CONFIDENTIAL

The contents of this file are the property of Dennis Murphy and the Fred Hollows Intraocular Lens Laboratory in Asmara, Eritrea, and are only to be used for the

purposes of discussing IOL lens design with people who are collaborating with FH Asmara on new lens design. As such, they are not to be disclosed to people outside of this

group without written authorization from the author

POSTERIOR EDGE FORM ON IOLs

By

Dennis Murphy15 July, 2005

Table of Contents

Scope...........................................................................................................................................3

Introduction...............................................................................................................................3

The Posterior edge terminology of an IOL.............................................................................4

SQUARE EDGE..........................................................................................................................4DISCONTINUOUS EDGE............................................................................................................4SHARP EDGE............................................................................................................................5A SAW TOOTH EDGE...............................................................................................................5

Engineering Data......................................................................................................................6

UNITS.......................................................................................................................................6STRENGTH OF MATERIALS......................................................................................................6FORCE....................................................................................................................................12

Stress Concentration...............................................................................................................13

The hydraulic wedge...............................................................................................................14

The wedge effect......................................................................................................................14

THE INCLINED PLANE............................................................................................................14THE INFINITE WEDGE.............................................................................................................16

Peel Strength of a Joint...........................................................................................................17

Why does a round posterior edge on the IOL contribute to PCO......................................17

WEDGE ANGLE VERSUS THE RADIUS ON THE POSTERIOR LENS EDGE...................................18THE LENS EPITHELIAL CELLS AS A HYDRAULIC WEDGE......................................................18CELL PENETRATION MECHANISM.........................................................................................19

Model of the Eye......................................................................................................................20

The Rim Effect........................................................................................................................22

CAD View of an IOL in the Capsular Bag...........................................................................23

LENS WITH A TURNED-UP RIM AROUND THE POSTERIOR SURFACE......................................24Turned-Up Rim around the posterior surface – 8 diopter.................................................26Turned-Up Rim around the posterior surface – 30 diopter...............................................27Summary – turned up rim IOL..........................................................................................28

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SHARP POSTERIOR LENS SURFACE WITH NO RIM AROUND IT................................................29Sharp posterior surface with no rim – 8 diopter...............................................................30Sharp posterior surface with no rim – 30 diopter.............................................................30Summary – sharp edge no rim IOL...................................................................................30

COMPARISON BETWEEN A TURNED UP RIM AND A SHARP EDGE WITH NO RIM.....................31

Lenses in the marketplace......................................................................................................32

Questions..................................................................................................................................34

1..) MAXIMUM ALLOWABLE RADIUS ON THE POSTERIOR IOL EDGE.....................................342..) CREASES IN THE CAPSULAR BAG.....................................................................................343..) A RIM OR NO-RIM ON THE POSTERIOR EDGE OF THE IOL............................................354..) MAXIMUM CLEAR OPTIC DIAMETER..............................................................................355..) STRESS LEVELS IN THE CAPSULE.....................................................................................356..) CAPSULAR BAG SHRINKAGE............................................................................................357..) Clinical Ophthalmic comments......................................................................................36

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Scope

The intent of this document is to explore the underlying mechanisms involved in a “sharp edge” on the posterior surface of an IOL that assist in preventing/delaying postoperative PCO.

It is clearly recognized that other mechanical design features related to the haptic design also interact with the sharp posterior edge in the IOL in helping to prevent PCO. However, this document will only discuss the “sharp edge” parameters and mechanisms. The haptic design will be addressed in a separate document.

Introduction

Conventional wisdom in the ophthalmic world seems to generally believe that a “sharp edge”, a “square edge” or a “discontinuous” edge on the posterior surface of the IOL can, under the “right” conditions, act as a barrier to the migration of residual lens epithelial cells across the anterior surface of the posterior surface of the capsular bag – and hence assist in delaying, or perhaps preventing the onset of postoperative PCO.

There are good engineering reasons for believing this. In addition, many studies have also tended to confirm the concept.

In attempting to design a suitable “sharp edge” on a new design of lens one rapidly discovers that there are many unknown factors and also some rather ambiguous definitions which seem to be commonly used in describing a “ sharp edge” on the IOL. In order to discuss the design of such a lens with both engineers and ophthalmologists it becomes necessary to establish a suitable set of standard terminology and working concepts in order that everyone is singing off the same song sheet (so to speak)

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The Posterior edge terminology of an IOL

The literature on preventing PCO is littered with expressions such as – square edge – discontinuous edge – sharp edge. This rather imprecise use of terminology leads to a fair amount of confusion as to exactly what is meant – and more importantly exactly what is needed on the posterior edge

Square edge

A square edge is a corner that forms a right angle (e.g. 90 degrees). It is clear that the posterior edge shown on the lens below is not truly a “square edge”.

It is possible to produce a square edge on an IOL by putting a rim around the edge of the clear optic diameter.

Discontinuous edge

The idea of continuity comes from mathematics – in particular, calculus. The underlying idea,

roughly speaking, is that we can say that a function is continuous on an interval I, if

the graph of is unbroken for all x in the interval I. In this description we will only be concerned with an intuitive understanding of continuity and won’t get bogged down in a mathematically rigorous discussion of the subject (interesting though it may be).

As an example, the graph below shows a function that has a sharp kink in it as well as a discontinuity.

Clearly we are not seeking a “discontinuous” edge on the posterior surface of the IOL.

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Sharp edge

In the picture below the difference between a “sharp” edge and a rounded edge is shown.

A “sharp” edge is what is actually required on an IOL in order to act as barrier to the migration of the epithelial cells across the anterior surface of the posterior capsule surface.

The reason for this statement will be explored below in some detail as it has a major bearing on the manufacturing specifications of the lens. It is also of interest to the clinical scene as well. Agreement on the design specification of this edge so that it assists in preventing the onset of PCO and at the same time ensures absolute patient safety is the prime reason for this document.

