Four Characteristics and a Model of an Effective Tear Film Lipid Layer (TFLL)

Abstract

It is proposed that a normal, effective tear film lipid layer (TFLL) should have the following four characteristics: 1) high evaporation resistance to prevent water loss and consequent hyperosmolarity; 2) respreadability, so it will return to its original state after the compression-expansion cycle of the blink; 3) fluidity sufficient to avoid blocking secretion from meibomian glands; 4) gel-like and incompressible structure that can resist forces that may tend to disrupt it. These characteristics tend to be incompatible; for example, lipids that form good evaporation barriers tend to be disrupted by compression-expansion cycles. It is noted that clues about the function and organization of the TFLL can be obtained by comparison with other biological lipid layers, such as lung surfactant and the lipid evaporation barrier of the skin. In an attempt to satisfy the conflicting characteristics, a “multilamellar sandwich model” of the TFLL is proposed, having features in common with the skin evaporation barrier.

I. COMPARISON OF BIOLOGICAL LIPID LAYERS

Deficiency of the tear film lipid layer (TFLL) is the basis of evaporative dry eye,¹ and therefore an understanding of this layer is fundamental to the diagnosis, management, and treatment of dry eye disorders. Here, it is proposed that a normal, effective TFLL should have the following four characteristics:

1. It should have a high evaporation resistance to prevent water loss and consequent hyperosmolarity.

2. It should have good respreadability, so that the lipid layer returns to its original state after the compression-expansion cycle of the blink.

3. It should be sufficiently fluid that it does not block secretion from meibomian glands.

4. It should be gel-like and incompressible so that it can resist forces that may tend to disrupt it.

Some of these characteristics tend to be incompatible. The gel-like, incompressible property (characteristic 4) would evidently tend to be at odds with fluidity (characteristic 3). Additionally, monolayers having high evaporation resistance (characteristic 1), such as saturated fatty acids and their esters,² tend to show poor respreadability (characteristic 2).^3,4 Thus, lipid layer composition and structure must involve compromise and trade-off between apparently conflicting characteristics.

Rantamaki et al discussed how a comparison of two biological lipid layers, namely, the TFLL and lung surfactant, can lead to insights into the relation of their function and composition.⁵ Both layers are “respreadable” in that they withstand compression-expansion cycles, either from breathing or from blinking. However, evaporation resistance is important for the TFLL, but not for the lung lipid layer; given the small size of the alveoli, the enclosed air would rapidly become saturated, even if the evaporation resistance were comparable to that of the tear film lipid layer. Here, we extend this approach to the comparison of biological lipid layers involved in the prevention of evaporation, as summarized in Table 1.

Table 1.

Comparison of different biological lipid layers by function and major components

Biological lipid layer	Respreadable?	Evaporative barrier?	Major components	Saturated hydrocarbon chain length ≥ 19?	References
Tear film lipid layer (TFLL)	Yes	Yes	Wax esters Cholesteryl esters Polar lipids Surfactant proteins	Yes	11,12,22
Lung surfactant	Yes	No	Phospholipids Surfactant proteins	No	13,15
Human skin lipid	No	Yes	Ceramides Cholesterol Fatty acids	Yes	98
Skin lipid secretions (tree frog)	No	Yes	Wax esters Triglycerides	Yes	10
Plant lipid layer (cuticle)	No	Yes	Hydrocarbons Ketones Alcohols	Yes	7
Arthropod lipid layer	No	Yes	Hydrocarbons	Yes	6

A. Function

Table 1 compares function and composition for six different biological lipid layers. Although the TFLL and lung surfactant are respreadable and withstand compression-expansion cycles, the other four layers are not subjected to such cycles. However, they, like the TFLL, are all thought to be barriers to evaporation,^6-10 as indicated in Column 3 of Table 1.

B. Composition

The TFLL and lung surfactant layer have some similarity of composition in that they both contain polar lipids (such as phospholipids)^11-15 and surfactant proteins, particularly the hydrophobic proteins SP-B and SP-C.^13,15-16 These surfactant proteins are thought to have a role in the respreading of lung surfactant during the breathing cycle,^13,15 and while their function in the tear film is unknown, they may play a corresponding role in the blink cycle.

