In-vivo characterization of scleral rigidity in myopic eyes using fundus-pulsation optical coherence elastography

The sclera plays an important role in the structural integrity of the eye. However, as myopia progresses, the elongation of the eyeball exerts stretching forces on the posterior sclera, which typically happens in conjunction with scleral remodeling that causes rigidity loss. These biomechanical alterations can cause localized eyeball deformation and vision impairment. Therefore, monitoring scleral rigidity is clinically important for the management and risk assessment of myopia. In this study, we propose fundus pulsation optical coherence elastography (FP-OCE) to characterize posterior scleral rigidity in living humans. This methodology is based on a choroidal pulsation model, where the scleral rigidity is inversely associated with the choroidal max strain obtained through phase-sensitive optical coherence tomography (PhS-OCT) measurement of choroidal deformation and thickness. Using FP-OCE, we conducted a pilot clinical study to explore the relationship between choroidal strain and myopia severity. The results revealed a significant increase in choroidal max strain in pathologic myopia, indicating a critical threshold beyond which scleral rigidity decreases significantly. Our findings offer a potential new method for monitoring myopia progression and evaluating therapies that alter scleral mechanical properties.


Introduction
The sclera, also known as the white of the eye, is a tough outer layer of the human eye.Composed primarily of collagen and essential elastic fibers [1], it plays an important role in supporting intraocular structures and protecting the eye from external trauma.Weakening of scleral tissue can make the eye susceptible to various diseases.
Myopia is a common eye disorder that affects an estimated 23% of the world's population [2].Myopia may alter scleral mechanical properties and lead to lesions that can impair vision and decrease quality of life [3].With myopia progression, the eye gradually elongates, and axial length increases.The biomechanical forces related to this axial elongation and scleral remodeling result in the stretching of the ocular layers and progressive thinning of the retina, choroid, and sclera [4].Scleral thinning compromises its ability to preserve the eye's original shape and can give rise to a localized outpouching on the posterior of the eye, known as posterior staphyloma.Posterior staphyloma is a hallmark of pathologic myopia [5] and a significant contributor to maculopathy [6,7].
Prior research has shown a decline in posterior scleral rigidity with myopia progression [8,9]; additionally, some researchers have explored the collagen crosslinking to increase the biomechanical strength of the sclera [10,11].However, there is also no clinical tool to assess change in scleral rigidity during disease progression or following interventions aimed at mitigating these changes.Although previous studies have attempted in-vivo characterization of ocular rigidity by assessing the ocular volume increase per unit change in intraocular pressure (IOP) [9,[12][13][14], these methods only provide a measure of the overall ocular rigidity and lack the specificity required to assess posterior scleral rigidity quantitatively.Moreover, these methods are impractical for tracking disease progression due to the invasive nature of the required procedures, such as concomitant cataract surgery [13] or continuous tonometry measurement [9,12].Consequently, a convenient and noninvasive technique that characterizes posterior scleral rigidity in routine clinical care is needed.
Optical coherence tomography (OCT) is a noninvasive imaging modality developed for imaging biological systems [15].The Doppler effect induced by the moving scattering medium can be carried by the measurement of OCT phase information, making it feasible to detect tiny motion with a sensitivity at the sub-nanometer scale [16][17][18].This feature has led to the evolution of optical coherence elastography (OCE) [19,20], an application of OCT that measures tissue deformation and rigidity [21][22][23][24][25][26][27][28][29].Essentially, OCE involves applying mechanical stimulation to a tissue and quantifying the resulting deformation to infer its elastic modulus, a measure of its rigidity [30,31].Mechanical stimulation can take on an active form, such as external ultrasound [32] or UV stimulation [33], or a passive form, like capitalizing on intrinsic cardiac pulsations [34][35][36].In the context of measuring the posterior sclera, the passive OCE that relies on the stimulation by fundus pulsations emerges as a suitable approach.
Fundus pulsation is induced by the cardiac pulse entering the eye vascular networks, especially the choroidal space, which accounts for 80% of the ocular blood supply.The expansion of the choroid applies a mechanical force onto other eye tissue, which results in the cyclic volume change of the eyeball and the fluctuation of IOP [37].Various studies have measured the ocular-pulsation-induced tissue deformation.Some have reported a correlation between the pulsation in the anterior chamber and the rigidity of the trabecular meshwork [38,39] and cornea [35].Others demonstrated the pulsation measurement on the fundus [40,41].Nevertheless, we are unaware of any prior report on a sensitive method to establish a correlation between fundus pulsation and posterior scleral rigidity in human subjects.
In this work, we propose a novel approach named fundus pulsation optical coherence elastography (FP-OCE).We characterized the posterior scleral rigidity in humans using a standard clinical OCT system and demonstrated the in vivo quantification of choroidal strain with repeated B-scans in pathologic and non-pathologic myopic eyes.

