Things to be Discussed

1
Things to be Discussed

• Previous work.
• Error representation, percentage or value - SD.

2
Simulation of Intrastromal Photo Refractive
Keratectomy with Picosecond Laser

• Presented By
• Ahmed Mohamed Abdul hameed
• Supervised By
• Dr. Yasser Mostafa Kadah
• Dr. Nahed Hussein Ali Solouma

3
Scope of the Work

• To model the process of the cavity collapse
  inside the cornea after the application of the
  laser, for myopic cases.
• To determine the accuracy of the model
  calculations and predictions.
• Show corneal deformation graphically.

4
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.
• Laser tissue interactions.
• ISPRK modeling.
• Finite element modeling.
• The model in steps for myopic cases.
• The model in blocks.
• Astigmatism modeling and simulation.
• Results.
• Conclusion and future work.

5
Eye Anatomy
6
The Cornea

• Functions
• Barrier protection.
• UV light filtration.
• Refraction
• Cornea provides 65-75 of eye's focusing power.
• Unlike lens, cornea's refraction power is fixed.

7
Corneal Layers

• Five distinct layers
• Epithelium
• Bowman's Membrane
• Stroma (90 of corneal thickness)
• Descemet's Membrane
• Endothelium

8
Eye refractive errors

• 1. Nearsightedness (myopia)Unfocused images
  results from light being focused before it
  reaches the retina.
• 2. Farsightedness (hyperopia)This results from
  light not being focused strongly enough to form a
  clear image on the retina.

9
Eye refractive errors

• 3. Astigmatism Cornea is football shaped, not
  round. This leads to images being unfocused.

10
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

11
Sight correction laser surgeries

• PRK Photorefractive Keratectomy.
• LASIK Laser Assisted In-Situ Keratomileusis.
• ISPRK Intrastromal photorefractive surgery.

12
PRK

• The surface of the cornea (surface epithelium) is
  reshaped using an Excimer laser.

13
Characteristics

• Advantages
• Good optical corrections is obtained.
• Disadvantages
• Regression of the achieved refractive power.
• Appearance of sub epithelial haze.
• Unpredictable healing of the cornea.

14
LASIK

• A thin surface flap of the cornea is created
  using a microkeratome (or Intralase laser) to
  expose underlying tissues (stromal bed).
• The surgeon then applies the Excimer laser beam
  to create the refractive ablation within the
  deeper layers of the cornea.
• The flap is returned to its preoperative position
  .

15
Characteristics

• Advantages
• Good optical corrections is obtained, specially
  for lower degree of refractive errors.
• Nearly no regression occurs.
• Disadvantages
• Dry eye syndrome commonly follows LASIK.
• Infections could occur as a result of the flap
  creation.

16
ISPRK

• A pulsed laser is used to photo disrupt a
  selected starting point in the stroma, then the
  beam is focused in a patterned sequence to other
  discrete points in the stroma.
• Each layer is created using subsequent laser
  pulses in a spiral pattern.

17
ISPRK

• The resultant photo disrupted tissue creates a
  layer which is centro symmetrical around the
  optical axis. A plurality of layers is removed to
  create a cavity in the stroma, that when it
  collapses, the corneal curvature is changed.

18
Characteristics

• Advantages
• No damage for corneal surface, as no flap is
  created.
• Nearly no regression or haze occurs.
• Can be used for higher degrees of refractive
  errors.
• Disadvantages
• It is not always possible to evaporate a
  homogenous cavity inside the cornea.

19
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

20
Laser tissue interactions

• Photo ablation, using Excimer lasers.
• Plasma induced ablation, using NdYLF.

21
Types of laser Photo ablation Laser

• Used in both PRK and LAISK surgeries.
• Laser pulses cause direct breaking of molecular
  bonds within the tissue by absorbing high energy
  UV photons
• (Photo ablation).
• Commonly used types Excimer lasers (ArF and
  KrF).

22
Types of laser Plasma induced ablation Laser

• Used in ISPRK surgery.
• Stromal tissue is ablated by the ionizing plasma
  formation (Plasma induced ablation).
• Plasma is formed by means of the inverse
  bremsstrahlung process, which results from the
  intense local electric field created by the laser
  beam.
• The local electric field must be intense enough
  to achieve optical breakdown.
• Commonly used laser types NdYLF, NdYAG.

23
Why using picosecond pulses?

• To photodisrupt stromal tissue, the irradiance of
  the laser pulses should be equal to the optical
  breakdown threshold of the stromal tissue.
• Irradiance pulse energy/(pulse duration spot
  size).
• To achieve optical breakdown we need the
  followings
• Sufficient pulse energy (About 40 micro Joules).
• Relatively short laser pulse (In the range of
  picoseconds).
• Relatively small spot size (About 10 micro
  meters).

