We investigate a type of one-dimensional quasi-exactly solvable double-well potential whose analytical solution can be constructed in terms of the Heun functions. It is shown that for certain special values of the potential parameters, two energy eigenvalues and eigenstates of the lowest part of the energy spectrum can be found exactly in explicit form. In addition, the Wronskian method has been applied to derive the conditions for the energy eigenvalues of the bound states. Our analytical results may find applications in the tunnelling problem for the double-well potentials.

There is a significant interest in the application of microneedles in intradermal drug delivery systems. Previous studies have demonstrated that skin permeation of drugs can be increased by orders of magnitude with microneedle insertion. In this study, emphasis is placed on the development of low cost, painless intradermal microneedle systems that can enhance the percutaneous drug permeation. Microneedles of octagonal pyramidal shape with the length of 150 mum were employed, and the capabilities of skin permeation enhancement under different delivery conditions were examined. The delivery parameters taken into account included the insertion time and the area of insertion. It was found that when solid microneedle arrays of 150 mum in length were pierced into human dermatomed skin for 5 to 60 s, microconduits with the depth of 50 to 80 mum were created to facilitate the percutaneous permeation of drugs. In percutaneous tests, it was demonstrated that the permeability coefficient of calcein (MW = 622.55) was significantly increased by 10(4) to 10(5) times compared to that on intact skin. In terms of biocompatibility, biological evaluation indicated a broad spectrum of safety for the microneedle system. These results suggest that the octagonal pyramidal microneedles can be an effective tool in developing novel intradermal drug delivery system.

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