Theory: the choroidal pulsation model
In this study, the posterior pole of the eye is simplified as a three-layer model, consisting of the retina, the choroid, and the sclera (Fig. 1).The space anterior to the retina is the vitreous humor, an incompressible fluid-like material [42].During systole, the choroid expands, pushing itself and the sclera away from the retina.The choroid reaches its maximum thickness in this phase, defined as d max = d 0 + ∆d, where d 0 is the static choroidal thickness, and ∆d is the choroidal max deformation due to the expansion.During diastole, the choroid recoils, bringing itself and the sclera towards the retina.The choroid reaches minimum thickness in this phase, defined as The sclera, made of relatively stiffer material, provides the main resistance to choroidal expansion.In eyes with a more rigid sclera, the choroid tends to expand less due to higher resistance, and vice versa.In other words, the magnitude of choroidal expansion could be a surrogate indicator of scleral rigidity.To quantitatively describe the magnitude of choroidal expansion, we employ the choroidal max strain ϵ, which is defined as the choroidal max  0 The parameters on the right side of eq. 1 can be measured using OCT.Typically, the choroidal thickness  0 is in the sub-millimeter scale, which is easily attainable on OCT structural images.In comparison, the choroidal max deformation Δ is typically several micrometers, below the level of OCT resolution, but is measurable by OCT phase information.
By acquiring Δ and  0 using OCT, we can readily derive the choroidal max strain and then evaluate the scleral stiffness.b1), (b2) The model in different heart cycles; during systole (b1), the choroid expands, while in diastole (b2), the choroid recoils.The sclera acts as a resistance to the choroidal expansion.  and  , the maximal and minimal thickness of the choroid, respectively;  0, the static choroidal thickness; Δ , the choroidal max deformation.

Subject recruitment summary
The study was approved by the institutional review board of the University of Washington (UW), and informed consent was obtained from all subjects before imaging.This study followed the tenets of the Declaration of Helsinki and was conducted in compliance with the Health Insurance Portability and Accountability Act.
Subjects with a diagnosis of non-pathologic and pathologic myopia were prospectively enrolled at the UW Eye Institute.Inclusion criteria encompassed individuals aged between 30 and 80 years old with a refractive error < 0 spherical equivalent.Exclusion criteria included significant media opacity preventing high-quality imaging and no history of scleral buckle, strabismus surgery, or tube shunt.If a patient had only one eligible eye, it would be selected for the study.If both eyes met the eligibility criteria, only the right eye would be chosen.There were 58 eyes in total meeting the criteria above and included into the analysis.
All subjects underwent a comprehensive ophthalmologic examination and fundus photographs at the time of enrollment, followed by OCT imaging as described in 2.2.2.Fundus photographs were taken with a fundus camera (Zeiss FF450, Carl Zeiss Meditec Inc., location) at least 20 minutes after pupillary dilation with 1% tropicamide and 2.5% phenylephrine.
Utilizing the META-PM classification system [44], fundus photos were categorized into the appropriate MMD grade by a trained ophthalmologist (JL).Grade 2 MMD, characterized by The parameters on the right side of Eq. ( 1) can be measured using OCT.Typically, the choroidal thickness d 0 is in the sub-millimeter scale, which is easily attainable on OCT structural images.In comparison, the choroidal max deformation ∆d is typically several micrometers, below the level of OCT resolution, but is measurable by OCT phase information.By acquiring ∆d and d 0 using OCT, we can readily derive the choroidal max strain and then evaluate the scleral stiffness.

Subject recruitment summary
The study was approved by the institutional review board of the University of Washington (UW), and informed consent was obtained from all subjects before imaging.This study followed the tenets of the Declaration of Helsinki and was conducted in compliance with the Health Insurance Portability and Accountability Act.
Subjects with a diagnosis of non-pathologic and pathologic myopia were prospectively enrolled at the UW Eye Institute.Inclusion criteria encompassed individuals aged between 30 and 80 years old with a refractive error < 0 spherical equivalent.Exclusion criteria included significant media opacity preventing high-quality imaging and no history of scleral buckle, strabismus surgery, or tube shunt.If a patient had only one eligible eye, it would be selected for the study.If both eyes met the eligibility criteria, only the right eye would be chosen.There were 58 eyes in total meeting the criteria above and included into the analysis.
All subjects underwent a comprehensive ophthalmologic examination and fundus photographs at the time of enrollment, followed by OCT imaging as described in 2.2.2.Fundus photographs were taken with a fundus camera (Zeiss FF450, Carl Zeiss Meditec Inc., location) at least 20 minutes after pupillary dilation with 1% tropicamide and 2.5% phenylephrine.Utilizing the META-PM classification system [45], fundus photos were categorized into the appropriate MMD grade by a trained ophthalmologist (JL).Grade 2 MMD, characterized by yellowish color in the posterior pole without discrete regions of RPE atrophy, was the threshold defined for pathologic myopia.
Based on the refractive error and the MMD grade, the eyes from all subjects were assigned to three groups: low-moderate myopia, high myopia, and degenerative myopic stages, using the criteria below.
Demographic and clinical information (age, gender, IOP, and refractive error) were collected from medical records.Refractive error for pseudophakic eyes was recorded before the date of their cataract surgery.The demographic profiles of three groups were summarized in Table 1.