Whereas the main components of lung surfactant are polar phospholipids,^13,15 the other five layers, which are all thought to be evaporation barriers, are composed mainly of nonpolar lipids.^6-10 There is considerable variation in the type of nonpolar lipids in different types of layer (Table 1). Whereas wax and cholesteryl esters are the main nonpolar lipids in the TFLL, other types of nonpolar lipids are common in the other four evaporation barrier layers. However, all five evaporation barriers have one striking feature in common; they all contain many, very long (≥19 carbons) saturated hydrocarbon chains.^6-10 The saturated chains in lung surfactant, which does not function as an evaporation barrier, have generally fewer than 19 carbons. The corresponding entries in Table 1, Column 5 match those in Column 3, to emphasize the correlation between saturated chain length and evaporation barrier function.

II. ROLE OF LONG, SATURATED HYDROCARBON CHAINS IN EVAPORATION RESISTANCE OF MEIBUM

A. In a normal eye, the lipid layer has a high evaporation resistance compared to lipid monolayers

“Evaporation resistance” is a measure of the ability of a surface layer to retard evaporation of water. It is described in the Appendix (Section VI), together with estimates of the evaporation resistance of rabbit and human tear film lipid layers. In Table 2, these estimates are compared with the evaporation resistance of monolayers of hexadecanol and octadecanol, which are the lipids most commonly used to retard evaporation from reservoirs.¹⁷ Evaporation resistance of monolayers is not significantly improved by increasing average thickness to more than that of a monolayer; either the regular array of molecules in a monolayer is disturbed in the thicker layer,¹⁸ or the additional lipid forms thick “lenses” within the monolayer.¹⁹

Table 2.

Evaporation resistance of tear film lipid layers and monolayers

Layer	Evaporation resistance, s/cm	Reference
Rabbit lipid layer#	37.3	59
Rabbit lipid layer	12.9	58
Human lipid layer#	20.2	61
Hexadecanol, C16H33OH#	0.70	17
Octadecanol, C18H37OH#	1.73	17

^#See Appendix

^*For 35°C and a surface pressure of 30mN/m on distilled water, based on the equations of Barnes and La Mer¹⁷

B. Evaporation resistance increases exponentially with saturated chain length.

Lipid monolayers that form good evaporation barriers have two characteristics. First, the molecule must contain saturated rather than unsaturated hydrocarbon chains. For example, Jarvis et al found that saturated fatty acids containing 16 or more carbon atoms, and saturated alcohols containing 14 or more carbon atoms, caused considerable resistance to evaporation at temperatures of 16 to 20°C.²⁰ For comparison, all the unsaturated fatty acids that they tested – elaidic, oleic, linoleic, and stearolic acids – showed no detectable resistance to evaporation. The second important characteristic is that evaporation increases greatly with increasing length of the saturated hydrocarbon chain. Figure 1 shows measurements of evaporation resistance of saturated fatty acids as a function of carbon chain length (from Archer and La Mer²¹). Evaporation resistance is an exponential function of chain length. Adding one carbon atom increases the evaporation resistance by a factor of 1.65, so increasing the chain length by 3 carbon atoms from 17 to 20 atoms increases evaporation resistance by a factor of 1.65³=4.5. Thus, the increase in evaporation resistance as a function of chain length is much greater than expected by simple proportionality between resistance and chain length, which would predict an increase in resistance of a factor of only 1.18 for an increase from 17 to 20 carbon atoms.

Figure 1.

Evaporation resistance as a function of carbon chain length for saturated fatty acids at 25°C. An exponential curve has been fitted to the experimental results. (Redrawn from Archer and LaMer.²¹)

C. Meibum contains long, saturated hydrocarbon chains.

Analysis of the lipid molecules in meibum shows that they have the two characteristics for forming a good barrier to evaporation, namely saturated hydrocarbon chains which are abnormally long. Thus, McCulley and Shine found that most of the fatty acids in cholesteryl esters are saturated, as are most of the fatty alcohols in wax esters.²² Additionally, they found that most of the fatty acids in cholesteryl esters and most of the fatty alcohols in wax esters have chain lengths greater than or equal to 19 carbons. (The fatty acids of wax esters differ in that they are often shorter and unsaturated.) More quantitative data has been provided by Butovich, who found that the most common fatty acids in cholesteryl esters are saturated and have 24, 25, and 26 carbon atoms, and the most common fatty alcohols in wax esters are also saturated and have 24, 25, and 26 carbon atoms.¹¹ Given the exponential increase in evaporation resistance as a function of chain length shown in Figure 1, it seems probable that these abnormally long chains help to provide the high evaporation resistance of the lipid layer (Table 2). A clinical implication is that any substitute for the natural lipid layer might need to contain long, saturated hydrocarbon chains in order to simulate natural meibum and provide a good barrier to evaporation.

