The brainloc package serves to describe a location on a brain surface mesh that is in MNI305 space, like the surfaces of the fsaverage standard brain templates used by FreeSurfer. Typical use cases of this package in the field of computational neuroimaging include:
Statistical results are often presented as significant clusters of activation on a brain surface mesh (sets of connected vertices). Typical use cases for working with clusters are:
This vignette describes how to perform these tasks with the brainloc package.
You will need a directory with the brain templates you want to use, typically these are the fsaverage subjects that come with the FreeSurfer neuroimaging software suite. There are 2 ways to get them:
When FreeSurfer is installed and configured properly on your system,
there is nothing you need to do. In that case, the environment variable
SUBJECTS_DIR points at the subjects directory
under the installation directory (FREESURFER_HOME), and it
will be used to find the templates by the get_subjects_dir
function. You can also set SUBJECTS_DIR to your custom
template directory, of course, and that will be used instead.
If you cannot or do not want to set environment variables, you can
set the option brainloc.subjects_dir in R to any directory
that contains the expected directory structure like this:
options("brainloc.subjects_dir"="~/my_fs_home/subjects/").
This would mean that ~/my_fs_home/subjects/ exists on your
system and holds the directories of the template subjects. We assume
that you have the fsaverage subject in there. Setting this
option takes precedence over any environment variables.
This requires that you have an internet connection and accept the FreeSurfer software license. See the code in the first example of this vignette below, which downloads the templates. The templates will be downloaded only if they cannot be found, and downloaded ones will be found on the next call to the function, of course.
Let’s say we have a coordinate in MNI305 surface space and want to
find the closest vertex. We first load brainloc and create
a brainparc object, which internally is a named list
holding the surfaces (the left and right hemisphere meshes) and the
surface parcellations (according to some brain atlas) for these meshes.
The parcellations assign to each vertex of a mesh a single region.
One can construct a brainparc manually from arbitrary loaded meshes
and parcellations using the brainparc function, but here we
use the function brainparc_fs, which is more convenient if
you want to read it from files in a SUBJECTS_DIR of
recon-all output data. We create a brainparc for the
fsaverage template:
library("brainloc");
# Searches for FreeSurfer SUBJECTS_DIR on machine and downloads if needed.
sjd = get_subjects_dir(allow_download = TRUE, accept_freesurfer_license = TRUE); ## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/lh.aparc.a2009s.annot' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/lh.aparc.a2009s.annot'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/rh.aparc.a2009s.annot' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/rh.aparc.a2009s.annot'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/lh.aparc.annot' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/lh.aparc.annot'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/rh.aparc.annot' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/rh.aparc.annot'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/lh.cortex.label' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/lh.cortex.label'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/label/rh.cortex.label' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/label/rh.cortex.label'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/mri/brain.mgz' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/mri/brain.mgz'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.white' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.white'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.white' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.white'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.pial' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.pial'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.pial' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.pial'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.inflated' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.inflated'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.inflated' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.inflated'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.curv' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.curv'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.curv' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.curv'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/ext/FreeSurferColorLUT.txt' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/ext/FreeSurferColorLUT.txt'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/LICENSE' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/LICENSE'
## Failed to download 7 of 17 file(s); retrying (attempt 1 of 2).
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.pial' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.pial'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.inflated' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.inflated'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.inflated' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.inflated'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/lh.curv' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/lh.curv'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/surf/rh.curv' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/surf/rh.curv'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/ext/FreeSurferColorLUT.txt' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/ext/FreeSurferColorLUT.txt'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage/LICENSE' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage/LICENSE'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage3/label/lh.cortex.label' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage3/label/lh.cortex.label'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage3/label/rh.cortex.label' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage3/label/rh.cortex.label'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage3/surf/lh.white' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage3/surf/lh.white'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage3/surf/rh.white' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage3/surf/rh.white'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/fsaverage3/LICENSE' from 'http://rcmd.org/projects/nitestdata/subjects_dir/fsaverage3/LICENSE'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/subject1/surf/lh.thickness.fwhm0.fsaverage3.mgz' from 'http://rcmd.org/projects/nitestdata/subjects_dir/subject1/surf/lh.thickness.fwhm0.fsaverage3.mgz'
## Download file to '/github/home/.local/share/R/brainloc/subjects_dir/subject1/surf/rh.thickness.fwhm0.fsaverage3.mgz' from 'http://rcmd.org/projects/nitestdata/subjects_dir/subject1/surf/rh.thickness.fwhm0.fsaverage3.mgz'By default, many functions in the brainloc package print
information to STDOUT, which is handy for creating command line clients
from the library. We do not want that here, so we disable it globally
here:
Note: One can also decide for each function that prints something,
they all have a silent parameter.
