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In flowcatchR: Tools to analyze in vivo microscopy imaging data focused on tracking flowing blood cells
Compiled date: r Sys.Date()
Last edited: 2018-01-14
License: r packageDescription("flowcatchR")[["License"]]
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Introduction {#intro}
This document offers an introduction and overview of the R/Bioconductor [@Rlang2014, @Gentleman2004] package r Biocpkg("flowcatchR"), which provides a flexible and comprehensive set of tools to detect and track flowing blood cells in time-lapse microscopy.
Why r Biocpkg("flowcatchR")?
\subsection{Why r Biocpkg("flowcatchR")?}
r Biocpkg("flowcatchR") builds upon functionalities provided by the r Biocpkg("EBImage") package [@Pau2010], and extends them in order to analyze time-lapse microscopy images. Here we list some of the unique characteristics of the datasets r Biocpkg("flowcatchR") is designed for:
- The images come from intravital microscopy experiments. This means that the Signal-to-Noise Ratio (SNR) is not optimal, and, very importantly, there are potential major movements of the living specimen that can be confounded with the true movements of the particles of interest [@Meijering2008]
- Cells are densely distributed on the images, with particles that can enter and leave the field of view
- The acquisition frame rate is a compromise between allowing the fluorescent cells to be detected and detecting the movements properly
- Cells can flow, temporarily adhere to the endothelial layer and/or be permanently adherent. Therefore, all movement modalities should be detected correctly throughout the entire acquisition. Cells can also cluster together and form (temporary) conglomerates
Essential features r Biocpkg("flowcatchR") delivers to the user are:
- A simple and flexible, yet complete framework to analyze flowing blood cells (and more generally time-lapse) image sets, with a system of S4 classes such as
Frames, ParticleSet, and TrajectorySet constituting the backbone of the procedures
- Techniques for aiding the detection of objects in the segmentation step
- An algorithm for tracking the particles, adapted and improved from the proposal of Sbalzarini and Koumoutsakos (2005) [@Sbalzarini2005], that reflects the directional aspect of the motion
- A wide set of functions inspecting the kinematic properties of the identified trajectories [@Beltman2009, @Meijering2012a], providing publication-ready summary statistics and visualization tools to help classifying identified objects
This guide includes a brief overview of the entire processing flow, from importing the raw images to the analysis of kinematic parameters derived from the identified trajectories. An example dataset will be used to illustrate the available features, in order to track blood platelets in consecutive frames derived from an intravital microscopy acquisition (also available in the package). All steps will be dissected to explore available parameters and options.
Purpose of this document
This vignette includes a brief overview of the entire processing flow, from importing the raw images to the analysis of kinematic parameters derived from the identified trajectories. An example dataset will be used to illustrate the available features, in order to track blood platelets in consecutive frames derived from an intravital microscopy acquisition (also available in the package). All steps will be dissected to explore available parameters and options.
Getting started
Installation
r Biocpkg("flowcatchR") is an R package distributed as part of the Bioconductor project. To install r Biocpkg("flowcatchR"), please start R and type:
if (!requireNamespace("BiocManager", quietly=TRUE))
install.packages("BiocManager")
BiocManager::install("flowcatchR")
In case you might prefer to install the latest development version, this can be done with these two lines below:
install.packages("devtools") # if needed
devtools::install_github("federicomarini/flowcatchR")
Installation issues should be reported to the Bioconductor support site (http://support.bioconductor.org/).
Getting help
The r Biocpkg("flowcatchR") package was tested on a variety of datasets provided from cooperation partners, yet it may require some extra tuning or bug fixes. For these issues, please contact the maintainer - if required with a copy of the error messages, the output of sessionInfo function:
maintainer("flowcatchR")
Despite our best efforts to test and develop the package further, additional functions or interesting suggestions might come from the specific scenarios that the package users might be facing. Improvements of existing functions or development of new ones are always most welcome! We also encourage to fork the GitHub repository of the package (https://github.com/federicomarini/flowcatchR), develop and test the new feature(s), and finally generate a pull request to integrate it to the original repository.
Citing r Biocpkg("flowcatchR")
The work underlying the development of r Biocpkg("flowcatchR") has not been formally published yet. A manuscript has been submitted for peer-review. For the time being, users of r Biocpkg("flowcatchR") are encouraged to cite it using the output of the citation function, as it follows:
citation("flowcatchR")
Processing overview {#overview}
r Biocpkg("flowcatchR") works primarily with sets of fluorescent time-lapse images, where the particles of interest are marked with a fluorescent label (e.g., red for blood platelets, green for leukocytes). Although different entry spots are provided (such as the coordinates of identified points in each frame via tab delimited files), we will illustrate the characteristics of the package starting from the common protocol starting point. In this case, we have a set of 20 frames derived from an intravital microscopy acquisition, which for the sake of practicality were already registered to reduce the unwanted specimen movements (Fiji [@Schindelin2012] was used for this purpose).
library("flowcatchR")
data("MesenteriumSubset")
# printing summary information for the MesenteriumSubset object
MesenteriumSubset
To obtain the set of trajectories identified from the analysis of the loaded frames, a very compact one-line command is all that is needed:
# one command to seize them all :)
fullResults <- kinematics(trajectories(particles(channel.Frames(MesenteriumSubset,"red"))))
On a MAC OS X machine equipped with 2.8 Ghz Intel Core i7 processor and 16 GB RAM, the execution of this command takes 2.32 seconds to run (tests performed with the R package r CRANpkg("microbenchmark"). On a more recent MacBook Pro (2017), the same benchmark took 1.78 seconds.
The following sections will provide additional details to the operations mentioned above, with more also on the auxiliary functions that are available in r Biocpkg("flowcatchR").
Image acquisition {#acquisition}
A set of images is acquired, after a proper microscopy setup has been performed. This includes for example a careful choice of spatial and temporal resolution; often a compromise must be met to have a good frame rate and a good SNR to detect the particles in the single frames. For a good review on the steps to be taken, please refer to Meijering's work [@Meijering2008, @Meijering2012a].
r Biocpkg("flowcatchR") provides an S4 class that can store the information of a complete acquisition, namely Frames. The Frames class extends the Image class, defined in the r Biocpkg("EBImage") package, and thus exploits the multi-dimensional array structures of the class. The locations of the images are stored as dimnames of the Frames object. To construct a Frames object from a set of images, the read.Frames function is used:
# initialization
fullData <- read.Frames(image.files="/path/to/folder/containing/images/", nframes=100)
# printing summary information for the Frames object
fullData
nframes specifies the number of frames that will constitute the Frames object, whereas image.files is a vector of character strings with the full location of the (raw) images, or the path to the folder containing them (works automatically if images are in TIFF/JPG/PNG format). In this case we just loaded the full dataset, but for the demonstrational purpose of this vignette, we will proceed with the subset available in the MesenteriumSubset object, which we previously loaded in Section \@ref(overview).
