Gates/filters in Flow Cytometry Data Visualization
abstract
The flowViz package provides tools for visualization of flow cytometry data. This document describes the support for visualizing gates (a.k.a. filters).
Introduction
Tools to read in and otherwise manipulate flow cytometry data are implemented in the flowCore package. The flowViz package provides visualization support for such data. In this document we give examples dealing with gated or filtered data. Please consult the online documentation for more details on the high-level visualization functions used here.
Filters and filter results
The flowCore package defines the concepts of
filters and filterResults. Filters are
abstract entities defined in terms of markers that are measured on the
flow instrument as different channels, whereas a filter result is the
result of applying a filter to one or more flowFrames (data
objects representing individual FCM experiments). Some filters are data
driven, while some are not. We will later see how this distinction has
an impact on their plotting. All abstractions of filters or gates
inherit from class filter, whereas objects generated as the
result of applying a filter inherit from class
filterResult.
Visualization
Before we discuss how to visualize gates in flowViz,
we need to point out that this may only be reasonable for certain types
of the many possible plots, namely one-dimensional density plots and
two-dimensional scatter plots. Over time we might add gate-plotting
support for other plot types as well. There are two principal ways to
add gates to a flow cytometry plot; either we render the outlines of the
gate region (for both one and two-dimensional plots), or we highlight
the points within a gate region by distinctive color, glyphs, or point
size (this applies for two-dimensional plots only). It only makes sense
to visualize the boundaries of a filter if it has a (one or two
dimensional) geometric representation. This is true for rectangle,
ellipsoid and polygon gates, which are all frequently used. It is also
true for some data driven gates, e.g. norm2Filter gates,
which have a (data dependent) spherical representation. Also, it makes
sense to draw gate boundaries only when plotting (some of) the channels
that define the gate.
Visualizing filterResults is more general. Specifically,
the result of applying a filter is usually a logical (TRUE
or FALSE) vector for each cell, or more generally, a
factor (as long as we restrict ourselves to non-fuzzy
filters). This can be used as a grouping variable within a display, also
when plotting channels other than those defining the gate.
All data-driven filters depend on the filterResult to be
computed in order to plot them. The user doesn’t have to worry about
this fact, as the software will implicitly compute these objects if
necessary. However, realizing filters and creating
filterResult is often computationally intense and
time-consuming, and in many cases makes sense to explicitly create the
filterResult once and pass it on to the plotting functions
instead of the input filter. In the course of this manual,
filter objects and filterResults may be used
interchangeably, unless stated otherwise.
Example Data
We use the GvHD data set to provide some examples. It
come as a serialized flowSet with the
flowViz package and the interested user is referred to
its documentation for details. For the purpose of this demonstration it
is sufficient to know that the phenoData slot of the
GvHD set contains several factor variables,
Patient and Visit two of the most descriptive
ones. In general, all flowSets contain an implicit
name variable which is is used as the default conditioning
variable in all of flowViz’s high-level plotting
functions.
## Patient Visit Days Grade name
## s5a01 5 1 -6 3 s5a01
## s5a02 5 2 0 3 s5a02
## s5a03 5 3 6 3 s5a03
## s5a04 5 4 12 3 s5a04
## s5a05 5 5 19 3 s5a05
## s5a06 5 6 26 3 s5a06The set is quite large and reducing it to a reasonable subset will speed up things for our interactive demonstration purpose. Due to various constrains (data size, complexity of computations, limitations in the grid software underlying the lattice and flowViz packages), rendering plots is usually not instantaneous. It usually takes a little bit of time to output complex panel layouts. When producing postscript output, the user should be aware that file size may become an issue, and we will address solutions for this problem at the end of this document.
The lattice package offers inline subsetting
capabilities for all high level plotting functions though the
subset argument, and this functionality (like most of the
other typical lattice concepts) is also available for
all derived plotting methods in flowCore. The general
idea here is that all symbols defined in either the formula or one of
the special arguments like subset are evaluated in the
context of the flowFrame's phenoData data
frame or the raw data matrix. This is a slight extension of the
fundamental lattice idea necessitated by the fact that
raw data and annotation data are stored separately in a
flowSet.
