Characterizing the Field of Fluidic Effect Around Vitrectomy Probes Using Particle Image Velocimetry

Abstract

Purpose: The shape and characteristics of the velocity fields around vitrectomy probes are unknown, resulting in an incomplete understanding of their surgical effects and behavior. The primary aim of this study was to define and measure with high spatial and temporal resolution the field of fluidic effect induced by vitrectomy probes, with assessment of both convective and temporal acceleration in a range of surgically relevant settings with an optimized particle image velocimetry (PIV) methodology.

Methods: This was a laboratory-based investigation using in vitro testing carried out at Newcastle University. Testing was conducted using a DORC EVA Nexus vitrectomy system with dual cutting action vitrectomy probes in three gauge sizes (23G, 25G and 27G). With the use of balanced salt solution (BSS), PIV measurements were conducted for various flow, vacuum, and cut rates. Experiments were conducted in a range of different probe orientations to reconstruct a three-dimensional representation of the flow fields.

Results: Using a variety of improvements in the PIV setup, including choosing an optimal time delay (dt) between the image pairs, the field of fluidic effect was measured with high spatial resolution up to the probe port. Fluid acceleration in the vicinity of the cutter was accurately resolved with values significantly higher than previously reported values. Two clinically relevant zones, high-flow and low-flow, were identified and defined. The high-flow zone (HFZ) had an acceleration of up to 400 m/s² and reached velocities of up to 1 m/s close to the port for the maximum aspiration setting. The low-flow zone (LFZ) extended approximately 2 to 2.5 mm from the port, or 3.5 to 4 times the diameter of the cutter (during maximum aspiration), with the mean velocity at the edge of the zone reaching 0.01 m/s. The extent of the HFZ was relatively constant with respect to gauge size and increased only marginally with both increased flow and vacuum settings. The LFZ increased in extent with both flow and vacuum. It varied in extent by gauge size with vacuum but was relatively unaltered by gauge size with fixed flow. Cut rate had no clinically relevant effect on the HFZ and LFZ extents and velocity fields.

Conclusions: Using optimized PIV measurements on an experimental in vitro vitrectomy setup, two clearly defined flow zones could be identified around the vitrectomy port. The study defined the shape of the two flow zones in BSS, outlined influencing factors, and correlated fluctuations with gauge, flow, and cut rates. These parameters enhance surgical understanding and provide a benchmark for future design evaluations. Further study using non-Newtonian fluids would be of interest to outline the differences in flow fields.

Translational Relevance: Understanding the flow patterns around the probe and the effect of key surgical parameters on their extent could assist in optimizing vitrectomy and reducing the risk of iatrogenic retinal trauma.

Introduction

Vitrectomy (i.e., removal of the vitreous gel from the eye) is an established and effective therapy for a range of common blinding retinal diseases, including retinal detachment and macular hole. To optimize the efficiency of surgery and reduce morbidity, vitrectomy cutter probe technology has advanced in several ways with higher cut speeds and new cutting actions to reduce retinal traction, as well as narrower gauges to reduce surgical trauma. During different phases of vitrectomy there are a range of varying fluidic requirements relating to the risks of vitreoretinal traction and retinal trauma, and the precise surgical demands at the time. 

Vitrectomy can be defined in terms of flow rates, but the field of fluidic effect or influence (referred to here as FOE) is a potentially more surgically useful representation of probe performance. The FOE can be broadly defined as the region around the vitrectomy port that is influenced by its induced fluid dynamics. At times, distant effects may be desirable, such as attracting fragments of retained lens matter to the probe after the vitrectomy has been completed. At other times, a very precise FOE may be useful for example trimming the internal limiting membrane during internal limiting membrane flap creation. 

The concept of a FOE was first introduced for vitrectomy by Dugel et al.,^1,2 which they referred to as the “sphere of influence.” Experimentally, they assessed its extent using the distance at which a vitrectomy probe attracted a suspended string. They described a reduction in the attraction distance with narrow-gauge cutters as compared to larger gauges, with matched vacuum settings potentially allowing more precise surgical effects and a reduced risk of distant tractional effects. Other parameters, including flow rate, cut rate, cutter action, and potentially port area, are also likely to affect the size of the field of effect and have not been clearly defined. Furthermore, the key characteristics defining and characterizing the induced flow field around a vitrectomy probe has not been defined for either clinical utility or comparative studies. 

In addition to the extent of the flow fields, two other parameters are also important—notably, fluctuations³ in the velocity field during the cutting action and the gradient of flow within it, both of which will affect the stability of vitrectomy and the surgical approach to tissue. Near-field flow fluctuations presumed secondary to blade action are observed as flow pulsatility, amplified by vitreous elasticity. Fluid acceleration during vitrectomy is known to be directly related to vitreoretinal traction,^4,5 although other factors, including the distance from the retina^6,7 and the connectivity and elasticity of the media joining the cutter to the retina, may also influence traction. A wide FOE with high flow acceleration into the cutter port, however, presents both danger and inefficiency⁸ when operating near the retina. 