24
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

25
Surgery Modeling

• 1. Geometric Modeling Based upon that the
  collapse of the cavity is equivalent to removing
  a lens of the same shape as the cavity, so thin
  lens formula is used.
• 2. Finite element modeling (FEM) The cornea is
  subdivided into a certain number of elements, the
  problem is solved for each one, then a total
  solution is obtained by assembling the individual
  solutions.
• Finite element modeling incorporates the
  biomechanical effects of the cornea into its
  structure.

26
Why using FEM

• Advantageous for irregular geometry.
• Suitable for unusual boundary conditions.
• Incorporates biomechanical properties.

27
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

28
Finite elements

• Each element consists of a number of nodes.
• Each element type has a specific shape function
  that is used to predict intermediate values
  between its nodes.

29
Finite element equations

• Each element has a set of equations describing
  its structural behavior, the main equations are
• The equations and shape functions are arranged to
  form the element stiffness matrix.

30
Finite element equations

• The material properties is substituted into the
  stiffness matrix.
• An assembly process is made to assemble all
  elements stiffness matrices to form the total
  stiffness matrix.
• Boundary conditions and loads are substituted
  into the total stiffness matrix.
• Solving the next equation is the solution stage

31
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

32
FEM basic steps

• Preprocessing
• Geometry building.
• Material properties.
• Meshing Create Nodes and Elements.
• Represent the solution elements with an
  approximate continuous function (shape function).
• Assemble elements to represent the entire
  problem.
• Apply boundary conditions and loads.
• Solution
• Solve a set of equations simultaneously to obtain
  nodal results.
• Postprocessing
• Obtain other important information.

33
Model Outlines

1. Nonlinear elastic isotropic model, using an
   exponential stress strain law.
2. Axisymmetric geometry with fixed boundary
   conditions at the limbus.
3. An overall material properties model for the
   cornea is used.
4. The cavity was modeled as a gap inside the
   cornea. The gap behavior was controlled using
   contact pairs of elements.
5. No temperature effects were considered.
6. ANSYS is used to implement the model.

34
ANSYS Main Features

• Large library for element types.
• Ability to solve multiphysics problems.
• Command driven program. Facility to create
  macros.
• Dimensionless program. The implementer is
  responsible for his units.
• Available contact technology.
• Building the geometry into ANSYS or importing it.
• Ability to animate results into video files.

35
ANSYS Overview
36
Geometry and Meshing

• Geometry building
• Bottom Up modeling.
• Top down modeling.
• Combination of both.
• Import geometry from other programs or images.
• Meshing Dividing the solution domain into a
  number of finite elements (structural elements)
• Element type.
• Material Model.
• Element size.
• Free or mapped meshing.

37
The used element type

• A ten node element is used (Solid92 in ANSYS)
  that is well suited to model irregular
  boundaries. Each node has three degrees of
  freedom, translations in the nodal x, y, and z
  directions.
• The element has structural capabilities, large
  deflection and large strain capabilities.
• The element is relatively accurate, but requires
  more solution time than other structural
  elements.

38
Cavity Geometry and meshing

• The cavity is created into the cornea, and its
  surfaces is meshed using contact elements.
• Appropriate contact parameters is set for the
  current model.

39
Corneal Material Properties

• Nonlinear stress strain curve.
• Poissons ratio of 0.49.
• Density 1.4e-6 Kg/mm3.
• Index of refraction1.376.

40
Boundary Conditions and Loads

• Apply Boundary Conditions Fixation of the cornea
  at the limbus. Applied on the attached nodes to
  the limbus.
• Apply Load Intraocular pressure (IOP). Applied
  on the elements attached to the inner surface of
  the cornea.

41
Solution

• Then the boundary conditions and loads are
  applied to following general equation
• Stiffness matrix Displacement matrix
  load matrix
• This equation is solved for the nodal
  displacement matrix, which is the solution step.

42
Postprocessing

• Postprocessing step follows to calculate other
  important information, e.g. reaction forces,
  strainsetc. Also it is used to represent results
  graphically.

43
Postprocessing

• Nodal displacement of the anterior surface of the
  cornea within 3.0mm diameter (Optical zone) is
  calculated, so new coordinates of the selected
  nodes is available.
• 4 mm diameter nodes where tested, but the 3 mm
  gave closer results to the clinical data.