It is important to note that lipids containing saturated hydrocarbon chains, particularly DPPC, play an important role also in lung surfactants.^13,15,23 These lipids are capable of reducing lung surface tension to low values, hence preventing collapse of alveoli, which is a major cause of respiratory disorders.²³ Although these saturated chains are not as unusually long as in the TFLL (palmitic acid has 16 carbons), the presence of saturated chains in both lung surfactants and the TFLL could raise problems for the respreading of the lipid layers in the breathing and blinking cycles, respectively, as discussed in the next section.

III. SPREADABILITY OF LIPID LAYER AFTER BLINK

During a blink, the TFLL does not pass under the lids but is trapped between the lids,²⁴ so it thickens considerably during the compression phase and thins during the expansion phase of the blink. Bron et al demonstrated that the TFLL often has a remarkable ability to return to its original pattern after a blink.²⁵ After other blinks, the lipid pattern does change considerably, but it is still expected that characteristics of the TFLL, such as its resistance to evaporation, are not consistently degraded by the blink cycle (otherwise extensive degradation would occur after the thousands of blinks that occur during a day).

The ability of meibum to withstand compression/expansion cycles can be studied using a Langmuir trough. A thin layer of meibum is spread on an aqueous sub-phase, and then the “surface pressure” (two-dimensional equivalent of pressure) of the meibum is measured as a function of its surface area as it is compressed and expanded through one or more cycles.³ Meibum is little altered by compression-expansion cycles; thus, for any surface area, surface pressure during expansion is not much different from the surface pressure during compression.³ More importantly, the surface pressure functions for repeated compression-expansion cycles are similar to that for the first cycle,^3-4,26 indicating that meibum is “respreadable.”

Although the TFLL is typically thicker than a monomolecular layer,²⁷ insights into its compression-expansion cycles can, nonetheless, be obtained from monolayer studies. The mechanisms involved in compression-expansion cycles of the TFLL can be elucidated by studying the “collapse” of monomolecular layers of lipids when they have been compressed so much that there is insufficient space for all the lipid molecules in the monolayer. Some of the lipid molecules must then be expelled from the plane of the monolayer. Monolayer collapse may be reversible (ie, expelled lipids are re-incorporated when the film is expanded again) or it may be irreversible (ie, expelled lipids are not re-incorporated on expansion); examples will be discussed below. As implied above, the collapse of a monolayer of meibum is largely reversible.⁴

Collapse of a lipid monolayer can occur by formation of a bilayer fold perpendicular to the surface, either extending upward into the air (Figure 2A)²⁸ or downward (Figure 2.B).²⁹ Collapse may also cause folds that are parallel to the surface, either above (Figure 2.C)³⁰ or below (Figure 2.D)³¹ the main monolayer. Folds can occur along straight lines,²⁹ or they can have a circular outline.³⁰ Respreading of lung surfactants after collapse is aided by the surfactant proteins, SP-B and SP-C.¹³

Figure 2.

Collapse of lipid monolayers. Circles represent polar headgroups of lipid molecules whereas attached lines represent hydrophobic hydrocarbon chains. A. Upward folding towards the air. B. Downward folding towards the aqueous sub-phase. C. A parallel fold above the main monolayer surface. D. A parallel fold below the main monolayer surface.

A. Some lipids collapse irreversibly on compression and do not return to their original state after expansion

Substances containing saturated hydrocarbon chains tend not to be respreadable in a Langmuir trough study. Thus, in the first compression-expansion cycle, the surface pressure during expansion is often much lower than for the original compression of the same surface area. Moreover, surface pressures in the second and later cycles are often much different from that of the first cycle. Example lipids include stearic acid, cholesteryl palmitate, and dipalmitoyl phosphatidylcholine (DPPC).³ In addition to the changes in surface pressure, the appearance of the lipid layer at the end of the first compression-expansion cycle may be quite different from the original appearance.⁴ If an artificial meibum substitute were composed of lipids that collapsed irreversibly, then the substitute would fail to provide a barrier to evaporation.

