Eye Pressure Model according to Ohm's Law� Application to stress-induced eye pressure peaks��Erhard Glötzl �erhard.gloetzl@gmail.com

Slide 1: Forms of stress-induced high eye pressure

Slide 2: Graphic of the eye pressure model according to Ohm's law (complete variant)

Slide 3: Explanations to the complete variant and simplified variant

Slide 4: Graphic of the eye pressure model according to Ohm's law (simplified variant)

Slide 5: Model equations for simplified variant, models A, B, C

Slide 6: Equations for eye pressure and stress sensitivity of eye pressure for the simplified variant, model A

Slide 7: Result as a graphic

Slide 8: Table: Eye pressure, affected areas, causes, measures

2 main forms of stress-related high eye pressure:

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1. Pupillary block / angle block: stress-induced increase of pupillary resistance RP and / or chamber angle resistance RK.
2. Claim:
1. Stress-induced high eye pressure can also occur if there is neither a pupillary block nor an angle block. This is the case for persons for whom the ion pump in the ciliary body is very sensitive to stress and at the same time there are additional disturbances in the drainage area (pupil, chamber angle, trabecular meshwork, episcleral veins). In healthy persons the total drainage resistance is in the normal range. Therefore, the eye pressure remains in the normal range even under high stress, even if the ion pump is very sensitive to stress.
2. In the case of the Posner-Schlossmann syndrome (= pressure peaks and inflammation of the trabecular meshwork), a stress component in the sense of a) is presumably often included.

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The eye pressure is modeled below in accordance with Ohm's law as a flow model for the aqueous humor.

Thereby 3 model variants are examined:

• Model A: Stress increases the power W of the ion pump 𝑊: = 𝑈.𝐼≅𝑎.𝑠
• Model B: The ion pump can be simplified seen as a voltage source,

i.e. stress acts directly on the pressure U 𝑈≅𝑏.𝑠

• Model C: The ion pump can be simplified seen as a power source,

i.e. stress has a direct effect on the ciliary water production I 𝐼≅𝑐.𝑠

The parameters a, b, c respectively correspond to the ion pump sensitivity at stress.

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Result:

All three models A, B, C lead qualitatively to the same result: stress-induced high eye pressure in the sense of 2 a) occurs only if stress, a sensitive ion pump and a higher drainage resistance occur simultaneously.

ciliary body

ion

pump

R2

R1

R4

R3

U2

U1

Eye pressure model according to Ohm's law (complete version)

eye

pressure

pressure

episcleral veins

ciliary body water

R flow resistance

U

inside the eye

U0+U1 eye pressure

U blood pressure

U0

heart

veins

R5

R9

arteries

R7

uveal-

skleral

R8

U3

R6

U0 episcleral

venous pressure

pupil

chamber angle

trabecular meshwork

aqueous humor

Explanations to the full version

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• The heart generates the blood pressure U.

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• The blood pressure U is reduced in the body via the resistor R9 to the venous pressure. Up to the ciliary body, the blood pressure U is first partially degraded via the vascular resistance R7, subsequently degraded via the further vascular resistance R6 to the episcleral venous pressure and further via R5 to the venous pressure.

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• The ion pump of the ciliary body produces an osmotic pressure at the level of U1 + U2, thereby overcoming the entry resistance R8 into the ciliary body.

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• The ciliary body water partially enters the inner eye via the resistance R2 and thus gives the aqueous humor. Partially, the ciliary body water also enters the episcleral venous system via the resistance R3.

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• The aqueous humor mainly passes through the series resistance R1 (consisting of the resistance of the pupil RP, resistance of the chamber angle RK and resistance of the trabecular meshwork RT, R1 = RP + RK + RT) and, to a lesser extent, also via the uveal-scleral drainage resistance R4 into the episcleral venous system.

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• The episcleral venous pressure is reduced via the vascular resistance R5 down to the venous pressure.

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• The eye pressure is the sum of U0 and U1.

U1 depends essentially on R1 and ion pump performance, U0 depends essentially on R5.

Explanations to the simplified version

R5, R6, R7, R8, R9 and heart as pump are ignored. U0 is considered constant.

ciliary body

ion

pump

pupil

chamber angle

trabecular meshwork

uveal-scleral

R2,I2

R1,I1

R4,I4

R3,I3

U2

U1

Eye pressure model according to Ohm's law (simplified version)

U0 episcleral

venous pressure

pressure

bloodstream

ciliary body water

aqueous humor

R flow resistance

I flow

​

U

inside the eye

U0 + U1

eye pressure

U pressure

I

U0

Model equations for simplified variant

Results for simplified variant: eye pressure = U0 + U1

The factors a, b, c respectively characterize the stress sensitivity of the ion pump.

At fixed r2, r3, r4, the eye pressure is high only when the sensitivities a, b, c are high and

the stress is high and the drainage resistance r1 is high.

The eye pressure sensitivity is high only when the sensitivities a, b, c are high and

the drainage resistance r1 is high.

Stress Sensitivity of eye pressure SS

as a function of ion pump sensitivity a and drain resistance r1

for the simplified variant, model A

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s=0.5

r2=1

r3=1

r4=1

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Complete and simplified variant are qualitatively the same

Models A, B, C are qualitatively the same

Interpretation:

High sensitivity of eye pressure to stress

only if high ion pump sensitivity a and at the same time high drainage resistance r1

high eye pressure

affected areas, causes, measures

R1 total drainage resistance

RP resistance of pupil

RK resistance of chamber angle

RT resistance of trabecular meshwork

𝑅1 = 𝑅𝑃 + 𝑅𝐾+ 𝑅𝑇

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R5 resistance between episcleral veins and veins

* also α2-agonists

(Alphagan, ..)