Mechanisms of Retinal Displacement After PFCL-Assisted Rhegmatogenous Retinal Detachment Repair: Insights From a Computational Model

Abstract

Purpose

To investigate the mechanical forces exerted by perfluorocarbon liquid (PFCL) during pars plana vitrectomy (PPV) for rhegmatogenous retinal detachment (RRD) using a computational model of retinal dynamics.

Methods

A continuous load was applied to the retina by simulating PFCL infusion into the vitreous cavity at a constant fill rate for varying PFCL densities. Using this loading condition, the model computed the corresponding movement of subretinal fluid (SRF) and the resulting retinal displacement throughout the reattachment process.

Results

In our model, the PFCL pushes the SRF against gravity, which displaces the fluid anteriorly away from the PFCL bubble. This flow of SRF induces shear stress, contributing to retinal stretching. In addition to the flow-induced stretching, the direct mechanical load from the PFCL will also directly result in retinal stretching. As a result, the retina undergoes a displacement or stretch of approximately 200 to 240 µm, and the residual stretch after the removal of PFCL is approximately 100 µm. The model, representative of a PPV setting, further demonstrates that PFCL with higher density can exert greater load on the retina, leading to increased residual displacement following retinal reattachment.

Conclusions

These simulations established a framework for investigating retinal displacement resulting from RRD repair using PPV with PFCL. The results suggest that a lower-density PFCL can help minimize retinal displacement by reducing mechanical loading on the retina. This model can be further extended to examine the influence of additional clinical variables, such as the location and size of retinal breaks, to support optimized surgical planning and improved visual outcomes.

Rhegmatogenous retinal detachment (RRD) is the accumulation of subretinal fluid between the neurosensory retina and the underlying retinal pigment epithelium (RPE), caused by a tear or a hole in the retina. Multiple surgical options can reattach the retina, including pars plana vitrectomy (PPV), scleral buckle, and pneumatic retinopexy (PnR).¹ Nevertheless, the “integrity” of the anatomic reattachment and the functional outcomes vary with surgical technique.^2–5 Over the last several years, multiple author groups have shown that retinal displacement may follow successful RRD repair and that displacement is influenced by the size and type of tamponade size and postoperative head positioning.^2,6–8

Retinal displacement can be evidenced postoperatively by the presence of retinal vessel printings (RVPs) on fundus autofluorescence (FAF) imaging⁹ or through superimposed infrared images pre-RRD (if available) and postoperatively following RRD repair using homography.¹⁰ One author group has defined low-integrity retinal attachment (LIRA) as the presence of RVPs following RRD repair, which indicates that the photoreceptors are significantly displaced from their original location with respect to the RPE.^4,9 A recent study⁴ showed that PPV was more commonly associated with LIRA with a relatively increased occurrence of retinal displacement when compared to PnR (44% vs. 7%, respectively). Some have suggested using PFCL in PPV to reduce the risk of retinal displacement.^11,12 However, Marafon et al.¹³ reported severe retinal displacement following RRD repair using intraoperative PFCL that was left in the eye as a short-term endotamponade. Importantly, the direction of retinal displacement corresponded precisely with the direction of flow of subretinal fluid during the PFCL-assisted drainage. Although this represents a unique scenario where the PFCL was left in the eye as a short-term tamponade agent, it begs the question whether even the short-term use as a surgical adjunct has negative effects on the retina. Although PFCL is widely used intraoperatively, the detailed biomechanical interactions between PFCL and retinal tissue are not yet fully understood.

This study aimed to develop a computational model to investigate retinal displacement during PFCL assisted reattachment. By simulating the dynamics of subretinal fluid (SRF) drainage and the resulting retinal deformation, we evaluated the influence of different PFCL liquids (i.e., different densities) on retinal displacement.

Methods

Mathematical Modeling

To investigate the fluid mechanical processes governing retinal reattachment during PFCL-assisted surgery for RRD, we developed a mathematical model similar to the model used to assess retinal displacement in the setting of a gas tamponade.¹⁴ This model captures the dynamic interaction among the PFCL, the SRF, and the detached retinal tissue. The geometric configuration used in the model is illustrated in Figure 1a. Because PFCL is denser than water, it tends to settle on the surface of the retina when injected in a fluid-filled eye. During surgery, PFCL is introduced at a controlled rate starting usually at the optic nerve until it fills the vitreous cavity, resulting in a time-dependent accumulation of PFCL. In this study, we assumed a relatively slow constant fill rate of 1% of the posterior segment volume per second, where the cavity volume is given by $V_o=\frac{4}{3}\pi R_i^3$, with V_o representing the posterior segment volume and R_i the radius of the inner retina.

