Tonometry, corneal thickness and biomechanics

4. Tonometry: Biophysical Principles & Clinical Methodologies

Tonometry is the clinical measurement of intraocular pressure. All clinical tonometers measure pressure indirectly by assessing the physical response of the ocular coats (cornea or sclera) to an applied external mechanical force.

The Imbert-Fick Law & Corneal Realities

The mathematical foundation of applanation tonometry is the Imbert-Fick law, which states that the internal fluid pressure ($P$) within an ideal, infinitely thin, dry, infinitely thin, perfectly flexible non-elastic spherical membrane equals the external mechanical force ($W$) required to flatten a given plane surface area ($A$):

$$W = P \times A \implies P = \frac{W}{A}$$

The human cornea violates every physical assumption of the Imbert-Fick law:

1. It possesses finite structural thickness ($540\,\mu\text{m}$) and bending stiffness (corneal rigidity, $M$), which actively resists flattening and requires extra applied force.
2. It is enveloped by a wet precorneal tear film that generates a surface tension capillary attraction (meniscus force, $S$), which pulls the tonometer tip inward toward the cornea.

Incorporating these opposing biological vectors yields the complete mechanical equation:

$$W + S = P \times A + M$$

Goldmann Applanation Tonometry (GAT): The Gold Standard

In the 1950s, Hans Goldmann discovered that when the external applanation contact area is precisely calibrated to a circular diameter of $3.06\text{ mm}$ (yielding an applanated surface area $A = 7.354\text{ mm}^2$):

• The inward capillary attraction of the tear film ($S \approx 0.45\text{ g}$) exactly balances and cancels the outward bending stiffness resistance of the normal human cornea ($M \approx 0.45\text{ g}$).
• Because $S = M$, the variables cancel out of the equation: $W = P \times A$
• Furthermore, because $A = 7.354\text{ mm}^2$, an internal pressure of $1\text{ mmHg}$ ($1.36\text{ g/cm}^2$) generates an applanating counter-force of exactly $0.1\text{ g}$. Therefore, the tonometer dial reading in grams is multiplied directly by $10$ to yield intraocular pressure in millimetres of mercury (e.g., $1.6\text{ g} = 16\text{ mmHg}$).

Clinical GAT Technique & Split-Prism Optics

The GAT applanation head houses a split-image biprism that optically divides the circular circular contact area into superior and inferior semicircles (mires) displaced laterally by exactly $3.06\text{ mm}$:

1. Illumination: The cobalt blue exciter filter is projected onto the biprism at an angle of $45^\circ$ at maximum slit-lamp illumination, exciting the instilled topical sodium fluorescein dye.
2. Fluorescein Mires: Two fluorescent green semicircles are visualized through the slit-lamp oculars. The applanation knob is rotated until the inner margins of the upper and lower semicircular mires just touch and overlap, oscillating symmetrically across each cardiac cycle (ocular pulsation).

Common Sources of GAT Measurement Error

• Excess fluorescein thickens the mires and can bias readings; too little produces thin mires. Standardise the endpoint and repeat inconsistent readings. | Insufficient Fluorescein | Thin, faint mires make apex visualization difficult; inner border measured prematurely. | Falsely Low IOP | | Corneal Epithelial/Stromal Oedema | Intrastromal fluid separates collagen lamellae, dramatically lowering corneal bending rigidity ($M$). | Falsely Low IOP | | High corneal astigmatism | Applanation shape changes | Use the instrument-recommended prism orientation (often the red mark at 43° to the minus-cylinder axis) or average appropriate meridians; the sign of bias depends on axis and technique | | Tight Neckwear / Valsalva / Breath-Holding | Compresses jugular venous return, directly elevating episcleral venous pressure ($P_e$). | Falsely Elevated IOP | | Eyelid Squeezing / Blepharospasm | Orbicularis oculi contraction exerts direct external mechanical globe compression. | Falsely Elevated IOP (can spike by $10–30\text{ mmHg}$) | | GAT Calibration Drift | Mechanical pivot fatigue. Calibrated using an eccentric calibration bar at $0, 20, \text{and } 60\text{ mmHg}$. | Systematic Under/Overestimation |

---

5. Central Corneal Thickness (CCT) & Corneal Biomechanics

Goldmann applanation is affected by corneal thickness and biomechanics, not thickness alone. A thin regular cornea can lead to underestimation and a thick regular cornea to overestimation, but oedema, scarring, surgery and stiffness can change this relationship. No fixed millimetre-of-mercury correction table reliably yields the “true” pressure in every eye. Measure pachymetry, note corneal pathology and interpret pressure with nerve and functional findings.

The Ocular Hypertension Treatment Study

OHTS established that pressure lowering can reduce conversion from ocular hypertension to glaucoma. Older age, higher pressure, thinner central cornea, larger vertical cup-to-disc ratio and greater field pattern standard deviation contributed to prediction. Thin cornea is a risk marker as well as a measurement issue; 555 micrometres is not a diagnostic boundary. Use a validated risk model only in an appropriate population and interpret its time horizon. Low-risk ocular hypertension may be observed, whereas higher-risk eyes may benefit from treatment after discussing life expectancy, preferences and adverse effects.

Non-Applanation Tonometers & Corneal Biomechanics

1. Dynamic Contour Tonometry (DCT / Pascal):
   • Employs a concave contact tip with a $10.5\text{ mm}$ contour radius matching the average cornea. A piezoresistive pressure sensor embedded flush within the contact face measures pressure transcorneally without bending or flattening the stroma.
   • Advantages: Virtually independent of CCT, corneal curvature, and post-refractive laser thinning. Accurately measures the Ocular Pulse Amplitude (OPA), reflecting pulsatile choroidal vascular perfusion.
2. Ocular Response Analyzer (ORA):
   • A dynamic, non-contact bidirectional pneumatic tonometer that fires a collimated air pulse, recording inward applanation pressure ($P_1$) and outward applanation pressure ($P_2$) as the cornea rebounds.
   • Corneal Hysteresis (CH): Calculated as the mathematical difference between the two applanation pressures: $\text{CH} = P_1 - P_2$. CH represents the viscoelastic viscous damping capacity of the corneal extracellular matrix.
   • Prognostic Value: A low Corneal Hysteresis ($< 9.5\text{ to }10.0\text{ mmHg}$) is an independent, powerful risk factor for glaucomatous structural and functional progression, reflecting increased biomechanical compliance and vulnerability at the lamina cribrosa.
   • Generates a Corneal-Compensated Intraocular Pressure ($IOP_{cc}$) that outperforms GAT in post-LASIK/PRK eyes.
3. Rebound Tonometry (iCare):
   • Propels a lightweight, magnetized, plastic-tipped probe ($1.7\text{ mm}$ diameter) against the cornea, measuring probe deceleration dynamics upon rebound.
   • Clinical Pearls: Requires no topical anaesthesia or fluorescein; highly convenient for pediatric examinations, bedridden patients, and home diurnal self-tonometry. However, readings remain moderately dependent on CCT (overestimating IOP in thick corneas).