Fig 1.
Obtained cytoskeleton image can include some degrees of blurring.
(a) Illustration of the cap and basal actin layers. (b) Image of a rat osteoblast (bone producing cell) with phalloidin (red) stained actin cytoskeleton and dapi stained nucleus (blue).
Fig 2.
Different analysis strategies will determine the amount of information to be extracted from the image.
(a) Possible fibers analysis strategies. (b) The strategy followed involve three sequential stages: directional filaments filtering and enhancement, filaments network segmentation and individual fibers extraction.
Fig 3.
The proposed framework is based on a specific three stage sequence of processing steps.
Fig 4.
(a) Schematics of the fluidic system we used to exert a constant shear stress on osteoblasts. 1: Ibidi culture chamber with osteoblasts attached to the lower plate (not depicted). 2: Container located under the culture chamber. 3: Peristaltic pump. 4: Container located above the culture chamber. Its position above the culture chamber permits to adjust the flow rate. 5: Microscope and camera (not shown). (b) Image of the culturing chamber showing the border of the micro-fluidic chip, and the direction of the shear stress flow at ≈ 80°.
Fig 5.
The decomposition process of the original image f into the artifacts image va, the fibers image uf and noise .
(a) Image f. (b) Artifacts image va. (c) Fibers image uf. (d) Reminder noise . Solution obtained after 100 iterations with δ = 3.
Fig 6.
Fibers enhancement of the fibers image uf provides sharpened filaments network.
(a) Fibers image uf after sparse multi-source separation. (b) Filaments enhanced image, uE, obtained with σ = 1.0, β = 10.0 and σdg = 10.0, for the Gaussian, Laplace and directional Gaussian, respectively.
Fig 7.
Linear response for width and length evaluation at certain orientation.
(a) Width evaluation. (b) Length evaluation.
Fig 8.
The binarization step provides the segmented filaments network.
(a) Multi-scale linear response uG. (b) Binary image uB obtained from uG. Width parameters set as W = 4.
Fig 9.
Fixed length segments are merged if they overlap and their angle difference is not too large θ < Tθ.
(a) Filament partitioned into fixed-length segments. (b) Overlapping and angle difference between segments.
Fig 10.
Individual filaments are extracted from the binarized image.
(a) Input defocused image f. (b) Fibers image uf. (c) Enhanced fibers image uE. (d) Fibers from uB. (e) Input well focused image x. (f) Fiber image uf. (g) Enhanced fibers image uE. (h) Fibers from uB. For each processing stage, the parameters were set as in Figs 5, 6 and 8, respectively.
Fig 11.
The proposed framework extract a higher number of filaments.
(a) Original image B2. (b) Method of [21]. (c) Proposed framework with W = 4 and L = 30.
Fig 12.
Zoomed area highlighting blurred filaments detected by the proposed framework.
(a) Zoomed image B2. (b) Method of [21]. (c) Proposed framework.
Fig 13.
(a) Original image B2. (b) Method of [21]. (c) Proposed framework with W = 8 and L = 60.
Fig 14.
Extracted fibers in the peri-nuclear area.
(a) Method of [21]. (b) Proposed framework.
Fig 15.
Most of errors accounted in the proposed framework consist of fibers longer than they should.
(a) Simulated image (S1). (b) Method of [21]. (c) Proposed framework.
Fig 16.
The models exhibit similar accuracy but a higher sensitivity, in 10 simulated images; Stars corresponds to method in [21] and Circles to the proposed framework results.
(a) Accuracy. (b) Sensitivity.
Table 1.
Top-row: the method of [21]; Bottom-row: the proposed framework (PF).
Table 2.
Specificity (Sp) comparison of method [21] in top-row and the proposed framework (PF) in bottom-row.
Fig 17.
Visually annotated osteoblasts for orientation validation.
(a-d) Images with fibers oriented to the left. (e-h) Images with fibers with fibers oriented to the right.
Fig 18.
Normalized angular distribution of the Left-Set, and Right-Set, respectively, considering the horizontal axis of the image as reference.
(a) Left-oriented fibers. (b) Right-oriented fibers.
Fig 19.
Normalized angular distribution of fibers grown in different stress conditions, taking as reference the horizontal axis of the image, and considering all images of each population.
(a) Osteoblasts grown in static conditions. (b) Osteoblasts grown under fluid shear stress.
Fig 20.
The proposed framework can properly extract highly overlapping fibers.
(a) and (d) Osteoblast image. (b) and (e) Extracted fibers located near the nucleus. (c) and (f) Detected filaments network. Top row: Osteoblasts grown in normal conditions; Bottom row: Osteoblasts grown under fluid shear stress. The arrows depict the shear stress flow direction around ≈ 80° (Fig 4b).