The Worm Project

The Worm module of FARSIGHT represents a robust multiple worm segmenting and tracking locomotion events in live worm time – lapse sequences in the presence of a pheromone. Worms are tracked according to their distance from the pheromone spots and intrinsic features are computed from the image data for each worm. We present the application of a physically motivated approach to modeling the dynamic movements of the nematode C. elegans exposed to an external stimulus as observed in time-lapse microscopy image sequences. Specifically, we model deformation patterns of the central spinal axis of various phenotypes of these nematodes which have been exposed to pheromone produced by wild type C. elegans Worms are tracked according to their distance from the pheromone spots and intrinsic features are computed from the image data for each worm. The features measured include those proposed by Nicolas Roussel and those provided in the FARSIGHT Toolkit.

A model based algorithm for simultaneously segmenting and tracking of an entire imaging field containing multiple worms previously proposed by Nicolas Roussel has been implemented an applied to model worm behavior. An extension to the work propped by Roussel et. al., is to create a map of the worm’s behavior over time similar to the kymographs used by biologists to improve the accuracy of multiple hypothesis tracking by eliminating hypothesis based on a Euclidean distance metric to the worm kymograph. Interaction between worms is typically modeled as a random walk. We seek to give biologists a new tool to isolate the paths of peristaltic progression of C. elegans leads to unpredictable behaviors that are resolved using a variant of multiple-hypothesis tracking. The net result is an integrated method to understand and quantify worm interactions. Experimental results indicate that the proposed algorithms allow for an integrated high throughput automated analysis of the locomotive behavior of C. elegans during exposure to a given pheromone. The results for this work are generated by a module of the FARSIGHT toolkit for segmentation and tracking of multiple biological systems. The features calculated during this work can be edited and validated using the tracking editor available in the FARSIGHT toolkit. Overall, the method provides the basis for a new range of quantification metrics for nematode social behaviors.

Contents 1 Modules 1.1 Detection 1.1.1 WormBinarization 1.2 Tracking 1.3 Features 1.3.1 Behaviors

Modules

The modules of The Worm Project are aimed at:
Exploiting complete worm track sequence to model movement and deformation in a correlated manner

• Modeling interaction and overlap using known locomotion events to exclude unfavorable hypothesis
• Extending existing probabilistic approach to measurement and prediction using track summary

Detection

Worms are modeled according to centerline and width profile. Information about the entire image sequence is obtained by projecting the maximum intensity of the sequence which is followed by a segmentation step.

Syntax:

 WormBinarization [StringBeforeFilename] [MaskFilename] [StartFrame] [EndFrame][Levell]
 TenickaSegment   [StringBeforeInputFilename] [StringBeforeDataFilename] [LabeledImageFilename] [StartFrame] [EndFrame]

WormBinarization

• WormBinarization accepts a series of grayscale images and returns a series of corresponding binary images

• The mask file used as an input is generated by performing a maximum intensity projection of the entire image sequence.
• The input images should be single-slice 8-bit TIFs. Other image formats have not been tested.
• The frame number must have n digits. We have tested this data with n == 4.
• The frame number must be at to the end of the image name.

See FARSIGHT Features

Tracking

Syntax:

  Tracker [StringBeforeLabeledImageFilename] [StringBeforeRawImageFilename] [StartFrame] [EndFrame]

A center-line is extracted for all of the ‘tracks’ in the summary view of the image sequence.
The Euclidean distance from the worm center-line in each time step to the center-lines in extracted in the summary view.
All hypothesis which are 1.2 times this distance are excluded from the possibilities used during tracking.

Example Input

To track worms with the following image sequence...

C:\data\Im0000.tif
C:\data\Im0001.tif
C:\data\Im0002.tif
C:\data\Im0003.tif
C:\data\Im0004.tif

...with their associated labeled image sequence...

C:\data\labeled0000.tif
C:\data\labeled0001.tif
C:\data\labeled0002.tif
C:\data\labeled0003.tif
C:\data\labeled0004.tif

Example Output

Features

Worms are tracked according to their distance from the pheromone spots and intrinsic features are computed from the image data for each worm.

Name	Description	Formula
Width	Model of worm Width
Area	Number of pixels in the worm	| Ω |
Minor Length	Minor axis length of an ellipse with the same area as the worm which has been fit to our worm model
Major Length	Major axis length of an ellipse with the same area as the worm which has been fit to our worm model
Eccentricity	Ratio of maximum to minimum distance of the center of mass from the worm’s surface
Orientation	Angle between the first principal axis of a given worm and the ‘x’ axis
t_start	Frame number that worm was initially detected	Ft(0)
t_end	Frame number that worm was last detected
t_length	Total number of frames worm was tracked in a given image sequence
Curvature	A metric to give an estimate of coiling as a worm behavior
Sum Squared Curvature	Average Curvature squared, gives an estimate of the worm’s bending energy
Intensity	The average intensity of the pixels in a worm	mean( | Ω | )
Peri_avg	The average worm speed	mean([ui,...,un]) i=1,2,...,15
Peri_std	The standard deviation of the worm speed. Gives users insight into irregularities of worm peristaltic progression	std([ui,...,un]) i=1,2,...,15
D_head_std	Standard deviation of the displacement of the worm’s head
D_tail_std	Standard deviation of the displacement of the worm’s tail
Reversal Rate	The frequency of backward progression by the worm’s head
Class	Each Phenotype is given a separate class from 1-N	N / A
Bearing	The angle between the velocity vector and the spatial vector from the worm’s position to the center of the pheromone spot(chemical gradient)
Instantaneous Turning Rate	The change in orientation over time

Behaviors

• Pierce-Shimomura JT, Morse TM, Lockery SR, "The Fundamental Role of Pirouettes in Caenorhabditis elegans Chemotaxis," The Journal of Neuroscience. 1999 Nov; 19(21):9557–9569.