A Saw Tooth Edge

Before we proceed we need to define another aspect of “sharp”. The general idea of a “sharp” edge is something that will cut into something else like a knife. Clearly this idea of “sharp” is totally unacceptable for an IOL.

“Sharp”, as in a knife, refers to a blade with a very narrow angle between the two surfaces of the sides of the knife. In a case such as this, the cutting action takes place by the intense buildup of local stress that is concentrated directly under the extremely small radius formed in the material as the knife edge is pushed into it. When the concentrated local stress formed at the cutting edge builds up to the point that it exceeds either the shear, compressive or the tensile strength of the material being cut (whichever parameter is appropriate in the case in point), then the material locally fails under the stress and is “cut”.

The other cutting mechanism is that of the saw tooth. The idea behind the saw tooth is to increase the local stress on the object to be cut by concentrating the force in a small area.

Clearly, a saw tooth is not acceptable to be superimposed onto the smooth surface (e.g. the surface texture of the optic surface) – or the posterior edge (e.g. a burr in the form of a series of saw teeth) – of the IOL. It needs to be stressed that the “sharp posterior edge” that is

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desired on the IOL is sharp only in the mathematical sense shown in the diagram above. e.g. you cannot draw an infinite series of closely spaced tangent lines around a curve that blends the two edges. In all other respects, the surface texture of the sides of the lens (edge & optic radius) – as well as the actual edge itself – is very smooth with no “feathery” saw tooth features to act as a cutting edge.

Engineering Data

This section will provide the basic definitions and explanations that are needed to understand the engineering terms that will be needed in the mechanical design process for a new intraocular lens. Any further information on these terms and subjects can easily be obtained from appropriate engineering text books that cover the subjects of Strength of Materials & Engineering Mechanics.

Units

When dealing with quantities such as forces, areas and volumes we must establish and use a standard system of terms and abbreviations. Below is a table showing a number of common descriptions for these quantities using the International system of units (SI).

Quantity Unit Symbol | Prefix Multiplier SymbolForce Newton N | tera TStress or Pressure Pascal Pa | giga GLength Meter m | mega MArea Square meter | kilo kVolume Cubic meter | milli m

Strength of Materials

Definition of Stress

Stress is defined as resistance to an external force. It is measured in terms of the force exerted per unit area. Using SI units the force is generally given in Newtons (see section on force for a definition) and the resisting area is given in square meters. The SI unit name for stress is the Pascal (one Pascal = one Newton per square meter (N/ )). Pressure is also defined in the same way as stress, and is equivalent. Normal engineering practice frequently specifies stress (pressure) as Newtons per square mm. This is gives the stress (pressure) in MPa. (One MPa = 1,000,000 Pascal N/ )

The Basic Stresses

Only two basic stresses exist:

1. Normal stresses, which always act normal (perpendicular) to the stressed surface under consideration. These stresses may be either tensile or compressive.

2. Shearing stresses, which act parallel to the stressed surface.

Other stresses are made up from a combination of these two basic forms. For example the stresses in a bent beam are referred to as “bending stresses”. They are in fact a combination of tensile, compressive and shearing stresses.

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Tensile stress. When a pair of axial forces pull on a part so trying to stretch or elongate the part. These tensile forces produce axial tensile stresses internally in the part on a plane lying perpendicular, or normal to its axis.

Tensile strength. The maximum load that a material can support without fracture when being stretched, divided by the original cross-sectional area of the material. Tensile strengths have dimensions of force per unit area and in the ISO system of measurement are expressed in units of MPa. When stresses less than the tensile strength are removed, a material returns either completely or partially to its original shape and size. As the stress reaches the value of the tensile strength, a material, if ductile, that has already begun to flow plastically rapidly forms a constricted region called a neck, where it then fractures.

Compressive stress. When a pair of axial forces push on a part and shorten or compress it. These compressive forces produce axial compressive stresses internally in the part on a plane lying perpendicular, or normal to its axis.

Compressive strength. Measured by a mechanical test to determine the maximum amount of compressive load a material can bear before fracturing. The test piece, usually in the form of a cube, prism, or cylinder, is compressed between the platens of a compression-testing machine by a gradually applied load. Brittle materials such as rock, brick, cast iron, and concrete may exhibit great compressive strengths; but ultimately they fracture. It is difficult to measure the compressive strength of ductile (able to be deformed) materials. When a load is applied to a ductile metal, it deforms elastically up to a certain point, and then plastic deformation occurs. Increasing loads may even completely flatten a test piece without any definite fracture occurring, so that no value can be obtained for the compressive strength.

Shear stress. This type of stress differs from tensile and compressive stresses in that the stressed plane (the shear plane) lies parallel to the direction of stress, rather than perpendicular to it, as in the case of tensile and compressive stresses.

Bearing Stress

This is also sometimes referred to as a contact stress (pressure). This is a compressive stress exerted on the external surface of a body when one object presses against another. In the case of an intraocular lens, it is the stress developed between the sides of the haptic that are in radial contact with the capsular bag, and the underside of the haptics in the axial direction. In addition it is also the stress between the posterior edge of the IOL and the posterior capsule.

Ultimate stress, permissible stress, factor of safety

Before any material can be safely used in a particular design a number of its properties must be known. The most important of these for our purposes include strength, elasticity, stiffness and toughness.

Ultimate stress, or strength is defined as the greatest stress a material can withstand without rupture. In the practical design of any structure we would never attempt to use the full strength of any material.

Permissible stress is that portion of the ultimate strength which may be safely used in any design. It is also sometimes referred to as working stress or allowable stress.

Factor of safety is the ratio of ultimate stress to permissible stress i.e.

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The appropriate factor of safety for any given design depends upon a number of considerations. Some of these factors that are applicable to the design of an IOL are:

1. The degree of safety required. That is, what dangers are there to a person if the IOL breaks.

2. Dependability of the material. Are flaws in the material easily detected? Do apparently similar pieces of the material behave similarly under stress? Does the material tend to snap suddenly such as hard brittle materials like glass, or does it tend to stretch first.

