Patent Application
20140118699
The invention relates to measurement and analysis of the ocular environment.
Dry eye disease affects approximately 12 million people in the US. The integrity of the tear film lipid and aqueous layers is critical for proper tear film function and avoidance of dry eye. Wavelength-dependent optical interferometry has been used to simultaneously measure tear film lipid and aqueous layers thicknesses at a single point at the apex of the cornea over a period of time. Such measurements can be used to diagnose sub categories of dry eye from (a) either lipid or aqueous deficiencies, or (b) time-profile changes in lipid and aqueous layer thicknesses after a blink.
Accurate and precise determination of lipid and aqueous layer thicknesses are critical for proper diagnosis of dry eye sub categories. Previous lipid and aqueous layer thickness calculation methods using interferometry data were conducted separately. This was due to the large differences in layer thicknesses (aqueous: 1-5 microns, lipid: 20-120 nanometers), basing aqueous thickness calculations upon spectral interference oscillations and absence of spectral oscillations from the lipid layer.
The latter absence of spectral oscillations from the lipid layer presents a difficulty in calculating tear film lipid layer thickness. Thus, there is a need for improvement in the accurate and precise determination of the thickness of the lipid layer. This improvement would be beneficial to the physician, and would allow researchers to better design lubricant eye drops for dry eye patients with meibomian gland dysfunction (MGD). Improved measurement methods may also allow researchers to design more comfortable contact lens and lens care solutions for contact lens wearers. Contact lens wear adversely affects the tear film lipid layer, which is thought to be responsible for the thinner, less stable tear film and resulting dryness among contact lens wearers than non-lens wearers.
Lastly, there are no known non-invasive diagnostic methods in the art for measuring the refractive index of the corneal epithelium at the precise boundary of the aqueous layer and the anterior surface of the corneal epithelium, known as the corneal glycocalyx. Anterior corneal surface refractive index is believed to be a parametric measurement directly related to the structure of the glycocalyx. The glycocalyx is comprised of transmembrane mucins and the integrity of the corneal glycocalyx is believed to be required for tear film stability and prevention of dry eye. Having such a diagnostic tool would assist researchers in the diagnosis of dry eye and development of compositions which could assist or restore a patient's glycocalyx function. Simultaneous in vivo measurements of this interface, along with tear film aqueous and lipid layer measurements, all of which comprise the ocular environment, may prove to be of use in dry eye diagnosis or elucidating dry eye etiology or ocular effects of topically-applied solutions.
This invention solves the problem of accurately and precisely measuring tear film lipid layer thickness by applying a new mathematical method to simultaneous tear film lipid and aqueous layer thicknesses and corneal refractive index calculations from interferometry data. The mathematical method is based upon electromagnetic and scalar scattering theories and thin film physics and includes two empirically-discovered factors, “bb” and “exp(−cc*1000/λ)”, wherein bb and cc are numbers, to account respectively for interferometer light losses/gains and light scattering at an optically rough surface.
The mathematical method for simultaneous tear film lipid and aqueous layers thicknesses and corneal refractive index calculations from interferometry data comprises the steps of: selecting a patient; aligning an eye of the patient with light originating from a light source; measuring tear film and ocular surface light reflectance of a patient; determining a value for tear film aqueous layer thickness, creating a mathematical construct of tear film and ocular surface light reflectance R based upon a characteristic mathematical matrix of a thin film stack comprising in sequence from top to bottom: air as a boundary, a tear film lipid layer, the tear film aqueous layer and a corneal epithelium as a semi-infinite substrate; multiplying R by two terms, bb and exp(−cc.*(1000./L).̂1.0), wherein bb and cc are numbers, to find lipid and aqueous layer thicknesses and corneal surface refractive index and determining whether the tear film and ocular surface is deficient.
This new mathematical method provides a better determination of tear film lipid layer thickness than previous more empirical methods. This new method also provides a more accurate calculation of tear film aqueous layer thickness determination and provides for the first time a value for the corneal epithelial refractive index at the precise boundary of the aqueous layer and the surface of the corneal epithelium, believed to be the corneal glycocalyx. This new method requires one to take under consideration all of the optical characteristics of interferometry measurements and the tear film as well as the optical characteristics of the corneal epithelial surface, which forms the underlying substrate for the tear film. Using this method, a practitioner may determine whether the tear film meets acceptable parameters, or whether it is deficient in any way by comparison to a reference value. By way of example, but not of limitation, such deficiencies may include aqueous deficiencies, lipid deficiencies or deficiencies of the corneal surface. If the practitioner is a doctor, the deficiency may be treated by way of an appropriate medication. If the practitioner is a researcher, this deficiency may be noted as a way to steer research and/or development of a new medication.