Particle image velocimetry (PIV) is an imaging technique that allows both spatial and temporal evolution of the velocity field around the vitrectomy probe to be precisely measured. Previous attempts to quantify the flow fields immediately around the vitrectomy port using PIV have been limited by shadow effects^9,10 and a variety of technical issues, resulting in a number of paradoxical representations and misinterpretations, including a zone of apparent low flow immediately at the port. 

In this paper, an optimized PIV technique is presented that has allowed the precise characterization of these near-flow fields with high spatial and temporal resolution, allowing both the convective and temporal acceleration profiles around the cutter port to be delineated for the first time.^3–5,8 This has also allowed the definition of specific parameters that can be used to describe the FOE. These include the recognition of two fluidically important zones around the port and fluctuations within the field, which can be used in future studies and device comparisons. Furthermore, the effect of a range of clinically relevant machine setting variables on these parameters is assessed to aid surgical interpretation, including the aspiration control mode used. 

Materials and Methods

To investigate the FOE of the vitreous cutters, an in vitro experimental setup was designed and assembled in the Fluid Dynamics Laboratory at Newcastle University. Figure 1a shows a schematic of the experimental setup. The study employed the EVA Nexus vitrectomy system (Dutch Ophthalmic Research Center [DORC], Zuidland, The Netherlands) with three different gauges (23G, 25G, and 27G), all using the same dual cutting action, spring return, guillotine vitrectomy probes. The cutter was secured in a custom-designed holder that allowed it to rotate about its axis with a resolution of 1°. This allowed a range of measurements around the cutter to be made. Moreover, the holder was mounted on a three-axis manual traverse system, offering precision positioning of 0.1 mm in the x and z directions and 1 mm in the y direction. The x and y directions are illustrated in Figure 1b, and the z direction extends into the paper. The cutter tip was immersed inside a transparent container (75 × 75 × 75 mm) containing balanced salt solution (BSS). The container used was intentionally large to avoid wall effects. We used BSS rather than water because BSS is the fluid typically used during surgical procedures to closely match the physiological conditions in the eye. BSS provides essential ions and nutrients, making it more representative of the intraocular environment than water. The fluid temperature was maintained at 25°C by regulating the room temperature; the viscosity of BSS, as specified by the manufacturer, is similar to that of water, ensuring consistent flow properties. The setup was mounted on an aluminum rig and leveled to ensure stability and accuracy during the experiment. 

Figure 1.

 

(a) Schematic of the experimental setup. (b) Cutter schematic and the coordinate system used in the paper; θ = 0 for the present orientation, which increases in the direction of the arrow. (c) Zoomed-in view of the high-speed pulsed laser and camera.

Particle Image Velocimetry

The flow field around the cutter was measured using PIV. The PIV system was equipped with a Phantom VEO-E 310L high-speed camera (Vision Research, Wayne, NJ) with a maximum resolution of 1280 × 800 pixels and a high-speed double-pulsed neodymium-doped yttrium lithium fluoride (Nd:YLF) laser (Litron, Agawam, MA) with a wavelength of 527 nm and energy of 15 mJ/pulse at 1 kHz. The laser light was transported from the laser head to the experimental rig using a light guide arm, which passed through divergent optics to form a two-dimensional planar sheet, with an approximate sheet thickness of 0.5 mm. The spread of the laser sheet is illustrated in Figure 1c. Further, to prevent the shadow of the cutter from obstructing the flow field, the laser sheet was directed from underneath the cutter (shown in Fig. 1c), rather than through the lateral sides.^9,10 The BSS was seeded with neutrally buoyant red fluorescent polymer microspheres, which had a nominal diameter of 8 µm and density of 1050 kg/m³. The maximum absorption and emission wavelengths of these particles are 542 nm and 612 nm, respectively. An optical bandpass filter with wavelength of 600 ± 50 nm was fitted to the high-speed camera to remove all background laser glare and allow PIV measurements up to the probe port. 

The Stokes number (S_k = particle response time/characteristic time scale of the flow¹¹) for the seeding particles was calculated as 0.06, meeting the acceptable limit (S_k < 0.1) for accurate flow tracing.¹² The number of particles added ranged from approximately 150 to 200 particles/mm², meeting the requirement of having a sufficient number of particles (6–10) within the interrogation window to accurately resolve the velocity. 