Let’s say we have some query coordinates in surface space and want to
find the closest vertex in the brainparc for each of the
coordinates. Here is how we can do that:
## [,1] [,2] [,3]
## [1,] 1.1 2.1 3.1
## [2,] 4.1 5.1 6.1
## [3,] 7.1 8.1 9.1## query_x query_y query_z lh_closest_vertex lh_distance rh_closest_vertex
## 1 1.1 2.1 3.1 126954 0.8923483 111013
## 2 4.1 5.1 6.1 69364 3.7896230 20707
## 3 7.1 8.1 9.1 39537 6.7494234 45778
## rh_distance both_closest_vertex both_distance both_hemi
## 1 0.4535498 111013 0.4535498 rh
## 2 2.9344436 20707 2.9344436 rh
## 3 6.2132350 45778 6.2132350 rhThis assumes that the query coordinates are in the surfaces space and uses Euclidean distance. It works for all subjects and meshes.
This assumes that you query vertex (or coordinate) is in MNI305
space. This is true for all FreeSurfer standard template subjects, like
fsaverage, fsaverage6, etc. Our
brainparc is for fsaverage, so we can use the
coordinates of its vertices to query.
query_vertices = c(10L, 145029L);
query_hemis = c("lh", "rh"); # vertex 10 on left hemi and 145029L on right hemi.
query_coords = get_surface_coords(bp, query_vertices, query_hemis);
query_coords## [,1] [,2] [,3]
## [1,] -26.305798 23.81276 -6.026234
## [2,] 8.849497 -35.22620 65.073280## $mni305
## [,1] [,2] [,3]
## [1,] -26.305798 23.81276 -6.026234
## [2,] 8.849497 -35.22620 65.073280
##
## $mni152
## [,1] [,2] [,3]
## [1,] -26.56283 25.01419 -4.704241
## [2,] 10.18691 -33.73528 66.281128
##
## $talairach
## [,1] [,2] [,3]
## [1,] -26.29720 24.03707 -5.160009
## [2,] 10.08504 -29.63502 62.541625Note: If you have the regfusionr package installed, have
a look at the method parameter of the
coord_MNI305_info function: you can use the more accurate
regfusionr method to transform from MNI305 to MNI152 then.
Open the docs with ?coord_MNI305_info to learn more.
We can easily find the regions a vertex is assigned to in all atlases of a brain parcellation:
query_vertices = c(10L, 145029L);
query_hemis = c("lh", "rh"); # vertex 10 on left hemi and 145029L on right hemi.
regions = vertex_regions(bp, query_vertices, query_hemis);
regions## vertex hemi atlas vertex_region
## 1 10 lh aparc lateralorbitofrontal
## 2 145029 rh aparc postcentralOne can also compute the distance of a vertex to all atlas regions. Several definitions for the distance of a vertex to a region are available, here we go with the defaults:
query_vertices = c(10L, 145029L);
query_hemis = c("lh", "rh"); # vertex 10 on left hemi and 145029L on right hemi.
region_dists = vertex_closest_regions(bp, query_vertices, query_hemis, num_regions_to_report=5L);
region_dists## vertex hemi linkage distance atlas vertex_region_direct vertex_region_nth
## 1 10 lh single euclidean aparc lateralorbitofrontal 1
## 2 10 lh single euclidean aparc lateralorbitofrontal 2
## 3 10 lh single euclidean aparc lateralorbitofrontal 3
## 4 10 lh single euclidean aparc lateralorbitofrontal 4
## 5 10 lh single euclidean aparc lateralorbitofrontal 5
## 6 145029 rh single euclidean aparc postcentral 1
## 7 145029 rh single euclidean aparc postcentral 2
## 8 145029 rh single euclidean aparc postcentral 3
## 9 145029 rh single euclidean aparc postcentral 4
## 10 145029 rh single euclidean aparc postcentral 5
## vertex_region_n_name vertex_region_n_distance vertex_region_n_point_x
## 1 lateralorbitofrontal 0.000000 -26.305798
## 2 insula 5.483304 -29.827978
## 3 parstriangularis 10.907174 -34.240818
## 4 parsorbitalis 14.363726 -39.584057
## 5 medialorbitofrontal 16.396578 -12.834730
## 6 postcentral 0.000000 8.849497
## 7 precentral 1.547366 7.996873
## 8 paracentral 4.240139 9.425453
## 9 precuneus 6.363814 12.051294
## 10 superiorparietal 8.489906 16.539742
## vertex_region_n_point_y vertex_region_n_point_z
## 1 23.81276 -6.026234
## 2 20.04161 -4.171691
## 3 30.83913 -3.450967
## 4 29.04067 -7.661278
## 5 20.36029 -14.712927
## 6 -35.22620 65.073280
## 7 -33.93639 65.134644
## 8 -39.40303 64.624718
## 9 -39.72830 68.232040
## 10 -37.11887 68.132111One can change the distance definition with the parameters
distance and linkage of the
vertex_closest_regions function. Open the docs with
?vertex_closest_regions to learn more.