B. Other lipids return close to their original states after a compression/expansion cycle

Substances containing unsaturated hydrocarbon chains tend to show more respreadability than those containing saturated chains. Thus, in the first compression-expansion cycle, the surface pressure during expansion is usually similar to that during compression for the same surface area. Additionally, surface pressures in the second and later cycles are usually similar to the first cycle. As an example, cholesteryl nervonate, derived from the mono-unsaturated nervonic acid, has much more repeatable compression-expansion cycles than cholesteryl palmitate, derived from the saturated palmitic acid.⁴

In simulations of lung surfactants, lipids containing unsaturated chains (eg, palmitoyl– oleoyl phosphatidylcholine) improve the respreadability of lipids containing only saturated chains, such as DPPC.^13,15,23,32 It thus is possible that the unsaturated chains in meibum, particularly the fatty acid components of wax esters, which are commonly oleic acid,¹¹ aid in the respreading of the TFLL after blinking. Since surfactant proteins SP-B and SP-C aid in the respreading of lung surfactant during breathing,^13,15 they may have a similar role for the TFLL in blinking.

IV. VISCOSITY OF MEIBUM

Obstructive meibomian gland dysfunction (MGD) may involve an obstruction of the gland orifice and duct by hyperkeratinization,³³ but it may also involve a pathological, more viscous or rigid meibum.³⁴ In young normal subjects, expressed meibum is a clear fluid, but in eyes with advanced MGD, it can appear opaque and thick, like toothpaste.³⁵ Borchman et al have quantified the difference between meibum from MGD and normals by comparing the “phase transition temperatures” above which hydrocarbon chains change from a rigid, ordered “trans” configuration to a more fluid, disordered “gauche” configuration.³⁶ The phase transition temperature was significantly increased from 28.9°C in normals to 32.2°C in MGD. Correspondingly, the degree of chain order was significantly increased in MGD (at 33.4°C, close to the surface temperature of the eye).³⁷ These results indicate that meibum in MGD is typically more rigid or less fluid than in normals. It should be noted, however, that Raman and NMR spectroscopies do not support the suggestion that the increased viscosity observed in meibomian gland dysfunction is due to an increase in the ratio of saturated to unsaturated chains.^38-39

A. Unsaturation and branching of hydrocarbon chains affect melting temperature of lipids

Lipids containing unsaturated chains melt at lower temperatures than those with saturated chains and therefore tend to be more fluid. Thus, as Table 3 shows, for 18 carbon fatty acids, the melting point of mono-unsaturated oleic acid is about 55°C lower than for the saturated stearic acid. Similarly, branched-chain lipids tend to have lower melting points than the corresponding straight-chain lipids. In the simplest example, the melting point of branched iso-butane is 21°C lower than for the normal, straight-chain butane (Table 3).

Table 3.

Melting temperatures of unsaturated and branched-chain substances

Molecule	formula	type	Melting point
Stearic acid	C17H35COOH	Saturated	71.5°C
Oleic acid	C17H33COOH	Mono-unsaturated	16°C
N-butane	C4H10	Straight-chain	−138°C
Iso-butane	C4H10	Iso-branched	−159°C

B. Meibum contains unsaturated and branched hydrocarbon chains

In human meibum, the majority of fatty acid components in cholesteryl esters and the majority of fatty alcohol components in wax esters have saturated hydrocarbon chains.^11,22 However, 82% of fatty acid components of wax esters are unsaturated⁴⁰ of which 90% are oleic acid. Additionally, the majority of the saturated fatty acid components in wax esters are branched.⁴⁰ In conclusion, meibum contains both unsaturated and branched hydrocarbon chains, which can be expected to lower the melting point and make it more fluid at the temperature of the lipid layer.³⁶ These considerations have relevance to the development of artificial tears with a lipid supplement – addition of unsaturated and/or branched lipids may help to maintain lipid fluidity.

V. “DEWETTING” OF THE LIPID LAYER WITH EXCESSIVE FLUIDITY OF MEIBUM

A. The normal lipid layer resists “leveling” (smoothing) by surface tension, indicating a gel-like structure

The floating lipid layer, comprised of meibum and other ingredients from elsewhere on the ocular surface,^11-12,41 is much more viscous than the aqueous layer. Using a capillary tube to estimate the viscosity of meibum, Tiffany and Dart found that it was 10³ to 10⁴ times more viscous that water.⁴²