To prevent aggregation of the seeding particles in BSS, a non-ionic detergent (polysorbate 20; Thermo Fisher Scientific, Waltham, MA) was added to the mixture. This aided in maintaining a uniform particle dispersion, crucial for accurate measurements. The amount of detergent added was fixed at 0.125% in all experiments. Rheometry confirmed that the viscosity of the solution was unaltered. The flow field was captured using a 60-mm lens with a field of view of 5.5 mm × 5 mm. For each measurement, 2000 image pairs were acquired at 2 to 5 KHz. To achieve the desired acquisition frequency, the camera resolution was reduced to 832 × 760 pixels. The acquired images were processed using LaVision DaVis software with a multi-pass cross-correlation scheme and final interrogation area of 32 × 32 pixels at an overlap of 75%, yielding 95 × 104 velocity vectors with a spatial resolution of 0.053 mm. Each experimental case was repeated three times. 

In general, the flow due to the vitreous cutter can be classified as a sink flow, as fluid surrounding the cutter is drawn into the port. Therefore, the origin of the coordinate system was taken at the port, and the axes defined as in Figure 1c. According to the defined coordinate system, the aspirated flow is directed along the negative x, y directions. To aid interpretation, the velocity moving into the cutter is represented as a positive value throughout the paper. The instantaneous velocities in the horizontal and vertical directions are denoted by u and v, respectively. The time-averaged velocities in the horizontal and vertical directions are represented by \(\bar{u}\) and \(\bar{v}\), respectively. Similarly, fluctuation velocities in the horizontal and vertical directions are represented as u′ and v′, respectively. The time-averaged velocity magnitude is denoted as \(U = \sqrt{(\overline{u^{2} + v^{2}})}\). 

Parameter Settings and Analysis

The effect of various aspiration parameters was investigated over a range of settings in both vacuum- and flow-controlled aspiration modes with a fixed cut rate of 16,000 cuts per minute (CPM), as detailed in the Table. In flow-controlled mode, the vacuum was set to maximum and the flow set to the desired level. Additionally, a separate set of experiments was conducted to investigate the effect of cut rate with a fixed vacuum of 300 mm Hg with vacuum-controlled aspiration. 

Table.

 

Settings Used in the Experiments

 

In previously published studies, spatial acceleration has typically been determined by averaging the acceleration measurements over a circular area centered around the cutter port, with a radius ranging from 3 to 5 mm.⁵ We observed that velocity increased significantly within 0.5 mm from the cutter as flow approached the aspiration port, creating a steep spatial acceleration gradient in that region. To resolve the convective acceleration in this region, the instantaneous convective acceleration was calculated based on the vector spacing (53 µm) for each frame and then averaged over the entire sampling time. Similarly, temporal acceleration (i.e., ∂u/∂t) was calculated by measuring the difference in velocity between consecutive frames and then averaged over the entire sampling period. 

Effect of dt Settings and the Influence of Cutter Orientation on Velocity Field

PIV enables the fluid velocity fields to be resolved in space and in time by analyzing pairs of consecutive images captured over a specific time interval, referred to as dt. By comparing the average displacement of a pattern of particles within each interrogation window between these two images, the velocity vectors throughout the field of view can be calculated.¹³ The significance of dt settings has had limited discussion in the previous vitrectomy literature. After removing the glare of the laser sheet from the cutter, it was possible to set a dt value that allowed the velocity field up to the cutter port to be obtained. In the present study, particular attention was given to identifying the optimal dt value for each case. Figure 2 shows the time-averaged mean velocity field, U, obtained for different dt settings for the same flow conditions: 25G, vacuum-controlled aspiration set at 100 mm Hg, and a cut rate of 1000 CPM. It can be seen that at dt = 20 µs the maximum velocity is situated in proximity to the aspiration port, as would be expected. As dt is increased, the velocity magnitude progressively diminishes. With higher values of dt, the velocity near the suction port is lower in comparison to the velocity at a farther distance. This discrepancy indicates an incorrect representation of the flow behavior, and it can be attributed to particle disappearance between image pairs, resulting in spurious vectors. Additionally, it may also arise from particle movement in and out of the plane of the light sheet. Hence, careful selection of the dt value is essential to ensure accurate and reliable velocity field measurements. Therefore, in this experiment, for each case in the Table, the PIV measurements were conducted for a range of dt values, and the one that captured the maximum velocity in proximity to the aspiration port was used. In addition to the dt settings, the number of particles within the interrogation window and the particle displacement are also of high importance. In this study, the smallest interrogation window utilized was 32 × 32 pixels, and the seeding density was designed to ensure the presence of eight to 10 particles within each interrogation window. In addition, the PIV settings were optimized to allow the particle pattern to move approximately 25% over the 32 × 32-pixel interrogation window at the location where there was maximum velocity (i.e., by the port). 

Figure 2.

 

Effect of various dt settings on the flow field: (a) dt = 20 µs, (b) dt = 50 µs, (c) dt = 200 µs, (d) dt = 600 µs. Settings: 25G, vacuum-controlled aspiration 400 mm Hg, 10,000 CPM.