A cluster is a set of vertices on a surface, and the statistical values that are assigned to the cluster’s vertices. Clusters are used in vertex-wise analyses to define activated brain regions (where the exact meaning of activated depends on the context). A clusters has a freeform label or name, but typically only consecutive numbers are used.
The data structure used to store clusters in brainloc is
called clusterinfo. The following two concepts are relevant
to understanding how a clusterinfo instance is typically
constructed:
cluster overlay is an integer vector that assigns to
each surface vertex a cluster number (zero is assigned to
background/non-cluster vertices).statistical map contains arbitrary values, one for
each surface vertex (a.k.a. per-vertex data). A thresholded map
only contains values for the cluster vertices, the values for all
non-cluster vertices are set to an arbitrary value (typically
0.0).A clusterinfo object can be constructed for a subject in
two ways:
cluster overlay and the
statistical map (thresholded or unthresholded), use the
clusterinfo function.statistical map, use the
clusterinfo_from_thresholded_overlay function instead.In the following example, we construct a clusterinfo
instance from a cluster overlay and the statistical map:
lh_tmap_file = system.file("extdata", "lh.tmap.mgh", package = "brainloc", mustWork = TRUE);
rh_tmap_file = system.file("extdata", "rh.tmap.mgh", package = "brainloc", mustWork = TRUE);
lh_overlay_file = system.file("extdata", "lh.cluster.overlayID.mgh", package = "brainloc", mustWork = TRUE);
rh_overlay_file = system.file("extdata", "rh.cluster.overlayID.mgh", package = "brainloc", mustWork = TRUE);
clinfo = clusterinfo(lh_overlay_file, rh_overlay_file, lh_tmap_file, rh_tmap_file, template_subject = "fsaverage", subjects_dir = sjd);
is.clusterinfo(clinfo);## [1] TRUEOne can extract the clusters from the `clusterinfo`` instance like this:
This returns a named list, where the keys are cluster names and the
values are integer vectors containing the vertices that belong the the
respective cluster. See ?get_clusters for more options,
like returning only the clusters for a specific hemisphere.
The clusterinfo object can now be used to compute
various information on the clusters. We will start by computing
information on the location of the clusters:
## Download file to '/github/home/.local/share/R/brainloc/talairach/talairach.nii' from 'http://www.talairach.org/talairach.nii'
## Download file to '/github/home/.local/share/R/brainloc/talairach/labels.txt' from 'http://www.talairach.org/labels.txt'## cluster hemi num_vertices extremum_value extremum_vertex mni152_r
## 1 lh_cluster_2 lh 15889 -3.612464 36395 -56.44855
## 2 lh_cluster_1 lh 1949 3.034767 124693 -38.24387
## mni152_a mni152_s talairach_r talairach_a talairach_s talairach_label_lvl1
## 1 -31.87322 40.38953 -55.88407 -29.02201 38.65962 Left Cerebrum
## 2 25.68162 -14.75147 -37.86143 24.26172 -13.62192 *
## talairach_label_lvl2 talairach_label_lvl3 talairach_label_lvl4
## 1 Parietal Lobe Inferior Parietal Lobule Gray Matter
## 2 * Inferior Frontal Gyrus *
## talairach_label_lvl5
## 1 Brodmann area 40
## 2 *
## talairach_label_full
## 1 Left Cerebrum.Parietal Lobe.Inferior Parietal Lobule.Gray Matter.Brodmann area 40
## 2 *.*.Inferior Frontal Gyrus.*.*
## atlas_region
## 1 supramarginal
## 2 lateralorbitofrontalNote that the clusterinfo object contains a brain
parcellation (a brainparc object, see at the top). We can
also compute the overlap of the cluster with its atlas regions:
## region num_shared_vertices percent_shared_vertices
## 3 postcentral 4880 30.713072
## 4 precentral 4224 26.584429
## 7 supramarginal 3963 24.941784
## 6 superiorparietal 1501 9.446787
## 1 caudalmiddlefrontal 609 3.832840
## 2 inferiorparietal 371 2.334949
## 5 rostralmiddlefrontal 341 2.146139
## 21 lateralorbitofrontal 1146 58.799384
## 31 parsorbitalis 629 32.272960
## 41 parstriangularis 115 5.900462
## 11 insula 59 3.027193
## cluster_percent_of_region hemi cluster atlas
## 3 51.265889 lh lh_cluster_2 aparc
## 4 39.329609 lh lh_cluster_2 aparc
## 7 46.081395 lh lh_cluster_2 aparc
## 6 14.355394 lh lh_cluster_2 aparc
## 1 16.300857 lh lh_cluster_2 aparc
## 2 4.713505 lh lh_cluster_2 aparc
## 5 4.707994 lh lh_cluster_2 aparc
## 21 27.363897 lh lh_cluster_1 aparc
## 31 65.794979 lh lh_cluster_1 aparc
## 41 5.620723 lh lh_cluster_1 aparc
## 11 1.128323 lh lh_cluster_1 aparcSometimes one wants to find all peaks of a cluster. A peak exists at vertices which have the most extreme value in their neighborhood. For a brain mesh, the neighborhood of a vertex is defined as all vertices which are reachable by one hop along the mesh edges.
