Dk, Dk/t, Thermal Conductivity & Holden-Mertz

Oxygen Transmissibility: Dk, Dk/t, Thermal Conductivity & Holden-Mertz

Quick Answer: Oxygen permeability (Dk) is an intrinsic material property; oxygen transmissibility (Dk/t) is what the cornea actually experiences once lens thickness is factored in. The classic Holden-Mertz criteria — Dk/t ≥24 for daily wear and Dk/t ≥87 for extended wear — are the clinical thresholds calibrated to keep overnight corneal edema at or below ≈4% (the no-lens overnight baseline in the 1984 study). Later reviews revise the no-lens baseline downward (~3.2%) and push the extended-wear target toward Dk/t ≥125.

Oxygen Permeability (Dk)

Oxygen permeability (Dk) is an intrinsic property of a contact lens material, independent of lens thickness or design. The ANSI unit is ×10⁻¹¹ (cm²/s)(mL O₂/mL·mmHg). Dk measures how easily oxygen molecules diffuse through the polymer matrix.

• D = diffusion coefficient (how fast O₂ moves through the material)
• k = solubility coefficient (how much O₂ the material can hold)

Traditional hydrogels rely on water to carry oxygen. Because water has a Dk of about 80, raising water content raises Dk — but only up to a ceiling near Dk 40. Silicone hydrogels break this rule: silicone itself is highly oxygen-permeable, so SiHy lenses achieve high Dk with low water content.

Oxygen Transmissibility (Dk/t)

The cornea does not "see" Dk — it experiences oxygen transmissibility (Dk/t), which is Dk divided by lens thickness (t, in centimeters):

Dk/t = Dk / t(cm)

Conventionally, Dk is reported in ×10⁻¹¹ units and Dk/t is reported in ×10⁻⁹ units (the thickness division shifts the exponent). The same material with two different center thicknesses produces two different Dk/t values. A −3.00 D lens is thinner than a +3.00 D lens of the same material, so the minus lens has higher Dk/t. Manufacturers therefore quote Dk/t at a reference thickness (commonly −3.00 D at t = 0.09 mm or 0.06 mm).

Dk Reference Table by Material

Holden-Mertz Criteria

The Holden & Mertz (1984) study established the minimum Dk/t required to limit overnight corneal edema to ≈4% — the average physiologic edema level they measured during overnight eye closure with no lens in place. Later literature revised that no-lens baseline and argued the extended-wear critical Dk/t should be raised to about 125 ×10⁻⁹.

A daily-wear lens is removed before sleep, so a lower Dk/t is tolerated because the cornea recovers overnight. An extended-wear lens stays on the eye for 6+ consecutive nights, so it must deliver near-physiologic oxygen to avoid chronic hypoxia.

Consequences of Sub-Threshold Dk/t

• Corneal edema (stromal swelling, striae at >5%, folds at >8%)
• Epithelial microcysts (appear during extended-wear recovery)
• Limbal hyperemia and neovascularization
• Reduced epithelial barrier → higher infection risk (Pseudomonas, Acanthamoeba)
• Endothelial polymegethism (chronic hypoxic stress)
• Myopic creep in long-term hypoxic pediatric wear

Silicone Hydrogel vs Traditional Hydrogel

Silicone hydrogel (SiHy) materials were engineered to break the water-content/Dk coupling. Silicone provides oxygen permeability; water provides wettability and on-eye mobility. SiHy Dk values range from 60 to 140+, versus traditional hydrogels at 8 to 40.

Because silicone is hydrophobic, SiHy lenses require surface treatment or internal wetting agents to be comfortable (covered in §7.2). First-generation SiHy (lotrafilcon A, balafilcon A) used plasma surface treatment and high modulus; modern generations use internal wetting agents and lower modulus.

Thermal Conductivity

Thermal conductivity is the rate at which a lens material transfers heat between the warm cornea/tear film and the cooler ambient environment. Materials with poor thermal conductivity (low water, high silicone content) can cause a mild cooling sensation or, in extreme cases, contribute to low-grade corneal cooling during extended wear. PMMA, traditional hydrogels, and SiHy conduct heat differently; this is a minor but tested point on the CLRE.

Measuring Dk: Polarographic Method

The ANSI Z80.20 standard method is the polarographic electrode technique:

1. A lens sample is placed on a polarographic oxygen sensor.
2. The sensor consumes oxygen at a known rate, creating a current proportional to O₂ flux.
3. Dk is calculated from the steady-state current after correcting for edge effects and boundary-layer resistance.

The coulometric method is an alternative that measures oxygen that passes through the lens to a sensor on the far side — useful for very high Dk materials where polarographic edge corrections become unreliable. Both methods apply edge correction (because oxygen diffuses laterally at the lens edge, inflating apparent flux) and boundary-layer correction (the tear-film boundary layer itself resists oxygen flux). Without these corrections, Dk is overestimated, especially for high-Dk SiHy.

Worked Dk/t Example

A patient wears a senofilcon A lens (Dk 103) at −3.00 D with center thickness 0.07 mm. Convert t to centimeters: 0.07 mm = 0.007 cm. Then Dk/t = 103 / 0.007 ≈ 147 — comfortably above both Holden-Mertz thresholds, so this lens qualifies for extended wear on oxygen criteria alone (final decision also depends on surface chemistry, modulus, and follow-up). Now consider the same material at +10.00 D where center thickness rises to 0.20 mm (0.020 cm): Dk/t = 103 / 0.020 ≈ 51 — below the extended-wear threshold. A high-plus patient who was told their lens is "extended-wear approved" may actually be hypoxic at their personal Rx.

Clinical Bottom Line

• Dk is the material; Dk/t is the lens.
• Use SiHy for extended wear, high Rx, and edema-prone patients.
• Verify Dk/t at the patient's actual Rx, not the −3.00 D marketing number — high-plus lenses have much lower Dk/t than the brochure.
• For a fragile dry-eye patient, the silicone advantage (high Dk, low dehydration) often outweighs the modulus and surface issues that come with SiHy.