Figure 1.

Left: Schematic representation of PFCL within the posterior segment of radius R_i, where shaded regions illustrate the increasing volume and corresponding shape of the PFCL interface. Right: Variation of the Bond number (Bo) with PFCL volume fill percentage for PFCL densities of 1200 kg/m³, 1500 kg/m³, and 2000 kg/m³.

As the PFCL volume (V) increases over time, the corresponding Bond number (Bo) evolves according to:

$$\begin{array}{c}\hfill Bo=\frac{\Delta \rho g{a}^2}{\sigma }\end{array}$$ (1)

where ∆ρ = ρ_P − ρ_o is the density difference between the PFCL and the ocular fluid, ρ_P is the density of PFCL, ρ_o = 993 kg/m³ is the density of the ocular fluid, g is the gravitational acceleration, σ = 45 mN/m is the interfacial tension between the PFCL and ocular fluid,¹⁵ and $a={\left(\frac{3V}{4\pi }\right)}^{\frac{1}{3}}$ is the effective radius associated with the PFCL volume.

The variation of the Bond number with the PFCL volume fill ratio is given by V/V_o is presented in Figure 1b for PFCL densities of 1200 kg/m³, 1500 kg/m³, and 2000 kg/m³. In clinical practice, commonly used PFCLs such as perfluoro-n-octane (PFO) and perfluorodecalin (PFD) have densities within a relatively narrow range, approximately 1770 kg/m³ and 1930 kg/m³, respectively. The broader range of densities considered in our simulations was intended to systematically explore the influence of density on retinal biomechanics within a controlled, theoretical framework. In particular, the lower density value (e.g., 1200 kg/m³) was included as a hypothetical case to better understand the sensitivity of retinal deformation to PFCL density, rather than to represent a clinically available agent. A density below 1200 kg/m³ approaches a neutrally buoyant condition, which is not favorable for effective reattachment. As shown in Figure 1b, the Bond number ranges from below 1 to approximately 28 for the various densities of PFCL. For Bo < 1, the PFCL remains nearly spherical, resulting in point contact with the retina. In contrast, when Bo > 1, the PFCL flattens and forms surface contact with the retina, as indicated by the shaded regions in Figure 1a.

The contact area between the PFCL and the retinal surface is governed by a balance between interfacial energy and gravitational potential energy associated with the PFCL (see Supplementary Materials for the detailed derivation). Figure 2a presents the variation of the contact angle θ_C with the PFCL volume fill ratio. At low fill ratios, θ_C remains small, indicating a point contact configuration corresponding to Bo < 1, as previously shown in Figure 1b. Additionally, the values of θ_C with V/V_o are less pronounced for a density of 1200 kg/m³ compared to 2000 kg/m³, due to the reduced gravitational potential energy in the system.

Figure 2.

(a) Variation of the contact angle θ_C with PFCL volume fill percentage for PFCL densities of 1200 kg/m³, 1500 kg/m³, and 2000 kg/m³. The contact angle increases with both PFCL volume and density difference, indicating enhanced spreading behavior. (b) Distribution of contact pressure P_C as a function of angular position θ for different PFCL volume fill percentages 1% (blue), 20% (red), 40% (green), 60% (magenta), 80% (purple), and 93% (black) for PFCL density of 2000 kg/m³. The pressure distribution becomes broader and more intense with increasing fill volume, indicating greater surface contact with the retina.

Figure 2b presents the angular distribution of contact pressure P_C for various PFCL volume fill percentages: 1%, 20%, 40%, 60%, 80%, and 93% for a PFCL density of 2000 kg/m³. The pressure profile is symmetric about θ = 0°, which corresponds to the bottom-most point of the cavity. At a low fill percentages (e.g., 1%), the pressure is sharply localized near the droplet apex, indicating limited contact area with the retina. With increasing fill volume, the peak pressure becomes more pronounced, and the spatial extent of the distribution widens, suggesting a transition from point contact to surface contact between the PFCL and the retinal surface. This transition is consistent with the increasing Bond number and contact angle trends observed in Figures 1b and 2a, respectively.