3. Permanency of the design. Lower factors of safety are permissible in temporary designs where personal injury from a failure is not a consideration. This is not the case in IOLs.

4. Load conditions. Is the design subject to steady, varying or shock loads? A load that varies or is subject to shocks needs a greater safety factor.

5. The exactness with which the probable loads and stresses can be predicted or determined. In the case of an IOL the actual stresses are not as easily predicted as those in metals because of the greater variability in plastic materials such as the PMMA material used in their manufacture.

6. Accessibility of the parts for inspection or replacement. In the case of an IOL this will require high safety margins as it is extremely difficult to surgically fix any problems.

The permissible stresses and safety factors which may be safely used in a particular design are usually based upon extensive laboratory tests and verified by a large amount of accumulated experience. In structural members in buildings, this data is laid out in the various ISO design standards. In the case of IOL designs this information is not readily available. ISO 11979-3 gives some guidance, but not a lot.

A factor of safety of two may be sufficient for a temporary structure that is only subject to steady loads and whose failure would not cause any danger to life or limb. On the other hand, a design that is subject to unpredictable shock loads and whose failure would cause death or injury may require a safety factor of ten. For designs that are subject to steady loads, a factor of safety of three or four is often used.

The direct stress formula

The types of stresses described so far are often referred to as direct stresses, in order to distinguish then from torsional (twisting), bending and other stresses.

In many, but not all cases, the maximum and minimum stresses do not vary greatly from the average stress. This is particularly true in many situations involving simple tension or compression stresses, except where there are holes in the part or changes in the cross sectional area of the part. However for bending stresses and torsion stresses, this is rarely, if ever, the case.

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Using the above stated general situation of even stresses throughout the part, a relationship can be established between the average intensity of stress ‘f’ produced by an externally applied force ‘P’ on each unit of stressed area ‘A’. This can be summarized as shown below.

P = f A or f = or A =

Where : f = average stress. N/ , (MPa)P = total external force or load, NA = stressed area,

If you are given any two of the f, P or A, then you can use one of the above formula to find the third quantity.

Strain or Deformation

The meaning of the term strain, as used in engineering is often misunderstood. Strain is deformation per unit length and is often used wrongly by people to describe the force which produces some form of deformation in an object.

All material bodies which are subjected to external forces, with internal stresses produced as a consequence, will be deformed (strained) to some extent, however small this may be. For example, a long rod subjected to an axial tensile load would be stretched or elongated, while a column supporting an axial load would be compressed or shortened. The total deformation produced in an object is designated by the Greek letter (delta). If the length of the object is L, the deformation per unit length, expressed by the Greek letter (epsilon), is

Strain = 0r

The quantities of total deformation and L are generally given in mm. Consequently strain will be mm per mm. This means that the quantity unit deformation is dimensionless as

The amount of deformation produced in a given material by a given force, will vary with the stiffness of the material. The stiffer the material, the less the deformation!

Elasticity

Another important property of materials is the ability, after having been deformed by the application of a force, to return to its original dimensions after the removal of the deforming force. A material that has this ability is said to be elastic.

There is a misconception regarding the true technical meaning of elasticity. It is commonly believed that an “elastic” material will withstand a high percentage of deformation, without sustaining any harm. Thus rubber is considered to be highly elastic. However, technically speaking, a material is elastic only if it has the ability to return to its original dimensions after removing the deforming force. In this respect both glass and steel are highly elastic materials, within their elastic limits.

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Hooke’s law & The Modulus of elasticity

According to Hooke’s law, stress is proportional to strain – within the elastic limit of the material.

For example, to verify the proportionality of stress to strain, and to determine the elastic limit of a particular material, a standard bar of the material is clamped into a testing machine that is capable of exerting a gradually increasing pull on the bar. A series of readings are taken of the elongation of the test bar for a series of equally spaced increasing known forces that are being applied to the bar. These are then tabulated. It will be found that equal increments of stress are found to produce equal increments of strain up to a certain value of stress. For stresses beyond this point, the elongations will be found to be increasing at a faster rate than the stresses, thus indicating that the elastic limit has been passed.

Careful measurement will also show that just before the elastic limit has been reached there is another point that is reached known as the proportional limit. In practice, this can usually be ignored as the elastic limit is the more important point for most designs.

Elastic limit

The elastic limit stress is the stress intensity at which the material retains its property of perfect elasticity. If the material is stressed beyond this point, it will not return to its original size or shape when the deforming force that is producing the stress is removed.

Proportional limit

As the term implies, this is the stress value at which the proportional law of Hooke breaks down. In most cases little practical distinction need be made between this stress and the elastic limit stress.

Yield point

In a ductile material (i.e. a material that will stretch), there is a point just above the limit of proportionality where a considerable increase in strain will be observed to occur for little increase in the stress level. The stress value at which this big increase takes place is known as the yield point of the material. Once this stress point has been reached, the material will tend to “flow” into a new shape under the applied stress and will remain in that shape after the deforming force has been removed.

Creep limit

The linear relationship of stress and strain for elastic materials is essentially constant over the stress range up to the elastic limit of the material. More particularly, this statement is strictly speaking true only for forces that are applied over a short period of time. If a force is applied over a long period of time, the resulting stress value, although less than the elastic limit, will cause the material to slowly but progressively undergo a permanent deformation (strain) over this period of time. This effect is temperature dependant. The higher the temperature, the faster the material will creep.

In steel, temperatures above 300° C are usually needed in order for creep to become a problem. As an example, the turbine blades in a jet engine are subjected to very high temperatures and tensile (stretching) forces due to the centrifugal forces from the high rotational speeds of the turbine. Over time the turbine blades will become longer due to creep from the centrifugal force. Unless the blades are checked and changed periodically, they

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would stretch and rip the outer casing of the turbine housing apart. Not a good thought if you happen to be in the aircraft at the time.

