Development of a procedure for periodization of the radial artery pulse signal for medical diagnostics

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Development of a procedure for periodization of the radial artery pulse signal for medical diagnostics

Guchuk V.V.; PhD in Engineering, Senior Researcher, Laboratory of dynamic information-control systems V.A. Trapeznikov Institute of control sciences Russian academy of sciences

Keywords: pulse signal, radial artery, periodization, amplitude-time characteristics, composite algorithm.

Аннотация

Разработка процедуры периодизации пульсового сигнала лучевой артерии для медицинской диагностики

Гучук В.В. (Российская Федерация)

Гучук Владимир Всеволодович - кандидат технических наук, старший научный сотрудник, Лаборатория динамических информационно-управляющих систем,

В статье рассмотрены алгоритмические вопросы процесса разделения периодов в импульсном сигнале лучевой артерии. Алгоритм периодизации - это набор различных процедур для обработки импульсного сигнала, которые позволяют уверенно распределять периоды в сигнале. Он предшествует остальным этапам анализа. Описываются процедуры, используемые в алгоритме. Обсуждается целесообразность их применения. Приведена структурная схема разработанного алгоритма периодизации импульсного сигнала. Проверка разработанного алгоритма проводилась на репрезентативной выборке.

Ключевые слова: пульсовой сигнал, лучевая артерия, периодизация, амплитудновременные характеристики, составной алгоритм.

When solving problems of computer pulse diagnostics [1], at the first stage it is necessary to develop an the periodization algorithm. The periodization algorithm is a set of various procedures for processing an impulse signal that can confidently allocate periods in a signal. There are no detailed descriptions of periodization algorithms with practical attractiveness in the literature. The types of algorithms discussed below are “sequential”, “statistical” and “composite” (“combined”, “mixed”). In the sequential algorithm, after finding S-peak (the systolic peak of the pulse signal), the next S-peak is searched for the interval [T_min...T_max] provided that its amplitude is not less than A_min. To increase the stability of the algorithm to the variability of the heart rate (HRV), it is necessary to use additional procedures, for example, logical analysis in a situation where there is no certainty that it was possible to find a really next S-peak.

The statistical algorithm analyzes the statistics of peak level distributions on the pulse signal, is analyzes only the amplitude component. An algorithm of this type usually gives a more adequate picture than a sequential algorithm. The composite algorithm uses a mixed search strategy for periods and can include additional procedures for correcting the results of periodization, combining the positive qualities of different procedures for more successful periodization. Among the procedures from which the periodization algorithms are arranged, the low-frequency filtration, smoothing, amplitude sieve, binding to reference points, adaptation of parameters for a particular signal, are the most productive, as the practice shows. The procedure "amplitude sieve" filters out peaks with a small level and allows simplify the periodization process.

The amplitude sieve can also be used to ensure the selection of "privileged" Speaks, clearly related to (by the amplitude level) to the S-peaks. Such S-peaks are used by the binding to reference points procedure which is the procedure for using the nearest preferred S-peak in an ambiguous situation. For a sequential algorithm, the use of privileged S-peaks allows to continue the periodization in case of premature stopping of the algorithm due to the absence of a suitable peak in the search zone. Adaptation of parameters for a specific signal consists of the preliminary periodization and the determination on its basis of the average or typical length of the period, as well as the level of S-peaks in periods with a length close to typical. It is necessary to control the correctness of the results of the application of certain procedures. For example, by using the simplest smoothing filter, A_i = k_JA_i-i + k₀A_i + kiA_i+i, where Aj is the amplitude of the j-th signal, k_n is the weighting factor, kj+ko+kj = 1, the coordinate of the maximum can shift. Besides, the application of a filter with several iterations sometimes leads to a bias, which is very significant for a diagnostic evaluation.

An important role is played by the very possibility of adjusting the parameters of the algorithm, and the ease of tuning. The sequential algorithm contains a larger number of configurable parameters, which can positively affect the periodization of signals which have a complex structure. In the presence of cardinal artifacts in the signal, the periodization process can give not only an inaccurate representation of the pulse, but also lead to inadequate estimates; therefore, in certain known software implementations, the signal is divided into separate fragments based on visual control (inspection). Fragments with sufficiently stable characteristics both in terms of pulse amplitude and heart rate are highlighted and excluded from further consideration periods, for example, the ones that do not correspond to the "threshold of prudence" [4].

If HRV is of a single-factor (single-module) nature, then it is not difficult to construct a periodization algorithm that takes into account such fairly simple variations. For example, with amplitude instability of the rhythmic pulse, sequential periodization algorithms are more effective, and in the case of a pronounced temporal arrhythmia with a stable level of Speaks, statistical algorithms and algorithms using an amplitude sieve work more efficiently. Practice shows that single-module (single-factor) variations are rare. More often the transition of the pulse to the rapid rhythm is accompanied by a decrease in signal power and vice versa, prolonging the duration of the current period can substantially increase the amplitude of the next S-peak. It is also necessary to take into consideration the belonging of the pulse signal to one of the archetypes [3].

The construction of the periodization algorithm was carried out according to a representative sample (~ 300 signals). More than 10 different of periodization algorithms of different types were realized, the testing of which allowed to determine the effectiveness or hopelessness of various signal processing procedures. As a result, a composite algorithm was chosen that combined the statistical algorithm and the corrective procedure a configurable amplitude sieve. At first, the algorithm searches for peaks uniquely related to S-peaks. The distribution of the identified S-peaks on the time scale is then analyzed. If the distance between some neighboring S-peaks is more than KaTc, where Tc is the average (typical) duration of the period, and Ka is the arrhythmia coefficient (1,5 ... 2,5) [5], then this correction is performed for this non-periodical region.