OCT scanning protocol
All eyes were scanned using a commercial swept source OCT (PLEX Elite 9000, Carl Zeiss Meditec Inc.) with a central wavelength of 1050 nm and a spectral bandwidth of 100 nm, delivering an approximate axial resolution of 5 µm in tissue.The system operates at an A-scan rate of 100 kHz, offering an A-scan depth of 3.0 mm in tissue.
The OCT scanning protocol for scleral strain measurement was the BM-mode (repeated B-scan).An M-scan consists of an ensemble of 3000 B-scans that were continuously acquired at one consistent cross-section centered at the fovea.Each B-scan consists of 300 A-scans, covering a 3-mm line field.Each A-scan consists of 1536 pixels, covering a depth range of 3 mm.Therefore, the dimension of the OCT data volume is 1536 × 300 × 3000 (A-scan x B-scan x M-scan).The frame rate was 220 frames per second.Thus, the 3000-frame M-scan is equal to a duration of 13.64 seconds.With this setting, the maximum velocity that the system can detect is 83 µm/s in tissue if evaluated between adjacent B-scans (t = ∼4.5 ms).
During the scanning, subjects were allowed to move their eyes or blink if necessary because the integrated FastTrac module of the OCT machine compensates for eye motion in real time to keep the OCT B-scan plane centered on a consistent fundus cross-section.If large eye motion is detected, the tracking module discards the affected frames, recenters the scanning field, and resumes the scan.This process is termed re-scan event, which typically extends the duration of a complete scan to 14 to 30 seconds.

Data processing framework
The OCT raw data cube was stored as complex-valued interferometric signal.ĨRAW (x, z, t), which can be written as ĨRAW (x, z, t where z is the depth position on A-scan direction, x is the lateral position on B-scan direction, t is the time of the B-scan being acquired, and j is the imaginary unit; A RAW (x, z, t) is the magnitude, while ϕ RAW (x, y, t) is the phase.
The data processing framework is summarized in Fig. 2. As shown in the top figure, the first step was to correct the OCT raw data cube for bulk tissue motion.The magnitude part A RAW (x, z, t) was co-registered using a correlation-based image registration algorithm [43], where the pixel-level axial and lateral bulk motion between every two adjacent B-scans was minimized.And the phase part ϕ RAW (x, y, t) was corrected for bulk phase shift between two adjacent B-scans using a histogram-based phase compensation algorithm [44].The resultant corrected data cube Ĩ(x, z, t) [Fig.2(a)] can be written as, where A(x, z, t) and ϕ(x, z, t) are the magnitude and phase after correction, respectively.
In the left column of Fig. 2, the magnitude A(x, z, t) was averaged along t-axis to result in the structure image Ā(x, z) (Fig. 2(b)), on which an automatic segmentation was conducted to find the depth of Bruch's membrane (BM), z BM (x), and choroid-sclera interface (CSI), z CSI (x), for every x position.Thereafter, the A-scans were evenly divided into three sections, labeled as i = 1, 2, 3.At this point, the cube would be processed section by section.Essentially, the sectional approach aids in the precise fitting of BM inclination and the effective removal of choroidal tailing artifacts through spatial averaging.More details about the tailing artifacts can be found in section 2.3.2 and the determination of section number will be discussed in chapter 4.
In each cube section i, the choroidal thickness d [i]  0 was calculated as the z distance between BM and CSI corrected by the angle of inclination of BM in that section θ [i]  BM , which can be written as: where N [i]  x is the number of A-scans in section i. θ [i]  BM was calculated by fitting a linear regression model to the BM depth profile in section i. Assume the slope obtained is α [i] ; then As depicted in the right column of Fig. 2, the phase ϕ(x, z, t) was differentiated between every two adjacent B-scans by calculating the complex conjugate product P(x, z, t), where * represents the complex conjugate, and ∆t is the time elapsed between two adjacent B-scans.
The phase part of P(x, z, t) contains the phase shift information, i.e., ∆ϕ(x, z, t) = arg[ P(x, z, t)], where arg[•] denotes the principal argument.The phase shift induced by the choroidal deformation can be obtained by calculating the difference between the phase shift near the choroidal inner boundary and that near the outer boundary.Specifically, the choroidal inner boundary region was defined as a retinal pigment epithelium (RPE) slab next to BM (between z BM (x) and z BM (x)−30 µm), while the choroidal outer boundary region was a scleral slab next to CSI (between z CSI (x) + 10 µm and z CSI (x) + 40 µm).The RPE slab and scleral slab representing the choroidal boundaries were highlighted using blue and red in Fig. 2(c), respectively.The conjugate products within these two slabs were averaged using, ∑︁ z∈Scleral slab P(x,z,t) Num of summed(x,z)pixels (5) where P[i] RPE (t) and P[i] Scl (t) stand for the spatially averaged time trace of complex product in the i th section of RPE and scleral slabs, respectively.The data processing framework is summarized in Fig. 2. As shown in the top figure, the first step was to correct the OCT raw data cube for bulk tissue motion.The magnitude part  (,,) was co-registered using a correlation-based image registration algorithm [42], where the pixel-level axial and lateral bulk motion between every two adjacent B-scans was minimized.And the phase part  (,,) was corrected for bulk phase shift between two adjacent B-scans using a histogram-based phase compensation algorithm [43].The resultant corrected data cube (,,) [Fig.2(a)] can be written as, where (,,) and (,,) are the magnitude and phase after correction, respectively.
In the left column of Fig. 2, the magnitude (,,) was averaged along t-axis to result in the structure image (,) (Fig. 2b), on which an automatic segmentation was conducted to find the depth of Bruch's membrane (BM),  () , and choroid-sclera interface (CSI),  () , Then, the phase shift induced from the choroidal deformation was obtained using: where ∆ϕ [i]  cho (t) is the time trace of phase shift from choroidal deformation in i th section.The obtained phase shift ∆ϕ [i]  cho (t) then went through non-uniform low pass (NULP) filtering to address for time discontinuity and noise.The resultant smooth trace was denoted as ∆ϕ [i]  cho,flt (t) .The details of our NULP filtering can be found in 2.3.2.
The filtered phase shift is converted to velocity using the Doppler theorem, • ∆ϕ [i]   cho,flt (7) where v [i]  cho (t) is the time trace of choroidal deforming velocity in i th section, λ 0 is the OCT center wavelength, n is the refractive index, and ∆T is the time elapsed between two adjacent B-scans.The cosine factor in the denominator corrects the influence of Doppler angle.Next, the time trace of choroidal deformation d [i]  cho (t) was obtained by time accumulation of the velocity, and the choroidal max deformation ∆d [i] can be extracted as the amplitude of the time trace, Ultimately, the choroidal max strain ϵ can be computed as the average of the ratio of ∆d [i] and d [i]  0 over all the three sections, ϵ = 1 3 Additionally, the averaged choroidal max deformation ∆d and thickness d 0 were also calculated by averaging ∆d [i] and d [i]  0 over i, respectively.In general, we computed three values from each OCT scan in our dataset: the choroidal max deformation ∆d, the choroidal thickness d 0 , and the choroidal max strain ϵ.These values served as the inputs for any subsequent statistical analyses.