Inline subsetting is useful to change plots on the fly, or to play
around with various panel arrangements. However, we still pass the whole
GvHD object down to the plotting function, potentially
increasing memory usage and decreasing performance due to unnecessary
heavy copying operations. Since we only want to use the subset for
patient 6 in the following examples, it makes sense to directly subset
the flowSet.
We also want to transform some of the fluorescence channels to an
adequate log-like scale. A good choice is the asinh
function which can deal with negative values.
For details on this step, please see the documentation of the
transformList and \%on\% functions in the
flowCore package.
Filters in scatter plots
Trellis scatter plots are created using xyplot methods.
The xyplot method for flowSet objects supports
filters through the filter argument. As mentioned before,
its value can either be an object inheriting from class
filter or a filterResult (a
filterResultList of multiple filterResults for
flowSets).
The key concepts here are that
filtersandfilterResultscan be used interchangeably. ProvidingfilterResultsdirectly may increase performance for data-driven filters.visualization of
filtersdepends on the type of rendering. For example, withsmooth=TRUE, filters are visualized geometrically, which makes sense only under certain circumstances (e.g. display axes matching filter parameters, thefilterclass has a geometric represention). For scatter plots of individual dots for all events (smooth=FALSE), filters are visualized through grouping and/or geometric filter outlines; the former makes sense more generally, as display variables need not match filter parameters. Grouping has the drawback of overplotting. The effect of overplotting can be reduced somewhat using transparency, but scalability issues remain. We may try dealing with this at some point if it becomes enough of a hassle.the software will check for matching parameters and available visualization representations as much as possible, yet finally it is up to the user to construct reasonable calls to the plotting functions.
Simple Geometric Filter Types
Visualization of most of the typical FCM filter types is straight
forward and doesn’t require the computation of
filterResult. All parameters (e.g. min and max values in a
recangular gate) are unambigously defined in the filter
object. We will start with a simple rectangleGate in the
FSC-H and SSC-H dimensions.
As default for smoothed scatter plots, the gate boundaries are drawn.
Orientation of the gate will be handled by the plotting function and the
user doesn’t have to worry about the order of arguments when defining
the filter. The software also decides on a reasonable
two-dimensional geometric representation of more complex filters. E.g.,
we can add a third dimension to the rectangleGate and still
achive the same visualization in the FSC-H and
SSC-H dimensions.
rgate2 <- rgate * rectangleGate("FL1-H"=c(2, 4))
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=rgate2)
Most of the customization options defined in the lattice package will also work here. A more detailed discussion about the filter-specific graphical settings will follow in one of the later sections.
For the non-smoothed rendering (i.e., all events are plotted as individual points).
Sometime non-smoothed plots can be slow for large number of events. We provide hexbin version of xyplot for faster rendering.
Additionally, We can add statistics of gated population along with
the filter to the plot using the stat
argument.pos and abs(whether the position is
absolute or relative to filter boundary ) are used to control the label
position.
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=rgate,
smooth=FALSE, stat=TRUE,pos=0.5,abs=TRUE)
Sometime it is necessary to display multipe filters/gates in one panel to represent multiple sub-populations gated from the same parent populatuion.
recGate1<-rectangleGate("FL4-H"=c(3.3,5.3),"FL2-H"=c(2.5,5))
recGate2<-rectangleGate("FL4-H"=c(4,6),"FL2-H"=c(6,8))
filters1<-filters(list(recGate1,recGate2))
xyplot(`FL2-H` ~ `FL4-H`
,data=GvHD[[1]]
,filter=filters1
,stat=TRUE
,margin=FALSE
) 
The constraint for a valid two-dimensional representation doesn’t
apply any more for this type of rendering. Since each event is
represented by a single point on the plot, we can visualize arbitrarily
complex filters using different colors or point glyphs for
the different sub-populations. However this implies that we need to
evaluate each filter, i.e., we need to figure out which of the events
are in and which are outside of the filter. We will see in a minute how
we can optimize these operations. Going back to our three-dimensional
rectangle, we notice that not all points within the rectangle are also
color red, because the additional third dimension further reduced the
selection of positive events in the FSC-H and
SSC-H dimensions.
