Application of the semiimplicit method (MPS) of moving particles on a retrooily fluid using threedimensional models of vitreous cavity resulting from magnetic resonance imaging
Patient selection
This study was approved by the Institutional Review Board of Fukui University Hospital, Fukui, Japan, and adhered to the principles of the Declaration of Helsinki. Written informed consent was obtained from all patients after a detailed explanation of the procedures involved. Patients aged ≥20 years who underwent orbital MRI at Fukui University Hospital between December 1, 2014 and March 31, 2016 were included. Patients with a history that could affect the shape of the vitreous cavity at the time of MRI, such as scleral buckling, ocular trauma, vitreous hemorrhage, and ocular tumor, were excluded.
MRI
Highresolution orbital images were obtained using a 3 Tesla scanner (Discovery MR 750 3.0T; GE Healthcare, Milwaukee, WI) in combination with a 32element phasedarray head coil with sequences of fast imaging using cycled phases of steadystate acquisition. The imaging parameters were as follows: repetition time, 5.6 ms; echo time, 2.7 ms; field of view, 180mm; and matrix size, 320 × 288; and slice thickness, 0.6 mm with overlapping thickness perpendicular to the plane containing the two optic nerves. Subjects were repeatedly instructed to avoid unnecessary movements during scanning.
Creation and design of the 3D model of the vitreous cavity from MRI examinations
First, we extracted the 3D vitreous cavity model from the MRIs in all cases as a standard triangulated language format and measured the vitreous volume using Expert INTAGE (Cybernet systems Co., Ltd., Tokyo, Japan). Next, we defined the intersection of the line perpendicular to the angle with the ocular surface as the surgical limbus on the MRIs. Then, the 3D vitreous cavity model was imported and designed using threedimensional (3D) modeling software (3D Builder; Microsoft Corporation, WA, USA). First, the 3D vitreous cavity was hollowed out to generate particles inside while maintaining the original shape of the vitreous cavity. Next, we separated the 3D vitreous cavity at 1:30, 4:30, 7:30, and 10:30 into four quadrants, and then defined the position of the ora serrata of the inferior retina as 6.7 mm anatomical differences. behind the limb. Next, we set the equator 6.5 mm posterior to the ora serrata in the lower region of the retina, according to the vortex vein ampullae.^{15.16}. Therefore, the lower quadrant of the retina was separated into two parts, loweranterior and lowerposterior (Fig. 1).
CFD Analysis
Relevant equations and resolution methodology
Particleworks 7.1 (Prometech Software Inc., Tokyo, Japan) was used as a solver to simulate SO and retrooil fluid streams using the MPS method. The fundamental equations governing the MPS method are a continuous equation (law of conservation of mass) and NavierStokes equations (law of conservation of momentum) written as follows:
$$ begin{array}{*{20}c} {frac{{Dvec{u}}}{Dt} = 0} end{array} $$
(1)
$$ begin{array}{*{20}c} {frac{{Dvec{u}}}{Dt} = – frac{1}{rho }nabla P + upsilon nabla^ {2} vec{u} + vec{g}} end{array} $$
(2)
or (rho) is the density, (lived}) is the speed, (P) is the pressure, (upsilon) is the kinematic viscosity coefficient, and (vec{g}) is the acceleration due to gravity. The acceleration added to the surface was calculated from the curvature of the fluid surface as follows:
$$ begin{array}{*{20}c} {frac{{Dvec{u}}}{Dt} = – frac{1}{rho }nabla P + upsilon nabla^ {2} vec{u} + vec{g} + frac{1}{rho }sigma kappa delta vec{n}} end{array} $$
(3)
or (sigma) is the surface tension coefficient, (kappa) is the curvature, (delta) is a delta function to ensure that surface tension only works on the surface, and (vec{n}) is a unit vector in the direction vertical to the surface. Moreover, the wettability can be controlled by modifying the contact angle between the fluids and the walls.
Boundary condition
The slip condition of the wall was nonslip. The MPS method does not use a wall as a calculation point; therefore, the noslip condition is expressed by the viscosity between the fluid and the wall as follows:
$$ begin{array}{*{20}c} {upsilon_{fs} = upsilon_{f} } end{array} $$
(4)
or (upsilon_{fs}) is the kinematic viscosity coefficient between the fluid and the wall and (upsilon_{f}) is the kinematic viscosity coefficient of the fluid.
The 3D vitreous cavity of each case was imported and filled with combinations of 80% SO and 20% retrooil fluid, and 95% SO and 5% retrooil fluid. Particleworks 7.1 cannot measure shear stress but can analyze the absolute velocity gradient which is proportional to shear stress in Newtonian fluids such as SO and water. Therefore, in this study, the absolute velocity gradient (1/s) caused by saccadic eye and head movements in a seated position in which the lower retina was at the lowest position was measured in each combination of SO and retrooily fluid. The properties of SO were as follows: temperature, 37°C; density, 970 kg/m^{3}; kinematic viscosity, 0.001 m^{2}/s; and surface tension, 0.021 N/m. The properties of the retrooily fluid were the same as those of water as follows: temperature, 37°C; density, 1000 kg/m^{3}; kinematic viscosity, 1e6 m^{2}/s; and surface tension, 0.072 N/m. The contact angle of the SOretina interface was 18.2°. The setting values were as follows: particle size (initial distance between particles), 0.35 mm; gravity, −9.8 m/s^{2}.
Setting Eye Movement Parameters
Particleworks 7.1 (Prometech Software Inc., Tokyo, Japan) was used to examine the three types of saccadic eye movement^{5} in a seated position.