It is possible to inspect the images composing a Frames object with the function inspect.Frames (Fig. \@ref(fig:inspectRaw)).
inspect.Frames(MesenteriumSubset, nframes=9, display.method="raster")
By default, display.method is set to browser, as in the r Biocpkg("EBImage") function display. This opens up a window in the predefined browser (e.g. Mozilla Firefox), with navigable frames (arrows on the top left corner). For the vignette, we will set it to raster, for viewing them as raster graphics using R's native functions.
Importantly, these image sets were already registered and rotated in such a way that the overall direction of the movement of interest flows from left to right, as a visual aid and also to fit with some assumptions that will be done in the subsequent step of particle tracking. To register the images, we recommend the general purpose tools offered by suites such as ImageJ/Fiji [@Schneider2012, @Schindelin2012].
For the following steps, we will focus on the information contained in the red channel, corresponding in this case to blood platelets. We do so by calling the channel.Frames function:
plateletsMesenterium <- channel.Frames(MesenteriumSubset, mode="red")
plateletsMesenterium
This creates another instance of the class Frames, and we inspect it in its first 9 frames (Fig.\@ref(fig:inspectPlatelets)).
inspect.Frames(plateletsMesenterium, nframes=9, display.method="raster")
Image preprocessing and analysis {#prepro}
Steps such as denoising, smoothing and morphological operations (erosion/dilation, opening/closing) can be performed thanks to the general functions provided by r Biocpkg("EBImage"). r Biocpkg("flowcatchR") offers a wrapper around a series of operations to be applied to all images in a Frames object. The function preprocess.Frames is called via the following command:
preprocessedPlatelets <- preprocess.Frames(plateletsMesenterium,
brush.size=3, brush.shape="disc",
at.offset=0.15, at.wwidth=10, at.wheight=10,
kern.size=3, kern.shape="disc",
ws.tolerance=1, ws.radius=1)
preprocessedPlatelets
The result of this is displayed in Fig.\@ref(fig:inspectSegm). For a detailed explanation of the parameters to better tweak the performances of this segmentation step, please refer to the help of preprocess.Frames. To obtain an immediate feedback about the effects of the operations performed in the full preprocessing phase, we can call again inspect.Frames on the Frames of segmented images (Fig.\@ref(fig:inspectSegm).
inspect.Frames(preprocessedPlatelets, nframes=9, display.method="raster")
The frames could be cropped, if e.g. it is needed to remove background noise that might be present close to the edges. This is done with the function crop.Frames.
croppedFrames <- crop.Frames(plateletsMesenterium,
cutLeft=6, cutRight=6,
cutUp=3, cutDown=3,
testing=FALSE)
croppedFrames
If testing is set to true, the function just displays the first cropped frame, to get a feeling whether the choice of parameters was adequate. Similarly, for the function rotate.Frames the same behaviour is expected, whereas the rotation in degrees is specified by the parameter angle.
rotatedFrames <- rotate.Frames(plateletsMesenterium, angle=30)
rotatedFrames
If desired, it is possible to select just a subset of the frames belonging to a Frames. This can be done via the select.Frames function:
subsetFrames <- select.Frames(plateletsMesenterium,
framesToKeep=c(1:10,14:20))
subsetFrames
If required, the user can decide to perform a normalization step (via normalizeFrames), to correct for systematic variations in the acquisition conditions, in case the overall intensity levels change, e.g., when the acquisition spans long time scales. In this case, the median of the intensity sums is chosen as a scaling factor.
normFrames <- normalizeFrames(plateletsMesenterium,normFun = "median")
The user can choose any combination of the operations in order to segment the images provided as input, but preprocess.Frames is a very convenient high level function for proceeding in the workflow. It is also possible, as it was shown in the introductory one-liner, to call just particles on the raw Frames object. In this latter case, particles computes the preprocessed Frames object according to default parameters. Still, in either situation, the output for this step is an object of the ParticleSet class.
platelets <- particles(plateletsMesenterium, preprocessedPlatelets)
platelets
The function particles leverages on the multi-core architecture of the systems where the analysis is run, and this is implemented via r Biocpkg("BiocParallel") (updated since Version 1.0.3).
As it can be seen from the summary information, each ParticleSet stores the essential information on all particles that were detected in the original images, alongside with a complete set of features, which are computed by integrating the information from both the raw and the segmented frames.
A ParticleSet can be seen as a named list, where each element is a data.frame for a single frame, and the image source is stored as names to help backtracking the operations performed, and the slot channel is retained as selected in the initial steps.
It is possible to filter out particles according to their properties, such as area, shape and eccentricity. This is possible with the function select.particles. The current implementation regards only the surface extension, but any additional feature can be chosen and adopted to restrict the number of candidate particles according to particular properties which are expected and/or to remove potential noise that went through the preprocessing phase.
selectedPlatelets <- select.particles(platelets, min.area=3)
selectedPlatelets
This step can be done iteratively, with the help of the function add.contours. If called with the parameter mode set to particles, then it will automatically generate a Frames object, with the contours of all particles drawn around the objects that passed the segmentation (and filtering) step (Fig.\@ref(fig:checkSelection)).
paintedPlatelets <- add.contours(raw.frames=MesenteriumSubset,
binary.frames=preprocessedPlatelets,
mode="particles")
inspect.Frames(paintedPlatelets, nframes=9, display.method="raster")
To connect the particles from one frame to the other, we perform first the detection of particles on all images. Only in a successive phase, we establish the links between the so identified objects. This topic will be covered in detail in the following section.
Particle tracking {#tracking}
To establish the connections between particles, the function to be called is link.particles. The algorithm used to perform the tracking itself is an improved version of the original implementation of Sbalzarini and Koumotsakos [@Sbalzarini2005]. To summarize the method, it is a fast and efficient self-initializing feature point tracking algorithm (using the centroids of the objects as reference) [@Chenouard2014]. The initial version is based on a particle matching algorithm, approached via a graph theory technique. It allows for appearances/disappearances of particles from the field of view, also temporarily as it happens in case of occlusions and objects leaving the plane of focus.
