# Scientists apply control theory to analyze the dynamics of photochemical reactions in light therapies

Researchers in China recently applied control theory for the first time to the analysis of photochemical reaction dynamics in light therapies and developed the first mathematical model of light-induced singlet oxygen in the treatment of fungal infections . The results were published in *IEEE Transactions on Biomedical Engineering*.

Photodynamic therapies (PDTs) are non-antibiotic alternatives for the treatment of localized infectious diseases due to their rapid action and lack of drug resistance. Similar to PDT, blue light therapies that rely solely on endogenous pigments, i.e. porphyrins and flavins, pathogens are also effective and even safer to use.

Antifungal blue light (ABL) has been widely studied as a new approach to treating fungal infections. Calculating the quantum yield of singlet oxygen is the key to determining the applied light dose in both PDT and ABL.

In order to study the dynamics of photosensitized oxidation reactions in PDT and ABL, and to develop an effective modeling approach, Dr. Dong Jianfei’s team at the Suzhou Institute of Biomedical Engineering and Technology ( SIBET) of the Chinese Academy of Sciences applied fundamental principles of control theory to analyze these processes and derived the linearization condition for the nonlinear PDT model from the first principle.

The mechanism of the antifungal effect of PDT and ABL is light exciting either the exogenous photosensitizer in the first case or the endogenous pigments in the second, which in turn produce reactive oxygen species (ROS ) from triplet oxygen (^{3}O_{2}) molecules.

ROS are very reactive and can cause cytotoxicity. Singlet oxygen (^{1}O_{2}) typically accounts for 80% of all light-induced ROS; while hydroxyl radicals and other types of ROS take up the remaining 20%. Additionally, singlet oxygen is a precursor to most other ROS.

Dong and colleagues linearized the nonlinear first-principle PDT model to a set of equilibrium points along the trajectory of its dynamic response to light stimuli.

This resulted in a set of linear time-invariant (LTI) state-space models. These models are all of the third order and contain three poles and a zero. Among these, a pole is constantly located at the origin of the complex plane.

Further analysis showed that the zero can approximately cancel the pole at the origin, leading to second-order models containing two poles. The locations of these two remaining poles are closely related to the concentration of ^{3}O_{2}i.e. the main ingredient to produce ^{1}O_{2}.

According to the researchers, when the concentration of ^{3}O_{2} is ample, the root loci at the different points are condensed into a much smaller cluster than those in the oxygen-deficient case. This indicates that the local LTI systems in the oxygen-rich case are more identical to each other; and that is, the original nonlinear first-principle PDT model tends to be linear.

“It’s an interesting observation,” Dong said. In fact, the oxygen concentration in the blood is sufficient for photochemical reactions in most cases.

Inspired by this, the team analyzed and solved the first-principle PDT model and obtained a closed-form analytical solution under oxygen-rich conditions. The significance of this analytical solution is that it is a nonlinear algebraic equation with only four parameters, which can be easily fitted to experimental data.

They further proposed a data-driven modeling approach for the photochemical reaction process of light therapies. The model obtained a good fit result on the measured ABL experimental data.

This is the first attempt to apply control theory to analyze the dynamics of photochemical reactions of light therapies in terms of nonlinearity. The proposed modeling techniques also offer opportunities to determine light doses in the treatment of fungal infectious diseases, especially those on the surface tissues of the human body.

**More information:**

Tianfeng Wang et al, Data-Based Analysis and Modeling of Photochemical Reaction Dynamics of Induced Singlet Oxygen in Light Therapies,

*IEEE Transactions on Biomedical Engineering*(2022). DOI: 10.1109/TBME.2022.3170541

**Quote**: Scientists apply control theory in analyzing the dynamics of photochemical reactions in light therapies (May 6, 2022) retrieved on May 6, 2022 from https://techxplore.com/news/2022-05-scientists -theory-analysis-photochemical-reaction.html

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