Aggregation susceptibility on phototransformation of hematoporphyrin derivatives

Photosensitizers used in PDT suffer degradation by light. In this work, photobleaching of Photogem((R)) (PG), Photofrin((R)) (PF), and Photosan((R)) (PS), hematoporphyrin derivatives, were induced by light in the presence or absence of 1% Triton X-100. The degradation efficiency in the absence of 1% Triton X-100 follows the sequence: Pf > PF > Ps, which means that PF presented a greater degradation than PF and PS. Forever, in the presence of the surfactant the degradation efficiency is different: PF congruent to PS > PF. Besides aggregation susceptibility, studies in cell culture (tumor and non tumor cells) and in animals (depth of necrosis) were performed, trying to correlate the stability of these photosensitizers with their photodynamic effect. The results suggest that PF presents higher light induced photo-cytotoxicity than PF and PS for both types of cells. For the depth of necrosis studies, more aggregated photosensitizer showed a longer time to accumulate in liver (30 min for PG, 120 h for PF and 720 h for PS). The, to establish an ideal dosimetry in PDT, one must consider the intrinsic physical chemistry characteristics of the photosensitizer as well as their ability to undergo photobleaching.

Can efficiency of the photosensitizer be predicted by its photostability in solution?

We have investigated a possible correlation between the photostability and photodynamic efficacy for different photosensitizers; hematoporphyrin derivatives and chlorines. To perform such analysis, we combined the depth of necrosis (d (nec)) measurement, expressed by the light threshold dose and a photodegradation parameter, measured from investigation of photosensitizer degradation in solution. The d (nec) analysis allows us to determine the light threshold dose and compare its value with the existent results in the literature. The use of simple models to understand basic features of Photodynamic Therapy (PDT) may contribute to the solid establishment of dosimetry in PDT, enhancing its use in the clinical management of cancers and others lesions. Using hematoporphyrin derivatives and chlorines photosensitizers we investigated their properties related to the photodegradation in solution and the light threshold dose (D (th)) in rat livers.

Influence of pH on the phototransformation process of PhotogemA (R)

PhotogemA (R) is a hematoporphyrin derivative that has been used as a photosensitizer in experimental and clinical Photodynamic Therapy (PDT) in Brazil. Photosensitizers are degraded under illumination. This process, usually called photobleaching, can be monitored by decreasing in fluorescence intensities and includes the following photoprocesses: photodegradation, phototransformation, and photorelocalization. Photobleaching of hematoporphyrin-type sensitizers during illumination in aqueous solution is related not only to photodegradation but is also followed by the formation of photoproducts with a new fluorescence band at around 640-650 nm and with increased light absorption in the red spectral region at 640 nm. In this study, the influence of pH on the phototransformation process was investigated. PhotogemA (R) solutions, 40 mu g/ml, were irradiated at 514 nm with intensity of 100 mW/cm(2) for 20 min with different pH environments. The controls were performed with the samples in the absence of light. The PhotogemA (R) photodegradation is dependent on the pH. The behavior of photodegradation and photoproducts formation (monitored at 640 nm) is distinct and depends on the photosensitizer concentration. The processes of degradation and photoproducts formation were monitored with Photogemin the concentration of 40 mu g/mL since that demonstrated the best visualization of both processes. While below pH 5 the photodegradation occurred, there was no detectable presence of photoproducts. The increase of pH led to increase of photoproducts formation rate with photodegradation reaching the highest value at pH 10. The increase of photoproducts formation and instability of PhotogemA (R) from pH 6 to pH 10 are in agreement with the desired properties of an ideal photosensitizer since there are significant differences in pH between normal (7.0 < pH < 8.6) and tumor (5.8 < pH < 7.9) tissues. It is important to know the effect of pH in the process of phototransformation (degradation and photoproduct formation) of the molecule since low pH values promotes increase in the proportion of aggregates species in solution and high pH values promotes increase in the proportion of monomeric species. There must be an ideal pH interval which favors the phototransformation process that is correlated with the singlet oxygen formation responsible by the photodynamic effect. These differences in pH between normal and tumor cells can explain the presence of photosensitizers in target tumor cells, making PDT a selective therapy.

A combination of techniques to evaluate photodynamic efficiency of photosensitizers

Photodynamic therapy, used mainly for cancer treatment and microorganisms inaction, is based on production of reactive oxygen species by light irradiation of a sensitizer. Hematoporphyrin derivatives as Photofrin (R) (PF) Photogem (R) (PG) and Photosan (R) (PF), and chlorin-c6-derivatives as Photodithazine (R)(PZ), have suitable sensitizing properties. The present study provides a way to make a fast previous evaluation of photosensitizers efficacy by a combination of techniques: a) use of brovine serum albumin and uric acid as chemical dosimeters; b) photo-hemolysis of red blood cells used as a cell membrane interaction model, and c) octanol/phosphate buffer partition to assess the relative lipophilicity of the compounds. The results suggest the photodynamic efficient rankings PZ > PG >= PF > PS. These results agree with the cytotoxicity of the photosensitizers as well as to chromatographic separation of the HpDs, both performed in our group, showing that the more lipophilic is the dye, the more acute is the damage to the RBC membrane and the oxidation of indol, which is immersed in the hydrophobic region of albumin.

Phototransformation of hematoporphyrin in aqueous solution: Anomalous behavior at low oxygen concentration

The photoactivation of a photosensitizer is the initial step in photodynamic therapy (PDT) where photochemical reactions result in the production of reactive oxygen species and eventually cell death. In addition to oxidizing biomolecules, some of these photochemical reactions lead to photosensitizer degradation at a rate dependent on the oxygen concentration among other factors. We investigated photodegradation of Photogem A (R) (28 mu M), a hematoporphyrin derivative, at different oxygen concentrations (9.4 to 625.0 mu M) in aqueous solution. The degradation was monitored by fluorescence spectroscopy. The degradation rate (M/s) increases as the oxygen concentration increases when the molar ratio of oxygen to PhotogemA (R) is greater than 1. At lower oxygen concentrations (< 25 mu M) an inversion of this behavior was observed. The data do not fit a simple kinetic model of first-order dependence on oxygen concentration. This inversion of the degradation rate at low oxygen concentration has not previously been demonstrated and highlights the relationship between photosensitizer and oxygen concentrations in determining the photobleaching mechanism(s). The findings demonstrate that current models for photobleaching are insufficient to explain completely the effects at low oxygen concentration.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Modified alternating direction methods for solving a two-dimensional non-continuous seepage flow with fractional derivatives

In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Do derivatives have a role in the risk-shifting behaviour of fund managers?

In this paper we examine the extent to which derivatives are used to affect the risk-shifting behaviour of Australian equity fund managers. We find, after periods of good and poor performance, the risk-shifting behaviour of fund managers is different between derivative users and non-users. Our results support the gaming and active competition hypotheses but there is little support for the cash flow hypothesis. The study also allows for a complex reporting environment by analysing data across three alternate time periods: the calendar year, financial year and quarterly frames. Given that our results are not consistent across time periods for users and non-users of derivatives, some caution in interpretation is required.