For higher density, both the magnitude and growth rate of maximum contact pressure P_C,max increased, indicating stronger localized pressure exerted on the retinal surface during later stages of PFCL injection. The corresponding evolution of the maximum contact pressure P_C,max is shown in Figure 3 for different PFCL densities. Notably, a local minimum in P_C,max is observed at low fill percentages, particularly for lower density PFCLs. This behavior indicates a transitional regime wherein the PFCL changes from a localized droplet exerting pressure at a single point to a configuration exerting distributed pressure across a broader area. As the PFCL volume continues to increase, the maximum pressure rises significantly, especially for higher density PFCLs, highlighting the importance of carefully balancing fluid properties and injection volume to avoid excessive mechanical stress on the retinal surface.

Figure 3.

Variation of the maximum contact pressure P_C,max with PFCL volume fill percentage for different densities of 1200 kg/m³, 1500 kg/m³, and 2000 kg/m³.

Simulations

To understand the deformation of the retina under PFCL-induced loading, three-dimensional simulations were performed using COMSOL Multiphysics, interfaced with MATLAB (MathWorks, Natick, MA, USA). All simulations were performed on version 5.6 of COMSOL Multiphysics on a workstation equipped with an Intel Core i3-2120 CPU (Intel Corporation, Santa Clara, CA, USA) at 3.30 GHz and 12-GB RAM. The typical computational time for each simulation was approximately 1 to 3 hours, depending on the mesh resolution and parameter settings. The geometry used in the simulations is shown in Figure 4a. The inner retinal radius was taken as R_i = 1.045 cm, and, assuming a retinal thickness of H = 250 µm, the outer retina is of the radius R_o = 1.07 cm. The retina was modeled as a linear elastic material with Young's modulus = 20 kPa¹⁶ and Poisson's ratio ν = 0.5. The retina swept an angular span of θ_o = 115°, corresponding to the anatomical location of the ora serrata within the eye.

Figure 4.

(a) Geometry used for the COMSOL simulations. (b) Schematic illustrating the locations of the retinal break and macula within the simulation domain. The red arrows indicate three different views of the three-dimensional diagram. View-1 corresponds to the x–z plane with the positive y-axis pointing outward; View-2 corresponds to the y–z plane with the negative x-axis direction; and View-3 represents the x–z plane viewed along the negative y-axis, from which the break is not visible. (Note that points P and D coincide when the retina is not detached.) (c, d) Schematic representing the retinal displacement where point P is a surface point that indicates the attachment site between the retina and the RPE, point D marks the detached configuration of point P, point A corresponds to the reattached state of point P after PFCL application in c, and point Q represents the point in unattached area due to accumulation of SRF.

For the purpose of detachment and reattachment modeling, the retinal break was positioned at θ = 90°, ϕ = 90°, and the macula was located at θ = −15°, ϕ = 6°. The break was assumed to be circular and have a diameter of 1 cm. In addition to the retina, the RPE was included in the model as a rigid boundary with radius R_RPE = 1.12 cm. The subretinal space between the RPE and the outer retina was filled with SRF, with an initial uniform height of h = 500 µm. It is important to note that we assumed the retinal stretch due to the detachment to be zero. The SRF was assumed to have viscosity μ = 10^–3 Pa·s and density ρ_o = 993 kg/m³.

During surgery, PFCL is injected into the posterior segment. In the simulations, it was assumed that PFCL is introduced at a fill rate of 1% of the posterior segment volume V_o per second, until the fluid reaches the retinal break. Because the break is located at θ = 90°, ϕ = 90°, as shown in Figure 4b, the total PFCL volume injected was taken to be 60% of V_o and the corresponding contact angle is shown in Figure 2a. The corresponding pressure distribution (as shown in Figure 2b) was applied as a time-dependent load on the inner retinal surface. Specifically, the pressure corresponding to 1% of V_o was applied during the first second, 2% during the second, and so on, until the distribution corresponding to 60% of of V_o was reached at 60 seconds. This load was then held constant from 60 seconds to 900 seconds, after which the pressure was linearly released over the final 30 seconds (900 seconds to 930 seconds), simulating PFCL removal.

For boundary conditions, the retina was fixed at the ora serrata. At the outer retina and SRF interface, a balance of normal elastic and hydrodynamic stresses was enforced. The pressure at the break location was set to zero. The RPE was treated as a rigid, stationary surface with no fluid absorption during the simulation.