1.
Rotation around a vertical axis (horizontal jerky movements)

2.
Rotation around a horizontal axis (vertical jerky movements)

3.
Movement in the horizontal plane of the whole eye (rectilinear movement of the head)
The angular displacement (for rotation around the vertical and horizontal axes) was set to ⊿θ (dtheta) = 30°, while the maximum angular velocity was vtheta = 500°/s. We have described the analysis script by Particleworks 7.1 as follows:
The function derives the value (you) {var dtheta = 30; var vtheta = 500; var t0 = 1.5 if (youyou−you0)/dtheta)); otherwise returns dtheta;}.
We applied the same values for horizontal and vertical saccades.
When the head moves, the eye has both rectilinear and angular acceleration components. The contribution of rectilinear acceleration was examined separately by considering the case of an eye moving over a distance dX of about 0.1 m, with a maximum speed of vX = 1 m/s, over a period dX/ vX of about 0.05 seconds^{5}. To describe the rectilinear and unsteady movement of the eye caused by the movement of the head, we have described the analysis script by Particleworks 7.1 as follows:
function getvalue( you) {var dX = 100; var vX = 1000; varyou0 = 1.5 if (youyou×you0)/dX)); otherwise returns dX;}.
Direction of the 3D vitreous cavity
Figure 1 shows the rest positions of the 3D vitreous cavity, which represents the postoperative positions, and each position is reproduced by 3D Builder (Microsoft Corporation, WA, USA). We have previously reported that even though patients superficially maintain a strict prone position with eyes closed, the mean angle of supraduction (degrees) of the eyeball from the perpendicular line is positive (16.1°)^{15}. Therefore, the six resting positions of the eyeball examined were:

1.
Lying: The direction of the eyeball is 90° up from the horizontal line.

2.
Sitting: The direction of the eyeball is parallel to the horizontal line.

3.
Prone position with eyes closed: The angle of supraduction of the eyeball in relation to the perpendicular line is 16.1°.

4.
Inclined: The direction of the eyeball is 90° downward from the horizontal line.

5.
Inferior temporal: The eyeball is rotated 90° from the sitting position so that the temporal retina is on the horizon side.

6.
Inferior nasal: The eyeball is rotated 90° from the sitting position so that the nasal retina is on the horizon side.
Measurement of lower retinal oil coverage levels
Blender 2.90 (https://www.blender.org/) was used for the measurement of oil coverage ratios (%) of the inferioranterior and inferiorposterior retina (Fig. 2). The result of the CFD simulation analysis and the 3D vitreous cavity wireframe are simultaneously displayed, and the oilcovered area where the SO particles were in contact with the retinal wall was measured. The oil coverage rate of the lower retina with 80% and 95% SO was calculated as (oil covered area)/(total lower retina areaanterior and lowerposterior) × 100% in supine position dorsal, seated, lower nasal, lower temporal, “lying with eyes closed” and prone positions.
statistical analyzes
Statistical analyzes were performed using JMP 14 (SAS Institute Inc., Tokyo, Japan). Tukey’s honestly significant difference test was used to compare oil coverage rates in each position in the 95% and 85% oil groups. Wilcoxon’s signed rank test was used to compare the 95% and 80% oil coverage rates in each position. P values
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