The maximum stress that can be steadily applied to a material at a given temperature and during a specified period of time without causing a specified deformation to be exceeded is called the creep limit of the material. The maximum creep limit usually used in engineering is the maximum stress at which the dimensional creep will not exceed one (1) percent in 100,000 hours of constant stress, equal to about 11.4 years – and even this depends on the particular design application..

In plastics, including PMMA, the material from which IOLs are manufactured, creep can become a consideration at temperatures well below 30° C. This is less that the body temperature in humans of 37° C (98.6° F).

Creep will cause the shape of the haptics and the vaults to deform over a period of time. This deformation will be in such a direction as to try and reduce the stress. The only way to do this is for the haptics and vaults to bend. This in turn will reduce the deflection force as the haptics are now not being compressed by the same amount as they were initially, due to the permanent change in their shape over time. For this reason, attention must be paid to the design to ensure that the internal stresses produced in the haptics and vaults will keep the creep rate to an acceptable level, so that the forces holding the lens in position do not reduce to an unacceptable level over a period of time. ISO 11979-3 specifies a test to check this problem. (Annex F - Measurement of compressive force decay)

Modulus of elasticity

The proportionality of stress to strain is expressed as the ratio of the increment of stress to the increment of strain. In a stiff but elastic material such as steel, we find that a given stress produces a relatively small deformation. In a softer, but still elastic material such as bronze, the deformation caused by the same intensity of stress is about twice that of steel, and in aluminium it is about three times that of steel. Plastics such as PMMA would deform approximately about sixty five times as much as steel under the same intensity of stress.

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Consequently the ratio of stress f to strain of any given material, which can be determined experimentally, then gives us a measure of its stiffness, or elasticity, which is called the modulus of elasticity of the material, denoted by the symbol E.

Modulus of elasticity = or E =

We now have a fixed relationship between the modulus of elasticity, stress and strain.

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Newton

The basic unit of force in the SI system is known as the Newton. It is defined as that force, which will, if it is constantly applied to a mass of one kilogram, cause the mass to undergo a continuous acceleration of one meter per second squared.

Resolving a force into rectangular components

In order to solve many problems in engineering, we often need to be able to collect several forces acting on a body into one composite force that can be used to replace the other forces acting on the body. At other times we need to be able to decompose (or resolve) a particular force into a number of separate components of force, which taken together will produce the same result as the one single force we are trying to analyze.

A given force can be resolved into an indefinite number of components. However in the design of an IOL we are mainly concerned with resolving a force into what is known as a “triangle of forces”. This procedure will be required when you come to calculate the component of force that is causing the vault to deflect when the haptics are compressed.

When a force is resolved into two components and these two components are at right angles to each other, they are called rectangular components. The term resolved parts is also sometimes used to describe them. The important thing to remember when considering one rectangular component of a force, that there is always another component of force that is acting at right angles to the first component.

If we resolve a force into two components at right angles to each other, each component has no effect in the direction of the other component. In such a case each component represents the total effect of the original given force in the particular component direction. Rectangular components are not merely components – each rectangular component represents a net effective value of the given force under consideration.

As a practical example consider a person walking along a path at the side of a canal pulling a boat along in the picture below. On the boat is a man steering, keeping it in the center of the canal. As the drawing shows, the man on the path has to exert a certain pulling force to keep the boat moving. However not all of this is directed toward pulling the boat along the canal. In addition, there is also a force at right angles to the component of the force parallel to the canal that is trying to pull the boat into the side of the canal. This force acting towards the side of the canal is counteracted by the man on the boat steering against this sideways force.

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The diagram below shows how to calculate the magnitude of the two components of force, one parallel to the center of the canal, and one directed into the bank, as a function of the force that the man on the bank is exerting.

Stress Concentration

Without any details of the mathematics of stress concentrators, the picture below shows the main features of the phenomenon. No further explanation is needed.

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The hydraulic wedge

Why does a round posterior edge on the IOL contribute to PCO? The short answer is simply that a “rounded” edge allows the epithelial cells to push past it and continue their migration across the anterior surface of the posterior capsule and cover the clear optic area of the IOL.

In order to develop the theory of how the penetration of the lens edge occurs, we need to first understand how the roots of a plant can cause so much damage to pipes buried in the ground and concrete paths. I am sure that most of us are familiar with this sort of everyday damage.

The reason that plant roots cause so much damage is simple. A very small root is capable of penetrating a very small crack in a pipe of concrete slab. Once inside the structure, the root then begins to expand as the root grows in diameter. The root is essentially a hydraulic wedge that allows it to flow into the shape of the crack. It then applies a sideways pressure on the crack as it grows.

Because it is a crack, the radius at each end of the crack is very small (maybe only in the region of a few tens on microns at the microscopic level). The radius at the end of the crack is the major factor in determining how much it will amplify the peak stress level right at the radius – in comparison to the average stress in the fracture area. The smaller the radius, the greater the stress concentration factor!

The same type of mechanism applies to the posterior edge of the IOL where the capsular bag should be laying tightly against the edge of the lens.

The wedge effect

The inclined plane

This concept is the key to understanding why the sharp edge is important. For that reason a short explanation is necessary in order to develop the design concepts involved in the square edge idea on an IOL.

Most people are familiar with the idea of a wedge as a simple machine and how it is used to translate a motion in the direction parallel to the base to another direction, usually at right angle to the inclined plane.

The inclined plane on a wedge is a simple machine that is used to obtain a mechanical force advantage in a similar manner to that of a lever and fulcrum or a pulley system.

In the case of the inclined plane the system is easiest to understand by the concept of doing “work” according to the following simple equation.

Work (Joules) = Force (Newtons) * the distance through which the force acts (meters).

