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Laboratory science

Mechanical model of human eye compliance for volumetric occlusion break surge measurements

Dyk, David W. BS; Miller, Kevin M. MD*

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Journal of Cataract & Refractive Surgery: February 2018 - Volume 44 - Issue 2 - p 231-236
doi: 10.1016/j.jcrs.2017.10.052
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Anterior chamber stability is an essential requirement for surgical safety during phacoemulsification. It is achieved by maintaining a nearly constant anterior chamber volume throughout the various stages of the procedure. Irrigating fluid is added to the anterior chamber only as needed to replace the volume of fluid and disassembled lens fragments that are removed from the eye. Any fluid surging from an eye after an occlusion break can compromise the stability of the anterior chamber and lead to complications such as posterior capsule rupture, vitreous loss, dropped lens fragments, endophthalmitis, and cystoid macular edema.1,2

An occlusion event initiates when fluid flow through the tip of a phacoemulsification probe is obstructed by lens fragments, iris tissue, or an ophthalmic viscosurgical device. As a phacoemulsification pump evacuates fluid from the aspiration line, negative pressure or vacuum builds relative to atmospheric pressure and stores potential energy in the walls of the aspiration tubing and cassette as a function of their compliance; entrapped air also expands in response.3,4 An occlusion break surge event follows when this obstructing material abruptly clears the tip. The aspiration line and cassette suddenly expand, the entrapped air collapses, and fluid is pulled from the anterior chamber faster than the irrigation supply can replenish it. On occasion, the volume of an occlusion break surge might be sufficient to collapse the anterior chamber and risk structural damage to the eye.5 Accurate measurements of the surge volume for a given eye can, therefore, predict the expected chamber stability after an occlusion break for any given system and its corresponding settings.

Factors that affect surge volume include surgical system characteristics, surgeon-controlled machine settings, and eye compliance. Compliance is the change in volume associated with a corresponding change in pressure (Δ volume/Δ pressure). Its inverse is stiffness. Eye compliance is nonlinear, a factor that has to be taken into consideration when addressing occlusion break surge characteristics. Previous tests of surge volume were limited by the lack of a human eye compliance model, difficulty and complexity of setup, and limited reproducibility of results.1

Eye compliance was first measured by Friedenwald.6 He described a volume–pressure relationship for the eye and proposed a constant ocular rigidity coefficient to characterize this nonlinear relationship. Other authors have since suggested alternatives to this proposed relationship.7

The purpose of this study was to develop a mechanical model of human eye compliance that can be used for volumetric studies of the occlusion break surge response of different phacoemulsification systems. This study shows experimental data to support a new independently derived mathematical human eye compliance model that forms the basis of a new mechanical eye model. The mechanical model enables direct surge-volume measurements after simulated occlusion breaks and standardizes surgical system comparisons. Unlike models that rely on donor eyes, which might require repeated freezing and thawing and be subject to retesting fatigue, a mechanical model provides consistent results for repeated measurements and can be used for testing over time as systems are improved. In addition, a mechanical model of human eye compliance provides the ability to clarify the impact of surgical settings on surge characteristics.

Materials and methods

This study was performed in a laboratory setting using human cadaver eyes. No living patients or animals were involved.

Human Eye Compliance Model

Human donor eyes with intact lenses were used to obtain compliance data. Intraocular pressure (IOP) was varied from 5 mm Hg to as high as 100 mm Hg. The setup (Figure 1) included a calibrated pressure controller (model CPC6000, Mensor) connected to the top of a 1 mL glass pipette with a 0.0016-inch ruby orifice at its junction for flow-rate control (model RB-82675-0016, Bird Precision). The glass pipette outlet was connected to a short piece of polyvinyl chloride tubing terminating at a flow sensor (model ME4PXN212, Transonic Systems, Inc.) that measured changes in volume; the flow sensor outlet was connected to a 25-gauge syringe needle. The pipette inlet, pipette outlet, and flow sensor all had intermediate stopcocks to facilitate priming of the syringe needle, flow sensor, and tubing. The pipette was primed to the height equivalent of eye level, and 2 pressure transducers (model XCL-072 transducer, Kulite Semiconductor Products, Inc.; model 1169-01-50-100 H programmable amplifier, Raetech Corp.) were mounted to either end of the pipette for verification of net-volume measurement from the flow sensor. The syringe needle of the primed system was inserted through a human donor eye’s corneal limbus and into the anterior chamber while the eye rested unconstrained on a Styrofoam base. A second syringe needle with a connected pressure transducer was primed and inserted through the limbus and into the anterior chamber opposite the first needle (Figure 2).

