, as the author noted, the method cannot recognize the artifacts. Another way to detect the onset is using a landmark of synchronous recorded signal, such as electrocardiogram (ECG) or ABP, to locate each pulse, afterwards the pulse onset on each pulse is identified [11,16]. The objective of this paper is to develop a robust ICP pulse onset detector without the synchronization such as ECG. In present work, a waveform descriptor is proposed to detect the minimum diastolic pressure of ICP pulses. The waveform descriptor is derived from the vectors connecting a given point on the pulse waveform and the local waveform samples around it. The onset identification proceeds by comparing the descriptor of each point with a customized template and then selecting the optimal one as the onset. Using an ICP dataset, we investigated the performance of the algorithm and compared it with three other algorithms. 2. Methods 2.1. Waveform descriptor

∗ Corresponding author. Tel.: +86 13658372167. E-mail address: [email protected] (L. Yang).

Shape context [17] is a widely adopted method in image retrieval and deformed shape matching [18–21], which can

1350-4533/$ – see front matter © 2011 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2011.07.008

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Fig. 1. Illustration of the log-polar transformation of a given point on ICP pulse. The upper panel shows the log-polar transformation of the vectors connecting to the onset (the star) of a representative segment of two consecutive pulses. The segment is first scaled, and then the vectors connecting the onset and other points on the segment are normalized, finally the normalized vectors are transformed into log-polar coordinates and ranked into uniform bins. As a comparison, the lower panel shows that of the global minimum (the triangle) around the starting time of the pulse. The segment of two inter-beat intervals (between the vertical dashed lines) is used to generate the vectors.

discriminatively describe a given point using the distribution of the relative positions of that point and the remaining points on the image edge. The construction of shape context is composed of several steps. First, vectors connecting a given point and all the other points on the edge of the image are generated. Then, the vectors are transformed into log-polar coordinates and ranked into uniform bins. The histogram of these ranked points is termed as the shape context. Following the idea of the shape context, a waveform descriptor is proposed to distinguish the onset from other points on the ICP pulse. For a given point pi , the waveform descriptor is constructed using the segment of two inter-beat intervals, one before and one after pi . The purpose of using of two inter-beat intervals is to capture the beat-by-beat nature of ICP. The construction of waveform descriptor consists of the following steps.

(1) Let H be the difference between the maximum and minimum pressure values of the signal segment. The time axis is scaled so that the duration of the segment equals H. Afterwards, vectors are generated by connecting pi to other successive points on the segment. The aim of scaling is to avoid the length of the vector predominantly determined by the time difference (horizontal direction) or the pressure difference (vertical direction) between the ends of the vector (see the middle portion of Fig. 1). (2) The length of these vectors is divided by their mean value while keeping their direction unaltered and then these vectors are transformed into log-polar coordinates and voted into uniform bins. The voting is performed as follows. The log-polar coordinates are first divided into bins by dividing the angle and the log transformation of the radial distance in a uniform way, and then the normalized vectors are voted to the corresponding bins. The

transformation from Cartesian to log-polar coordinates of the vectors of a point is illustrated in Fig. 1. Log-polar transformation: Consider a point (x,y) in Cartesian coordinate system. (x,y) can be represented by (,) in polar coordinate system, where  is the angle of the point from center and  is the radial distance. Let (x0 ,y0 )be the center of polar transformation, the relationship between Cartesian and polar coordinates is =



(x − x0 )2 + (y − y0 )2

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The log-polar transformation is a conformal mapping from the point (x,y) on the Cartesian plane to point (,log()) in the log-polar plane. 2.2. Similarity measure of waveform descriptor The similarity between two different points on the pulse waveform can be measured by comparing the similarity of their features extracted by waveform descriptor. In the present work, the similarity cost is calculated using the 2 test statistic 1  [hi (n) − ho (n)] , 2 hi (n) + ho (n) N

2

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where hi (n) and ho (n) denote the N-bin histogram at location i and o, respectively.