To investigate the velocity field around the vitrectomy probe, PIV measurements were conducted at various orientations of the vitrector. Figure 3 presents the PIV measurements obtained at three different orientations. At 0°, the maximum velocity observed at the aspiration port was 0.35 m/s, whereas, at 45° and 90°, the maximum velocities at the lateral edges of the cutter were approximately 0.2 m/s and 0.13 m/s, respectively. Here, the dt values were set to 60 µs for 0° and 45° cutter orientations and 120 µs for the 90° orientation, in order to correctly capture the fluid velocities. Furthermore, the mean velocity fields at all three orientations illustrated that the spatial distribution of the velocity field of fluidic effect (FOE) varied around the cutter. Specifically, the averaged velocity was notably higher in the direction of the port opening, but laterally the velocity dropped to approximately 35% of the maximum velocity. 

Uncertainty

Uncertainty from the calculations and repeated measurements is presented as uncertainty bars in figures throughout this article. The uncertainty of the velocities was estimated using the correlation statistics method.¹⁴ A correlation-based uncertainty quantification method identified the individual pixels and their fluctuating contributions to the shape of the correlation peak from which an uncertainty estimate was derived. Based on this technique, the maximum uncertainty of the velocity field was calculated as ±0.0117 m/s, computed using LaVision DaVis Software. Subsequently, we calculated uncertainty in the acceleration based on earlier work by Kline and McClintock.¹⁵ 

To determine the uncertainty due to repeatability, all of the cases in the Table were repeated three times, and the corresponding mean quantities and uncertainties were obtained as described above. The results from all three measurements (including the uncertainty) were averaged, and the spread of the data is reported as uncertainty bars. 

Results

The flow rates achieved with the different applied vacuum levels for the three probe gauges were recorded and are illustrated in Figure 4. The data revealed a nearly linear association, indicating a high degree of approximation between these two variables. These findings served to validate the field of fluidic effect that is discussed in the later part of this section and allowed plotting of corresponding values under vacuum- and flow-controlled aspiration. 

Figure 3.

 

PIV velocity field measured at various positions of the vitrector: (a) θ = 0° (b) θ = 45° (c) θ = 90°. The corresponding dt values are 60 µs, 60 µs, and 120 µs, respectively. Flow parameters: 25G, 10 mL/min, 16,000 CPM.

Figure 4.

 

Variation of flow rate with respect to applied vacuum in the EVA Nexus system.

Field of Fluidic Effect

In order to explore the FOE under various vitrectomy settings, PIV measurements were conducted on the vitrector while maintaining a 0° orientation, as shown in Figure 5a. This orientation was chosen to capture the maximum spatial extent of the aspiration. 

The colormap of the mean velocity field illustrates a continuous velocity profile around the vitrector. In close proximity to the vitrector port, the velocity increases significantly, a region we refer to as the high-flow zone (HFZ), enclosed by a dashed line in Figure 5a. Farther away from the port, the velocity gradually decreases, approaching zero and forming what we describe as the low-flow zone (LFZ), depicted by a solid line in Figure 5a. The transition between the LFZ and the HFZ is smooth and continuous. A three-dimensional (3D) representation of these zones is provided in Figure 5b. 

Figure 5.

 

(a) Flow fields illustrated with the HFZ (enclosed by dashed line) and LFZ (enclosed by solid line). Settings: 25G, flow-controlled aspiration 10 mL/min, 16,000 CPM. (b) 3D schematic of the HFZ (red) and LFZ (transparent).

High-Flow Zone

To precisely define the boundaries of the HFZ, the mean horizontal velocity (\(\bar{u}\)) distribution along the x-axis at y = 0 was plotted (Fig. 6a), with the same flow conditions as in Figure 5. This plot clearly demonstrated a sharp increase in velocity as the vicinity of the cutter port was approached (x = 0). This rapid change in velocity resulted in a substantial increase in convective acceleration, plotted in Figure 6b. Here, the acceleration is defined as \({\bar{a}}_x = {\overline{u\frac{\partial u}{\partial x}}}\) as the other temporal and spatial quantities are negligible. For example, the two-dimensional instantaneous fluid acceleration in the horizontal and vertical directions can be defined, as  

\begin{eqnarray}{{a}_x} = \frac{{\partial u}}{{\partial t}} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}}\end{eqnarray}

(1)

 

\begin{eqnarray}{{a}_y} = \frac{{\partial v}}{{\partial t}} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}}\end{eqnarray}

(2)

 

Each quantity in the above equations was time averaged and is presented in Figure 7. Notably, the magnitude of \(\overline{u\frac{\partial u}{\partial x}}\) was significantly larger than the other terms. Although the temporal acceleration can reach values of approximately ±100 m/s² at the onset of the HFZ from an instantaneous perspective, time averaging these values results in near-zero contributions. As a result, further analysis concentrated on the dominant term \( (\overline{u\frac{\partial u}{\partial x}} )\). The time-averaged convective accelerations measured in this study were considerably higher than those reported in previous studies. This disparity is due to two reasons. First, in the present study, the velocity induced by the cutter was resolved up to the cutter port where the spatial velocity gradient was largest, resulting in large convective acceleration. Second, the acceleration fields were not spatially averaged over large areas of the flow field. 

