Equation-based models of dynamic biological systems

The purpose of this review is to introduce differential equations as a simulation tool in the biological and clinical sciences. This modeling technique is very mature and has been a preferred tool of physiologists and bioengineers and of quantitative scientists in general to describe and predict the behavior of complex interacting systems. However, this methodology has not been widely used within clinical medicine due to a lack of familiarity with highly quantitative methods and a greater acquaintance with statistical modeling approaches based on inference and empirical data analysis. We will describe various aspects of equation-based modeling, including underlying assumptions, strengths, and weaknesses and provide specific examples of simple models. We conclude that the usefulness of quantitative modeling, including equation-based models, is ultimately linked to the quality and abundance of observation obtained on the system being modeled. Equation-based modeling, although potentially an integrative approach, is complementary to and extends the potential of traditional statistically based approaches to inference.