A wavelength-dependent optical interferometer of the type developed by King-Smith et al and Huth (King-Smith P E, Fink B A, Fogt N, Nichols K K, Hill R M, Wilson G S. The thickness of the human precorneal tear film: evidence from reflection spectra. Invest Ophthalmol Vis Sci 2000; 41:3348-3359; Huth, U.S. Pat. No. 7,963,655 B2) was utilized. The tear film was modeled as a stack of 2 homogeneous films between air as a semi-infinite medium and the cornea as a semi-infinite substrate:
The refractive indices, nn, were derived from literature, where
n0=1,
n1=sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29)))), derived from a Sellmeier equation fit of data from Tiffany (Tiffany, J M. Refractive index of meibomian and other lipids. Current Eye Research, 5 (11), 1986, 887-889),
n2=1.32806+0.00306.*(1000./L).̂2 from Ewen King-Smith, personal communication. and
n3=b(2)+0.00306.*(1000./L).̂2, where b(2) starting value=1.338 since the cornea refractive index at the aqueous tear interface is unknown (n3 is expressed as v5 in software code, since it is a fitted term), and where
L=λ, nm for n1, n2 and n3
There are a total of 3 boundaries at the interfaces between media of differing refractive indices:
Boundary I: between air and the lipid layer of the tear film
Boundary II: between the lipid and aqueous layers of the tear film
Boundary III: between the aqueous layer of the tear film and the corneal epithelium
The angle of incidence θ onto the apex of the cornea of the incident light source in the interferometer was 0.091 radians. Other angles of refraction into a layer and incidence onto the succeeding layer are defined and expressed mathematically as follows from Snell's law:
n0 sin θ=n1 sin β;
n1 sin β=n2 sin γ and
n2 sin γ=n3 sin δ
and from the equations above for n0, n1, n2 and n3, and where:
angle of incident light onto the lipid layer, angle θ=0.091 radians;
angle of incident light onto the aqueous layer=angle β;
angle of incident light onto the corneal surface=angle γ and
angle of refracted light into the cornea=angle δ.
Refracted light in the lipid layer=incidence angle onto the aqueous layer=angle β, where β=asin(no sin θ/n1)=asin(1.*sin(0.091)./sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29)))));
Refracted light in the aqueous layer=incidence angle onto the corneal epithelium=angle γ, where γ=asin(n1 sin β/n2)=asin(n1 sin(asin(no sin θ/n1)/n2))=asin (sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29)))).*sin(asin(1.*sin(0.091)./sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29))))))./(1.32806+0.00306.*(1000./L).̂2)))); and
Refracted light in the corneal epithelium=angle δ, where δ=asin(n2 sin γ/n3)=asin ((1.32806+0.00306.*(1000./L).̂2).*sin(asin(sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29)))).*sin(asin(1.*sin(0.091)./sqrt(1+(((−851.03).*L.*L)./(L.*L−(816.139)))+(((420.267).*L.*L)./(L.*L−(−706.86)))+(((431.856).*L.*L)./(L.*L−(2355.29))))))./(1.32806+0.00306.*(1000./L).̂2)))./(b(2)+0.00306.*(1000./L).̂2)))). The last denominator here, (b(2)+0.00306.*(1000./L).̂2), is expressed as v5 in software code, as the program needs to iteratively fit the best value of n3 to the observed data and thus n3 also becomes a determined output.
The film stack is first treated mathematically as in Hecht (Optics, Eugene Hecht, 4th ed., pp. 426-428, Pearson Education, Inc., Addison Wesley, 1301 Sanome St., San Francisco, Calif. 94111, 2002). Electric and magnetic field intensities are designated conventionally, as E and H, respectively, with subscripts I, II or III referring to these fields at the respective boundaries. Thus, for a single thin dielectric film (layer) between two semi-infinite transparent media,
E
I
=E
II cos k0h+HII(i sin k0h)/Ω1
and
H
I
=E
IIΩ1i sin k0h+HII cos k0h,
where
and where h=2 n1d cos β, where d=layer thickness.
In matrix notation, these linear equations take the form,
Expansion of this equation using the values for EI, HI, EII and HII derived from the boundary condition requirements that the tangential components of both the electric and magnetic fields be equal across the boundaries yields the following expanded expression:
and Ω0 has its corresponding value based upon n0 and cos θ, e.g., Ω0=√∈0/μ0)*n0 cos θ.
