Backward stochastic differential equations with non-Markovian singular terminal values

We solve a class of BSDE with a power function [Formula: see text], [Formula: see text], driving its drift and with the terminal boundary condition [Formula: see text] (for which [Formula: see text] is assumed) or [Formula: see text], where [Formula: see text] is the ball in the path space [Formula: see text] of the underlying Brownian motion centered at the constant function [Formula: see text] and radius [Formula: see text]. The solution involves the derivation and solution of a related heat equation in which [Formula: see text] serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain, the BSDE has continuous sample paths with the prescribed terminal value.

Approximation of bounds on mixed-level orthogonal arrays

Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

Fucosphere—New microsphere carriers for peptide and protein delivery: Preparation andin vitrocharacterization

PURPOSE

Fucoidan is a complex polysaccharide containing sugars and high amounts of sulphate derived from marine brown algaes. In this study, a new microsphere-delivery system based on cross-linking of fucoidan with chitosan, named Fucosphere, was evaluated as a drug carrier. Bovine serum albumin (BSA) was used as a model protein. The effect of fucoidan (1.5, 1.75, 2.0 and 2.5%), chitosan (0.25, 0.50 and 0.75%) and protein (0.25, 0.50 and 0.75%) concentrations, the origin of chitosan and the preparation methods of the particles on the microsphere characteristics were evaluated.

METHODS

The microspheres were prepared by a simple method based on the cross-linking of the opposite charged biopolymers. The shape and surface morphologies of the particles were evaluated by scanning electron microscopy (SEM) and the size, charge and encapsulation capacity of the microspheres were determined. The released amount of BSA from the microspheres into phosphate buffered saline (PBS pH 7.4) was determined spectrophotometrically by the Bradford method. SDS-PAGE was performed to check the structural integrity of BSA after the preparation.

RESULTS

Smooth and spherical microspheres between the size ranges of 0.61-1.28 microm were obtained. BSA was efficiently encapsulated into the microspheres (51.8-89.5%). All formulation parameters affected the encapsulation capacity of Fucosphere (p < 0.05). The highest encapsulation was obtained with microspheres containing 2.5% of fucoidan (89.5%).

CONCLUSIONS

The extent of drug release from the microspheres was dependent on the concentrations of polymers and BSA, chitosan origin and type of preparation method. When the addition methods of protein compared, BSA encapsulated into Fucosphere released slower than the adsorbed protein (E) (p < 0.05). The electrophoretic mobility values of Fucospheres changed between +6.9 and +32.3 mV. In general, BSA release from Fucosphere showed a three-phasic release curve. In conclusion, this new fucoidan microsphere system may be a potential delivery of macromolecular drug such as peptide and protein.

Release characteristics of chitosan treated alginate beads: II. Sustained release of a low molecular drug from chitosan treated alginate beads

The aim of this paper was to investigate the possible applicability of chitosan treated alginate beads as a controlled release system of small molecular drugs with high solubility. Timolol maleate (mw 432.49) was used as a model drug. The beads were prepared by the ionotropic gelation method and the effect of various factors (alginate, chitosan, drug and calcium chloride concentrations, the volume of external and internal phases and drying methods) on bead properties were also investigated. Spherical beads with 0.78-1.16 mm diameter range and 10.8-66.5% encapsulation efficiencies were produced. Higher encapsulation efficiencies and retarded drug release were obtained with chitosan treated alginate beads. Among the different factors investigated such as alginate, drug, chitosan and CaCl2 concentrations, the volumes of the external and internal phases affected bead properties. The drying technique has an importance on the bead properties also. The release data was kinetically evaluated. It appeared that chitosan treated alginate beads may be used for a potential controlled release system of small molecular drugs with high solubility, instead of alginate beads.

Release characteristics of chitosan treated alginate beads: I. Sustained release of a macromolecular drug from chitosan treated alginate beads

Alginate and chitosan treated alginate beads were prepared and compared as an oral controlled release system for macromolecular drugs. Dextran (M.W. 70,000) was used as a model substance. The beads were prepared by the ionotropic gelation method and the effect of various factors (alginate, chitosan, drug and calcium chloride concentrations, the volume of external and internal phases and drying methods) on bead properties were investigated. The addition of chitosan increased the drug loading capacity of the beads, and larger beads were obtained in the presence of chitosan. On the other hand, addition of chitosan in the gel structure reduced the drug release from beads. The erosion of the beads was suppressed by chitosan treatment. The drying method was important to the properties of the chitosan-alginate beads. It is proposed that chitosan treated alginate beads may be used as a potential controlled release system of such macromolecules.