Ocular Rigidity, Ocular Pulse Amplitude, and Pulsatile Ocular Blood Flow: The Effect of Axial Length

Abstract

Purpose.: Previous studies have shown a negative correlation between axial length (AL) and pulsatile ocular blood flow (POBF). This relation has been questioned because of the possible confounding effect of ocular volume on ocular rigidity (OR). The purpose of this study was to investigate the relation between AL, as a surrogate parameter for ocular volume, and OR, ocular pulse amplitude (OPA), and POBF.

Methods.: Eighty-eight cataract patients were enrolled in this study. A computer-controlled device comprising a microdosimetric pump and a pressure sensor was used intraoperatively. The system was connected to the anterior chamber and used to raise the intraocular pressure (IOP) from 15 to 40 mm Hg, by infusing the eye with a saline solution. After each infusion step, the IOP was continuously recorded for 2 seconds. Blood pressure and pulse rate were measured during the procedure. The OR coefficient was calculated from the pressure volume data. OPA and POBF were measured from pressure recordings.

Results.: Median AL was 23.69 (interquartile range 3.53) mm. OR coefficient was 0.0218 (0.0053) μL⁻¹. A negative correlation between the OR coefficient and AL (ρ = −0.641, P < 0.001) was documented. Increasing AL was associated with decreased OPA (ρ = −0.637, P < 0.001 and ρ = −0.690, P < 0.001) and POBF (ρ = −0.207, P = 0.053 and ρ = −0.238, P = 0.028) at baseline and elevated IOP, respectively.

Conclusions.: Based on manometric data, increasing AL is associated with decreased OR, OPA, and POBF. These results suggest decreased pulsatility in high myopia and may have implications on ocular pulse studies and the pathophysiology of myopia.

Introduction

The prevalence of myopia is increasing, affecting approximately 1 billion people. ¹ Various theories have been proposed to explain its pathogenesis. Current approaches to myopia development suggest that the sclera plays a key role, with changes in biomechanical properties and biochemical environment occurring in the process of eye elongation. Both cellular factors and the extracellular matrix have been implicated in the pathogenesis of myopia. ² Various reports from studies in animal models of myopia have provided valuable information on the changes in biomechanics that occur during the process. Despite a significant difference in the in vivo elastic response of the sclera shown in some of them, ² other studies have failed to demonstrate a change in the modulus of elasticity during myopia development. ³ It is evident that besides the growing knowledge, the complete spectrum of induced biochemical changes, as well as the structural biomechanical alterations still have not been characterized. ³ Meanwhile, the sclera is a dynamic tissue that can adaptively alter its properties, and data on the biomechanical properties of human eyes in vivo remain very limited. ^4,5  

Evidence from animal models has also led researchers to suggest a role for the richly vascularized choroid in the process of emmetropization. Choroidal thickening and thinning may aid in tuning the defocus on the retina and secreting factors that can influence the process of eye elongation. ⁶ Studies have also shown decreased blood flow measurements in myopic eyes compared to emmetropic eyes by means of pneumotonometry and color Doppler imaging, suggesting that decreased blood flow may underlie the pathologic changes seen in degenerative myopia. ⁷ These differences have also been reported in young healthy myopes, without signs of degenerative disease. ^8,9 Interestingly, all these techniques hold limitations in axially elongated eyes. 

Ocular rigidity (OR) has been used in the literature as a clinical concept that characterizes the biomechanical properties of the ocular coats. It is generally assumed to be a surrogate parameter related to the biomechanical properties of the whole globe. It measures the extensibility of the ocular wall as the relationship between a change in intraocular pressure (IOP) and a change in intraocular volume. 

Data from animal models as well as postmortem studies have shown that the pressure volume relation does not conform to a simple law. Several mathematical formulations were proposed thereafter to quantify this relation. Many of them are dependent on the internal volume of the globe, IOP, corneal biomechanics, and thickness of the corneoscleral shell. ¹⁰ Sometimes this is extended to biomechanical properties of the ocular vasculature and perfusion pressure. ¹¹ The formula suggested by Friedenwald, ¹² using the OR coefficient based on a logarithmic pressure volume relationship, and the one proposed by Silver and Geyer ¹³ are the most extensively used formulae. Recently, Kotliar et al. ¹⁴ also suggested a biomechanical model, based on three-dimensional elasticity theory, that they validated with their experimental results from intraoperative Schiotz tonometry. 

