Theoretical evaluation of the light distribution and PDT dose for a multi-wavelength light source

Abstract

The broad absorption spectrum of Protoporphyrin IX (PpIX) allows being activated by a source with an emission spectrum in the visible region. Also, PpIX can be activated simultaneously by two or more sources whose emission spectrum overlaps with its absorption spectrum. Sources with a wide spectrum of illumination, such as lamps and Sun, have a different light-tissue interaction, and the constant monitoring of the dose of light and the total damage caused by photodynamic therapy (PDT) becomes difficult. The main objectives of this study were to simulate the distribution of light in the tissue for a multiwavelength source and determine the total theoretical photodynamic dose. This study is composed of three parts. First, photobleaching experiments of PpIX using different light sources and the development of a mathematical model was used to explain the change in PpIX concentration. Second, Monte Carlo simulation using MCX (Monte Carlo eXtreme) was performed to know the light distribution through in a human skin model. Finally, the theoretical photodynamic dose was determined using the two steps mentioned previously. The experimental results show that the decrease in the concentration of PpIX is mainly dependent on the dose of photons absorbed. Therefore, for a multi-wavelength source, the total damage is calculated by partial damages caused by each wavelength that active the PpIX. The simulation of the light distribution in the human skin phantom demonstrated that the energy fluence rate decrease as a function of the depth. The mathematical model estimates that the efficacy of PDT, where it is guaranteed there is necrosis, has a diameter and depth of about 0.3 and 0.2 mm respectively. This model can be expanded to other biological media, other photosensitizers and even to any source of illumination.

Theoretical study of the conditions for acoustic nucleation and cavitation in biological tissue for its application in sono-photodynamic therapy

“…Such a diagram shows the energy transfer of molecular oxygen, and the products of this reaction, which can be quantified using rate equations. 3 The effectiveness of PDT depends on some factors, such as the characteristic of the incident light and the medium's capacity to absorb energy. 1 Ultraviolet light, for example, is usually applied to treat superficial lesions, due to its high absorption by the first layers of the epidermis, while red and near-infrared are used to treat lesions more deeply located in the tissue.…”

Sobre as condições e probabilidades para a nucleação e cavitação acústicas no tecido biológico - uma análise teórica

“…(18) As características dessa interação podem ser modeladas matematicamente através das equações de taxa, baseadas no diagrama de Jablonski, e visualizadas por meio de simulações computacionais relativas à distribuição de luz no tecido. (19) As equações de taxa consistem em equações diferenciais utilizadas na descrição das transições energéticas das moléculas que compõe o FS, interações entre tais moléculas e a morte celular (20,21), através do aumento ou diminuição de concentração devido à variações na energia do sistema.…”

“…Para que a bolha comece a se expandir é necessário que seja fornecida uma quantidade mínima de energia, ou seja, o US deve ter uma amplitude de pressão negativa mínima ou pressão de limiar. A partir da equação (1.41) é possível obter a figura (19). Fonte: Elaborada pela autora.…”

“…A figura (19) representa a variação da pressão de limiar, ou seja, a quantidade mínima de energia que o US deve entregar ao meio para que ocorra a expansão de bolhas de cavitação, segundo o modelo de Blake em função do raio inicial da bolha em água (σ = 70 mN/m) e em sangue/tecido mole/pele (σ = 16 mN/m).…”

“…De acordo com as curvas obtidas na figura (19) é possível observar que para o sangue/tecido mole/pele (σ = 16 mN/m) a pressão de limiar é superior à da água (σ = 70 mN/m) para todos os valores de raio inicial analisados. Considerando bolhas com raio inicial de R 0 = 1µm, a pressão de limiar para a condição de Blake é -53,38 kPa em água e -35,89 kPa em sangue/tecido mole/pele.…”