The simulations were conducted using the Solid Mechanics interface under the Structural Mechanics module and the Thin-Film Flow¹⁷ interface from the Computational Fluid Dynamics module in COMSOL. The governing lubrication equation for the SRF and the solid deformation equations for the retina were coupled and solved using a time-dependent solver over a total simulation duration of 930 seconds.

The meshing for the coupled solid fluid simulations was carried out in COMSOL Multiphysics with an emphasis on balancing computational efficiency and numerical accuracy. The final mesh consisted of 29,398 tetrahedral elements and 20,454 triangular surface elements, with a total of 10,245 mesh vertices. The average element quality, based on skewness, was 0.5761, with a minimum element quality of 0.1091, indicating an overall well-structured mesh suitable for capturing the physics of retinal deformation and subretinal fluid flow. The element volume ratio was maintained at 0.0398, and the total mesh volume was approximately 2.501 × 10^–7 m³. To better resolve the region around the break, a finer mesh was applied locally, and a coarser mesh was used in regions with relatively uniform behavior.

Results

The pressure exerted by the PFCL on the retina during the filling process induces significant mechanical responses within the subretinal space. As the PFCL fills the posterior segment, it applies a spatially varying pressure on the inner retinal surface, with the maximum pressure typically occurring at the pole, corresponding to θ = 0°, as shown in Figure 2b. This localized pressure drives the displacement of the SRF¹⁸ away from the posterior pole toward the ora serrata.

The movement of SRF in response to the PFCL-induced pressure gradient results in the generation of shear or tangential stresses along the interface between the retina and the RPE. These tangential stresses contribute to the lateral deformation of the retinal tissue, manifesting as stretch in the plane of the retina. The extent of this tangential stress depends on the pressure gradient, viscosity of the SRF, and the geometric constraints of the vitreous cavity. Moreover, the retina experiences additional axial or radial stretching due to the normal loading applied by the PFCL. Because the edge of the retina is anatomically anchored at the ora serrata, it acts as a fixed boundary.

The deformation of the retina during the reattachment process with PFCL leads to permanent tissue stretching, causing it to deviate from its original position even after repositioning the retina against the RPE and after removing the PFCL. To quantify this residual deformation, we define a representative point on the retina, initially in contact with the RPE, as point P with coordinates (x_P, y_P, z_P) as indicated in Figure 4c. Upon detachment, this point is displaced to a new location, point D (x_D, y_D, z_D), such that the radial distance between P and D corresponds to the SRF height of approximately 500 µm After the retina reattaches, the corresponding material point does not return to P but instead relocates to a new position, A (x_A, y_A, z_A), due to elastic stretching or it can be at point Q in the regions where SRF can be accumulated.

The residual displacement, d, arising purely from retinal stretching, is quantified as the Euclidean distance between the mapped point P and its reference location either A or R, depending on the spatial location of the point. In the attached region, the residual displacement is purely meridional and occurs between points P and A, as expressed in Equation 2a. In contrast, within the detached region, the residual displacement is comprised of both meridional and radial components and is measured between points P and Q as defined in Equation 2b. Mathematically, this is expressed as

$$\begin{array}{c}\hfill d=\sqrt{{\left(x_A-x_P\right)}^2+{\left(y_A-y_P\right)}^2+{\left(z_A-z_P\right)}^2}\end{array}$$ (2a)

or

$$\begin{array}{c}\hfill d=\sqrt{{\left(x_Q-x_P\right)}^2+{\left(y_Q-y_P\right)}^2+{\left(z_Q-z_P\right)}^2}\end{array}$$ (2b)

Figure 5a presents simulation snapshots of the reattachment process under a PFCL density of 2000 kg/m³ in the x–z plane. In this computational model, the initial configuration of the detached retina is taken as the reference state, and all subsequent displacements are measured relative to this baseline. At t = 0 seconds, the displacement is zero, as indicated by the uniform blue color across the retinal surface. As time progresses, PFCL-induced loading drives the retina toward the RPE, initiating reattachment. At an intermediate stage, a displacement of approximately 500 µm is observed at the pole (θ = 0°), corresponding closely to the height of the SRF layer.

Figure 5.