Observations at relatively low resolution with color interferometry show that the lipid layer may not spread evenly in the presence of MGD or other dry eye conditions.^1,43,44 High resolution images from King-Smith et al show some of the details of this poor spreading and may suggest at least some causes.⁴⁵ Broadband interferometry from a strobe is used to catch images of lipid layer dynamics during the blink and in subsequent interblinks. In some images, such as those in Figures 5 and 11 from that paper,⁴⁵ it can be clearly seen that there are so-called "droplets" with corners and edges that appear within the lipid layer; these droplets are often quite thick compared to the lipid layer. They may also be quite long-lived, over 10 seconds with no apparent change in aspect. Thus, one may reasonably conclude that these objects are definitely not a Newtonian liquid (like water), and that they may be more like a gel (or "jello"), in that they can support mechanical stresses and not deform like a liquid. We propose that the source of these droplets may be the organized lipid droplets observed in the acinar cells of the meibomian gland as seen in electron micrographs and discussed in Section VI.^46-47

B. Dewetting of the lipid layer can occur when the lipid layer is unusually fluid

A healthy lipid layer is generally spread to a fairly uniform thickness rapidly after a blink. In some cases, the rapid spreading does not occur or is very rapidly undone. As depicted in Figures 8 and 9 of King-Smith et al,⁴⁵ for less than 10% of the subjects they observed, the lipid layer was liquid enough that it could dewet and separate into liquid “islands” on the surface of the aqueous layer. The dynamics of this process can be quite rapid. One liquid island shaped like an upper case "C" (shown in their Figure 8⁴⁵) relaxes to a circular outline in a subsequent image that is 0.27s later. The process may begin from a complete or majority coverage of the lipid layer; Figure 13 in that paper shows an image that would correspond to an earlier stage in this dewetting process because much of the lipid is still connected.⁴⁵

Why does this dewetting occur in only some cases? We propose that the cause is an abnormal chemistry of the lipid layer; there appear to be two contributing factors, and either or both may be critical to these cases. The first factor is that such subjects may have lower concentrations of polar lipids or other surface active components of the tear film than are present in healthy subjects. The lack of an adequate amount of these surface active components would hinder spreading of the lipid layer on the aqueous tear film in the first place and fail to assist in maintaining the layer spread. The second factor could be a lack of higher melting point lipids that increase the viscosity of the lipid layer; a lower viscosity of the lipid layer would enable it to retract more quickly after being spread. Both factors could be present, especially in severe cases, such as those shown in Figures 8, 9, and 13 of King-Smith et al.⁴⁵

VI. CONCLUSIONS – IMPLICATIONS FOR LIPID LAYER STRUCTURE: A MULTILAMELLAR SANDWICH MODEL

Good biological barriers to evaporation involve dense, rigid, two-dimensional arrays of long, saturated hydrocarbon chains (Table 1 and Figure 1). However, monolayers of lipids with saturated chains, such as cholesteryl palmitate, tend to be rigid and poorly respreadable.^3,4 These observations imply that the TFLL should include dense arrays of long, saturated chains, organized in such a way that the overall TFLL structure is fluid and not disrupted by blinking. We propose a “multilamellar sandwich model” as a way of satisfying these requirements.

Two possible structures for the lamellae are proposed in Figure 3. In both cases, stacks of lamellae are represented by blue lines running parallel to the TFLL plane. Therefore, evaporating water must pass through several lamellae, thus increasing the evaporation resistance compared to a single lamella. The skin lipid barrier has been shown to have a rather similar multilamellar structure by electron microscopy.⁹ Given the saturated hydrocarbon chains in the lamellae, they may be relatively rigid, but the binding between faces of neighboring lamellae may be relatively weak, allowing them to slip over each other during blinking. In Figure 3.A, the lamellae are organized as flat plates. During the compression phase of the blink, the plates may slip between each other, like a deck of cards being shuffled. In Figure 3.B, the lamellae are derived from foldings of one or more larger sheets. In this case, compression during a blink may produce new lamellae by generating additional folds, as may occur during compression of lung surfactants.¹³ Leiske et al have used X-ray reflectivity on meibum spread on saline to demonstrate a multilamellar structure with lamellae parallel to the film surface⁴⁸; this supports the models of Figure 3.

Figure 3.

Possible structures of the tear film lipid layer. Red lines represent polar lamellae and blue lines represent nonpolar lamellae. A. “Plate” model of nonpolar lamellae. B. Folded model of nonpolar lamellae. See text for details.

Our model includes the proposal that polar lipids form an interface between nonpolar lipids and the aqueous layer.²² The red lines in Figure 3 represent polar lipids such as (O-acyl) omega hydroxy fatty acids^11,12 and phospholipids.¹⁴ The polar lipids have been represented as a folded sheet, and additional folds could be generated during blinking. Folds are shown both above and below the main monolayer surface, as in Figures 2.C and D, respectively, but it is possible that only one of these types could exist.

