As mentioned above, the calculation results of the MC method are closer to the experimental data rather than those calculated by the DSF method. When applying DSF,
20,24,25,30 researchers first assess the scattering effect of a single fibril, then combine the effects of all fibrils. The DSF method is simple and intuitive but overlooks the continuous attenuation of incident light and multiple scattering among fibrils. Our improved MC method tracks incident particles as they undergo complex scattering among the fibrils, simulating realistic light intensity attenuation during transmission. Using the developed image recognition program, we accurately capture the size and distribution of corneal fibrils. The obtained fibril radius in porcine corneas is well agreed with the results measured by X-ray scattering.
31 The existing research suggests the main causes of corneal transparency loss due to edema are (1) increases in corneal thickness and fibril radius; (2) greater differences in refractive indices between fibrils and the extracellular matrix; and (3) increased short-range disorder in fibril distribution, leading to a more uneven arrangement.
14,25 Figure 8 illustrates microscopic mechanisms of the main causes obtained from the improved MC method. After edema occurs, the radius of the corneal fibrils as scatterers slightly increases. Because the scattering ability of the fibrils grows with the fourth power of their radius, their scattering capacity is enhanced significantly. Additionally, as the cornea hydrates, its thickness increases, leading to a longer path for transmitted light and less transparency. This phenomenon can be described by
Equation 5. Both fibrils and the extracellular matrix absorb water. According to observation of TEM images, the volume increase of the extracellular matrix is much greater than that of the fibrils, indicating that more water is absorbed by the extracellular matrix. The difference in water-binding capacities disrupts the already existing refractive index imbalance, making light transmission less efficient, because hydration reduces the refractive indices of both the fibrils and the extracellular matrix.
15 The short-range arrangement of corneal fibrils is crucial for enhancing light transmission.
12 Over a hydration period of 0 to 10 hours, the short-range zone of the fibril distribution expands significantly, over 30%, increasing the free path of scattered particles. Incident particles are more likely to escape the boundaries rather than being received.
The common DSF theory uses the Born approximation to solve the Schrödinger equation for scattering, which is only accurate when the scattering is a perturbation relative to the incident light. When the wavelength of the incident light is short, according to
Equation 2, the scattering cross-section of fibrils increases sharply. Moreover, when highly edematous cornea occurs, scattering cross-section of fibrils also increases. These will induce that Born approximation is not satisfied, leading to a large deviation between the calculation result and the experimental result. Compared to the DSF theory, our improved MC method has merits: (1) tracking the trajectories of incident light particles rather than using the Born approximation; (2) considering multiple scattering among fibrils. As shown in
Figure 9, prediction errors of the MC method are much lower than those of the DSF method, especially in the conditions of high hydration and short wavelengths. The predicted errors of the MC method are less than 4%, even in the conditions of low hydration and longer wavelengths.
In summary, this article presents an improved MC method for predicting corneal transparency. This method tracks the trajectories of incident light particles and considers multiple scattering among fibrils. It can elucidate the microscopic mechanisms underlying the reduced transparency of edematous corneas and well predict the corneal transparency with errors less than 4%. We also developed an image recognition program to accurately detect the characteristic of the fibrils. These results help understanding of scattering abnormalities in edematous corneas and effective supporting advancements in biomedical imaging.