(a) Snapshots of distance moved by the retina surface obtained from the simulations at different time stamps represent the stretching of the retina towards the load direction. The color bar represents the distance moved by the retina from the detached position (in µm) in the x–z plane (View-1). (b) Snapshots obtained from the simulations at different time stamps represent the attachment of the retina near the break. The color bar represents the distance moved by the retina from the detached position (in µm) in the y–z plane (View-2) for the PFCL density of 2000 kg/m³.

Figure 5b shows snapshots at the same time points as in Figure 5a but in the y–z plane. It is evident that SRF accumulates in regions far from the break, resulting in displacements exceeding 500 µm, as indicated by the color scale. In contrast, the region near the break undergoes reattachment, facilitated by the drainage of SRF back into the vitreous cavity.

Using the simulation output from COMSOL, the displacement of each material points on the retinal surface from its original configuration (P) is computed using Equation 2. This computation is repeated for all points across the retinal surface to map the fullfield residual displacement. The results corresponding to the time points illustrated in Figure 5 are presented in Figures 6a and 6b in the x–z and y–z planes, respectively, highlighting the spatial variation of retinal displacement over time.

Figure 6.

(a, b) Displacements in the retina calculated using Equation 2 and the distance results obtained from the COMSOL at the same time stamps shown in Figure 5 in the x–z plane (View-1) (a), and the y–z plane (View-2) (b) for the PFCL density of 2000 kg/m³.

From a medical perspective, Figures 5 and 6 describe two distinct but complementary aspects of retinal behavior during PFCL-assisted reattachment. Figure 5 illustrates the overall movement of the retina relative to its detached position as PFCL is introduced, representing the gross intraoperative reattachment process in which the retina is drawn toward the RPE through the displacement of subretinal fluid. Figure 6 quantifies the residual displacement of the retina relative to its original pre-detachment anatomical position, thereby isolating deformation caused by retinal stretching rather than simple radial motion. Clinically, this distinction is essential because a retina that appears fully reattached may still be mechanically stretched and imperfectly realigned with the underlying RPE, which helps explain postoperative findings such as retinal vessel printings and subtle photoreceptor misalignment on fundus autofluorescence or OCT imaging. A key limitation of this analysis is that the model assumes the retina to be unstretched in its detached state and therefore does not account for any pre-existing stretch that may occur during the detachment process itself. In reality, retinal detachment can already induce mechanical deformation before surgery, and this preoperative stretch may contribute to the total postoperative displacement observed clinically. Consequently, the residual displacement reported here likely represents a lower bound; future models incorporating detachment-induced retinal stretch would provide a more comprehensive representation of retinal biomechanics during RRD repair. However, the actual postoperative retinal displacement is therefore likely the cumulative effect of detachment related stretch and the additional deformation introduced during surgical manipulation and PFCL loading. To better understand the displacement profiles shown in Figure 6, a FAF image (Figure 7a) was used as the reference retinal image prior to PFCL injection. The displacement fields obtained from the simulations in Figure 6 were artificially imposed onto Figure 7a to generate the displaced retinal image shown in Figure 7b. Figure 7c shows the overlay of Figures 7a and 7b, where the red vessel locations correspond to the original retinal position before PFCL injection, and the green vessel locations correspond to the displaced retinal position after PFCL injection. The generated overlay qualitatively demonstrates the displacement patterns predicted by the simulations in Figure 6, with larger displacement observed toward the periphery and smaller displacement near the optic nerve head. In addition, the displacement magnitude is relatively smaller in the vicinity of the retinal hole. These projected Optos-like images provide a clinically relatable representation of the simulated retinal displacement patterns after PFCL injection. Figure 7d is a magnified version of the central macular area of Figure 7c and demonstrates the retinal displacement in the vicinity of the fovea. Figure 7e shows an enlarged view of the foveal region where the displacement between the pre-PFCL and post-PFCL retinal positions is clearly visualized. Figure 7f is an enlarged view of the supertemporal vascular arcade and shows that the retinal displacement is greater in the peripheral retina than at the posterior pole. Finally, Figure 7g schematically shows the displacement vector at the fovea, which represents the magnitude and direction of retinal movement after PFCL injection, thus providing a quantitative visualization of the simulated retinal displacement.

Figure 7.