Taking a situation where we exert a certain force in a direction parallel to the base of the wedge, for a certain distance parallel to the base, of say 3mm (0.003 meter), then on a 20 degree inclined plane the object being pushed along the inclined plane would lift by 1.0919 mm (0.0010919 meter) in the vertical direction. (See picture below)

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Then assuming a force of say 3 Newton was exerted for the full 3 mm, then the work done in the horizontal plane =

Work (J) = 3 (N) * 0.003 meter = 0.009 Joules of work in the horizontal plane.

It is clear that (ignoring losses due to friction) the work done in the vertical plane cannot be greater than 0.009 Joules in this case because that is what we actually expended.

Then:

0.009 Joules = X Newtons in the vertical plane * 0.0010919 meter

Then.

The above explanation is intended to give the understanding of the basic mechanism of the wedge effect. There is a simpler method of calculating the force multiplier effect and is shown in the picture below. Looking at the picture on the right hand side (20 degree inclined plane) you will see that the numbers agree with the “work” method of calculation above because they have used the same horizontal force of 3 Newtons on a 20 degree inclined plane.

In the method below we simply use the “triangle of forces” to resolve a force acting in one direction – in this case, horizontal to the bas of the inclined plane – into its components acting at other specified direction. The problem is then solved simply by using the force (in Newtons) in the specified direction, and then solving for the resultant force(s) in the other planes by simple trigonometry.

Looking at the diagram below, it is clear that the side force generated by the wedge for a given horizontal force becomes greater as the wedge angle becomes smaller.

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The infinite wedge

The concept of the infinite wedge is important when discussing the maximum allowable radius on the posterior edge of the IOL.

The idea is simple. As the angle of the inclined plane on the wedge approaches zero degrees, the force that is exerted in the plane at right angles to the base of the wedge tends to increase to an infinitely large value in theory. In practice it is limited by many factors. Nonetheless the force increases to a value that is many times greater that the force parallel to the base. The reason for the infinitely small wedge angle developing is show in the picture below.

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Peel Strength of a Joint

If you try and pull two objects apart that are glued together you will normally fail to separate the two objects. The reason for this is simple. The adhesive strength is stated as being able to resist a force – acting at right angles (90 degrees) to the glue line – as so many Newtons (the S.I unit of force) per square millimeters of the glued surface area. Even glues that have a low adhesive force per square mm can – if the glued surface area is large enough – withstand very high forces trying to separate the two objects (under the right conditions, a glued joint in fact is much stronger than a bolted joint)

The situation changes dramatically however if you try and peel the two objects apart as shown in the drawing below. In this situation, it normally becomes fairly easy to separate the two objects. The reason for the ease of separation is because of the high stress concentration that forms at the very small radius in the glue line right at the “peel point”. This stress level is then large enough to cause the glue line to fail locally at that point. The general situation is shown in the two pictures below.

Why does a round posterior edge on the IOL contribute to PCO

The information that is available (to me) is that the lens epithelial cells are about ten (10) microns in diameter. In order to understand the mechanism of why a radius on the posterior

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edge of the optic body of the lens allows the epithelial cells to pass across the junction of the lens and the capsular bag, we need to investigate the situation from the point of view of the epithelial cells.

Wedge angle versus the radius on the posterior lens edge

As the drawing below shows, the larger the radius on the posterior edge of the optic body on the lens, the smaller the wedge angle that is formed between the tangent at the point of contact of the round cell body and the radius on the lens on one side and the capsular bag on the other point of contact.

In the drawing directly below, the capsular bag has been drawn tangent to the vertical edge of the lens purely in order to demonstrate the relationship between the wedge angle and the radius on the posterior edge of the lens.

The lens Epithelial Cells as a Hydraulic Wedge

In reality the epithelial cells – being a soft biological entity – are almost certain to act as a hydraulic wedge. By this it is meant that the cells are able to deform themselves and penetrate further into the space between the posterior capsule and any radius that may exist on the posterior edge of the IOL. In so doing, the effective wedge angle is then reduced as per the drawing below.

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Cell Penetration Mechanism

Mechanical analysis fairly clears shows the mechanisms that allow the epithelial cells to penetrate across the anterior surface of the posterior capsule past the posterior edge of the lens as being influenced by two factors.

The existence of a radius on the posterior edge of the lens that allows the epithelial cells to act as a hydraulic wedge in the space formed by the tangent to the capsular bag and the posterior edge of the lens.

If the posterior lens edge was “sharp”, then although the cells may be able to push the capsular bag away from the side of the lens (if it had in fact shrunk in around the side of the lens) there would be no space on the edge of the lens into which the cells could move. In other words, the sharp edge on the lens acts as a scraper (in the same way as the windscreen wipers on a car work)

The second mechanism that is at work is the “peeling effect whenever there is a radius on the posterior edge of the lens. In this case the hydraulic wedge effect is generating forces that are acting at right angles to the point of cell contact on the radius on the posterior

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edge of the IOL. These sideways acting forces are then “peeling” the capsule away from the surface of the lens – hence allowing the cell’s migration to continue on around the radius on the posterior edge of the lens.

In some cases the lens material may tend to stick to the capsular bag. My understanding is that hydrophobic IOL materials have this property. In cases such as this the adhesion between the lens material and the capsule surface will be increased – hence requiring greater wedge effect forces to separate the lens from the capsule.

In the case of PMMA and hydrophilic IOLs – as far as I am aware – the lens materials do not tend to naturally adhere to the capsule. Because of this it would be more important to maintain a sharp edge on the posterior surface of the lens than would appear to be the case with hydrophobic materials.

Model of the Eye

http://hyperphysics.phy-astr.gsu.edu/hbase/vision/eyescal.html

As the drawing above shows, the natural crystalline lens in the human eye is very different to the design of an IOL. These differences include:

1. The fact that both the anterior (front) and the posterior (rear) surfaces of the natural lens are strongly aspheric (not spherical) whereby the local radius of the lens continually varies across its diameter - as opposed to most IOLs that normally have spherical surfaces on both sides of the lens. It should be noted that some new IOLs are now being produced with aspheric surfaces.