Possible molecular arrangements of cholesteryl and wax esters in the nonpolar lamellae are shown in Figure 4. It is proposed that the lamellae are in the form of “sandwiches” made from “interdigitated bilayers,”⁴⁹ where the center of the lamellar thickness consists of a dense array of the long, saturated hydrocarbon chains of cholesteryl and wax esters. The proposed structure is similar to the “sandwich model” of the skin lipid barrier, in that the core of the sandwich consists of densely packed, saturated chains providing the evaporation resistance.⁵⁰ In Figure 4.A, the interdigitation of saturated fatty acid chains of cholesteryl esters is similar to that in cholesteryl ester films deduced by Alonso et al,⁴⁹ and is also consistent with the “bilayer” type of structure observed in crystals of long-chain, saturated cholesteryl esters.⁵¹ Rectangles in Figure 4.A represent the cholesterol rings, while the side chain of cholesterol is represented by short lines at top and bottom of the lamellae. The long, saturated chains have a cross-sectional area of 0.18 to 0.2 nm², whereas the cross section of the cholesterol ring structure is 0.38 nm² – about twice as large⁴⁹; thus, the interdigitated structure of Figure 4.A, where a section through the saturated chains contains twice as many molecular cross-sections as a section through the cholesterol rings, is a compact, stable form. The long saturated chains slope at an angle of 24° corresponding to the molecular tilt observed in meibum films by grazing incidence X-ray diffraction.⁴⁸

Figure 4.

Possible molecular arrangement of cholesteryl and wax esters in the proposed nonpolar lamellae. For both cholesteryl and wax esters, the center of the lamellar thickness consists of interdigitated long, saturated chains. A. Cholesteryl esters. Long, saturated chains come from the fatty acid component. Rectangles correspond to the cholesterol rings, and the cholesterol side chain is represented by short lines at top and bottom. B. Wax esters. Long, saturated chains come from the alcohol component. The combining oxygen atoms are represented by circles, while unsaturated fatty acids (eg, oleic) are represented by kinked chains at top and bottom. C. Overall structure consisting of “domains” of cholesteryl and wax esters. D. An alternative overall structure where cholesteryl and wax esters are densely mixed on a molecular scale. E. A structure in which cholesteryl and wax esters are arrayed on opposite sides of the interdigitated chains.

For a cholesteryl ester based on typical saturated fatty acid chain lengths of 24-27 carbon atoms,⁵² the total thickness of this lamella would be about 5.5-6 nm. However, this value might be reduced if there was bending of the cholesterol side chains. It may be noted that small angle X-ray scattering of bulk human meibum⁵³ indicates multilamellar structures with a lamellar thickness of 4.9 nm, and multilamellar structures of a similar thickness have been demonstrated in meibum spread on saline.⁴⁸ It may also be noted that a small quantity of human meibum spread on saline at 20°C (20 μg over 80 cm²) forms a uniform layer (with included “lakes”) of about 5.2 nm thick.⁴ For a TFLL lipid layer thickness of 40-50 nm,^27,54 there could thus be about 10 lamellae, as in the models of Figure 3. Given the considerable variation in TFLL thickness,²⁷ there could be a corresponding variation in the number of lamellae.

A possible corresponding interdigitated bilayer of wax esters is proposed in Figure 4.B, where, in this case, the long, saturated chains come from the alcohol components; connecting oxygen atoms are given as circles, and unsaturated fatty acids (eg, oleic) are represented at top and bottom. The overall structure of a lamella might consist of “domains” of cholesteryl and wax esters (Figure 3.C), or a dense intermixing of the two ester molecules (Figure 3.D). It is also conceivable that cholesteryl and wax ester might be arrayed on opposite sides of the interdigitated chains (Figure 3.E). (It should be noted that, at a molecular level, the lamellae are three-dimensional structures and so are difficult to represent on a two-dimensional figure; thus, for example, the bent tails of the wax ester acids, which appear to collide with cholesterol side chains in Figures 3.C and D, could actually extend into the third dimension, in or out of the figure.) An important aspect of these lamellae might be that, whereas the long, saturated chains are bound strongly together to form a good barrier to water penetration, the outer surfaces of neighboring layers will not have such strong, regular binding and so may readily slip over each other during the blink. The unsaturated fatty acids of wax esters, and the iso-branching of the cholesterol side chain, which are both at the lamellar surfaces, may help to increase fluidity in the interface region between two lamellae (cf. Table 3).