Optos-like representation of simulated retinal displacement following PFCL injection. (a) FAF image used as the reference retinal image prior to PFCL injection. (b) Artificially displaced retinal image generated by deforming the reference image according to the displacement patterns predicted by the computational simulations. (c) Overlay of the reference and displaced retinal images demonstrating the relative retinal vessel displacement. In the overlay image, the red vessel locations correspond to the original retinal position before PFCL injection, and the green vessel locations correspond to the displaced retinal position after PFCL injection. (d) Magnified view of the central macular region from the overlay image highlighting the superotemporal retinal displacement. (e) Enlarged view of the foveal region showing the simulated foveal displacement. (f) Enlarged view of the superotemporal arcade demonstrating the corresponding retinal displacement. (g) Schematic representation of the simulated foveal displacement vector, indicating the magnitude and direction of retinal movement between the pre-PFCL and post-PFCL configurations.

Figure 8 illustrates the displacement of the retina under different PFCL densities of 1200 kg/m³, 1500 kg/m³, and 2000 kg/m³ corresponding to Figures 8a, 8b, and 8c, respectively. As described in the previous section, PFCL is injected at a fill rate of 1% of the posterior segment volume V_o per second for a duration of 60 seconds. At t = 0 seconds, the displacement is uniformly 500 µm throughout the retina, representing the initial detachment height. As PFCL loading progresses, a pressure gradient develops, with the maximum pressure applied at θ = 0°. This causes the retina to reattach to the RPE at θ = 0° initially, displacing SRF toward the periphery. The fluid in proximity to the break flows back into the vitreous cavity, whereas fluid located farther away accumulates in the subretinal region, creating the bulged regions. In the reattached zone, at 900 seconds, the displacement of the retina, which is now in contact with the RPE, lies in the range of 200 to 600 µm, representing the deviation from the original attached configuration. In contrast, regions that remain detached exhibit displacements exceeding 600 µm, which include both the stretching-induced deformation and the radial separation from the RPE. When the PFCL filling is done by 60 seconds, it is left in the posterior segment until 900 seconds. Due to this fixed load, the fluid displacement continues to happen, as it is evident from Figure 8 that the displacement at θ = 90° has increased from t = 60 seconds and t = 900 seconds. Furthermore, the color bar in Figure 8 at 900 seconds indicates that the displacement is greater when a heavier PFCL is used. From 900 seconds to 930 seconds, the PFCL is being removed, resulting in removal of the loading. Due to the reduction in the load, some of the SRF tries to flow backward, and the retina tries to relax. It is evident from Figure 8 between the time stamps of 900 seconds and 930 seconds that there is a reduction of the subretinal region height in the bulged region and a decrease in the displacement. The displacement profile shown in Figure 8 until 900 seconds (loading and holding stage) is similar to the finding of Marafon et al.,¹³ where the retina was found to be substantially displaced in the direction of subretinal fluid flow toward the open retinal break.

Figure 8.

Temporal evolution of retinal displacement for different PFCL densities in the x–z plane (View-3) shown in Figure 4b: (a) 1200 kg/m³, (b) 1500 kg/m³, and (c) 2000 kg/m³. Each row shows the displacement profiles at key time points of 0, 30, 60, 900, and 930 seconds during PFCL injection, holding, and removal. Initially, the displacement is uniform (500 µm) across the retina due to detachment. With progressive PFCL loading, the retina begins to reattach near θ = 0°, causing the subretinal fluid to redistribute and bulge in peripheral regions.

The displacement at the macula region, located at θ = −15°, ϕ = 6°, as obtained from the simulations, is presented in Figure 9. As shown in Figure 8a, macular displacement increases steadily until a dynamic equilibrium is reached between the applied load and the fluid-induced stresses. This progressive rise is initially governed by the increasing PFCL volume being introduced into the vitreous cavity over the first 60 seconds, resulting in a growing pressure load on the retina. Beyond 60 seconds, the applied load remains constant, allowing the system to reach a quasi-steady state where the mechanical deformation of the retina balances the hydrodynamic resistance from the SRF. The maximum displacement observed at the macula varies from approximately 210 µm to 240 µm, depending on the density of the PFCL, highlighting the significant role of PFCL density in modulating the mechanical response of the retina. A denser PFCL leads to higher pressure, resulting in greater deformation. In contrast, a PFCL with lower density induces less pressure, leading to reduced macular displacement up to 30 µm lower than the denser counterpart.

Figure 9.

Temporal evolution of retinal displacement for PFCLs of varying densities. (a) Displacement at the macula region located at θ = –15°, ϕ = 6°, showing progressive increase followed by stabilization and eventual drop during PFCL removal. (b) Displacement at the location of the retinal break at θ = 90°, ϕ = 90°, capturing the dynamics of immediate reattachment and subsequent stabilization throughout the PFCL injection and removal phases.

