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.

Anti-fungal blue light (ABL) therapies are based on the photochemical reaction of endogenous photosensitizer (PS) in fungal cells. Knowing the spectral sensitivity of these cells for the ability to generate singlet oxygen is thus important to determine the most effective wavelength of such light therapies, and thereby to design ABL therapeutic devices, e.g., by light emitting diodes. We propose a modeling method of such spectral sensitivity in this work, based on the absorption spectra of cells and other inherent characteristic parameters, i.e., singlet oxygen quantum yield and the extinction coefficient of the endogenous PS. Specifically, the absorption spectra are determined by the PSs inside the fungus Candida albicans and human epithelial cells. Then, the concentration of PS in those two types of cells was measured by high-performance liquid chromatography (HPLC) assays. The HPLC assays show that the coproporphyrin (CP) is the main PS in C. albicans, accounting for 60% of the total PS. The simulation results demonstrate that the 390420nm light can stimulate the PS in the cells to generate more singlet oxygen in C. albicans than in epithelial cells; and this range is the same as the CP Soret band. In contrast, the light with wavelengths >450nm is less effective in exciting the PS in C. albicans, and leads to more singlet oxygen generation in V.E. cells than shorter wavelength. We thus conclude that 390420nm light is the most effective range for inhibiting C. albicans with the least damage to human host cells.

Objective: The goal of this study is to investigate the efficacy, safety, and mechanism of ABL for inactivating Candida albicans (C. albicans), and to determine the best wavelength for treating candida infected disease, by experimental measurements and dynamic modeling. Methods: The changes in reactive oxygen species (ROS) in C. albicans and human host cells under the irradiation of 385, 405, and 415nm wavelengths light with irradiance of 50mW/cm2 were measured. Moreover, a kernel-based nonlinear dynamic model, i.e., nonlinear autoregressive with exogenous inputs (NARX), was developed and applied to predict the concentration of light-induced ROS, whose kernels were selected by a newly developed algorithm based on particle swarm optimization (PSO). Results: The ROS concentration was increased respectively about 10-12 times in C. albicans and about 3-6 times in human epithelial cells by the ABL treatment with the same fluence of 90J/cm2. The NARX models were respectively fitted to the data from the experiments on both types of cells. Besides, four different kernel functions, including Gaussian, Laplace, linear and polynomial kernels, were compared in their fitting accuracies. The errors with the Laplace kernel turned out to be only 0.2704 and 0.0593, as respectively fitted to the experimental data of the C. albicans and human host cells. Conclusion: The results demonstrated the effectiveness of the NARX modeling approach, and revealed that the 415nm light was more effective as an anti-fungal treatment with less damage to the host cells than the 405 or 385nm light. Significance: The kernel-based NARX model identification algorithm offers opportunities for determining the effective and safe light dosages in treating various fungal infection diseases.

Light therapies can be used to treat fungal infections. A general mechanism is attributed to the generation of cytotoxic reactive oxygen species (ROS) due to light stimulation. The effectiveness of these therapies has been widely studied in the literature via conducting biological experiments, where fungi are exposed to light with various wavelengths and power. However, despite the large amount of work reporting the experimental results, few efforts have been given to build a mathematical model that describes the amount of generated ROS as a function of the photon energy and power of the stimulating light. The lack of such a model still hinders the optimization of the light doses. In this work, we propose a novel modeling method based on experimental data, so as to establish a mathematical relationship between the ROS concentration and the stimulating photon energy and light fluence (energy density). The anti-fungal experiments were performed on Candida {}albicans (C. {}albicans) using four LED light sources with different wavelengths ranging from 385nm to 450nm. Both the viability of the fungi and the ROS concentration therein were measured during the experiments. High fitting accuracy has been achieved by the model, which therefore demonstrates the effectiveness of the proposed modeling techniques.

Dynamic photovoltaic (PV) greenhouses integrate sustainable energy generation with plant cultivation, offering more possibilities of energy production and microclimate control by adjusting the sun-tracking angles. Previous studies on PV greenhouses barely paid attention to the PV partial shading effects, and rarely recorded the performance across the full range of rotation angles. In this study, we first build computer simulation models of typical greenhouses with high-density (1/2 roof area) and low-density (1/3 and 1/4 roof area) PV layouts. Then four special sun-tracking positions are found in the model of equivalent global irradiance, which is defined as the quotient of the total input power divided by the area of PV module under partial diffuse shadows. Simulation models are also built in terms of PV modules and interior irradiance. Simulations are conducted using the climate data of Delft, the Netherlands (52.01°N,4.36°E). Results show that high-density PVs under no-shading sun tracking generate 6.91% more energy than that under conventional (quasi-perpendicular) sun-tracking. Meanwhile, no-shading sun tracking allows more diffuse sunlight to enter the greenhouse mounted with high-density PV panels, resulting in 10.96% and 10.68% improvement on the annual average global irradiance and uniformity on the target plane compared to the fixed PV panels in the closed position. Regarding low-density PV layouts, which barely suffer from partial shading problems, quasi-perpendicular sun tracking improves the annual energy generation by 7.40% relative to the closed position. However, the average global irradiance reaches the minimum in this position because more sunlight is blocked by PVs. Meanwhile, the average uniformity of global irradiance reveals good (but not the best) performance, resulting in up to 9.80% (1/3 coverage) and 4.70% (1/4 coverage) improvement respectively compared to the closed position. The proposed methods and simulation results provide guidelines for the initial design and daily operation of PV greenhouses, aiming to balance the PV power generation and food production.