Original research••

Simulation of fluid dynamics and turbulence during phacoemulsification using the new propeller turbo tip

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Abstract

Purpose To investigate the fluid dynamics and turbulence in the anterior chamber during phacoemulsification with a new propeller turbo tip using computational fluid dynamics methods.

Methods A theoretical study, three-dimensional model with the corresponding mathematical equations for the propeller turbo phaco tip, anterior chamber and lens capsular bag was developed. A simulation was performed for the new propeller turbo tip with various parameter settings (vacuum, irrigation bottle height and phaco power). Fluid dynamics and turbulence in the anterior chamber, lens capsular bag and phaco tip were evaluated. The linear relationship between the different setting parameters and a stable anterior chamber pressure was assessed.

Results The fluid dynamic turbulence was mainly symmetrically distributed in the anterior chamber. Propeller turbo phaco tip vibration caused increased fluid velocity and asymmetrical fluid turbulence in the metal lumen but had little influence on dynamic intraocular pressure. Reasonable phaco machine parameter settings can maintain a stable intraocular pressure during phacoemulsification.

Conclusions Evaluation of phacoemulsification fluid dynamics using computational simulation methods could provide detailed information about the influence of the propeller on dynamic intraocular pressure during phacoemulsification, which is useful for a better understanding of this procedure.

What is already known on this topic

Using a computational simulation model, the bimanual and coaxial irrigation/aspiration procedures were shown to cause different levels of flow turbulence in the corneal endothelium.

What this study adds

Computational flow dynamics simulations could improve our understanding of fluid mechanisms during phacoemulsification.
Phacoemulsification with turbo phaco-tip coaxial vibration could cause various degrees of flow turbulence.
Proper vacuum and irrigation fluid settings could provide a stable intraocular pressure for the Venturi pump.

How this study might affect research, practice or policy

A better understanding of the working mechanism and fluid dynamics with different phaco tip designs can help optimise surgical machine parameters setting, improve surgical safety and improve patients’ postoperative visual quality.

Introduction

Phacoemulsification cataract surgery, a new surgical technique, has gained popularity since it was first described by Kelman.1 Because of the fixed direction of the side holes on the installed irrigation sleeve and the different types of tip vibration, surgical steps related to phacoemulsification and irrigation/aspiration (I/A) can cause fluid dynamic turbulence in the anterior chamber and capsular bag.2–6 Therefore, inner ocular structures such as the corneal endothelium, iris, suspensory ligaments and capsulorhexis margin can be influenced or damaged by unstable fluid dynamics during phacoemulsification and I/A.7 8

In comparison with I/A, phacoemulsification fluid dynamics are much more complex and show the combined effects of irrigation, vacuum, flow rate and phaco tip vibration during the surgical procedure. Previous studies have evaluated the fluid velocity or dynamics changes (known as acoustic streaming) of torsional and longitudinal phacoemulsification, or provided visual comparison of ultrasonic tip vibrations by different ultrasound modes using high-resolution digital ultrasound imaging systems and high-speed video systems.4 5 9 In addition, researchers have been trying to use different phaco tip designs to improve phaco efficiency and safety.10 11 In 2018, Dr Tadahiko Kozawa introduced a new propeller turbo phaco tip, in which a vertical plate (named the propeller) is embedded into the tip lumen to minimise unwanted damage to the ocular tissue (https://www.aao.org/clinical-video/new-propeller-turbo-tip-torsional-phacoemulsificat). Although some online videos have demonstrated the ability of this system to handle the lens nucleus using a high-speed video system (https://vjcrgs.com/volume34-issue2/new-propeller-turbo-tip-for-torsional-pea), no previous study has tested its actual fluid dynamics during phacoemulsification using a computational simulation model.

Previous studies have demonstrated the details of fluid dynamics differences during I/A using coaxial and bimanual handpieces.12 13 With the rapid advancements in computational fluid dynamics methods and algorithms, the simulation model could be a vital tool for demonstrating fluid flows in complex conditions.14

This study aimed to use a computational fluid dynamics (CFD) simulation model to investigate and analyse the fluid dynamics in the anterior chamber during phacoemulsification with the new propeller turbo phaco tip. Detailed information about the flow velocity distribution, intraocular pressure (IOP) changing tendency, turbulence intensity and anterior chamber stability was assessed using various parameter settings. In addition, the relationship between machine parameter settings (vacuum and irrigation bottle height) and anterior chamber stability was also studied.