2. The refractive index of the natural lens varies across its diameter as opposed to all IOLs which have a constant refractive index throughout the lens material

3. The natural lens has a much greater thickness than a normal IOL.

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The end result of these differences is that all IOLs are an inferior optical device to the natural lens. However, for this study the main difference of interest is the fact that because of the very different shapes and sizes of the natural lens and an IOL, the IOL does not fill the capsular bag in the same way as the natural lens does. This has certain mechanical effects on the capsular bag – such as unsupported areas and creasing in the bag which in turn can provide a “gateway” for the lens epithelial cells to migrate through irrespective of how sharp the posterior surface if the IOL may be.

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The Rim EffectBelow are three photographs that demonstrate the “rim effect”. We can consider the photograph directly below of a spherical ball sitting in the top of a jar as a model of the posterior surface and edge of an IOL. The ball represents the spherical posterior surface of the IOL and the top rim of the glass represents the rim around the posterior edge of the IOL. (See many of the CAD pictures and drawings below in this document to see the similarities)

You can use a rubber balloon as a model of the capsular bag as it is very thin and pliable such as the capsular bag is reported to be an elastic structure about 10 to 25 µm thick.

Quote - Steven Cains

Clinically, it is remarkably thin, One often describes it as glad-wrap, but it is much thinner than that. One can poke it and polish it, and a continuous circular tear in it has a very strong edge, which can resist significant stretching

Quote - Suresh Pandey (referring to rabbits eyes)

The elastic lens capsule is thick anteriorly (varying from 10 to 25 µm without epithelium), with the maximum thickness a little closer to the equator than at the anterior pole. At the equator, it can be from 8 to 17.5 µm thick; and it thins gradually to a minimum thickness of 4 to 6 µm at the posterior pole.

In the two photographs below a normal child’s balloon has been draped over the ball in the glass and then held in place by the rubber band. The significant points here are:

The radius of the ball is significantly different to the radius of the balloon – with the balloon radius being measured by inflating – but not stretching the balloon.

Despite the major mismatch in the radii of the ball and the balloon – and the consequent ripples in the balloon as it sits over the ball – where the balloon passes over the rim of the glass there is a definite stretching of the balloon at this point which then fits tightly around the rim of the glass.

As will be seen in the next section showing CAD models of the IOL after insertion in the capsular bag, this same arrangement of a major radii mismatch between the IOL and capsular bag exists along with the rim effect that comes about as a result of the haptics forcing the posterior rim of the IOL against the posterior capsule.

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CAD View of an IOL in the Capsular Bag

Below are a series of pictures of two (2) PMMA IOLs with different forms of sharp edges on their posterior surfaces. In both of these models the sharp edge extends all the way around the posterior surface of the lens – including across the haptics.

The CAD system is not capable of deforming the CAD model from its manufactured diameter of 13.00 mm across the haptics down to the compressed diameter of 9.60 mm diameter. Because of this the CAD model was redrawn to show the haptics in the calculated deformed position. There is always the risk that the real life situation will be a little different to the calculated form, but I don’t believe (at this stage) that there will be a significant departure in the manufactured IOLs from the deformed IOL shape shown below.

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Lens with a Turned-Up Rim around the posterior surface

The rim on the posterior surface of this lens design is the result of ensuring that the diamond cutting tool continues profiling across the optic surface so that the full clear 6.00 mm optic diameter is maintained with the required spherical form. The form that results is shown in the dimensioned sketch below.

A variation on this form could be that instead of the 11.54 degree tangent angle formed by the 0.50 mm radius on the diamond cutting tool – the cutter could machine straight out away from the edge of the 6.00 mm clear optic diameter, so producing a rim with zero angulation on the rim e.g. a 90 degree sharp edge – instead of the 78.46 degree corner as shown.

The cutting tool is likewise carried completely across the anterior surface of the lens past the 6.00 mm clear optic diameter so that the full clear optic diameter of 6.00mm on both the anterior and posterior surfaces is maintained.

The milling operation that produces the haptics must be carried out at a radius of about 0.15 mm greater than the rim diameter around the posterior edge so that the milling cutter does not damage the very smooth clean sharp edge that has been produced on the posterior edge by the 0.050 mm tip radius cutting tool on the lathe. This has the effect of producing a stepped ridge effect on the edge of the IOL which will be clearly seen in the pictures below.

A note of caution is needed at this point in relation to viewing the pictures below. The CAD models of both the IOLs and the capsular bag that are shown below are accurate models (to thousandths of a millimeter). However because the images are zoomed up for easy viewing purposes, the dimensions of the rims on the IOLs appear to be exaggerated in size. Please bear this in mind and make the appropriate mental corrections when assessing the pictures

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Turned-Up Rim around the posterior surface – 8 diopter26

Turned-Up Rim around the posterior surface – 30 diopter

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Summary – turned up rim IOL

There is a large mismatch between the posterior IOL radius of (8 diopter = 38.8 mm, 30 diopter = 10.3 mm) and the capsular bag rad of 6.3mm. This means that the center of the capsular bag has nothing to support it – and hence will sag and crease, unless the posterior surface of the IOL is pushed against the capsular bag by the action of the haptics.

Because of the “rim effect” (e.g. the haptics push the rim of the posterior edge of the IOL into the posterior capsule), the capsular bag should be tightly stretched across the sharp posterior edge of the IOL. Because of the rim formed around the edge of the posterior lens surface and the fact that there is a constant included angle of 78.46 degrees – or an included angle of 90 degrees if the flat topped rim was preferred – and the fact that this in turn produces a constant surface area of contact between the lens and the bag irrespective of the dioptric power of the IOL – the contact stress (pressure) between surface of the lens in contact with the capsular bag is constant irrespective of the dioptric power of the lens. Because the contact stress is constant, then so is the force required from the lens epithelial cells to peel the bag away from the edge of the lens – irrespective of the dioptric power of the IOL.