Non-uniform low pass (NULP) filtering of the phase
There were two motivations for performing NULP filtering.(1) Eye-tracking caused time discontinuity.A typical time trace of phase shift is shown in Fig. 3(c), where the re-scan events causing the discontinuity are marked with orange circles.The time accumulation of a discontinued trace would introduce error in the calculation of ∆d and d 0 .(2) The phase noise was too high in the scleral slab.The choroid has a dense vascular network, where the intense dynamic scattering from the blood introduces considerable phase fluctuation and casts tailing artifacts onto the scleral slab.Figure 3(b) shows a representative phase noise map, where the yellowish color (suggesting high phase noise) dominates the choroid-sclera complex.Even though we averaged the traces from a large number of spatial pixels (reflected in Eq. ( 5)), the phase shift (Fig. 3(c)) still carried significant noise.To address the two challenges mentioned above, we developed a NULP filtering algorithm that consists of a non-uniform Fourier transform (NUFT) and a frequency-domain low-pass filtering.The algorithm was summarized in Fig. 3 as a flowchart.
where iFT{ ⋅ } denotes the inverse Fourier transform, NUFT{ ⋅ }  denotes the NUFT with respect to time , () = 1/ 1 + (/6 1 ) 12 is the transfer function of the low-pass filter, and  is the frequency.After the filtering, the time trace became noise-suppressed and continuous in the time domain.Fig. 4(a) displays the structural image, followed by two phase shift maps showcased at distinct time points: one during systole (Fig. 4b) and the other during diastole (Fig. 4c).The phase shift values were overlaid onto the OCT structural image using pseudo color encoding.The yellowred colors in Fig. 4(b) indicate a downward motion of the choroid and sclera, suggesting choroidal expansion, while the blue color in Fig. 4(c) suggests the opposite motion.The dynamic nature of fundus pulsation over time is demonstrated in the M-scan view (z-t plane) displayed in Fig. 4(d), with the structure and velocity of all A-scans averaged to minimize the speckle and noise.Discernible periodic velocity alterations can be observed.Fig. 4(e) presents the time trace of choroidal motion, where the strain rate (time derivative of strain) is depicted in blue and the strain in orange.Notably, the strain exhibits a ~90° phase lag compared to the strain rate due to the time accumulation.

Fundus pulsation imaging and repeatability evaluation
To assess the repeatability of FP-OCE, three low-moderate myopia eyes (25-year-old male, -1D; 30-year-old female, -4D; 36-year-old female, -4D) were measured for choroidal max strain.Each eye was consecutively measured three times.The distribution is demonstrated in the left column of Fig. 4(f).The coefficients of variance (CoV, standard deviation divided by arithmetic mean) of the three subjects were 16.9%, 10.9%, and 14.7%, respectively.The intraclass correlation coefficient (ICC) of agreement between individual measurements was 0.841.Both CoV and ICC suggested good repeatability.First, the phase shift ∆ϕ [i]  cho (t) induced by the choroidal deformation was transformed to obtain the frequency domain spectra (Fig. 3(d)) using non-uniform Fourier transform (NUFT).Note that the time trace is not continuous, so we employed NUFT instead of the conventional Fourier transform to handle the time discontinuity.The MATLAB routine nufft() was used for the computation.
Next, a 12-order Butterworth low-pass filter (Fig. 3(e)) was applied to the spectra, and the filtered spectra were inverse Fourier transformed (iFT) to achieve a filtered time trace (Fig. 3(f)).The -3 dB bandwidth of the filter was 6f 1 , where f 1 is the fundamental heartbeat frequency that maximizes the spectrum.The mathematical description of the NULP process can be summarized as, where iFT{•} denotes the inverse Fourier transform, NUFT{•} t denotes the NUFT with respect to time t, H(f is the transfer function of the low-pass filter, and f is the frequency.After the filtering, the time trace became noise-suppressed and continuous in the time domain.

