An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe

Mutation or loss of Wilms' tumor gene 1 (WT1) are not major reasons for immune escape in patients with AML receiving WT1 peptide vaccination

<p>Abstract</p> <p>Background</p> <p>Efficacy of cancer vaccines may be limited due to immune escape mechanisms like loss or mutation of target antigens. Here, we analyzed 10 HLA-A2 positive patients with acute myeloid leukemia (AML) for loss or mutations of the WT1 epitope or epitope flanking sequences that may abolish proper T cell recognition or epitope presentation.</p> <p>Methods</p> <p>All patients had been enrolled in a WT1 peptide phase II vaccination trial (NCT00153582) and ultimately progressed despite induction of a WT1 specific T cell response. Blood and bone marrow samples prior to vaccination and during progression were analyzed for mRNA expression level of WT1. Base exchanges within the epitope sequence or flanking regions (10 amino acids N- and C-terminal of the epitope) were assessed with melting point analysis and sequencing. HLA class I expression and WT1 protein expression was analyzed by flow cytometry.</p> <p>Results</p> <p>Only in one patient, downregulation of WT1 mRNA by 1 log and loss of WT1 detection on protein level at time of disease progression was observed. No mutation leading to a base exchange within the epitope sequence or epitope flanking sequences could be detected in any patient. Further, no loss of HLA class I expression on leukemic blasts was observed.</p> <p>Conclusion</p> <p>Defects in antigen presentation caused by loss or mutation of WT1 or downregulation of HLA molecules are not the major basis for escape from the immune response induced by WT1 peptide vaccination.</p

Fractional dynamics pharmacokinetics–pharmacodynamic models

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics