digressions on (mouse) brain imaging - Developmental analyses, part 2

Here we pick up from part 1, and get into some RMINC and friends code to apply these different longitudinal models to every part of the hierarchical anatomical tree.

First, let’s reconstruct the data by loading Tiffany’s data files as before.

# load all the libs we will need
library(data.tree)
library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.2     ✔ purrr   1.0.1
✔ tibble  3.2.1     ✔ dplyr   1.1.2
✔ tidyr   1.3.0     ✔ stringr 1.5.0
✔ readr   2.1.3     ✔ forcats 0.5.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

library(RMINC)
library(lme4)

Loading required package: Matrix

Attaching package: 'Matrix'

The following objects are masked from 'package:tidyr':

    expand, pack, unpack

library(splines)
library(emmeans)
library(broom)
library(MRIcrotome)


Attaching package: 'MRIcrotome'

The following object is masked from 'package:graphics':

    legend

library(gt)
library(gtExtras)

load("brain_analysis_data_2023nov2.RData")

# the suppress warnings bit deals with a comparison in the data.tree
# library that throws far too many warnings.
hvols <- suppressWarnings(addVolumesToHierarchy(hdefs, structvols))

We’ll skip the simple straight line models, and dive right into fitting the splines and deriving information from them.

Functional programming with hierarchical trees

The anatomical hierarchies in RMINC use the data.tree package, which uses environments under the hood. There are a series of hanat prefixed functions that make it easier to work with these trees, but those functions can only take you so far. Here I will therefore focus on using standard R tools for the most part.

Environments are great for navigating trees, but for purposes of fitting multiple models it is easier to work with lists, however, as they play nicely with tidyverse functional programming. In simpler language, once we have a list of ROIs we can repetitive apply the same function to them.

The process we’ll walk through is the following:

Generate a list of brain ROIs
run a linear mixed effects model on every ROI
compute the estimated marginal means for every ROI
compute the pairwise t statistics over the estimated marginal means
put the results back into the hierarchical tree
visualize

So let’s start:

brainstructs <- Traverse(hvols)

The Traverse function creates a list of all entries in the tree. These lists now feed nicely into tidyverse’s map function. So let’s now compute the same linear mixed effects model that we used in the previous post across all structs.

# estimate the interaction model for every node
sexModels <- map(brainstructs, ~ lmer(roi ~ ns(age,3) * Sex + (1|subject_id), 
                                      gf %>% mutate(roi = .x$volumes)))

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The only trick here is that lmer expects the dependent variable to be inside the dataframe with the independent variables; hence that last line where we use mutate to assign the volumes entry from each ROI to the roi variable.

A bunch of the singular boundary fits errors popped up again. For the moment we can ignore them.

Now we have a list of 590 (the number of ROIs in our anatomical tree) statistical models. Let’s take a look at a random one

sexModels[[40]]

Linear mixed model fit by REML ['lmerMod']
Formula: roi ~ ns(age, 3) * Sex + (1 | subject_id)
   Data: gf %>% mutate(roi = .x$volumes)
REML criterion at convergence: -901.9437
Random effects:
 Groups     Name        Std.Dev.
 subject_id (Intercept) 0.01309 
 Residual               0.02671 
Number of obs: 224, groups:  subject_id, 37
Fixed Effects:
     (Intercept)       ns(age, 3)1       ns(age, 3)2       ns(age, 3)3  
        0.166201          0.068117          0.278469          0.148887  
            SexM  ns(age, 3)1:SexM  ns(age, 3)2:SexM  ns(age, 3)3:SexM  
        0.003463         -0.017298         -0.004661          0.011820

Which ROI were we looking at?

brainstructs[[40]]$name

[1] "left Cortex-amygdala transition zones"

Now remember from the more detailed discussion in the previous post that, when fitting a spline, the parameters themselves are fairly hard to interpret. So we turn back to the emmeans package to compute marginal means at different ages.

emmeansSexModels <- map(sexModels, ~ emmeans(.x, ~ Sex | age, at = list(age=c(7, 21, 65))))
emmeansSexModels[[40]]

age =  7:
 Sex emmean      SE    df lower.CL upper.CL
 F    0.227 0.00498  60.3    0.217    0.237
 M    0.229 0.00466  59.2    0.220    0.238

age = 21:
 Sex emmean      SE    df lower.CL upper.CL
 F    0.292 0.00527  70.3    0.282    0.303
 M    0.287 0.00504  76.8    0.277    0.297

age = 65:
 Sex emmean      SE    df lower.CL upper.CL
 F    0.378 0.00788 184.3    0.362    0.393
 M    0.391 0.00784 193.8    0.376    0.407

Degrees-of-freedom method: kenward-roger 
Confidence level used: 0.95

So now we have a list of 590 emmeans objects. Let’s compute the pairwise t statistics again.

emmeansSexModelsPairs <- map(emmeansSexModels, ~ pairs(.x, reverse=TRUE))
emmeansSexModelsPairs[[40]]

age =  7:
 contrast estimate      SE    df t.ratio p.value
 M - F     0.00168 0.00682  59.8   0.246  0.8065

age = 21:
 contrast estimate      SE    df t.ratio p.value
 M - F    -0.00567 0.00729  73.4  -0.778  0.4389

age = 65:
 contrast estimate      SE    df t.ratio p.value
 M - F     0.01365 0.01111 189.1   1.229  0.2208

Degrees-of-freedom method: kenward-roger

This will prove to be somewhat hard to parse. The wonderful broom package can help

tidy(emmeansSexModelsPairs[[40]])

# A tibble: 3 × 9
    age term  contrast null.value estimate std.error    df statistic p.value
  <dbl> <chr> <chr>         <dbl>    <dbl>     <dbl> <dbl>     <dbl>   <dbl>
1     7 Sex   M - F             0  0.00168   0.00682  59.8     0.246   0.807
2    21 Sex   M - F             0 -0.00567   0.00729  73.4    -0.778   0.439
3    65 Sex   M - F             0  0.0137    0.0111  189.      1.23    0.221

We will want one more modification to turn it into a single entry list, so that our map operation can return a dataframe.

tidy(emmeansSexModelsPairs[[40]]) %>% 
  select(age, estimate, statistic, p.value) %>%
  pivot_wider(names_from = age, values_from = c(estimate, statistic, p.value))

# A tibble: 1 × 9
  estimate_7 estimate_21 estimate_65 statistic_7 statistic_21 statistic_65
       <dbl>       <dbl>       <dbl>       <dbl>        <dbl>        <dbl>
1    0.00168    -0.00567      0.0137       0.246       -0.778         1.23
# ℹ 3 more variables: p.value_7 <dbl>, p.value_21 <dbl>, p.value_65 <dbl>

Putting that all together to return a dataframe rather than a list:

emmeansSexModelsPairs <- map_dfr(emmeansSexModels, ~ pairs(.x, reverse=T) %>%
                                   tidy() %>%
                                   select(age, 
                                          estimate, 
                                          statistic, 
                                          p.value) %>%
                                   pivot_wider(names_from = age, 
                                               values_from = c(estimate,
                                                               statistic, 
                                                               p.value)))

Now what remains to be done is to put the variables we care about back into the tree.