## cluster hemi peak_vertex peak_value
## 1 lh_cluster_2 lh 17 -2.744687
## 2 lh_cluster_2 lh 48 -1.858908
## 3 lh_cluster_2 lh 167 -3.017634
## 4 lh_cluster_2 lh 188 -2.706193
## 5 lh_cluster_2 lh 368 -3.061095
## 6 lh_cluster_2 lh 844 -2.856204
## 7 lh_cluster_2 lh 1059 -2.536362
## 8 lh_cluster_2 lh 1443 -2.452701
## 9 lh_cluster_2 lh 1570 -2.675941
## 10 lh_cluster_2 lh 1818 -3.056978
## 11 lh_cluster_2 lh 2096 -2.821692
## 12 lh_cluster_2 lh 2633 -2.942444
## 13 lh_cluster_2 lh 2939 -3.173836
## 14 lh_cluster_2 lh 2946 -2.900167
## 15 lh_cluster_2 lh 3368 -1.801927
## 16 lh_cluster_2 lh 3382 -2.089746
## 17 lh_cluster_2 lh 3445 -2.607287
## 18 lh_cluster_2 lh 4006 -2.744771
## 19 lh_cluster_2 lh 4482 -2.015952
## 20 lh_cluster_2 lh 4507 -2.937274
## 21 lh_cluster_2 lh 4604 -2.673632
## 22 lh_cluster_2 lh 4609 -2.855095
## 23 lh_cluster_2 lh 5774 -2.092039
## 24 lh_cluster_2 lh 6137 -2.874391
## 25 lh_cluster_2 lh 6138 -2.841173
## 26 lh_cluster_2 lh 6140 -2.883987
## 27 lh_cluster_2 lh 6145 -2.785391
## 28 lh_cluster_2 lh 6446 -2.985426
## 29 lh_cluster_2 lh 7220 -2.988027
## 30 lh_cluster_2 lh 7227 -2.464265
## 31 lh_cluster_2 lh 7492 -2.424789
## 32 lh_cluster_2 lh 7504 -2.538386
## 33 lh_cluster_2 lh 7695 -3.172078
## 34 lh_cluster_2 lh 8081 -3.030712
## 35 lh_cluster_2 lh 8115 -2.020023
## 36 lh_cluster_2 lh 8125 -2.621741
## 37 lh_cluster_2 lh 8151 -1.715064
## 38 lh_cluster_2 lh 8733 -3.057757
## 39 lh_cluster_2 lh 8827 -2.437251
## 40 lh_cluster_2 lh 8834 -1.913942
## 41 lh_cluster_2 lh 8836 -2.157695
## 42 lh_cluster_2 lh 8854 -2.799692
## 43 lh_cluster_2 lh 8858 -2.493563
## 44 lh_cluster_2 lh 10358 -2.780647
## 45 lh_cluster_2 lh 10454 -2.474493
## 46 lh_cluster_2 lh 10619 -3.218110
## 47 lh_cluster_2 lh 10647 -1.899229
## 48 lh_cluster_2 lh 11048 -1.802100
## 49 lh_cluster_2 lh 11071 -2.285401
## 50 lh_cluster_2 lh 11123 -2.745003
## 51 lh_cluster_2 lh 11671 -2.953016
## 52 lh_cluster_2 lh 11731 -1.866850
## 53 lh_cluster_2 lh 11890 -2.089939
## 54 lh_cluster_2 lh 12287 -2.859982
## 55 lh_cluster_2 lh 13449 -1.874903
## 56 lh_cluster_2 lh 13528 -2.266294
## 57 lh_cluster_2 lh 13616 -2.872344
## 58 lh_cluster_2 lh 13656 -2.923451
## 59 lh_cluster_2 lh 14073 -2.930758
## 60 lh_cluster_2 lh 14124 -2.218930
## 61 lh_cluster_2 lh 14580 -3.094419
## 62 lh_cluster_2 lh 14588 -3.006916
## 63 lh_cluster_2 lh 15891 -2.470590
## 64 lh_cluster_2 lh 15893 -2.477159
## 65 lh_cluster_2 lh 16094 -2.643576
## 66 lh_cluster_2 lh 16330 -2.195119
## 67 lh_cluster_2 lh 16381 -3.135160
## 68 lh_cluster_2 lh 16386 -2.641017
## 69 lh_cluster_2 lh 16468 -2.387602
## 70 lh_cluster_2 lh 17688 -1.885616
## 71 lh_cluster_2 lh 17729 -3.053454
## 72 lh_cluster_2 lh 17731 -3.057509
## 73 lh_cluster_2 lh 17735 -3.044742
## 74 lh_cluster_2 lh 17739 -3.058966
## 75 lh_cluster_2 lh 17781 -1.703062
## 76 lh_cluster_2 lh 