Figure 1
Figure 1:
Eye compliance test setup diagram of the equipment and connections required to perform the compliance tests on human donor eyes.
Figure 2
Figure 2:
Syringe needle insertion into human donor eye. One syringe was connected to a flow sensor and provided the flow path for fluid inflow and outflow. The second syringe facilitated IOP measurement with an external pressure transducer.

Eye pressure was initially maintained at 5 mm Hg with the pressure controller while the fluid height in the pipette remained at eye level. Fluid flow into the eye was initiated by setting the controlled air pressure to 60 to 100 mm Hg while a digital oscilloscope (Waverunner 606Zi, Lecroy Corp.) captured changes in IOP and flow rate from the pressure transducer and flow sensor, respectively. After the eye pressure and fluid flow reached equilibrium at approximately 30 seconds, the controlled air pressure was set to 5 mm Hg. No fluid leakage from the syringe needle insertion sites was observed during testing.

Twenty-one phakic eyes from 12 donors ranging in age from 51 to 94 years (mean age 71 years) were tested on the same day they were received. Wetting drops were added between cycles to ensure proper eye hydration. Pressurization–depressurization test cycles were repeated up to 12 times per human donor eye. Data from 6 of the 21 eyes were rejected. Data were rejected from 4 eyes because air bubbles in the syringe needle at the limbus, which communicated IOP to the pressure transducer, impaired IOP measurements. Data were rejected from 1 eye because it was damaged during needle insertion. Data from another eye were mistakenly rejected along with the data from its paired eye (originally rejected because of an air bubble affecting measurement) and erroneously excluded from the final overall average. Data from the remaining 15 eyes were used for the final average eye curve-fit measurement.

For the mechanical model, a fluid chamber was created that was sealed with a thin polyethylene membrane that transmitted pressure to a piston surface (Figure 3). A confocal laser displacement sensor (model LT-9030M, Keyence Corp.) was used to measure piston displacement. The digital oscilloscope converted output voltage to volume (cm3) using the known laser sensitivity value and known piston diameter. A spring fixture with 3 springs, which could be used to stiffen piston displacement at variable pressures, was incorporated into a test bed (Figure 4). A phacoemulsification handpiece was mounted within an acrylic block. The acrylic block formed a sealed cylindrical fluid chamber with the block’s inner diameter sealing the handpiece sleeve’s compressed outer diameter. In addition, the acrylic block held a lever with a sealed ball joint to form an occlusion on a phaco tip’s distal end. A piece of soft natural rubber tubing fixed to the lever’s end could rotate against the cutting surface of the phaco tip to establish full occlusion (Figure 5). The acrylic block had a connection to the spring fixture through stiff polyurethane tubing, and the handpiece was made to rest slightly above the spring fixture’s fluid chamber to provide the head pressure necessary to offset the piston and spring mass.

Figure 3
Figure 3:
Cross-section of the compliance spring fixture with staged engagement. At low pressures, spring 1 resists chamber volume change due to increased IOP. At mid-range pressures, springs 1 and 2 resist volume changes. At elevated pressures, springs 1, 2, and 3 resist volume changes. The gaps between the top stop (blue) and springs 2 and 3 determine the pressures at which the springs become engaged.
Figure 4
Figure 4:
A spring fixture is mounted within the occlusion break test bed. The fixture is connected to the rigid fluid block via rigid tubing. The fixture’s volume is displaced as a result of IOP changes during the simulated occlusion.
Figure 5
Figure 5:
Mechanical model of the occlusion. Rubber tubing establishes occlusion at the phaco needle tip. The occlusion break event occurs when the lever, actuated through an electronically controlled pneumatic cylinder, releases the blockage formed from the rubber tubing.