Our implementation adds to the existing one by redefining the cost function used in the optimization phase of the link assignment. It namely adds two terms, such as intensity variation and area variation, and mostly important implements a function to penalize the movements that are either perpendicular or backwards with respect to the oriented flow of cells. Small unwanted movements, which may be present even after the registration phase, are handled with two jitter terms in a defined penalty function. Multiplicative factors can further influence the penalties given to each term.
In its default value, the penalty function is created via the penaltyFunctionGenerator. The user can exploit the parameter values in it to create a custom version of it, to match the particular needs stemming from the nature of the available data and phenomenon under inspection.
defaultPenalty <- penaltyFunctionGenerator()
print(defaultPenalty)
As mentioned above, to perform the linking of the particles, we use link.particles. Fundamental parameters are L and R, named as in the original implementation. L is the maximum displacement in pixels that a particle is expected to have in two consecutive frames, and R is the value for the link range, i.e. the number of future frames to be considered for the linking (typically assumes values between 1 - when no occlusions are known to happen - and 3). An extended explanation of the parameters is in the documentation of the package.
linkedPlatelets <- link.particles(platelets,
L=26, R=3,
epsilon1=0, epsilon2=0,
lambda1=1, lambda2=0,
penaltyFunction=penaltyFunctionGenerator(),
include.area=FALSE)
linkedPlatelets
As it can be seen, linkedPlatelets is an object of the LinkedParticleSet class, which is a subclass of the ParticleSet class.
After inspecting the trajectories (see Section \@ref(trajanal)) it might be possible to filter a LinkedParticleSet class object and subsequently reperform the linking on its updated version (e.g. some detected particles were found to be noise, and thus removed with select.particles).
r Biocpkg("flowcatchR") provides functions to export and import the identified particles, in order to offer an additional entry point for tracking and analyzing the trajectories (if particles were detected with other routines) and also to store separately the information per each frame about the objects that were primarily identified.
An example is provided in the lines below, with the functions export.particles and read.particles :
# export to csv format
export.particles(platelets, dir="/path/to/export/folder/exportParticleSet/")
# re-import the previously exported, in this case
importedPlatelets <- read.particles(particle.files="/path/to/export/folder/exportParticleSet/")
Trajectory analysis {#trajanal}
It is possible to extract the trajectories with the correspondent trajectories function:
trajPlatelets <- trajectories(linkedPlatelets)
trajPlatelets
A TrajectorySet object is returned in this case. It consists of a two level list for each trajectory, reporting the trajectory as a data.frame, the number of points npoints (often coinciding with the number of nframes, when no gaps ngaps are present) and its ID. A keep flag is used for subsequent user evaluation purposes.
Before proceeding with the actual analysis of the trajectories, it is recommended to evaluate them by visual inspection. r Biocpkg("flowcatchR") provides two complementary methods to do this, either plotting them (plot or plot2D.TrajectorySet) or drawing the contours of the points on the original image (add.contours).
By plotting all trajectories in a 2D+time representation, it's possible to have an overview of all trajectories.
The following command gives an interactive 3D (2D+time) view of all trajectories (Fig.\@ref(fig:cubeTrajs)):
plot(trajPlatelets, MesenteriumSubset)
The plot2D.TrajectorySet focuses on additional information and a different "point of view", but can just display a two dimensional projection of the identified trajectories (Fig.\@ref(fig:overviewTrajs)).
plot2D.TrajectorySet(trajPlatelets, MesenteriumSubset)
To have more insights on single trajectories, or on a subset of them, add.contours offers an additional mode called trajectories. Particles are drawn on the raw images with colours corresponding to the trajectory IDs. add.contours plots by default all trajectories, but the user can supply a vector of the IDs of interest to override this behaviour.
paintedTrajectories <- add.contours(raw.frames=MesenteriumSubset,
binary.frames=preprocessedPlatelets,
trajectoryset=trajPlatelets,
mode="trajectories")
paintedTrajectories
As with any other Frames object, it is recommended to take a peek at it via the inspect.Frames function (Fig.\@ref(fig:inspectTrajs)):
inspect.Frames(paintedTrajectories,nframes=9,display.method="raster")
To allow for a thorough evaluation of the single trajectories, export.Frames is a valid helper, as it creates single images corresponding to each frame in the Frames object. We first extract for example trajectory 11 (Fig.\@ref(fig:traj11)) with the following command:
traj11 <- add.contours(raw.frames=MesenteriumSubset,
binary.frames=preprocessedPlatelets,
trajectoryset=trajPlatelets,
mode="trajectories",
trajIDs=11)
traj11
inspect.Frames(traj11, nframes=9, display.method="raster")
The data for trajectory 11 in the TrajectorySet object can be printed to the terminal:
trajPlatelets[[11]]
After that, it can also be exported with the following command (the dir parameter must be changed accordingly):
export.Frames(traj11, dir=tempdir(), nameStub="vignetteTest_traj11",
createGif=TRUE, removeAfterCreatingGif=FALSE)
export.Frames offers multiple ways to export - animated gif (if ImageMagick is available and installed on the system) or multiple jpeg/png images.
Of course the user might want to singularly evaluate each trajectory that was identified, and this can be done by looping over the trajectory IDs.
evaluatedTrajectories <- trajPlatelets
for(i in 1:length(trajPlatelets))
{
paintedTraj <- add.contours(raw.frames=MesenteriumSubset,
binary.frames=preprocessedPlatelets,
trajectoryset=trajPlatelets,
mode="trajectories",
col="yellow",
trajIDs=i)
export.Frames(paintedTraj,
nameStub=paste0("vignetteTest_evaluation_traj_oneByOne_",i),
createGif=TRUE, removeAfterCreatingGif=TRUE)
### uncomment the code below to perform the interactive evaluation of the single trajectories
# cat("Should I keep this trajectory? --- 0: NO, 1:YES --- no other values allowed")
# userInput <- readLines(n=1L)
# ## if neither 0 nor 1, do not update
# ## otherwise, this becomes the value for the field keep in the new TrajectoryList
# evaluatedTrajectories@.Data[[i]]$keep <- as.logical(as.numeric(userInput))
}
Always using trajectory 11 as example, we would set evaluatedTrajectories[[11]]$keep to TRUE, since the trajectory was correctly identified, as we just checked.
