SEARCH

SEARCH BY CITATION

Keywords:

  • electrocardiography;
  • longitudinal eye movements;
  • ocular pulse;
  • phase estimation

Abstract

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

Background

The aim was to establish phase relationships between the principal harmonic, related to the heart rate, of synchronically registered longitudinal corneal apex displacement (LCAD), blood pulsation (BP) and electrical heart activity signals in a group of healthy subjects.

Methods

Longitudinal corneal apex displacement was non-invasively measured using an ultrasonic distance sensor. Synchronously, electrocardiographic (ECG) and blood pulsation signals were acquired. As all considered signals are non-stationary (that is, their spectral characteristics vary in time), a reliable and repeatable phase estimation method was sought. For this, a range of phase estimators were tested in the windowed regime of simulated non-stationary signals. Two robust estimators that showed minimum mean square error performance, were selected for further analysis of real signals registered for seven subjects participating in the study.

Results

The windowed cross-correlation and the windowed minimum sum of squared error method achieved the best results among the estimators considered and their outputs were averaged to arrive at a robust phase estimator. Across the subjects, it was found that an increase in the time delay between the principal harmonic of BP and ECG signals, θ(BP,ECG), corresponds to a slight time delay increase between the corresponding harmonics of longitudinal corneal apex displacement and blood pulsation signals, θ(LCAD,BP) and a decrease in the time delay between those of longitudinal corneal apex displacement and ECG signals, θ(LCAD,ECG). Significant correlation (paired t-test, p < 0.05) were found between θ(BP,ECG) and θ(LCAD,BP) as well as between θ(BP,ECG) and θ(LCAD,ECG). There was no significant correlation found between θ(LCAD,BP) and θ(LCAD,ECG).

Conclusion

The results indicate that longitudinal corneal apex displacement and correspondingly the ocular pulse phenomenon have not only a vascular origin but could also be influenced by the electrical activity of the heart.

Variations in intraocular pressure (IOP) and pulsatile ocular blood flow (POBF) affect a phenomenon known as the ocular pulse,[1] which is characterised by some minute quasi-periodical deformations of the eye globe and expansion of the corneal surface.[2] Variability of the amplitude of the IOP depends on POBF[3-5] and the cardiac circle.[6] Ocular blood flow is also significantly conditioned by the cardiovascular activity.[7] In consequence, the ocular pulse reflects a valid component of the heart activity,[8, 9] which was found to also modulate the steady-state accommodation[10, 11] and affect the dynamics of wavefront aberrations.[12, 13]

The majority of techniques for measuring IOP (Goldman, Schiotz)[14, 15] and ocular haemodynamics[16] are semi-invasive and uncomfortable for the patient. Nevertheless, several non-invasive methods of measuring ocular pulse exist.[1, 17, 18]

Spectral analysis has been successfully applied to studies of IOP-related ocular blood pulsation (BP).[19, 20] The technique also has the potential to differentiate diseased from healthy eyes. In particular, Evans and colleagues[21] found that the second, third and the fourth harmonic of the ocular pulse signal can differentiate patients with glaucoma from normal subjects. It was speculated that non-invasive measurement of longitudinal eye movements[17, 19, 22] and investigation of their spectral correlation with cardiac activity[2, 20] could lead to the development of a non-invasive technique for measuring IOP. Correlation between the ocular pulse amplitude and the degree of carotid stenosis has been found in animal studies,[22, 23] in which it was shown that the ocular pulse amplitude decreases with carotid artery occlusion. No phase dependencies, which are known to be more sensitive than their amplitude counterparts, between such signals were studied.

The main goal of this study was to establish phase relationships between longitudinal corneal apex displacement (LCAD), BP and electrical heart activity in a group of healthy subjects.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

Subjects

Seven healthy subjects (aged from 23 to 35 years) participated in the study. The subjects had no corneal or eyelid pathology, no symptoms of dry eye and were not contact lens wearers. Before the experiments, the blood pressure of all subjects was measured with the Blood Pressure Monitor HEM 780 (Omron Healthcare Co. Ltd, Kyoto, Japan). The diastolic and systolic values were normal and ranged from 72 to 83 mmHg and from 110 to 125 mmHg, respectively. Additionally, the IOP of the subjects was measured with the Reichert 7CR auto-tonometer (Reichert, Inc, Depew, NY, USA). All subjects exhibited normal levels of IOP (mean and standard deviation of 14.0 ± 2.4 mmHg).

