An Echocardiographic Approach to the Analysis of the Variability in Cardiac Cycle Phases

Enrico G Caiani^a, Alberto Porta^b, Maurizio Turiel^c, Giuseppe Baselli^a, Sergio Cerutti^a

^aDipartimento di Bioingegneria, Politecnico di Milano, Milano, Italy
^bDipartimento di Scienze Precliniche, LITA di Vialba, Università degli Studi di Milano, Italy
^cDipartimento di Scienze Cliniche “L.Sacco” - Università degli Studi di Milano -
Istituto Ortopedico Galeazzi, Italy

Correspondence: EG Caiani, Dipartimento di Bioingegneria, Politecnico di Milano, P.zza L. da Vinci 32, 20133 Milano, Italy.
E-mail: caiani@biomed.polimi.it, phone +39 02 23993302, fax +39 02 23993360

1.  Introduction

Measurement of heart rate variability (HRV) is a noninvasive approach based on ECG monitoring that allows an indirect evaluation of cardiovascular neuro-autonomic control. Spectral analysis of HRV series provides a quantitative noninvasive means of assessing the functioning of the short-term cardiovascular control systems [Akselrod et al., 1981]: by this processing tool, sympathetic and parasympathetic activity has been related to low frequency (LF) and high frequency (HF) spectral component, respectively.

The modulations of heart periods are naturally not the only manifestation of the autonomic regulatory mechanisms [Task Force, 1996]. Currently, commercial equipment exists that enables simultaneous recording of ECG, respiration, blood pressure, and so forth. Among them, echocardiographic automated endocardial border detection technique [Perez et al., 1993] , based on acoustic quantification (AQ), provides a novel opportunity to assess LV function by means of a noninvasive and real-time measure of LV area or volume, obtained as a byproduct of routine echocardiographic examination [Bednarz et al., 1995]. As confirmed by literature [Chenzbraun et al., 1993], AQ technique may enhance the evaluation of diastolic function, which is important to understand the relationship between alterations of filling phases of ventricle and cardiac failure.

The analysis of the AQ signal was primarily focused on the extraction of LV function parameters (LV chamber dimensions, ejection fraction, peak filling and ejection rates) averaged over a few cardiac cycles [Mor-Avi et al., 1995] , in order to obtain reliable measures despite the variability contained in the signal, due to artifacts and physiologic LV beat-to-beat changes.

Recently, particular attention was given in trying to study the fluctuations present in the AQ signal [Akselrod et al., 2000] and in the beat-to-beat variability of LV volume function parameters [Caiani et al., 2000; Caiani et al., 2002a], in order to exploit the complex interactions between neural control of heart rate and mechanical influence of respiration.

The aim of this study is to apply a method we recently developed [Caiani et al., 2002b], based on a time-warping technique [Sakoe and Chiba, 1978], to track beat-by-beat some fiducial points on the LV volume waveforms, otherwise not easily detectable, in order to extract new variability series related to the time duration of different diastolic phases (rapid filling, diastasis and atrial contraction) inside the heart beat. In fact, the RR period computed on the electrocardiogram corresponds to different mechanical phases of the heart, in which autonomic control could act in different ways. Studying the variability of diastolic phases with their spectral components could add new insight into HRV, exploiting potentially different relationships between mechanical phases and autonomic nervous system activation.

Comparison between a group of normal young versus a group of normal adult subjects will be performed, to evaluate the effects of ageing on the variability of these new LV function indices.

2.  Material and Methods

2.1. Study Protocol and Data Acquisition

Data were obtained in 10 normal young (NY) subjects (mean age±SD, 24±6 years) and in 10 normal adult (N) subjects (63±6 years).

Cardiac imaging was performed by an expert sonographer in apical 4 chamber view using a Sonos 5500 ultrasound imaging system (Philips, Andover, MA, USA) equipped with a transthoracic S4 probe, AQ software and analogue output port. The LV volume signal was computed by the imaging system on each frame (25 Hz) in real time by using the disc model available in the system; samples were interpolated by cubic spline and sent as output to the analogue port.

ECG was obtained from precordial lead V2 while respiration was monitored by a piezoelectric thoracic belt (Marazza, Monza, Italy). All signals were simultaneously sampled at 300 Hz (DT300 A/D, Data Translation, Marlboro, MA, USA) for at least 3 minutes and stored in a personal computer for further processing.

To reduce the broad band noise, the AQ signal was filtered with a low-pass FIR filter (150 coefficients, cut-off frequency 15 Hz). Then, each i-th LV volume cycle was extracted from the AQ signal starting from the i-th end systolic volume (ESV(i)) to the next one (ESV(i+1)). This choice was made because the automatic detection of this fiducial point is the most robust one.

