**Purpose**:
To determine the riboflavin concentration gradient in the anterior corneal stroma when using the Dresden protocol with different dextran solutions.

**Methods**:
Three different groups of porcine corneas, five each, were compared regarding the riboflavin concentration in the anterior stroma. Before all experiments, stable hydration conditions were established for the corresponding solution. All groups were treated with 0.1% riboflavin in different dextran solutions (15%, 16%, 20%). After imbibition, two-photon microscopy was used to determine fluorescence intensity. For signal attenuation and concentration determination corneas were saturated and measured a second time by two-photon microscopy. Additionally, the distribution was calculated mathematically and compared to the empiric results.

**Results**:
Riboflavin concentration is decreasing with depth for all dextran solutions. A nearly constant concentration could be determined over the first 75 μm. Analysis of the fit functions leads to diffusion coefficients of *D* = 2.97 × 10^{−7} cm^{2}/s for the 15% dextran solution, *D* = 2.34 × 10^{−7} cm^{2}/s for the 16% dextran solution, and *D* = 1.28 × 10^{−7} cm^{2}/s for the 20% dextran solution. The riboflavin gradients of the 20% dextran group were statistically significantly different from 15% dextran starting at a depth of 220 μm and deeper (*P* = 0.047). The 16% dextran group differed statistically at a depth of 250 μm and deeper (*P* = 0.047). These results show a significant difference to those published previously.

**Conclusions**:
With correct settings two-photon microscopy is a precise way to determine the concentration of riboflavin in cornea. The measured gradient is excellently fit by a Gaussian distribution, which comes out as a solution of Fick's second law.

^{1–3}In clinical routine, cross-linking is achieved by using the Dresden protocol: After removing the epithelium, riboflavin is applied to the surface of the cornea.

^{1,4}Diffusion leads to a spreading of riboflavin in the stroma of the cornea and anterior chamber. Since riboflavin acts as a photosensitizer, it can be activated by ultraviolet A (UV[A]) light and forms new chemical bonds within the extracellular matrix.

^{1,5}These newly formed bonds (cross-links) increase the mechanical stiffness of the cornea. The riboflavin acts also as UV(A) light protection for the endothelium, lens, and retina.

^{6–8}Therefore, the success of the cross-linking is highly dependent on an adequate riboflavin concentration in the cornea. In several publications, the distribution of riboflavin through the corneal stroma has been investigated with different approaches, such as (two-photon) fluorescence microscopy

^{9–11}and high-performance liquid chromatography.

^{12,13}In our described work, two-photon fluorescence microscopy was used for this purpose as well, but the methodology was changed in comparison with previous publications.

^{14,15}Two-photon absorption transfers a molecule (here, riboflavin) into an excited state, that returns to the ground state by emission of fluorescence. Since two-photon absorption is restricted to the focal volume, the laser can be scanned in a defined plane and a consecutive pointwise signal detection results in a two-dimensional image. Variation of the focal position over depth (z-position) allows imaging in different planes and facilitates a three-dimensional reconstruction of a defined volume.

^{16–18}Generated fluorescence light is absorbed by the extracellular matrix and by the riboflavin itself on its way back to the surface. In addition, scattering occurs at keratocytes and collagen inhomogeneities.

^{19}These losses must be compensated by an appropriate correction model.

^{9–11}However, due to methodical errors all three groups underestimated or did not address all different sources of loss of the fluorescence and, therefore, come to erroneous conclusions.

**Figure 1**

**Figure 1**

^{10,20}For signal detection, the microscope system was equipped with two photomultiplier tubes arranged in backward direction (behind the objective lens). To restrict the detectable wavelength range, bandpass filters were used in front of every photomultiplier tube. For detecting the riboflavin fluorescence, a bandpass filter with a transmission window of 525 ± 25 nm was used. In the second detection pathway, second harmonic signals generated at the stromal collagen could be detected simultaneously when using a bandpass filter with a transmission window of 450 ± 35 nm in front of the second photomultiplier tube. A scheme of the total setup is shown in Figure 1c. For each cornea, images were recorded in z-stacks with a step size of 10 μm over a depth of 350 μm. One single image inside the stack covered an area of 400 × 400 μm

^{2}with a pixel resolution of 1042 × 1042. In addition, one dark image (same settings, but without laser irradiation) was taken after every z-stack. After saturation, each cornea was imaged again in a z-stack with the same parameters as described before. The saturation process was necessary to correct our data for absorption and scattering effects.

*c*(

*z*,

*t*) stands for the riboflavin concentration,

*D*for the diffusion coefficient,

*z*for the depth in the cornea, and

*t*for time. To solve this differential equation, useful boundary conditions must be assumed. Taking the experiments into account, it can be assumed that

*c*(

*z*,0) = 0 for all

*z*that are not equal to 0. The concentration

*c*tends to infinity for

*z*= 0. This means that all molecules whose number can be described by

*N*are located in an infinitesimal volume

*V*at the surface of the stroma. Since

*c = N/V*and

*V →*0, the concentration is tending to infinity. With these boundary conditions, Fick's second law can be solved by

*B*stands for

*N*/2 and reduces the number of factors.