Subjects were familiarised with the measurement set-up. The experiments were conducted in accordance with the Declaration of Helsinki. Informed consent was obtained from all subjects included in this study.

Measurements

Longitudinal corneal apex displacement was measured in left eyes of the subjects using an ultrasonic distance sensor, working at a frequency of 0.8 MHz, with an accuracy below 2 μm. The transducer was placed around 15 mm in front of the corneal surface, so the measurement was non-contact and non-invasive. Technical details of this technique have been reported earlier.[2, 24] Head movement is one of the main factors affecting accurate measurement of corneal displacement.[24] Therefore, a heavy headrest and a rigid bite bar were applied to stabilise the head position during measurements. It is not possible to completely eliminate head movements but the proposed technique allowed a significant reduction in their amplitude. Breathing is also reflected in the longitudinal movements of the eye and head. Therefore, to control the influence of this factor, all subjects were instructed to breathe on a metronome at a frequency of 0.3 Hz, close to the average rate of natural breathing for a healthy adult at rest.[25]

To monitor heart activity, the electrocardiographic (ECG) signal was synchronously registered using a three-lead system, known as the Einthoven's triangle.[26] Two skin electrodes were attached to the right and to the left wrist and a third to the left ankle of each subject. To record the ECG, the Multifunction Data Acquisition module (DAQm, National Instruments, Budapest, Hungary) was used. Additionally, the signal of BP was registered using a pulse oximeter placed on the right earlobe of each subject. This signal represents oxygen saturation in the blood during each blood inflow. The LCAD, ECG and BP signals were sampled at a frequency of 100 Hz. The recording time was set to 10 seconds. During that time, the subjects were asked to abstain from blinking and fixate on a designated stationary target which was placed at a far point. Signals with blinks were not considered in the analysis. Measurements were carried out ten times for each subject. A representative example of the three measured signals is shown in Figure 1, where normalised amplitudes of raw LCAD, pulse and ECG signals (left column) are presented with the corresponding power spectra (right column). The power spectrum, computed using fast Fourier transform, represents the distribution of a signal power in the frequency domain.[27]

figure

Figure 1. Normalised amplitudes of longitudinal corneal apex displacement (LCAD), pulse and electrocardiographic (ECG) signals (left column) and the corresponding power spectra (for LCAD its first derivative) (right column). The dashed-line box encompasses the first harmonic of the signals, for which phase relationships are being sought.

Download figure to PowerPoint

To better visualise the higher frequency content of the LCAD signal in comparison to those of the ECG and pulse signals, the power spectrum of its first derivative is shown. The dashed-line box encompasses the principle frequency (first harmonic) of the signals, for which phase relationships are being sought.

Data analysis

Longitudinal corneal apex displacement, ECG and BP signals were numerically processed using a custom-written program in Matlab (MathWorks, Inc., Natick, MA, USA). First, the signals were linearly detrended and a linear phase band-pass filter (in the range from 0.1 Hz to 20 Hz) was applied to minimise the very low frequency baseline drift and to enhance the performances of the subsequent time delay estimators by broadening the QRS complex of the ECG signal. The QRS complex is a section of the electrocardiogram containing three deflections corresponding to the depolarisation of the heart ventricles. Estimating phase relationships between the considered signals proved to be intricate. First, all signals are non-stationary,[20] meaning that their frequency content varies in time. Applying time delay estimation methods using a cross-correlation function calculated between the total lengths of the signals was somewhat ambiguous.[28] On the other hand, an off-the-shelf phase estimation method for non-stationary signals proved to be difficult to find. Hence, a variety of phase estimators from those calculated in the time domain[29] to those calculated in the frequency[30] and Hilbert space domains,[31] were first tested in the windowed regime of simulated non-stationary signals using the Monte Carlo method. Estimators expected to work well, in terms of their mean-square error performance; for narrowband signals, small time delays and small samples were selected for establishing the phase relationships between LCAD, ECG and BP signals.