Figure 6.

 

(a, b) Mean horizontal velocity (a) and mean acceleration (b) along the line y = 0. Settings: 25G, flow-controlled aspiration 10 mL/min, 16000 CPM. The inset figure in (b) illustrates the method used to determine the boundary of the HFZ.

To establish the boundary of the HFZ, a dual-slope technique was used on the acceleration data. The dual-slope method is widely used in research concerning laminar–turbulent transitions.^16–18 This technique involves identifying the point where the slope of sharp acceleration intersects with the slope of acceleration observed at a considerable distance from the cutter, as depicted in the zoomed-in plot in Figure 6b. The horizontal distance from the cutter at which this intersection occurred was considered the boundary of the HFZ. 

The dual-slope technique was applied to determine the HFZ boundaries for all of the cases detailed in the Table, and the results are presented in Figure 8. As the aspiration settings were increased for both flow and vacuum, the boundary of the HFZ gradually expanded slightly, although the zone of high-velocity aspiration was confined within a region of approximately 0.5 mm from the aspiration port for all conditions. 

An alternative approach to identifying the point where the flow transitions into a region of significant convective acceleration (i.e., the beginning of the HFZ, as shown in Figure 6b) is to plot the velocity data on a logarithmic scale and fit it to the known velocity profile for a 3D point sink flow, which follows u ∼ 1/x². By identifying the point where the data deviate from this idealized profile, one can highlight the onset of near-port effects. Although the results of this method are not shown here for brevity, they are consistent with the location of the HFZ depicted in Figure 8, with both techniques, yielding similar results. 

The uncertainty bars in Figure 8 were determined by considering the minimum and maximum uncertainties of the acceleration. From these uncertainty limits, it was possible to identify the uncertainty in the HFZ, as indicated in Figure 9 by the intersection of red dashed lines at a_x = 0. 

Figure 7.

 

(a–f) Mean temporal and mean spatial acceleration along the x-axis (a–c) u-component of acceleration and (d–f) v-component of acceleration. Settings: 25G, flow-controlled aspiration 10 mL/min, 16,000 CPM.

Figure 8.

 

(a, b) Boundaries of the HFZ obtained for various flow rates under flow-controlled aspiration (a) and vacuum settings under vacuum-controlled aspiration (b).

Figure 9.

 

Uncertainty estimation method for HFZ. The intersection of the two vertical red dashed lines at a_x = 0 indicates two HFZs.

Another interesting observation was that, when the horizontal velocity distribution was normalized with the corresponding maximum velocity and the boundaries of the HFZ, all of the profiles collapsed to a single curve. This is graphically depicted in Figure 10 for various flow rates. 

Figure 10.

 

Mean horizontal velocity measured at y = 0 for various flow rates with flow-controlled aspiration normalized with the corresponding maximum velocity and boundaries of the HFZ. Settings: 25G, 16,000 CPM.

Low-Flow Zone

During surgery it is also important to understand the physical distance at which the vitrectomy probe has any effect on flow. Therefore a second FOE zone, the LFZ, was defined. 

In the context of fluidic influence, it is worth noting that aspiration at any point tends to have some effect, albeit tending to zero, on its surrounding region, making it challenging to identify where flow rates become less important. At a threshold velocity of T_h = 0.01 m/s, the frequency of the cutter was not discernible in the velocity field, verified through power spectral density analysis, discussed below. Therefore this velocity was used to define the outer extent of the LFZ. The distance x from the cutter port where the velocity reached this threshold value was designated as the boundary of the LFZ. 

Figure 11 presents the velocity profiles for various flow rates using the 25G cutter. The red dashed line represents the threshold velocity of T_h = 0.01 m/s, as defined for the LFZ. In Figure 12, the LFZ is the x distance from the aspiration port where the velocity reached the threshold value for various flow rates and vacuum settings. An interesting observation is that, when using flow-controlled aspiration, as the flow rate increased the LFZ appeared to be independent of the gauge size. However, in vacuum-controlled aspiration settings, LFZ tended to increase with an increase in vacuum or a decrease in gauge size. 

Figure 11.

 

Mean horizontal velocity measured along y = 0, for various flow rates. Settings: 25G, flow-controlled aspiration 10 mL/min, 16,000 CPM.

Figure 12.

 

(a, b) FOE of the LFZ obtained for various flow rates (a) and vacuum settings (b).