2.2. Tracking by Time Warping Technique

Given two waveforms W₁(t_i) and W₂(t_j), each mapped on its time axis t_i e t_j:

the correspondence between their points is described by the warping function (WF), defined as the sequence of points w(k) = (i(k),j(k)) on the (i,j) plane

where w(k) represents the optimal link between the point i(k), on the t_i time basis, with the point j(k), on the t_j time basis. In this way, WF(k) would allow to properly compare the points of W₁(t_i) with those of W₂(t_j), representing their optimal correspondence given an appropriate dissimilarity function [Sakoe and Chiba, 1978].

Once q points of interest W₁(i_x), …., W₁(i_y), …..,  W₁(i_z) have been identified on W₁(t_i), corresponding to samples i_x,….., i_y, ….., i_z, it will be possible to individuate the samples j_x, …, j_y, …, j_z on W₂(t_j)having similar characteristics, by the non linear alignment defined by the points of the WF:

If the WF has been computed without imposing a slope constraint [Gupta et al., 1996], it will be possible to have horizontal and vertical segments in the WF, so allowing a non univocal correspondence between ix and j_x. Thus, more points i_x1, i_x2, …, i_xm could correspond to a single point j_x and vice versa. In this case, to obtain an univocal extraction of the q points of interest, the first point i_x1  will be assumed as the corresponding one to j_x.

To properly define the points of interest to be tracked beat-by-beat, we decided to select these points not from a generic waveform W_n of the sequence but from their average AW computed with time warping, as described in [Caiani et al., 2002b], thus avoiding the results to be independent from the initial choice.

Once the q points have been identified on AW, the procedure illustrated above can be iterated on all the waveforms of the sequence, computing the WF between AW and the i-th waveform W_i and extracting the q beat-by-beat variability series (see Fig. 1).

Figure 1. Correspondence between points of interest selected on the average waveform AW with samples on the W₁ waveform, as expressed by the warping function WF.

2.3. Selection of Points of Interest

On the AW, the following points were identified semi-automatically: the end-systolic volume (ESV) as its minimum, the temporal locations of diastasis onset (DO) and end (DE), and the end-diastolic point (EDV) as its last point. By projecting these points on all the waveforms of the sequence, the beat-to-beat variability series of the duration of rapid filling (RF, time interval between ESV and DO), diastasis (DS, time interval as DO and DE) and atrial contraction (AC, time interval between DE and EDV) were obtained, together with the whole diastolic (time interval between ESV and EDV) and systolic phase durations (time interval between previous EDV and ESV).

2.4. Autoregressive Spectral Analysis

The extracted beat-to beat variability series, together with RR, were analyzed with autoregressive spectral analysis (Levinson-Durbin iterative algorithm [Kay, 1988] for parameters identification, Akaike criterion for the model order). Power spectral density (PSD) was decomposed in order to calculate the power connected with the identified rhythms: these were classified as low-frequency (LF: from 0.04 to 0.14 Hz) and as high frequency rhythm (HF: at respiratory frequency). Statistical analysis was performed by unpaired t-Student test, with significance for p<0.05.

3.  Results

Comparing the results relevant to the mean duration of the measured sub-intervals of the cardiac cycle obtained in N and NY, a significant increase in the duration of the systolic phase with age was evidenced (387±11 vs. 345±8 ms), together with a marked reduction in the diastasis duration (145±35 vs. 224±32 ms), while mean RR was unchanged (920±45 vs. 927±48 ms). The shortening of the diastolic phase with age (531±51 vs. 592±43 ms) appeared to be due to a DS shortening, while RF and AF phase durations were unchanged (246±19 vs. 238±8 ms and 136±10 vs. 130±9 ms respectively).

The variance of RR was significantly decreased in N (442±110 vs. 2734±772 ms²), together with a significant reduction in the variability of the diastolic phase (1662±251 vs. 3890±1062 ms²), of diastasis (1075±260 vs. 3575±991 ms²) and of atrial contraction (627±138 vs. 1343±225 ms²), while that of rapid filling (1585±242 vs. 1508±238 ms²) and of the systolic phase (1209±136 vs. 1634±246 ms²) remained unchanged. In NY, the diastolic phase had a variability greater than the systolic phase, due to the large variability of DS; in N, the reduction of variability in DS was accompanied with a reduction of variability in the whole diastole.

