Transient diffusion of oxygen through the cornea and the covering membrane to the POS electrode has been analyzed previously.
40 The distinction here is that the steady profile of oxygen in the cornea before POS placement (see curve
P(0,
x) in
Fig. 1) is that corresponding to SCL wear in the environment rather than to that of a bare cornea exposed to the environment. As shown in Appendix A, the oxygen-tension profile across an SCL is linear following Fick's second law. The tension profile of the contact lens–covered cornea also follows Fick's second law, but now including a first-order reactive loss of oxygen (see
Equation 6 in Takatori et al.
40). The resulting steady tension profiles in the SCL and in the cornea are given by Equations A1 and A2. The desired steady oxygen flux through the lens and into the cornea follows directly as described in Appendix A:
where
D is the average diffusivity of oxygen in the cornea;
k is the average partition coefficient of oxygen in the cornea (i.e., the product
Dk is the corneal oxygen permeability); and
L is the average corneal thickness.
D and
k are taken here as characteristic of the stroma,
1–3,67 and are reported in
Table 2 along with
L, and membrane properties.
68,69Po (155 mm Hg) is the open-eye oxygen tension in the environment, and
PAC (24 mm Hg) is the oxygen tension at the anterior chamber. Oxygen tensions at the endothelium/anterior chamber interface may take on much lower values during contact-lens wear
70 than that listed in
Figure 1 with no impact on our results.
φ2 = k1L2/
Dk is the square of the Thiele modulus
71 or the Damköhler number,
72 with
k1 the first-order rate constant or the zero-tension slope of the Monod rate expression for oxygen consumption.
40,67 The parameter
βL = DkLL/(
DLkLL) is the ratio of diffusion resistance of oxygen in the SCL to that in the cornea. Values for the SCL oxygen diffusivities,
DL, and partition coefficients,
kL, are from Chhabra et al.,
66 as listed in
Table 2. Thus, the only unknown parameter in
Equation 1 is the first-order metabolic consumption rate constant,
k1 (embedded in the Thiele modulus). Once
k1 is obtained for each subject with each lens, in vivo oxygen uptake by the cornea during contact-lens wear can be determined.
Equation 1 applies also to no–contact lens wear. In the limit of zero lens thickness, it correctly reduces to the previous result that
40 Comparison of
Equations 1 and
2 shows that SCL wear reduces oxygen uptake into the cornea so that
< 1. High SCL oxygen transmissibility (i.e., a large value of
DLkL/
LL), reduces the parameter
βL toward zero resulting in unimpeded oxygen flow into the cornea.