17798 -1.951260
## 77 lh_cluster_2 lh 17819 -1.723828
## 78 lh_cluster_2 lh 17877 -1.749732
## 79 lh_cluster_2 lh 17878 -1.769274
## 80 lh_cluster_2 lh 19085 -1.838858
## 81 lh_cluster_2 lh 19139 -2.318835
## 82 lh_cluster_2 lh 19150 -1.908982
## 83 lh_cluster_2 lh 19242 -3.534949
## 84 lh_cluster_2 lh 19250 -2.790674
## 85 lh_cluster_2 lh 19266 -2.932451
## 86 lh_cluster_2 lh 19267 -2.913095
## 87 lh_cluster_2 lh 19278 -2.867075
## 88 lh_cluster_2 lh 19317 -1.953748
## 89 lh_cluster_2 lh 19517 -2.446122
## 90 lh_cluster_2 lh 19583 -2.817948
## 91 lh_cluster_2 lh 19599 -2.159396
## 92 lh_cluster_2 lh 23052 -1.897364
## 93 lh_cluster_2 lh 23448 -1.892832
## 94 lh_cluster_2 lh 23552 -2.558031
## 95 lh_cluster_2 lh 23689 -1.806096
## 96 lh_cluster_2 lh 23719 -3.149762
## 97 lh_cluster_2 lh 23720 -3.107920
## 98 lh_cluster_2 lh 23725 -3.252490
## 99 lh_cluster_2 lh 23727 -3.067868
## 100 lh_cluster_2 lh 24488 -1.851189
## 101 lh_cluster_2 lh 24490 -1.823261
## 102 lh_cluster_2 lh 24504 -2.965343
## 103 lh_cluster_2 lh 24518 -2.093884
## 104 lh_cluster_2 lh 24777 -1.797602
## 105 lh_cluster_2 lh 24850 -2.212785
## 106 lh_cluster_2 lh 24853 -2.454756
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## 513 lh_cluster_2 lh 121179 -3.151238
## 514 lh_cluster_2 lh 121183 -3.215775
## 515 lh_cluster_2 lh 121235 -2.945282
## 516 lh_cluster_2 lh 121243 -2.884675
## 517 lh_cluster_2 lh 121250 -2.856719
## 518 lh_cluster_2 lh 121276 -1.781689
## 519 lh_cluster_2 lh 121310 -2.107559
## 520 lh_cluster_2 lh 121434 -1.746353
## 521 lh_cluster_2 lh 121441 -1.739218
## 522 lh_cluster_2 lh 121443 -1.713047
## 523 lh_cluster_2 lh 121449 -1.688209
## 524 lh_cluster_2 lh 123102 -1.981119
## 525 lh_cluster_2 lh 123178 -2.245620
## 526 lh_cluster_2 lh 123185 -2.294299
## 527 lh_cluster_2 lh 123316 -2.870781
## 528 lh_cluster_2 lh 123326 -3.123764
## 529 lh_cluster_2 lh 123331 -2.795111
## 530 lh_cluster_2 lh 123358 -2.925398
## 531 lh_cluster_2 lh 123362 -2.925673
## 532 lh_cluster_2 lh 123379 -2.851797
## 533 lh_cluster_2 lh 123426 -1.877161
## 534 lh_cluster_2 lh 123468 -2.076707
## 535 lh_cluster_2 lh 123743 -2.443603
## 536 lh_cluster_2 lh 123767 -2.732703
## 537 lh_cluster_2 lh 123785 -2.897136
## 538 lh_cluster_2 lh 123791 -2.872825
## 539 lh_cluster_2 lh 123808 -2.372777
## 540 lh_cluster_2 lh 125527 -1.814749
## 541 lh_cluster_2 lh 128669 -1.834998
## 542 lh_cluster_2 lh 128702 -2.308194
## 543 lh_cluster_2 lh 128740 -1.884908
## 544 lh_cluster_2 lh 128754 -2.332346
## 545 lh_cluster_2 lh 128974 -2.406472
## 546 lh_cluster_2 lh 129418 -2.699180
## 547 lh_cluster_2 lh 129425 -2.821688
## 548 lh_cluster_2 lh 129454 -2.747772
## 549 lh_cluster_2 lh 129460 -2.669875
## 550 lh_cluster_2 lh 129468 -2.778847
## 551 lh_cluster_2 lh 129981 -2.826816
## 552 lh_cluster_2 lh 129987 -2.769923
## 553 lh_cluster_2 lh 130923 -2.736296
## 554 lh_cluster_2 lh 130932 -2.824289
## 555 lh_cluster_2 lh 131061 -2.770342
## 556 lh_cluster_2 lh 131213 -1.856283
## 557 lh_cluster_2 lh 131232 -2.187672
## 558 lh_cluster_2 lh 131261 -1.713503
## 559 lh_cluster_2 lh 131862 -2.120339
## 560 lh_cluster_2 lh 132829 -2.178810
## 561 lh_cluster_2 lh 132903 -2.196242
## 562 lh_cluster_2 lh 132937 -2.962943
## 563 lh_cluster_2 lh 132947 -2.777386
## 564 lh_cluster_2 lh 132955 -2.883126
## 565 lh_cluster_2 lh 132957 -2.922586
## 566 lh_cluster_2 lh 132958 -3.126752
## 567 lh_cluster_2 lh 133048 -1.903787
## 568 lh_cluster_2 lh 133050 -1.896930
## 569 lh_cluster_2 lh 133059 -1.752161
## 570 lh_cluster_2 lh 133067 -1.670437
## 571 lh_cluster_2 lh 133266 -2.295657
## 572 lh_cluster_2 lh 133318 -2.077978
## 573 lh_cluster_2 lh 133353 -2.748770
## 574 lh_cluster_2 lh 133363 -2.778066
## 575 lh_cluster_2 lh 133388 -2.457157
## 576 lh_cluster_2 lh 133396 -2.388834
## 577 lh_cluster_2 lh 137766 -2.465033
## 578 lh_cluster_2 lh 137801 -1.855743
## 579 lh_cluster_2 lh 137853 -3.067700
## 580 lh_cluster_2 lh 137867 -2.974158
## 581 lh_cluster_2 lh 137869 -2.929076
## 582 lh_cluster_2 lh 137930 -1.877492
## 583 lh_cluster_2 lh 137942 -2.456002
## 584 lh_cluster_2 lh 137947 -2.299135
## 585 lh_cluster_2 lh 137964 -2.365802
## 586 lh_cluster_2 lh 138030 -2.259001
## 587 lh_cluster_2 lh 138050 -1.972327
## 588 lh_cluster_2 lh 138071 -1.909967
## 589 lh_cluster_2 lh 138078 -2.105213
## 590 lh_cluster_2 lh 138083 -1.941128
## 591 lh_cluster_2 lh 138090 -1.823496
## 592 lh_cluster_2 lh 138677 -2.668877
## 593 lh_cluster_2 lh 138680 -2.613598
## 594 lh_cluster_2 lh 138703 -2.625983
## 595 lh_cluster_2 lh 138712 -2.634187
## 596 lh_cluster_2 lh 139548 -2.139704
## 597 lh_cluster_2 lh 139571 -2.116695
## 598 lh_cluster_2 lh 139576 -2.215816
## 599 lh_cluster_2 lh 139680 -2.473578
## 600 lh_cluster_2 lh 139721 -3.084668
## 601 lh_cluster_2 lh 139723 -3.114415
## 602 lh_cluster_2 lh 139727 -3.065696
## 603 lh_cluster_2 lh 139738 -3.157661
## 604 lh_cluster_2 lh 140010 -1.873192
## 605 lh_cluster_2 lh 140022 -2.428306
## 606 lh_cluster_2 lh 140053 -2.360365
## 607 lh_cluster_2 lh 140081 -2.549805
## 608 lh_cluster_2 lh 140091 -2.649093
## 609 lh_cluster_2 lh 140095 -2.699740
## 610 lh_cluster_2 lh 140138 -2.578142
## 611 lh_cluster_2 lh 140152 -2.367616
## 612 lh_cluster_2 lh 144364 -1.877462
## 613 lh_cluster_2 lh 144392 -2.797173
## 614 lh_cluster_2 lh 144395 -2.834889
## 615 lh_cluster_2 lh 144409 -2.667339
## 616 lh_cluster_2 lh 144427 -1.869190
## 617 lh_cluster_2 lh 144442 -1.802146
## 618 lh_cluster_2 lh 144449 -2.543071
## 619 lh_cluster_2 lh 144451 -2.584459
## 620 lh_cluster_2 lh 144513 -1.768680
## 621 lh_cluster_2 lh 144526 -1.876261
## 622 lh_cluster_2 lh 144540 -1.740638
## 623 lh_cluster_2 lh 144651 -2.649130
## 624 lh_cluster_2 lh 144653 -2.673120
## 