The ability to quantify the parameter of OR is important because it can transform pressure wave recordings, which are easily recordable, to volume changes in the eye, which are difficult to quantify, and thus permit estimating the pulsatile component of blood flow. In our previous report, we suggested that the pressure volume relation, as well as ocular pulse amplitude (OPA) and pulsatile ocular blood flow (POBF), is influenced by the level of IOP. ⁴ The purpose of this study was to investigate the relation between axial length (AL), as an easily accessible surrogate parameter for ocular volume, and OR. Moreover, in this study we examine whether ocular pulsatility, as reflected in OPA and POBF, is altered in high myopia. 

Methods

Patients and Procedures

Measurements were performed in the Ophthalmology Departments of the University Hospital of Heraklion and the University Hospital of Larissa. Eighty-eight patients undergoing cataract surgery were enrolled. One eye per patient was measured. Exclusion criteria were presence of ocular disease other than cataract and myopia, history of previous ophthalmic surgery, or systemic medical conditions, including severe cardiovascular or pulmonary disease. However, medically treated systemic hypertension and diabetes were not exclusion criteria. All participants underwent a comprehensive ocular examination including slit lamp biomicroscopy and dilated fundoscopy. IOP was measured with Goldmann applanation tonometry the day before surgery. AL and central corneal thickness (CCT) were measured with A-scan biometry and pachymetry with Ocuscan (Alcon Laboratories, Irvine, CA). 

The study protocol adhered to standards outlined in the Declaration of Helsinki and was approved by the Review Boards of the University Hospitals of Heraklion and Larissa. All patients participating in the study were informed about the purpose, the procedures, and the consequences of this study and signed an informed consent. 

The measurement procedure has been presented in detail elsewhere. ⁴ A computer-controlled device was used, comprising three units: a pressure sensor (sampling rate 200 Hz, effective pressure sensitivity 0.05 mm Hg), a dosimetric syringe drive unit (volume sensitivity 0.08 μL per step), and a circuit of sterile inextensible tubes (Vygon, Ecouen, France) filled with saline solution. 

The usual protocol for pupil dilation with tropicamide and phenylephrine drops for patients undergoing cataract surgery was followed. Briefly, the measurement procedure was performed in the operating theater, under sterile conditions, in the supine position, under local anesthesia with proparacaine drops. In the beginning of the measurement, the system was calibrated and the anterior chamber was cannulated with a 21-gauge needle, allowing for free communication between the eye and the measurement system. The initial IOP was recorded, and with appropriate saline solution–aqueous humor exchange, the IOP was controlled at the level of 15 mm Hg. The system was used to raise the IOP from 15 to 40 mm Hg by infusing the eye with a saline solution in increments of 4 μL. After each infusion step, the IOP was continuously recorded for 2 seconds in order to measure the pulsatile change in IOP during this interval. Starting from an initial level of 40 mm Hg, an IOP decay curve was recorded. Systemic blood pressure and pulse rate were monitored throughout the procedure. 

Data Analysis

The pressure–volume data, after an initial correction for outflow, were fitted with an exponential curve, in order to calculate the OR coefficient K, according to the equation IOP = initial IOP × (expK × ΔVolume). ⁴ In order to quantify OPA, which corresponds to the maximum IOP fluctuation in synchrony with the heart rate, an algorithm based on the standard deviation of the pressure tracings during each 2-second recording was used. The mean IOP as well as the OPA in each measurement window was calculated. To estimate POBF, an algorithm based on a theoretical model proposed by Silver and Farrell ¹⁵ was used. While the raw signal was used in all other calculations, a low-pass filter was applied to the real-time pressure signal in order to measure POBF. For each measurement window, dIOP/dt versus time was calculated and transformed to dV/dt with the use of the pressure volume data. POBF was estimated as the lowest value of volume flow dV/dt, during each 2-second tracing. Data processing was performed with a customized software algorithm (Labview; National Instruments, Inc., Austin, TX). 