# call the Set function with every column of our variable
do.call(hvols$Set, emmeansSexModelsPairs)

So far we did each step one at a time, creating separate variables for every output. This is great if you want to inspect intermediate outputs, but can also be skipped for conciseness if you are comfortable with your pipeline. Putting it all together it would look like this:

Traverse(hvols) %>% # start by traversing ROIs
  # then run lmer at every ROI
  map(~ lmer(roi ~ ns(age,3) * Sex + (1|subject_id), 
             gf %>% mutate(roi = .x$volumes))) %>%
  # compute the estimated marginal means
  map(~ emmeans(.x, ~ Sex | age, at = list(age=c(7, 21, 65)))) %>%
  # compute pairwise stats from the emmeans
  map(~ pairs(.x, reverse=TRUE)) %>%
  # now tidy the results
  map(tidy) %>%
  # keep just the interesting bits
  map(~ select(.x, age, estimate, statistic, p.value)) %>%
  # and create a dataframe after pivoting
  map_dfr(~ pivot_wider(.x, names_from = age, 
                    values_from = c(estimate, statistic, p.value))) %>%
  # and put it back into the tree
  do.call(hvols$Set, .)

boundary (singular) fit: see help('isSingular')
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Visualizing the outputs from the hierarchical tree

At this point we have our stats back in our hierarchical tree. Let’s first simply look at it (note the output should be horizontally scrollable in case you can’t see the values):

options(width = 5000) # to keep it on one line
print(hvols, "statistic_7", "statistic_21", "statistic_65", limit=Inf)

