Algorithm for identifying and separating beats from arterial pulse records
© Treo et al; licensee BioMed Central Ltd. 2005
Received: 02 March 2005
Accepted: 11 August 2005
Published: 11 August 2005
This project was designed as an epidemiological aid-selecting tool for a small country health center with the general objective of screening out possible coronary patients. Peripheral artery function can be non-invasively evaluated by impedance plethysmography. Changes in these vessels appear as good predictors of future coronary behavior. Impedance plethysmography detects volume variations after simple occlusive maneuvers that may show indicative modifications in arterial/venous responses. Averaging of a series of pulses is needed and this, in turn, requires proper determination of the beginning and end of each beat. Thus, the objective here is to describe an algorithm to identify and separate out beats from a plethysmographic record. A secondary objective was to compare the output given by human operators against the algorithm.
The identification algorithm detected the beat's onset and end on the basis of the maximum rising phase, the choice of possible ventricular systolic starting points considering cardiac frequency, and the adjustment of some tolerance values to optimize the behavior. Out of 800 patients in the study, 40 occlusive records (supradiastolic- subsystolic) were randomly selected without any preliminary diagnosis. Radial impedance plethysmographic pulse and standard ECG were recorded digitizing and storing the data. Cardiac frequency was estimated with the Power Density Function and, thereafter, the signal was derived twice, followed by binarization of the first derivative and rectification of the second derivative. The product of the two latter results led to a weighing signal from which the cycles' onsets and ends were established. Weighed and frequency filters are needed along with the pre-establishment of their respective tolerances. Out of the 40 records, 30 seconds strands were randomly chosen to be analyzed by the algorithm and by two operators. Sensitivity and accuracy were calculated by means of the true/false and positive/negative criteria. Synchronization ability was measured through the coefficient of variation and the median value of correlation for each patient. These parameters were assessed by means of Friedman's ANOVA and Kendall Concordance test.
Sensitivity was 97% and 91% for the two operators, respectively, while accuracy was cero for both of them. The synchronism variability analysis was significant (p < 0.01) for the two statistics, showing that the algorithm produced the best result.
The proposed algorithm showed good performance as expressed by its high sensitivity. The correlation analysis demonstrated that, from the synchronism point of view, the algorithm performed the best detection. Patients with marked arrhythmic processes are not good candidates for this kind of analysis. At most, they would be singled out by the algorithm and, thereafter, to be checked by an operator.
Outpatients coming daily for consultation to a general public hospital are often preventively checked for signs suggestive of infectious, cardiovascular and/or any other endemic disease. The positive detected fraction is derived for further confirmatory study, which may lead to eventual treatment. Within such concept, this project was specifically designed as an epidemiological aid-selecting tool for a small country health center serving a large rural area (see Acknowledgments). Essential requirements were low cost and simplicity. The general objective was to screen out possible coronary patients.
Peripheral artery function can be non-invasively evaluated by impedance plethysmography, either in lower or upper limbs . Changes in these vessels appear as good predictors of future coronary behavior [2, 3]. Basically, impedance plethysmography detects volume variations due to the pulsating blood flow that, after simple mechanical occlusive maneuvers, may show indicative modifications in arterial/venous responses [4, 5].
Pulse plethysmographic analysis, based on variations of its amplitude or waveform , requires the averaging of several beats.
There are specific algorithms for the detection of the dicrotic notch ; some papers make a beat-to-beat analysis of the arterial pressure [8–11]. Commercial equipment (like Complior ®SP, Artech Medical, http://www.artech-medical.com y SphygmoCor ® Vx, Atcor Medical, http://www.atcormedical.com) carry out the above mentioned type of plethysmographic signal analysis. Schroeder et al , by means of MATLAB, developed a cardiovascular package (named HEART), which permits beat identification using two sequential processes (one of coarse approximation and a second one of fine adjustment). Unfortunately, none of these procedures offer detailed descriptions.
Besides, several algorithms have been developed to detect electrocardiographic beats, by and large based on the recognition of the QRS complex . However, our design has been thought to operate independently of the ECG signal; for these reasons they are not applicable in this case.
Thus, the objective here is to describe an algorithm to identify and separate out beats from a plethysmographic record during an occlusive maneuver. As a secondary objective, we intended to compare the output given by human operators (trained and not trained) against the algorithm. The method herein proposed is potentially applicable to other cardiac signals.
An occluding cuff produces a limb short ischemia. Basal and post-occlusion plethysmographic arterial pulse records are compared searching for either amplitude and/or waveform modifications or both. Since the possible change in a single beat record does not supply enough information, valid results call for averaging of a series of pulses and this, in turn, requires proper determination of the beginning and end of each beat. In other words, good beats must be identified and singled out discarding abnormal pulses.