Mean arterial pressure (MAP) was calculated from systolic (SBP) and diastolic (DBP) blood pressure as follows  

 

 

Statistical Analysis

One eye from each patient was examined. Normality of distribution was assessed with the Shapiro-Wilk test. Normally distributed data are presented as mean (standard deviation) and skewed variables are given as median (interquartile range). Correlation analysis was performed with calculation of the Pearson correlation coefficient r when at least one of the variables tested followed a normal distribution and with the Spearman correlation coefficient ρ if both variables were skewed. Multiple linear regression analysis was used to control for parameters that may also have affected the outcome variable. The level of significance was set at 0.05. The SPSS software package was used for all analyses (version 16; SPSS, Inc., Chicago, IL). 

Results

Median AL was 23.69 (range, 20.35–32.49) mm. Patients' characteristics are presented in the Table. Six of the patients had signs of degenerative myopia; three being diagnosed with a myopic cone, two with chorioretinal atrophic lesions, and one with myopic maculopathy. None of the participants in the study experienced any intra- or postoperative complications related to the procedure (up to a minimum follow-up of 6 months in all patients). 

The median OR coefficient was 0.0214 (0.0084) μL⁻¹. The mean measured OPA was 2.00 (0.67) mm Hg at measurements performed at 15 mm Hg increasing to 3.66 (1.40) mm Hg at 40 mm Hg. Median POBF was 876 (282) μL/min at an IOP of 15 to 20 mm Hg, 787 (306) μL/min at 20 to 25 mm Hg, 686 (284) μL/min at 25 to 30 mm Hg, 642 (268) μL/min at 30 to 35 mm Hg, and 607 (215) μL/min at an IOP of 35 to 40 mm Hg. 

Table.

 

Demographic Characteristics

Sex, males/females	35/53
Age, y	60.2 (14.1)*
Axial length, mm	23.69 (3.53)†
CCT, μm	537.3 (27.9)*
Pulse, rate per minute	65 (14)†
MAP, mm Hg	98.2 (14.8)*
Preoperative IOP, mm Hg	14.0 (5.0)†

*  Data are presented as mean (standard deviation).

†  Data are presented as median (interquartile range).

A negative correlation between the OR coefficient K and AL (ρ = −0.641, P < 0.001) was documented (Fig. 1). No statistically significant relation was found between K and CCT values (r = 0.071, P = 0.549). Data analysis showed a positive correlation between K and age (r = 0.230, P = 0.031). However, in our sample AL also correlated with age (r = −0.460, P < 0.001), but not with CCT (r = 0.092, P = 0.433). In multiple regression analysis (significance of the model, P < 0.001, R ² = 0.342), AL (P < 0.001) was the only statistically significant parameter to predict the variance of the OR coefficient, with age (P = 0.747), CCT (P = 0.662), MAP (P = 0.863), and pulse rate (P = 0.594) also being considered in the model. 

Figure 1

 

Scatterplot of the relation between the ocular rigidity coefficient and AL. Based on the relationship between IOP and AL proposed by Kotliar et al. ¹⁴ and taking into account Friedenwald's pressure–volume relationship, ¹² a logarithmic function was used to fit the data.

Due to the linear relation between OPA and IOP, which was evident in all measurements, we chose to examine and report the correlation between OPA and AL at two IOP levels, the baseline IOP of our measurement, which was 15 mm Hg and also the increased level of 40 mm Hg. Increasing AL was indeed associated with decreased OPA (r = −0.639, P < 0.001 and r = −0.661, P < 0.001) at baseline and elevated IOP, respectively (Fig. 2). Moreover, OPA positively correlates with the OR coefficient at baseline and elevated IOP (r = 0.596, P < 0.001 and r = 0.522, P < 0.001, respectively). 

Figure 2

 

OPA in relation to AL at baseline (15 mm Hg) and elevated (40 mm Hg) IOP.