                                                                                          levelName  statistic_7  statistic_21 statistic_65
1   root2                                                                                            1.554178788  1.4623880721  0.582970075
2    ¦--Basic cell groups and regions                                                                1.449040816  1.4251563619  0.394304116
3    ¦   ¦--Cerebrum                                                                                 1.418345444  1.8626836271  0.237294406
4    ¦   ¦   ¦--Cerebral cortex                                                                      1.336647652  1.7472158382  0.341015721
5    ¦   ¦   ¦   ¦--Cortical subplate                                                                1.109311863  1.7729834001  0.606775564
6    ¦   ¦   ¦   ¦   ¦--Cortical subplate-other                                                      0.972877057  1.7183563971  0.521564590
7    ¦   ¦   ¦   ¦   ¦   ¦--left Cortical subplate-other                                             0.591334841  1.3375002921  0.847828622
8    ¦   ¦   ¦   ¦   ¦   °--right Cortical subplate-other                                            1.208057965  1.8525215228  0.144700317
9    ¦   ¦   ¦   ¦   ¦--Claustrum                                                                    1.113914275  1.0384739647  0.892730929
10   ¦   ¦   ¦   ¦   ¦   ¦--Claustrum-other                                                          0.663558218 -0.7753881638  2.063137042
11   ¦   ¦   ¦   ¦   ¦   ¦   ¦--left Claustrum-other                                                 0.333190825 -0.9878038718  0.767952479
12   ¦   ¦   ¦   ¦   ¦   ¦   °--right Claustrum-other                                                1.086014532 -0.0947630639  3.718327788
13   ¦   ¦   ¦   ¦   ¦   ¦--Claustrum: dorsal part                                                   0.710558796  0.8499593672  0.240630678
14   ¦   ¦   ¦   ¦   ¦   ¦   ¦--left Claustrum: dorsal part                                          0.703275039  1.3204478342 -0.146579861
15   ¦   ¦   ¦   ¦   ¦   ¦   °--right Claustrum: dorsal part                                         0.432976987 -0.3652189535  0.855687740
16   ¦   ¦   ¦   ¦   ¦   °--Claustrum: ventral part                                                  1.104379977  1.6259693766  0.245779703
17   ¦   ¦   ¦   ¦   ¦       ¦--left Claustrum: ventral part                                         0.662411545  2.2003257095  0.024642346
18   ¦   ¦   ¦   ¦   ¦       °--right Claustrum: ventral part                                        1.017813074  0.2403218473  0.307859571
19   ¦   ¦   ¦   ¦   °--Endopiriform nucleus                                                         1.211663436  1.7867521888  0.384925773
20   ¦   ¦   ¦   ¦       ¦--Endopiriform nucleus, dorsal part                                        1.211022204  1.7204799871  0.184579808
21   ¦   ¦   ¦   ¦       ¦   ¦--Dorsal nucleus of the endopiriform                                   0.684064701  1.5509642471  0.090865506
22   ¦   ¦   ¦   ¦       ¦   ¦   ¦--left Dorsal nucleus of the endopiriform                          0.250037221  1.6624797773  0.848863175
23   ¦   ¦   ¦   ¦       ¦   ¦   °--right Dorsal nucleus of the endopiriform                         0.857911074  1.1602216455 -0.524447936
24   ¦   ¦   ¦   ¦       ¦   °--Intermediate nucleus of the endopiriform claustrum                   2.353450525  1.7690747719  0.405583870
25   ¦   ¦   ¦   ¦       ¦       ¦--left Intermediate nucleus of the endopiriform claustrum          2.313014842  1.6526800267  1.114713001
26   ¦   ¦   ¦   ¦       ¦       °--right Intermediate nucleus of the endopiriform claustrum         1.756831625  1.3951306635 -0.519143996
27   ¦   ¦   ¦   ¦       °--Endopiriform nucleus, ventral part                                       0.873573870  1.5070349810  0.968249054
28   ¦   ¦   ¦   ¦           ¦--left Endopiriform nucleus, ventral part                              1.142391078  1.1500975240  0.867743712
29   ¦   ¦   ¦   ¦           °--right Endopiriform nucleus, ventral part                             0.254063877  1.2969709526  0.727652476
30   ¦   ¦   ¦   °--Cortical plate                                                                   1.341041592  1.7278471368  0.313991354
31   ¦   ¦   ¦       ¦--Olfactory areas                                                              1.057050008  1.4456274906  3.066738012
32   ¦   ¦   ¦       ¦   ¦--Olfactory areas-other                                                    1.160247774  1.5398093875 -0.616486194
33   ¦   ¦   ¦       ¦   ¦   ¦--left Olfactory areas-other                                           0.451393326  0.8901338859 -1.669627717
34   ¦   ¦   ¦       ¦   ¦   °--right Olfactory areas-other                                          1.517564328  1.8138834621  0.406009180
35   ¦   ¦   ¦       ¦   ¦--Postpiriform transition area                                             0.407635267  0.7973577892  0.334844129
36   ¦   ¦   ¦       ¦   ¦   ¦--left Postpiriform transition area                                    0.804938011  1.4120351044 -0.795815417
37   ¦   ¦   ¦       ¦   ¦   °--right Postpiriform transition area                                  -0.043730681  0.0028581022  1.430723653
38   ¦   ¦   ¦       ¦   ¦--Piriform area                                                            0.469670951  0.5566548325  1.214127664
39   ¦   ¦   ¦       ¦   ¦   ¦--Cortex-amygdala transition zones                                     1.124160992 -1.2881114280  1.489944386
40   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Cortex-amygdala transition zones                            0.245991689 -0.7782547562  1.228576544
41   ¦   ¦   ¦       ¦   ¦   ¦   °--right Cortex-amygdala transition zones                           1.276899709 -1.0335125369  0.947996078
42   ¦   ¦   ¦       ¦   ¦   °--Piriform cortex                                                      0.389518045  0.7197527108  1.099113619
43   ¦   ¦   ¦       ¦   ¦       ¦--left Piriform cortex                                             0.146543507  0.9270184916  0.659795589
44   ¦   ¦   ¦       ¦   ¦       °--right Piriform cortex                                            0.611657605  0.3866705536  1.174643738
45   ¦   ¦   ¦       ¦   ¦--Taenia tecta                                                             0.139293344  0.2799544991 -3.570937775
46   ¦   ¦   ¦       ¦   ¦   ¦--Taenia tecta, dorsal part                                            0.059729276  0.1370835727 -3.727153054
47   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Taenia tecta, dorsal part                                  -0.103012943 -0.2262635081 -3.982354315
48   ¦   ¦   ¦       ¦   ¦   ¦   °--right Taenia tecta, dorsal part                                  0.211577975  0.4834703587 -3.112188416
49   ¦   ¦   ¦       ¦   ¦   °--Taenia tecta, ventral part                                           0.304553239  0.6840882537  1.232678934
50   ¦   ¦   ¦       ¦   ¦       ¦--left Taenia tecta, ventral part                                 -0.088843617  0.8149311095  0.565163555
51   ¦   ¦   ¦       ¦   ¦       °--right Taenia tecta, ventral part                                 0.570742900  0.4103735912  1.603310615
52   ¦   ¦   ¦       ¦   ¦--Cortical amygdalar area                                                  0.425909615  1.2122507262  2.349771471
53   ¦   ¦   ¦       ¦   ¦   °--Cortical amygdalar area, posterior part                              0.425909615  1.2122507262  2.349771471
54   ¦   ¦   ¦       ¦   ¦       ¦--Cortical amygdalar area, posterior part, lateral zone            0.535338822  0.3662754837  1.849055467
