deletions | additions       diff --git a/subsection_Image_analysis_Pharyngeal_pumping__.tex b/subsection_Image_analysis_Pharyngeal_pumping__.tex  index e3796d2..07d3728 100644  --- a/subsection_Image_analysis_Pharyngeal_pumping__.tex  +++ b/subsection_Image_analysis_Pharyngeal_pumping__.tex 
...
\subsection{Image analysis}  Pharyngeal pumping motion is most easily detected through the motion of the grinder -- a cuticle region of the pharynx inside the terminal bulb that is used to crush bacteria to aid digestion \cite{avery199724}. At low magnifications, directly tracking the position of the grinder is ineffective: the amplitude of grinder motion is small and any translation or deformation of the head will compromise the data. Therefore, our approach relied on intensity differences between consecutive images and on the separation of timescales between head motion and pumping (Fig. \ref{fig:entropy}A-B). Key to this approach is a high imaging rate, 62.5 fps, as compared with more than 10 times faster than  the maximal instantaneous rate of pumping, 6 Hz. The position of the head is maintained by mounting the animals into the WormSpa microfluidic device such that tracking a moving animal is not required and the motion of the head is dampened without a major impact on feeding \cite{kopito2014durable}. Subtracting consecutive frames that were captured 16 ms apart isolates fast-changing features, i.e., the motion of the grinder. Examples of distributions of intensity differences in the presence or absence of a pump are shown in Fig. \ref{fig:entropy}C. Notably, rapid motion affects the tail of this distribution. Therefore, a measure that preferentially weighs the tail would enhance the signal to noise ratio of motion detection. Using the entropy, $\sum_i p_i \log p_i$ (where $p_i$ is the probability of observing intensity $i$ in the difference image), to enhance the significance of motion achieves this goal \cite{jing2004foreground}. An additional advantage of this method as compared to tracking the grinder is that no model of the background needs to be calculated. In a high frame-rate movie of grinder motion, the entropy of intensity differences peaks sharply when pumping occurs while contributions of slower head motions are minor. In our hands, imaging conditions did not require fine tuning in order to maintain a signal to noise ratio that exceeded $200\%$ (\ref{fig:entropy}D-E).