Fig 1.
Typical PIV methods, a topology-based tracking and the current cPTV fail to track a large, local deformation.
(A) Ground-truth traction map, designed with a large, local traction force in the center, mimicking the force from a large focal adhesion. (B) A color-merged image of a synthetic bead image (8000 beads on 512x512 pixel area) in a relaxed configuration (red) and another image of beads where displacements in A is applied (green). (C,D) Ground-truth displacement magnitude map (C) and vector field (D) calculated from the ground-truth traction distribution. Yellow polygon overlaid represents the region of displacement by the small forces whereas the red ellipse represents the region of displacements by the large force. (E-P) Displacement magnitude map (E,G,I,K,M,O) and corresponding vector field (F,H,J,L,N,P) of the pair of bead images from panel B, tracked by multiple PIV methods such as PIV Suite (E,F), Tseng’s PIV (G,H) and mpiv (I,J), a correlation-based PTV, or cPTV (K,L), cPTV where vector outliers are filtered (M,N), and a topology-based particle tracking, or T-PT method (O,P). Red circles in the vector fileds represent the seed points that have failed to track the deformation. Green arrows represent falsely-tracked vectors that show more than 10% mean-squared-deviation. Scale bars in A-P: 5 μm assuming 108 nm/pixel. (Q-R) Bar plots of the mean-squared-deviation (MSD) for the measured displacement fields by the six tracking methods, quantified over the entire field of view (Q), large force area (R), and small force area (S).
Table 1.
Parameters used for PIV methods.
Fig 2.
Large displacement shows a correlation score smaller than global correlation maximum.
(A-L) Cross correlation score maps (A, E, I), the synthetic reference images of the reference (undeformed) configuration with a yellow box indicating the template window around the center position of a bead of interest (B,F,J), the bead images of the deformed configuration with a red box indicating a shifted location of the measured displacement, a purple box indicating a shifted location of the ground-truth displacement, and a dotted white box indicating the original unshifted position of the template window (C,G,K), and the cropped and enlarged views of the templates with boxes whose color matches those in the bead images (D,H,L) for a small (<10 px in magnitude) displacement representative vector (A-D), a large (>50 px in magnitude) displacement vector (E-H) and another large (~30 px in magnitude) displacement vector that was determined to be missing (I-L).
Fig 3.
(A) Flowchart of the main algorithm of cPTV-based retracking. See the main text or Methods section for detailed description of this chart. (B) An example of a masked correlation score map (right) compared to a full score map (left), which is used in step 4 of the flowchart. A white arrow on the masked score map, unei, is the averaged neighboring vector. The range of the radius of the mask was determined as 0.5*|unei| ≤ |u| ≤ 3*|unei|, and the range of the angle was deteremined as mean(∠unei)-2*std(∠unei) ≤ ∠u ≤ mean(∠unei)+2*std(∠unei) where the symbol, ∠, represents the orientation of each vector. (C) A series of displacement vector fields at representative iterations, showing how progressively missing vectors are found. Red vectors represent the newly-found vectors at the specific iteration. At zeroth iteration, the field is filtered by a vector median filter with a strict threshold so that the retracking is performed based on the confident neighboring vectors. The last field at iteration = 317 is the result from the last iteration, i.e., when there was no single retracked vector for 30 consecutive iterations.
Fig 4.
Containing the enlargement factor increases the possibility of identification of the large displacement vectors and the accuracy of the tracking.
(A) A flowchart of an algorithm that adaptively retrack displacement vectors using the enlargement factor. See the main text for the details. (B,C) Final displacement fields (top) and associated displacement maps (bottom) resulted from cPTVR with a median vector as a model vector (B) and with a progressive enlargement in the model vector (C). Green arrows represent vector outliers determined by ones showing more than 10% MSD. (B) was converged in 317 iterations whereas (C) converged in 119 iterations. (D,E) Bar plots of MSD for the measured displacement fields in the entire field of view (D) or in the large force area defined in Fig 1C (E). Note that cPTVR with enlargement factor has much smaller MSD than the filtered cPTV or cPTVR with a median model vector. (F) A bar plot of the accuracy at the large force area between three PIV methods and three cPTV methods.
Fig 5.
cPTV-retracking method with the enlargement factor leads to the most accurate traction reconstruction for large forces.
(A) The ground-truth traction map, the same as in Fig 1A. (B) The ground-truth traction vector field. (C-P) the traction maps (C,E,G,I,K,M,O) and the traction vector fields (D,F,H,J,L,N,P) reconstructed from displacement fields by PIV Suite (C,D), mpiv (E,F), Tseng’s PIV (G,H), T-PT (I,J), cPTV with outlier filtering (K,L), cPTV-Retracking with a median model vector (M,N), and cPTV-Retracking with the enlargement factor (O,P). (Q-S) Bar plots of the mean-squared-diviation (MSD) for the measured force fields by the six tracking methods quantified over the entire field of view (Q), large force area (R), and small force area (S). (T) A bar plot of accuracy for the measured force fields by the six tracking methods over the large force area.
Fig 6.
cPTVR leads to a traction field resolving a larger range of the force magnitude than PIV or cPTV.
(A) A color-merged image of beads on a 4 kPa silicone gel, taken under cell presence (green) and absence (red) via total internal reflection fluorescence microscope. Scale bar: 5 μm (B-D) Displacement maps tracked by PIV Suite (B), cPTV (C) and cPTVR with the enlargement factor (D). (E) An image of paxillin-GFP of a U2OS cell, overlaid with nascent adhesions (NAs, yellow circles), detected with Gaussian misture model, focal complexes (FCs, green segmentations), and focal adhesions (FAs, red segmentations). Background inside a cell (BGin) represents the area in the cell excluding adhesions whereas background outside the cell (BGout) represents the area outside of the cell. (F-H) Traction mpas reconstructed from the displacement fields in B,C,D, respectively. White outlines overlaid on the maps represents cell boundary. Magenta arrowheads indicate areas of tracking failure. Scale bar: 5 μm (I) A bar graph of the average traction magnitude by PIV Suite, cPTV and cPTVR per NAs, FCs and FAs. Note that larger forces are meausred for FCs and FAs by cPTVR compared to the other two methods whereas forces at NAs stay the same. **: p<0.01, *: p<0.05, tested by unpaired student t-test. Scale bars: 5 μm. (J-L) Box plots of tractions quantified at FAs, FCs, NAs, BGin and BGout by PIV Suite (J), cPTV (K), and cPTVR (L). Note that only by cPTVR-based traction can resolve forces at FAs larger than forces at both FCs and NAs whereas other methods result in the force at FAs not necessarily larger than forces at either or both of FCs and NAs. ***: p<1e-5, *: p<0.5, tested by unpaired student t-test.