Fig 1.
Analyzing movies of contracting human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs): (a) Still image of a beating hiPSC-CM movie. As per the schematic, z-discs, which define the ends of an ≈ 2 μm sarcomere, are fluorescently labeled; (b) Movie still with a schematic illustration of deformation gradient Favg and tracked sarcomeres overlaid, sarcomere color corresponds to contraction level with red indicating the highest level of contraction; (c) Magnitudes of average principal stretches (λ1, λ2) computed from Favg with respect to the movie frame number; (d) Average normalized sarcomere length with respect to the movie frame number. We note that the definitions of Favg, λ1, and λ2 are introduced in this text.
Fig 2.
Creating synthetic data to test the image analysis code: (a) Define the geometry of z-discs (points) and sarcomeres (line segments) in three-dimensional (3D) space and prescribe the ground truth deformation for each sarcomere; (b) Approximate each z-disc as an oriented cylinder in 3D space; (c) Convert the 3D geometry into a voxel array with higher resolution in the x and y directions than the z direction; (d) Slice and project the voxel array to obtain a two-dimensional (2D) image. Image noise and blur can be added to the voxel array, 2D image, or both.
Table 1.
Summary of experimental examples included in this paper (E1, E2, E3, E4, and E5).
We note that Examples E1 and E2 have already been published and made publicly available at https://github.com/HMS-IDAC/SarcTrack [10].
Fig 3.
Segmenting and tracking the z-discs and sarcomeres: (a) An example of a raw synthetic two-dimensional (2D) input image; (b) The Laplacian of the input image is used to detect the high gradients present at the edge of every z-disc [27]; (c) z-discs are identified as closed contours where the value of the Laplacian exceeds the threshold computed with Otsu’s method [28]; (d) Sarcomeres are procedurally identified from the segmented z-discs; (e) Sarcomeres and z-discs are tracked independently between frames with the Python trackpy package [29]; (f) The algorithm to segment sarcomeres is based on linking the approximately parallel z-discs to their closest neighbors in the direction perpendicular to the z-disc; (g) Sarcomere properties are computed from the pair of associated z-discs; (h) Tracking each sarcomere leads to multiple spatially resolved time series.
Fig 4.
Data analysis from segmentation and tracking: (a) Tracked elements are treated as fiducial markers and used to construct an average deformation gradient F (see Eqs 1–4); (b) z-discs and sarcomeres are tracked independently and used to construct a spatial graph (z-discs are “nodes” and sarcomeres are “edges”, edge color corresponds to sarcomere orientation, node color corresponds to correlation in sarcomere orientation) to measure correlations based on network distance; (c) Automated analysis of time series data is used to extract constants such as mean contraction time and number of peaks.
Fig 5.
For each image, the number of sarcomeres successfully segmented and tracked (out of 20 possible) is reported.
Running the algorithm on synthetic data shows that the code is robust to geometry and noise up to a limit: (a) Illustration of successful z-disc and sarcomere segmentation and tracking for a curved geometry in the presence of noise; (b) Performance degrades when the baseline geometry moves partially out of plane (here slanted in the z-direction), and when the sarcomere chain is too distorted (here high amplitude to period ratio for sinusoidal geometry); (c) Performance degrades in the presence of Perlin noise, in particular noise that is similar in size and brightness to the z-discs themselves.
Fig 6.
Example performance on synthetic data of increasing complexity with a known ground truth: Segmentation and tracking (marker color corresponds to sarcomere contraction in the illustrated frame); Constructing a spatial graph (line color corresponds to sarcomere orientation); Recovering individual time series data (both Sarc-Graph output and ground truth shown); Recovering average deformation behavior (both Sarc-Graph output and ground truth shown).
Table 2.
Comparison of Sarc-Graph computed , savg, OOP, Ciso, and C∥ with the ground truth values of these parameters for each synthetic data example.
Fig 7.
Example performance on experimental data E1 and E2: Raw image visualization; z-disc and sarcomere segmentation; Sarcomeres that are tracked for 1/3 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 20); Sarcomeres that are tracked for 3/4 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 20), note that these sarcomeres are included in the time series analysis; Individual time series data for normalized sarcomere length; Average deformation behavior; Illustration of the data represented as a spatial graph, color corresponds to sarcomere orientation; Normalized sarcomere time series cross-correlation score plotted as a function of the distance along the network. S1 and S2 Movies are included for further visualization.
Fig 8.
Example performance on experimental data E3 and E4: Raw image visualization; z-disc and sarcomere segmentation; Sarcomeres that are tracked for 1/3 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 50 for E3, frame 40 for E4); Sarcomeres that are tracked for 3/4 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 50 for E3, frame 40 for E4), note that these sarcomeres are included in the time series analysis; Individual time series data for normalized sarcomere length; Average deformation behavior; Illustration of the data represented as a spatial graph, color corresponds to sarcomere orientation; Normalized sarcomere time series cross-correlation score plotted as a function of the distance along the network. S3 and S4 Movies are included for further visualization.
Fig 9.
Example performance on experimental data E5: Raw image visualization; z-disc and sarcomere segmentation; Sarcomeres that are tracked for 1/3 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 50); Sarcomeres that are tracked for 3/4 or more of the movie, red corresponds to a contracted state, blue corresponds to a relaxed state (frame 50), note that these sarcomeres are included in the time series analysis; Individual time series data for normalized sarcomere length; Average deformation behavior; Illustration of the data represented as a spatial graph, color corresponds to sarcomere orientation; Normalized sarcomere time series cross-correlation score plotted as a function of the distance along the network. S5 Movie is included for further visualization.
Table 3.
Sarc-Graph computed , savg, OOP, Ciso, and C∥ for each experimental data example.