55   ¦   ¦   ¦       ¦   ¦       ¦   ¦--left Cortical amygdalar area, posterior part, lateral zone   0.422799432 -0.1564458496  1.181614810
56   ¦   ¦   ¦       ¦   ¦       ¦   °--right Cortical amygdalar area, posterior part, lateral zone  0.629491486  1.1897858224  2.713181860
57   ¦   ¦   ¦       ¦   ¦       °--Cortical amygdalar area, posterior part, medial zone             0.022381621  1.7721134234  1.567846679
58   ¦   ¦   ¦       ¦   ¦           ¦--left Cortical amygdalar area, posterior part, medial zone    0.056122514  1.9283300728  0.958750712
59   ¦   ¦   ¦       ¦   ¦           °--right Cortical amygdalar area, posterior part, medial zone  -0.038877174  1.0645481687  1.722327980
60   ¦   ¦   ¦       ¦   ¦--Piriform-amygdalar area                                                  0.474554093  0.8796195990  2.820685973
61   ¦   ¦   ¦       ¦   ¦   ¦--left Piriform-amygdalar area                                        -0.040236869 -0.0207593489  2.366453036
62   ¦   ¦   ¦       ¦   ¦   °--right Piriform-amygdalar area                                        0.616854260  1.2245157591  2.122667779
63   ¦   ¦   ¦       ¦   ¦--Main olfactory bulb                                                      1.083053179  1.4980732925  3.995371926
64   ¦   ¦   ¦       ¦   ¦   ¦--Main olfactory bulb, glomerular layer                                0.754457467  0.8498906997  4.000706834
65   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Main olfactory bulb, glomerular layer                       0.839328207  0.7059229655  4.145061245
66   ¦   ¦   ¦       ¦   ¦   ¦   °--right Main olfactory bulb, glomerular layer                      0.644712160  0.9523545961  3.719652908
67   ¦   ¦   ¦       ¦   ¦   ¦--Main olfactory bulb, outer plexiform layer                           0.270529662  1.0063018334  3.363204791
68   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Main olfactory bulb, outer plexiform layer                  0.347534226  1.3534406514  3.261733045
69   ¦   ¦   ¦       ¦   ¦   ¦   °--right Main olfactory bulb, outer plexiform layer                 0.187527716  0.6839523944  3.321958685
70   ¦   ¦   ¦       ¦   ¦   ¦--Main olfactory bulb, mitral layer                                    0.867706837  0.8973786411  3.841059064
71   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Main olfactory bulb, mitral layer                           0.930049108  0.8132004181  3.879886238
72   ¦   ¦   ¦       ¦   ¦   ¦   °--right Main olfactory bulb, mitral layer                          0.746941511  0.9838141644  3.674016496
73   ¦   ¦   ¦       ¦   ¦   ¦--Main olfactory bulb, inner plexiform layer                           0.894976773  1.0551838331  3.941575362
74   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Main olfactory bulb, inner plexiform layer                  0.785147580  1.2723355091  3.753259414
75   ¦   ¦   ¦       ¦   ¦   ¦   °--right Main olfactory bulb, inner plexiform layer                 0.926043801  0.8347703458  3.947188325
76   ¦   ¦   ¦       ¦   ¦   °--Main olfactory bulb, granule layer                                   1.760915739  2.3114959072  2.137291144
77   ¦   ¦   ¦       ¦   ¦       ¦--left Main olfactory bulb, granule layer                          1.839934856  2.0460435487  2.008888631
78   ¦   ¦   ¦       ¦   ¦       °--right Main olfactory bulb, granule layer                         1.569332729  2.4382644941  2.095090367
79   ¦   ¦   ¦       ¦   ¦--Accessory olfactory bulb                                                 0.624975298  0.9830240198  3.027844995
80   ¦   ¦   ¦       ¦   ¦   ¦--Accessory olfactory bulb, glomerular layer                           0.661541316  1.2418802035  3.136957139
81   ¦   ¦   ¦       ¦   ¦   ¦   ¦--left Accessory olfactory bulb, glomerular layer                  0.867276477  1.5998499161  3.077546089
82   ¦   ¦   ¦       ¦   ¦   ¦   °--right Accessory olfactory bulb, glomerular layer                 0.407269129  0.8114321746  2.874803489
83   ¦   ¦   ¦       ¦   ¦   °--Accessory olfactory bulb, granular layer                             0.442604802  0.4822540712  2.277446150
84   ¦   ¦   ¦       ¦   ¦       ¦--left Accessory olfactory bulb, granular layer                    0.827637155  0.4572730387  2.283772120
85   ¦   ¦   ¦       ¦   ¦       °--right Accessory olfactory bulb, granular layer                  -0.031305844  0.4547174674  1.768373502
86   ¦   ¦   ¦       ¦   °--Anterior olfactory nucleus                                               1.099978876  1.2025685726 -1.035080831
87   ¦   ¦   ¦       ¦       ¦--left Anterior olfactory nucleus                                      0.511733806  0.2207980258 -1.068937858
88   ¦   ¦   ¦       ¦       °--right Anterior olfactory nucleus                                     1.322820095  1.7008404446 -0.760055435
89   ¦   ¦   ¦       ¦--Hippocampal formation                                                        0.878343304  1.1240156209  1.084744302
90   ¦   ¦   ¦       ¦   ¦--Retrohippocampal region                                                  0.202024704  1.0015117620  0.759910916
91   ¦   ¦   ¦       ¦   ¦   ¦--Subiculum                                                           -0.273718971  0.4807324321  0.516468367
92   ¦   ¦   ¦       ¦   ¦   ¦   ¦--pre-para subiculum                                              -0.675158373  0.3160954526  0.089243885
93   ¦   ¦   ¦       ¦   ¦   ¦   ¦   ¦--left pre-para subiculum                                      0.020949740  0.8928175758  0.886026709
94   ¦   ¦   ¦       ¦   ¦   ¦   ¦   °--right pre-para subiculum                                    -0.968030073 -0.2434818644 -0.536530432
95   ¦   ¦   ¦       ¦   ¦   ¦   °--subiculum                                                        0.001387844  0.5277904213  0.735856634
96   ¦   ¦   ¦       ¦   ¦   ¦       ¦--left subiculum                                              -0.009628009  0.7270726692  1.074819939
97   ¦   ¦   ¦       ¦   ¦   ¦       °--right subiculum                                              0.001089564  0.2922541497  0.322035794
98   ¦   ¦   ¦       ¦   ¦   °--Entorhinal area                                                      0.329059586  1.1889371570  0.739705794
99   ¦   ¦   ¦       ¦   ¦       ¦--Entorhinal area, medial part, dorsal zone                        0.256047795  0.8936193450  0.022362715
100  ¦   ¦   ¦       ¦   ¦       ¦   ¦--left Entorhinal area, medial part, dorsal zone               0.595712381  1.1684921121  0.956080579
101  ¦   ¦   ¦       ¦   ¦       ¦   °--right Entorhinal area, medial part, dorsal zone             -0.262237783  0.4311167884 -1.114761190
102  ¦   ¦   ¦       ¦   ¦       ¦--Entorhinal area, lateral part                                    0.284639462  1.1673217527  1.097292269
103  ¦   ¦   ¦       ¦   ¦       ¦   ¦--Dorsal intermediate entorhinal cortex                        0.033618413  1.6109884953  1.627726132
104  ¦   ¦   ¦       ¦   ¦       ¦   ¦   ¦--left Dorsal intermediate entorhinal cortex               0.137961559  2.9046209211  1.805863904
105  ¦   ¦   ¦       ¦   ¦       ¦   ¦   °--right Dorsal intermediate entorhinal cortex             -0.039783071  0.3782782045  1.151061307
106  ¦   ¦   ¦       ¦   ¦       ¦   ¦--Dorsolateral entorhinal cortex                               0.417380854  0.6819608517  0.009376044
107  ¦   ¦   ¦       ¦   ¦       ¦   ¦   ¦--left Dorsolateral entorhinal cortex                     -0.046709407 -0.1099171898  0.231696125
108  ¦   ¦   ¦       ¦   ¦       ¦   ¦   °--right Dorsolateral entorhinal cortex                     0.734641050  1.1207049870 -0.125633488
