Eye Vessel Compliance as a Function of Intraocular and Arterial Pressure and Eye Compliance

Abstract

Purpose.: The purpose of our study is to develop and validate a methodology to measure the compliance of the vascular network in the eye using biomechanical parameters, namely arterial pressure, intraocular pressure (IOP), and ocular compliance of the eyeball (OC).

Methods.: In vitro experiments were conducted on 6 freshly enucleated rabbit eyes. An inflatable catheter was inserted in the posterior chamber. The balloon was inflated and its volume changed periodically at a rate of 1–2 Hz, yielding variations in the intraocular volume; thus, emulating the volume pulsations of the vascular network in the eye. The IOP was measured continuously with a pressure transducer and the OC was calculated using the outflow facility. The compliance of the balloon, mimicking the compliance of the vascular network, was estimated indirectly from the measurements of IOP, balloon pressure, and OC. The estimated balloon compliance was compared to direct estimates of balloon compliance, based on the balloon pressure-volume curve. In vivo study included 5 white New-Zealand rabbits. The method to estimate the vascular compliance of the eye was tested under normal conditions and after administration of norepinephrine, which induced a vasoconstriction leading to reduction in vascular compliance.

Results.: In vitro comparison of direct versus indirect estimates of compliance showed a difference that was not significant (0.075 vs. 0.077 μL/mm Hg, P = 0.86). Results from the in vivo study indicated that norepinephrine significantly increased the arterial pulse pressure amplitude, while compliance of vascular network of the eye decreased from 0.18 ± 0.12 to 0.10 ± 0.08 μL/mm Hg (P = 0.001).

Conclusions.: The eye vascular compliance can be predicted using the IOP, arterial pressure, and OC of the eyeball.

Introduction

Age-related macular degeneration (AMD) is a leading cause of blindness in industrialized countries. ¹ However, the causes of this complex disease are not yet well understood. Genetics ² and other risk factors, such as smoking, hypertension or elevated cholesterol, ^3,4 have been identified to have a role in the development of such disease. Among other causes, vascular factors also have been hypothesized to contribute to the onset of AMD pathophysiology. ^5,6 Retinal imaging technologies, such as color Doppler imaging, ⁷ laser Doppler flowmetry, ⁸ and angiographic techniques, ⁹ have shown abnormalities in the choroidal circulation by revealing reduced flow velocities and increased resistance indices in the central retinal artery of AMD patients. Several studies have reported that changes in ocular blood flow or in ocular vessel diameter can affect highly the development of the disease. Results of these studies support the hypothesis of an increase in choroidal vascular resistance due to a decrease in the ocular compliance. ^5,10 From that perspective, other studies demonstrated that the pulsatile amplitude of the blood flow pulse in retinal arteries was higher in the presence of AMD. ^11,12 Patients with AMD would likely have a stiffer, less compliant arterial vasculature feeding the eye, as a result of age-related degenerative changes in collagen and elastin. ¹³ Furthermore, the elastin layer composing the Brunch's membrane at the level of the macula, and the walls of large arteries analyzed in patients suffering from AMD was found to be thinner and more porous than that in controls. ¹⁴ These observations would reinforce the relationship between AMD and the stiffening of systemic vessels. Consequently, it seems that there probably should be a relationship between some cardiovascular diseases affected by low arterial compliance and AMD. 

Therefore, it is of interest to develop methodologies for noninvasive or minimally invasive monitoring of the compliance of the eye vessels, as this may prove useful in diagnosing retinal diseases, such as AMD. The purpose of our study was to develop and test a new methodology to assess the compliance of the eye vessels based on physiological parameters and biomechanical properties of the eye, specifically the intraocular pressure (IOP), arterial pressure, and ocular rigidity of the eyeball. 

Materials and Methods

Mathematical Model

The model developed in our study is based on the pressure-volume relationship of the eye and the ocular arteries. Volume compliance is defined by C = ΔV/ΔP, where ΔV is the change in volume for a given change in pressure (ΔP). Equation (1), below, defines the compliance for the arterial network (subscript a) and the eye (subscript e), respectively. C_e , in particular, defines the compliance of the entire eyeball, (combination of sclera and cornea). 