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2.3. Onset detection with waveform descriptor

Representative Segments

The onset detection procedure consists of the following stages. (1) The template is constructed using representative ICP segment of two consecutive pulses. The onset of the representative segment is first identified manually. Then the template is constructed using feature extracted from the onset by the waveform descriptor. The selection of the representative segment is according to the configurations of the characteristic sub-peaks [22] on ICP pulse. In present work, the representative segment is automatically selected by hierarchical clustering which is a standard unsupervised clustering technique primarily based on the similarity measure between individuals [23]. Agglomerative clustering [24] is performed using average linkage similarity measure [25]. The similarity between two ICP pulses is calculated by Euclidian distance. The similarities among ICP segments are evaluated and then these segments are partitioned into clusters by average linkage. Each cluster corresponds to a kind of configuration pattern. As a result, 43 representative segments are selected. (2) To identify the pulse onset of a test signal, the feature of each local minimum is first derived using waveform descriptor. pi is treated as a local minimum, if vi − 1 < vi > vi + 1 , vi is the pressure value of pi . To extract the feature, the initial value of the pulse interval is set as the mean inter-beat interval (e.g., 320 for 75 bpm, 400 Hz sample rate), and then the interval is updated using the average inter-beat interval of 6 nearest neighbor pulses. (3) The similarity between the feature of each local minimum and template is measured using 2 test statistic. The point with minimal similarity cost within 0.5–1.5 cycles of the estimated beat interval is selected as onset candidate. Noted that the trailing part of a pulse usually exhibits more fluctuations and is prone to noise [16] and the front part is more consistent. To capture this characteristic, different weights are assigned to the similarity cost of the waveform before and after each local minimum. Specifically, let Ci represent the similarity cost between pi and the template, Ci = ˛ * Cfi + (1 + ˛) * Cli ; ˛, i.e., the weight, a scale factor, 0 < ˛ < 1, Cfi is the similarity cost between the template and the histogram generated from the waveform before pi ; Cli , the similarity cost between the template and the histogram generated from the waveform after pi . (4) The onset is identified by comparing the similarity cost of onset candidate with a threshold. (5) To take advantage of the similar shape appearance of adjacent neighborhoods, the features of the 6 nearest neighbor pulses are incorporated into the original template to detect the next point. The construction of template using the representative pulses and the identification of ICP pulse are shown in Fig. 1. Fig. 2 illustrates the overall view of the onset detection procedure. 2.4. Evaluation criteria Two criteria are used to assess the performance of the algorithm. Sensitivity (Se) Se =

TP TP + FN

(4)

where TP (true positive) is the number of true onsets that are predicted to be true and FN (false negative) is the number of true

ICP Signal

Preprocess (Denoise and Resample) Derive the Local Minimum (LM)

Two-beat Pulses

Construct the Feature with WD Feature of LM

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Measure Similarity Compare the Similarity with the Threshold Onset Fig. 2. The flow chart of the overall view of the onset detection procedure. The procedure mainly consists of the following 4 stages. The template is constructed using representative segment of two consecutive pulses; the feature of each local minimum on the test pulse waveform is extracted; the similarity between the feature and template is measured; the optimal local minimum whose similarity cost below a threshold is identified as the onset.

onsets that are predicted to be not true. Positive predictive value (PPV), PPV =

TP TP + FP

(5)

where FP (false positive) is the number of false onsets that are predicted to be true. 2.5. Parameter determination To investigate how the performance of the algorithm is affected by the parameters, we studied the changes of sensitivity and positive predictive value when varying the algorithm parameters. With regard to the determination of the number of the bins in log-polar coordinates, Let p and q represent the uniformly divided angle and radial distance, respectively. The (p,q) was first coarsely tuned by grid search method from (1,1) to (50,50) with a large step length (e.g., 5). Then (p,q) was finely tuned together with varying the weight ˛, (˛, was varied from 0 to 1, with a step length of 0.05). As an example, Fig. 3 shows the performance (positive predictive value) changes with ˛ tuned under different (p,q).The threshold was determined after the determination of (p,q) and ˛. To establish the optimal parameters, the tradeoff between sensitivity and positive predictive value needs to be taken into account based on actual needs. Fig. 4 displays the change of positive predictive value versus specificity with different thresholds (the threshold was varied from 0.1 to 1, with a step length of 0.04). In present work, ˛, (p,q) and the threshold were set as 0.35, (11,15) and 0.46, respectively. 2.6. Patient data and onset annotation The ICP recordings were collected from bedside monitors in Department of Neurosurgery, Southwest Hospital of Third Military Medical University in China (intraparenchymal transducer

