Post on 15-Jan-2016
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
MTs
Fluorescence labeling in confocal microscopy, ≈200 nm/pixel
•Provide structure and support to the cell
Why are Microtubule Dynamics Interesting?
MT: tracks for granules (dark dots) in fish cell
•Dynamic ‘highways’ for trafficking of vesicles
MT: spindle in yeast cell
•Regulate cell migration and cell division
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
Microtubule end
Microtubule
pinner
1. Start from pinner to compute cost map Uo:
•P1 : Isotropic, favors MT fluorescence:
Cumulative Cost Over Valid Neighborhood
intensity maximum
1)(
max
max1
I
I
IxP x
21 PPUo
P1(x)
Ix
1
Imax
.
.
•P2 : Anisotropic, favors MT centerline:
2. Solve with one pass algorithm
Centerline Component
x
x rxe
xr
xeU
xr
xeUUxP
ii
at sderivative
2nd ofmatrix ofPCA )(),(
)(
)(.
)(
)(.),(
1
20
2
1002
11, re
22 , re
x.
Extraction of Curve Segment
3. Curve segment is streamline of U0
• Backtrack along Uo from starting point:
startpM
sM
Us
M
)0(
)(
,0
segmentMT
Extraction of First MT Segment
Null region of UloValid region for Ul
o,
r=5weff
MicrotubuleMicrotubule end
Valid region for Ulo,
r=5weff
Extraction of Subsequent MT Segments
2weff
Null region of Ulo
Microtubule
Most recently segmented point, pstart
MT tangent
Evaluation of Curve Segment
Contrast measure across its axis:
segment eMicrotubul
1I
I
outer
innercontrast
Inner zone
Outer zone
Outer zone
Microtubule segment
weff weff weff
Microtubule 2D Segmentation
Compute Ulo in segment
neighborhood
Backtrack along Ulo
to get segmentYes
Evaluate curve
Backtrack along Ulo
to get segment
Compute Ulo in segment
neighborhood
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
•Extract streamline Lt between pinner
and pouter
•Lt includes microtubule
pinner
MT
.
.pouter
Lt
Examples of Streamlines Through Microtubules
Compute MT End Feature
0UR u
For all t=tstart+1→tend:
• Compute end feature , R along streamline Lt,
R=directional derivative of Uo along tangent u of Lt:
pinner
pouter
u
. .Lt
.
MT End Point Trajectory
tstart
Lt-1
Lt
tend
t
.
.
.
.etstart
.etend
..et-1
.et
•Condition 1: Limit motion shift:
|et-et-1| < shift
et -MT end at time t
•Condition 2: Point of maximum R along Lt:
tLt Re maxarg
L1
Outline of Motion Tracking Algorithm
MT end
Microtubule
tstart
Segment microtubules to get pinner
Extrapolate microtubules to get pouter
For all t: Extract streamline, Lt
btw pinner and pouter
For all t: Compute MT end feature, R
Form MT end point trajectory
t
tend pouter
.
pinner
. .
Preprocessing
Next subsequence
•Implementation in C++•Enhancement for visualization
Phantom Sequence for Noise
Size=150x150x100, Time=2 min 45 sec
•Green: Ground truth•Red: Algorithm
Phantom Sequence for Proximity
•Size=150x150x100, •Time=2 min 38 sec
•Green: Ground truth•Red: Algorithm
Examples 1 of Real Sequence
Example 1: Ground Truth
•Size=635x471x100, •Time=30 min 6 sec• Error=3.3 pixels
•Green: Ground truth•Red: Algorithm
Example 2 of Real Sequence
Example 2: Ground Truth
•Green: Ground truth•Red: Algorithm
•Error in MTs tracked=17/19•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
Light source
Beam splitter
CCD
Specimen
Objective lens
Beam splitter
CCD
Specimen
Laser illumination
Objective lensWide field of view
Narrow field of view
Confocal vs Conventional Microscopy
Widefield Microscopy Confocal Microscopy
ApertureNo aperture
Quantification of Microtubule Motion
•Specification of tips at first frame
•Motion tracking of ends•Measure average (de)-polymerization:
–Duration,–Rates
C
C
Quantification of Microtubule End Motion
•Microtubule states: –Polymerization, –Depolymerization, –Quiescent
P D
Q
•Statistics:–States:(de)polymerization rates, avg time duration–State transitions: Rescue, catastrophe
RR
Examples of Motion Statistics
Example 2: Statistics
•Size=636x472x100, •Time= min sec