SH Lecture 2

What is Lecture 2 mainly about?

Structural and fluid mechanics of the eye: the eye as a pressurised shell, ocular rigidity, eye fluids, IOP regulation, and glaucoma.

Why does the eye need to maintain its shape?

To preserve its optical properties.

What maintains the eye’s shape mechanically?

Internal pressurisation by intraocular pressure, IOP.

What simple structural model is used for the eye?

A thin-walled spherical shell.

Which tissues give the wall properties in the shell model?

The sclera and cornea.

What structural details are omitted in the simple shell model?

Detailed structural features at the cornea and optic nerve.

What material assumptions are made in the simple eye shell model?

The tissue is treated as linear elastic and time-independent.

What stress assumption is made for the eye shell model?

The sphere has no bending stresses, giving biaxial wall stresses.

What is the thin-walled spherical pressure vessel stress formula for the eye?

σ = pR/(2h), where p is IOP, R is radius, and h is wall thickness.

What does σ represent in the shell model?

Biaxial wall stress in the eye wall.

What is the normal IOP value given in the notes?

About 15.5 mmHg.

What conversion is given for mmHg?

1 mmHg = 133 Pa.

What extreme IOP value is mentioned?

About 50 mmHg.

What IOP can occur when rubbing the eyes?

About 80 mmHg.

What other activities can load the eye?

Accommodation, blinking, and rubbing the eyes.

Using p = 15.5 mmHg, h = 0.78 mm, R = 12 mm, what wall stress is estimated?

σ ≈ 16 kPa.

For equal biaxial stress, what strain relation is used?

ε = σ(1 − ν)/E.

Using E = 3 MPa and ν = 0.5, what eye-wall strain is estimated at normal IOP?

ε ≈ 0.26%.

Why is ocular rigidity important?

It helps explain tonometry, resistance to aqueous humour outflow, myopia development, and the ocular pulse.

What does the coefficient of rigidity K characterise?

The effect of IOP on change in eye volume.

Is ocular rigidity K a material property only?

No. It is a structural property depending on both geometry and material properties.

For a sphere, how is small volume change related to radial strain?

dV/V = 3dR/R = 3ε.

How is wall stress proportional to IOP in the shell model?

σ/IOP = R/(2h), so dσ/d(IOP) = R/(2h).

What is the ocular rigidity formula from the shell model?

K = d(IOP)/dV = 2hE/[R(1 − ν)3V].

What typical calculated value of K is given?

K ≈ 0.27 mmHg/µL.

What measured value of K is given for comparison?

About 0.46 mmHg/µL.

What disease is linked to changes in IOP?

Glaucoma.

What is tonometry?

A technique for indirectly measuring IOP by deforming the cornea.

Why is direct IOP measurement by pressure tapping usually inappropriate?

It is invasive and not normally suitable for routine measurement.

What is the basic Goldmann tonometry idea?

A force W flattens a corneal area A, and IOP is estimated as W/A.

In Goldmann tonometry, why is a correction needed?

Tear film effects and corneal bending stresses affect the measured force.

At what flattened area do tear film and bending corrections empirically cancel?

A = 7.35 mm².

What extra correction may be needed in tonometry?

Correction for abnormal corneal thickness.

What are the main fluid types in the eye discussed?

Blood flow, aqueous humour, and interstitial flow in the ECM.

Why do the lens and cornea lack vasculature?

To maintain transparency.

How are the lens and cornea nourished despite lacking blood vessels?

By aqueous humour.

What is the role of blood flow in the eye?

It transports oxygen and nutrients and removes waste products.

Why does the choroid have very high perfusion?

The retina/choroid region has high metabolism needed to detect photons.

What is interstitial fluid?

Fluid contained in tissue spaces and pores.

What is the Starling resistor idea in ocular blood flow?

A soft vessel can collapse under external pressure, constricting flow.

Why does pressure fall along a blood vessel?

Because of pipe friction.

What happens when external pressure collapses an ocular blood vessel?

The vessel constricts and controls flow.

In the Starling resistor model, what pressure controls flow?

IOP controls flow more than venous pressure.

What is the vascular waterfall analogy?

Like a waterfall or supersonic throat, downstream pressure has little effect once constriction controls flow.

Why does ocular blood flow need autoregulation?

To maintain flow despite differences or changes in IOP.

What example arterial pressure range is given?

About 75/35 mmHg.

What example venous pressure range is given?

About 8–10 mmHg.

What is poroelasticity used to model?

Time-dependent material response due to fluid flow through a porous solid matrix.

In linear poroelastic theory, what is assumed about the solid phase?

It is linearly elastic and isotropic.

In poroelasticity, what causes time-dependence?

Flow of fluid through the porous matrix.

In the ECM context, what flow is poroelasticity describing?

Interstitial flow in the extracellular matrix.