*U*tests were performed (Winstat; R Finch, Bad Krozingen, Germany). Significance was accepted if

*P*< 0.05.

**Table**

*z*-axis measured from riboflavin-treated corneas were corrected by data obtained from the same corneas in a saturated state. Figure 2 shows exemplarily the fluorescence intensities obtained from a cornea treated with 15% dextran after 30 minutes of riboflavin application and the corresponding data obtained from the same cornea in a saturated state. As expected, measured intensities from the saturated cornea are higher compared to intensities after applying riboflavin for 30 minutes. To determine the riboflavin concentration as a function of corneal depth, the resulting intensity values in the various depths were divided pairwise (fluorescence intensity after 30 minutes of treatment/fluorescence intensity of saturated cornea) and multiplied with the concentration of the riboflavin solution [0.1%]).

**Figure 2**

**Figure 2**

*n*= 5 corneas treated with 15% dextran,

*n*= 5 corneas treated with 16% dextran, and

*n*= 5 corneas treated with 20% dextran. In all cases, the experimentally obtained data (means ± SE) and the corresponding fit functions (solution of Fick's second law) are displayed.

**Figure 3**

**Figure 3**

*D*= 2.97 × 10

^{−7}cm

^{2}/s for the 15% dextran solution,

*D*= 2.34 × 10

^{−7}cm

^{2}/s for the 16 % dextran solution, and

*D*= 1.28 × 10

^{−7}cm

^{2}/s for the 20% dextran solution. To compare the results of the different groups with each other, Figure 4 shows line diagrams of the mean values from Figure 3.

**Figure 4**

**Figure 4**

*P*= 0.917). The riboflavin gradients of the 20% dextran group were statistically significantly different from 15% dextran starting at a depth of 220 μm and deeper (

*P*= 0.047). The 16% dextran group differed statistically from the 20% dextran group at a depth of 250 μm and deeper (

*P*= 0.047).

^{11}that proposed an exponential gradient with steep slope at the surface, or that of Gore et al.,

^{10}who found a relatively constant concentration throughout the whole corneal thickness after 30 minutes.

*D*= 1.28 × 10

^{−7}cm

^{2}/s for the 20% dextran solution compared to

*D*= 2.97 × 10

^{−7}cm

^{2}/s for the 15% dextran solution. From x-ray scattering experiments

^{21}in corneal stroma, we know that primarily the collagen molecule is superficially cross-linked. However, Hayes et al.

^{21}also found cross-links within and between the proteoglycans. In a deswollen cornea, proteoglycans and collagen are more densely packed and, therefore, intermolecular cross-links are facilitated. Therefore, for clinical efficacy of corneal cross-linking (CXL) a higher concentration of dextran is preferable. On the other hand, a steep gradient avoids sufficient riboflavin concentration in the deeper layer, and, therefore, causing less cross-linking in the posterior cornea.

^{22}We assumed that the slight reduction in thickness results from a constant dextran concentration throughout the experiments, because we refilled the riboflavin/dextran reservoir with fresh solution after each measurement step.

^{−7}cm

^{2}/s. In the literature, diffusion coefficients of the stroma are reported with a magnitude of 10

^{−7}cm

^{2}/s as well.

^{23}Thus, the diffusion coefficients obtained from the fit functions are comparable to those reported by Araie et al.

^{23}

^{11}used an excitation wavelength of 880 nm in their studies and detected the riboflavin fluorescence as well as the second harmonic signal generated at collagen fibrils present in the stromal region simultaneously. To correct for scattering effects of laser light and fluorescence emission, the intensity loss of the second harmonic was determined and used as a reference for the depth-associated reduction of signal. An incident laser wavelength of 880 nm leads to a resulting second harmonic generation at 440 nm. Since riboflavin has an absorption maximum at 445 nm the generated second harmonic is absorbed by the riboflavin itself. Thus, using the second harmonic signal is not a good reference signal to compensate scattering effects in riboflavin treated corneas.

^{10}tried to correct the two-photon fluorescence signal by imaging a cornea that was treated with riboflavin for 50 minutes. In their setup, riboflavin was stored in a sole reservoir on top of the cornea during the treatment. After 50 minutes of treatment, they assumed an uniformly soaked cornea, as fluorescence signals almost did not change any more, and used the signal obtained from this for signal correction over depth. This assumption is wrong, especially when considering the relatively big volume of the anterior chamber, which acts as a sink during the diffusion process. As they used full globes, the concentration gradient after 50 minutes cannot be constant and the assumption of a uniformly soaked cornea after 50 minutes cannot be made.

^{9}used confocal microscopy to estimate the riboflavin distribution inside the cornea before cross-linking. In their experiments, an excitation wavelength of 458 nm was used. This wavelength is absorbed strongly by corneal tissue.

^{9}The results obtained were not corrected for absorption and scattering effects in the cornea. Thus, the data presented mainly demonstrated a loss of signal over the depth due to absorption of the incident light only (Lambert Beer's Law).

**T.G. Seiler**, None;

**T. Ehmke**, None;

**I. Fischinger**, None;

**D. Zapp**, None;

**O. Stachs**, None;

**T. Seiler**, None;

**A. Heisterkamp**, None

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