After 900 seconds, the removal of the PFCL begins, resulting in a rapid drop in the applied pressure on the inner retina. This causes a reversal in the fluid flow direction, with some SRF moving back toward the macula. In doing so, it separates the retina from the RPE, leaving approximately 15% to 20% of the SRF remaining. This backward flow results in a residual bleb of fluid, particularly in locations far from the drainage site, which will take some time to reabsorb by the RPE. In Figure 9, to isolate the surface deformation of the retina from the total displacement, the radial distance between the retina and the RPE has been subtracted from the displacement values. The resulting plot captures the net surface displacement in the macula (i.e., the deviation from its original attached configuration) rather than the absolute distance from the RPE. The final displacement is in the range of 100 µm, indicating a residual stretch in the retina even after the PFCL is removed. Because the retina has been modeled as a linearly elastic material, it exhibits elastic recovery upon the removal of PFCL loading. However, the recovery is incomplete, indicating residual deformation. This lasting deformation can have clinical relevance, particularly in relation to post-operative functional and anatomic outcomes.

Similarly, the temporal variation of displacement at the location of the break, positioned at θ = 90°, ϕ = 90°, is illustrated in Figure 9b. During the initial phase (0–60 seconds), a gradual increase in displacement can be observed, corresponding to the accumulation of SRF and the subsequent increase in the height of the subretinal space. This increase results from the progressive loading of the PFCL, which drives the fluid toward peripheral regions, temporarily elevating the retina in the vicinity of the break. Beyond 60 seconds, as the PFCL filling ceases and the applied load stabilizes, the displacement begins to decline. This reduction is attributed to the gradual drainage of the subretinal fluid through the break and the corresponding settling of the retina toward the RPE. The displacement eventually reaches a plateau, indicating the point at which the break is in contact with the RPE, signifying local reattachment.

As observed in the macular region, a sharp drop in displacement occurs after 900 seconds, when PFCL removal begins. This decline is due to the reversal of the pressure gradient, which induces a backward flow of fluid, leading to a transient separation between the retina and the RPE. This behavior emphasizes the dynamic mechanical response of the retina during both PFCL injection and removal, highlighting the sensitivity of reattachment to changes in fluid pressure and PFCL density. Such variations of displacement near the break can be seen in Figure 6b. In addition to the displacement, PFCL injection and removal can also lead to stretching of the break, as shown in Figure 5a. This stretching transforms the circular break into an elliptical shape during injection, after which it tends to regain its circular form during removal. However, it should be noted that the break may not be perfectly circular initially, as assumed in the model.

The current model treats the retina as a linear elastic tissue, meaning that recovery occurs instantly after the load is removed and deformation is proportional to the applied load. Both the direct compressive load from the PFCL and the shear stresses caused by pressure-driven subretinal fluid flow deform the retina during PFCL injection. When the PFCL is removed, these external loads are eliminated, allowing the retina to relax. However, the simulations show that the retina does not fully return to its original pre-detachment configuration.

This incomplete recovery is partly explained by the presence of residual SRF, with approximately 10% to 15% of the fluid remaining trapped in the subretinal space after PFCL removal. Even in the absence of PFCL, this residual fluid maintains a separation between the retina and the RPE, continuing to impose geometric and mechanical constraints on the tissue. Within the framework of linear elasticity, these constraints are sufficient to prevent complete reversal of strain, resulting in a persistent surface displacement of roughly 100 µm.

It is essential to emphasize that this residual deformation may not be interpreted as permanent retinal damage. The linear elastic formulation used here does not account for time-dependent tissue behavior¹⁹ such as viscoelastic relaxation, creep, or biological remodeling, nor does it include active absorption of SRF by the RPE. In the clinical setting, these processes promote further relaxation of the retina over time. As such, the residual stretch predicted by the model likely represents a short-term mechanical outcome following PFCL use rather than a final long-term anatomical state.

Discussion

From the simulation results shown in Figures 9a and 9b, it is evident that the displacement of the retina at both the macula and the break regions is lower when using PFCL with a lower density. This indicates that lighter PFCL exerts less force on the retina, leading to reduced deformation during reattachment. However, it is important to note that the density of the PFCL should not fall below 1200 kg/m³, as the density of the SRF is approximately 993 kg/m³.