109  ¦   ¦   ¦       ¦   ¦       ¦   °--Ventral intermediate entorhinal cortex                       0.142601863  1.1238648153  2.580144677
110  ¦   ¦   ¦       ¦   ¦       ¦       ¦--left Ventral intermediate entorhinal cortex              0.555126605  2.4183699544  2.252376489
111  ¦   ¦   ¦       ¦   ¦       ¦       °--right Ventral intermediate entorhinal cortex            -0.264556879 -0.2262704474  2.225118794
112  ¦   ¦   ¦       ¦   ¦       °--Entorhinal area, medial part, ventral zone                       0.533478445  1.4065439564  1.493862346
113  ¦   ¦   ¦       ¦   ¦           ¦--left Entorhinal area, medial part, ventral zone              0.712491268  2.0032201477  2.022884019
114  ¦   ¦   ¦       ¦   ¦           °--right Entorhinal area, medial part, ventral zone             0.227085538  0.5346458288  0.663095620
115  ¦   ¦   ¦       ¦   °--Hippocampal region                                                       1.392180657  1.1577358610  1.235471166
116  ¦   ¦   ¦       ¦       ¦--Ammon's horn                                                         1.117722887  0.6606689992  1.305386598
117  ¦   ¦   ¦       ¦       ¦   ¦--Field CA1                                                        1.211155192  0.3934869180  1.219899888
118  ¦   ¦   ¦       ¦       ¦   ¦   ¦--Field CA1, stratum oriens                                    0.547404366 -0.1365590728  0.719414290
119  ¦   ¦   ¦       ¦       ¦   ¦   ¦   ¦--left Field CA1, stratum oriens                           0.983718655  0.2312357287  0.342001625
120  ¦   ¦   ¦       ¦       ¦   ¦   ¦   °--right Field CA1, stratum oriens                         -0.021623869 -0.5587484434  1.072563209
121  ¦   ¦   ¦       ¦       ¦   ¦   ¦--Field CA1, stratum lacunosum-moleculare                      1.550936342  1.6209940161  0.821617670
122  ¦   ¦   ¦       ¦       ¦   ¦   ¦   ¦--left Field CA1, stratum lacunosum-moleculare             1.345633994  1.2747469823  0.922974522
123  ¦   ¦   ¦       ¦       ¦   ¦   ¦   °--right Field CA1, stratum lacunosum-moleculare            1.691134101  1.9230181470  0.647010627
124  ¦   ¦   ¦       ¦       ¦   ¦   ¦--Field CA1, stratum radiatum                                  0.731025084 -0.2901539168  1.075915585
125  ¦   ¦   ¦       ¦       ¦   ¦   ¦   ¦--left Field CA1, stratum radiatum                         0.677601903 -0.0648093531  0.814537704
126  ¦   ¦   ¦       ¦       ¦   ¦   ¦   °--right Field CA1, stratum radiatum                        0.710655211 -0.4422905492  1.218190689
127  ¦   ¦   ¦       ¦       ¦   ¦   °--Field CA1, pyramidal layer                                   1.043816836 -0.0117843922  2.081256723
128  ¦   ¦   ¦       ¦       ¦   ¦       ¦--left Field CA1, pyramidal layer                          1.027417612 -0.1068622529  1.819455161
129  ¦   ¦   ¦       ¦       ¦   ¦       °--right Field CA1, pyramidal layer                         0.859550730  0.0747584726  1.917622495
130  ¦   ¦   ¦       ¦       ¦   ¦--Field CA2                                                       -0.075470241 -0.1729647069  1.265933260
131  ¦   ¦   ¦       ¦       ¦   ¦   ¦--Field CA2, pyramidal layer                                  -0.112612488  0.1790860947  1.173633940
132  ¦   ¦   ¦       ¦       ¦   ¦   ¦   ¦--left Field CA2, pyramidal layer                         -0.278140860  0.0923482755  0.358478333
133  ¦   ¦   ¦       ¦       ¦   ¦   ¦   °--right Field CA2, pyramidal layer                         0.106814386  0.2541952142  1.916770188
134  ¦   ¦   ¦       ¦       ¦   ¦   ¦--Field CA2, stratum oriens                                    0.344990451  0.2180972226  1.167956544
135  ¦   ¦   ¦       ¦       ¦   ¦   ¦   ¦--left Field CA2, stratum oriens                           0.197121320  0.5105639057  0.781210492
136  ¦   ¦   ¦       ¦       ¦   ¦   ¦   °--right Field CA2, stratum oriens                          0.429441625 -0.0879504201  1.386227490
137  ¦   ¦   ¦       ¦       ¦   ¦   °--Field CA2, stratum radiatum                                 -0.480534440 -0.6335486238  1.168871165
138  ¦   ¦   ¦       ¦       ¦   ¦       ¦--left Field CA2, stratum radiatum                        -0.488931033 -0.3890821041  0.073539187
139  ¦   ¦   ¦       ¦       ¦   ¦       °--right Field CA2, stratum radiatum                       -0.297269051 -0.6985426151  1.878539821
140  ¦   ¦   ¦       ¦       ¦   °--Field CA3                                                        0.854098154  1.0937102306  0.894497976
141  ¦   ¦   ¦       ¦       ¦       ¦--Field CA3, pyramidal layer                                   1.059175375  0.7156266582  0.540310024
142  ¦   ¦   ¦       ¦       ¦       ¦   ¦--CA3Py Inner                                              1.299812593  1.1155756984  0.324444651
143  ¦   ¦   ¦       ¦       ¦       ¦   ¦   ¦--left CA3Py Inner                                     2.133105666  1.0733493281  0.382301816
144  ¦   ¦   ¦       ¦       ¦       ¦   ¦   °--right CA3Py Inner                                    0.353195181  0.8772957682  0.187480774
145  ¦   ¦   ¦       ¦       ¦       ¦   °--CA3Py Outer                                              0.949517821  0.6158981428  0.511907175
146  ¦   ¦   ¦       ¦       ¦       ¦       ¦--left CA3Py Outer                                     1.445520839  1.2430188857  1.113758089
147  ¦   ¦   ¦       ¦       ¦       ¦       °--right CA3Py Outer                                    0.166822178 -0.2335855360 -0.250150835
148  ¦   ¦   ¦       ¦       ¦       ¦--Field CA3, stratum oriens                                    0.472451173  0.8475182938  0.260938447
149  ¦   ¦   ¦       ¦       ¦       ¦   ¦--left Field CA3, stratum oriens                           0.731119250  0.8650259167  1.099752984
150  ¦   ¦   ¦       ¦       ¦       ¦   °--right Field CA3, stratum oriens                          0.141731066  0.6708809087 -0.552870242
151  ¦   ¦   ¦       ¦       ¦       ¦--Field CA3, stratum radiatum                                  1.198712559  1.3619407427  1.522117486
152  ¦   ¦   ¦       ¦       ¦       ¦   ¦--left Field CA3, stratum radiatum                         1.048506793  0.7236989617  1.937150249
153  ¦   ¦   ¦       ¦       ¦       ¦   °--right Field CA3, stratum radiatum                        1.201143562  1.7725563562  0.946612336
154  ¦   ¦   ¦       ¦       ¦       °--Field CA3, stratum lucidum                                   0.037868658  0.9627972039  1.900296398
155  ¦   ¦   ¦       ¦       ¦           ¦--left Field CA3, stratum lucidum                          0.565621299  0.8913482937  2.491107528
156  ¦   ¦   ¦       ¦       ¦           °--right Field CA3, stratum lucidum                        -0.574354301  0.8016504875  0.865550329
157  ¦   ¦   ¦       ¦       °--Dentate gyrus                                                        1.793971945  2.2323992940  0.717449838
158  ¦   ¦   ¦       ¦           ¦--Dentate gyrus, molecular layer                                   1.691151483  2.0347318454  0.574504404
159  ¦   ¦   ¦       ¦           ¦   ¦--left Dentate gyrus, molecular layer                          1.664789573  1.8907383184  1.225943545
160  ¦   ¦   ¦       ¦           ¦   °--right Dentate gyrus, molecular layer                         1.598438526  2.0455512577 -0.145528216
161  ¦   ¦   ¦       ¦           °--Dentate gyrus, granule cell layer                                1.860317102  2.4895784663  0.893218815
162  ¦   ¦   ¦       ¦               ¦--GrDG                                                         1.847614523  2.4225154090  0.997684166
163  ¦   ¦   ¦       ¦               ¦   ¦--left GrDG                                                2.051180910  2.1532149678  0.717370791
164  ¦   ¦   ¦       ¦               ¦   °--right GrDG                                               1.229995242  2.3720462688  1.193153205