It is possible that the lamellae in Figure 4 could form spontaneously by self-assembly. For example, McIntosh et al showed that the in vivo structure of the skin lipid layer, with a laminar repeat period of 13.0 nm, may be replicated in vitro by a mixture of ceramides, cholesterol and fatty acid in proportions similar to those found in vivo (other mixtures deviated from the in vivo structure).⁵⁵

An alternative origin of the nonpolar lamellae in Figure 4 may be proposed. Sirigu et al used freeze-fracture electron microscopy to study “fat droplets” in human meibomian glands, which are the main source of meibum lipid.⁴⁷ These fat droplets were seen to have an onion-like structure of very thin lamellae (perhaps similar in thickness to the proposed lamellae). Jester et al used transmission electron microscopy to show how the fat droplets (or “meibomian vesicles”) are generated by concentric layers of smooth endoplasmic reticulum which surround the droplets.⁴⁶ It thus seems possible that the proposed lamellae are derived from the lamellae of the fat droplets in the meibomian glands and that their structure, as in Figure 4, is generated and controlled by the smooth endoplasmic reticulum.

A remarkable finding about the evaporation resistance of the TFLL (Appendix and Table 2) is that it has not been possible to reproduce it in vitro by spreading meibum on saline.^56,57 Similarly, artificial TFLL compositions have little or no effect on evaporation.^58,59 Herok et al therefore proposed that prevention of evaporation by the TFLL requires a complex interaction between components of aqueous tears and meibum.⁵⁷ The in vitro evaporation resistance of meibum may also be readily disturbed by experimental procedures. In this respect, it may be noted that high evaporation resistance is difficult to achieve even in laboratory conditions. For example, in determining the evaporation resistance of a monolayer of a saturated fatty acid, the measured value increased by up to a factor of 20 with improved experimental procedure.⁶⁰ Particularly relevant to the TFLL is the finding that low concentrations (eg, 0.0125 molar fraction) of cholesterol can greatly reduce the evaporation resistance of a monolayer of octadecanol⁶¹; it seems possible that breakdown of cholesteryl esters in the TFLL by bacterial esterases could cause a similar reduction of the evaporation resistance of the TFLL.

It should be emphasized that the current model is proposed as a basis for discussion, and the model will need further development and analysis. The role of less common lipids, such as triglycerides,^11,12 needs to be considered. Additionally, studies of wax ester structures^62,63 have not shown the interdigitation of chains in Figure 4.B, so the origin of such an organization of wax esters needs to be considered; eg, can the known interdigitated structure of cholesteryl esters in Figure 4.A^49,51 form a “framework” for a similar interdigitation of wax esters in Figure 4.B?

In summary, the proposed lamellar structure of the TFLL avoids the potential incompatibility between the rigid arrays of long saturated chains needed for evaporation resistance and the fluidity required for respreading of the TFLL after a blink. The rigid evaporation barrier forms the central thickness of the nonpolar lamellae, while the surfaces of these lamellae allow easy slippage and provide the fluidity needed for respreading the TFLL. It would have an important clinical implication if the lamellae were disrupted by factors such as biosynthetic anomalies in meibomian glands,⁶⁴ inclusion of keratin proteins,⁶⁵ structural disorder associated with TFLL deposition on contact lenses,⁶⁶ or the ocular surface, bacterial lipases⁶⁷ and oxidative stress.⁶⁸ Such lamellar disruption could lead to increased evaporation, hyperosmolarity and dry eye.

VII. APPENDIX: EVAPORATION RESISTANCE OF THE TEAR FILM LIPID LAYER

In this appendix, rough estimates of the evaporation resistance of the lipid layer of the tear film are given, so that the values obtained can be compared with published values for lipid monolayers used in evaporation control.

A useful analogy to evaporation from the tear film is the flow of electric current through a chain of resistors. For a given potential difference between the ends of the chain, the current is given by Ohm’s Law, namely:

Current = (potential difference) / (total resistance).

Correspondingly, evaporation rate is given by a similar equation^21,69:

$$\mathrm{Flux}=\left(\mathrm{water}\mathrm{vapor}\mathrm{concentration}\mathrm{difference}\right)∕\left(\mathrm{total}\mathrm{evaporation}\mathrm{resistance}\right),$$ (A1)

where flux is the rate of flow of water per unit area, in g/(s.cm²), “water vapor concentration difference” is the difference between saturated water vapor concentration at the anterior eye temperature and the concentration for room air, in g/cm³, and “total evaporation resistance” is the sum of resistances for the lipid film and the overlying air; units of evaporation resistance are s/cm (reciprocal velocity).