Once all trajectories have been selected, we can proceed to calculate (a set of) kinematic parameters, for a single or all trajectories in a TrajectorySet object. The function kinematics returns the desired output, respectively a KinematicsFeatures object, a KinematicsFeaturesSet, a single value or a vector (or list, if not coercible to vector) of these single values (one parameter for each trajectory).
allKinematicFeats.allPlatelets <- kinematics(trajPlatelets,
trajectoryIDs=NULL, # will select all trajectory IDs
acquisitionFrequency=30, # value in milliseconds
scala=50, # 1 pixel is equivalent to ... micrometer
feature=NULL) # all kinematic features available
As it is reported from the output, the function raises a warning for trajectories which have 3 or less points, as they might be spurious detections. In such cases, no kinematic features are computed.
allKinematicFeats.allPlatelets
A summary for the returned object (in this case a KinematicsFeaturesSet) shows some of the computed parameters.
By default, information about the first trajectory is reported in brief, and the same parameters are evaluated on average across the selected trajectories. The true values can be accessed in this case for each trajectory by the subset operator for lists ([[]]), followed by the name of the kinematic feature (e.g., $totalDistance).
A list of all available parameters is printed with an error message if the user specifies an incorrect name, such as here:
allKinematicFeats.allPlatelets <- kinematics(trajPlatelets, feature="?")
When asking for a single parameter, the value returned is structured in a vector, such that it is straightforward to proceed with further analysis, e.g. by plotting the distribution of the curvilinear velocities (Fig.\@ref(fig:allVelos)).
allVelocities <- kinematics(trajPlatelets, feature="curvilinearVelocity")
hist(allVelocities, breaks=10, probability=TRUE, col="cadetblue",
xlab="Curvilinear Velocities Distribution",
main="Trajectory Analysis: Curvilinear Velocities")
lines(density(allVelocities, na.rm=TRUE), col="steelblue", lwd=2)
For this code chunk, we are suppressing the warning messages, as they would be exactly the same as in the former where all features were computed for each trajectory.
Interactive tools for a user-friendly workflow solution
To enhance the Frames objects and deliver an immediate feedback to the user, the function snap leverages on both the raw and binary Frames, as well as on the corresponding ParticleSet and TrajectorySet objects. It integrates the information available in all the mentioned objects, and it plots a modified instance of the Frames object, identifying the particles closest to the mouse click, and showing additional trajectory-related information, such as the trajectory ID and the instantaneous velocity of the cell. The function can be called as in the command below:
snap(MesenteriumSubset,preprocessedPlatelets,
platelets,trajPlatelets,
frameID = 1,showVelocity = T)
An example output for the snap is shown below in Fig.\@ref(fig:snapExample), where the information (trajectory ID, as well as the velocity in the selected frame) is shown in yellow to offer a good contrast with the fluorescent image.
display(readImage(system.file("extdata/snapExp.jpg",package="flowcatchR")),
method = "raster")
The shinyFlow Shiny Application
Additionally, since Version 1.0.3, r Biocpkg("flowcatchR") delivers shinyFlow, a Shiny Web Application ([@Shiny2013]), which is built on the backbone of the analysis presented in this vignette, and is portable across all main operating systems. The user is thus invited to explore datasets and parameters with immediate reactive feedback, that can enable better understanding of the effects of single steps and changes in the workflow.
To launch the Shiny App, use the command below to open an external window either in the browser or in the IDE (such as RStudio):
shinyFlow()
r Biocpkg("flowcatchR") in Jupyter notebooks
A further integration are a number of Jupyter/IPython notebooks ([@Perez2007]), as a way to provide easy reproducibility as well as communication of results, by combining plain text, commands and output in single documents. The R kernel used on the back-end was developed by Thomas Kluyver (https://github.com/takluyver/IRkernel), and instructions for the installation are available at the Github repository website. The notebooks are available in the installation folder of the package r Biocpkg("flowcatchR"), which can be found with the command below.
list.files(system.file("extdata",package = "flowcatchR"),pattern = "*.ipynb")
The notebooks are provided as template for further steps in the analysis. The user is invited to set up the IPython notebook framework as explained on the official website for the project (http://ipython.org/notebook.html). As of February, 3rd 2015, the current way to obtain the Jupyter environment is via the 3.0.dev version, available via Github (https://github.com/ipython/ipython). The notebooks can be opened and edited by navigating to their location while the IPython notebook server is running; use the following command in the shell to launch it:
$ ipython notebook
Alternatively, these documents can be viewed with the nbviewer tool, available at http://nbviewer.ipython.org/.
r Biocpkg("flowcatchR") in Docker containers
r Biocpkg("flowcatchR") is now (as of September 2015) available also in Docker images that are the components of the dockerflow proposal (https://github.com/federicomarini/dockerflow). This includes:
flowstudio - https://github.com/federicomarini/flowstudio, a command-line/IDE interface to RStudio where r Biocpkg("flowcatchR") and its dependencies are preinstalledflowshiny - https://github.com/federicomarini/flowshiny a Shiny Server running the shinyFlow web applicationflowjupy - https://github.com/federicomarini/flowjupy, a Jupyter Notebook interface
These three images can be run simultaneously, provided the system where the containers are running supports the docker-compose tool. For more information on how to install the single components, please refer to their repositories.
Supplementary information {#supplinfo}
For more information on the method adapted for tracking cells, see Sbalzarini and Koumotsakos (2005) [@Sbalzarini2005].
For additional details regarding the functions of r Biocpkg("flowcatchR"), please consult the documentation or write an email to marinif@uni-mainz.de.
Due to space limitations, the complete dataset for the acquired frames used in this vignette is not included as part of the r Biocpkg("flowcatchR") package.
If you would like to get access to it, you can write an email to marinif@uni-mainz.de.
Acknowledgements
This package was developed at the Institute of Medical Biostatistics, Epidemiology and Informatics at the University Medical Center, Mainz (Germany), with the financial support provided by the TRP-A15 Translational Research Project grant.
r Biocpkg("flowcatchR") incorporates suggestions and feedback from the wet-lab biology units operating at the Center for Thrombosis and Hemostasis (CTH), in particular Sven Jäckel and Kerstin Jurk. Sven Jäckel also provided us with the sample acquisition which is available in this vignette.
We would like to thank the members of the Biostatistics division for valuable discussions, and additionally Isabella Zwiener for contributing to the first ideas on the project.
