1. Introduction

The heart beat affects the ocular hemodynamics in the elastic eyeball, particularly the vascular volume changes of the choroid. The vascular volume change in the eye leads to the periodic axial movement of ocular tissues [1,2]. The periodic axial movement of ocular tissues caused by the heart beat is known as the ocular pulsation [3,4]. It helps to characterize the biomechanical properties incorporating stiffness, strain, stress, elasticity of ocular tissue [5]. Evidence increasingly suggests that abnormal biomechanical properties of the ocular tissue may play an important role in the development of a number of eye diseases, such as glaucoma, age-related macular degeneration, and diabetic retinopathy [6,7]. The ocular pulsation is highly correlated with the biomechanical properties of the eye [8]. As such, research on the ocular pulsation may be of great significance for the monitoring of eye disease development [9,10].

Researchers are trying to explore the correlation between temporal ocular pulsation and the development of eye diseases using state-of-art techniques. Since reported in 2007 [11], phase-sensitive optical coherence tomography (PhS-OCT) has become a routine diagnostic tool to measure micro-motion, such as ocular pulsation. The phase of ocular tissue movement can be detected in PhS-OCT. In 2012, the trabecular meshwork pulsation of monkey eyes was evaluated in ex vivo by PhS-OCT [12]. Several parameters of trabecular meshwork pulsation, such as speed, displacement, and strain rate, were quantitatively measured under different mean IOP conditions. In 2013, the first measurements of pulsation of the trabecular network in human eyes was realized in vivo by a phase compensation algorithm [5]. The 2D cross-correlation algorithm was developed to remove the eye motion, and then, the motion strength was extracted from the frequency which is related to heart rate. The results measured from 10 healthy human subjects with 20 healthy eyes indicated that the pulsating motion of trabecular meshwork correlated with digital/cardiac pulse. The pulsating motion of the trabecular meshwork follows the digital pulse with a certain time delay. Further, it has been proposed that glaucoma caused by high IOP is likely related to the abnormal circulation of the trabecular meshwork.

. It has potential use for biomechanical properties of ocular tissue. For the measurement of pulsation in the anterior chamber, the aThe anterior chamber is filled with aqueous humor, and plays an important role in the ocular fluid circulation. When the ocular fluid circulation is blocked, the intraocular pressure (IOP) will increase [13]. High IOP increase the risk of developing eye diseases. Change of ocular pressure is closely related to ocular pulsation. Therefore, the pulsation measurement in the anterior chamber is valuable for diagnosis of eye diseases with biomechanical properties damage, such as glaucoma [14] interior chamber pulsation (aOP) is used as the biomarker. Here, aOP is defined as the relative change of the periodic axial displacement between the cornea and the lens. In 2014, Li et al.. [15] explored the connection between aOP and heart beat by using PhS-OCT. They proposed a phase-based method to accurately measure the aOP. M-mode phase images along the center A-line of the frame were performed, and then the relative displacement between the cornea and lens was visualized and quantified in vivo in mice in 5 s. The experiment demonstrated that the measurement of the relative displacement between the cornea and lens can provide a new approach to evaluate the pulsation movement in the anterior chamber. However, the aOP method has been applied to measurements in the eyes of mice. Therefore, our study is to measure the aOP in vivo in the human eyes, and evaluate the phase relationships between displaced tissues in the anterior chamber due to bulk tissue motion.

In this study, the axial displacement movement in the anterior chamber of healthy people was measured and demonstrated to be associated with heart beat. The data was firstly collected by a spectral domain optical coherence tomography (SD-OCT) system with full-range complex imaging function and phase sensitive feature, and then was processed by a pulsation measurement algorithm. The full-range imaging technology was used to extend OCT imaging depth. The pulsation measurement algorithm tracks the relative displacement between the cornea and lens by extracting the phase difference between adjacent images. To obtain effective experimental data for the measurement of aOP, BM mode which means repeated B-scans taken at the same position, was used as the imaging scanning mode. In order to reduce the interference caused by human subject movement for pulse phase extraction, the imaging range should be controlled within 3 mm within a 5 s measuring time. The elimination of eye jitter was an important part of the measurement process. Our work realized phase compensation between the cornea and lens by a high-order histogram algorithm.

