Microtubule Tracking by KXj29n54

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									  Tracking the Motion of the Outer
       Ends of Microtubules
Stathis Hadjidemetriou, Derek Toomre, James S.
                    Duncan

      Yale University, School of Medicine,
            New Haven, CT 06520
        Microtubule (MT) Assembly
•Self-assembling biopolymers of cytoplasm,width≈25 nm

•Provide structure and support to the cell




                            MTs

                        Fluorescence labeling in confocal
                        microscopy, ≈200 nm/pixel
  Why are Microtubule Dynamics
          Interesting?
•Dynamic ‘highways’ for     •Regulate cell migration
trafficking of vesicles     and cell division




 MT: tracks for granules     MT: spindle in yeast cell
 (dark dots) in fish cell
        Importance in Cell Pathology
• Anticancer drugs (e.g. Taxol®, Taxotere®) inhibit
  polymerization of MTs to retard:
  – Cancer growth through cell division
  – Cancer spread through cell migration


• Deficient neurotransmitter transport implicated in
  neurodegenerative diseases, e.g. Alzheimer’s
                          Objective




 Fibroblast & epithelial cells


•Segment of MTs [Hadjidemetriou et al, 05]
•Tracking of MTs motion [Hadjidemetriou et al, 04]
    Previous Work in Segmentation of
    Biomedical Curvilinear Structures

•Microscopy:
  –Actin, chromosomes [Noordmans et al, 98]

•Organ imaging:
  –Colon [Cohen et al, 01]
  –Vasculature [Chung et al, 01] , bronchial tree [Fridman et al, 03]
  –White matter tractography [Parker et al, 02][Jackowski et al, 04]
   Previous Work in Motion Tracking of
          Biomedical Structures
• Microscopy:
   – Manual: Annotation of video [Waterman et al, 00]
   – Automated: Single molecules, cytoplasmic particles
     [Cheezum et al 01]

• Organ imaging:
   – Lungs, heart [Papademetris et al, 02]
   – Cineangiography of coronary arteries [Shechter et al, 03]
• Registration of longitudinal data [Weiner et al, 2004]
              Confocal Microscopy
• Pinhole microscopy, 2D or 3D
• Resolution:
  x-y≈200 nm/pixel, z≈500 nm/pixel, weff≈2-3 pixels
• Laser causes photobleaching




 I:D→[0, Imax], fluorescence
                  Preprocessing
• Filtering: Largest eigenvalue of matrix of 2nd
  derivatives
    MT Segmentation in Initial Frame
• Segment MTs starting from the ends
• Get pinner

                          pinner




                              Microtubule
            Microtubule end
         Cumulative Cost Over Valid
              Neighborhood
1. Start from pinner to compute cost map Uo:

                U o  P  P2
                        1


•P1 : Isotropic, favors MT fluorescence:

                        Ix
                                            1   .
        P ( x)  1 
         1
                       I max        P1(x)
        I max  maximum intensity
                                                          .
                                                         Imax
                                                    Ix
                 Centerline Component

•P2 : Anisotropic, favors MT centerline:
                                                    
                                          
                                                    e1 , r1
                      U 0 .e1 ( x) U 0 .e2 ( x)              
  P2 ( x, U 0 )                                             e2 , r2
                       r2 ( x)        r1 ( x)
  
  ei ( x), ri ( x)  PCA of matrix of 2nd                     .x
  derivative s at x



2. Solve with one pass algorithm
       Extraction of Curve Segment

3. Curve segment is streamline of U0
• Backtrack along Uo from starting point:

                  M
                        U 0 ,
                   s
                  M ( s)  MT segment
                  M (0)  pstart
Extraction of First MT Segment

Valid region for Ulo,          Null region of Ulo
r=5weff




          Microtubule end
                            Microtubule
Extraction of Subsequent MT Segments
                                           MT tangent
     Valid region for   Ul   o,
     r=5weff
                                            2weff




                                                            Null region of Ulo
    Microtubule
                                  Most recently
                                  segmented point, pstart
       Evaluation of Curve Segment
Contrast measure across its axis:

                     Microtubule segment


                                               I inner
                                    contrast          1
                                               I outer
                                             
                                    Microtubul e segment

    weff    weff    weff
  Outer    Inner   Outer
  zone      zone   zone
Microtubule 2D Segmentation
       Compute Ulo in segment
           neighborhood


