Modeling Oxygen Flow through Continuous Wear Contact Lens-Cornea
System with Increasing Protein Layer Build-up
Semyung Choi
David Day
Jonathan Kuo
Nancy Lee
Nansae Lim
BEE 453 Final Project
5/6/05
98
I. EXECUTIVE SUMMARY
The cornea requires a minimum amount of oxygen concentration to maintain normal
metabolic activity; insufficient amounts of oxygen can result in corneal edema, swelling of
cornea, and other harmful conditions. In our project design, we chose to model the Ciba Vision’s
Focus Night & Day contact lenses to determine whether or not sufficient amounts of oxygen can
diffuse into the cornea even in the presence of protein buildup. When developing our model, we
considered four different scenarios in which a variable amount of protein layers could be added;
zero to three layers to be exact. In doing so, we hoped to determine whether or not a dangerous
level of protein buildup could be reached for these specific lenses and their parameters. From our
results, we can conclude that even under the most severe protein buildup conditions, the cornea
receives adequate amounts of oxygen for proper metabolic activity. To determine whether our
assumptions were appropriate for our parameters, we performed three specific sensitivity
analyses; varying initial oxygen concentration in cornea, varying diffusivity of oxygen, and node
intervals. When varying the initial oxygen concentration in the cornea, we found that in all
scenarios the tolerable amount of oxygen was obtained. Next, when varying the diffusivity, the
time needed to reach steady state differed only by an insignificant amount. Lastly, after varying
interval count for protein layers, the mesh was shown to converge because no significant
difference resulted. After analyzing of our data and taking into consideration financial needs, we
have determined that the Ciba Vision’s Focus Night & Day contact lenses are cost effective and
a safe product for the general public.
99
II. INTRODUCTION & DESIGN OBJECTIVES
Background Information
Focus Night & Day contacts, made from a new super-permeable silicone hydrogel
material, is claimed to improve oxygen permeability by optimizing the diffusion coefficient and
oxygen solubility of the lens material, as well as the lens thickness. It is also claimed to reduce
protein buildup due to its unique biocompatible properties. Research has been conducted to
show that immediately upon insertion of the lens, protein begins to build up, and that after eight
hours of wear, about 90% of the surface area is likely to be covered with deposits. The protein
deposits come mostly from tears, which are predominantly composed of lysozyme. The contact
lens coupled with the issue of protein buildup provides a substantial resistance to oxygen
transmission to the cornea. Insufficient oxygen level in the eye tissues inhibit normal eye
functions and may cause corneal swelling, which leads to irritated, red eyes and uncomfortable
lens wear. In our project, we aim to model the oxygen flow through a Focus Night & Day
contact lens. We will monitor the oxygen gradient through the lens-protein-cornea system for 30
seconds, and determine whether the cornea is receiving a sufficient amount of oxygen at the end
of the time period to maintain its normal metabolic activity.
Design Objectives
Many studies are currently being performed to test the effects of protein deposition on the
surface of contact lenses. We believe that the presence of a growing protein layer will provide
an added resistance to oxygen transmission to the tissues in the eye. The aim of our project is to
model the changes in the oxygen being transmitted to the eye due a layer of increasing protein
buildup on the lens. This model serves to reflect a situation where a protein layer is continually
increasing, because the user is not replacing nor cleaning the lens throughout the 30 day wear
period. We aim to show how the oxygen concentration in the cornea decreases due to the
continuous growth of a protein layer between the cornea and the lens. In addition, we will
determine if the protein layer inhibits oxygen transmission to the cornea enough to become
harmful to the user.
100
Problem Schematic & Geometry:
O2 Flow
O 
2
y 0.3875
 7.944e - 6 kg / m 3
Lens = 0.08mm
cO2
y
Protein/Cornea = 0.0075mm
(each layer 0.0025mm)
0
x 0
Width = 0.3875mm
cO2
y
0
x  0.3875
Cornea = 0.3mm
5mm=0.5mm
y
cO2
x
0
y 0
x
Figure 1: Problem schematic and geometry.