When the components of this matrix are expanded, one obtains the reflection (r) and transmission (t) coefficients:
The characteristic matrix, M, above, also written as MI, relates the fields at the two adjacent boundaries in the above system with a single film between two semi-infinite transparent media. If there are two overlying films on a substrate, e.g., the tear film lipid and aqueous layers on the corneal epithelial substrate, the resultant system matrix is calculated by multiplication of the individual matrices of the lipid and aqueous layers.
where h1 (lipid layer 1)=2 n1dlip cos β, h2 (aqueous layer 2)=2 n2daq cos γ, where dlip is the thickness of the tear film lipid layer (expressed as “a” in software code), daq is the thickness of the tear film aqueous layer (expressed as “d” in software code), where Ω1 and Ω2 have their previous definitions and where k0=π/λ. From this, reflectance is calculated from:
R=|r|2=|(Ω0m11+Ω0Ω3m12−m21−Ω3m22)/(Ω0m11+Ω0Ω3m12+m21+Ω3m22)|, where Ω2 is replaced by Ω3, since our substrate is the corneal epithelium, and where Ω3 has its corresponding value based upon n3 and cos δ, e.g., Ω3=√(∈0/μ0)*n3 cos δ. Reflectance is a measure of the proportion of intensities rather than field amplitudes. Reflectance is calculated since measurements can only be made of intensities. Matrix terms m11, m12, m21 and m22 are calculated from standard matrix algebra as follows:
Thus, ae+bg=m11; af+bh=m12; ce+dg=m21; and cf+dh=m22.
An example of matrix term calculation and expansion follows. From matrix algebra, m11=cos k0h1*cos k0h2+i sin k0h1/Ω1*Ω2i sin k0h2=cos((2.*π)./λ).*n1dlip cos β)*cos ((2.*π)./λ).*n2daq cos γ+((i sin((2.*π)./λ).*n1dlip cos β)/(√(∈0/μ0)*n1 cos β))*(√(∈0μ0)*n2 cos γ*i sin((2.*π)./λ).*n2daq cos γ).
Thus, Ω0m11=√(∈0/μ0)*n0 cos θ.*cos((2.*π)./λ).*n1dlip cos β)*cos((2.*π)./λ).*n2daq cos γ+√(∈0/μ0)*n0 cos θ.*((i sin((2.*π)./λ).*n1dlip cos β)/(√(∈0/μ0)*n1 cos β))*(√(∈0/μ0)*n2 cos γ*i sin((2.*π)./λ).*n2daq cos γ).
In the software code for calculating R=|r|2, the equation for the first term, Ω0m11, is expanded using values and equations above for n0, n1, n2, θ, β and γ to:
Other terms for calculating R=|r|2 are calculated and expanded similarly, yielding the final equation:
The final equation and software require that an initial value for tear film aqueous layer thickness be used. This initial value for tear film aqueous layer thickness can be derived from methods disclosed in U.S. Pat. No. 7,963,655 B2, which is incorporated herein by reference. Alternatively, since the aqueous layer thickness of the tear film averages about 3000 nm for non-contact lens wearers, this can be used as an input starting value for non-contact lens wearers. Since the aqueous layer thickness of the tear film averages about 2500 nm for contact lens wearers, this can be used as an input starting value for contact lens wearers.
Note the final equation also includes two additional terms, bb and exp(−cc.*(1000./L).̂1.0), wherein bb and cc are numbers, not described by the theory for the characteristic matrix for a film stack. The first term, bb, was determined to be required to increase or decrease the mathematically-fitted reflectance, R, at each measured wavelength, to achieve a better fit to measured reflectance. This is necessary since the interferometer measures only relative reflectance of the tear film, relative to the measured reflectance of a glass lens standard, not absolute reflectance. Thus, interferometer instrument raw data are quotients of measured reflectance of the tear film divided by the measured reflectance of the glass lens standard. Measured tear film reflectance is subject to changes in light intensity, depending upon focus and eye alignment, since the instrument is designed to reflect only a small spot of light from the apex of the cornea.