2. Methods and materials

2.1 Methods for extracting phase information

Due to the symmetry of the Fourier transformation, the OCT image reconstructed by Fourier transformation is symmetrical with spatial inversion as to the zero-delay line [9]. As the Fourier symmetry causes overlays of positive and negative images, it limits the reliability of phase extraction of the anterior chamber. To overcome the shortcoming, a full-range imaging technology was proposed [16]. The technology was used to extend OCT imaging depth. Herein, a modulation phase was introduced by a galvanometer. The modulation phase was used to eliminate the negative frequency component of Fourier transformation and retain the positive frequency component. Thus, a full-range image with extended imaging depth could be achieved. The complex signal of the image acquired by the FRC-SDOCT system can be expressed as:

Here, $A(x,z,t)$ denotes the structural signal of OCT conveyed as a position and time dependent amplitude in reflectivity. The symbol θ denotes the modulation phase introduced by the full range reconstruction technology, and $\varphi (x,z,t)$ denotes the phase difference of OCT. The complex signal that describes the complex reflectivity signals multiplies with its conjugate term. Phase differences $\varphi (x,z,t)$ can be obtained from the arctangent function of the multiplication result. Because the modulation phases are equal in all A-lines of one B-scan, it can be eliminated in the multiplication process. Here, $\varphi (x,z,t) - \varphi (x,z,t - \tau ) = \Delta \varphi + {\varphi _B}$. Therefore, phase difference change of cornea and lens can be expressed as Eq. (2).

Here, $\Delta {\varphi _{CL}}$ was designate as the pulsation phase in the anterior chamber. The value of $\Delta {\varphi _{CL}}$ is between [−π, π] because of phase wrapping. The true value of $\Delta {\varphi _{CL}}$ could be greater than n times that of 2π radians. An unwrapping algorithm will be illustrated in section 3.1. $\Delta {\varphi _C}$ represents the phase difference of cornea caused by heart pulse movement. The process of phase extraction is illustrated in Fig. 1. It should be noted that the bulk tissue movement requires compensation for the second frame between the two adjacent frames, as the phase of the eyeball bulk motion ${\varphi _B}$ is presumed in the second frame by default. After eliminating the phase of the eyeball bulk motion ${\varphi _B}$, the phase difference change between adjacent B-scans can be used to calculate the phase of aOP by Eq. (3).

 

Fig. 1. Diagram for extraction of the pulsation of the anterior segment of the eye. ${\varphi _C}(t )$, $\; {\varphi _C}({t - \tau } )$, ${\varphi _L}(t )$, $\; {\varphi _L}({t - \tau } )$ are the phases of cornea (C) and lens (L), where τ is the time interval of capture; ${\varphi _B}$ is the phase shift due to the bulk motion of the eye; $\Delta {\varphi _C}$, $\; \Delta {\varphi _L}$ are the phase differences between the t and t-τ intervals that correspond to the cornea and lens, respectively, and $\Delta {\varphi _{CL}}$ is the phase difference between the cornea and lens.

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The phase change of the anterior segment of eye $\Delta \varphi $ is estimated by a histogram algorithm [17,18]. The bin width for the histogram was determined by the Freedman & Diaconis rule. However, the resulting histogram is often inaccurate if the bin that is evaluated is too large. In order to obtain an accurate phase evaluation, an additional histogram with five different phase origins was calculated [19]:

2.2 System setups

The schematic diagram of the SD-OCT system for anterior chamber imaging is shown in Fig. 2. The center wavelength of the light source (super luminescent diode, SLD) is 840 nm, and the bandwidth is 49 nm. The broadband light reaches the control arm and the sample arm through a fiber optic coupler (with a coupling ratio of 50:50). The fiber entrance of the sample arm (with collimator CFC-8X-B by Thorlabs) is installed on a three-dimensional movable platform to precisely adjust the position of the light incident on the X oscillating mirror. The diameter of the light spot after collimator is ∼2.4 mm. The collimated beam incident at 1.0 mm above X oscillating mirror center. Phase modulation is introduced by the optical difference caused by the optical offset on the X oscillating mirror. The repeating B-scan mode is adopted in the experiment. The light returning through the two arms interferes in the fiber coupler and is passed on to the spectrometer. The spectrometer consists of a light collimating lens (f = 40 mm), a grating (1200 lines/mm), a focusing lens (f = 100 mm), and a camera with 2048 pixels,12 bits depth and 56% quantum efficiency (TELEDYNE e2v, OCTOPLUS). The collimated interference light is split by the grating according to the wavelength and is then focused by the lens onto the 2048 photosensitive pixel points on the camera. The camera has a maximum line acquisition rate of 130 KHZ. The detection depth of spectrometer is 3.6 mm, and the optical power at the eye is 1.2 mW. As long as the oscillating mirror is in the initial fixed state, the sensitivity fall-off from zero delay is 14 dB at the imaging depth of 2.5 mm (in the air). The maximum OCT image SNR (dynamic range) and absolute sensitivity values of system are 85 dB and 105 dB respectively. The axial resolution of the system is 5 $\mu m$, the lateral resolution is 15 $\mu m$.The two-dimensional structural image of the anterior chamber collected by this SD-OCT system is shown in Fig. 3(a). The two-dimensional image of the anterior chamber acquired by the full-range imaging system is shown in Fig. 3(b).