625 lh_cluster_2 lh 144678 -3.003641
## 626 lh_cluster_2 lh 144682 -3.030228
## 627 lh_cluster_2 lh 144684 -2.988099
## 628 lh_cluster_2 lh 144691 -3.092796
## 629 lh_cluster_2 lh 144697 -3.114132
## 630 lh_cluster_2 lh 144699 -3.025141
## 631 lh_cluster_2 lh 144705 -3.005927
## 632 lh_cluster_2 lh 144718 -3.012284
## 633 lh_cluster_2 lh 144733 -3.074111
## 634 lh_cluster_2 lh 144752 -3.081471
## 635 lh_cluster_2 lh 144771 -2.844472
## 636 lh_cluster_2 lh 144785 -2.831925
## 637 lh_cluster_2 lh 144807 -2.809669
## 638 lh_cluster_2 lh 144811 -2.759856
## 639 lh_cluster_2 lh 144917 -1.705038
## 640 lh_cluster_2 lh 144975 -1.935498
## 641 lh_cluster_2 lh 145018 -2.004066
## 642 lh_cluster_2 lh 145019 -1.960363
## 643 lh_cluster_2 lh 145074 -2.692695
## 644 lh_cluster_2 lh 145087 -2.799384
## 645 lh_cluster_2 lh 145090 -2.845287
## 646 lh_cluster_2 lh 145094 -2.894552
## 647 lh_cluster_2 lh 145188 -2.306647
## 648 lh_cluster_2 lh 145225 -1.855943
## 649 lh_cluster_2 lh 149824 -2.013308
## 650 lh_cluster_2 lh 150004 -1.877636
## 651 lh_cluster_2 lh 150009 -1.840493
## 652 lh_cluster_2 lh 150076 -2.418087
## 653 lh_cluster_2 lh 150112 -2.223941
## 654 lh_cluster_2 lh 150155 -3.594900
## 655 lh_cluster_2 lh 150161 -3.420627
## 656 lh_cluster_2 lh 150173 -2.852933
## 657 lh_cluster_2 lh 150260 -2.888609
## 658 lh_cluster_2 lh 150272 -2.915713
## 659 lh_cluster_2 lh 150275 -2.899922
## 660 lh_cluster_2 lh 150279 -2.885434
## 661 lh_cluster_2 lh 150301 -3.127359
## 662 lh_cluster_2 lh 150304 -3.053297
## 663 lh_cluster_2 lh 150310 -2.841323
## 664 lh_cluster_2 lh 150399 -2.940142
## 665 lh_cluster_2 lh 150421 -1.964484
## 666 lh_cluster_2 lh 150494 -3.081033
## 667 lh_cluster_2 lh 151055 -1.668231
## 668 lh_cluster_2 lh 151166 -2.402683
## 669 lh_cluster_2 lh 151228 -2.136434
## 670 lh_cluster_2 lh 151259 -2.220501
## 671 lh_cluster_2 lh 151311 -2.758924
## 672 lh_cluster_2 lh 151314 -2.776259
## 673 lh_cluster_2 lh 151413 -2.767905
## 674 lh_cluster_2 lh 155934 -2.029620
## 675 lh_cluster_1 lh 4821 2.963625
## 676 lh_cluster_1 lh 5425 1.997769
## 677 lh_cluster_1 lh 9117 2.490170
## 678 lh_cluster_1 lh 9841 2.063780
## 679 lh_cluster_1 lh 11366 2.144142
## 680 lh_cluster_1 lh 12627 2.008087
## 681 lh_cluster_1 lh 22057 2.075435
## 682 lh_cluster_1 lh 22060 1.963660
## 683 lh_cluster_1 lh 22065 1.781243
## 684 lh_cluster_1 lh 22066 1.780069
## 685 lh_cluster_1 lh 22067 1.807639
## 686 lh_cluster_1 lh 23990 1.910698
## 687 lh_cluster_1 lh 28193 1.899689
## 688 lh_cluster_1 lh 28211 2.097919
## 689 lh_cluster_1 lh 29200 2.083483
## 690 lh_cluster_1 lh 30848 2.565757
## 691 lh_cluster_1 lh 30851 1.985112
## 692 lh_cluster_1 lh 31010 1.854087
## 693 lh_cluster_1 lh 33265 2.018873
## 694 lh_cluster_1 lh 37564 1.845441
## 695 lh_cluster_1 lh 37582 2.767477
## 696 lh_cluster_1 lh 37594 2.417317
## 697 lh_cluster_1 lh 