Quantification of choroidal strain in myopia patients
Now that we have the choroidal strain, a preliminary clinical study can be readily conducted to validate our method.Previous studies found that the scleral rigidity decreases with the progression of myopia stages [8].Therefore, according to our model, it is expected that an elevated choroidal strain in subjects with severe myopic stages should be observed.To test this hypothesis, we divided the recruited subjects into different groups according to their myopic stages.In each group, the choroidal strain  was counted, and the mean value difference of  among groups were analyzed.To assess the repeatability of FP-OCE, three low-moderate myopia eyes (25-year-old male, -1D; 30-year-old female, -4D; 36-year-old female, -4D) were measured for choroidal max strain.Each eye was consecutively measured three times.The distribution is demonstrated in the left column of Fig. 4(f).The coefficients of variance (CoV, standard deviation divided by arithmetic mean) of the three subjects were 16.9%, 10.9%, and 14.7%, respectively.The intraclass correlation coefficient (ICC) of agreement between individual measurements was 0.841.Both CoV and ICC suggested good repeatability.

Demonstration of choroidal biomechanics alterations in myopia
Additionally, the inter-day reproducibility of FP-OCE was evaluated on the same eye from the 25-year-old male.FP-OCE measurements of this eye were conducted on three separate days, with three repeats collected for each day.The distribution of choroidal max strain is demonstrated in the right column of Fig. 4(f).The average CoV of three days was 13.6%.The mean values of the three days showed no significant difference in one-way analysis of variance (ANOVA, p = 0.48), demonstrating excellent inter-day consistency.

Quantification of choroidal strain in myopia patients
Now that we have the choroidal strain, a preliminary clinical study can be readily conducted to validate our method.Previous studies found that the scleral rigidity decreases with the progression of myopia stages [8].Therefore, according to our model, it is expected that an elevated choroidal strain in subjects with severe myopic stages should be observed.To test this hypothesis, we divided the recruited subjects into different groups according to their myopic stages.In each group, the choroidal strain ϵ was counted, and the mean value difference of ϵ among groups were analyzed.

Demonstration of choroidal biomechanics alterations in myopia
Figure 5 presents representative images from three subjects with varying degrees of myopia severity, illustrating the alterations in choroidal thickness, deformation, and strain.The first row depicts the eye of a 58-year-old male with low myopia.A thick choroid (Fig. 5(a)) and large choroidal deforming velocity (Fig. 5(d)) can be observed.In contrast, the eye of a 46-year-old male with high myopia in the second row shows a thinner choroid (Fig. 5(b)) and smaller choroidal deforming velocity (Fig. 5(e)).The eye of a 63-year-old male subject with pathologic myopia, shown in the third row, displays an even thinner choroid (Fig. 5(c)) and smaller choroidal deforming velocity (Fig. 5(f)).Notably, the pathologic myopic eye appears to have an excessively stretched eyeball, resulting in large fundus curvature and extremely thin sclera.This permits the OCT beam to penetrate down to the extraocular tissue (see the yellow arrow in Fig. 5(c)).Interestingly, the choroidal strain showed an inverted trend than the choroidal thickness and deformation, as can be observed in Fig. 5(g)-5(i), with higher choroidal strain linked to more severe myopia.

Statistical analysis
Statistical analysis confirmed the trend in choroidal biomechanical alterations.Among the three myopic groups, the choroidal thickness, choroidal max deformation, and choroidal max strain were compared using multiple comparisons, and the results were displayed in Fig. 6.The p-value was calculated using the Tukey multiple comparison test.The parameter that showed the most significant difference was the choroidal thickness, which decreased as the myopic stage increased (Fig. 6(a)).The choroidal max deformation also showed a significant decreasing trend (Fig. 6(b)), which can be attributed to the thinning of choroid.The choroidal max strain, defined as the choroidal max deformation normalized with thickness, is shown in Fig. 6(c).The group mean of choroidal max strain from the high myopia group is slightly higher than the low-moderate myopia group but is not significant (p = 0.6511).By contrast, the pathologic myopia group has significantly higher choroidal max strain than both the low-moderate (p = 0.0006) and high myopia groups (p = 0.0036).This result was in accordance with our hypothesis that elevated choroidal strain should be observed in subjects with more severe myopia.
male with high myopia in the second row shows a thinner choroid (Fig. 5b) and smaller choroidal deforming velocity (Fig. 5e).The eye of a 63-year-old male subject with pathologic myopia, shown in the third row, displays an even thinner choroid (Fig. 5c) and smaller choroidal deforming velocity (Fig. 5f).Notably, the pathologic myopic eye appears to have an excessively stretched eyeball, resulting in large fundus curvature and extremely thin sclera.
This permits the OCT beam to penetrate down to the extraocular tissue (see the yellow arrow in Fig. 5c).Interestingly, the choroidal strain showed an inverted trend than the choroidal thickness and deformation, as can be observed in Fig. 5(g) -5(i), with higher choroidal strain linked to more severe myopia.