Because of the rim that is formed around the posterior edge of the IOL, this means that the milling surface has to also be offset a further 0.15 mm out from this rim in order to ensure that the sharp posterior edge on the lens is not damaged during the milling operation. This means that because this extra milling rim sits against the capsular bag then it should also provide some extra level of protection against the migration of the lens epithelial cells as they attempt to migrate across the posterior capsular bag. However, there are two conditions with this statement. One is the fact that this milling rim does not extend fully around the lens as the haptics break this continuity. The other condition is that because this milling edge is not protected during the tumble polishing operation, that – depending on certain circumstances – it may be that this edge is rounded and is not sharp so being able to act as a “scraper” – or in fact may not even touch the posterior capsule, depending on how large the radius is.

The other factor is the fact that the capsular bag will bear against the top of the haptics at the point at which the haptics join onto the central optic body of the lens. As the pictures above show, this effect is a little more pronounced on the higher diopter power IOLs (e.g.30 diopter) than with lower (8) diopter power lenses. This mechanical interference will have the effect of reducing the contact stress between the capsular bag and the posterior edge of the IOL at the points where the haptic join the optic body of the IOL. This in turn will reduce the peel strength of the capsular bag off of the lens at these points. However, the CAD models show

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that there should still be a continuous line of contact between the posterior edge of IOL and the capsular bag completely around the circumference of the IOL.

Sharp posterior lens surface with no rim around it

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Sharp posterior surface with no rim – 8 diopter

Sharp posterior surface with no rim – 30 diopter

Summary – sharp edge no rim IOL

There is a large mismatch between the posterior IOL radius of (8 diopter = 38.8 mm, 30 diopter = 10.3 mm) and the capsular bag rad of 6.3mm. This means that the center of the capsular bag has nothing to support it – and hence will sag and crease, unless the posterior surface of the IOL is pushed against the capsular bag by the action of the haptics.

Because of the “rim effect”, the capsular bag should be tightly stretched across the sharp posterior edge of the IOL. However an examination of the dimensioned drawing and pictures above clearly show that the angle of contact between the capsular bag and the posterior edge

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of the IOL with this design is always greater than 90 degrees – whereas the turned up rim version is never more than 90 degrees –and in fact should only be 78.46 degrees. Furthermore, this angle of contact becomes greater as the dioptric power of the lens increases e.g. the angle with a 30 diopter lens is grater than with a 10 diopter lens.

Because this design does not have a rim around the posterior edge – then the angle that the capsular bag makes with the posterior edge of the IOL varies according to the dioptric power of the IOL. This in turn produces a variable surface area of contact between the lens and the bag depending on the dioptric power of the IOL – the contact stress (pressure) between surface of the lens in contact with the capsular bag is variable according to the dioptric power of the lens. Because the contact stress is variable, then so is the force required from the lens epithelial cells to peel the bag away from the edge of the lens – depending on the dioptric power of the IOL.

The other factor is the fact that the capsular bag will bear against the top of the haptics at the point at which the haptics join onto the central optic body of the lens. As the pictures above show, this effect is a little more pronounced on the higher diopter power IOLs (e.g.30 diopter) than with lower (8) diopter power lenses. This mechanical interference will have the effect of reducing the contact stress between the capsular bag and the posterior edge of the IOL at the points where the haptic join the optic body of the IOL. This in turn will reduce the peel strength of the capsular bag off of the lens at these points. However, the CAD models show that there should still be a continuous line of contact between the posterior edge of IOL and the capsular bag completely around the circumference of the IOL. However the interference, and hence the reduction in the contact stress, with this edge form is much greater that the turned-up edge rim form on the posterior IOL edge.

Comparison between a turned up rim and a sharp edge with no rim

In order to present a constant barrier effect to the migration of the lens epithelial cells across the anterior surface of the posterior capsule, the lens capsular bag interface should have certain mechanical properties. These are:

The barrier effect – in terms of the contact stress – should be constant and not be dependent on the dioptric power of the IOL. This in turn effectively means that the posterior edge of the IOL should have a rim around on which the majority of the contact between the lens and the capsule takes place.

The barrier effect should be formed by the scraper effect of a sharp edge that does not allow the epithelial cells to act as a hydraulic wedge that peels the capsular bag off of the posterior edge of the IOL

The sharper the angle that the capsular bag has to conform to around the posterior edge of the IOL – and the tighter that the capsule is stretched around the IOL edge- the smaller the radius that will form on the anterior surface of the capsular bag as it turns around the sharp corner on the posterior surface of the IOL. The smaller this radius, the less space there is for the epithelial cells to enter and act as a hydraulic wedge.

The point at which the haptics joins onto the central optic body should not act to reduce the contact stress between the capsular bag and the posterior edge of the IOL to the point where the peel strength of the capsule from the lens is significantly reduced because of mechanical interference between the haptics and the posterior capsule surface.

On all three counts above, the lens with the turned up rim around the posterior surface has the advantage over the IOL which simply has a sharp posterior edge with no rim on it.

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Lenses in the marketplace

A short look on the internet reveals that there are IOLs offered for sale that have a rim on them although the reason for the rim is not explicitly stated.

In the example below the posterior edge is a plus 90 degree sharp edge where the angle will vary according to the dioptric power of the IOL. The anterior surface of the IOL has a turned up rim and a rounded edge. The turned up rim is almost certainly the result of making the radius of the cutting tool continue on over the clear optic diameter of the anterior surface of the lens so that it maintains the full 6.00mm clear optic diameter.

The radiused anterior edge (along with the angled side of the IOL) is stated as assisting to reduce off-axis light beam glare within the lens. In the proposed new FH Asmara designs the anterior surface of the lens will have a naturally occurring radius (as the current FH105 & FH106 lenses do simply because the polishing mask will not protect that edge. At this stage I am not proposing an angled edge on the IOL.

