Objective: The use of mathematics in the study of phenomena and systems of interest to medicine has become quite popular in recent years, but not much progress has been made as a result of these efforts. The aim of this article is to identify the reasons for this failure and to suggest procedures for more successful outcomes.
Methods: We review and assess a variety of mathematical modeling procedures, from microscopic (at the level of molecular behavior) to macroscopic standpoints, from lumped-parameters to distributed-parameters approaches. Using examples that are as simple as possible, we elucidate the difference between the predictive and the explanatory powers of mathematical models, as well as the uses (and abuses) of analogy in their construction.
Results: Mathematical medicine is a truly interdisciplinary area that brings together medical researchers, engineers, and applied mathematicians whose vast differences in expertise and background make collaboration difficult.
Conclusion: The lack of a common language and a common way of understanding what a mathematical model is, and what it can do, is identified as the main source of the slow progress to date, and constructive suggestions are made to improve the situation.