Session info {.unnumbered}
This vignette was generated using the following package versions:
sessionInfo()
References {.unnumbered}
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set.seed(42) knitr::opts_chunk$set( comment='##' ) # knitr::opts_chunk$set(comment=NA, # fig.align="center", # fig.width = 7, # fig.height = 7, # warning=FALSE)
Introduction {#intro}
This document offers an introduction and overview of the R/Bioconductor [@Rlang2014, @Gentleman2004] package r Biocpkg("flowcatchR"), which provides a flexible and comprehensive set of tools to detect and track flowing blood cells in time-lapse microscopy.
Why r Biocpkg("flowcatchR")?
\subsection{Why r Biocpkg("flowcatchR")?}
r Biocpkg("flowcatchR") builds upon functionalities provided by the r Biocpkg("EBImage") package [@Pau2010], and extends them in order to analyze time-lapse microscopy images. Here we list some of the unique characteristics of the datasets r Biocpkg("flowcatchR") is designed for:
- The images come from intravital microscopy experiments. This means that the Signal-to-Noise Ratio (SNR) is not optimal, and, very importantly, there are potential major movements of the living specimen that can be confounded with the true movements of the particles of interest [@Meijering2008]
- Cells are densely distributed on the images, with particles that can enter and leave the field of view
- The acquisition frame rate is a compromise between allowing the fluorescent cells to be detected and detecting the movements properly
- Cells can flow, temporarily adhere to the endothelial layer and/or be permanently adherent. Therefore, all movement modalities should be detected correctly throughout the entire acquisition. Cells can also cluster together and form (temporary) conglomerates
Essential features r Biocpkg("flowcatchR") delivers to the user are:
- A simple and flexible, yet complete framework to analyze flowing blood cells (and more generally time-lapse) image sets, with a system of S4 classes such as
Frames,ParticleSet, andTrajectorySetconstituting the backbone of the procedures - Techniques for aiding the detection of objects in the segmentation step
- An algorithm for tracking the particles, adapted and improved from the proposal of Sbalzarini and Koumoutsakos (2005) [@Sbalzarini2005], that reflects the directional aspect of the motion
- A wide set of functions inspecting the kinematic properties of the identified trajectories [@Beltman2009, @Meijering2012a], providing publication-ready summary statistics and visualization tools to help classifying identified objects
This guide includes a brief overview of the entire processing flow, from importing the raw images to the analysis of kinematic parameters derived from the identified trajectories. An example dataset will be used to illustrate the available features, in order to track blood platelets in consecutive frames derived from an intravital microscopy acquisition (also available in the package). All steps will be dissected to explore available parameters and options.
Purpose of this document
This vignette includes a brief overview of the entire processing flow, from importing the raw images to the analysis of kinematic parameters derived from the identified trajectories. An example dataset will be used to illustrate the available features, in order to track blood platelets in consecutive frames derived from an intravital microscopy acquisition (also available in the package). All steps will be dissected to explore available parameters and options.
Getting started
Installation
r Biocpkg("flowcatchR") is an R package distributed as part of the Bioconductor project. To install r Biocpkg("flowcatchR"), please start R and type:
if (!requireNamespace("BiocManager", quietly=TRUE)) install.packages("BiocManager") BiocManager::install("flowcatchR")
In case you might prefer to install the latest development version, this can be done with these two lines below:
install.packages("devtools") # if needed devtools::install_github("federicomarini/flowcatchR")
Installation issues should be reported to the Bioconductor support site (http://support.bioconductor.org/).
Getting help
The r Biocpkg("flowcatchR") package was tested on a variety of datasets provided from cooperation partners, yet it may require some extra tuning or bug fixes. For these issues, please contact the maintainer - if required with a copy of the error messages, the output of sessionInfo function:
maintainer("flowcatchR")
Despite our best efforts to test and develop the package further, additional functions or interesting suggestions might come from the specific scenarios that the package users might be facing. Improvements of existing functions or development of new ones are always most welcome! We also encourage to fork the GitHub repository of the package (https://github.com/federicomarini/flowcatchR), develop and test the new feature(s), and finally generate a pull request to integrate it to the original repository.
Citing r Biocpkg("flowcatchR")
The work underlying the development of r Biocpkg("flowcatchR") has not been formally published yet. A manuscript has been submitted for peer-review. For the time being, users of r Biocpkg("flowcatchR") are encouraged to cite it using the output of the citation function, as it follows:
citation("flowcatchR")
Processing overview {#overview}
r Biocpkg("flowcatchR") works primarily with sets of fluorescent time-lapse images, where the particles of interest are marked with a fluorescent label (e.g., red for blood platelets, green for leukocytes). Although different entry spots are provided (such as the coordinates of identified points in each frame via tab delimited files), we will illustrate the characteristics of the package starting from the common protocol starting point. In this case, we have a set of 20 frames derived from an intravital microscopy acquisition, which for the sake of practicality were already registered to reduce the unwanted specimen movements (Fiji [@Schindelin2012] was used for this purpose).
library("flowcatchR") data("MesenteriumSubset")
# printing summary information for the MesenteriumSubset object
MesenteriumSubset
To obtain the set of trajectories identified from the analysis of the loaded frames, a very compact one-line command is all that is needed:
# one command to seize them all :) fullResults <- kinematics(trajectories(particles(channel.Frames(MesenteriumSubset,"red"))))
On a MAC OS X machine equipped with 2.8 Ghz Intel Core i7 processor and 16 GB RAM, the execution of this command takes 2.32 seconds to run (tests performed with the R package r CRANpkg("microbenchmark"). On a more recent MacBook Pro (2017), the same benchmark took 1.78 seconds.
The following sections will provide additional details to the operations mentioned above, with more also on the auxiliary functions that are available in r Biocpkg("flowcatchR").
Image acquisition {#acquisition}
A set of images is acquired, after a proper microscopy setup has been performed. This includes for example a careful choice of spatial and temporal resolution; often a compromise must be met to have a good frame rate and a good SNR to detect the particles in the single frames. For a good review on the steps to be taken, please refer to Meijering's work [@Meijering2008, @Meijering2012a].
r Biocpkg("flowcatchR") provides an S4 class that can store the information of a complete acquisition, namely Frames. The Frames class extends the Image class, defined in the r Biocpkg("EBImage") package, and thus exploits the multi-dimensional array structures of the class. The locations of the images are stored as dimnames of the Frames object. To construct a Frames object from a set of images, the read.Frames function is used:
# initialization fullData <- read.Frames(image.files="/path/to/folder/containing/images/", nframes=100) # printing summary information for the Frames object fullData
nframes specifies the number of frames that will constitute the Frames object, whereas image.files is a vector of character strings with the full location of the (raw) images, or the path to the folder containing them (works automatically if images are in TIFF/JPG/PNG format). In this case we just loaded the full dataset, but for the demonstrational purpose of this vignette, we will proceed with the subset available in the MesenteriumSubset object, which we previously loaded in Section \@ref(overview).