Human Eye Compliance Model

Figure 6 shows the human eye compliance curves from the 15 of 10 donors. Pressurization and depressurization cycles were analyzed separately. To model human eye volume (V) changes due to IOP, the curve V = C1 × exp(C2 × IOP) + C3 × exp(C4 × IOP) − V0, was fit to individual pressure cycles, where C1, C2, C3, and C4 were coefficients, and V0 was chosen such that V = 0 at 7 mm Hg for each individual cycle. This 2-term exponential fit was chosen as a practical approximation of the following 2 regions observed in the test data: a highly compliant region at low IOP and a rigid nonlinear region at high IOP. Note that V0 was chosen for convenience; the final output result was independent of this value because V0 was updated in the final curve to correspond to 0 mm Hg. Any volume change detected by the flow sensor while the eye pressure remained constant was excluded from the curve-fit because the small volume changes without corresponding IOP changes were attributed to fluid leakage. The curve-fit results were averaged to produce an overall individual eye’s pressurization and depressurization curves. The individual eyes’ resulting volume versus pressure data were averaged using datapoints extrapolated from these curves. The final mean pressurization and depressurization curves were generated for each individual eye; the final overall depressurization curve was generated from the mean of each eye’s averaged results.

Figure 6
Figure 6:
Individual compliance curves for depressurization in human donor eyes were derived from the individual curve fittings based on the equation V = C1 × exp(C2 × IOP) + C3 × exp(C4 × IOP) − V0. All curves were referenced to volume at 7 mm Hg as a baseline for display; however, the final overall curve was independent of the chosen reference pressure. The final overall depressurization (overall mean of each eye’s individual averaged depressurization curves) is represented by the heavy line (IOP = intraocular pressure; V = volume).

The depressurization curve was selected for its similarity to an occlusion break event. The equation V = C1 × exp(C2 × IOP) + C3 × exp(C4 × IOP) − V0 was fitted to the final depressurization curve, where C1 = −0.07141, C2 = −0.23055, C3 = −0.14972, C4 = −0.02006, and V0 was chosen so that V = 0 cc at 110 mm Hg (Figure 6). The mechanical eye compliance model was subsequently developed using this equation.

Mechanical Eye Compliance Model

A fluid chamber with a displaceable piston was selected to model the depressurization compliance curve. Three springs were carefully selected to stiffen piston displacement in the fluid chamber to simulate the curve. At low fluid chamber pressures (0 to 11 mm Hg), the first spring resisted piston displacement by itself. At intermediate pressures (11 to 53 mm Hg), the second spring engaged and further stiffened piston displacement. At high pressures (>53 mm Hg), the third spring engaged and all 3 springs resisted volume changes. The resulting compliance curve from the spring fixture mechanical model mimicked the depressurization curve derived from the human donor eye model reasonably well (Figure 7, A).

Figure 7
Figure 7:
A: Comparison of the spring fixture mechanical model with the human donor eye model. Compliance curve derived from the mechanical model and the final overall depressurization curve derived from the human donor eyes are shown. Both curves were referenced to volume at 0 mm Hg for convenience. B: Mechanical model of the occlusion. Changes in volume are shown as a function of time.

To simulate an occlusion break, the occluding lever’s movements were controlled through a timer relay, 2 solenoid valves, and a pneumatic cylinder. The timer relay engaged the 2 solenoid valves for a controlled duration of 3.5 seconds. These, in turn, supplied a regulated 3.5 psig air pressure to the pneumatic cylinder, which then applied an actuating force to the lever for occlusion. Occlusion formation and occlusion break speed were controlled through adjustable needle valves at the pneumatic cylinder’s air inlet and outlet (Figure 7, B).

Last, the pressurization and depressurization curves derived from the eye model were compared with the published compliance curve from living human eyes using a common reference volume of 5 mm Hg. The human eye compliance model characteristically agreed with data in a previous report that used living human eyes (Figure 8). With increasing pressure, the model curves derived from enucleated eyes showed slightly greater volume than previously published curves from living human eyes.

Figure 8
Figure 8:
Derived compliance curves for pressurization and depressurization in human donor eyes compared with pressure-volume relationship in living human eyes.9 All curves were referenced to volume at 5 mm Hg as a baseline to match reference pressure used by Silver and Geyer.9 In living human eyes, the average eye’s dimensions were used to identify average coefficients.


We present a new mechanical eye model that enables direct volumetric surge measurements after simulated occlusion breaks. It differs from the current method of characterizing postocclusion break surge as a pressure transient, which is not clinically relevant. The mechanical model was developed from compliance data derived from human cadaver eye testing. The compliance model simulates the known nonlinear relationship between human eye volume and IOP, which fits a 2-term exponential function.

In the current study, pressurization and depressurization curves were obtained from human cadaver donor eyes. Although Friedenwald’s data for ocular rigidity were also derived from enucleated eyes,6 he found a linear relationship between the 2 variables (volume and pressure). Differences in ocular rigidity were reported between live eyes and enucleated donor eyes in 1 study.8 However, model compliance curves derived from the enucleated human eyes were similar to compliance curves generated from living human eyes in another study9 (Figure 8).