Analysis of the POBF versus IOP data showed different patterns of their relation, and we chose to group and average POBF values at five different IOP levels. In order to investigate the relation between AL and POBF, we looked at correlation coefficients at these five IOP levels. There was a marginally nonsignificant relation between the two variables at lower IOP levels (ρ = −0.207, P = 0.053; ρ = −0.169, P = 0.115; and ρ = −0.195, P = 0.069 at IOP levels of 15–20, 20–25, and 25–30 mm Hg, respectively), while increasing AL was significantly associated with lower POBF values at higher IOP levels (ρ = −0.258, P = 0.017 and ρ = −0.238, P = 0.028 at 30–35 mm Hg and 35–40 mm Hg, respectively) (Fig. 3). 

Figure 3. 

 

POBF values in relation to AL at baseline (15–20 mm Hg) and elevated (35–40 mm Hg) IOP.

Discussion

The purpose of this study was to assess and quantify the role of AL on the pressure volume relation and on parameters that reflect pulsatility, such as OPA and POBF. This study demonstrates that the OR coefficient as well as OPA and POBF decreases with increasing AL. This is the first study that relates the OR coefficient measured intraoperatively in a large number of human eyes to AL, suggesting that AL alone could account for some of the interindividual differences in the above parameters. 

OR is a macroscopic parameter that characterizes the relationship of pressure to volume changes. It is commonly accepted that it is related to the elasticity of the sclera. The OR coefficient is a measure of this relation, without considerations of possible diverse morphology and material properties of the different ocular tissues. Volume is a parameter in many mathematical formulations of OR including those proposed by Friedenwald ¹² and Silver and Geyer. ¹³ The ocular volume depends on the shape of the eye. In the present study, we measured the AL, which represents the anteroposterior diameter. The shape of the eye is not spherical, and indeed, in highly myopic or hyperopic eyes, the lateral and vertical diameters may not be nicely approximated by the AL. As a result, a percentage of the variance seen in the relation between AL and OR in the present study may be explained by the variation in eye dimensions relative to AL. This argument is reinforced by the findings of the study by Tabernero and Schaeffel, ¹⁶ who were able to analyze peripheral refraction profiles and concluded that the peripheral retinal shape is more irregular in cases of low myopia compared to emmetropic eyes. In fact, using a swept source optical coherence tomography device and three-dimensional magnetic resonance imaging, Ohno-Matsui et al. ¹⁷ were able to study the shape of the sclera in a large number of eyes and reported that myopic retinochoroidal lesions also occurred more frequently in eyes with irregular curvature. As a result of this study, it can be assumed that regional variations in the stresses and deformation of the sclera can lead to susceptible areas that exhibit pathologic changes. 

However, Silver et al. (Silver DM, et al. IOVS 2010;51:ARVO E-Abstract 5019) have studied human eyes postmortem and proposed mathematical expressions that relate the volume to the AL of the eye, suggesting that this approximation may not induce large errors in the calculations. This might be true for emmetropic eyes with average AL, but it remains uncertain whether deviations may occur in highly myopic eyes. 

In addition, Perkins ¹⁸ investigated the relation between ocular volume and OR in human eyes postmortem and suggested that the decreased value of OR coefficient seen in high myopia is primarily a consequence of their larger ocular volume. He calculated a coefficient of rigidity that included the volume of the individual eye and suggested that myopic eyes do not exhibit apparent changes in scleral distensibility. Reanalyzing his data, a positive correlation of borderline significance (P = 0.043) between this metric and AL is found. Applying this approach to our sample, which includes a large number of living eyes and a wider range of ALs, and calculating an OR coefficient in which ocular volume is incorporated reveals a highly significant positive correlation between this new OR parameter and AL (ρ = 0.472, P < 0.001). 

In general, the concept of OR has been used with different units with different physical meanings in the literature. ^19–21 Recently, the use of the ocular response analyzer has introduced new metrics of corneal biomechanical properties, and studies with this technology suggest that high myopes manifest reduced corneal hysteresis, compared to controls, whereas no difference between the two groups was found for the corneal resistance factor. ²² These parameters are thought to represent mainly corneal properties, and many aspects regarding these new metrics are still not completely understood. As a result, direct comparison of these parameters to OR is not possible because OR is a measure that reflects geometry and material properties from the whole eye. 