 

 

 

During the heart cycle, pulsatile imbalances of blood into and out of the eye lead to changes in the volume of blood within the ocular space. Similarly, imbalances in aqueous production and aqueous outflow may create volume fluctuations, but in the short time scale of a single heartbeat, such imbalances in the production and outflow of aqueous humor are assumed to be negligible. Hence, the variation in ocular volume during the heartbeat is identical to blood volume variation, so that: 

 

 

 

These volume variations are related to changes in arterial and ocular pressure via their corresponding volume compliances:  

 

 

 

 

From equations (2) and (3) we obtain the following simple relationship between changes in volume of the heartbeat and the volume compliances of eye and ocular vascular bed: 

 

 

 

which permits the estimation of intraocular vascular bed compliance C_a based on estimated of eye compliance C_e and measurements of intraocular and arterial pressure variations. 

 

 

 

In Vitro Study

Six freshly enucleated eyes (post-mortem time less than 4 hours) from white New Zealand rabbits were obtained from a local farm. The eye was held on a brace, and the anterior chamber was cannulated with a 24 gauge catheter (Optiva W; Smiths Medical, Rossendale, UK) filled with a saline solution. The catheter was placed between the anterior plane of the iris and the inner surface of the cornea. This perfusion set-up was connected to an electronic pressure transducer (BLPR2; World Precision Instruments, Sarasota, FL) by a stopcock to measure the IOP corresponding to ΔP_e (equation 1). 

A 3 French Fogarty artery embolectomy catheter balloon (Fogarty; Edwards Lifesciences, Irvine, CA) was used to induce volume changes within the eye, mimicking the volume changes of the vascular network of the eye during a heartbeat. The catheter was inserted in the posterior chamber and connected to a microsyringe pump (SP210iw; World Precision Instruments) filled with a saline solution. The volume of the balloon was changed periodically and at a rate of 1–2 Hz, producing variations in intraocular volume in a range of 10 to 20 μL. These changes in volume correspond to ΔV_a in equation 1, and are accompanied by changes in pressure (ΔP_a , equation 1) in a range of 150 to 350 mm Hg. 

The perfusion set-up was connected to a data acquisition card (DAQPad-6015; National Instruments, Austin, TX) that collected and displayed the signals using a custom made LabView interface (National Instruments). The IOP and balloon pressure were measured in this experiment, whereas the compliance of the eyeball (C_e , equation 1) was determined in a companion experiment as described below. The compliance of the balloon (representing the compliance of the vascular network of the eye, C_a , equation 1) was estimated experimentally based on relation (equation 5) using data of IOP, balloon pressure and compliance of the eyeball (this method was defined as the indirectly measured compliance). The indirectly measured balloon compliance was compared to balloon compliance estimated directly from pressure-volume obtained from the differential volume injected in the balloon and the corresponding change in intra-balloon pressure (equation 1, Fig. 1). 

Figure 1.

 

Estimation of the compliance of the Fogarty balloon. In the direct method, the volume of the balloon was changed periodically (ΔV_a ) and the resulting pressure (ΔP_a ) was measured with a pressure transducer. In the indirect method, changes of ΔV_a produced variations in intraocular volume (ΔV_e ) resulting in changes in intraocular pressure (ΔP_e ). The compliance of the eyeball (C_e ) was determined with a companion experiment involving the measurement of the outflow facility.

Eyeball Compliance

The eyeball compliance was calculated from outflow facility using the method described by Pallikaris et al. ¹⁵ In brief, the IOP was increased artificially and recorded from 10 to 25 mm Hg using a micropump at a rate of 100 μL/minute. The net volume into the eye was estimated by subtracting outflow from inflow, the outflow being estimated from the outflow facility, as explained in the following paragraph. The eye compliance then was determined as the ratio of the net volume of the eye and the increase in IOP. For the calculation of the balloon compliance, individual-specific eyeball compliance was used. 

