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A theoretical comparison of macroscopic and microscopic modeling of singlet oxygen during Photofrin and HPPH mediated-PDT

机译：光荧土素和HPPH介导 - PDT术期单次氧气和微观造型的理论比较

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摘要

Mathematic models were developed to simulate the complex dynamic process of photodynamic therapy (PDT). Macroscopic or microscopic modeling of singlet oxygen (1O2) is particularly of interest because it is the major cytotoxic agent causing biological effects during PDT. Our previously introduced macroscopic PDT model incorporates the diffusion equation for the light propagation in tissue and the macroscopic kinetic equations for the production of the 1O2. The distance-dependent distribution of 3O2 and reacted 1O2 can be numerically calculated using finite-element method (FEM). We recently improved the model to include microscopic kinetic equations of oxygen diffusion from uniformly distributed blood vessels and within tissue. In the model, the cylindrical blood capillary has radius in the range of 2–5 μm and a mean length of 300 μm, and supplies oxygen into tissue. The blood vessel network is assumed to form a 2-D square grid perpendicular to a linear light source. The spacing of the grid is 60 μm. Oxygen can also diffuse along the radius and the longitudinal axial of the cylinder within tissue. The oxygen depletion during Photofrin-PDT can be simulated using both macroscopic and microscopic approaches. The comparison of the simulation results have reasonable agreements when velocity of blood flow is reduced during PDT.
机译：开发了数学模型来模拟光动力疗法（PDT）的复杂动力过程。单线态氧（ 1 O2）的宏观或微观建模尤其令人感兴趣，因为它是导致PDT期间生物效应的主要细胞毒性剂。我们先前介绍的宏观PDT模型结合了光在组织中传播的扩散方程和产生 1 O2的宏观动力学方程。 3 O2和反应的 1 O2的距离相关分布可以使用有限元方法（FEM）进行数值计算。我们最近改进了该模型，以包括从均匀分布的血管和组织内扩散的氧气的微观动力学方程。在该模型中，圆柱形毛细血管的半径范围为2–5μm，平均长度为300μm，并向组织供氧。假设血管网络形成垂直于线性光源的二维正方形栅格。网格的间距为60μm。氧气还可以沿着圆柱体的半径和纵向轴线在组织内扩散。可以使用宏观和微观方法模拟Photofrin-PDT中的氧耗竭。当PDT期间血流速度降低时，模拟结果的比较具有合理的一致性。

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