Statistical analysis
Statistical analysis confirmed the trend in choroidal biomechanical alterations.Among the three myopic groups, the choroidal thickness, choroidal max deformation, and choroidal max strain were compared using multiple comparisons, and the results were displayed in Fig. 6.The pvalue was calculated using the Tukey multiple comparison test.The parameter that showed the most significant difference was the choroidal thickness, which decreased as the myopic stage increased (Fig. 6a).The choroidal max deformation also showed a significant decreasing trend (Fig. 6b), which can be attributed to the thinning of choroid.The choroidal max strain, defined as the choroidal max deformation normalized with thickness, is shown in Fig. 6(c).The group mean of choroidal max strain from the high myopia group is slightly higher than the low- moderate myopia group but is not significant (p = 0.6511).By contrast, the pathologic myopia group has significantly higher choroidal max strain than both the low-moderate (p = 0.0006) and high myopia groups (p = 0.0036).This result was in accordance with our hypothesis that elevated choroidal strain should be observed in subjects with more severe myopia.

Discussion
Fundus pulsation opens a new pathway for investigating the biomechanical properties of the human eye.Leveraging our proposed choroidal pulsation model, we successfully established a connection between the magnitude of fundus pulsation (quantified by the choroidal max strain) and the posterior scleral rigidity.This connection provides a potentially powerful diagnostic tool for diseases with progressively changing ocular rigidity.We conducted a preliminary clinical study on eyes with myopia, a disease characterized by decreasing posterior scleral rigidity as myopia progresses.According to our hypothesis, we anticipated reduced choroidal strain with increasing myopic severity due to scleral weakening.The experimental results, as illustrated in Fig. 6, validated this hypothesis.Interestingly, the difference between high and