From the daily inflow of hospital outpatients, we obtained 800 records out of which 40 supradiastolic-subsystolic occlusive ones were randomly selected without any preliminary diagnosis. All patients accepted and signed the informed consent. The attending physician, including the measurements leading to the quantitative data mentioned above, carried out routine clinical interrogation. Blood pressure was obtained with the oscillometric method using the contra-lateral arm to that where the test was to be performed. Patients rested for at least 5 min in the supine position prior to the test.
Impedance Plethysmography and Recording System
Radial pulse was picked up with two metallic electrodes (ECG standard type) placed over the forearm artery line, 2 cm below the ante-cubital fold, and 5 to 10 cm apart. The forearm was always at the left atrial level. Besides, a simultaneous standard ECG was obtained. Impedance was obtained with a custom-made laboratory apparatus .
Digital acquisition (sampling frequency sf = 200 Hz, at 16 bits) was carried out using a commercial system (BIOPAC System Inc, AcqKnowledge II for MP100WSW). Each occlusive maneuver record included basal plethysmographic pulses (PRE), a period of 2 to 3 minutes of occlusive cuff inflation (INTRA), and a post-occlusive (POST) after release; the overall duration was always in the order of 5–6 min (Figure 1).
The original signal is derived twice applying the well-known iterative series of subtractions , that is,
S'(n) = S(n + 1) - S(n)
S"(n) = S'(n + 1) - S'(n) 
The sequence of maximum spikes after multiplication (Figs. 2 and 3) can be used as a filtering criterion to separate out the true beats. Whenever the interval between two pulses is much smaller than the cardiac period (for example, less than one half), it can be assumed that the two spikes are too close together and cannot represent a beginning (and ending) of a whole cycle. Consequently, one must be removed.
Since, by and large, the beginning of a cycle corresponds to a steep rise time, the second derivative has more weight, and the multiplication result clearly indicates to retain that particular spike (Fig. 3, trace W2).
Mathematically, this is treated as
t(Si+1) - t(Si) <Tol1 × T c 
where t(Si+1) and t(Si) are, respectively, the time of appearance of spikes i+1 and i in signal W1, Tol1 is a preset tolerance value and T c = 1/fc stands for the cardiac period expressed in seconds. Each pair of adjacent spikes is analyzed and, if the comparison result is true, the smallest is removed and the new pair of contiguous spikes is now chosen. If the result is false, i is incremented. The process repeats until no true result is obtained. Adjusting the tolerance value Tol1, the number of removed spikes can be increased or decreased.
Once all small spikes have been removed, the remaining spikes must be analyzed to check if they correspond to the beginning and end of a cycle. Figure 3 (fifth trace W2) shows the peaks remaining after the weighed filter. Spike 4 is a misdetection that must be removed. A second filter matches pairs of peaks (not necessarily consecutive) checking whether they correspond to a beat limits or not; the distance between them should be fixed between T c ± Tol2, where the latter is a second tolerance value, generally chosen close to 20%.
Starting from the first detected spike 1 at time t (Fig. 3, fifth trace), and assuming it corresponds to the beginning of a cycle, a second spike should be located within the interval t + T c ± 20%. If this second spike exists, the time corresponding to both spikes is stored as the limits of a cardiac cycle. In fact, this second spike exists in Figure 3, marked as 2. The process is repeated starting now from 2 and so on. Now, let us consider that the first spike detected was 4. When searching its partner spike ahead, the algorithm will not find it because 5 and 6 are, respectively, too close and too far from 4. In this case, 4 is discarded and the process continues to the next one.
Cardiac period has been assumed constant up to now, however, it is known to be modulated by the respiratory heart rate response. To have a better estimation of T c , each time two spikes are found to be (T c ± Tol2) seconds apart, their difference is used to update a new value of T c to be applied in the following calculations.
For each of the 40 patients, a 30 s trace was chosen at random, which was analyzed by two operators. One of them (operator 1) was trained and familiar with the procedure and another (operator 2) without any previous training. Both operators received the same instructions regarding the analysis to be performed. Each operator marked manually the beginning and end of each beat as the 30 s sample was presented on the monitor. The selection criterion was to identify that point previous to the rapid rising of the ejective period, not necessarily coincident with the previous minimum. In this way, there were two marks that clearly bounded each positive cycle. When the beat limits were not clearly defined or the signal was lost due to circuit saturation, the portion between the last observed beat and the following beginning was classified as negative (i.e., rejected). Thereafter, the algorithm was applied and coincidences with the operators' results were searched.