Assumptions




The eye is open at all times and the concentration of oxygen at the outer surface
of the lens is equivalent to the concentration of oxygen adsorbed on the lens as given by
Henry’s Law.
Protein layer is modeled as lysozyme, with D=1.079E-06 cm2/s1
No resistance to oxygen diffusion between layers.
Lens/Protein/Cornea are modeled as a perfect slab.
101
III. RESULTS AND DISCUSSION
Mesh
Magnified Section Below
Figure 2A: Mesh used for FIDAP simulations; generated in Gambit.
Protein/Cornea 1
Protein/Cornea 2
Protein/Cornea 3
Figure 2B: Magnified section of mesh detailing Protein/Cornea regions.
102
The simulation was run four times, modeling scenarios with 0, 1, 2, or 3 layers of
protein buildup, for a duration of 30 seconds. The simulation was only run for thirty seconds
because after running the simulation for longer periods of time we noticed that a steady state
oxygen profile was reached shortly after thirty seconds. Since we are most interested in the
changes in oxygen concentration with time we decided to focus on the short time span in which
oxygen diffusion is changing. Taking this into consideration the oxygen concentration profiles
were assessed at 5seconds and 30 seconds for each scenario.
Below (Figure 4) is the concentration profile for the three protein layer scenario at the
end of the simulation and that for 0 layers of protein (Figure 3) for reference.
Figure 3: Contour plot of illustrating oxygen concentrations with 0 protein layers at t=30s.
Figure 4: Contour plot with 3 layers of protein at t=30s. Note that the concentration of oxygen
remains above 7.944e-7 kg/ m3 everywhere in the system and that the presence of the protein
layer does visibly impede oxygen transmission.
103
Even with the maximum amount of protein buildup (3 layers) one can observe that the
concentration of oxygen in the cornea remains above the required amount of 7.944e-7 kg/ m3 to
maintain healthy eye tissue. More over the whole system appears to retain a concentration of
oxygen above this minimum amount, providing evidence that, in terms of oxygen transmittance
to the cornea, neither the lens nor the protein build up is harmful to the user.
The overall effect of the protein layers on the other hand, is clearly seen if one compares
the scenario with 0 protein layers with that of 3 protein layers. Once the oxygen reaches the
protein layer its flow is instantly impeded, as indicated by the distinct yellow region in Figure 4.
This is in contrast to the situation with no protein, in which the oxygen concentration profile
gradually changes throughout the length of the system.
The Concentration vs. Time plots (Figure 5) give a better quantitative indication of how
oxygen concentration in the cornea varies with time. Nodes were chosen to approximate a
location at the start of the corneal layer regardless of scenario. From the plots it can be seen that
the effects of increasing protein layers is to slow the rate oxygen transmission to the cornea, this
clearly seen at the earlier times of the simulation (0-.5s) in which the approximate slope of the
curves decreases with increasing protein layers. Also the same steady state is eventually
reached, regardless of scenario. Finally, it should be noted that as mentioned previously the
oxygen concentration remains above the minimal requirement in all four scenarios.
Concentration vs Time
9.00E-06
8.00E-06
7.00E-06
Concentration
6.00E-06
No Protein
5.00E-06
1 Protein
2 Protein
4.00E-06
3 Protein
3.00E-06
2.00E-06
1.00E-06
0.00E+00
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
Time
Figure 5: Concentration of oxygen vs. Time with 0, 1, 2, 3 protein layers. See Figure
below for nodes chosen for plots –location of nodes were altered to reflect
same physical location between scenarios.
104
Approximate location of nodes
where above plots were generated.
Figure 6: Zoomed in mesh of protein layers with approximate location of node used to generate
above concentration plot. Colors of circled nodes correspond to respective plot color.