The second term, exp(−cc.*(1000./L).̂1.0), was discovered empirically to achieve a better fit of the measured reflectance data to the mathematically-fitted reflectance, R, at each measured wavelength, L. This term evolved from an initial failed attempt to use scalar light scattering theory and a theoretical Gaussian distribution of substrate (e.g., the corneal epithelium in our case) surface height variation, which involved multiplying R by exp(−cc.*(1000./L).̂2.0). Scalar scattering theory is based upon the principle that longer light wavelengths are scattered by a rough surface less than shorter wavelengths, resulting in interference peak and trough amplitude modulation. In other words, interference spectra of thin films overlying rough surfaces are expected to have larger oscillations at longer wavelengths, due to variation of thickness of the thin film layer caused by variation of surface roughness (height) of the underlying surface.
We believe, without wishing to be bound by this explanation, that the second term, exp(−cc.*(1000./L).̂1.0), accounts for an empirically-discovered non-Gaussian distribution of substrate surface roughness. This is believed due to the macroscopic size of the imaged area of the tear film (12.5×133 um) which would encompass multiple corneal epithelial cell surfaces, cell borders and corneal surface microplicae.
In some cases, a second term to account for substrate surface roughness of exp(−a(1000/λ)+b(1000/λ)2), wherein a and b are numbers, was found to provide a better fit of the measured reflectance data to the mathematically-fitted reflectance, R. The format of this second term accounts for both non-Gaussian and Gaussian distributions in surface roughness. It is anticipated that other non-Gaussian surface roughness distributions will have to be accounted-for when using the methods of the present invention. Such surface roughness distributions can be mathematically modeled using mathematics terms as in Rakels J. Influence of the surface height distribution on the total integrated scatter (TIS) formula. Nanotechnology 7 (1996): 43-46, which is incorporated herein in its entirety by reference. Alternatively, any non-Gaussian height distribution function or single mathematical term may be employed, whose relevance can be determined by the goodness of fit methods of the present invention, comparing a fitted function R comprising a non-Gaussian height distribution function or single mathematical term to experimentally measured interference spectra.
Given the length of the equation, changing wavelength and requirements for fitting calculated R to measured R, a least squares minimization technique is preferably employed, where an error function is evaluated and minimized. Software was developed using the MatLab® software platform from The MathWorks, Inc. The software of the present invention uses the Gauss-Newton method to find the optimal values for the refractive index of the corneal epithelium, thickness of the lipid layer and “bb” and “cc” parameters. The software requires starting values for aqueous layer thickness, lipid layer thickness (using a value selected from 20 to 140 nm), refractive index of the corneal epithelium (starting with 1.338+0.00306.*(1000./L).̂2) and bb parameter (set=1 to start). Other fitting-error minimization methods other than the Gauss-Newton method may also be employed, which are well-known in the art, such as the Levenberg-Marquardt algorithm.
Thus, the mathematical method for simultaneous tear film lipid and aqueous layers thicknesses and corneal refractive index calculations from interferometry data comprises the steps of: selecting a patient; aligning an eye of the patient with light from a light source; measuring tear film and ocular surface light reflectance of a patient; determining a value for tear film aqueous layer thickness, fitting the light reflectance from the eye of the patient to a mathematical construct of tear film and ocular surface light reflectance R based upon a characteristic mathematical matrix of a thin film stack comprising in sequence from top to bottom: air as a boundary, a tear film lipid layer, the tear film aqueous layer and a corneal epithelium as a semi-infinite substrate; multiplying R by two terms, bb and exp(−cc.*(1000/L).̂1.0), wherein bb and cc are numbers, to find lipid and aqueous layer thicknesses and conical surface refractive index and determining whether the tear film and ocular surface is deficient by comparing the obtained thickness and refractive index values to reference values representing a normal eye without any deficiencies or an eye with deficiencies.
Alternatively, depending on the patient being tested, since the aqueous layer thickness of the tear film in non-contact lens wearers averages about 3000 nm, this can be used as an input starting value and the step for determining a value for aqueous layer thickness in the method above can be omitted.
Alternatively, depending on the patient being tested, since the aqueous layer thickness of the tear film in contact lens wearers averages about 2500 am, this can be used as an input starting value and the step for determining a value for aqueous layer thickness in the method above can be omitted.
Also, if interferometer instrument optical reflectance measurement errors are eliminated, the bb term becomes 1, and thus can be omitted.
This new method provides a value for the conical epithelial refractive index at the precise boundary of the aqueous layer and the surface of the corneal epithelium, believed to be the corneal glycocalyx. The glycocalyx is comprised of the membrane-spanning mucin MUC16. When MUC16 is lost or shed, a dry spot can form. Since the integrity of the corneal glycocalyx is known to be required for tear film stability and prevention of dry eye, this new method offers a potential new diagnostic tool for the diagnosis of dry eye.