It is possible to inspect the images composing a Frames object with the function inspect.Frames (Fig. \@ref(fig:inspectRaw)).
inspect.Frames(MesenteriumSubset, nframes=9, display.method="raster")
By default, display.method is set to browser, as in the r Biocpkg("EBImage") function display. This opens up a window in the predefined browser (e.g. Mozilla Firefox), with navigable frames (arrows on the top left corner). For the vignette, we will set it to raster, for viewing them as raster graphics using R's native functions.
Importantly, these image sets were already registered and rotated in such a way that the overall direction of the movement of interest flows from left to right, as a visual aid and also to fit with some assumptions that will be done in the subsequent step of particle tracking. To register the images, we recommend the general purpose tools offered by suites such as ImageJ/Fiji [@Schneider2012, @Schindelin2012].
For the following steps, we will focus on the information contained in the red channel, corresponding in this case to blood platelets. We do so by calling the channel.Frames function:
plateletsMesenterium <- channel.Frames(MesenteriumSubset, mode="red") plateletsMesenterium
This creates another instance of the class Frames, and we inspect it in its first 9 frames (Fig.\@ref(fig:inspectPlatelets)).
inspect.Frames(plateletsMesenterium, nframes=9, display.method="raster")
Image preprocessing and analysis {#prepro}
Steps such as denoising, smoothing and morphological operations (erosion/dilation, opening/closing) can be performed thanks to the general functions provided by r Biocpkg("EBImage"). r Biocpkg("flowcatchR") offers a wrapper around a series of operations to be applied to all images in a Frames object. The function preprocess.Frames is called via the following command:
preprocessedPlatelets <- preprocess.Frames(plateletsMesenterium, brush.size=3, brush.shape="disc", at.offset=0.15, at.wwidth=10, at.wheight=10, kern.size=3, kern.shape="disc", ws.tolerance=1, ws.radius=1) preprocessedPlatelets
The result of this is displayed in Fig.\@ref(fig:inspectSegm). For a detailed explanation of the parameters to better tweak the performances of this segmentation step, please refer to the help of preprocess.Frames. To obtain an immediate feedback about the effects of the operations performed in the full preprocessing phase, we can call again inspect.Frames on the Frames of segmented images (Fig.\@ref(fig:inspectSegm).
inspect.Frames(preprocessedPlatelets, nframes=9, display.method="raster")
The frames could be cropped, if e.g. it is needed to remove background noise that might be present close to the edges. This is done with the function crop.Frames.
croppedFrames <- crop.Frames(plateletsMesenterium, cutLeft=6, cutRight=6, cutUp=3, cutDown=3, testing=FALSE) croppedFrames
If testing is set to true, the function just displays the first cropped frame, to get a feeling whether the choice of parameters was adequate. Similarly, for the function rotate.Frames the same behaviour is expected, whereas the rotation in degrees is specified by the parameter angle.
rotatedFrames <- rotate.Frames(plateletsMesenterium, angle=30) rotatedFrames
If desired, it is possible to select just a subset of the frames belonging to a Frames. This can be done via the select.Frames function:
subsetFrames <- select.Frames(plateletsMesenterium, framesToKeep=c(1:10,14:20)) subsetFrames
If required, the user can decide to perform a normalization step (via normalizeFrames), to correct for systematic variations in the acquisition conditions, in case the overall intensity levels change, e.g., when the acquisition spans long time scales. In this case, the median of the intensity sums is chosen as a scaling factor.
normFrames <- normalizeFrames(plateletsMesenterium,normFun = "median")
The user can choose any combination of the operations in order to segment the images provided as input, but preprocess.Frames is a very convenient high level function for proceeding in the workflow. It is also possible, as it was shown in the introductory one-liner, to call just particles on the raw Frames object. In this latter case, particles computes the preprocessed Frames object according to default parameters. Still, in either situation, the output for this step is an object of the ParticleSet class.
platelets <- particles(plateletsMesenterium, preprocessedPlatelets) platelets
The function particles leverages on the multi-core architecture of the systems where the analysis is run, and this is implemented via r Biocpkg("BiocParallel") (updated since Version 1.0.3).
As it can be seen from the summary information, each ParticleSet stores the essential information on all particles that were detected in the original images, alongside with a complete set of features, which are computed by integrating the information from both the raw and the segmented frames.
A ParticleSet can be seen as a named list, where each element is a data.frame for a single frame, and the image source is stored as names to help backtracking the operations performed, and the slot channel is retained as selected in the initial steps.
It is possible to filter out particles according to their properties, such as area, shape and eccentricity. This is possible with the function select.particles. The current implementation regards only the surface extension, but any additional feature can be chosen and adopted to restrict the number of candidate particles according to particular properties which are expected and/or to remove potential noise that went through the preprocessing phase.
selectedPlatelets <- select.particles(platelets, min.area=3) selectedPlatelets
This step can be done iteratively, with the help of the function add.contours. If called with the parameter mode set to particles, then it will automatically generate a Frames object, with the contours of all particles drawn around the objects that passed the segmentation (and filtering) step (Fig.\@ref(fig:checkSelection)).
paintedPlatelets <- add.contours(raw.frames=MesenteriumSubset, binary.frames=preprocessedPlatelets, mode="particles") inspect.Frames(paintedPlatelets, nframes=9, display.method="raster")
To connect the particles from one frame to the other, we perform first the detection of particles on all images. Only in a successive phase, we establish the links between the so identified objects. This topic will be covered in detail in the following section.
Particle tracking {#tracking}
To establish the connections between particles, the function to be called is link.particles. The algorithm used to perform the tracking itself is an improved version of the original implementation of Sbalzarini and Koumotsakos [@Sbalzarini2005]. To summarize the method, it is a fast and efficient self-initializing feature point tracking algorithm (using the centroids of the objects as reference) [@Chenouard2014]. The initial version is based on a particle matching algorithm, approached via a graph theory technique. It allows for appearances/disappearances of particles from the field of view, also temporarily as it happens in case of occlusions and objects leaving the plane of focus.