Discussion
Fundus pulsation opens a new pathway for investigating the biomechanical properties of the human eye.Leveraging our proposed choroidal pulsation model, we successfully established a connection between the magnitude of fundus pulsation (quantified by the choroidal max strain) and the posterior scleral rigidity.This connection provides a potentially powerful diagnostic tool for diseases with progressively changing ocular rigidity.We conducted a preliminary clinical study on eyes with myopia, a disease characterized by decreasing posterior scleral rigidity as myopia progresses.According to our hypothesis, we anticipated reduced choroidal strain with increasing myopic severity due to scleral weakening.The experimental results, as illustrated in Fig. 6, validated this hypothesis.Interestingly, the difference between high and low-moderate myopia was not significant, while pathologic cases displayed significantly higher choroidal strain than both low-moderate and high myopia.This observation suggests that reaching myopic macular degeneration (MMD) category 2 may represent a critical threshold, beyond which scleral mechanical properties deteriorate significantly-a plausible interpretation as MMD category 2 also marks the first stage of pathologic myopia and the onset of the degradation of visual acuity [46].
Notably, the high myopia group exhibits higher variability in choroidal max strain values compared to the low-moderate myopia group (see the inter-quartile range of the high myopia group in Fig. 6(c)).This variance is potentially attributable to the varying rate of progression in myopia, i.e., different risk of pathologic myopia.Over time, some individuals with high myopia may progress to pathologic myopia.This subset of the myopic population experiencing rapid progression may potentially exhibit distinct choroidal max strain patterns.A longitudinal follow-up study on individuals with high myopia is warranted to provide validation for this hypothesis.
Effective control of eye motion is essential for accurate in-vivo human eye measurements.We proposed a hardware-and-software combined solution to suppress the bulk eye motion in our FP-OCE measurement.On the software side, the commonly used image registration and phase compensation were applied.On the hardware side, we utilized the built-in eye tracking module of the clinical OCT machine, which allowed real-time minimization of eye motion during scanning.However, we encountered the challenge of time discontinuity when the tracking module paused the scan for motion compensation.To avoid potential frequency error, we utilized the NULP filtering to handle time traces with time discontinuity.This approach reconstructed a continuous time axis (Fig. 3(f)) and more accurate fundamental cardiac frequencies (Fig. 3(d)).
Moreover, effectively addressing tailing artifacts due to overlying blood flow is crucial to achieve a precise estimation of fundus pulsation.As illustrated in Fig. 3(b), the strong tailing artifact in the choroid and sclera significantly deteriorated the clarity of the Doppler phase shift.Our strategy was to average multiple spatial locations in a slab to cancel the random noise.Theoretically, a higher number of samples to be averaged results in a more definitive phase shift; thus, the ideal condition is to average all points within the slab.However, due to the curvature of the retina, calculating the phase shift must be done by sections to correct the local Doppler angle; and the precision of Doppler angle estimation benefits from a larger number of sections, which unfortunately, opposes the optimization of phase noise suppression.We ultimately opted for three segments to strike a satisfactory balance in the precision of Doppler angle estimation and phase noise suppression.
Of note, the spatial averaging may de-emphasize the lateral resolution of the choroidal strain.Given that the FP-OCE protocol evaluates the overall choroidal strain within a 3-mm imaging field, it cannot detect localized scleral weakening smaller than 3 mm in diameter.Fortunately, posterior staphylomas commonly have a diameter in the range of 10 mm [47], making them potentially distinguishable by FP-OCE.In future research, we intend to explore localized differences in choroidal strain between staphylomatous and non-staphylomatous regions.
One limitation of our clinical study is the absence of axial length data.Instead, we relied on refractive error as a suboptimal indicator to categorize myopic severity, resulting in less accurate grouping and somewhat impaired differentiation sensitivity.Encouragingly, despite this limitation, FP-OCE still effectively characterized the difference in scleral rigidity in myopia.We expect that by incorporating axial length data in future studies, we can enhance the sensitivity of FP-OCE in differentiating myopia severity and discover a more significant difference between low-moderate and high-myopia eyes.Besides, the axial-length dependency of choroidal strain is another topic worth investigating.
It should be noted that the choroidal pulsation model was remarkably simplified, with the assumption that the choroidal strain is negatively correlated with scleral rigidity.An important underlying prerequisite is that the force causing the choroidal expansion -the ocular perfusion pressure -should stay constant.However, the intraocular pressure and blood pressure vary from person to person.Therefore, this prerequisite can only be satisfied in specific contexts.In our preliminary clinical study, we compared the group mean values, with each group consisting of a considerable number of 9∼26 eyes.This allowed us to assume quasi-constant ocular perfusion pressures among the group averages reasonably.Another circumstance that the constant-pressure prerequisite can be satisfied is the longitudinal studies that track the myopia progression or treatment in the same individual.In our future work, we will consider adding more parameters to our model to make it more generalizable.Potential candidates include axial length, ocular perfusion pressure, and IOP.We foresee that our model can become more sensitive to subtle changes in scleral weakening with additional parameters.
FP-OCE offers a wide array of research and clinical applications with significant benefits, such as monitoring myopia progression and early detection of possible progression to pathologic myopia and/or posterior staphyloma.By continuously tracking scleral rigidity in follow-up visits, this technique can identify abnormal rates of scleral weakening and facilitate timely clinical interventions.Furthermore, FP-OCE is competent for the efficacy assessment of the developments of scleral crosslinking treatment options.Given that crosslinking modifies scleral rigidity while preserving ocular perfusion strength, changes in choroidal strain would directly reflect treatment efficacy.Above all, our methodology seamlessly integrates into clinical practice, as it only requires a standard clinical OCT system with a customized scanning protocol.Implementing our methods in clinical settings can be as straightforward as a software update, and the FP-OCE eye examinations closely resemble standard clinical OCT exams.

Conclusion
In conclusion, we propose fundus pulsation optical coherence elastography (FP-OCE) for assessing scleral rigidity in living humans.By quantifying choroidal strain, we establish a novel approach to evaluate scleral rigidity.Despite some limitations, our preliminary clinical study effectively differentiated pathologic myopia from non-pathologic cases, highlighting its sensitivity and potential avenues for improvement in our methodology.The straightforward integration into clinical practice, with standard clinical OCT equipment and a simple examination procedure, makes it a potentially revolutionary tool in myopia diagnosis and management.

Fig. 1 .
Fig. 1.The choroidal pulsation model.(a) The schematic shows the blood being pumped into the "posterior sandwich".(b1), (b2) The model in different heart cycles; during systole (b1), the choroid expands, while in diastole (b2), the choroid recoils.The sclera acts as a resistance to the choroidal expansion.d max and d min , the maximal and minimal thickness of the choroid, respectively; d 0 , the static choroidal thickness; ∆d, the choroidal max deformation.

Fig. 2 .
Fig. 2. The data processing framework.The OCT raw data cube was first corrected for bulk motion to get (a) the corrected data cube.The magnitude of the corrected data cube was averaged along the t-axis to generate (b) the structure image, on which the segmentation was conducted to get the choroidal thickness.(c) The phase shift showing the tissue motion, obtained by computing the complex conjugate product between successive B-scans.(d) The time trace of choroidal deformation, computed from the difference of the phase shifts between a RPE slab and a scleral slab located next to the choroidal boundaries.BM, Bruch's membrane; CSI, choroidsclera interface, RPE, retinal pigment epithelium.

Fig. 2 .
Fig. 2. The data processing framework.The OCT raw data cube was first corrected for bulk motion to get (a) the corrected data cube.The magnitude of the corrected data cube was averaged along the t-axis to generate (b) the structure image, on which the segmentation was conducted to get the choroidal thickness.(c) The phase shift showing the tissue motion, obtained by computing the complex conjugate product between successive B-scans.(d) The time trace of choroidal deformation, computed from the difference of the phase shifts between a RPE slab and a scleral slab located next to the choroidal boundaries.BM, Bruch's membrane; CSI, choroid-sclera interface, RPE, retinal pigment epithelium.