The outflow facility is used to determine the eyeball compliance in the in vitro and in vivo experiments. Details of outflow facility measurement have been reported previously. ^16,17 Briefly, the anterior chamber was perfused at first with a defined flow rate (2 μL/minute). After a stable IOP level was reached, the flow rate was changed to a higher value until another stable IOP level was reached. The value of the change in flow rate divided by the IOP change measured represents the outflow facility (OF). The outflow facility, thus, is calculated using the Goldman equation 

 

 

 

where Q ₁ and Q ₂ are successive inflow rates (μL/minute), and ΔIOP = (P ₂-P ₁), where P ₁ and P ₂ represent IOP at Q ₁ and Q ₂, respectively (mm Hg). 

In Vivo Study

Five white New Zealand rabbits (3.5–4.5 kg) were used for this study. General anesthesia was performed using a mixture of a 3 mg/kg (body mass) Xylazine and a 35 mg/kg ketamine intramuscular injection. Under general anesthesia, the central ear artery was cannulated using a 24 gauge catheter (Smiths Medical), and a 1 French gauge diameter intra-arterial pressure guide (ComboWire; Volcano, San Diego, CA) was inserted through the 24 gauge catheter. Systolic, diastolic, and blood pressures were measured using the intra-arterial pressure guide at a rate of 100 Hz, and the arterial pulse pressure amplitude was measured taking the diastolic-systolic pressure difference. The pressure sensor was located at about 10 cm from the heart. 

Using the same type of Optiva W catheter, the anterior chamber of the eye was cannulated to measure the IOP after the lids were kept open using a wired lid speculum. The catheter was connected to a pressure sensor (World Precision Instruments). Intraocular pressure was kept in the range of 10–25 mm Hg to be close to physiological pressure values. Mean arterial pressure and IOP amplitude were acquired to establish baseline conditions. Then, norepinephrine (10 μg/bolus) was administrated intra-arterially, and the mean arterial pressure and IOP amplitude were acquired. The eyeball compliance was determined for each eye before and after norepinephrine injection. The compliance of the vascular network of the eye was calculated using the IOP amplitude, pulse pressure amplitude, and eyeball compliance before and after norepinephrine injection. After acquiring data on one eye, the second eye was cannulated the same way and the same experimental procedure was followed. At the end of the experimentation the animal was sacrificed with a 120 mg/kg pentobarbital intra-arterial injection. All experiments conformed to the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research, and were reviewed and approved by the institutional committee for animal studies in Lausanne, Switzerland. 

Statistics

The results were expressed as the mean and SD. The paired Student's t-test was used to assess significant differences and effects of norepinephrine administration on the results. P < 0.05 was considered statistically significant. 

Results

In Vitro Study

The outflow facility was 0.35 ± 0.07 μL/mm Hg/minuteand the compliance of the eyeball was equal to 14.13 ± 4.03 μL/mm Hg (Table 1). 

Table 1.

 

Summary of the In Vitro Fogarty Balloon Compliance Measurements

Enucleated Eye #	Ocular Compliance of the Eyeball (μL/mm Hg)	Fogarty Balloon Compliance
		Indirect Method (equation 5, μL/mm Hg)	Direct Method (from pressure-volume curve, equation 1, μL/mm Hg)	Difference
1	18.1	0.062 ± 0.009	0.06 ± 0.005	3.3%
2	13.35	0.059 ± 0.011	0.058 ± 0.007	2%
3	20.06	0.096 ± 0.019	0.105 ± 0.015	−9%
4	11.12	0.088 ± 0.016	0.091 ± 0.009	−2.7%
5	12.05	0.086 ± 0.015	0.091 ± 0.009	−4.9%
6	10.11	0.06 ± 0.01	0.058 ± 0.005	3.7%
Mean ± SD	14.13 ± 4.03	0.075 ± 0.015	0.077 ± 0.02	4.2%

Variations in pressure of the Fogarty balloon, from 150 ± 10 to 350 ± 37 mm Hg, resulted in IOP variation from 0.6 ± 0.1 to 3.2 ± 0.4 mm Hg. 