165  ¦   ¦   ¦       ¦               °--PoDG                                                         1.733972908  2.4476645715  0.568100465
166  ¦   ¦   ¦       ¦                   ¦--left PoDG                                                2.156627696  2.0404266943  0.478106514
167  ¦   ¦   ¦       ¦                   °--right PoDG                                               1.061935141  2.4361448374  0.528854900
168  ¦   ¦   ¦       °--Isocortex                                                                    1.474192157  1.8809772456 -0.931198035
169  ¦   ¦   ¦           ¦--Anterior cingulate area                                                  2.890415082  3.7664991852 -0.092956490
170  ¦   ¦   ¦           ¦   ¦--Anterior cingulate area, ventral part                                2.810951971  4.0150532874  0.287881923
171  ¦   ¦   ¦           ¦   ¦   ¦--Cingulate cortex: area 24a                                       1.949903179  3.2260104361  0.495689971
172  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Cingulate cortex: area 24a                              1.721721847  2.6021901603 -0.146880923
173  ¦   ¦   ¦           ¦   ¦   ¦   °--right Cingulate cortex: area 24a                             1.960717425  3.4037699180  0.903126033
174  ¦   ¦   ¦           ¦   ¦   °--Cingulate cortex: area 24a'                                      3.621458790  4.0823868275 -0.482377653
175  ¦   ¦   ¦           ¦   ¦       ¦--left Cingulate cortex: area 24a'                             3.390652083  3.7478369870 -0.609395812
176  ¦   ¦   ¦           ¦   ¦       °--right Cingulate cortex: area 24a'                            3.187788019  3.6981857337 -0.236146429
177  ¦   ¦   ¦           ¦   °--Anterior cingulate area, dorsal part                                 2.547919108  2.8973677806 -0.529072115
178  ¦   ¦   ¦           ¦       ¦--Cingulate cortex: area 24b                                       2.531205643  3.1487736384 -0.523440619
179  ¦   ¦   ¦           ¦       ¦   ¦--left Cingulate cortex: area 24b                              2.055255000  2.3545223620 -0.891604826
180  ¦   ¦   ¦           ¦       ¦   °--right Cingulate cortex: area 24b                             2.477638954  3.2597401864 -0.156533931
181  ¦   ¦   ¦           ¦       °--Cingulate cortex: area 24b'                                      1.071752564  0.2360420770 -0.216693450
182  ¦   ¦   ¦           ¦           ¦--left Cingulate cortex: area 24b'                             0.816540854 -0.4596428309 -0.401684388
183  ¦   ¦   ¦           ¦           °--right Cingulate cortex: area 24b'                            1.065845718  0.9866059455  0.050585964
184  ¦   ¦   ¦           ¦--Infralimbic area                                                        -0.098618166  0.6882661095  0.165281589
185  ¦   ¦   ¦           ¦   ¦--left Infralimbic area                                               -0.585003068 -0.0523203645  0.069426123
186  ¦   ¦   ¦           ¦   °--right Infralimbic area                                               0.810328197  1.5690019794  0.221580157
187  ¦   ¦   ¦           ¦--Retrosplenial area                                                       2.046862848  2.0737768863  0.311427224
188  ¦   ¦   ¦           ¦   ¦--Retrosplenial area, ventral part                                     2.454870201  2.9819644605  0.050104265
189  ¦   ¦   ¦           ¦   ¦   ¦--Cingulate cortex: area 29a                                       0.608691818  2.0439367364 -0.181179015
190  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Cingulate cortex: area 29a                             -0.189573117  0.8692720461 -0.200878451
191  ¦   ¦   ¦           ¦   ¦   ¦   °--right Cingulate cortex: area 29a                             1.238786387  2.5264772569  0.004481050
192  ¦   ¦   ¦           ¦   ¦   ¦--Cingulate cortex: area 29b                                       0.872842529 -0.1196575122  0.155111593
193  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Cingulate cortex: area 29b                              1.171701286 -0.1582802920  0.326541719
194  ¦   ¦   ¦           ¦   ¦   ¦   °--right Cingulate cortex: area 29b                             0.218412439 -0.0124884629 -0.078486782
195  ¦   ¦   ¦           ¦   ¦   °--Cingulate cortex: area 29c                                       2.604429638  3.0030942289  0.005246101
196  ¦   ¦   ¦           ¦   ¦       ¦--left Cingulate cortex: area 29c                              2.266272552  2.2353457969 -0.760420352
197  ¦   ¦   ¦           ¦   ¦       °--right Cingulate cortex: area 29c                             2.577585569  3.3180790541  0.663005258
198  ¦   ¦   ¦           ¦   °--Retrosplenial area, dorsal part                                      1.328605004  0.8068815956  0.526738417
199  ¦   ¦   ¦           ¦       ¦--left Retrosplenial area, dorsal part                             1.832591883  0.9227943516 -0.199321672
200  ¦   ¦   ¦           ¦       °--right Retrosplenial area, dorsal part                            0.368867511  0.4416998129  0.883314077
201  ¦   ¦   ¦           ¦--Prelimbic area                                                           0.855572689  0.6311325659 -0.495767296
202  ¦   ¦   ¦           ¦   ¦--left Prelimbic area                                                  0.900007855  0.6916878111 -0.602885490
203  ¦   ¦   ¦           ¦   °--right Prelimbic area                                                 0.716541865  0.4804167650 -0.290500712
204  ¦   ¦   ¦           ¦--Auditory areas                                                           0.609161786  0.5483005283 -0.331452998
205  ¦   ¦   ¦           ¦   ¦--Primary auditory area                                                0.900100812  0.5042905221 -0.494303851
206  ¦   ¦   ¦           ¦   ¦   ¦--left Primary auditory area                                       0.349211738  0.0563075165  0.108071195
207  ¦   ¦   ¦           ¦   ¦   °--right Primary auditory area                                      1.254283438  0.9005995607 -1.152019355
208  ¦   ¦   ¦           ¦   ¦--Dorsal auditory area                                                 0.576056871  0.8373467267 -0.005799054
209  ¦   ¦   ¦           ¦   ¦   ¦--left Dorsal auditory area                                        0.752550064  1.3210695797 -0.125061943
210  ¦   ¦   ¦           ¦   ¦   °--right Dorsal auditory area                                       0.141732555  0.0382212699  0.131094805
211  ¦   ¦   ¦           ¦   °--Ventral auditory area                                                0.306718206  0.2591959583 -0.314613879
212  ¦   ¦   ¦           ¦       ¦--left Ventral auditory area                                       0.327649460  1.1089941011  1.027443275
213  ¦   ¦   ¦           ¦       °--right Ventral auditory area                                      0.176829778 -0.4467741394 -1.202911362
214  ¦   ¦   ¦           ¦--Agranular insular area                                                   0.075853585  0.7282501730  1.336971677
215  ¦   ¦   ¦           ¦   °--Agranular insular area, dorsal part                                  0.075853585  0.7282501730  1.336971677
216  ¦   ¦   ¦           ¦       ¦--left Agranular insular area, dorsal part                         0.056948850  0.1985161459  0.638848885
217  ¦   ¦   ¦           ¦       °--right Agranular insular area, dorsal part                        0.081571868  1.0409608099  1.665189515
218  ¦   ¦   ¦           ¦--Ectorhinal area                                                         -0.076210786 -0.2821656546 -2.620086064