37601 2.274525
## 698 lh_cluster_1 lh 39777 2.397180
## 699 lh_cluster_1 lh 45741 2.006130
## 700 lh_cluster_1 lh 46226 2.439538
## 701 lh_cluster_1 lh 47540 2.152936
## 702 lh_cluster_1 lh 50933 1.855518
## 703 lh_cluster_1 lh 50938 2.877723
## 704 lh_cluster_1 lh 52757 2.076313
## 705 lh_cluster_1 lh 52781 1.998772
## 706 lh_cluster_1 lh 57017 1.965328
## 707 lh_cluster_1 lh 60568 1.815858
## 708 lh_cluster_1 lh 60916 2.006209
## 709 lh_cluster_1 lh 62357 2.056747
## 710 lh_cluster_1 lh 67749 1.996794
## 711 lh_cluster_1 lh 69551 2.376573
## 712 lh_cluster_1 lh 69558 2.451164
## 713 lh_cluster_1 lh 73522 2.716175
## 714 lh_cluster_1 lh 73524 2.764723
## 715 lh_cluster_1 lh 73528 2.547196
## 716 lh_cluster_1 lh 83668 1.821302
## 717 lh_cluster_1 lh 83740 2.489569
## 718 lh_cluster_1 lh 89147 2.045287
## 719 lh_cluster_1 lh 89203 2.460077
## 720 lh_cluster_1 lh 89220 1.969035
## 721 lh_cluster_1 lh 89223 1.948439
## 722 lh_cluster_1 lh 89227 1.816426
## 723 lh_cluster_1 lh 94116 1.932315
## 724 lh_cluster_1 lh 94191 2.072604
## 725 lh_cluster_1 lh 97316 1.963499
## 726 lh_cluster_1 lh 97325 1.700736
## 727 lh_cluster_1 lh 100763 1.929818
## 728 lh_cluster_1 lh 100767 2.004781
## 729 lh_cluster_1 lh 101638 2.424464
## 730 lh_cluster_1 lh 110103 1.764825
## 731 lh_cluster_1 lh 110142 2.678272
## 732 lh_cluster_1 lh 110164 2.095730
## 733 lh_cluster_1 lh 113392 2.018968
## 734 lh_cluster_1 lh 113426 2.341359
## 735 lh_cluster_1 lh 113437 1.979370
## 736 lh_cluster_1 lh 113440 1.792273
## 737 lh_cluster_1 lh 117414 1.957137
## 738 lh_cluster_1 lh 119928 2.003705
## 739 lh_cluster_1 lh 124674 1.854382
## 740 lh_cluster_1 lh 124676 1.819994
## 741 lh_cluster_1 lh 124693 3.034767
## 742 lh_cluster_1 lh 124710 2.346529
## 743 lh_cluster_1 lh 124713 2.297761
## 744 lh_cluster_1 lh 124726 2.009181
## 745 lh_cluster_1 lh 127229 1.925664
## 746 lh_cluster_1 lh 127232 1.958064
## 747 lh_cluster_1 lh 127234 2.055418
## 748 lh_cluster_1 lh 129885 1.925981
## 749 lh_cluster_1 lh 134634 1.817920
## 750 lh_cluster_1 lh 134671 1.918198
## 751 lh_cluster_1 lh 134674 1.970797
## 752 lh_cluster_1 lh 136499 1.985039
## 753 lh_cluster_1 lh 136504 2.051935
## 754 lh_cluster_1 lh 136517 2.007598
## 755 lh_cluster_1 lh 141347 1.929966
## 756 lh_cluster_1 lh 141377 2.666265
## 757 lh_cluster_1 lh 153697 2.753929
## 758 lh_cluster_1 lh 153701 2.992773
## 759 lh_cluster_1 lh 153710 2.540332
## 760 lh_cluster_1 lh 153722 2.390890
## 761 lh_cluster_1 lh 153727 2.651097
## 762 lh_cluster_1 lh 160228 2.073562
## 763 lh_cluster_1 lh 160232 1.979324
## 764 lh_cluster_1 lh 160235 2.088021
## 765 lh_cluster_1 lh 160302 2.003011
## 766 lh_cluster_1 lh 160304 2.030677
## 767 lh_cluster_1 lh 160322 2.036019
## 768 lh_cluster_1 lh 160334 1.702631
## 769 lh_cluster_1 lh 160338 1.757455This concludes the package vignette, thanks for reading.