In general, although the presence of protein buildup does affect the oxygen transmission in
the system, it either does not have a small enough diffusivity or the buildup is not great enough
to substantially impede oxygen transmission to have harmful effects to the user.
Sensitivity Analysis
1. Initial Concentration of Oxygen in the Cornea
The oxygen concentration required to avoid corneal edema for humans was estimated to
be 10% of the concentration of oxygen in the atmosphere. One study on 8 subjects showed that
one individual required 7% O2, four required 10.1% O2, and three required 21% O2
concentrations in the cornea to avoid damage. The way this was modeled in our experiment was
by changing the value of O2 concentration in the cornea as an initial condition, and making sure
the value never decreased below the set percentage determined by the research. Contours and
nodal Concentration vs. Time plots were all provided for the three protein layer case to provide
the most significant distinction.
105
7%: [O2]=5.56e-7 kg/m3
3 protein layers, t=30s
3 Protein layers, node 321
21%: [O2]- 1.668e-7
3 protein layers, t=30s
3 Protein layers, node 321
Analysis of varying Initial Concentration of Oxygen
Varying the value of initial concentration of O2 in the cornea had no significant effect on
if the cornea O2 value fell below the threshold for damage. The contour plots show that the
Oxygen diffusion through the lens, protein, and cornea is largely unaffected by how much initial
Oxygen is present in those layers. At the time, we were unable to graph the two Time vs.
Concentration plots together, but from observation the values vary only slightly showing that the
effect is insignificant. The 7% O2 plot approaches steady state at a value of 0.70633 while the
21% O2 plot approaches a steady state value of 0.70185. This slight difference is caused by the
addition of 14% of the atmospheric O2 value inside the cornea, which shifts the plot accordingly.
This variable has little to no effect on the oxygen diffusion through to the cornea, so no negative
consequences can be shown to occur in the cornea from lack of O2.
106
2. Diffusivity of Oxygen through Cornea
The diffusivity value of Oxygen through the cornea depends on a number of factors: the
metabolic depletion, the temperature, and the density of the cornea. To insure that the value
chosen for diffusivity did not have a significant effect on the amount of oxygen reaching the
cornea, we varied the diffusivity +/- 10% as well as by +/- magnitudes of 10. The nondimensionalized value originally used was 0.199 while the new values were 0.1791, 0.2189,
1.99, and 0.0199 for the previously mentioned instances.
Contour Plots for 3 Protein Layers, t = 30s
Diffusivity of Cornea (–10%) = 0.1791
Diffusivity of Cornea (+10%)= 0.2189
Diffusivity of Cornea (by degree of 10)= 1.99
Diffusivity of Cornea (by degree of 1/10)= .0199
107
Concentration of Oxygen through Cornea vs. Time
concentration of oxygen through cornea
.
8.00E-06
7.00E-06
6.00E-06
5.00E-06
degree of 10: 1.99
4.00E-06
degree of 1/10: .0199
normal: .199
3.00E-06
-10%: .1791
+10%: .2189
2.00E-06
1.00E-06
0.00E+00
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
time
Figure 7: Graph of varying concentration of oxygen through cornea (+/-10%, degree
of 10, and degree of 1/10, and normal) against time.
Analysis of varying Diffusivity of Oxygen through Cornea
The comparison of +/- 10% with the original value shows that no significant difference
occurs for both the contour and nodal plots. This would model the situation of comparing a
single individual’s diffusivity for different times of day which would cause very slight changes
to the value. On the plot for all of the various diffusivities, +10%, -10%, and normal are almost
the same line and roughly achieve the same steady state concentration over time. Significant
variation was shown when +/- magnitudes of 10 were used which would model substantial
variation between two individuals with completely different variables. The contour for 10 times
greater diffusivity shows that almost no oxygen diffuses from the protein layer into the cornea
which would result in severe depletion of O2 over time. The contour of 1/10 the original value
shows that the O2 concentration reaches a farther depth over the course of the same time, but it is
not significantly deeper in the model. A comparison of the Time vs. Concentration plots (shown
in Figure 3) shows that the 1/10 diffusivity reaches steady state at a faster rate while the 10 times
magnitude would eventually reach a higher steady state. The sensitivity analysis for varying the
diffusivity values by small percentages has almost no effect on the diffusion of O2, but when
varying it by entire magnitudes would result in altering the concentration profile for small
increments of time.