219  ¦   ¦   ¦           ¦   ¦--Ectorhinal cortex                                                    0.108984984  0.0120922335 -1.610914078
220  ¦   ¦   ¦           ¦   ¦   ¦--left Ectorhinal cortex                                           0.378334587  1.4804157383 -0.002647473
221  ¦   ¦   ¦           ¦   ¦   °--right Ectorhinal cortex                                         -0.124393138 -1.1222090393 -2.161095501
222  ¦   ¦   ¦           ¦   °--Insular region: not subdivided                                      -0.192584836 -0.3857659735 -2.393819072
223  ¦   ¦   ¦           ¦       ¦--left Insular region: not subdivided                             -0.167421358 -0.0744677391 -1.089013718
224  ¦   ¦   ¦           ¦       °--right Insular region: not subdivided                            -0.130330555 -0.4827503156 -2.546811622
225  ¦   ¦   ¦           ¦--Somatomotor areas                                                        2.282466025  2.2433353025 -0.186638610
226  ¦   ¦   ¦           ¦   ¦--Primary motor area                                                   2.143786798  2.1862491030 -0.416752777
227  ¦   ¦   ¦           ¦   ¦   ¦--Frontal cortex: area 3                                           1.371404864  0.8380844006  1.870032325
228  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Frontal cortex: area 3                                  0.572905684  0.5367037331  2.729838053
229  ¦   ¦   ¦           ¦   ¦   ¦   °--right Frontal cortex: area 3                                 1.414434541  0.7888445177  1.000978735
230  ¦   ¦   ¦           ¦   ¦   °--Primary motor cortex                                             2.099399889  2.1933401806 -0.591792198
231  ¦   ¦   ¦           ¦   ¦       ¦--left Primary motor cortex                                    1.908665104  1.8342484895 -0.988263152
232  ¦   ¦   ¦           ¦   ¦       °--right Primary motor cortex                                   1.859907234  2.0695280534 -0.073733785
233  ¦   ¦   ¦           ¦   °--Secondary motor area                                                 2.096902305  1.8328346544  0.384400838
234  ¦   ¦   ¦           ¦       ¦--left Secondary motor area                                        1.543582562  1.1052164161 -0.449746725
235  ¦   ¦   ¦           ¦       °--right Secondary motor area                                       1.636239572  1.6420847045  0.956143048
236  ¦   ¦   ¦           ¦--Frontal pole, cerebral cortex                                            0.223667401  0.2987130997 -0.749108808
237  ¦   ¦   ¦           ¦   ¦--left Frontal pole, cerebral cortex                                   0.078952518 -0.2175291417 -0.835159489
238  ¦   ¦   ¦           ¦   °--right Frontal pole, cerebral cortex                                  0.284458759  0.7342992392 -0.536083948
239  ¦   ¦   ¦           ¦--Orbital area                                                             0.791975811  2.2478007008 -0.392504840
240  ¦   ¦   ¦           ¦   ¦--Orbital area, lateral part                                           0.829905976  2.1056359225 -0.649403540
241  ¦   ¦   ¦           ¦   ¦   ¦--left Orbital area, lateral part                                  0.529645272  1.6934590535 -1.373698539
242  ¦   ¦   ¦           ¦   ¦   °--right Orbital area, lateral part                                 1.014904735  2.2107263628  0.124041205
243  ¦   ¦   ¦           ¦   ¦--Orbital area, medial part                                            0.208982279  1.4819319700  0.058420861
244  ¦   ¦   ¦           ¦   ¦   ¦--left Orbital area, medial part                                  -0.182425621  1.1331448375 -0.641817051
245  ¦   ¦   ¦           ¦   ¦   °--right Orbital area, medial part                                  0.623678768  1.6135088165  0.893618979
246  ¦   ¦   ¦           ¦   °--Orbital area, ventrolateral part                                     1.218442748  2.4121804825 -0.130135607
247  ¦   ¦   ¦           ¦       ¦--left Orbital area, ventrolateral part                            0.657797253  1.6230694740 -0.810236184
248  ¦   ¦   ¦           ¦       °--right Orbital area, ventrolateral part                           1.584691332  2.7475152630  0.598515679
249  ¦   ¦   ¦           ¦--Posterior parietal association areas                                     2.293739827  1.1509115323  0.093526181
250  ¦   ¦   ¦           ¦   ¦--Lateral parietal association cortex                                  1.682385678  0.1869812830 -1.219089250
251  ¦   ¦   ¦           ¦   ¦   ¦--left Lateral parietal association cortex                         1.549643323  0.2955894011 -1.089783484
252  ¦   ¦   ¦           ¦   ¦   °--right Lateral parietal association cortex                        0.662591066 -0.2817543585 -0.561962661
253  ¦   ¦   ¦           ¦   ¦--Medial parietal association cortex                                   1.994680325 -0.0376276715  0.161742843
254  ¦   ¦   ¦           ¦   ¦   ¦--left Medial parietal association cortex                          2.000872363  0.4373136824  0.534527413
255  ¦   ¦   ¦           ¦   ¦   °--right Medial parietal association cortex                         1.003222139 -0.6616801573 -0.416326959
256  ¦   ¦   ¦           ¦   ¦--Parietal cortex: posterior area: rostral part                        1.998769115  0.2218662364 -0.688751475
257  ¦   ¦   ¦           ¦   ¦   ¦--left Parietal cortex: posterior area: rostral part               1.882671697  0.2336970244 -0.608388485
258  ¦   ¦   ¦           ¦   ¦   °--right Parietal cortex: posterior area: rostral part              0.688723242  0.0009733674 -0.360556770
259  ¦   ¦   ¦           ¦   °--Secondary visual cortex: mediomedial area                            2.040759026  1.5727697368  0.313046815
260  ¦   ¦   ¦           ¦       ¦--left Secondary visual cortex: mediomedial area                   2.259491985  1.2604542590 -0.061516255
261  ¦   ¦   ¦           ¦       °--right Secondary visual cortex: mediomedial area                  0.688189479  1.2113519164  0.679398406
262  ¦   ¦   ¦           ¦--Perirhinal area                                                         -0.018407200  0.5713141525 -0.907412691
263  ¦   ¦   ¦           ¦   ¦--left Perirhinal area                                                -0.031432213  0.9768904270 -0.188307882
264  ¦   ¦   ¦           ¦   °--right Perirhinal area                                                0.106853635  0.0681486837 -1.165584537
265  ¦   ¦   ¦           ¦--Somatosensory areas                                                      1.140519932  1.4480435734 -1.159939358
266  ¦   ¦   ¦           ¦   ¦--Primary somatosensory area                                           1.347404697  1.7939773430 -0.757365666
267  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area-other                                 0.644316325  2.1174833919 -0.562347667
268  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Primary somatosensory area-other                        1.081189930  2.4841750857  0.022708242
269  ¦   ¦   ¦           ¦   ¦   ¦   °--right Primary somatosensory area-other                       0.166388374  1.3551403893 -0.995899663
270  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area, barrel field                         1.573580125  1.6446997825 -0.902168835
271  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Primary somatosensory area, barrel field                1.527886853  1.5006529591 -0.757635456
272  ¦   ¦   ¦           ¦   ¦   ¦   °--right Primary somatosensory area, barrel field               1.423465205  1.5692167406 -0.916418627
273  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area, trunk                                1.099904928 -0.3536063980 -1.052650553