The chosen threshold value of 0.01 m/s was validated by investigating the boundaries of the LFZ for a range of threshold values. Figure 13 illustrates the LFZ for various values of T_h, revealing that, as the T_h value decreased, the LFZ boundary expanded. This expansion continued until T_h = 0.007 m/s; for further decreases in T_h, the boundaries of the LFZ no longer followed the same trend and instead became nonlinear and paradoxical. This suggested that selecting a value for T_h below 0.01 m/s would lead to wide inaccuracies in measuring its extent, reducing its validity and utility. A value of 0.01 m/s was also the uncertainty limit within the PIV setup for this investigation. Further research is needed to determine an optimal clinically relevant value for T_h. 

The uncertainty bars in Figure 12 were estimated by computing the distance where the LFZ threshold value was T_h ± 0.0117 m/s. 

Figure 13.

 

Boundaries of the LFZ obtained for various threshold values (m/s) using a 25G vitrector.

Effect of Cut Rate on the Surrounding Fluid

It has been previously reported^5,19 that cut rate has no discernible influence on flow rate or vacuum with dual cutting action vitrectomy probes. The impact of cut rate in BSS was investigated by measuring the velocity fields and their spectral characteristics. Figure 14 displays the mean horizontal velocity profiles obtained at y = 0 for various cut rates with a fixed vacuum-controlled aspiration at 300 mm Hg. All of the profiles collapsed to a single profile, indicating that the surrounding flow remained largely unaffected by changes in the cut rate. 

Figure 14.

 

Values of \(\overline{u}\) measured at y = 0 for various cut rates. Settings: 25G, vacuum-controlled aspiration 300 mm Hg.

The horizontal (Fig. 15) and vertical (Fig. 16) fluctuation velocities at the boundaries of the HFZ (depicted by black lines) and the LFZ (depicted by red lines) were plotted with the corresponding power spectrum (ϕ_u′ and ϕ_v′, respectively). These fluctuation velocity signals were taken at y = 0 points, denoted by the black and red dots in Figure 5a. Notably, the periodic signals at the boundary of the HFZ suggested the influence of cutting action on the surrounding fluid, clearly captured in the spectral plot. The frequency of the selected cut rate correlated well with the frequency of the spectral peaks observed. For example, 16,000 CPM is 266 cuts per second and thereby 133 blade cycles per second, creating a frequency of 133 Hz at the border of the HFZ (see black lines in Figs. 15b and 16b). In contrast, the fluctuation signals from the LFZ boundary did not exhibit any effects of blade motion. 

Figure 15.

 

(a) Fluctuating horizontal velocities measured at the boundaries of the HFZ (black) and the LFZ (red). (b) Corresponding power spectral densities. Black and red dashed lines in (a) represent the standard deviations of the fluctuations at the HFZ and the LFZ, respectively. Settings: 25G, vacuum-controlled aspiration 300 mm Hg.

Figure 16.

 

(a) Fluctuating vertical velocities measured at the boundaries of the HFZ (black) and the LFZ (red). (b) Corresponding power spectral densities. Black and red dashed lines in (a) represent the standard deviations of the fluctuations at the boundaries of the HFZ and the LFZ, respectively. Settings: 25G, vacuum-controlled aspiration 300 mm Hg.

The data in Figures 14, 15a, and 16a clearly indicate that changes in cut rates did not significantly impact the mean velocity, but they did affect the velocity fluctuations (i.e., the instantaneous flow field). Furthermore, the influence of the cutter on the surrounding fluid was predominantly localized within the HFZ, whereas the LFZ appeared to remain relatively unaffected by these changes. This is evident in Figure 17, where the standard deviation of the fluctuations in both horizontal and vertical directions at the border between the zones and edge of LFZ are plotted for various cut rates. This figure clearly indicates that the flow fluctuations at the edge of the LFZ were lower than at the border of the HFZ and did not vary with cut rate. Horizontal fluctuation was greater than vertical fluctuation at the HFZ border, and they both gradually increased with cut rate. 

Figure 17.

 

Standard deviations of the fluctuation in both the horizontal (red) and the vertical (blue) directions obtained for various cut rates at a vacuum of 300 mm Hg, measured at the edge of the LFZ (solid lines) and at the border between the LFZ and HFZ (dashed lines).

Fluctuations at the HFZ

To examine the impact of both flow and vacuum on fluid fluctuations, Figure 18 illustrates the standard deviation of horizontal fluctuations measured at the edge of the HFZ for all three gauges at 16K CPM. The blue and red curves denote the flow- and vacuum-controlled aspiration conditions, respectively. To more clearly assess the intensity of the horizontal fluctuations between gauges and aspiration conditions, the horizontal fluctuations were normalized with the local mean velocity, shown in Figure 19. Under both aspiration modes the normalized fluctuation values showed higher magnitudes at low flows, particularly for 27G, but, as aspiration increased, the fluctuation values reached a saturation point. There were no clinically relevant differences in the fluctuations between the two aspiration modes or between gauges when saturation was reached. 

Figure 18.