108
3. Reduced and Finer Mesh
From the original interval count of 10, we decided to vary the interval count to 5 and 20 per
protein/cornea layer.
Reduced Mesh in 3 Protein/Cornea Layers (Interval Count: 5)
Figure 8: Reduced mesh, using interval count of 5 per protein/cornea layer; generated in
Gambit.
Reduced Mesh- Interval Count: 5
3 Protein Layers
Normal- Interval Count: 10
109
Analysis of the Reduced Mesh (Interval Count: 5)
After reducing the mesh from interval count of 10 to 5 per protein/cornea layer, there was
no change in the oxygen concentration contours after 30 seconds of simulation. This indicated
that we could have used an interval count of 5 per protein/cornea layer instead of 10, and still
achieved the same results. It would have saved the computer from performing some extra
computations; however, the time it would have taken to run the program would not have had
changed by a noticeable amount, because our system of the original meshing took less than a
minute to run to start with.
Finer Mesh in 3 Protein/Cornea Layers (Interval Count: 20)
Figure 9: Finer mesh, using interval count of 20 per protein/cornea layer; generated in
Gambit.
110
Finer Mesh- Interval Count: 20
3 Protein Layers
Normal- Interval Count: 10
Analysis of the Finer Mesh (Interval Count: 20)
After increasing the mesh from interval count of 10 to 20 per protein/cornea layer, there
was no change in the oxygen concentration contours after 30 seconds of simulation. This
indicated that we could have used a finer mesh, which would have made the computer perform
some extra computations and run a little longer, and still end up getting the same results.
Therefore, it was not necessary to have an interval count of more than 10 per protein/cornea
layer.
Originally we had expected that the oxygen concentration levels would change greatly
with increasing protein layers. Furthermore, we also originally developed the hypothesis that at
the greatest protein build up, the cornea would not receive the required amount of oxygen to
maintain normal metabolic activities. Our results, however, contradict both of our expectations in
that even with the greatest amount of protein build, the oxygen diffusion rate is impeded only by
a small amount in comparison to the no protein build up scenario. Furthermore, our data shows
that even with three layers of protein build up the cornea was still able to receive healthy
amounts of oxygen. We have concluded that these unexpected results may have occurred
because the oxygen concentration in the atmosphere is considerably greater than the
concentration in the eye. Therefore, diffusion will easily occur through to the cornea and the
protein layers are not a limiting factor; at least not a significant limiting factor.
IV. CONCLUSION AND DESIGN RECOMMENDATIONS
In the beginning we aimed to model the oxygen flow through the contact lenses and into
the cornea, and to determine whether the increasing presence of protein build would prevent the
necessary amount of oxygen to diffuse into the cornea. From our four modeled scenarios, we can
conclude that in every case the cornea was able to receive more than the required amount of
oxygen to maintain normal metabolic activities. We would like to emphasize that even in the
most severe protein build up scenario of three full layers, the oxygen concentration retained
111
within the cornea was above the minimum requirement. This proves that in regards to oxygen
concentration needs, neither the lens nor the protein build up is harmful to the user. In terms of
changes oxygen diffusion through the protein layer(s) to the cornea, our four modeled scenarios
prove that the oxygen diffusion rate is impeded a slight bit as the protein layers increase causing
a slight decrease in oxygen diffusion. However, once again, even with the greatest amount of
protein build, the eye was able to retain sufficient amount of oxygen to maintain normal
metabolic activities; proving that protein build up is of little concern in regards to oxygen
diffusion into the cornea.