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(Camino 110-4B, Integra LifeSciences, NJ, USA)). The ICP signals were recorded from 48 patients, including 15 traumatic brain injury (TBI) patients, 14 normal pressure hydrocephalus (NPH) patients and 19 hydrocephalus patients. The duration of these signals ranged from 15 min to 1 h and the sample rate was set at 400 Hz. The study was approved by the institutional review board of the Southwest Hospital of Third Military Medical University and was conducted with informed written consents from the patients enrolled. Typically useful frequency components of ICP signal are below 5 Hz [3,26]. The signal was filtered by a low-pass filter with a cutoff frequency of 25 Hz to eliminate high frequency noise. The onset of ICP pulses was identified automatically by the proposed algorithm and then re-checked and corrected by an expert with the help of a customized Matlab software which was developed for visual inspection and annotation of physiological signals, such as ICP, ABP and ECG. 3. Algorithm validation and comparison The waveform descriptor describes the onset using the distribution of the relative positions of the onset and the remaining points

on the pulse waveform. It aims to discriminate the normal pulse from the artifacts and the true onset from the global minimum using the overall shape of the pulse waveform (around the onset). To investigate whether the waveform descriptor shows the effectiveness on identifying the onset, we evaluated the performance of the proposed algorithm on an expert-annotated ICP dataset and compared it with three other pulse onset detectors. To evaluate the performance of the waveform descriptor, the ICP data was separated into three patient groups: template set, training set and test set, which were used to build the template, train the model parameters and validate of the algorithm, respectively. The performance of the other three detectors was also investigated on the test set. The algorithms first predicted the onset of each pulse and then the predicted results were compared with the ground truth. The template was built from the dataset consisting of 996 segments that were randomly selected from 22 patients. Each segment was with two consecutive beats that started from one onset and ended with another. The training dataset consisted of 122,800 normal beats and 674 segments of artifacts and noise from 15 patients. The test dataset consisted of 40,933 normal beats and 306 segments artifacts and noise from 11 patients.

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Table 1 Sensitivity (Se), positive predictive values (PPV) and error rates of the four algorithms at each tolerance level from 10 ms to 60 ms. (GM, global minimum within a sliding window; SSF, slope sum function; PUD, pulse waveform delineator; WD, waveform descriptor.) Interval (ms)

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3.1. Related algorithms 3.1.1. ABP pulse onset detectors As mentioned in the introduction, the existing ICP onset detection methods either require the synchronization such as ECG [11,16] or are subject to artifacts [15]. Due to both ICP and ABP belonging to beat-by-beat pulse pressure signals and highly correlating with each other [27,28], ABP onset detector may be extended to ICP signal. We investigated the performance of two algorithms proposed for ABP signal by Zong et al. [29] and Li et al. [30] on ICP signal. For simplicity, the algorithms proposed by Zong et al. and Li et al. are referred to as SSF (slope sum function) and PUD (pulse waveform delineator), respectively. The SSF employs a slope sum function (SSF) to transform the ABP signal into SSF signal. By this transformation, the upslope of ABP is enhanced and the remainder is suppressed. The ABP onset is identified by locating corresponding SSF pulse onset. Several parameters need to be adjusted proportional to the sample rates of the ABP signal. Note that the SSF was not designed for detecting the diastolic point as the other two algorithms. To facilitate comparison, we treated the nearest local minimum to the point detected by SSF as onset. The PUD was proposed as an ABP pulse delineator aiming to identify the onset, peak and notch of ABP pulse. The PUD uses the pair of inflection and zero-crossing points in the derivative of ABP signal. The onset is identified by searching and comparing the zero-crossing points before and after the maximal inflection in each estimated beat of the derivative. Given initial values, the amplitude and interval threshold of PUD are estimated adaptively. There are no tunable parameters in both algorithms.

3.1.2. Global minimum within sliding window One goal of the waveform descriptor is to select the optimal local minimum that may not be a global minimum as the onset. To evaluate the robustness to the global minimum that is not but close to the onset, the proposed algorithm was compared to the approach treating the global minimum around the starting time of a pulse as onset. In present work, the approach to find the global minimum proceeded by identifying the following points (Pmin1, Pmin2, Pmin3, Pmax1 and Pmax2) on the ICP waveform using a sliding window. The window length is the inter-beat interval of ICP pulse (the initial value of the inter-beat interval is set as the mean interval (e.g., 320 for 75 bpm, 400 Hz sample rate)). (1) Pmin1, the minimum from the start point within the window. (2) Pmax1, the maximum within the window starting at Pmin1. (3) Pmin2, the minimum within the window starting at Pmax1. (4) Pmax2, the maximum in the window starting at Pmin1. (5) Pmin3, the minimum between Pmax1 and Pmax2. If the distance

between the two is within the 0.5–1.5 of the interval, the Pmin3 is regarded as the onset. The window length is updated as the average of the distance between each two adjacent onsets, if the number of identified onset is larger than a value (e.g., 60); (6) Pmin1, Pmin3 identified in step (5); (7) go to step (2). This method is referred to as GM (global minimum) and the waveform descriptor is referred to as WD.

