INVERSION OF LAPLACE TRANSFORMS ON MICROCOMPUTERS

微机上拉普拉斯变换的反演

• 批准号: 3509396
• 负责人: MYLES L LAMSON
• 金额: $ 24万
• 依托单位: MICROMATH, INC.
• 依托单位国家: 美国
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-04-01 至 1991-03-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/3509396
• 关键词: biological models; computer graphics /printing; computer human interaction; computer program /software; computer simulation; mathematical model; membrane model; model design /development; online computer; physiology

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 in 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.

物理化学原理在生物学中的应用 系统经常导致量化的情况 概念上简单的模型的处理被 系统的复杂性。情况就是如此，例如，在 的渗透(和可能的同时代谢)的研究 药物通过复合生物膜，生理上 药物在体内的分布的模型，以及在 流体流动与并发的处理 扩散/新陈代谢。 这些问题中的每一个都可以通过 容易开发的拉普拉斯变换和表达式 问题解的拉普拉斯变换。的倒置 利用拉普拉斯变换恢复问题的解是经常遇到的 足够难，以至于排除了使用这个原本优雅的 技术。 该项目的目的是利用最近发布的算法 为了可靠和准确地进行拉普拉斯数值反演 将转型作为开发 交互式和易于使用的微型计算机程序 拉普拉斯变换的逆变换。现在需要一天或一天时间的问题 更多需要手工解决的问题将在几秒钟或几分钟内解决， 以适当的结果图形输出完成。这个 拉普拉斯变换将承担日常工具的角色， 对于许多科学家来说，这不是一种好奇心，而是 一点实用价值都没有。