As for economic constraints, “Focus Night & Day Contact Lenses” we found that these
lenses are more consumer friendly; in regards to cost of course. From our research, we calculated
that the thirty day wear contact lenses are potentially one hundred and fifty dollars cheaper than
daily disposable contact lens, and approximately the same cost as weekly disposable contact
lenses; of course these numbers will vary with different brands and different discounts offered
between competing stores. For the most part, we strongly recommend that “Focus Night & Day
Contact Lenses” are the more economically sound buy for the consumer. In regards to
manufacturability, we see no problem in the mass production of these contact lenses considering
CIBA clearly already produces and distributes these contacts lenses to the general consumer.
From our computer generated models, we see that with respect to oxygen diffusion to the
cornea, these contact lenses are safe and maintain normal health conditions for the user.
However, our model only puts into consideration the required amounts of oxygen for the cornea,
but does not consider the danger levels that could occur with increasing amounts of protein build
up. Thus for future designs, we strongly recommend that the future models put into consideration
the increasing build up of protein with increasing usage. In other words, future models should
also program for the increasing build of protein concentration and determine at what time the
contact lenses are unsafe for the user to wear. Furthermore, these simulations must model contact
lenses more realistically; such as they should be three dimensional meshes, consider possible
lament or turbulent flow of oxygen, moisture content of lenses, include a tear layer, and more.
Lastly, for additional design recommendation, we feel that it would be worth the effort to model
possible ways for new and improved contact lenses to absorb the protein build up within the
lenses. This would eliminate the dangers of protein build up for the user and possibly increase
the life span for each contact lens.
112
Appendix A: Mathematical Statement of the Problem
A.1 Governing Equations
To model the diffusion of oxygen through the lens-protein-cornea system, the species equation is
employed. Internal fluid flow is assumed to be negligible, and so the convection term is crossed
out:
cO2
t
u
cO2
x
D
 2 cO2
x 2
 rA
Because property values differ for each layer of the system, a governing equation is necessary for
each. Reaction is only present in the cornea (zeroth order):
rA  kc
A.2 Boundary Conditions
The concentration of oxygen at the outer surface of the lens is calculated using the partial
pressure of oxygen in the atmosphere (21%) and Henry’s Law. The oxygen concentration at y =
0.3875 mm was calculated to be 7.944e-6 kg/m3. Since we are modeling the system as semiinfinite, the flux at the cornea end (y = 0 mm) is zero. The flux at x = 0 mm and at x = 0.3875
mm are also set to zero, because the geometry of the slab has an axis of symmetry along the
center axis.
A.3 Initial Conditions
Since 10% of oxygen in the air is assumed to be in the cornea, the initial concentration of oxygen
in the cornea is calculated to be 7.944e-7 kg/m3. The initial concentration of oxygen in the other
layers is assumed to be zero.
A.4 Input parameters
Table A1 details all of the constants that are employed, along with their appropriate units, and
the nondimensionalized values when necessary, for each input parameter that is entered into
FIDAP.
113
Table A1: Summary of constants used and their respective nondimensionalized equivalents.
