Table 1.
Description of the software packages included in OpenCASA.
Fig 1.
The software architecture was designed to facilitate the subsequent development of new features, so the code was separated in different packages depending on its functionality. Using these packages, the program allows user to carry out four different sperm analyses through the corresponding modules: Chemotaxis, Motility, Morphometry and Viability. In addition, a fifth module was implemented to generate simulations of chemotactically attracted sperm populations.
Table 2.
Mathematical definition and meaning of the kinematic parameters implemented in the OpenCASA software.
Fig 2.
Definition of the instantaneous directionality angle.
ψ is the angle between the vector of the cell frame-to-frame displacement () and the gradient direction
. In the example above, the gradient has been set to
.
Fig 3.
Definition of two different options in order to analyse the chemotaxis phenomena.
It is important to count the number of instantaneous displacements pointing in the chemotaxis gradient direction
and the number of those displacements not pointing to the gradient.
being the angle between the instantaneous displacement of a cell and the gradient direction; N+ is defined as count{ψ∈[−γ,+γ]}, where γ is a parameter defined by the user and represents the amplitude of the chemoattractant concentration gradient. The developed software allows users to choose two options to define which displacements not pointing to the gradient are taken into account. In option 1, N− is defined as count{ψ∉[−γ,+γ]}, whereas in option 2 only displacements in the opposite direction of the gradient are considered (N− = count{ψ∈[180°−γ,180°+γ]}). The images above show graphically which angles are taken into account for the sum N+(green color) and N−(red color), depending on the option specified by the user.
Fig 4.
Two examples of the distribution of the instantaneous directionality angles ψ.
(a) Simulated sperm population without chemotaxis. (b) Simulated sperm population chemoattracted to θ = 0° (right). The ch-index provides information about the percentage of the angles ψ that point in the gradient direction with respect to the total number of angles taken into account (the total number of angles will depend on the option specified by the user). The parameters used to generate the simulation on the right were β = 1 and Responsiveness = 50%.
Fig 5.
Determination of the O.R. threshold used to discriminate between chemotaxis and no chemotaxis in the bootstrapping method.
The histogram comes from 10000 O.R. ratios, each one calculated by the odds value of two disjointed subsets of trajectories randomly sampled over all detected trajectories in 100 control simulations. Each simulation consisted of a 500 frames length video (800x800 pixels each frame) containing 100 virtual cells randomly located at the beginning of the simulation. Each cell was defined as an ellipse (10x8 pixels size) and behaved following a persistent random walk equation with parameters Drot = 0.1, v0 = 3,β = 0, Reponsiveness = 0 and ψ0 = 0°.
Fig 6.
Membrane integrity module workflow.
The module receives an RGB image as input, splits the image into red and green channels, identifies viable and non-viable cells depending on the channel and finally merges all the results showing all the detected cells in the same image. The module identifies the viable cells in green and the non-viable cells in red.
Table 3.
Definition of the morphometric parameters implemented in the OpenCASA software.
Fig 7.
Verification of the ch-index in a non-chemotaxis condition.
The ch-index provides information about the percentage of the angles ψ that point in the gradient direction with respect to the total of angles taken into account. In the case of a non- chemotaxis condition, a uniform distribution of the instantaneous directionality angles is expected, so defining γ = 30° and considering the angles ψ in the range [−30°,+30°] as chemotactical responses to the gradient, theoretically the percentage of those angles with respect to the total number of angles would be . Analysing the histogram, as expected, the ch-index was centred close to the theoretical value (17.90±0.46%) with some variation due to the sampling and the noise of the system (e.g. intersection of trajectories).
Table 4.
Comparison between the motility parameter values given by ISAS or by OpenCASA using a Pearson’s correlation test and a Bland-Altman test.
Table 5.
Comparison between the membrane integrity results obtained by flow cytometry or by OpenCASA using a Pearson’s correlation test and a Bland-Altman test.
Table 6.
Comparison between the values of the morphometry parameters given by CASMA-F or by OpenCASA using a Pearson’s correlation test and a Bland-Altman test.