Results of the estimation of compliance of the Fogarty balloon using direct and indirect methods are depicted in Table 1. Direct and indirect estimates of balloon compliance were 0.075 ± 0.017 and 0.077 ± 0.021 μL/mm Hg, respectively. The mean ratio between the directly and indirectly measured compliances was 0.99 ± 0.05, suggesting there is no significant difference between the two methods (P = 0.86, Fig. 2). 

Figure 2.

 

Compliance of the Fogarty balloon. Bland-Altman graph comparing the indirect and direct estimates of balloon compliance.

In Vivo Study

The mean outflow facility of the 10 rabbit eyes was equal to 0.209 ± 0.09 μL/mm Hg/minute. Norepinephrine increased the mean arterial pressure by 70%, an effect that was highly significant compared to the baseline (P < 0.001, Fig. 3A). As expected, this increase in mean arterial pressure was accompanied by a 60% increase (P < 0.001) in arterial pulse pressure amplitude (Fig. 3B). The mean ocular pulse pressure amplitude (IOP pulse) increased after norepinephrine administration from 1.21 ± 0.24 to 1.55 ± 0.2 mm Hg (P < 0.05, Fig. 3C). Finally, the arterial compliance significantly decreased after administration of norepinephrine from 0.18 ± 0.12 to 0.10 ± 0.08 μL/mm Hg (P < 0.05, Fig. 3D). 

Figure 3.

 

Effects of norepinephrine on the arterial pressure amplitude (A), mean arterial pressure (B), IOP pulse (C), arterial compliance (D), and ocular compliance (E). Data are presented as means and SD values. P values are calculated from paired t-tests comparing baseline data with data after administration of norepinephrine.

Eye compliance was significantly reduced after norepinephrine injection (P < 0.05), with compliance being equal to 4.07 ± 1.49 and 2.93 ± 1.48 μL/mm Hg before and after injection, respectively (Fig. 3E). 

Discussion

We developed a new method to predict the compliance of the vascular network of the eye. Based on the principle of continuity, and variations of IOP and arterial pressure over the cardiac cycle, we derived a simple relationship that gives the compliance of the vascular network of the eye, C_a , as the product of eyeball compliance, C_e , times the ratio of IOP variation over arterial pulse pressure (ΔP_e /ΔP_a ). The eyeball compliance was characterized in a parallel experiment following the outflow facility measurements. 

An in vitro approach, where a Fogarty catheter with a compliant balloon simulating the compliance of the ocular vessels was inserted in enucleated rabbit eyes, was used to validate the proposed model. The experiment showed that inflation of the Fogarty catheter induced an increase of the IOP. The results showed that the compliance of the Fogarty catheter balloon can be predicted using our formula (equation 5) quite precisely, with the average error being statistically insignificant and always less than ±5% (Table 1). 

After validating the model in vitro, we performed animal experiments to determine the compliance of the vascular system of the eye under control conditions and after administration of norepinephrine. Norepinephrine is a hormone that causes strong arterial vasoconstriction. ¹⁸ Consequently, the mean arterial pressure and arterial pressure amplitude have increased significantly, as expected. ¹⁹ According to our results, the arterial compliance has decreased significantly, meaning that elevation of the systemic blood pressure changed the effective elastic properties of the arterial system. These findings are plausible, as we expect that contraction of vascular smooth muscles (VSM) and increase in pressure would lead to decrease in vascular compliance. ²⁰  

Ocular compliance is a physical parameter of the eye that expresses the elastic properties of the eyeball upon inflation. ²¹ Based on observations by Langham et al., the coefficient of ocular compliance reflects the elastic properties of the sclera and the cornea in cadaveric eyes, where no blood circulation prevails. ²² In contrast, when measured in vivo on animal models, ocular rigidity seems to be affected by ocular blood volume. In our study, the coefficient of ocular compliance was higher in enucleated eyes (14.13 μL/mm Hg) compared to living eyes (4.07 μL/mm Hg). We postulate that the blood circulation and resulting vascular tone possibly could have contributed to the observed increase in the eye rigidity. It is worth mentioning that the ocular compliance, C_e , which is needed to calculate the intraocular vascular compliance, cannot be obtained noninvasively. Our in vivo measurements of the pressure-volume relationship of the rabbit eyeball were in accordance with the results presented by Kymionis et al., who evaluated the ocular rigidity of 16 rabbit eyes after photorefractive keratectomy. ²³ Dastiridou et al. studied the pressure-volume relationship in the living human eye, and found that the pulsatile change in IOP is related directly to the rigidity of the ocular layers that dampen the pulsations. ²⁴ The latter suggests that higher ocular pulse amplitude may be found in eyes with increased rigidity, due to either a higher rigidity coefficient or a higher IOP. In our study, administration of norepinephrine increased the coefficient of ocular rigidity, raising the ocular pulse pressure amplitude. This observation consolidates the statement made by Dastiridou et al. ²⁴  