 

Fig. 2. Schematic of the full-range spectral-domain OCT system. Sample arm: the light from collimator shines on the position above the center of the X oscillating mirror; Reference arm: coherence with sample arm; Spectrometer: analyze interference spectrum.

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Fig. 3. The B-scan of the anterior chamber of a healthy woman, (a) the image acquired by spectral-domain OCT system without full-range, (b) the image acquired by spectral-domain OCT system with full-range. The white frame is the region of interest of scanning in the below experiment.

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5 healthy subjects for imaging (10 eyes) with no history of eye disease were recruited and their informed consent from all subjects prior to the experiment were obtained. To assess the relative movement between the cornea and lens of each eye, and to make sure the scan speed is 5 ms per frame, the scanning range of the FRC SD-OCT system was set to 3 mm. The anterior chamber was scanned at the center of the anterior chamber within the scope of the cornea and lens. The scanning time frame for one data set was 5 s. The data set incorporates 1000 B-scans. There are 400 A-lines per B-scan and 200 B-scans per second. The time interval between adjacent B-scans is 5 ms. To ensure the reliability and stability of corneal and lens imaging, the chin rest and forehead bracket were used to fix subjects’ head. The system is adjustable to allow for adjustment in height and distance according to the position of subject. During the process of data collection, the subject's anterior chamber was located at the focus of the focusing lens. The subject was required to look straight ahead at a fixed point without blinking. The fixed point was the light spots emitted by a visible light source. A finger blood oxygen meter was clamped on the finger to collect the frequency of heart beat simultaneously. The frequency of the heart beat was 1.2 Hz. According to above setup, the factors adversely affecting aOP extraction could be greatly reduced. Those factors include breath-driven head movement, eye scanning from side to side, and changes in lens thickness due to focus change. Subsequently, an image alignment algorithm based on the reflectivity amplitudes of the image was applied. The algorithm was used to analyze the spatial and temporal changes in the structure diagram in Fig. 3. The algorithm performed functions for correction of rigid translation of the tissues caused by the left and right eye scanning. It enabled extraction of phase difference from the anterior chamber [20].

3. Results and discussion

3.1 Results

The process for phase compensation is illustrated in Fig. 1. The images are filtered to eliminate the effect of Gaussian noise before applying the algorithm to phase processing [21] on phase extraction. By Eq. 2, the phase difference values in the anterior segment between the adjacent 40th and 41st frames are shown in Fig. 4(a). Without any phase compensation processing, Fig. 4(a) exhibits a phase difference ${\varphi _B}$, $\; $ which is caused by the movement of large tissues, the phase difference $\Delta {\varphi _C}$, which is caused by the pulsation of the cornea itself and the phase difference $\Delta {\varphi _L}$, which is caused by the pulsation of the lens itself. To obtain the phase caused by aOP, histogram algorithm is required to be applied on all the A-lines. The histogram of the corneal phase difference of the 20^th A-line is shown in Fig. 4(b). The phase value with maximum frequency is the phase value of the 20^th A-line. The phase of each A-line in Fig. 4(a) is counted by the histogram. It should be noted that the histogram algorithm were performed in cornea and lens separately. The separate performances were to avoid the phase interference between cornea and lens during extraction. In order to obtain accurate phase extraction, the estimation algorithm of higher-order phase processes is needed. Phase value of the 20^th A-line is obtained from the five loops of the histogram algorithm. The blue curve line in the Fig. 4(c) denotes the phase difference map of the cornea between two adjacent frames after applying the high order histogram algorithm. From the blue curve line in Fig. 4(c), it can be visualized that there is a step in the phase curve map. The step represents phase-wrapped. The phase-wrapped is due to the 2π-modulo in the arctangent function. To obtain the true corneal phase changes information caused by corneal movement, an unwrapping algorithm is required. The unwrapped result is marked by red curve in the Fig. 4(c).

 

Fig. 4. Phase difference estimation within 5 ms, (a) the phase difference image between the 40^th and 41^st frame of the anterior segment. (b) the result of the phase histogram performed in the 20^th A-line for corneal segment. (c) the result of histogram statistics between each A-line for corneal segment.

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The method used for the cornea phase difference was applied to obtain the lens phase difference $\Delta {\varphi _L}$. The phase describing positions of the cornea and lens calculated from the 40^th and 41^st frames are shown in Fig. 5(a). In Fig. 5(a), the blue curve line represents the phase changes of the cornea, and the red curve line represents the phase changes of the lens. The X-axis is time lapse. The Y-axis is phase difference. The phase difference between the lens and cornea can be used to describe the pulsation of the anterior chamber. The value of the pulsation of the anterior chamber was calculated by the Eq. (3). It is worth noticing that the calculated phase value is the difference compared to the phase in the adjacent frames. In other words, the phase difference obtained can be used to characterize the displacement occurring within 5 ms. To visualize the axial movement between the cornea and lens within 5 s, the curve of the phase change along time lapse should be observed. A total of 999 phase differences within 5 ms intervals were collected to observe the movement of the anterior chamber. The result is shown in Fig. 5(b). The phase differences between the cornea and the lens cumulatively calculated from the 1000 B-scan frames with 999 phase differences. The color bar represents the phase difference of aOP. The X-axis represents 300 A-lines in one B-scan.