Location/Property
Value
Nondimensionalized Value
2
Lens Diffusivity
9.9e-9 m /s
1
Lens Depth
0.08 mm
0.2065
Protein Diffusivity
Protein Depth
1.079e-10 m2/s
0 - 0.0075 mm
Cornea Diffusivity
Cornea Depth
Corneal Oxygen Reaction Rate
(Elimination)
Corneal Oxygen Activation
Energy
1.08e-9 m2/s
0.3 - 0.3075 mm
0.10909
0.7742 - 0.79355
2.475e-5 kg/m3s
3.90e-13
1.09e-02
0 - 0.01936
3.313 J/kg
N/A
PROBLEM Statement:
Geometry Type
Flow Regime
Simulation Type
Flow Type
Convective Term
Momentum Equation
Species Dependence
Temperature Dependence
Surface Type
Fluid Type
2-D Axis-symmetric
Incompressible
Transient
Linear
No convection
No momentum
Species=1 (oxygen)
Isothermal
Fixed
Newtonian
SOLUTION Statement:
Solution Method
Relaxation Factor
Successive Substitution=50
ACCF=0
TIMEINTEGRATION Statement:
Time integration
No. Time steps
Starting Time
Ending time
Time Increment
Time Stepping Algorithm
Backward
100
0 sec
2
1.9779 sec (non-dimensional= Do*t/L )
Dt=.659
Fixed
114
Concentration of Oxygen
[O2] in Air = 7.944e-6 kg/cm3
[O2] in Cornea = 7.944e-7 kg/cm3
[O2] in Lens = 0 kg/cm3
[O2] in Protein = 0 kg/cm3
Time
Nondimensionalized Time = ( D * Normal Time ) / L2
D = 9.9e-9 m2/s
L = 0.3875 mm
FIDAP Commands: INPUT FILE
/
/ INPUT FILE CREATED ON 28 Apr 05 AT 23:35:09
/ *** FICONV Conversion Commands ***
/ *** Remove / to uncomment as needed
/
/ FICONV(NEUTRAL,NORESULTS,INPUT)
/ INPUT(FILE= "tproj.FDNEUT")
/ END
/ *** of FICONV Conversion Commands
/
TITLE
/
/ *** FIPREP Commands ***
/
FIPREP
PROB (AXI-, ISOT, NOMO, TRAN, LINE, FIXE, NEWT, INCO, SPEC = 1.0)
PRES (MIXE = 0.100000000000E-08, DISC)
EXEC (NEWJ)
SOLU (S.S. = 50, VELC = 0.100000000000E-02, RESC = 0.100000000000E-01,
SCHA = 0.000000000000E+00, ACCF = 0.000000000000E+00)
TIME (BACK, FIXE, TSTA = 0.000000000000E+00, TEND = 1.9779,
DT = 0.659000000000E-02, NSTE = 300)
OPTI (SIDE)
DATA (CONT)
PRIN (NONE)
POST (RESU)
SCAL (VALU = 1.0)
ENTI (NAME = "LENS", SOLI, PROP = "mat1", SPEC = 1.0, MDIF = "C1_LENS")
ENTI (NAME = "PROCORINTERFACE1", SOLI, PROP = "mat2", SPEC = 1.0,
MDIF = "C1_PROCORINTERFACE1")
ENTI (NAME = "PROCORINTERFACE2", SOLI, PROP = "mat3", SPEC = 1.0,
MDIF = "C1_PROCORINTERFACE2")
ENTI (NAME = "PROCORINTERFACE3", SOLI, PROP = "mat4", SPEC = 1.0,
115
MDIF = "C1_PROCORINTERFACE3")
ENTI (NAME = "CORNEA", SOLI, PROP = "mat5", SPEC = 1.0, MDIF = "C1_CORNEA")
ENTI (NAME = "BOTTOMCORNEA", PLOT)
ENTI (NAME = "LEFTCORNEA", PLOT)
ENTI (NAME = "RIGHTCORNEA", PLOT)
ENTI (NAME = "TOPCORNEA", PLOT)
ENTI (NAME = "TOPLENS", PLOT)
ENTI (NAME = "LEFTLENS", PLOT)
ENTI (NAME = "RIGHTLENS", PLOT)
ENTI (NAME = "BOTTOMLENS", PLOT)
ENTI (NAME = "LEFTINTERFACE1", PLOT)
ENTI (NAME = "LEFTINTERFACE2", PLOT)
ENTI (NAME = "LEFTINTERFACE3", PLOT)
ENTI (NAME = "RIGHTINTERFACE1", PLOT)
ENTI (NAME = "RIGHTINTERFACE2", PLOT)
ENTI (NAME = "RIGHTINTERFACE3", PLOT)
ENTI (NAME = "INTERFACE1", PLOT)
ENTI (NAME = "INTERFACE2", PLOT)
DIFF (SET = "C1_LENS", CONS = 1.0)
DIFF (SET = "C1_PROCORINTERFACE1", CONS = 0.109000000000E-01)
DIFF (SET = "C1_PROCORINTERFACE2", CONS = 0.109000000000E-01)
