INVERSION OF LAPLACE TRANSFORMS ON MICROCOMPUTERS

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 TREATMENTOF FLOW OF FLUIDS AND CONCURRENT DIFFUSION/METABOLISM. EACH OF THESE PROBLEMS CAN BE APPROACHED BY THE TECHNIQUE OFLAPLACE 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.