         Backtrack along Ulo
           to get segment


       Compute Ulo in segment
           neighborhood



         Backtrack along Ulo    Yes
           to get segment


           Evaluate curve
Examples of Segmentations of 2D
              MT
  MT Extrapolation in Average Frame
• Compute average image over time:
  MT Extrapolation in Average Frame
• Extrapolate MTs starting from the outer ends
• Get pouter
              Thresholding of Data
•Estimate mean and st.dev. of intensities on MT centerlines
                 Threshold=mean-st.dev.
  Streamline Passing from Microtubule

For all t=tstart+1→tend:
   •Compute local U0t starting from
   pinner                                               Lt   .p
   •Extract streamline Lt between pinner   MT
                                                                  outer

   and pouter                               .
                                            p
   •Lt includes microtubule                     inner
Examples of Streamlines Through
         Microtubules
           Compute MT End Feature
For all t=tstart+1→tend:
• Compute end feature , R along streamline Lt,
  R=directional derivative of Uo along tangent u of Lt:

                            R  uU 0
                        u
           pinner   .         Lt        .p   outer




    .
            MT End Point Trajectory

•Condition 1: Limit motion shift:
           |et-et-1| < shift
                                     etend
                                              . .t   end

                                        .
                                      e .
et -MT end at time t
                                            L              t

                                      e . L
                                       t                       t
                                                      t-1

•Condition 2: Point of maximum R
                                          .
                                        t-1


                                          . L           1
 along Lt:
                                    e    .t
                                    tstart      start
           et  arg max R
                     Lt
   Outline of Motion Tracking Algorithm
        Preprocessing

                                                                          tend     pouter
   Segment microtubules
       to get pinner                                                      t
                                                         Microtubule
                                                                  . .
                                                                .
                                    Next subsequence
  Extrapolate microtubules                                                tstart
         to get pouter

                                                                          MT end
For all t: Extract streamline, Lt
       btw pinner and pouter                                     pinner


    For all t: Compute MT                              •Implementation in C++
        end feature, R
                                                       •Enhancement for
Form MT end point trajectory
                                                       visualization
    Phantom Sequence for Noise




                        •Green: Ground truth
                        •Red: Algorithm




Size=150x150x100,
Time=2 min 45 sec
Phantom Sequence for Proximity



                      •Green: Ground truth
                      •Red: Algorithm




•Size=150x150x100,
•Time=2 min 38 sec
Examples 1 of Real Sequence
       Example 1: Ground Truth




•Size=635x471x100,
                        •Green: Ground truth
•Time=30 min 6 sec      •Red: Algorithm
• Error=3.3 pixels
Example 2 of Real Sequence
Example 2: Ground Truth




•Green: Ground truth   •Error in MTs tracked=17/19
•Red: Algorithm        •Error in tracking=2.6 pixels
    Example 3 of Real Sequence




•Size=136x112x100,
•Time=5 min 7 sec
     Example 4 of Real Sequence




•Size=350x262x36,
•Time=3 min 25 sec,
•Error in MTs tracked=17/19
•Error in tracking=2.6 pixels
                                •Green: Ground truth
                                •Red: Algorithm
                    Summary

•Preprocessing
•MT segmentation and extrapolation:
  –First and average image
  –Consecutive MT segments


•MT end feature ≡ derivative of Uo along streamline
•Form MT end trajectory
                     Discussion

•Evaluate:Phantom, real
•Robust:
   –Noise,
   –Deformation,
   –Proximity
   –MT end polymerization
•Sensitive:
   –Intersections,
   –Lateral motion
End
Example 4 of Real Sequence
  Confocal vs Conventional Microscopy
   Widefield Microscopy                Confocal Microscopy

CCD                              CCD
                 Beam splitter                      Beam splitter

No aperture                      Aperture




                  Light source                      Laser illumination


Wide field        Objective lens Narrow field       Objective lens
of view                          of view
                  Specimen                          Specimen
  Quantification of Microtubule Motion
•Specification of tips at first frame




•Motion tracking of ends
•Measure average (de)-polymerization:
  –Duration,
  –Rates
    Quantification of Microtubule End
                  Motion
                                               C
•Microtubule states:                 P               D
  –Polymerization,                             R
  –Depolymerization,                       R
  –Quiescent                                        C

                                               Q


•Statistics:
   –States:(de)polymerization rates, avg time duration
   –State transitions: Rescue, catastrophe
Examples of Motion Statistics
    Example 2: Statistics




•Size=636x472x100,
•Time= min sec

								
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