DIFF (SET = "C1_PROCORINTERFACE3", CONS = 0.109000000000E-01)
DIFF (SET = "C1_CORNEA", CONS = 0.199)
BCNO (SPEC = 1.0, CONS = 0.794400000000E-05, ENTI = "TOPLENS")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "BOTTOMCORNEA")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LEFTCORNEA")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "RIGHTCORNEA")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LEFTLENS")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "RIGHTLENS")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LEFTINTERFACE1")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LEFTINTERFACE2")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LEFTINTERFACE3")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "RIGHTINTERFACE1")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "RIGHTINTERFACE2")
BCFL (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "RIGHTINTERFACE3")
ICNO (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "LENS")
ICNO (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "PROCORINTERFACE1")
ICNO (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "PROCORINTERFACE2")
ICNO (SPEC = 1.0, CONS = 0.000000000000E+00, ENTI = "PROCORINTERFACE3")
ICNO (SPEC = 1.0, CONS = 0.166800000000E-06, ENTI = "CORNEA")
EXTR (ON, AFTE = 5, EVER = 5, ORDE = 3, NOKE, NOFR)
END
/ *** of FIPREP Commands
CREATE(FIPREP,DELE)
CREATE(FISOLV)
PARAMETER(LIST)
116
Appendix C: Additional plots and figures
Figure C1: Oxygen concentration profile: 0 protein layers, 5 seconds.
Figure C2: Oxygen Concentration profile: 1 protein layer, 5 seconds.
117
Figure C3: Oxygen Concentration profile: 1 protein layer, 30 seconds.
Figure C4: Oxygen Concentration profile: 2 protein layers, 5 seconds.
118
Figure C5: Oxygen Concentration profile: 2 protein layers, 30 seconds.
Figure C6: Oxygen Concentration profile: 3 protein layers, 30 seconds.
119
Oxygen Concentration at Lens Surface Calculation:
(350 textbook, pg.251)
21% Oxygen in air
H=47,000 atm/mole fraction
55.56e-3 molesO2/cm3 of cornea
PA=HXA
0.21atm= (47,000 atm/mole fraction)(XA)
XA=4.468e-6 mole fraction



4.468e  6molefraction 5.563 e  3moleO2  32 gO2 
1kg 
kg
  7.944e  6 3
cm
 cm molefraction  molO2  1000 g 
120
Appendix D: References
BA Holden, DF Sweeney and G Sanderson. 1984. “The minimum precorneal oxygen
tension to avoid corneal edema”. Investigative Ophthalmology & Visual
Science, Vol 25, 476-480. Association for Research in Vision and
Ophthalmology.
Brennan, Noel A. "A Model of Oxygen Flux Through Contact Lenses".
Cornea, 20, no.1, (2001): 104-108
C. Steven Bailey. “Contact Lens Complications”. 15 April 2005.
<http://www.optometry.co.uk/articles/19990604/Bailey.pdf>
Datta, A.K. 2002. Biological and Bioenvironmental Heat and Mass Transfer.
Marcel Dekker, Inc. New York.
“Focus Night & Day Contacts”. Ciba Vision, Night & Day. 2003. 10 March 2005.
<http://www.nightanddaycontacts.co.uk/index.shtml?cv>
J. Garcia de la Torre, M.L. Huertas and B. Carrasco. 2000. Calculation of
hydrodynamic properties of globular proteins from their atomic-level
structure. Biophys. J. 78, 719-730.