%
Overplotting is a potential problem for this representation. As a matter of fact, it is problematic for all visualization approaches of high-volume FCM data that try to display individual events rather than some form of summary statistic like density estimates. Partial transparency can alliviate some of these shortcomings but this approach does not scale well and has certain technical limitations on graphic devices that don’t support transparency. We will see in one of the following sections how to enable partial transparency in scatter plots.
Data-Driven Filters
Data-driven filters don’t have a natural geometric representation a
priori; they are data-driven. Once all parameters are estimated, we can
usually derive such a representation from the filterResult.
There is only a small subet of filter classes for which
this is not directly possible (kmeansFilter,
timeFilter), although one might be able to fall back to
approximations like convex hulls or similar. So far,
flowViz has nor support for plotting gate outlines of
these filter types, and they are silently ignored when passed on as
argument filter to any of the high-level plotting
functions. As shown in the previous example, the absence of a
two-dimensional spherical representation only poses a problem when
trying to plot filter boundaries, the non-smooth representation of
individual events is available for virtually all filter
types.
In the following example, we first compute the
filterResults of a norm2Filter in
FSC-H and SSC-H for each frame in our
GvHD flowSet and plot their geometric elliptic
representation.
n2Filter <- norm2Filter("SSC-H", "FSC-H", scale=2, filterId="Lymphocytes")
n2Filter.results <- filter(GvHD, n2Filter)
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=n2Filter.results)
%
There are data-driven filter types that may result in more than just
one sub-population. curv1Filters and
curv2Filters are a prominent example. In the next code
chunk we use a curv2Filter to identify high-density areas
in the FSC-H and FL4-H projections of the
data.
library(flowStats)
c2f <- curv2Filter("FSC-H", "FL4-H", bwFac=1.8)
c2f.results <- filter(GvHD, c2f)
xyplot(`FL4-H` ~ `FSC-H` | Visit, data=GvHD, filter=c2f.results)
%
This is a good example for a case where passing the
filterResult instead of the filter helps to
optimize computation time. Depending on the hardware it can take quite a
while to complete the extensive computations necessary for the
identification of siginficant high-density areas in two dimensions.
Imagine you want to make slight changes to your plot (and producing good
graphical output is almost always an iterative approach); having to
recompute the filterResult on each iteration would be
very time-cosuming and annoying at best.
Filters in one-dimensional density plots
The lattice package provides the high-level
densityplot function to draw one-dimensional Kernel density
estimates of univariate data. Density estimates are a generalization of
the well-known histograms; instead of drawing boxes of relative or
absolute frequencies of binned observations, a continous relative
density is displayed, usually beautified by applying a smoother function
with an appropriate bandwidth. The densityplot methods in
the flowViz package assume an implicit conditioning
variable (the measurement channel or channels) and display the density
estimates of all frames for one channel as a stacked layout. This has
proven to be a useful visualization, since the direct comparison of
univariate channel distributions is of great interest in many FCM
application, however the typically large number of samples makes
superimposing in a single display impratical. See the documention of
densityplot for more details.
In one-dimensional density plots it only makes sense to plot filter
boundaries. The densities are basically a summary of the distribution of
events for a particular channel, and there is no real notion of
individual events any more. Similar to the xyplot methods,
we can pass filters or filterResults to the
function as optional argument filter. We decided to
indicate gate boundaries by different shading of the the respective
integrals of the density regions rather than simply adding vertical
lines. These tend to be distracting in the stacked layout or are often
partly masked by overplotting of neighbouring density areas.
The situation gets slightly more complex when we are conditioning on
multiple FCM channels. In this case, filter has to be a list of equal
length as the number of channels that are supposed to be displayed
(i.e., the number of panels). Each list item may contain one of the
familiar objects of class filter,
filterResult, filterResultList, or
NULL in case no filter should be plotted at all for a given
panel.
densityplot(~ ., GvHD, channels=c("FSC-H", "SSC-H", "FL1-H"),
filter=list(curv1Filter("FSC-H"), NULL, rgate2))
%
Note that by default the scale of the x axis has been adjusted for
each panel. This is contrary to the default settings in the
lattice package and can be reversed using appropriate
settings in in the scales argument.