 

Standard deviations of the fluctuation in horizontal direction, measured under both flow-controlled (blue) and vacuum-controlled (red) aspiration at 16K CPM, measured at the corresponding edges of the HFZ.

Figure 19.

 

Standard deviations of the horizontal fluctuation normalised to the local mean velocity for flow-controlled (blue), and vacuum-controlled (red) aspiration and the three different gauges obtained for 16K CPM at the HFZ.

Discussion

Understanding the fluidic effects of vitrectomy probes is key to optimizing their use.²⁰ The main findings of this paper are the accurate representation of the FOE around a vitrectomy probe port using an optimized PIV approach and the recognition of two clinically relevant flow zones that are surgically useful. The flow fits the pattern of a classic “sink” flow. An area of high flow was identified immediately adjacent to the port, and this HFZ merged into an area of gradually diminishing flow, the LFZ. The LFZ has an outer border where the flow rate tends to zero and the vitrectomy probe has no fluidic influence. The event horizon of a black hole is defined by the border at which the escape velocity matches the speed of light and hence nothing can escape. The outer border of the HFZ can be considered as a “surgical event horizon,” as it represents the point at which acceleration rapidly increases and mobile structures such as vitreous and retina are drawn into the vitrectomy port, beyond the ability of the surgeon to react. Determining the two borders that define these zones and the fluctuations during cutting action at the borders, has set a benchmark which will allow other instruments and design modifications to be evaluated. Specifically, we have shown that the HFZ is restricted to the area immediately in front of the port with a relatively sharp reduction laterally, forming a crescent shape in BSS when looking axially down the shaft. The HFZ is symmetric around the port on perpendicular viewing. 

Several other papers have used PIV to explore the near-field flow characteristics around the port of vitreous cutters. Romano et al.⁵ and Rossi et al.⁸ used PIV to assess the differences in fluidic effects between dual-blade and single-blade cutters and BSS versus artificial vitreous but did not define the convective acceleration and near field around the cutter port. They concentrated on flow rates, and average fluid accelerations and descriptions of the shape of the flow fields. Similarly, Stocchino et al.²¹ used PIV to assess the differences between guillotine and ultrasonic vitreous cutting and concentrated on the differences between the two cutting mechanisms, particularly in artificial vitreous, but they did not attempt to define the flow field. Inoue et al.⁹ studied the fluidic effects of beveled-tip versus flat-tip cutters and found changes in the angle and rate of flow between the two cutter shapes. In a second study, Inoue et al.¹⁰ evaluated the near-field fluidic effects of single-action versus dual-action cutting guillotine beveled tip blades and described differences in maximal flow at the proximal and distal ends of the cutter ports. None of these studies detailed the effect of dt on the derived fields, nor did they derive the flow field immediately adjacent to the cutter tip. In this investigation, three innovations allowed improved visualisation of the flow field immediately next to the port: (1) using a laser system positioned below the cutter to avoid the shadow effects visible in the above-mentioned studies; (2) using fluorescent particles coupled with a bandpass filter attached to the PIV camera to remove the glare from the laser sheet as it makes contact with the vitrectomy probe, thereby reducing visual noise; and (3) optimizing dt to accurately obtain maximum velocity across the near field. Previous studies have not detailed the parameters that can be used to define the FOE, as done here; rather, they have described the fields purely in descriptive terms, limiting the ability to compare them across differing conditions and machines. Defining the FOE allowed two distinct zones to be differentiated, which concurs with clinical experience. Flow starts around the cutter at about 1 to 2.5 mm perpendicular to the port depending on flow rate and rises slowly to a point approximately 0.5 mm from the port, where it rapidly and exponentially increases. 

Understanding the shape and the existence of the two flow zones has direct relevance to surgery, including reducing the risk of iatrogenic retinal break formation. When tissue enters the HFZ, reaction speed will not aid a surgeon no matter how low the flow rate is, and understanding the one probe width extent of the HFZ serves as a useful guide to its border location. Similarly, when trying to attract tissue to the port, increasing vacuum will not extend the HFZ significantly and has a relatively small effect on the LFZ. The surgeon has to move the probe toward the tissue to utilize the LFZ in the case of vitreous and retina and the HFZ to engage denser material such as retained lens matter. Our findings also explain how, when the vitreous is being trimmed, the tissues jump as they enter the HFZ and rapidly accelerate. Cut rate does not eliminate this effect. The HFZ is tightly defined by the port; hence, approaching tissue from the side or rear of the probe will partially shield the surgeon from inadvertent retinal cutting. 