How does a fluid-like material behave in the notes’ poroelastic example?

E(∞)/E(0) ≪ 1, meaning the long-time stiffness is much smaller.

How does a solid-like material behave in the notes’ poroelastic example?

E(∞)/E(0) ≈ 1, meaning little stiffness change with time.

What is Darcy’s law for fluid flow through a specimen?

Q = κAΔp/h.

In Darcy’s law, what does Q mean?

Rate of volume discharge across area A.

In Darcy’s law, what does Δp mean?

Pressure difference applied across the specimen.

In Darcy’s law, what does h mean?

Specimen thickness.

What is hydraulic permeability κ?

A measure of how easily fluid flows through a porous material; units m⁴/(N s).

What is intrinsic permeability k?

k = ηκ, where η is fluid viscosity.

What are the units of intrinsic permeability k?

m².

What physical meaning does intrinsic permeability k have?

It estimates the internal pore size or internal surface area associated with pores.

What viscosity values are given for water and aqueous humour?

Water: about 1 mPa s. Aqueous humour: about 0.75 mPa s.

What is the poroelastic time constant formula?

τ = h²/(Eκ).

What does a larger hydraulic resistance imply for flow?

For a given pressure gradient, less fluid flows through the tissue.

What is Bruch’s membrane?

A five-layer barrier limiting transport between the choroid and outer retina.

What drives water movement across Bruch’s membrane?

Hydrostatic and osmotic pressure gradients.

What ageing change is linked to Bruch’s membrane hydraulic resistance?

Lipid accumulation increases hydraulic resistance.

What disease mechanism is hypothesised from increased Bruch’s membrane resistance?

It may contribute to age-related macular degeneration by causing retinal detachment.

How can Darcy’s law be written as a hydraulic resistance relation?

Δp/(Q/A) = h/κ.

Why is corneal drug delivery difficult?

The cornea is a strong transport barrier and lacks vasculature.

Why might scleral drug delivery to the retina be attractive?

It may provide a route to the retina, but transport rates must be checked.

What two transport mechanisms are compared for scleral drug delivery?

Convection flow using Darcy’s law versus diffusional transport.

What quantity is compared with the diffusion coefficient D in dimensional analysis?

κΔp, which has units m²/s.

What estimate is given for κΔp in scleral drug transport?

κΔp ≈ 5 × 10⁻¹² m²/s.

What diffusion coefficient range is given?

D ≈ 2 × 10⁻¹⁰ to 4 × 10⁻¹³ m²/s.

What are the main roles of aqueous humour?

It pressurises the eye, nourishes the cornea and lens, and clears debris.

What is the typical aqueous humour production rate?

About 2.4 µL/min.

Where is aqueous humour produced?

By the ciliary body.

What fraction of anterior chamber volume is produced per minute?

About 1% per minute.

When is aqueous humour production highest and lowest?

It peaks in the morning and is minimum at night.

Why must aqueous humour flow be regulated?

To maintain IOP; high IOP can lead to glaucoma.

What are the two main aqueous humour drainage routes/components?

The trabecular meshwork and Schlemm’s canal.

Where is the principal aqueous drainage route located?

At the junction of the iris, cornea, and sclera.

What is the typical outflow resistance value?

About 3–4 mmHg/(µL/min).

What gives resistance in the trabecular meshwork?

Proteoglycan-rich gels causing interstitial flow resistance.

What gives resistance in Schlemm’s canal?

Endothelial lining bulging into the canal lumen, causing channel flow resistance.

What is mechanobiology?

The study of how living/reactive materials respond biologically to mechanical conditions.

What happens experimentally when perfusion of media is increased?

IOP increases immediately, then returns to baseline after about 150 hours.

What was found in the perfusate after increased perfusion experiments?

Increased gelatinase A, also called MMP-2.

What does increased MMP-2 suggest about IOP control?

ECM material is linked to the control of IOP.

What is wall shear stress, WSS?

The shear stress exerted by flowing fluid on a vessel or channel wall.

How do large arteries respond to wall shear stress?

They remodel by changing diameter over time.

What cells sense WSS in arteries?

Endothelial cells.

What is mechanotransduction?

Conversion of a mechanical stimulus into a biological response.

What typical WSS range is given?

2–20 dynes/cm².

Why can Poiseuille flow be assumed in Schlemm’s canal estimate?

The vessels/channels are very small, so Reynolds number is small and viscous forces dominate.

What example WSS is calculated for Schlemm’s canal?

τf ≈ 2.7 dynes/cm².

What formula is given for wall shear stress between plates?

τf = 6ηQ/(Wh²).

What is the flow formula between two plates?

Q = −Wh³/(12η) · dp/dx.

What observation supports WSS-related regulation in Schlemm’s canal?

Preferential alignment of endothelial cells in Schlemm’s canal.