Methods

Dimensions and schematics of model data

The new propeller turbo phaco tip, irrigation sleeve and ocular anterior segment were included in the numerical simulation model. No propeller phaco tip was used in the traditional comparison model. The dimensions and schematics of the model data were designed to be similar to the anterior segment of the human eye: corneal diameter, 12 mm; radius of the corneal curvature, 7.7 mm; distance between the anterior cornea surface and posterior lens capsule, 7.0 mm; anterior lens capsule opening, 6.0 mm; and lens diameter, 9.0 mm (figure 1). The inner diameter of the 30° bevel-up phaco tip was 1.0 mm and the central propeller thickness was 0.05 mm, while the inner diameter of the irrigation sleeve was 2.75 mm and the two-side orifice diameter for irrigation fluid was 1.0 mm (figure 1).

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Figure 1

The human eye dimensions and schematics in the model (A) and the corresponding simulation model (B).

Computational fluid dynamics

CFD was used to obtain flow field and static pressure data of the eye under different inlet and outlet pressures and sensor movement conditions. Moreover, since the CFD method based on the Arbitrary Lagrangian Eulerian Reynolds-averaged Navier-Stokes (ALE-RANS) equations can analyse complex unsteady flows very accurately, this method was used in this study.

The FLUENT software package (V.6.3; Fluent, Lebanon, New Hampshire, USA) includes pressure-based and density-based solvers according to the ALE-RANS equations. In general, a pressure-based solver is suitable for low-speed incompressible flows, whereas the density-based approach is primarily used for high-speed compressible flows. Considering the low-flow speed during phacoemulsification, we used a pressure-based solver with a coupled-implicit formulation in FLUENT.

For the ALE-RANS formulation, turbulence models are required to determine additional unknown variables. FLUENT provides the following turbulence models: the Spalart-Allmaras (SA) one-equation model, inline graphic two-equation model, two-equation model, Reynolds stress model and large eddy simulationmodel. The SA one-equation model13 can obtain relatively accurate results with less time and higher robustness. This turbulence model has been successfully used in commercial applications.15 Therefore, the SA turbulence model was used in this study. The three-dimensional (3D) fine-mesh flow field and boundary conditions of the simulation model are shown in figure 2.

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Figure 2

The boundary condition and three-dimensional fine-mesh flow field for phacoemulsification.

Data setting for propeller and no-propeller comparisons

In this study, we used a Venturi fluid pump as the phaco machine model. Irrigation fluid (cmH₂O) and vacuum (mm Hg) were the two main setting factors during phacoemulsification. The setting ranges for irrigation fluid and vacuum were 20–140 cmH₂O and 100–600 mm Hg, respectively. The interconversion formula of pressure units was as follows: 1 mm Hg=133 Pa, 1 cmH₂O=ρgh=97.804 Pa.

For dynamic IOP investigation in a cycle, the following computational conditions were used: continuous ultrasound model, inlet pressure=irrigation bottle height=110 cmH₂O=10 758.44 Pa, outlet vacuum=300 mm Hg=−39900 Pa, frequency of vibration=28.5 kHz, vibration period=3.50877E-05 s, 200 time steps for each cycle, corresponding calculation time=1.75439E-07 s, number of 3D fine meshes=3219105, and amplitude of oscillation for the coaxial vibration=10° for each side.

Statistical analyses

Statistical analyses were performed using commercial software (SPSS V.22.0; IBM). A paired-sample t-test was performed to compare quantitative data between the propeller and no-propeller groups. A linear regression model was used to determine the relationships between the irrigation fluid, vacuum and IOP. All tests were performed with a significance level of 5%.

Results

Propeller and no-propeller flow patterns during vibration

The intraocular flow pattern during phacoemulsification is shown in figure 3. A ‘butterfly’ vortex morphology can be clearly seen from the top view (figure 3A). The pathway of irrigation fluid was mainly separated into two parts: (1) the symmetrical red pathway in figure 3A, in which the flow was perpendicular to the irrigation sleeve orifice, changed direction and moved along the posterior corneal surface after contacting the corneal endothelium, and showed symmetrical merged fluid aspiration into the phaco tip; and (2) the symmetrical yellow pathway in figure 3A, in which the fluid was above the phaco tip and irrigation sleeve after contacting the corneal endothelium and could change direction and form relatively small eddies.