44
Corneal power calculation

• Curve fitting is used to calculate the new
  corneal curvature (R), using the previously
  calculated nodal coordinates
• Using least squares method, we find (R, a, b) to
  minimize
• Corneal power in Diopters
• To determine the power change, we first run the
  model with no cavity inside the cornea, then run
  it with the cavity and the change in corneal
  power is the difference between the two runs
• ?D Dnew-Dold

45
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

46
The Model in blocks
2.Geometry
1.Type of model (Structural)
3.Material properties
4.Element type
5.Meshing
No
Adequate element size
Yes
7.Create Contact Elements on the cavity
9.Apply Boundary conditions
6.Check elements
8.Apply Loads
No
No
Revise from step 2
Results acceptable
Graphical Results acceptable
12. Calculate Corneal power change
10.Solution
11.Post processing
Yes
47
Problems faced during Modeling

• Uniformity of units for material properties load,
  geometry.
• Selecting a suitable element type, with a
  sufficient number of nodes.
• Cavity creation inside the cornea (geometry
  problem).
• Contact management between anterior and posterior
  surfaces of the cavity.

48
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

49
Astigmatism Modeling

• The previous steps was followed except for the
  geometry, which is different.

50
Astigmatism Correction

• The cavity shape is different too

51
Simulation
52
Power Change

• Now we calculate curvature in the horizontal and
  vertical directions, using also curve fitting.
  Then we get the difference between them.
• For the current simulation the difference was
  -7.4 D.
• After the solution was done the difference became
  2 D.
• This shows that the cavity needs to be modified
  to achieve the appropriate correction, as an
  overcorrection has occurred.

53
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

54
Results
 

• Model results for three cavity dimensions,
  compared with an old 2D FEM model
• The first column contains three actual clinical
  treatment categories.

Error 3D FEM (D) Error 2D FEM (D) Diopter change (D) Cavity Dimensions
3.54 11.7 28.3 14.5 11.3 100?m, 4mm 1
0.64 13 27.6 16.7 13.083 120?m, 4mm 2
3.06 19 14.8 22.5 19.6 120?m, 3.2mm 3
55
Results

• The following table compares the results with the
  actual individual 9 cases

Error 3 D Model Error 2 D Model Power Change Cavity Dimensions
0.4 11.7 3.2 14.5 11.3 100?m, 4mm 1
0.4 11.7 3.2 14.5 11.3 100?m, 4mm 2
0.12 12.62 4.2 16.7 12.5 120?m, 4mm 3
1.32 12.62 5.4 16.7 11.3 120?m, 4mm 4
1.38 12.62 2.7 16.7 14 120?m, 4mm 5
3.18 12.62 0.9 16.7 15.8 120?m, 4mm 6
2.89 13.01 0.8 16.7 15.9 120?m, 4mm 7
1 19 4.5 22.5 18 120?m, 3.2mm 8
2.2 19 1.3 22.5 21.2 120?m, 3.2mm 9
56
Results

• Average error with respect to the 9 individual
  cases shows that our model has a 9.3 error, and
  the 2D model has an error of 22.2 .
• This data can be more judging on our model with
  the knowledge of the individual IOP values.

57
Intraocular pressure effect

• The following table shows the effect of
  increasing the intraocular pressure (IOP), which
  is lowering the predicted power change.
• Results agree with previous studies on IOP effect.

Difference Predicted (D) 20mmHg Predicted (D) 15mmHg Cavity Dimensions
0.6 11.1 11.7 100?m, 4mm 1
0.5 12.5 13 120?m, 4mm 2
0.65 18.35 19 120?m, 3.2mm 3
58
Presentation Agenda

• The human eye and refractive errors.

• Refractive surgeries.

• Laser tissue interactions.

• ISPRK modeling.

• Finite element modeling.

• The model in steps for myopic cases.

• The model in blocks.

• Astigmatism modeling and simulation.

• Results.

• Conclusion and future work.

59
Conclusion

• A relatively accurate model of the intrastromal
  photorefractive keratectomy procedure was built,
  using finite element modeling, and predictions
  was compared with actual clinical treatments.
  Model error is 2.5 compared to categories, and
  less than 10 compared to individual cases.
• A virtual astigmatic case was simulated, and
  correction was predicted but no clinical
  verification was made.

60
Future work

• Verify the model with more clinical data,
  especially for the astigmatism cases.
• Compare model results with laser experiments.
• Modify the model to be a probabilistic one, this
  leads to results with an error range.
• Wound healing effect modeling.
• Include sclera deformation into the model.

61
Thank you very much.