SBIR-STTR Award

The application of physical-chemical principles to biological systems frequently leads to situations in which the quantitative treatment of conceptually simple models is confounded by the complexity of the system. Such is the case, for example, in the study of the permeation (and possible concurrent metabolism) of drugs through complex biological membranes, the physiological modeling of the distribution of drugs throughout the body, and the treatment of flow of fluids and concurrent diffusion/metabolism.Each of these problems can be approached by the technique of Laplace transforms and expressions readily developed for the Laplace transform of the problem's solution. The inversion of the Laplace transform to recover the problem solution is often sufficiently difficult to preclude the use of this otherwise elegant technique.The aim of this project is to utilize a recently published algorithm for the reliable and accurate numerical inversion of the Laplace transform as a building block for the development of an interactive and easy-to-use microcomputer program for the inversion of Laplace transforms. Problems that now take a day or more to solve by hand will be solved in seconds or minutes, complete with appropriate graphical output of results. The Laplace transform will assume the role of a routine everyday tool, rather than remain a curiosity that, for many scientists, is of little practical worth.

Thesaurus Terms:
Computer (General) Incl Computer Data Processing (General), Computer, Design And Evaluation Of Computers (Incl. Hardware), Information And Communication, Systems Analysis, Computer Programming, Computer Simulation Division of Research Resources (NCRR)

This project will utilize a recently published algorithm for the reliable and accurate numerical inversion of the Laplace transform as a building block for the development of an interactive and easy-to-use microcomputer program for the inversion of Laplace transforms. A graphical interface will enable models to be rapidly constructed and tested without the user being aware of the underlying mathematics. Problems that now take many hours to solve by hand will be solved in seconds or minutes, complete with appropriate graphical output of results. The application of physical-chemical principles to biological systems frequently leads to situations in which the quantitative treatment of conceptually simple models is confounded by the complexity of the mathematics. Such is the case, for example, in the study of the permeation of drugs through complex biological membranes, in the physiological modeling of drug distribution throughout the body, and in the treatment of fluid flow and concurrent diffusion and metabolism. These problems can be approached using Laplace transforms. However, frequently the inversion of the Laplace transform to recover the problem solution is sufficiently difficult to preclude the use of this technique. Thus, the Laplace transform will assume the role of a routine everyday tool.

Anticipated Results:
The software developed in this project would be available to and useful to a broad range of scientific, engineering, and technical personnel. Individuals in chemical and biological sciences, and in various engineering fields, would be able to employ Laplace transformation for problems that would otherwise be impractical to solve. The program could be utilized on microcomputers in the user's own office.

Thesaurus Terms:
Computer Programs (Software), Computer, On-Line Computers, Models, Design And Development Of Models, Models, Mathematical, Physiology Biological Transport, Membrane Models, Biological Transport, Passive Transport, Diffusion, Computer Printing-Graphics, Computer, Man-Computer Interaction, Models, Biological, Computer Simulation Division of Research Resources