Now lowered the A*min level to search S-peaks. The correction procedure can be organized in an iterative way - in the non-periodic region, a peak with maximum amplitude is sought and it is included in the list of S-peaks. Then, the distribution of the peaks at the timeline is again analyzed, etc. In the first case, the difficulty lies in the choice of A*min, and the general problem is the uncertainty of the arrhythmia coefficient.

Fig. 1. Dependence of the amplitude A on the number of the period n

Fig. 2 illustrates the dependence of the amplitude of the peak A(n), and Fig. 3 dependence of the duration of the period T(n) on the number of the period n for real signals on which the periodization algorithms were being debugged. The illustrations give a visual representation of the complexity of solving the problem of periodization, in particular, given the fact that the signals have a fundamentally different amplitude-time structure, and the periodization algorithm cannot be absolutely universal.

In practice, the most important factor is the very technical implementation of the procedures used by the periodization algorithms. For example, in the initial procedure for finding extremums (peaks) it is useful not just to determine local maxima, but to immediately search for a global maximum in the tolerance zone [(t - D)... (t + D)], where t is the current time and D is a half zone of tolerance. This allows to simplify further procedures, as it will clear nearby maxima (ie, get rid of the "palisade"). Naturally, it is necessary to control the correctness of the results of the application of certain procedures.

When choosing the type of algorithm for periodization, the very possibility of adjusting the parameters of the algorithm plays an important role along with the ease of tuning. The sequential algorithm contains a larger number of configurable parameters, which can positively affect the periodization of signals which have a complex structure. At the same time, there should be some compromise, since, as practice has shown, adjusting the parameters to the most qualitative periodization can improve the efficiency of the algorithm only for the sample that was tuned, significantly worsening the results of the periodization of other signals.

When given the cardinal artifacts, the periodization process can give not only an inaccurate picture of the signal, but also lead to inadequate estimates. To prevent the occurrence of such collisions, prior to the periodization, in some known software implementations, the signal is divided into separate fragments based on their visual control (inspection). At the same time, fragments with sufficiently stable characteristics both in terms of the amplitude level and in the frequency of pulsations are singled out, and also quasi-periods, for example, which do not correspond to a certain prematurity threshold, are excluded from further consideration. If the variations of the signal periods are one-factor (single-module), then it is easy to construct a periodization algorithm that takes into account such variations. For example, for signals with amplitude instability of the teeth, sequential algorithms of periodization are more effective. With pronounced temporal variations and a stable level of prongs, statistical algorithms and "amplitude sieve" algorithms work well. The practice of analysis shows that single-module (single-factor) variations are rare.

More often the transition from one stationarity (in the sense of the duration of the period) to another is accompanied by a decrease in the signal power and vice versa, the tightening of the duration of the current period can substantially increase the amplitude of the next wave. Regarding the above-mentioned signal splitting into separate fragments based on a visual inspection, this procedure can be useful in a number of cases. However, there are often signals in which periods of vigorous operation and low-power periods are mixed either spontaneously or with some periodicity, which predetermines the inexpediency of their fragmentation. The construction of the periodization algorithms was carried out heuristically with testing on a representative sample (~ 10³) of the signals.

More than 10 versions of the periodization algorithms related to the sequential, statistical and composite type have been implemented. The results of testing algorithms allowed to determine the effectiveness or hopelessness of various signal processing procedures, as well as to identify the possibilities of setting the parameters of periodization. Synthesis of algorithms and their debugging were carried out based on the work of the constructed algorithm of periodization in an autonomous mode without human participation. Based on the results of the research, a composite algorithm was chosen for further use and modification, combining the statistical algorithm and the corrective procedure with a configurable amplitude sieve. In Fig. 5 is a simplified block diagram of the developed periodization algorithm.

Fig. 2. Simplified block diagram of the developed periodization algorithm

The statistical algorithm is realized in a truncated form. With its help, peaks of large amplitude are sought, which makes it possible to reliably relate them to S-peaks. Then the distribution of the detected peaks on the time scale is analyzed. If the distance between certain neighboring S-teeth are more than K_aT_c (T_c is the average duration of the period, K_a is the arrhythmia coefficient), then correction is performed in this region. The A_min level is set, above which maxima are sought, claiming the status of peaks. The correction procedure can be organized in an iterative way. In the non-periodic region, a maximum is sought with the largest amplitude and it is included in the list of peaks. Then, the distribution of the maxima on the timeline is again analyzed, and so on.

The verification of the developed periodization algorithm was carried out on a representative sample. Several variants of the composite algorithm were implemented. As a result, an algorithm was chosen that combined the statistical algorithm and the corrective procedure - a configurable amplitude sieve. The analysis of the results of the developed algorithm has confirmed the acceptable efficiency of the periodization process for very diverse pulse signals [6]. The author expresses gratitude to Mikhail Coen from Matea Valley school (St. Illinois, USA) for assistance in preparing materials for publication.

References

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2. Zhaopeng Fan, Gong Zhang, Simon Liao. Pulse Wave Analysis // Advanced Biomedical Engineering, 2011. P. 21-40.

3. Guchuk V.V. Fragmentary imitation modeling of the pulse signal of the radial artery // European science, 2016. № 12. P. 85-88.

4. Desova A.A., Guchuk V.V., Dorofeyuk A.A. Spectral Density Analysis of Dynamic Sequences of Radial Artery Pulsation // Biomedical Engineering. Munich, London: Springer Science, 2012. Vol. 45. Iss. 6. P. 240-244.

5. Desova A.A., Guchuk V.V., Pokrovskaya I.V., Dorofeyuk A.A. Intelligent Analysis of Quasiperiodic Bioosignals in Medical Diagnostic Problems (with the Example of a Pulse Signal) // Automation and Remote Control, 2018. Vol. 79. Iss. 11. P. 1953-1962

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