Sensitivity of the procedure was defined as the percentage of beats correctly selected by the algorithm with respect to the total number of beats marked as true by the operator, that is,
s [%] = tp /(tp + fn) × 100 
Accuracy, instead, was defined as the total number of sections correctly rejected by the algorithm with respect to the total number of sections discarded by the operator,
a [%] = tn /(tn + fp) × 100 
Bounding of the beats is also important for the correct synchronization of the averaging procedure. Thus, those beats correctly classified by all three methods (operators 1 and 2 and the algorithm) were selected to compare the synchronization ability. For that matter, the time between the beginning and the first maximum coincident with ventricular ejection was measured for each beat. This time was, of course, different for the operators and the algorithm, each with a specific coefficient of variation. The latter was taken as the statistical estimator.
Moreover, for each patient a correlation analysis was carried out between all possible combinations of the tp beats. For each pair of beats a correlation factor was obtained, thus producing a non-normal distribution when all combinations are considered, which is usually characterized by the median value. In the end, we obtained three of these values for each patient according to the classification methods (two operators and algorithm).
The coefficient of variation (also with a non-Gaussian distribution) and the median should be analyzed by non-parametric techniques. In our case, we used Friedman's ANOVA and Kendall Concordance.
Results of the statistical analysis for both operators.
Accuracy for both operators was 0 because traces marked as negative were somehow classified by the algorithm, thus, producing fp beats.
The detection routine for the average cardiac frequency was a critical factor in the analysis of the algorithm; any failure in it can produce an error that would propagate to any subsequent processing. Thus, this parameter was checked by visual inspection of the 40 signals and their frequency spectra.
This algorithm allows the averaging of non-invasively obtained arterial pulses for the evaluation of the vascular response to peripheral occlusive maneuvers employing only the plethysmographic signal. The ECG served as monitor of cardiac activity and was used to help the operators in their task. Since the algorithm was designed thinking of a possible commercial equipment based only on the plethysmographic signal, the ECG, cannot be included in the analysis.
The algorithm is based on the analysis of the maximum systolic slope discarding pulses not consistently separated out from their respective previous beats or when the derivative value is too low. Usually, beat separation in blood pressure records is obtained by the minimum value previous to the dicrotic notch. Noise, however, may perturb this kind of determination. When pulses selected by this criterion are overlapped for their averaging, the systolic maximum does not temporally coincide in all beats and a small shift, unpredictable and unknown, shows up. Low amplitude noise, when present, tends to interfere with the temporal location of the valve opening point. The maximum second derivative criterion does not really represent valve opening but rather represents maximum rise during systole. In most of the patients, in our experience, the latter reference showed better periodicity and seems to be a better time reference when averaging is required. The second event seems to be less sensitive to interferences because signal growth during systole is larger than noise changes. This observation was supported by the variability analysis. Kendall coefficient indicates that correlation is a reliable statistic and its variability is similar in the three methods.
The algorithm, due to its philosophy of design, does not have to identify all beats, so conferring to it a practical characteristic, i.e., rather frequently, due to patient's movements, the system's electronics may saturate. In such case, the algorithm disregards the piece resuming the search after signal recovery. However, the two filtering criteria are based on the cardiac frequency and, when the latter is too variable (for example, due to arrhythmias) the sensitivity falls drastically (figure 5D).
Tolerances, in turn, are useful to modify the algorithm's performance according with the prevalent conditions (noise, drift, saturation). However, sensitivity higher than 90% is enough when the recording time is long (say, 5–6 min or more). The tolerance values suggested here produced in our opinion the best results.
Interested investigators are encouraged to request the algorithm in order to test it using signals obtained from other sources. These authors would be happy to make it available.
The proposed algorithm showed good performance as expressed by its high sensitivity. The correlation analysis demonstrated that, from the synchronism point of view, the algorithm performed the best detection. Patients with marked arrhythmic processes are not good candidates for this kind of analysis. At most, these patients would be singled out by the algorithm to be checked by an operator.
We deeply thank the medical and paramedical staff of the General Lamadrid Hospital (City of Monteros, Province of Tucumán, Argentina) for their collaboration during the clinical tests reported here. We also thank Dr. Elena Bru for her useful contributions and discussions, especially in aspects regarding to the statistical analysis. Preliminary partial results were communicated to the III Latin American Congress of Biomedical Engineering and XIX Congresso Brasileiro de Engenharia Biomédica, João Pessoa (Brazil), September 22–25, 2004. This work was partially supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, PID#3134-700-88) and by the Consejo de Investigaciones de la Universidad Nacional de Tucumán (CIUNT, E349/2005).
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