Project

Overview

Introduction

The vitreous humor is a clear, gel-like substance that fills the space between the lens of the eye ​and the retina. It helps maintain the round shape of the eye and allows light to pass through to ​the retina, where images are formed.

The vitreous humor is composed mainly of water (approximately 99%), along with a network of ​collagen fibers, hyaluronic acid, and various electrolytes. Here's a breakdown of its composition:

1. Water: Approximately 99%.
   
2. Collagen fibers: Provide structural support.
   
3. Hyaluronic acid: A clear, gooey substance that gives the vitreous humor its gel-like ​consistency.
   
4. Electrolytes: Including sodium, potassium, chloride, and bicarbonate ions
   

The viscosity and density of vitreous humor can vary slightly among individuals, but ​generally, the viscosity of vitreous humor is about 4 to 5 centipoise (cP), and its density ​is approximately 1.004 g/cm3.

Vitreous humor has complex viscoelastic properties, and although there have been ​several attempts to characterize its properties experimentally (Lee et al. 1992, ​Nickerson et al. 2008, Swindle et al.2008, Zimmerman 1980), its rheology is not fully ​understood.

It is known that the vitreous humor becomes progressively liquefied with age; ​approximately 20% of the vitreous humor is liquid in 14–18-year-olds, and this rises to ​more than 50% in subjects aged 80–90 years (Bishop 2000).

In approximately 25%–30% of subjects, liquefaction can lead to a process in which the ​retina

detaches, risking loss of sight.

Saccadic Motion

In this context, it is also important to note that the eye is not normally stationary, even when ​apparently focused on a fixed point. Instead, the eye constantly executes a series of extremely ​rapid angular rotations (300◦ s−1 or more) known as saccades (Rayner 1998)

Saccadic eye movements are quick, simultaneous movements of both eyes in the same ​direction. They're used to obtain the best possible vision by directing the line of sight to a new ​location.

During a saccadic eye movement, the rotation of the eyeball is typically very rapid. The ​rotation angle can vary, but it's usually between 1 and 60 degrees, and the duration of ​the movement is typically between 20 and 200 milliseconds.

So, during a saccade, the eyeball can rotate anywhere from 1 to 60 degrees, depending ​on factors such as the distance of the target and the individual's eye movement ​characteristics.

During reading, for example, saccadic movements direct the eyes from word to word. ​These movements are rapid and usually cannot be voluntarily controlled.

Why study vitreous humor dynamics

Vitrectomy, a surgical procedure involving the removal of some or all of the vitreous ​humor from the eye, is commonly used to treat various eye conditions such as retinal ​detachment, macular holes, diabetic retinopathy, and vitreous hemorrhage

. After vitrectomy, the removed vitreous humor is often substituted with silicone oil ​to maintain the shape of the eye and provide support to the retina. This silicone oil is ​gradually replaced over time, first with balanced salt solution (BSS), and eventually ​with the eye's natural aqueous humor.

The effects of eye motion on the dynamics of the vitreous humor, both in aged ​individuals and in those who have undergone vitrectomy, are of interest to ​researchers. Understanding these dynamics is crucial for optimizing surgical ​techniques, improving patient outcomes, and developing new treatments for various ​eye conditions

Motion of the vitreous humor during the wall ​rotation due to eye saccadic movements

During saccadic eye movements, the motion of the vitreous humor against the wall of ​the eye can be described as follows: Slightly turbulent flow

Saccadic eye movements induce a turbulent flow within the vitreous humor.

The hypothesis currently followed is that the motion of the vitreous humor during wall ​motion, particularly induced by saccadic eye movements, is influenced by factors such ​as chamber shape, saccade amplitude, size of lens indentations, and viscosities

MODEL ​DECRIPTION

MODEL SHAPE

MODEL SHAPE :: Sphere shape , radius 12 mm

Enclosure sphere ( boundary FOR THE sclera ( EYE WALL ))

Inner Sphere for the Vitrous Humor

No Space between the spheres ( 0 mm )

Automatic mesh is applied ( across the boundaries )

GOVERNING EQUATIONS::

The k−ω model is a two-equation model commonly used in computational fluid dynamics (CFD) ​simulations.

In this model, the transport equations for kinetic energy (k) and specific dissipation rate (ω) are ​solved. The governing equations for the k−ω model are as follows:

GOVERNING EQUATION ::k w model

THIS IS MORE APPROPRIATE MODEL THAN NAVIER STOKES , AS PROVED IN THE ​RESEARCH PAPERS

These equations, along with appropriate initial and boundary conditions, are solved numerically ​to simulate the fluid flow.

These boundary conditions depend on the specifics of your simulation setup and the behavior ​of the fluid at the walls. Typically, for "no-slip" walls, the boundary conditions for kk and ωω are ​set to zero gradient.

∂k/∂n=0( kinetic energy normal to the direction of the wall is zero )

∂ω/∂n=0(specific turbulent dissipation rate is zero )

N is the normal direction to the wall

BOUNDARY CONDITIONS :

The vitreous cavity is moved with a specified angular velocity

for the boundary.

The no-slip boundary condition was set for the wall which

means the fluid adjacent to the wall has the same velocity.