Results from in vivo experiments have shown that norepinephrine significantly altered not only the compliance of the vascular network in the eye, C_a , but also the elastic properties of the eyeball, C_e . This possibly could suggest that decrease in compliance of ocular vessels leads to a more rigid and less compliant eyeball. Previous studies have shown that ocular and vascular compliance of the eye are affected by retinal disease. Friedman et al. suggested that ocular rigidity has a role in the development of AMD. ¹⁰ They stated that the coefficient of scleral rigidity of age-related macular degeneration patients was higher than that of controls, meaning that a more rigid sclera likely would alter compliance of vessels embedded in a less compliant surrounding. Later, Pallikaris et al. also measured the ocular rigidity in patients suffering from AMD, distinguishing between the different types of AMD. ²⁵ Their results draw conclusions comparable to Friedman et al., as they showed that the eye rigidity data were significantly higher in presence of neovascular AMD in comparison with the non-neovascular form and the group of control patients. Sato et al. stated that patients with AMD have a less compliant arterial network in the eye. ^11,12 They showed that the pulse wave velocity and pressure associated with the central aortic blood pressure waveform were higher in patients with AMD compared to controls, ¹² implying that an increase in vascular rigidity would lead to a stiffer scleral wall. All these findings suggest that AMD may be associated with increased vascular and eye rigidity. As stated before, Friedman et al. ¹⁰ and Pallikaris et al. ²⁵ suggested that an increasingly rigid sclera would affect the arterial compliance, encapsulating the ocular vasculature in a less compliant compartment. However, in our study, we demonstrated that a deliberate increase in the systemic arterial rigidity resulted in a corresponding elevation of the eye rigidity (Fig. 3E). Consequently, we could suggest that a stiffer ocular arterial network could result in stiffer eyeballs. We further may add that the parameter C_a (arterial compliance) should be considered as a component of the overall eyeball compliance C_e . That is, C_a reflects not only the compliance of the vessel branches within the posterior chamber, but also incorporates the choroidal vasculature and intra-scleral vasculature. Hence, modifying the stiffness of this extended vasculature would impact necessarily overall eyeball stiffness, as they are inter-related. When considering previous studies on AMD and eyeball rigidity, a question remains unresolved: are the AMD-related hemodynamic abnormalities the result of an increase in the scleral rigidity, or would elevation of the systemic vascular stiffness lead to further scleral rigidity? Further studies are needed to clarify this question. 

In conclusion, we proposed a method to estimate the compliance of the ocular vascular network, based on measurements of eyeball compliance, IOP, and arterial pressure. The stiffness of the arterial network in the eye may be an important factor in the initiation and development of retinal disease. Age-related macular degeneration is a good example of how abnormalities in elastic properties of the choroidal blood vessels can alter the structure of the retina and, ultimately, the sight. The method to estimate compliance of the ocular vascular network may be of interest not only to researchers and clinicians focusing on AMD, but also to a broader audience working on ophthalmic diseases affecting or affected by the properties of the eyeball vascular network. Further studies should include human subjects to assess the link between changes in ocular vascular network compliance to retinal disease, such as AMD. 

Acknowledgments

The staff from Hôpitaux Universitaires de Genève (HUG) and Reda Hasballa contributed to this study. 

Footnotes

 Presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, May 2011.

Footnotes

 Disclosure: A. Villamarin, None; S. Roy, None; N. Stergiopulos, None