This new method can be used for both non-contact lens wearers and contact lens wearers. The method can be used to evaluate the efficacy and retention time of novel lubricant eye drops such as those based upon oil-in-water emulsions and which are designed to supplement the lipid or lipid and aqueous layers of the tear film.
The code we constructed on the Matlab® software platform follows:
The following examples illustrate the method of the invention:
An interferometric reflectance spectrum of a human subject's right eye baseline tear film is taken, as described in U.S. Pat. No. 7,963,655 B2. Measured reflectance data are processed according to the method of the present invention without and with the application of the correction with the (exp (−cc*10001×)) term in the equation for total reflectance, R, wherein cc is a number.
An interferometric reflectance spectrum of a human subject's right eye baseline tear film is taken, as described in U.S. Pat. No. 7,963,655 B2. Measured reflectance data are processed according to the method of the present invention without and with the application of the correction with the (exp (−cc*1000/λ)) term in the equation for total reflectance, R.
An interferometric reflectance spectrum of a human subject's right eye baseline tear film is taken, as described in U.S. Pat. No. 7,963,655 B2. Measured reflectance data are processed according to the method of the present invention without and with the application of the correction with the (exp (−cc*1000/λ)) term in the equation for total reflectance, R.
An interferometric reflectance spectrum of a human subject's right eye baseline tear film is taken, as described in U.S. Pat. No. 7,963,655 B2. Measured reflectance data are processed according to the method of the present invention without and with the application of the correction with the term (exp (−a(1000/λ)+b(1000/λ)2), wherein a and b are numbers, in the equation for total reflectance, R.
Interferometric reflectance spectra of human subject's right eye baseline tear films are taken, as described in U.S. Pat. No. 7,963,655 B2. Measured reflectance data are processed according to the method of the present invention with the application of the correction with either the (exp (−cc*1000/λ)) or (exp (−a(1000/λ)+b(1000/λ)2; subject 2, scans CJ through CN) term and consistently with the bb termin the equation for total reflectance, R. Table 1 presents results of simultaneous measurements and calculations of tear film lipid and aqueous layer thicknesses and corneal surface refractive index. Tear film lipid and aqueous layer thickness values are consistent with literature (King-Smith P E, Fink B A, Fogt N, Nichols K K, Hill R M, Wilson G S. The Thickness of the Human Precorneal Tear Film Evidence from reflection Spectra. Invest Ophthalmol Vis Sci. 2000; 41:3348-3359; Korb D R, Baron D F, Herman J P, Finnemore V M, Exford J M, Hermosa J L, Leahy C D, Glonek T, Greiner W. Tear film lipid layer thickness as a function of blinking. Cornea. 1994; 13(4): 354-359). Lipid thickness range=34-119 nm, mean=74 nm, stdev=23 nm and aqueous thickness range=1546-3870 nm, mean=2639 nm and stdev=403 nm. A tear lipid layer thickness of 34 nm potentially represents a tear lipid deficiency. An aqueous layer thickness of 1546 nm potentially represents a tear aqueous deficiency. Corneal surface refractive index range=1.3288-1.3386, mean=1.3328 and stdev=0.0024. Intrasubject refractive index stdev for 6 subjects, n≧5 measurements, were: 0.0010, 0.0009, 0.0006, 0.0009, 0.0010 and 0.0027.
Table 2 and
Table 3 presents average corneal surface refractive index calculations taken from data in Table 1, along with refractive index data from subjects wherein a single measurement was taken.
An interferometric reflectance spectrum of a human subject's (rh33) baseline tear film is taken, as described in U.S. Pat. No. 7,963,655 B2, while the subject was wearing an ACUVUE® 2 soft hydrogel contact lens. Measured reflectance data are processed according to the method of the present invention with the application of the correction with the (exp (−cc*1000/λ)) and bb terms in the equation for total reflectance, R. The application of the method of the invention to contact lens wearers requires the use of the contact lens refractive index as a starting value for refractive index, instead of the refractive index starting value of 1.338+0.00306*(1000/λ)2 used for non-contact lens wearers. In this case, a value of 1.4053+0.00306*(1000/λ)2 was used, as this is the published value for refractive index of the ACUVUE® 2 soft hydrogel contact lens (1.4053), along with an assumed dispersion factor of 0.00306*(1000/λ)2.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 13310026 | Dec 2011 | US |
| Child | 14058564 | US |