Plotting parameters
Lattice graphics are a great tool to easily create informative and consise data visualization with a minimal amount of code. Most of its default graphical parameters are well thought through. However, there is also a wealth of customization available, and we refer readers to the package’s documentation as well as Deepayan Sarkar’s excellent book “Lattice: Multivariate Data Visualization with R” for details. With respect to flowViz, it should suffice to mention that customization follows the exact same principles defined in the lattice package. As a matter of fact, most customization actually happens at the level of the underlying lattice software. The facts to mention are:
There are session-wide global defaults that can be queried and set using the
flowViz.par.getandflowViz.par.setfunctions. These are extensions to thetrellis.par.getandtrellis.par.setfunctions in the lattice package, and work in exactly the same way. All graphical parameters that are not defined in flowViz are directly passed on to lattice.Parameters can also be set for a single function call using the
par.settingsargument. These setting take precedence over global settings.Parameters are split up into logical categories and have to be provided as named lists or lists of lists. The categories directly relevant for filter plotting are
gate,gate.density, andgate.text, the basic flowViz settings are controlled by theflow.symbolcategory. See the documentation forflowViz.par.setfor a complete list of available parameters. All additional graphical parameters (likecex,pchandcol) known from the lattice high-level plotting functions are also still available.
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=rgate,
par.settings=list(gate=list(fill="black", alpha=0.2)))
%
We could have achieved the same customization by changing the session defaults:
flowViz.par.set(gate=list(fill="black", alpha=0.2))
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=rgate)Depending on the rendering, the graphical parameters may have
slightly different effects. The col parameters for instance
sets the line color for filter boundaries and the point color for
non-smooth scatter plots (and also the outline if
outline=TRUE). In the following code sample we try to make
use of partial transparency to address the problem of overplotting.
Dense regions of the plot with many overplotted points will apprear
darker. Although this is better than using opaque colors, lots of the
underlying structure could still be hidden and we strongly emphasize the
advantages of smoothed scatter plots for vizualization of FCM data.
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=rgate,
smooth=FALSE,
par.settings=list(gate=list(col="orange", alpha=0.04,
pch=20, cex=0.7),
flow.symbol=list(alpha=0.04, pch=20, cex=0.7)))
For multiple population filters, R ordinary recycling rules apply,
and we can spice up out plot of the curv2Filter results by
using a different color for each sub-population.
xyplot(`FL4-H` ~ `FSC-H` | Visit, data=GvHD, filter=c2f.results,
par.settings=list(gate=list(fill=rainbow(10), alpha=0.5, col="transparent")))
Sometimes it helps to add population names to a plot.
flowCore provides default names for each
filter and their associated results, but the user is free
to pass their own custom names. The interface is very simple: argument
names either takes a logical scalar (default names are used
if TRUE) or a character vector. Again, recycing rules apply
when there are multiple sub-populations (unless default names are uses
in which case the software provides a reasonable choice).
xyplot(`SSC-H` ~ `FSC-H` | Visit, data=GvHD, filter=n2Filter.results,
names=TRUE,
par.settings=list(gate=list(fill="black", alpha=0.2,
col="transparent"),
gate.text=list(col="darkred", alpha=0.7, cex=0.6)))
Restrictions on the formula interface
We mentioned before that all elements of the formulae used in
flowViz are evaluated in the context of either the raw
data matrix or the phenoData slot. This implies that
formula components can themselves be valid R expressions including
function calls. To a certain extend this is true, and the user might be
able to produce reasonable graphical output by evaluating expressions on
existing data or annotation objects, however we strongly discourage this
use. The software makes certain assumptions on the relationship between
gate definitions and data, the most prominent one being that both are on
the same scale. The use of expressions in flowViz
potentially changes the scale of the raw data, in which case the gate
representation doesn’t make much sense anymore. Furthermore, FCM data is
naturally censored (by the available measurement range of the
instrument) and we try to protect the user from irritating visual
artifacts caused by the piling up of events on the margins of the data
range. This is most notable in the one-dimensional densityplots, where
densities are only computed within the data range, and margin events are
added as vertical bars. Similarily, in the two-dimensional smoothed
scatter plots, we display margin events as ticks around the actual data
display. Again, changing the scale of the data would potentially
invalidate many of the necessary computations.
In summary, lattice encourages the use of expressions in the formula interface and for the sake of customizability we didn’t want to exclude this feature completely in the flowViz methods. However, the tool has to be used with great care, particularly when plotting gates.