If the PFCL density is too close to that of the SRF, it becomes nearly neutrally buoyant, which significantly reduces its ability to apply sufficient downward pressure on the detached retina to facilitate proper reattachment. Such insufficient loading can compromise the effectiveness of the reattachment process, especially in critical areas such as the macula. Therefore, although higher PFCL densities are more effective in applying the required load for reattachment and the removal of SRF, they also result in larger retinal displacements that must be carefully managed.

These results show how important it is to choose the right properties for PFCL, especially its density, for retinal surgery. Using the optimal PFCL density would help to reduce displacement of the retina and improve the chances of a better “integrity” of anatomic reattachment. It is also important to consider if PFCL is needed at all, because, irrespective of its density, PFCL will always lead to some amount of retinal displacement. Other considerations such as patient head positioning and the type and size of the tamponade are also relevant. It is now well known that a large gas tamponade is the major cause of postoperative retinal displacement, typically in the inferior direction. It is important to highlight that the displacement/stretch occurring as a result of adjunctive intraoperative PFCL that is removed during surgery is different and in some ways unrelated to the displacement occurring postoperatively as a result of the buoyant force of the large gas bubble. Although they both result in stretching of the retina, they will occur in different directions related to the corresponding induced fluid flow. This highlights how every part of retinal detachment repair must be carefully examined to assess its inadvertent impact on the delicate elastic retinal tissue. Importantly, the present results are derived from an idealized, non–patient-specific computational framework rather than direct clinical observations. Although qualitative parallels may be drawn with phenomena such as retinal vessel printings or other biomarkers of retinal displacement, these associations remain hypothesis driven and require validation against case-specific clinical data.

Building on the insights gained from the present study, we are currently developing more comprehensive models to investigate the influence of various parameters on retinal displacement. These include the location and size of the retinal break, the rate of PFCL infusion, and the duration for which PFCL remains in the eye. Understanding these factors in an integrated manner will help improve surgical planning and outcomes in retinal reattachment procedures. Although the infusion rate was not explicitly varied in the present work, it is expected to primarily influence the transient evolution of pressure and SRF flow during the early stages of PFCL filling, with limited impact on the final deformation when equilibrium is reached. Similarly, although the site of injection may, in principle, affect local flow patterns, the high density of PFCL leads to rapid settling and the formation of a dependent layer within the vitreous cavity, making the overall pressure distribution and thus global retinal deformation largely independent of the initial injection location. Any effects of injection site are therefore likely to be confined to localized perturbations associated with the injection jet, with minimal influence on the overall displacement patterns. Understanding these factors in an integrated manner will help improve surgical planning and outcomes in retinal reattachment procedures.

Although the use of PFCL has significantly advanced the management of complex retinal detachments, there are limitations associated with mechanical interactions with retinal tissue. PFCL, due to its high density, applies substantial localized pressure on the retina, which can lead to residual retinal displacement/stretch. This computational model offers a framework to study these effects, allowing for the simulation of different PFCL properties and fluid dynamics to identify strategies that minimize retinal displacement and optimize reattachment outcomes.

Conclusions

The fluid mechanical mechanisms causing retinal displacement during PFCL-assisted RRD repair were examined in this work using a comprehensive computational framework. The simulations revealed that the maximum displacement at the macula ranges from approximately 210 µm to 240 µm, and the residual stretch after the removal of PFCL is approximately 100 µm, depending on the density of the PFCL. These findings underscore the critical role of PFCL density in modulating the mechanical response of the retina and aim to inform the development or selection of PFCLs that minimize postoperative displacement and improve anatomic outcomes. The simulations further showed that the retina is subjected to higher contact pressures from PFCLs with higher densities, which causes tissue stretching and residual displacement even after reattachment and PFCL removal. Conversely, if the density of the PFCL is very close to that of the SRF, it may lose its ability to effectively reattach the retina or remove the subretinal fluid, despite imposing less mechanical loading. Hence, there has to be a balance between the reattachment and mechanical loading. Also, it has been shown that PFCL removal leads to relaxation of the retina, resulting in elastic recovery, although there is still approximately 100 µm of residual stretch. In order to study how variations of surgical techniques for retinal detachment repair may maximize outcomes, future developments of this model will incorporate additional surgical parameters such as injection speed and duration of intraoperative PFCL use.