Fig. 3 .
Fig. 3.The schematic of the non-uniform low-pass (NULP) filtering.(a) The structural image of a retina with segmentation lines overlaid, and (b) The overlay of the phase noise (the standard deviation of phase shift over time) map on the structural image, where the RPE and scleral slabs were indicated using blue and red color, respectively.The yellow color suggests high phase fluctuation.(c) The time trace of the phase shift from choroidal deformation in the 3 rd section.The orange arrow indicates a typical re-scan event that caused a segment of discontinuity of ~0.1s.(d) The spectrum of the time trace.(e) The frequency domain low-pass filter.(f) The time trace after NULP filtering.NUFT, non-uniform Fourier transform; iFT, inverse Fourier transform.

Figure 4
Figure 4 presents an illustrative example of fundus pulsation imaging of a 47-year-old male.

Fig. 3 .
Fig. 3.The schematic of the non-uniform low-pass (NULP) filtering.(a) The structural image of a retina with segmentation lines overlaid, and (b) The overlay of the phase noise (the standard deviation of phase shift over time) map on the structural image, where the RPE and scleral slabs were indicated using blue and red color, respectively.The yellow color suggests high phase fluctuation.(c) The time trace of the phase shift from choroidal deformation in the 3 rd section.The orange arrow indicates a typical re-scan event that caused a segment of discontinuity of ∼0.1s.(d) The spectrum of the time trace.(e) The frequency domain low-pass filter.(f) The time trace after NULP filtering.NUFT, non-uniform Fourier transform; iFT, inverse Fourier transform.

Figure 4
Figure 4 presents an illustrative example of fundus pulsation imaging of a 47-year-old male.Figure 4(a) displays the structural image, followed by two phase shift maps showcased at distinct time points: one during systole (Fig. 4(b)) and the other during diastole (Fig. 4(c)).The phase shift values were overlaid onto the OCT structural image using pseudo color encoding.The yellow-red colors in Fig. 4(b) indicate a downward motion of the choroid and sclera, suggesting

Figure 4 (
Figure 4 presents an illustrative example of fundus pulsation imaging of a 47-year-old male.Figure 4(a) displays the structural image, followed by two phase shift maps showcased at distinct time points: one during systole (Fig. 4(b)) and the other during diastole (Fig. 4(c)).The phase shift values were overlaid onto the OCT structural image using pseudo color encoding.The yellow-red colors in Fig. 4(b) indicate a downward motion of the choroid and sclera, suggesting

Fig. 4 .
Fig. 4. Illustration and repeatability of the FP-OCE measurement.(a) Structural image.(b) Phase shift at a systolic time point and (c) phase shift at a diastolic time point.Phase shift values were pseudocolor-encoded and overlaid onto the structural image.(d) M-scan view, where the structural image and velocity map from all A-scans were averaged.(e) Time traces of choroidal motion, with the blue curve representing strain rate and the orange curve representing strain.(f) Results of the FP-OCE repeatability test in terms of choroidal max strain.Error bars depict the standard deviation of three repeated measurements of choroidal strain in the same day.

Fig. 5
Fig. 5 presents representative images from three subjects with varying degrees of myopia severity, illustrating the alterations in choroidal thickness, deformation, and strain.The first

Fig. 4 .
Fig. 4. Illustration and repeatability of the FP-OCE measurement.(a) Structural image.(b) Phase shift at a systolic time point and (c) phase shift at a diastolic time point.Phase shift values were pseudocolor-encoded and overlaid onto the structural image.(d) M-scan view, where the structural image and velocity map from all A-scans were averaged.(e) Time traces of choroidal motion, with the blue curve representing strain rate and the orange curve representing strain.(f) Results of the FP-OCE repeatability test in terms of choroidal max strain.Error bars depict the standard deviation of three repeated measurements of choroidal strain in the same day.

Fig. 5 .
Fig. 5. Representative images of eyes at different stages of myopia (from top to bottom: low, high, and pathologic myopia).(a)-(c) B-scan images showing Bruch's membrane (BM) in blue and the choroid-sclera interface (CSI) in orange.The yellow arrow in (c) indicates the extraocular tissue.(d)-(f) The M-scan views with all A-scans averaged, where the velocity values were overlaid onto the structural image using the colormap shown in the top middle.(g)-(i) Time traces of choroidal motion, with the choroidal strain rate (time derivative of strain) shown in blue and the choroidal strain in orange.

Fig. 5 .
Fig. 5. Representative images of eyes at different stages of myopia (from top to bottom: low, high, and pathologic myopia).(a)-(c) B-scan images showing Bruch's membrane (BM) in blue and the choroid-sclera interface (CSI) in orange.The yellow arrow in (c) indicates the extraocular tissue.(d)-(f) The M-scan views with all A-scans averaged, where the velocity values were overlaid onto the structural image using the colormap shown in the top middle.(g)-(i) Time traces of choroidal motion, with the choroidal strain rate (time derivative of strain) shown in blue and the choroidal strain in orange.