The outer limits of the two zones are both related to the flow rate of the cutter and are relatively little affected by gauge if flow is matched. However, higher vacuum, with variable flow increases the extent of the LFZ in relation to gauge. We found that larger gauges had wider LFZs than narrower gauges for the same vacuum. The HFZ is relatively unaffected by gauge size and vacuum-controlled flow. Cut rate did not alter the extent of the flow zones. Dual cutting action probes were used, and it has previously been shown that flow is largely unchanged with cut rate in BSS.⁵ Single-action guillotine cutters were not evaluated; however, because they typically have lower flow with higher cut rates related to a reduction in duty cycle, it would be expected that they would exhibit narrower fields of flow with higher cut rates. In addition to defining the convective acceleration field around the probe port in high resolution, we also studied temporal acceleration and flow fields. In the same way as previous papers have averaged spatial acceleration over a wide area, they also averaged temporal acceleration over the same areas. Previous work³ showed that flow fluctuation at the cutter was surprisingly approximately an order of magnitude greater than mean flow and at the same frequency as the cutter. By assessing temporal acceleration by location at the same resolution as for convective acceleration, it has been possible to map out changes in temporal acceleration at specific locations from the port. Fluctuations in flow of an order of magnitude less than the mean flow at the borders of the HFZ have been found (Fig. 19). The fluctuations at the HFZ border were consistently higher in the horizontal than vertical velocity vectors, with both increasing in absolute magnitude with flow and vacuum. Similarly, this relationship persisted with varying cut rates, with a visible but probably insignificant peak at 12,000 CPM (Fig. 17). These findings are in contrast with those of Rossi et al.,^3,4 who found higher fluctuations with peristaltic pumps and evidence of a possible resonance effect with increased amplitude fluctuations at specific cutting frequencies. The relative extent of the flow fluctuations in relation to mean flow stayed constant across flow rates and gauges except at low flows and vacuums, when they increased particularly for 27G. This is likely related to the larger relative size of the blade thickness to shaft area for the narrow 27G probes, suggesting that 27G may not be the optimum gauge in situations such as peripheral vitreous trimming with a detached retina. It is important to note that the EVA Nexus system utilizes a novel aspiration system that is neither a peristaltic nor a Venturi pump but allows for flow- or vacuum-based control. The DORC VacuFlow valve timing intelligence (VTi) technology incorporated in the EVA Nexus uses high-sensitivity pressure sensors and computer-controlled operating pistons. It is proposed to generate a fast vacuum response and reduce undesirable flow effects and this may generate different flow parameters to other aspiration pump systems. Further investigation is necessary to assess the exact mechanisms for the fluctuations in flow observed. 

It is accepted that this study has limitations. The variance of flow fields with non-Newtonian viscoelastic materials such as vitreous, which as others²² have shown vary in shape and extent from BSS, were not investigated but will be the subject of future studies. In our study, we utilized Newtonian fluids to simulate the behavior of vitreous cutter probes. Newtonian fluids, which have a constant viscosity irrespective of shear rates, serve as a simplified model to investigate fluid dynamics near the probe. However, human vitreous presents a more complex scenario. As a non-Newtonian viscoelastic substance, the vitreous exhibits shear-thinning properties, meaning its viscosity decreases under shear stress, unlike the constant viscosity in Newtonian fluids. This distinction has significant implications for fluid flow and acceleration patterns around the probe. 

In human vitreous, high- and low-flow acceleration regions are more variable and dependent on the viscoelasticity of the vitreous gel. When subjected to shear forces from a vitreous cutter, the vitreous may deform differently than a Newtonian fluid, altering the fluidic flow and stability near the probe tip. Understanding these viscoelastic properties is crucial to translating our findings to clinical applications, as they can affect surgical precision, efficacy, and the potential risk of iatrogenic retinal damage during procedures. 

Although our results provide valuable insights into the mechanics of vitreous cutters, we emphasize that interpretation in human tissue requires consideration of these non-Newtonian properties, which may further influence the dynamics under physiological conditions. 

The flow fields were studied in multiple two-dimensional planes rather than 3D, which limits the ability to reconstruct a full volumetric representation. However, this approach enables a reproducible methodology that can be easily replicated by others. Finally, only one vitrectomy system was examined along with one mode of cutting action, but principles have been established that allow other systems to be investigated. 

Conclusions

By applying an optimized PIV methodology to flow fields around vitrectomy probes, it was possible to define the FOE around the vitrectomy port and observe two identifiable zones with high- and low-flow areas separated by a region of intense acceleration, similar to an event horizon. The shapes and parameters that affect the extent of each zone are outlined here for the Newtonian fluid BSS. Vertical and horizontal fluctuations at the boundary of the HFZ have been defined and related to gauge, flow, and cut rates. Defining these parameters aids surgical understanding and also sets a benchmark by which future design changes can be evaluated. Future studies will evaluate the effect of different viscosity media and non-Newtonian fluids to understand the effects of vitreous cutting. 

Acknowledgments

Supported by DORC International (Zuidland, the Netherlands) through a research grant to Newcastle University. 

Disclosure: D. Veerasamy, None; D. Vedeniapina, None; M. Wilkes, None; D.H. Steel, DORC, BVI and Alcon (C); R.D. Whalley, DORC and BVI (P)