A formal mathematical framework for physiological observations, experiments and analyses

Experiments can be complex and produce large volumes of heterogeneous data, which make their execution, analysis, independent replication and meta-analysis difficult. We propose a mathematical model for experimentation and analysis in physiology that addresses these problems. We show that experiments can be composed from time-dependent quantities, and be expressed as purely mathematical equations. Our structure for representing physiological observations can carry information of any type and therefore provides a precise ontology for a wide range of observations. Our framework is concise, allowing entire experiments to be defined unambiguously in a few equations. In order to demonstrate that our approach can be implemented, we show the equations that we have used to run and analyse two non-trivial experiments describing visually stimulated neuronal responses and dynamic clamp of vertebrate neurons. Our ideas could provide a theoretical basis for developing new standards of data acquisition, analysis and communication in neurophysiology.