3.1.3. Computational cost When the onset detectors are used in real world settings, one of the key features is their real time performance. In present work, all the four algorithms were evaluated for their application for online onset detection. Using an ICP signal of 2429 pulses (around 36 min), the computational time was measured with Matlab 7.6 on a PC (Intel(R) Core(TM)2 Duo CPU P8400, 2.26 GHz, 32-bit operating system and 2.00 GB RAM). The running time was as follows (sec): GM, 3.0301; SSF, 0.5342; PUD, 2.9315; WD: 53.2132. WD ranked last mainly because a waveform descriptor needs to be generated for each local minimum, increasing the overall computational cost as compared to other detectors.

4. Results The waveform around the onset usually shows considerable irregularity and is prone to noise, which makes it very hard to pinpoint the labeled onset point exactly. In present work, we assessed the matching between the predicted and labeled onsets with tolerance level of 10 ms, 20 ms, 30 ms, 40 ms, 50 ms and 60 ms, i.e., the predicted and labeled onsets were considered as correctly matched if the distance between them was equal or less than the specified level). Table 1 reports the summary statistic of the onset identification. As can be seen, except for the relatively low positive predictive value at 10 ms tolerance level, the algorithms showed good performances. McNemar’s test [31] was used to examine if the performance of the algorithms showed statistically significant difference (considered significant when P < 0.001). As a result, the positive predictive values in Table 1 were statistically different. Specifically, the positive predictive value of WD was higher than that of the other four and that of GM was lowest at each tolerance level. Fig. 5 summarizes the results of McNemar’s test on sensitivity values of the algorithms. The sensitivity values of WD were higher than the other algorithms except there were no statistical differences between the sensitivity values of WD and SSF at a tolerance level of 20 ms, 30 ms and 40 ms. GM showed lowest sensitivity among the four at each tolerance level.

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Tolerance Level (ms) Fig. 5. Summary of the result of McNemar’s test on the sensitivity values of the four algorithms at each tolerance level from 10 ms to 60 ms. The left- and right-hand side of the equal sign (“=”) show equivalent sensitivity values by McNemar’s test. The left-hand side of the greater than sign (“>”) shows higher sensitivity than that of the right-hand side. P(SSF, WD) represents the P value of McNemar’s test between the sensitivity of SSF and WD (considered significant when P < 0.001). (SSF, slope sum function; GM, global minimum within a sliding window; PUD, pulse waveform delineator; WD, waveform descriptor.)

5. Discussion

tify the onset especially when the onset is not the global minimum around the starting time of the pulse [16]. In this study, we proposed a new algorithm to identify the pulse onset without using synchronization. The core of our algorithm is a waveform descriptor, which creates a signature for a given point using the vectors connecting that point and the local waveform samples around it. By comparing the similarity between the signature of each point on the waveform and the customized template, the optimal one is identified as the onset. Using an ICP dataset annotated by expert, the proposed algorithm was evaluated. We also investigated the performance of three other algorithms and compared them with our algorithm.

Automatic pulse onset identification is a fundamental stage of the beat-level analysis of ICP signal. With the onset of each pulse first identified, many other morphology features can be calculated and derived, such as slope and percussion peak. A common way to identify the onset of ICP pulses is using the landmark of a synchronous recorded signal such as ECG or ABP as a reference [16]. When the synchronization is not available or is contaminated by the noise, pulse onset detectors may be put into use. Even in the case that the pulse is located by the synchronization such as the QRS peak of ECG, an onset detector may also be necessary to iden-

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Fig. 6. Illustration of the robustness to the baseline drift, inter-beat interval variability and variation of pulse amplitude. The upper three panels show a challenging case in which both the inter-beat interval and pulse amplitude vary with cardiac arrhythmia. In addition, there are some pulses that the global minimum is not but close to the onset on each of them. The similarity cost of the onset is obviously smaller than that of the global minimum around the onset. The lower panels show an example of baseline drift and pulse amplitude diminishing. Despite the changes of the baseline and pulse amplitude, the similarity cost between each onset and template keeps relatively stable and below the threshold (0.46).

