Imbert-Fick law
Encyclopedia
The Imbert-Fick "law" was invented by Hans Goldmann (1899–1991) to give his newly marketed tonometer (with the help of the Haag-Streit Company) a quasi-scientific basis; it is mentioned in the ophthalmic
and optometric
literature, but not in any books of physics
. According to Goldmann, "The law states that the pressure in a sphere filled with liquid and surrounded by an infinitely thin membrane
is measured by the counterpressure which just flattens the membrane." "The law presupposes that the membrane is without thickness and without rigidity
...practically without any extensibility."
The problem is that a sphere
formed by such a membrane and filled with incompressible liquid (water) cannot be indented or applanated even when the pressure inside is zero, because a sphere contains the maximum volume with the minimum surface area. Any deformation
necessarily increases surface area
, which is impossible if the membrane is inelastic, such as aluminum foil.
The actual physical basis of tonometry is Newton's third law of motion: "If you press a stone eyeball with your finger, the finger is also pressed by the stone eyeball."
The law is this: Intraocular pressure = Contact force/Area of contact
The law assumes that the cornea
is infinitely thin, perfectly elastic, and perfectly flexible. None of these assumptions are true. The cornea is a membrane that has thickness and offers resistance when pressed.. Therefore, in Goldmann tonometry, readings are normally taken when an area of 3.06mm has been flattened. At this point the opposing forces of corneal rigidity and the tear film are roughly approximate in a normal cornea and cancel each other out allowing the pressure in the eye to be inferred from the force applied.
Ophthalmology
Ophthalmology is the branch of medicine that deals with the anatomy, physiology and diseases of the eye. An ophthalmologist is a specialist in medical and surgical eye problems...
and optometric
Optometry
Optometry is a health care profession concerned with eyes and related structures, as well as vision, visual systems, and vision information processing in humans. Optometrists, or Doctors of Optometry, are state licensed medical professionals trained to prescribe and fit lenses to improve vision,...
literature, but not in any books of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. According to Goldmann, "The law states that the pressure in a sphere filled with liquid and surrounded by an infinitely thin membrane
Biological membrane
A biological membrane or biomembrane is an enclosing or separatingmembrane that acts as a selective barrier, within or around a cell. It consists of a lipid bilayer with embedded proteins that may constitute close to 50% of membrane content...
is measured by the counterpressure which just flattens the membrane." "The law presupposes that the membrane is without thickness and without rigidity
Rigidity
Rigid or rigidity may refer to:*Stiffness, the property of a solid body to resist deformation, which is sometimes referred to as rigidity*Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges...
...practically without any extensibility."
The problem is that a sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
formed by such a membrane and filled with incompressible liquid (water) cannot be indented or applanated even when the pressure inside is zero, because a sphere contains the maximum volume with the minimum surface area. Any deformation
Deformation
In materials science, deformation is a change in the shape or size of an object due to an applied force or a change in temperature...
necessarily increases surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
, which is impossible if the membrane is inelastic, such as aluminum foil.
The actual physical basis of tonometry is Newton's third law of motion: "If you press a stone eyeball with your finger, the finger is also pressed by the stone eyeball."
The law is this: Intraocular pressure = Contact force/Area of contact
The law assumes that the cornea
Cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...
is infinitely thin, perfectly elastic, and perfectly flexible. None of these assumptions are true. The cornea is a membrane that has thickness and offers resistance when pressed.. Therefore, in Goldmann tonometry, readings are normally taken when an area of 3.06mm has been flattened. At this point the opposing forces of corneal rigidity and the tear film are roughly approximate in a normal cornea and cancel each other out allowing the pressure in the eye to be inferred from the force applied.