Focusing on the spectral components (see Fig. 2), HRV was characterized by a significant reduction of HF power with age (24±5 vs. 42±7 n.u.), while LF did not change (59±8 vs. 50±8 n.u.). In N, the diastolic phase was significantly less influenced by the LF fluctuations than in the younger subjects (18±4 vs. 32±5 n.u.), with a prevalent oscillation at HF (41±5 vs. 36±5 n.u.). More precisely, this reduction in older subjects of LF power in diastole could be related to the decrement of LF power relevant to the diastasis (21±5 vs. 33±7 n.u.). In fact, in N a low LF power in diastasis corresponded to a low LF power in diastole, while HF power in diastasis did not change (37±6 vs. 36±9 n.u.).

In both groups, a major contribution of respiration was observed in the RF phase, where LF power was minimum (8±3 vs. 10±4 n.u.) and HF power was maximum (40±4 vs. 45±4 n.u.); atrial contraction was characterized by 20±4 vs. 19±5 n.u. LF power and 30±2 vs. 39±6 n.u. HF power. In the systolic phase, HF was the prevalent rhythm (43±4 vs. 40±4 n.u.) compared to LF (15±5 vs. 19±6 n.u.).

4.  Discussion

This study shows an application of the dynamic time warping technique to locate on LV volume cycles the fiduciary points marked on the AW waveform. This method allowed us to carry on a tracking of reference points (DE and DO) difficult to detect using conventional automatic procedures and to extract beat-to-beat variability series of sub-interval cardiac phases duration.

Interestingly, the analysis of systolic and diastolic duration showed a different relation of each phase with HRV, with different LF and HF contributions and their modification with the ageing process. In particular, an increase in systolic duration was noted in N, probably due to the reduction in speed of contraction of myocardial cells due to the reduction in Calcium uptake in the sarcoplasmatic reticule [Lakatta et al., 1975]. Spectral analysis showed a prevalence of LF rhythm in the diastasis, which seemed to greatly reflect the LF modulation in heart rate, while a prevalent effect of respiration was found in RF and AC phases.

5.  Conclusions

The applied method, based on a time-warping technique, allows the beat-by-beat extraction of new variability series related to time duration of sub-interval cardiac phases. Spectral analysis applied to these series appears able to give a new insight of HRV, evidencing changes in LF and HF contributions relevant to the different cardiac phases and related with the ageing process.

References

Akselrod S, Amitayt Y, Lang RM, Mor-Avi V, Keselbrener L. Spectral analysis of left ventricular area variability as a tool to improve the understanding of cardiac autonomic control. Physiol Meas, 21: 319-331, 2000.

Bednarz JE, Marcus RH, Lang RM. Technical guidelines for performing automated border detection studies. J Am Soc Echocardiogr, 8: 293-305, 1995.

Caiani EG, Turiel M, Muzzupappa S, Porta A, Baselli G, Pagani M, Cerutti S, Malliani A. Evaluation of respiratory influences on left ventricular function parameters extracted from echocardiographic acoustic quantification. Physiol Meas, 21: 175-186, 2000.

Caiani EG, Turiel M, Muzzupappa S, Colombo LP, Porta A, Baselli G. Noninvasive quantification of respiratory modulation on left ventricular size and stroke volume. Physiol Meas, 23: 567-580, 2002a.

Caiani EG, Porta A, Baselli G, Turiel M, Muzzupappa S, Pagani M, Malliani A, Cerutti S. Analysis of cardiac left ventricular volume based on time warping averaging, Med&Biol Eng&Comp, 40: 225-233, 2002b.

Chenzbraun A, Pinto FJ, Popyulisen S, Schnittger I and Popp R. Comparison of acoustic quantification and Doppler echocardiography in assessment of left ventricular diastolic variables. Br Heart J, 70: 448-456, 1993.

Gupta L, Molfese DL, Tammana R, Simos PG. Nonlinear alignment and averaging for estimating the evoked potential. IEEE Trans Biom Eng, 43: 348-356, 1996.

Kay SM. Modern spectral analysis: theory and application. Prentice Hall, Englewood Cliffs, New Jersey, 1988.

Lakatta EG, Gerstenblith G, Angell CS, Shock NW, Weisfeldt ML. Prolonged contraction in aged myocardium. J Clin Invest, 55: 61-68, 1975.

Mor-Avi V, Gillesberg IE, Korcarz C, Sandelski J, Lang RM. Improved quantification of left ventricular function by applying signal averaging to echocardiographic acoustic quantification. J Am Soc Echocardiogr, 8: 679-689, 1995.

Perez JE, Waggoner AD, Barzilai B, Melton HE, Miller JG, Sobel BE. On-line assessment of ventricular function by automatic boundary detection and ultrasonic backscatter imaging. J Am Coll Cardiol, 19: 313-320, 1993.

Sakoe H, Chiba S. Dynamic programming algorithm optimisation for spoken word recognition. IEEE Trans Acoust Speech Sign Proc, 26: 43-49, 1978.