As a square edge is a corner that forms a right angle (e.g. 90 degrees), it is clear that the posterior edge shown on the lens below (Sensar OptiEdge) is not really a “square edge” – but should be described as a sharp edge.

http://www.revophth.com/index.asp?page=1_255.htm

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The Rayner C-flex hydrophilic lenshttp://www.rayner.com/products.php?PHPSESSID=7720cf46c1aa9d6bf26cc410d330d2ba

This lens has curved posterior edge that appears to be identical to the “turned up rim” described in this document as the preferred posterior edge style

Biotech “EYECRYL” with a “Fish Tail” e.g. a “curved up” posterior edgehttp://www.biotechvisioncare.com/eyecryl-01.html

This lens has curved posterior edge that appears to be the same as the “turned up rim” described in this document as the preferred posterior edge style

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Questions

It is clear that in order to ensure that the posterior surface of the IOL sits against the posterior capsule – and that the posterior capsule is not distorted e.g. creased – that the haptic design is also an integral part of the design of an intraocular lens. However haptics do not form part of the current discussion. For the purposes of this discussion the assumption is made that a suitable haptic design has ensured that the IOL is pressed against the capsule and that the capsular bag has no undue creasing in it because of asymmetrical radial haptic forces e.g. the radial haptic forces are reasonably constant around the circumference of the capsular bag.

The questions that we seek to answer in this document are the following.

1..) Maximum allowable radius on the posterior IOL edge

Common opinion within the ophthalmic profession seems to favour the idea of a sharp edge on the posterior surface of the IOL as a means of preventing or at least reducing, the incidence and severity of postoperative PCO.

As the mechanical analysis in this document confirms, there are well known and accepted engineering reasons for this characteristic of a sharp “scraper” type of edge preventing material passing across the sharp edge. The best known example for people who are not connected to the engineering world is the windscreen wiper on a car. These blades only work so long as they have a really sharp edge contacting the windscreen. As soon as this edge begins to wear and form a radius, water and road grime act as a hydraulic wedge at the point of contact between the blade and the windscreen, and simply lift the wiper blade off of the windscreen – hence making it useless and having to be replaced.

QUESTION 1-a Although many studies confirm the effectiveness of the “sharp edge” in assisting in PCO prevention, none of the studies that I have seen actually specify the maximum radius on the lens in the studies. What then is the maximum allowable radius on the posterior IOL edge that is acceptable for an IOL to claim that it has a “sharp posterior edge”?

2..) Creases in the capsular bag

From the mechanical analysis in this document it is clear that there is a mismatch between the radii on the posterior edge of the IOL and the posterior capsule. Unless the posterior edge of the IOL is pressed against the posterior capsule surface by the action of the haptics the rim effect of the sharp posterior edge of the IOL will not operate and hence any creases in the posterior capsule will act as gates through which the lens epithelial cells can migrate. Creases in the capsule can also form as a result of uneven pressure from the haptics around the circumference of the capsular bag. E.g. the haptics are stretching the bag in the radial direction – but not in the direction at right angles to that. This creasing effect is shown below.

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QUESTION 2-a I have not seen any of the full detailed studies of sharp edged IOLs versus PCO, but in the versions that I have read none of the studies seen to discuss – or report – the effect of creases crossing the sharp edge of the IOL as one of the contributing factors towards PCO. Have any of the studies reported on the effect of creasing in the posterior capsule on PCO?

3..) A Rim or No-Rim on the Posterior Edge of the IOL

The mechanical analysis in this document would indicate that a turned-up rim on the posterior edge of the IOL that presents a constant included angle around the rim of less that 90 degrees – or at least a rim that has a constant angle of 90 degrees – presents a more effective barrier to the migration of the lens epithelial cells than the same lens that merely has a sharp posterior edge on it.

The angle on the simple no-rim sharp edge posterior IOL is always greater than 90 degrees. In addition, this form of lens has a variable contract stress level between the posterior capsule and the posterior surface of the IOL depending on the dioptric power of the lens. It also has an increased mechanical interference effect between the capsule and the area where the haptics join the central optic body. Both of these effects cause a reduction in the peel strength of the capsule off of the IOL – hence leading to a reduction in the barrier effect.

QUESTION 3-a From the clinical viewpoint which of the two options would you prefer e.g. turned-up posterior rim or a simple “sharp posterior edged” IOL

4..) Maximum Clear Optic Diameter

Optic theory shows that a better image is formed when the effective lens diameter is at a maximum. In order to achieve this on a lens that is manufactured by machining, you need to have a rim around the anterior edge of the lens.

QUESTION 4-a Do you believe the existence of the rim around the anterior surface of the lens will affect either the lens in the clinical sense – or the attitude of ophthalmologists towards it – given that there are already samples of these IOLs in the market place?

5..) Stress levels in the capsule

Mechanical stress is a natural part of physical existence. However, there are always safe levels of tensile, compressive, shearing and contact stresses that must not be exceeded in any given design.

QUESTION 5-a Does the ophthalmic profession have tables that show maximum permissible stress levels within the capsular bag?

6..) Capsular bag shrinkage

Clinical studies seem to confirm that the capsular bag shrinks in the months following the removal of the natural crystalline lens. The bag is known to shrink in the radial direction. It presumably also shrinks in the axial direction as well. In this case we would expect to see some shrinkage of the posterior capsule to form a close fit around the contour of the posterior edge of the IOL and probably some shrinkage onto the posterior surface of the IOL as well.

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QUESTION 6-a Assuming that the capsule shrinks in both the axial and radial directions, are there any photographs available showing an IOL in place in the eye and where the relationship of the posterior capsule to the posterior edge and surface of the IOL is clearly demonstrated

7..) Clinical Ophthalmic comments

QUESTION 7-a Are there any general comments to be made on the current design options of the posterior edge – and./or haptic design (which will form a separate document – but any comments now will assist in the analysis of the haptics)

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