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Fig. 7. Illustration of the similarity cost without using the local minima as candidates. The upper panel shows the ICP signal and the lower panel shows the similarity cost between each point on the pulse and the template. The point around the true onset may generate more similar histograms to the template than the onset, which will be wrongly predicted as the onset (the stars indicate the predicted onset and the cycles indicate the wrong ones). Using local minima as candidates can improve the matching accuracy.

The matching between the predicted and labeled onsets was assessed at a set of tolerance levels [32] from 10 ms to 60 ms. As a result, the algorithms achieved good performance except that positive predictive values were relatively low at smaller tolerance levels (10 ms). WD achieved higher positive predictive value than the other detectors and GM ranked the lowest. WD achieved higher sensitivity than others except at a tolerance level of 20 ms, 30 ms and 40 ms, where its sensitivity was equivalent with that of SSF. GM showed lowest sensitivity. The lower positive predictive value at smaller tolerance level (10 ms) is probably because the waveform around onset always shows high irregularity and is prone to noise. It is challenging to match with the labeled onset accurately [16]. When applied to ICP waveform analysis, the onset identification at a tolerance level of 30 ms is acceptable. Therefore, all of the four algorithms are sufficient for the onset identification stage of ICP waveform analysis. Among the four detectors, WD showed overall better performance, in particular positive predictive value, and then the PUD and SSF, and GM ranked last. The reasons are the following. The SSF locates the onset by enhancing the upslope and suppressing the remainder of ICP pulse, which mainly makes use of the upslope phase of the pulse [29]. The PUD takes advantage of the derivative value (the inflection and zero-crossing points) of the pulse [30] and GM only uses the extreme values of the pressure and inter-beat interval of the signal. In contrast, the WD takes advantage of the overall shape of the pulse waveform around the onset to characterize the onset and discriminate between the onset and other points. The advantages of the WD are two folds. First, the normalization eliminates the effect of the pulse amplitude; second, the log-polar transformation makes the descriptor sensitive to the pulse morphology nearby and able to capture the overall shape of the pulse waveform. When the algorithm is applied to ICP signal, first, it is robust to the baseline drift and variability of inter-beat interval and signal amplitude. Fig. 6 illustrates the robustness to the pulse amplitude diminishing and the inter-beat interval variability. Second, it can distinguish the onset from the global minimum around it and can distinguish the normal pulse from the artifacts and noise. The selection of representative pulses for the template is a key factor affecting the performance of the algorithm. In present work,

the template was built from signals of intraparenchymal ICP monitoring. When the algorithm is applied to other types of signal, e.g., the signal recorded from ventricular or epidural space, the generation of the template from these types of signal needs to be done to achieve a required performance. In addition, the use of local minimum as the candidate of the onset is necessary for the waveform descriptor. First, it is much more time-consuming to generate waveform descriptor for each point on the pulse. Second, the point close to the onset may be mistaken as the onset because it usually generates almost the same histograms with the onset, which might be more similar to the template than the onset. Fig. 7 shows an example of this situation. In present work, the waveform descriptor was used to detect the minimum diastolic pressure point of ICP pulse. When applied to detect the onset of other definitions (such as the second derivative and tangent intercept method) without the synchronization, it can be used first to identify the minimum diastolic pressure point of each pulse and then the onset with corresponding definitions can be calculated. The proposed algorithm characterizes a given point by taking advantage of morphological feature of the waveform around the point. In consequence, it may be extended to identify the onset of other kinds of waveforms, such as ECG [33] and ABP [29] signal. Combined with other signal processing methods (e.g., wavelet analysis [34]), the waveform descriptor may be capable of identifying other characteristic points (e.g., the percussion peak of ICP pulse [35]). 6. Conclusion In this paper, we have presented an algorithm for automatic ICP pulse onset identification. The algorithm constructs a waveform descriptor to give a description of a given point using the distribution of the relative positions of that point and the local waveform samples around it. The algorithm was evaluated and compared with three other algorithms on an ICP dataset. The statistical significance of differences of the algorithms was examined by McNemar’s test. As a result, all the algorithms showed their effectiveness and WD showed overall better one. The assessment indicates that the algorithms are effective for identifying the onset of ICP pulses.

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