The "no-slip" boundary condition can be applied to the walls of the eye, which states that ​the velocity of the fluid at the wall is equal to the velocity of the wall:

MESH GENERATION ::

A structured 3-D numerical mesh was generated for numerical

model of the vitreous

MODEL STRUCTURE

enclosure sphere for eye ​wall

inner sphere for vitreous ​humor

MESH STRUCTURE

MATERIAL PROPERTIES

Static

In the actual motion a lot of intricate meshing needs to be ​done to get the accurate velocity and shear stress

This is the actual mesh used in the research paper

Understanding the ​Physics behind it

Eye Geometry

The diameter of the eye was considered to be 24 mm and will show only a variation of 1-2mm in ​the case of humans

Understanding the eye movement during saccadic movement

ANGULAR ​VELOCITY VS ​TIME

ANGULAR ​DISPLACEMENT ​VS TIME

velocity has ​acceleration , ​constant velocity ​( maximum ) and ​deceleration ​phases

Phases of Saccadic Movement:

1. Acceleration Phase:
   
• Angular Displacement: Rapid increase from initial fixation point to maximum ​displacement.
  
• Angular Velocity: Rapid increase to maximum velocity.
  
2. Maintained Velocity Phase:
   
• Angular Displacement: Maintained at maximum displacement.
  
• Angular Velocity: Remains constant at maximum velocity.
  
3. Deceleration Phase:
   
• Angular Displacement: Rapid decrease from maximum displacement to final ​fixation point.
  
• Angular Velocity: Rapid decrease from maximum velocity to zero.
  

Saccadic movements are defined based on the saccadic amplitude( maximum ​displacement of the eye ) , and time duration . A fifth order polynomial equation ​represents this

The saccadic amplitude that we have considered is 50 degrees ( in reality it lies ​between 10 to 40 degrees )

We set the angular displacement to 50 degrees under the rotational motion of angular ​velocity of 10 radian per sec

How did we calculate the shear stress

After modeling , in Ansys Fleunt , selected the inner vitreous sphere chamber ( surface ​selection ) and computed the shear stress at a point on the surface of the vitreous body ​vs time taken for the motion to complete

The time is automatically calculated using the velocity of the wall motion and the ​boundary ( saccadic displacement boundary ) from 0 to 50 degrees

Variation in the shear stress

The shear stress would increase and decrease as the eye moves, reaching maximum ​values at certain points in the eye movement cycle.

Increase in Shear Stress:

As the eye starts to rotate, the vitreous humor near the wall experiences a shearing ​force due to the motion of the wall.

Initially, as the eye begins to move, the shear stress increases rapidly because of ​the rapid change in motion.

Due to the "no-slip" boundary condition, the vitreous humor at the wall is stationary, ​resulting in zero velocity and shear stress at this point.

Maximum Shear Stress:

The shear stress reaches its maximum value when the eye movement is at its peak. At ​this point, the velocity difference between the vitreous humor and the wall is greatest, ​resulting in maximum shear stress.

This maximum shear stress corresponds to the moment when the eye movement is ​most rapid.

Due to the "no-slip" boundary condition, the velocity of the vitreous humor at the wall ​is equal to the velocity of the wall, resulting in maximum shear stress.

Decrease in Shear Stress:

As the eye movement slows down and eventually stops, the shear stress decreases.

When the eye movement reverses, the shear stress changes direction, but it still causes ​deformation in the vitreous humor.

Due to the "no-slip" boundary condition, the vitreous humor at the wall slows down as ​the wall slows down, resulting in a decrease in shear stress.

AT THE MAX ​AMPLITUDE ​THE ​VELOCITY ​AND SHEAR ​STRESS WILL ​MAXIMIZE

GRAPHS GENERATED IN THE RESEARCH PAPER

Both the graphs are vitreous humor shear stress vs time

decrease in shear stress

maximum shear stress

GRAPHS GENERATED USING THE MODEL

Two graphs(shear stress vs time) were generated for 2 particles on the surface of the vitreous humor as highlighted as the Red and the Blue lines

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GRAPH GENERATED WITH A DIFFERENT MODEL

Green Line shows the graph for the particle on the ​surface of the vitreous humor

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Reasons for the difference in the graph

1. Appropriate intricate meshing could not be done ( poor quality meshing ( automatic mesh ) ( ​static mesh ) , however the mesh needs to be applied at each position intricately
   
2. We consider a Newtonian fluid properties for the vitreous humor , when in reality it has non - ​newtonian dynamics
   
3. Appropriate conformations ( like the position of the lens , the position of the aqueous humor ​) also could not be added , thereby leading to certain discrepancies
   
4. Boundary conditions , also had to applied to multiple surfaces ( different boundary ​conditions ) , which we were not able to model
   
5. Certain model assumptions , were made , which lead to generalized movement , we could ​not consider the length of the lens , variation in saccades etc .
   

Reynold’s number calculation

Given ::

• Density of vitreous humor: 1.0053 g/cm^3 to 1.0089 g/cm^3
  
• Dynamic viscosity of vitreous humor: 4 centipoise(0.0004Pa⋅s)
  
• Angular velocity ω = 10 rad/s
  

The calculated Reynolds number indicate a slightly turbulent flow

Reason for the slightly turbulent flow of the vitreous ​humor in saccadic movement

In the vitreous humor, the flow is primarily laminar, but under certain conditions, ​such as during rapid eye movements like saccades, the flow can become slightly ​turbulent.

Turbulence in the vitreous humor is generally minimal due to its high viscosity and ​the relatively low velocities involved. However, during rapid eye movements, ​especially during saccades, the sudden acceleration and deceleration of the eye can ​lead to transient increases in flow velocity, causing localized turbulence

Therefore, while the predominant type of flow in the vitreous humor is laminar, slight ​turbulence can occur under specific conditions, such as during rapid eye ​movements.

BIBLIOGRAPHY :: Research Papers

Numerical simulation of the fluid dynamics in vitreous cavity due to saccadic eye

movement

Fluid Mechanics of the Eye Jennifer H. Siggers and C. Ross Ethier

Numerical simulation for unsteady motions of the human vitreous

humor as a viscoelastic substance in linear and non-linear regimes

Flow dynamics of Vitreous Humour during saccadic eye

movements