Mathematical modeling and rationale for identifying pupillary latency time: When is the nervous system starting to react?

Latency can be defined as the time between two causally related events. For example, in a biological system, the studied latency begins with a stimulus with an identifiable time record and ends with a time record of response from the system. Such response latencies can encompass at least three different time components; the time from stimulus onset to its detection by the biological system, followed by the time the biological system first reacts to the stimulus change, and ending with the more inclusive time required to form an ecologically effective and functional action. Additional time may be spent on the selection of the behavioral output and suppression of alternatives. Latencies are a highly malleable research tool that can be employed across a wide range of fundamental biological, physiological, psychological, pharmacological, and neuroscientific questions. If the stimulus is generated by the researcher, the identification of its time record may be well established via the digital system that is generating stimulation and time record marking. However, measuring the biological response onset can present significant issues of signal-to-noise ratios. In this article, we offer a general method of modeling the biological responses using a mathematical interpolation tool called splines. We propose that the change in response from baseline background can be modeled from a time-series through the analysis of the continuous data derivative functions. In this tutorial, we explain the underlying mathematical approach to estimating the emergence of a response trace from background activity. We later present an example using the pupillary light reflex with a change in luminance as stimulus and its reciprocal change in pupil diameter. We supply a small sample of pupillary reflex data as well as source code in R necessary for the analyses. Importantly, we present tests showing that the only operator-selected parameter for this analytic approach, the level of spline smoothing, is not systematically related to the estimated timestamp of the response and therefore the modeling technique appears to be unbiased.