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Figure 3

The fluid streamline map on the 2/4 time point of the vibration cycle during phacoemulsification. (A) Clear demonstration of the ‘butterfly’ morphology from the top view; and (B,C) the intraocular stereo fluid streamlines in the no-propeller and propeller groups, respectively. The green plane is the X–Z cross-sectional plane.

In addition, figure 3B,C show the intraocular fluid turbulence of the propeller and the no-propeller flows during phacoemulsification from a stereoscopic perspective. In comparison with the no-propeller group, the regular oscillation of the propeller phaco tip caused more irregular fluid turbulence, and some vortices demonstrated the opposite direction (red asterisk in figure 3B, black asterisks in figure 3C).

Inner fluid velocity of the phaco tip lumen in a cycle

Figure 4 demonstrates that the propeller and no-propeller conditions could influence the inner lumen fluid velocity at different cycle time steps. Owing to the coaxial propeller vibration, the inner lumen velocity exhibited asymmetrical changes, including different directional velocities around the propeller, when the propeller was considered as the boundary. The 0/4 and 4/4 time steps demonstrated similar changing tendencies and types, showing an opposite trend from that in the 2/4 time step (left side of figure 4B, D and F). The 1/4 and 3/4 time step velocities demonstrate a symmetrical model (left side of figure 4C and E). In contrast, the non-propeller group demonstrated similar, but not equal, velocity changes in the lumen during phacoemulsification in one cycle (right side in figure 4B–F).

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Figure 4

The phaco tip vibration period and corresponding velocity on the X–Z plane on each time point of the whole cycle. (A) The whole vibration cycle and the observed velocity cross-sectional position. (B) The 0/4 time point of a cycle; (C) 1/4 time point of a cycle; (D) 2/4 time point of a cycle; (E) 3/4 time point of a cycle; (F) 4/4 time point of a cycle. The yellow dotted square was magnified five times to show the detailed inner lumen fluid velocity information in (B–F).

Dynamic IOP

Online supplemental figure 1 shows the dynamic pressure on the posterior lens capsule and cornea in each group during phacoemulsification. Two similar symmetrical high-pressure locations (online supplemental figure 1A: 1, 2) accompanied by two obvious low-pressure locations (online supplemental figure 1A: 3, 4) on the posterior lens capsule and one notably different location (online supplemental figure 1A: 5) on the cornea were observed. Table 1 demonstrates that the dynamic pressure at location 1 in the propeller group was approximately 133 Pa (1 mm Hg) lower than that of the no-propeller group, and approximately 6 Pa (0.05 mm Hg) higher at location 4. No significant differences were observed in the other three locations between the two groups.

Table 1

Dynamic intraocular pressure in each group for a cycle

Balanced IOP during phacoemulsification

The phaco tip vibration caused less than 1 mm Hg (56–130 Pa) fluctuations in the dynamic IOP in a cycle. We used a static condition (without vibration) to determine the linear relationships among the IOP, irrigation bottle height and vacuum. Online supplemental figure 2 shows the correlations among the above-mentioned factors and provides the corresponding fitting equation for IOP (non-propeller group: IOP (mm Hg)=1.152+0.6712×(inlet cmH₂O)−0.08394×(outlet mm Hg); propeller group: IOP (mm Hg)=1.084+0.6756×(inlet cmH₂O)−0.08026×(outlet mm Hg)). We also found that when the range setting for the inlet was 20–140 cmH₂O and the vacuum range was 100–600 mm Hg, the average IOP fluctuation difference between the propeller and non-propeller groups was approximately 122–213 Pa (0.92–1.60 mm Hg).

Phaco tip clogged percentage and IOP

To test the relationship between the phaco tip clogged percentage and IOP in the propeller group, we set the irrigation bottle height to 110 cm and vacuum to 300 mm Hg. Online supplemental figure 3 demonstrates that as the phaco tip clogged area increased, the IOP increased linearly. Moreover, the propeller itself has little effect on IOP fluctuations.

Discussion

Some of the significant findings observed in this study were as follows: (1) ‘butterfly’ symmetry and some irregular vortexes exist during phacoemulsification; (2) the propeller has minimal influence on the phaco tip lumen velocity and intraocular dynamic pressure; and (3) the target-specific stable IOP could be achieved by reasonable regulation of the machine setting parameters.