The mechanical model implements a 2-term exponential mathematic relationship between volume and pressure for use in phacoemulsification system occlusion break testing. Advantages of this mechanical model include simple setup, repeatable testing, and relevant volumetric surge measurements.

It is possible to calculate a percentage change in aqueous volume after an occlusion break in the phakic or aphakic state if the magnitude of the transient volume change within a compliant eye model can be measured and the volume of aqueous humor in these states can be determined. Information about the percentage change in aqueous volume is clinically relevant; for example, a 100% loss of aqueous volume indicates complete collapse of the anterior chamber. Although it is easier to measure, the corresponding change in aqueous or anterior chamber pressure is not nearly as relevant to cataract surgeons. Hence, laboratory comparisons of the surge response of phacoemulsifiers from different companies are difficult to translate into clinical practice when the measured variable is a pressure transient.10

Other mechanical models for use in occlusion break measurements have been designed, including a collapsible anterior chamber model that provided a volumetric model of compliance.1,11 The collapsible anterior chamber model was compared with a single enucleated pig eye and found to be equivalent. The mechanical model described in this report was designed with a priori knowledge of average eye compliance and used staged springs to achieve a high-fidelity mechanical equivalent. The earlier anterior chamber model only mimicked a near infinite compliance region (<5 cm water) and a stiff region (>5 cm water).1

Our mechanical eye model is limited in its ability to detect large surge volumes that require large displacements of the piston. The piston will not displace beyond its resting point at atmospheric pressure. The volume available to measure the surge depends on the IOP before the occlusion break; specifically, a large initial IOP would push the piston into a large initial displacement. In the normal fixture design, a 55 mm Hg initial IOP provides enough piston displacement to measure a surge up to approximately 0.17 cc.

In addition, the piston does not provide response to small fluctuations in pressure (approximately <5 mm Hg). Spring and piston inertia and friction at the piston’s outside surface restrict the piston’s response to these small-force fluctuations. The fluid chamber’s sealing membrane also requires careful attention. If the membrane is secured with internal tension, the film tension will compound with spring forces to resist pressure changes, flattening the volume response curve. The mechanical model’s spring design could be improved to further imitate the experimentally derived compliance curve. Modifications to the fixture pistons could also decrease friction, which currently leads to hysteresis when changing from pressurization to depressurization. This would improve the piston’s displacement response to smaller IOP changes. Finally, the relevance of the mechanical eye model could be extended by correlating the measured volume surge with clinically meaningful values, such as posterior capsule movement.

Large myopic eyes are generally more compliant than small hyperopic eyes. To reflect the range of compliance encountered in different clinical settings, it might be possible to build other model eyes to simulate these variations. Also, to better fit the current mechanical model to the cadaver compliance data as it is depressurized from 10 to 0 mm Hg, an additional spring could be fit to the model, increasing the number of springs from 3 to 4.

Application of the mechanical model described in this report is not limited to occlusion break testing; it could also address other ocular volumetric changes. Advances in phacoemulsification technologies have led to a variety of systems with different properties, including percentage power, machine-indicated flow, and vacuum regulation.12 The mechanical eye model provides a standardized and reproducible test fixture for intra-phacoemulsification machine comparisons with each advancement. In addition, a significant correlation between ocular rigidity and patient age was previously reported.13 The mechanical eye model could be used to address compliance correlations with patient characteristics such as age and medical history.

The spring fixture-based mechanical eye model described in this report provides a simple, repeatable, and reproducible method for measuring volume changes, such as occlusion break surge. It has the potential to generate consistent results in studies addressing improvements in ocular surgery.

What Was Known

  • Occlusion break surge events can cause a sudden drop in anterior chamber volume.
  • Surge magnitude depends on system characteristics, operating settings, and the compliance of the eye being tested.

What This Paper Adds

  • Quantitative analysis of mean human eye compliance enables the creation of a mechanical spring eye test model.
  • This mechanical compliance eye model allows for measurement of the occlusion break surge response in volumetric terms.
  • The ability to study volumetric occlusion break surge events in a controlled manner allows for comparison of system characteristics across different phacoemulsification platforms.


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Mr. Dyk is an Alcon employee. Dr. Miller is an investigator for and consultant to Alcon Laboratories, Inc.

© 2018 by Lippincott Williams & Wilkins, Inc.