In algebraic terms, Equation A1 may be written

$$F_{LA}=(C_E-\rho C_A)∕(r_L+r_A)$$ (A2)

where F_LA is flux through lipid and air layers, C_E is saturated water vapor concentration at the anterior eye temperature, r_L is the evaporation resistance of the lipid layer, r_A is the evaporation resistance of the overlying air, ρ is fractional relative humidity of room air and C_A is saturated water vapor concentration at room air temperature (thus ρC_A is the water vapor concentration of room air).

The evaporation resistance of the lipid layer can be derived as follows. Equation A2 can be re-written

$$r_L=(C_E-\rho C_A)∕F_{LA}-r_A$$ (A3)

The evaporation resistance of the overlying air, r_A, can be derived from Equation A2 by setting r_L=0,

$$r_A=(C_E-\rho C_A)∕F_A$$ (A4)

where F_A is the corresponding evaporative flux (i.e., no lipid resistance).

Substituting this expression into Equation A3 gives

$$r_L=(C_E-\rho C_A)(1∕F_{LA}-1∕F_A)$$ (A5)

Equation A5 shows that estimation of lipid resistance requires knowledge of five quantities: 1/. evaporative flux when lipid is present, F_LA; 2 and 3/. eye and room air temperatures (hence determining saturated water vapor concentration at these temperatures, C_E and C_A); 4/. relative humidity of room air, ρ; 5/. flux from a lipid free surface, F_A. In practice, not all these quantities are usually well known.

Mishima and Mauricemeasured evaporative flux from the rabbit tear film before and after removal of the lipid layer allowing a relatively complete estimate of lipid evaporation resistance using Equation A5.⁷⁰ Measured values of flux were:

F_LA = 7.78 × 10⁻⁷ g/(s.cm²)

F_A = 1.18×10⁻⁵ g/(s.cm²)

Other parameters in Equation A5 were not recorded, so the following values were assumed, based on an equation for saturated water vapor density⁷¹:

C_E = 3.97 × 10⁻⁵ g/cm³ based on anterior eye temperature of 35°C³⁷

C_A = 1.73 × 10⁻⁵ g/cm³ for assumed room temperature of 20°C

ρ = 0.5 (i.e., 50%) assumed relative humidity

Substituting all the above 5 values into Equation A5 gives a lipid resistance of 37.3 s/cm. This value, of course, depends on the assumed values of temperature and relative humidity. For example, an increase in anterior eye temperature of 1°C would increase the calculated lipid resistance by 6.8%, and increase in room temperature of 1°C would reduce the resistance by 1.7%, and an increase in humidity of 10% would reduce the resistance by 5.6%.

Iwata et al estimated the evaporation resistance of the lipid layer of the rabbit tear film to be 12.9 s/cm, only 35% of the above value.⁶⁹ Their procedure, which involved gluing a plastic chamber to the cornea, seems more invasive than the above method. It may also be noted that disturbance of the lipid layer of the tear film is likely to reduce evaporation resistance. Both these observations indicate that the higher resistance calculated above is closer to the true value. However, it is certainly possible that the higher value is an overestimate, eg, if the eye temperature was less than 35°C. It may be noted again that only approximate values of lipid evaporation resistance are needed here, for order-of-magnitude comparison with corresponding values for monolayers used for evaporation control.

From a review of published values, Tomlinson et al found an average evaporation rate for normal human eyes of F_LA = 13.57 × 10⁻⁷ g/(s.cm²).⁷²If the other four parameters in Equation A5 have the values given above, then evaporation resistance, r_L , would be 20.2 s/cm. King-Smith et al have argued that published evaporation rates are underestimates because of the restriction of air flow over the cornea by the pre-ocular chambers used in the measurements⁷³; it has been proposed that the thinning rate of the tear film between blinks may be a more accurate measure of evaporation rate which does not suffer from this restriction of air flow.⁷⁴ While a histogram of thinning rates⁷⁵ is a skewed distribution with a few cases of very rapid thinning, thus increasing the mean rate, the most common thinning rates give an evaporation rate similar to Tomlinson’s value above, which will therefore be retained for comparison with monolayer studies.