 

Fig. 5. (a) The unwrapped phase difference of cornea and lens within 5 ms. (b) Phase difference map between cornea and lens within 5 s. (c) The average pulsation of the anterior segment within 5 s. (d) The frequency spectrum of the average pulsation of the anterior segment within 5 s.

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In Fig. 5(c), the X-axis represents time lapse, and the Y-axis represents average phase difference of aOP calculated along the X axis of Fig. 5(b). From the Fig. 5(c), the curve line represents the pulsation of the anterior chamber fluctuates up and down regularly. The periodic pulsation of phase difference change was obvious. Fourier transformation was performed on the curve shown in Fig. 5(c) to obtain the frequency spectrum of the pulsation motion of the anterior chamber. Result from Fourier transform is shown in Fig. 5(d). From the Fig. 5(d), it can be seen that the first harmonic frequency is 1.2 Hz, which is consistent with the frequency of the heart beat measured at the same time.The measured frequency 1.2 Hz of the heart beat is the oscillation frequency of a normal human heart pulse reported in [22,23].

3.2 Discussion

The ocular pulsation parameters caused by heart beat can be used to explore the biomechanical parameters of ocular tissues, it is of great significance for the pathological study of eye diseases, such as glaucoma. In the anterior segment, the trabecular meshwork is a key part. Researches have explored the relationship between the trabecular meshwork pulsation and the biomechanical parameters of ocular tissues. The earliest trabecular meshwork pulsation was measured from isolated animals, and then was measured in vivo experiments. Xin et al. [19] studied the synchronous relationship between trabecular meshwork movement and eye pulsation by using phase sensitive OCT system, and it helps to explain the measurement significance of eye pulsation for biomechanical properties. Li et al. [3] explored ocular pulsation in anterior segment by measuring the axial movement between lens and cornea. The experiments is performed on anesthetized mice. The eye movements and relative parameter was not considered in their study.

In our study, we perform in vivo experiment in human eye with inevitable movement. The phase compensation algorithm was applied to remove bulk tissue motion. The phase difference and time-lapse phase differences between two adjacent frames were extracted for the cornea and the lens. The phase differences curves of the cornea and the lens were performed by subtraction.The final pulsation waveform of aOP was generated. Therefore, we overcome the eye movement interference and extract the axial movement between lens and cornea in the presence of body movement. Our results show that optical phase difference extracted from FRC-SDOCT instrumentation can be used to characterize the movement of tissues in response to pulsation in the anterior chamber. The heart rate measured by a finger pulse oximeter was used as the reference signal. The heart rate is used to discriminate and detect coherence reflections that characterize pulsation motion of cornea and lens structures in the ocular anterior chamber. Here, it was confirmed that the regular movement of the cornea and lens in the eyes of healthy people correlates with normal heart beat.

Whereas, our study requires further improvement. In future work, the velocity of the anterior chamber movement can be measured quantitatively. Also, to explore the influence of varying IOP on anterior chamber movement, IOP may be controlled to induce the relative movement of the lens and the cornea in the eyes of isolated animals. Furthermore, FRC-SDOCT will be used for pulsation measurement of the anterior segment to evaluate biomechanical properties of the eye. In addition, the number of subjects and the testing time should be increased to acquire more data and statistical capability. With the increase of the measurement time, there will be greater eye twitch, squibbing from side to side, and breathing-associated motion to the head. Subsequently, the amplitude of eye movements may be increased. Eye-tracking technology will be introduced to solve these problems.

4. Conclusion

The method for measuring the aOP of the human eye in vivo was proposed in this study. Imaging of the anterior chamber is achieved with FRC-SDOCT. A pulsation measurement algorithm is employed. In the algorithm, according to different optical phases associated with lens and cornea motion, the bulk tissue motions of the cornea and lens were separately computed during the process of phase extraction. The bulk tissue motion was compensated by the high-order phase compensation algorithm. Then the phase difference were extracted for the cornea and the lens, as well as the phase difference change between two adjacent frames. The pulsation waveform of aOP was generated by subtracting the two phase differences change curves of the cornea and the lens. Finally, the micro-motion of anterior chamber tissue pulsation was detected and quantified in vivo. The frequency of the micro-motion of anterior chamber tissue pulsation is closely related to the heart rate. The pulsation measurement algorithm provides a useful method to visualize the deformations of the anterior chamber.