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.

Each applied maneuver consists of a supradiastolic and subsystolic occlusion; thus, it permits inflow of blood while stops outflow, which leads to limb volume increase. A typical record is showed in Figure 1. The pulse 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.

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.

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 14.

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).

Figure 2 summarizes the sequential steps the recorded signal S went through. The first step is the detection of the average cardiac frequency fc, which is expected to be within the 0.5 Hz – 2.5 Hz range, and is divided in two stages: First, the signal goes through a band-pass FIR (Finite Impulsive Response) filter, with cut-off frequencies of 0.8 Hz and 2.8 Hz, and attenuation at least of -50dB at 0.25 Hz and 3.25 Hz. Thereafter, the Power Spectral Density function (PSD, an averaging variant of the Fast Fourier Transform), is applied to find fc. The first minute of data acquisition corresponds to the basal or pre-occlusion stage (Fig. 1). This period is divided into overlapping sections; each is linearly detrended, then windowed with a Hanning function (4,096 samples) and, thereafter, zero-padded to a length of 8,192 samples. The magnitude squared of the Fast Fourier Transform of each section is averaged to form P_xx, the Spectral Density Function. Each section overlaps with the previous 2000 samples. The maximum value for the first harmonic component corresponds to the cardiac frequency fc (see Signal Processing Toolbox for Use with MATLAB, The MathWorks, Inc, Natick, MA).

The original signal is derived twice applying the well-known iterative series of subtractions 15, that is,

S'(n) = S(n + 1) - S(n)

S"(n) = S'(n + 1) - S'(n)     [1]

where S'(n) and S"(n) stand, respectively, for the first and second derivative and n represents the sample number. Figure 3, upper trace, shows 6 beats of a typical plethysmographic record. Thereafter, both signals are processed binarizing the first derivative and rectifying the second derivative. Binarization means to replace 1's for positive values and 0's for negative ones. The process of rectification leaves only the positive excursions. Clearly, the product of the binarized and rectified signals is a trace showing large peaks and some significantly lower ones in between, which is called the weighing signal W₁. When the latter product is compared with the original S signal, one can easily see that the large peaks are obviously coincident with true good beats while the small spikes correspond to other changes (not pulses) in that signal. A spike detection routine based on the first derivative sign change identifies all maxima, including both the large and the small spikes; thus, filtering is required to remove the small spikes and preserve the large ones.

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(S_i+1) - t(S_i) <Tol₁ × T_c     [2]

where t(S_i+1) and t(S_i) 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.

Since an exact coincidence is almost nil, we adopted a threshold level to specify the maximum difference to be accepted between the limits marked by the operators and the algorithm. A program was developed to determine the beginning and ending points closest to those selected by the operator (Fig. 4). When the addition of the differences (Δt₁ + Δt₂) was lower than 10% of the cardiac period, the beat was considered as true positive (tp). If the difference was larger, the beat was classified as false negative (fn). However, when the operator could not bound the beat there is an undetermined signal length, which must not be processed. If coincidently the algorithm did not classify any beat within that same length, the selection is marked as true negative (tn). Instead, if the algorithm picked up at least one beat, the selection is considered as false positive (fp).

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     [3]

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     [4]

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.