Another result of this study is the negative correlation between OPA and AL. This finding is in accordance to previous studies in large numbers of patients. ^23–26 Shih et al. ²⁷ also reported a negative correlation between the OPA and AL in a study in 376 eyes, but in contrast to our results, the authors found a poor correlation between OPA and scleral rigidity. This may be due to differences in sample characteristics and in measurement procedures, since the measurement procedure used in the present study may provide more accurate results. Finally, the correlation between AL and OPA highlights the limitations inherent in the use of OPA as a hemodynamic index in between-subject comparisons since differences in AL could account for differences in OPA without representing real differences in blood flow. 

Moreover, the present study suggests a borderline relation between POBF and AL at lower IOPs, which becomes significant at elevated levels of IOP. Reduced POBF has been previously reported in myopia with the use of pneumotonometry. ^26,28–30 In all these studies, the correlation was significant, and moderate correlation coefficients were reported. Additionally, in a study of 80 patients, in which the factors that may influence POBF values in normal subjects were evaluated, the AL was the only parameter significantly associated with POBF, while age, systolic and diastolic blood pressure, IOP, and refractive error were not statistically significant factors in the model. ²⁹ However, these findings may have arisen from the use of a pressure volume relation for all eyes, irrespective of differences in ocular volume or scleral distensibility. The effort of the present study was to calculate POBF values in different IOP levels, using each individual eye's measured OR coefficient in order to minimize the error induced in the calculations when assuming a uniform pressure–volume relation. For this purpose, we also included eyes with a wide range of ALs and we compared the values of POBF under both lower and higher levels of IOP. The findings of the present study support the presence of compromised pulsatile hemodymanics in high myopia. It remains unknown whether reduced POBF values in high myopia also reflect an altered ratio of pulsatile to nonpulsatile flow. 

The major limitation of this study is the invasive and dynamic nature of the measurement procedure that provides data under non–steady state conditions. However, it should be considered that for a given eye, both the pressure volume relation and blood flow can be characterized. Moreover, pulse–pressure and flow–pressure curves can be obtained with each measurement. Additionally, the same range of pressures was used in every eye, in order for measurements to be readily comparable between subjects. In this context, the adherence to the same measurement protocol and the ability to manipulate the IOP and the volume change in the eye should provide us with useful considerations regarding the physiology of the eye and could reveal differences that may have pathophysiological implications. An important advantage of this study is also the wide range of ALs in our series of measurements. We chose, however, not to analyze data for spherical equivalent, since the subjects were all cataract patients and the results would be misleading because refraction is influenced by other parameters as well. Another limitation of the study is that we did not perform measurements of scleral thickness. It is known that highly myopic eyes manifest decreased scleral thickness in the posterior pole, ³¹ and the measurement of this parameter could possibly characterize the relation between the OR coefficient and scleral thickness. Additionally, it would be interesting to relate our findings to the volume of the vascularized choroid in our series of eyes. A negative correlation between AL and choroidal volume with evident choroidal thinning in highly myopic eyes has recently been reported by means of enhanced depth imaging optical coherence tomography. ³²  

Finally, AL is a determinant of ocular rigidity, OPA, and POBF. Our study provides a normative database for OR, which may also be useful for future studies, especially for tonography and pneumotonometry. POBF is shown to be reduced in high myopia after incorporating the OR coefficient of each eye in the calculation algorithms. These results may have implications for ocular pulse studies and the pathophysiology and clinical ramifications of myopia, suggesting compromised pulsatile hemodynamics in high myopes. A larger, longitudinal study with the use of noninvasive technology may highlight the time course of changes accompanying the development of degenerative myopia. 

Footnotes

 Disclosure: A.I. Dastiridou, None; H. Ginis, None; M. Tsilimbaris, None; N. Karyotakis, None; E. Detorakis, None; C. Siganos, None; P. Cholevas, None; E.E. Tsironi, None; I.G. Pallikaris, None

Footnotes

 Part of the data reported in this article was presented as an ARVO abstract: Dastiridou A, et al. IOVS 2009;50:ARVO E-Abstract 414.