Principles of Corneal Cross-Linking





Introduction


Originally, corneal cross-linking (CXL) was introduced to prevent the progression of keratoconus. However, during in vitro and in vivo experiments, in addition to the biomechanical stabilization of the cornea, an increased resistance of tissue against melting enzymes may occur. Consequently, the first publication on clinical application of CXL was about melting disease in the cornea. Between 2000 and 2003, our group in Dresden reported on CXL for keratoconus at several meetings and Gregor Wollensak presented the first prospective study on corneal CXL in 23 eyes with a follow-up of 1 year and longer. He reported stabilization and even regression of keratoconus as detected by corneal topography in all cases. Based on this publication, the international community took notice of CXL of the cornea and prospective studies were launched in countries such as Italy and Australia. During the following years, the technique was improved: the Dresden Protocol (30 minutes riboflavin/dextrane application, 30 minutes ultraviolet [UV] light application of 3 mW/cm 2 , 7 mm in diameter) was established and safety limits defined.




Basic Principles


During the CXL process, hyperactive radicals are generated that produce new chemical bonds within the cornea. Four ingredients are necessary to accomplish corneal CXL: riboflavin, oxygen, UV light, and the extracellular matrix of the cornea. Seconds after switching on the UV light, the pool of oxygen diluted in the cornea is exhausted ; therefore the oxygen-dependent CXL pathway may play only a minor role. The remaining participants in the CXL process (extracellular matrix, riboflavin, and UV light) and their interaction can be modeled using a mathematical model that was developed in material science.


The intensity I of the UV light at a point P inside the cornea is dependent on the depth z = z r •cos α and the local concentration of riboflavin c(z). The Lambert-Beer law leads to


<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='I(z)=I0·exp(−ε·c(z)·z/cosα),’>?(?)=?0·exp(−?·?(?)·?/cos?),I(z)=I0·exp(−ε·c(z)·z/cosα),
I(z)=I0·exp(−ε·c(z)·z/cosα),
with I 0 being the (homogenous and perpendicular to the surface) light intensity in the corneal plane. Owing to the oblique incidence in the periphery of the UV light, a reduced intensity/area I c follows a simple cosine law:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='Ic=I0·cosα.’>??=?0·cos?.Ic=I0·cosα.
Ic=I0·cosα.
For simplification, a linear decrease of the riboflavin concentration from the front to the rear surface of the cornea (thickness d) is assumed:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='c(z)=c0·(1−z/d).’>?(?)=?0·(1−?/?).c(z)=c0·(1−z/d).
c(z)=c0·(1−z/d).
However, this assumption is not correct: Ehmke et al. measured the riboflavin gradient inside the cornea by means of 2 photon microscopy and found a sinusoidal decay toward deeper layers of the stroma that, in first order, may be approximated by a linear function.


Following the theory of polymerization, the local radical formation rate R(z,α) is proportional to the square root of the product of riboflavin concentration and light intensity:


<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='R(z,α)=k·(c(z)·I(z))1/2′>?(?,?)=?·(?(?)·?(?))1/2R(z,α)=k·(c(z)·I(z))1/2
R(z,α)=k·(c(z)·I(z))1/2

<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='=k·(c0(1−z/d))1/2·Ic1/2·exp(−ε·c(z)·z/2·cosα).’>=?·(?0(1−?/?))1/2·??1/2·exp(−?·?(?)·?/2·cos?).=k·(c0(1−z/d))1/2·Ic1/2·exp(−ε·c(z)·z/2·cosα).
=k·(c0(1−z/d))1/2·Ic1/2·exp(−ε·c(z)·z/2·cosα).

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Oct 10, 2019 | Posted by in OPHTHALMOLOGY | Comments Off on Principles of Corneal Cross-Linking

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