Our implementation adds to the existing one by redefining the cost function used in the optimization phase of the link assignment. It namely adds two terms, such as intensity variation and area variation, and mostly important implements a function to penalize the movements that are either perpendicular or backwards with respect to the oriented flow of cells. Small unwanted movements, which may be present even after the registration phase, are handled with two jitter terms in a defined penalty function. Multiplicative factors can further influence the penalties given to each term.
In its default value, the penalty function is created via the penaltyFunctionGenerator. The user can exploit the parameter values in it to create a custom version of it, to match the particular needs stemming from the nature of the available data and phenomenon under inspection.
defaultPenalty <- penaltyFunctionGenerator() print(defaultPenalty)
As mentioned above, to perform the linking of the particles, we use link.particles. Fundamental parameters are L and R, named as in the original implementation. L is the maximum displacement in pixels that a particle is expected to have in two consecutive frames, and R is the value for the link range, i.e. the number of future frames to be considered for the linking (typically assumes values between 1 - when no occlusions are known to happen - and 3). An extended explanation of the parameters is in the documentation of the package.
linkedPlatelets <- link.particles(platelets, L=26, R=3, epsilon1=0, epsilon2=0, lambda1=1, lambda2=0, penaltyFunction=penaltyFunctionGenerator(), include.area=FALSE) linkedPlatelets
As it can be seen, linkedPlatelets is an object of the LinkedParticleSet class, which is a subclass of the ParticleSet class.
After inspecting the trajectories (see Section \@ref(trajanal)) it might be possible to filter a LinkedParticleSet class object and subsequently reperform the linking on its updated version (e.g. some detected particles were found to be noise, and thus removed with select.particles).
r Biocpkg("flowcatchR") provides functions to export and import the identified particles, in order to offer an additional entry point for tracking and analyzing the trajectories (if particles were detected with other routines) and also to store separately the information per each frame about the objects that were primarily identified.
An example is provided in the lines below, with the functions export.particles and read.particles :
# export to csv format export.particles(platelets, dir="/path/to/export/folder/exportParticleSet/") # re-import the previously exported, in this case importedPlatelets <- read.particles(particle.files="/path/to/export/folder/exportParticleSet/")
Trajectory analysis {#trajanal}
It is possible to extract the trajectories with the correspondent trajectories function:
trajPlatelets <- trajectories(linkedPlatelets) trajPlatelets
A TrajectorySet object is returned in this case. It consists of a two level list for each trajectory, reporting the trajectory as a data.frame, the number of points npoints (often coinciding with the number of nframes, when no gaps ngaps are present) and its ID. A keep flag is used for subsequent user evaluation purposes.
Before proceeding with the actual analysis of the trajectories, it is recommended to evaluate them by visual inspection. r Biocpkg("flowcatchR") provides two complementary methods to do this, either plotting them (plot or plot2D.TrajectorySet) or drawing the contours of the points on the original image (add.contours).
By plotting all trajectories in a 2D+time representation, it's possible to have an overview of all trajectories.
The following command gives an interactive 3D (2D+time) view of all trajectories (Fig.\@ref(fig:cubeTrajs)):
plot(trajPlatelets, MesenteriumSubset)
The plot2D.TrajectorySet focuses on additional information and a different "point of view", but can just display a two dimensional projection of the identified trajectories (Fig.\@ref(fig:overviewTrajs)).
plot2D.TrajectorySet(trajPlatelets, MesenteriumSubset)
To have more insights on single trajectories, or on a subset of them, add.contours offers an additional mode called trajectories. Particles are drawn on the raw images with colours corresponding to the trajectory IDs. add.contours plots by default all trajectories, but the user can supply a vector of the IDs of interest to override this behaviour.
paintedTrajectories <- add.contours(raw.frames=MesenteriumSubset, binary.frames=preprocessedPlatelets, trajectoryset=trajPlatelets, mode="trajectories") paintedTrajectories
As with any other Frames object, it is recommended to take a peek at it via the inspect.Frames function (Fig.\@ref(fig:inspectTrajs)):
inspect.Frames(paintedTrajectories,nframes=9,display.method="raster")
To allow for a thorough evaluation of the single trajectories, export.Frames is a valid helper, as it creates single images corresponding to each frame in the Frames object. We first extract for example trajectory 11 (Fig.\@ref(fig:traj11)) with the following command:
traj11 <- add.contours(raw.frames=MesenteriumSubset, binary.frames=preprocessedPlatelets, trajectoryset=trajPlatelets, mode="trajectories", trajIDs=11) traj11 inspect.Frames(traj11, nframes=9, display.method="raster")
The data for trajectory 11 in the TrajectorySet object can be printed to the terminal:
trajPlatelets[[11]]
After that, it can also be exported with the following command (the dir parameter must be changed accordingly):
export.Frames(traj11, dir=tempdir(), nameStub="vignetteTest_traj11", createGif=TRUE, removeAfterCreatingGif=FALSE)
export.Frames offers multiple ways to export - animated gif (if ImageMagick is available and installed on the system) or multiple jpeg/png images.
Of course the user might want to singularly evaluate each trajectory that was identified, and this can be done by looping over the trajectory IDs.
evaluatedTrajectories <- trajPlatelets for(i in 1:length(trajPlatelets)) { paintedTraj <- add.contours(raw.frames=MesenteriumSubset, binary.frames=preprocessedPlatelets, trajectoryset=trajPlatelets, mode="trajectories", col="yellow", trajIDs=i) export.Frames(paintedTraj, nameStub=paste0("vignetteTest_evaluation_traj_oneByOne_",i), createGif=TRUE, removeAfterCreatingGif=TRUE) ### uncomment the code below to perform the interactive evaluation of the single trajectories # cat("Should I keep this trajectory? --- 0: NO, 1:YES --- no other values allowed") # userInput <- readLines(n=1L) # ## if neither 0 nor 1, do not update # ## otherwise, this becomes the value for the field keep in the new TrajectoryList # evaluatedTrajectories@.Data[[i]]$keep <- as.logical(as.numeric(userInput)) }
Always using trajectory 11 as example, we would set evaluatedTrajectories[[11]]$keep to TRUE, since the trajectory was correctly identified, as we just checked.
