Huang Naiyan, Cheng Gang, Li Xiaosong, Gu Ying, Liu Fanguang, Zhong Qiuhai, Wang Ying, Zen Jin, Qiu Haixia, Chen Hongxia
Department of Laser Medicine, Chinese PLA General Hospital, Beijing 100853, China.
Photodiagnosis Photodyn Ther. 2008 Jun;5(2):120-6. doi: 10.1016/j.pdpdt.2008.05.006. Epub 2008 Jun 24.
We established mathematical models of photodynamic therapy (PDT) on port wine stains (PWS) to observe the effect of drug-light-interval (DLI) and optimize light dose.
The mathematical simulations included determining (1) the distribution of laser light by Monte Carlo model, (2) the change of photosensitizer concentration in PWS vessels by a pharmacokinetics equation, (3) the change of photosensitizer distribution in tissue outside the vessels by a diffuse equation and photobleaching equation, and (4) the change of tissue oxygen concentration by the Fick's law with a consideration of the oxygen consumption during PDT. The concentration of singlet oxygen in the tissue model was calculated by the finite difference method. To validate those models, a PWS lesion of the same patient was divided into two areas and subjected to different DLIs and treated with different energy density. The color of lesion was assessed 8-12 weeks later.
The simulation indicated the singlet oxygen concentration of the second treatment area (DLI=40 min) was lower than that of the first treatment area (DLI=0 min). However, it would be increased to a level similar to that of the first treatment area if the light irradiation time of the second treatment area was prolonged from 40 min to 55 min. Clinical results were consistent with the results predicted by the mathematical models.
The mathematical models established in this study are helpful to optimize clinical protocol.
我们建立了鲜红斑痣（PWS）光动力疗法（PDT）的数学模型，以观察药物 - 光间隔（DLI）的效果并优化光剂量。
数学模拟包括通过蒙特卡罗模型确定（1）激光光的分布，（2）通过药代动力学方程确定PWS血管中光敏剂浓度的变化，（3）通过扩散方程和光漂白方程确定血管外组织中光敏剂分布的变化，以及（4）考虑PDT期间的氧消耗，通过菲克定律确定组织氧浓度的变化。采用有限差分法计算组织模型中单线态氧的浓度。为验证这些模型，将同一患者的PWS病变分为两个区域，给予不同的DLI并采用不同的能量密度进行治疗。8 - 12周后评估病变颜色。
模拟表明，第二个治疗区域（DLI = 40分钟）的单线态氧浓度低于第一个治疗区域（DLI = 0分钟）。然而，如果将第二个治疗区域的光照时间从40分钟延长至55分钟，其单线态氧浓度将增加至与第一个治疗区域相似的水平。临床结果与数学模型预测的结果一致。
本研究建立的数学模型有助于优化临床方案。