Monte Carlo simulations

Two chirp signals, which are sinusoidal waves linearly modulated in frequency over time, with frequencies changing from 0.9 to 1.3 Hz in the period of 10 seconds were numerically generated. Three factors were considered: the phase shift (time delay) between the signals, the level of additive noise (assumed to be white Gaussian and independent from the signals) and a multiplicative amplitude component of frequency 0.2 Hz simulating the modulating effect of respiration on considered physiological signals. Further, a time window size of the chirp signals was selected as the period of the lowest frequency of signals. Although initially a wider variety of phase estimators was considered, the most applicable to our scenario proved to be the cross correlation (CC), the minimum sum of square errors (SSE), generalised CC and an estimator based on Hilbert transformation. These were the methods that could handle the desired degree of non-stationarity of the signals within the given range of signal-to-noise ratios.

Figure 2 shows the performance of the considered four estimators in terms of their mean square error for a given phase shift of 0.3 seconds. It is evident that in the range where the signal-to-noise ratio does not fall below -5 dB, the best performance is achieved by the CC and SSE methods. Similar results were achieved for a range of time delays showing a certain degree of robustness (in a colloquial sense) of the considered estimators. As a consequence, for further analysis of measured LCAD, ECG and BP signals only these two methods were applied. To arrive at a more robust phase estimator, the average from the CC and SSE methods has been considered as the final estimator of the phase interdependencies between the three considered signals. Finally, it should be clarified that, although in general we seek phase relationships between considered signals, the analysis described above only pertains to time delay estimation because only the single harmonic component of each signal is considered.

figure

Figure 2. Mean squared error performance of the four considered phase estimators

Download figure to PowerPoint

Results

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

Real signal measurements

For real signals, the phase examinations were carried out for the principal harmonic related to the heart rate (from 0.9 to 1.3 Hz) of the analysed signals. The length of the sliding window, in which the signal should be assumed to be stationary, was estimated as the period of the selected harmonic based on the Fourier spectra, individually for each subject. Next, the time window of the two considered signals for the chosen harmonic was shifted with a step of 0.01 second and the time delay between them estimated using the CC and the SSE methods in each window area. Finally, the estimate of the phase shift between the two given signals (θ) was calculated as an average of individual phase shift obtained in each position of the time window. Figure 3 shows the estimates of the phase shifts between LCAD, ECG and BP signals (that is, θ[LCAD,BP], θ[LCAD,ECG] and θ[BP,ECG]) for the main harmonic related to the heart rate, using the CC and SSE methods, obtained for all subjects' measurements.

figure

Figure 3. Correlation analysis (left column) and the Bland-Altman plots (right column) for the three considered phase relationships (θ[LCAD,BP], θ[LCAD,ECG] and θ[BP,ECG]) estimated by the cross correlation and sum of squared errors methods for all measurements of all subjects. LCAD: longitudinal corneal apex displacement, BP: blood pulsation, ECG: electrocardiographic signal.

Download figure to PowerPoint

The left column of Figure 3 shows the correlation plots, while the right column shows the corresponding Bland and Altman plots.[32] Linear orthogonal fits showed moderately significant correlations between the phase estimates obtained with the CC and SSE methods (r = 0.44, p = 0.019 for θ[LCAD,BP], r = 0.89, p < 0.001 for θ[LCAD,ECG] and r = 0.97, p < 0.001 for θ[BP,ECG]). Some bias has been observed toward the CC method which for all three cases resulted in higher phase estimates than the SSE method (linear slopes of 0.39, 0.68, and 0.97 for θ[LCAD,BP], θ[LCAD,ECG] and θ[BP,ECG], respectively).

Figure 4 shows the correlation analysis between the three considered phases (θ[LCAD,BP], θ[LCAD,ECG] and θ[BP,ECG]). Linear orthogonal fits showed moderate significant correlations between phases θ(LCAD,BP) and θ(BP,ECG), r = 0.47, p = 0.001 and between θ(LCAD,ECG) and θ(BP,ECG), r = 0.39, p = 0.008; however, no significant correlation was observed between θ(LCAD,BP) and θ(LCAD,ECG), r = 0.17, p = 0.26.

figure

Figure 4. Correlation analysis between the three considered phases (θ[LCAD,BP], θ[LCAD,ECG] and θ[BP,ECG]) estimated from the average of cross correlation and sum of squared errors methods. LCAD: longitudinal corneal apex displacement, BP: blood pulsation, ECG: electrocardiographic signal.