Once all trajectories have been selected, we can proceed to calculate (a set of) kinematic parameters, for a single or all trajectories in a TrajectorySet object. The function kinematics returns the desired output, respectively a KinematicsFeatures object, a KinematicsFeaturesSet, a single value or a vector (or list, if not coercible to vector) of these single values (one parameter for each trajectory).
allKinematicFeats.allPlatelets <- kinematics(trajPlatelets, trajectoryIDs=NULL, # will select all trajectory IDs acquisitionFrequency=30, # value in milliseconds scala=50, # 1 pixel is equivalent to ... micrometer feature=NULL) # all kinematic features available
As it is reported from the output, the function raises a warning for trajectories which have 3 or less points, as they might be spurious detections. In such cases, no kinematic features are computed.
allKinematicFeats.allPlatelets
A summary for the returned object (in this case a KinematicsFeaturesSet) shows some of the computed parameters.
By default, information about the first trajectory is reported in brief, and the same parameters are evaluated on average across the selected trajectories. The true values can be accessed in this case for each trajectory by the subset operator for lists ([[]]), followed by the name of the kinematic feature (e.g., $totalDistance).
A list of all available parameters is printed with an error message if the user specifies an incorrect name, such as here:
allKinematicFeats.allPlatelets <- kinematics(trajPlatelets, feature="?")
When asking for a single parameter, the value returned is structured in a vector, such that it is straightforward to proceed with further analysis, e.g. by plotting the distribution of the curvilinear velocities (Fig.\@ref(fig:allVelos)).
allVelocities <- kinematics(trajPlatelets, feature="curvilinearVelocity") hist(allVelocities, breaks=10, probability=TRUE, col="cadetblue", xlab="Curvilinear Velocities Distribution", main="Trajectory Analysis: Curvilinear Velocities") lines(density(allVelocities, na.rm=TRUE), col="steelblue", lwd=2)
For this code chunk, we are suppressing the warning messages, as they would be exactly the same as in the former where all features were computed for each trajectory.
Interactive tools for a user-friendly workflow solution
To enhance the Frames objects and deliver an immediate feedback to the user, the function snap leverages on both the raw and binary Frames, as well as on the corresponding ParticleSet and TrajectorySet objects. It integrates the information available in all the mentioned objects, and it plots a modified instance of the Frames object, identifying the particles closest to the mouse click, and showing additional trajectory-related information, such as the trajectory ID and the instantaneous velocity of the cell. The function can be called as in the command below:
snap(MesenteriumSubset,preprocessedPlatelets, platelets,trajPlatelets, frameID = 1,showVelocity = T)
An example output for the snap is shown below in Fig.\@ref(fig:snapExample), where the information (trajectory ID, as well as the velocity in the selected frame) is shown in yellow to offer a good contrast with the fluorescent image.
display(readImage(system.file("extdata/snapExp.jpg",package="flowcatchR")), method = "raster")
The shinyFlow Shiny Application
Additionally, since Version 1.0.3, r Biocpkg("flowcatchR") delivers shinyFlow, a Shiny Web Application ([@Shiny2013]), which is built on the backbone of the analysis presented in this vignette, and is portable across all main operating systems. The user is thus invited to explore datasets and parameters with immediate reactive feedback, that can enable better understanding of the effects of single steps and changes in the workflow.
To launch the Shiny App, use the command below to open an external window either in the browser or in the IDE (such as RStudio):
shinyFlow()
r Biocpkg("flowcatchR") in Jupyter notebooks
A further integration are a number of Jupyter/IPython notebooks ([@Perez2007]), as a way to provide easy reproducibility as well as communication of results, by combining plain text, commands and output in single documents. The R kernel used on the back-end was developed by Thomas Kluyver (https://github.com/takluyver/IRkernel), and instructions for the installation are available at the Github repository website. The notebooks are available in the installation folder of the package r Biocpkg("flowcatchR"), which can be found with the command below.
list.files(system.file("extdata",package = "flowcatchR"),pattern = "*.ipynb")
The notebooks are provided as template for further steps in the analysis. The user is invited to set up the IPython notebook framework as explained on the official website for the project (http://ipython.org/notebook.html). As of February, 3rd 2015, the current way to obtain the Jupyter environment is via the 3.0.dev version, available via Github (https://github.com/ipython/ipython). The notebooks can be opened and edited by navigating to their location while the IPython notebook server is running; use the following command in the shell to launch it:
$ ipython notebook
Alternatively, these documents can be viewed with the nbviewer tool, available at http://nbviewer.ipython.org/.
r Biocpkg("flowcatchR") in Docker containers
r Biocpkg("flowcatchR") is now (as of September 2015) available also in Docker images that are the components of the dockerflow proposal (https://github.com/federicomarini/dockerflow). This includes:
flowstudio- https://github.com/federicomarini/flowstudio, a command-line/IDE interface to RStudio wherer Biocpkg("flowcatchR")and its dependencies are preinstalledflowshiny- https://github.com/federicomarini/flowshiny a Shiny Server running theshinyFlowweb applicationflowjupy- https://github.com/federicomarini/flowjupy, a Jupyter Notebook interface
These three images can be run simultaneously, provided the system where the containers are running supports the docker-compose tool. For more information on how to install the single components, please refer to their repositories.
Supplementary information {#supplinfo}
For more information on the method adapted for tracking cells, see Sbalzarini and Koumotsakos (2005) [@Sbalzarini2005].
For additional details regarding the functions of r Biocpkg("flowcatchR"), please consult the documentation or write an email to marinif@uni-mainz.de.
Due to space limitations, the complete dataset for the acquired frames used in this vignette is not included as part of the r Biocpkg("flowcatchR") package.
If you would like to get access to it, you can write an email to marinif@uni-mainz.de.
Acknowledgements
This package was developed at the Institute of Medical Biostatistics, Epidemiology and Informatics at the University Medical Center, Mainz (Germany), with the financial support provided by the TRP-A15 Translational Research Project grant.
r Biocpkg("flowcatchR") incorporates suggestions and feedback from the wet-lab biology units operating at the Center for Thrombosis and Hemostasis (CTH), in particular Sven Jäckel and Kerstin Jurk. Sven Jäckel also provided us with the sample acquisition which is available in this vignette.
We would like to thank the members of the Biostatistics division for valuable discussions, and additionally Isabella Zwiener for contributing to the first ideas on the project.
Session info {.unnumbered}
This vignette was generated using the following package versions:
sessionInfo()
References {.unnumbered}
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