Without phaco tip vibration, the working scenarios of the phaco handpiece (irrigation and vacuum functions) were similar to those of the coaxial I/A system, except for a difference in the aspiration port position. Similar to previous studies, the anterior chamber fluid dynamics and turbulence can result in inconsistent pressure on different positions of the posterior corneal surface, iris, suspensory ligament and posterior lens capsular bag.12 13 In contrast to the coaxial I/A fluidic findings, the vibration of the propeller or the absence of a propeller could potentially disturb the phaco tip inner lumen velocity distribution and produce different levels of vacuum, which may affect the holding power of the lens nucleus during phacoemulsification.

Peristaltic and Venturi pumps are the most common types of commercial phaco machines and have different working principles and clinical parameter settings.16 Because fewer parameters make it easier to obtain reliable results with the simulation model (peristaltic and Venturi=4 and 3 parameters, respectively), we chose the Venturi pump in this study. Moreover, different setting values may result in different flow rates and unstable anterior chamber pressure.17 We identified linear relationships among irrigation bottle height, vacuum and IOP, which will be clinically useful for surgeons to set a relatively stable IOP during surgery and avoid drastic post-occlusion vacuum surges, especially for complex situations such as post-vitrectomy eyes and eyes with extremely high myopia.18–20

With the traditional torsional phaco tip, high-frequency tip movement can cause severe cavitation outside the tip, which can cause heavy mechanical damage (including local high pressure and temperature resulting from microjets, sonoluminescence and shock waves) to ocular tissue within a certain distance.21 22 These damaging effects were also confirmed by long-term erosion of the surface using a phaco tip and other materials.6 23 24 In contrast, using the coaxial vibration simulation model, cavitation mainly existed in the lumen of the turbo tip but less so outside the turbo tip, which could greatly reduce collateral damage to the ocular tissue and enhance the efficiency of smashing the lens nucleus during phacoemulsification. This phenomenon was confirmed by video observations using a high-speed camera (https://vjcrgs.com/volume34-issue2/new-propeller-turbo-tip-for-torsional-pea#).

Unlike cavitation, coaxial rotation of the turbo phaco tip could also cause a small increase in the lumen fluid velocity of the outflow, which could potentially improve nucleus followability. Moreover, the motion curve difference between torsional/longitudinal and coaxial rotation turbo phaco tips resulted in different effects on unintentional contact with the ocular tissue, which demonstrated that coaxial rotation was much safer than the other two modalities, even in the capsule survival test (https://vjcrgs.com/volume34-issue2/new-propeller-turbo-tip-for-torsional-pea).

The differences in lumen fluid velocity at a fixed rotation length with and without the turbo plate were small, indicating that the turbo plate had a little influence on the lumen fluid velocity. Therefore, we conclude that the function of the turbo plate is to mainly smash the lens nucleus.

As an extension of previous simulation studies on the I/A procedure, this is the first study to focus on fluid dynamics using a computational simulation model to demonstrate the details of the flow and dynamic pressure in the anterior chamber during phacoemulsification. The flow velocity, ocular pressure distribution and turbulence kinetic energy fields of the anterior segment of the ocular tissue during phaco tip vibration were investigated. The results of this study will improve the current understanding of the entire flow system in the anterior chamber during phacoemulsification.

There are some limitations of the study. First, we only investigated the use of the Venturi pump and no lens nucleus was involved in this study; a peristaltic pump and lens nucleus dynamic information will be evaluated in a future study. Second, simulation model analysis could show the details of the whole procedure, but the boundary data are relatively fixed, which might not be the same as that in real surgical procedures.

In conclusion, we investigated the fluid dynamics of the propeller turbo phaco tip during phacoemulsification using a computational simulation model, which provided a priori detailed fluid turbulence and dynamic information and evaluation for this new phaco tip. The findings will be helpful in creating more updated phaco tip designs in the future. This study also highlights the usefulness of simulation models for complex fluid dynamic analysis in medical situations. Further studies should assess peristaltic systems and add lens nucleus dynamic information to enhance the understanding of more detailed information during phacoemulsification.

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Overview

Abstract
Introduction
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Discussion
References
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