Download figure to PowerPoint

Across the subjects, it was found that an increase in the time delay between the harmonics of BP and ECG signals, θ(BP,ECG), corresponds to a slight time delay increase between the corresponding harmonics of LCAD and BP signals, θ(LCAD,BP) and a decrease in the time delay between those of LCAD and ECG signals, θ(LCAD,ECG).

Similar relationships can be derived for the following harmonics of the three considered signals by setting a linear phase band pass filter centred on the multiples of the principle harmonic.

Discussion

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

The signals of pulse, ECG and LCAD are non-stationary[19, 20] and their analyses require non-standard tools. Although in our study with generated synthetic signals two potential methods have been identified as good phase estimators, the practical implementation of those estimators showed very good correlation only in the case of the time delay between BP and ECG signals (Figure 3). The reason for this is that those signals are less non-stationary than the LCAD signal. The number and amplitudes of frequency components of the LCAD signal as well as its degree of non-stationarity depend on each individual subject's characteristics, such as their ocular blood flow, heart rate, IOP propagation and biomechanical properties of the ocular tissue. This clearly indicates that phase estimation of non-stationary signals is not trivial and should be approached with caution.

It is worth noting that the corneal indentation pulse and changes in time intervals computed between the base and the peak of its pulse wave (known as crest time) correspond to the alteration in ocular blood supply related to many pathologies.[33] The proposed non-invasive ultrasonic method of LCAD measurements and calculation of time delays between LCAD signal and cardiovascular activity signals might be helpful to better understand the ocular haemodynamics and the pathogenesis of several ocular diseases, such as normal tension glaucoma.

At first glance, the results of our study could have appeared counterintuitive. One could imagine a simplified cardiovascular system, in which after the rapiddepolarisation of the right and left ventricles (signified by the R peak in the so-called QRS complex), there would be a certain time delay (isovolumic contraction) before the aortic valve opens and the increase in the aortic pressure appears. In such a model, the estimated time between the BP and ECG signals would correspond to the time between the R peak and the maximum aortic pressure in the ejection phase. Correspondingly, if one viewed LCAD as a purely mechanical response to blood pressure, one would expect the estimated time between the LCAD and BP (measured on the ear) signals would be proportional to the blood travel path difference (heart-ear minus heart-eye). Our results showed that such a simplified model is not valid as the increase in the time delay between the LCAD and BP signals not only corresponded to the increase in the time delay between the BP and ECG signals but also to the decrease in the time delay between LCAD and ECG signals. This indicates that the blood-travel-path-difference proportionality approach cannot be used as the only mechanism generating those time delays.

Correlation analyses add more insight into the problem. We note that the estimated phases θ(BP,ECG) and θ(LCAD,BP) as well as θ(BP,ECG) and θ(LCAD,ECG) are moderately and significantly correlated. In comparison, no significant correlation was found between θ(LCAD,BP) and θ(LCAD,ECG). This indicates that the influence of ECG and BP signals, which are highly correlated, on the LCAD signal is not straightforward and that the longitudinal corneal movement and subsequently, the corneal pulse, may have an intricate relationship with blood pulse and electrical activity of the heart. These premises lead us to speculate that the ECG component visible in the corneal pulse may be uncorrelated with that of the blood pulse, indicating a substantial role of that electrical signal in axial eye movements.

Interestingly, using an ultrasonic technique van der Heijde, Beers and Dubbelman[34] found that the high frequency component of accommodative microfluctuations, believed to be related to the blood pulse, was visible in the axial length measurements but not in those related to anterior chamber depth and lens thickness. In contrast, the low frequency accommodation component, believed to have neurological origins, was visible in anterior chamber depth and lens thickness measurements but not in axial lens changes. Our results complement this work, suggesting that besides purely mechanical and neurologic determinants, the electrical activity of the heart could be an additional factor to ocular accommodation.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

We thank the anonymous reviewers and the Associate Editor for their constructive comments, which helped improve the manuscript.

Grants and Financial Assistance

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References

Part of this work was supported by funds from the Foundation for Polish Science (project VENTURES/2011-7/4 to M.E.D.) and by the Grant of Polish Ministry of Science, number NN518423336.

References

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. Grants and Financial Assistance
  8. References