Analysis and data-based modeling of the photochemical reaction dynamics of the induced singlet oxygen in light therapies

Objective: The macroscopic singlet oxygen (MSO) model for quantifying the light-induced singlet oxygen ($^{1}O_{2}$) always contain a set of nonlinear dynamic equations and therefore are generally difficult to be applied. This work was devoted to analyze and simplify this dynamic model. Methods: Firstly, the nonlinearity of the MSO model was analyzed with control theory. The conditions, under which it can be simplified to a linear one, were derived. Secondly, in the case of ample triplet oxygen concentration, a closed-form exact solution of the $^{1}O_{2}$ model was further derived, in a nonlinear algebraic form with only four parameters that can be easily fitted to experimental data. Finally, in vitro experiments of anti-fungal light therapies were conducted, where the fungi, Candida albicans, were irradiated respectively by the 385, 405, 415, and 450 nm wavelength light. The singlet oxygen concentration levels in the fungi were measured, and then used to fit the developed models. Results: The parameters of the closed-form exact solution were estimated from both the simulated and the measured experimental data. Based on this model, a functional relationship between the photon energy, fluence rate and singlet oxygen concentration was also established. The fitting accuracy of this model to the data was satisfactory, which therefore demonstrates the effectiveness of the proposed modeling techniques. Conclusion: The results from simulating the closed-form model indicate that the photon energy within the range of either 2.7 $\sim$ 2.8 eV or 3.0 $\sim$ 3. 2 eV (388 $\sim$ 413 nm or 443 $\sim$ 459 nm in wavelength) is more effective in generating singlet oxygen in the fungi studied in this work. Significance: It is the first attempt of applying control theory to analyze the photochemical reaction dynamics of light therapies in terms of their nonlinearity. The proposed modeling techniques also offer opportunities for determining the light dosages in treating fungal infection diseases, especially those on the surface tissues of human body.