274  ¦   ¦   ¦           ¦   ¦   ¦   ¦--Primary somatosensory cortex: dysgranular zone               0.394601642  0.2110789024  0.079381249
275  ¦   ¦   ¦           ¦   ¦   ¦   ¦   ¦--left Primary somatosensory cortex: dysgranular zone      0.581546258  0.1050837997  0.803603309
276  ¦   ¦   ¦           ¦   ¦   ¦   ¦   °--right Primary somatosensory cortex: dysgranular zone     0.075218505  0.3043095319 -1.376757639
277  ¦   ¦   ¦           ¦   ¦   ¦   ¦--Primary somatosensory cortex: shoulder region                0.619759674 -0.5391275011 -0.383584749
278  ¦   ¦   ¦           ¦   ¦   ¦   ¦   ¦--left Primary somatosensory cortex: shoulder region       0.734528301 -1.2920873683 -0.937267669
279  ¦   ¦   ¦           ¦   ¦   ¦   ¦   °--right Primary somatosensory cortex: shoulder region      0.365674673  0.1384181433  0.138447093
280  ¦   ¦   ¦           ¦   ¦   ¦   °--Primary somatosensory cortex: trunk region                   0.918394557 -0.4947214231 -1.612345910
281  ¦   ¦   ¦           ¦   ¦   ¦       ¦--left Primary somatosensory cortex: trunk region          0.866032743 -0.5178837706 -1.628333697
282  ¦   ¦   ¦           ¦   ¦   ¦       °--right Primary somatosensory cortex: trunk region         0.446481409 -0.2421295579 -0.621370465
283  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area, upper limb                           1.799911038  2.1665312058 -0.458151461
284  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Primary somatosensory area, upper limb                  1.716755309  1.3495684617 -0.545007493
285  ¦   ¦   ¦           ¦   ¦   ¦   °--right Primary somatosensory area, upper limb                 1.453250684  2.3733281254 -0.255831412
286  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area, lower limb                           1.358195251  0.9941153140 -0.198782349
287  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Primary somatosensory area, lower limb                  1.617358844  1.1074456838 -0.294413918
288  ¦   ¦   ¦           ¦   ¦   ¦   °--right Primary somatosensory area, lower limb                 0.673119897  0.5307238679 -0.018462606
289  ¦   ¦   ¦           ¦   ¦   ¦--Primary somatosensory area, mouth                               -0.130289118  0.9795777877  1.557412161
290  ¦   ¦   ¦           ¦   ¦   ¦   ¦--left Primary somatosensory area, mouth                       0.114570074  0.9404591668  0.731210293
291  ¦   ¦   ¦           ¦   ¦   ¦   °--right Primary somatosensory area, mouth                     -0.353684310  0.8191556148  2.082549849
292  ¦   ¦   ¦           ¦   ¦   °--Primary somatosensory area, nose                                -0.043935559  1.0264508089 -0.876241045
293  ¦   ¦   ¦           ¦   ¦       ¦--left Primary somatosensory area, nose                        0.216416375  1.0061465131 -1.047440564
294  ¦   ¦   ¦           ¦   ¦       °--right Primary somatosensory area, nose                      -0.240574039  0.7955416327 -0.500213242
295  ¦   ¦   ¦           ¦   °--Supplemental somatosensory area                                      0.273937294  0.0537405088 -2.193598726
296  ¦   ¦   ¦           ¦       ¦--left Supplemental somatosensory area                            -0.271799062  0.1509869070 -1.235020615
297  ¦   ¦   ¦           ¦       °--right Supplemental somatosensory area                            0.813088725 -0.0825049774 -2.481148664
298  ¦   ¦   ¦           ¦--Temporal association areas                                               0.775326085  1.3513789829 -1.922225199
299  ¦   ¦   ¦           ¦   ¦--left Temporal association areas                                      0.354191548  1.7422602550 -0.555287370
300  ¦   ¦   ¦           ¦   °--right Temporal association areas                                     0.841965501  0.2947462097 -2.141010829
301  ¦   ¦   ¦           °--Visual areas                                                             1.627552733  2.6796387418 -0.232924936
302  ¦   ¦   ¦               ¦--Primary visual area                                                  0.544443497  2.8271672471 -0.366128430
303  ¦   ¦   ¦               ¦   ¦--left Primary visual area                                         1.038335838  2.4996183376  0.168716196
304  ¦   ¦   ¦               ¦   °--right Primary visual area                                       -0.204745406  2.1800664153 -0.804949551
305  ¦   ¦   ¦               ¦--Lateral visual area                                                  1.379326704  2.0475110563  0.588044319
306  ¦   ¦   ¦               ¦   ¦--left Lateral visual area                                         1.176169638  1.4657136482 -0.204674776
307  ¦   ¦   ¦               ¦   °--right Lateral visual area                                        1.193525059  1.9365079190  0.959168099
308  ¦   ¦   ¦               ¦--posteromedial visual area                                            1.452513955  1.9677738244  0.105730804
309  ¦   ¦   ¦               ¦   ¦--left posteromedial visual area                                   1.534404888  2.2532879330 -0.093135073
310  ¦   ¦   ¦               ¦   °--right posteromedial visual area                                  0.884184252  0.9429250813  0.258230427
311  ¦   ¦   ¦               ¦--Anterolateral visual area                                            1.494090732  2.4425759185 -0.875735807
312  ¦   ¦   ¦               ¦   ¦--left Anterolateral visual area                                   1.854976381  2.0064088839 -1.920221055
313  ¦   ¦   ¦               ¦   °--right Anterolateral visual area                                  0.902151954  2.5443023191  0.409875161
314  ¦   ¦   ¦               °--Anteromedial visual area                                             2.339250126  1.6479433186 -0.229944973
315  ¦   ¦   ¦                   ¦--left Anteromedial visual area                                    2.360607567  1.7961278969 -0.192907200
316  ¦   ¦   ¦                   °--right Anteromedial visual area                                   1.290620969  0.7302901415 -0.163175803
317  ¦   ¦   °--Cerebral nuclei                                                                      1.631478523  2.1511768969 -0.190005636
318  ¦   ¦       ¦--Pallidum                                                                         1.363232398  1.3116254807  0.171417210
319  ¦   ¦       ¦   ¦--Pallidum, ventral region                                                     1.284243686  0.7771977786  0.019869927
320  ¦   ¦       ¦   ¦   ¦--left Pallidum, ventral region                                            1.328221760  0.6884114687 -0.687131392
321  ¦   ¦       ¦   ¦   °--right Pallidum, ventral region                                           1.059156096  0.7275694520  0.597221084
322  ¦   ¦       ¦   ¦--Pallidum, caudal region                                                      1.523448429  2.6491120307  1.479175636
323  ¦   ¦       ¦   ¦   °--Bed nuclei of the stria terminalis                                       1.523448429  2.6491120307  1.479175636
324  ¦   ¦       ¦   ¦       ¦--left Bed nuclei of the stria terminalis                              1.687109215  2.9730261673  1.602933125
325  ¦   ¦       ¦   ¦       °--right Bed nuclei of the stria terminalis                             1.061164126  1.8169351021  1.031114688
326  ¦   ¦       ¦   ¦--Pallidum, dorsal region                                                      1.255210751  1.1419431453 -0.121620950
327  ¦   ¦       ¦   ¦   ¦--left Pallidum, dorsal region                                             2.051319777  1.5274562136  0.322436206
328  ¦   ¦       ¦   ¦   °--right Pallidum, dorsal region                                            0.292772539  0.6001838327 -0.532744909
329  ¦   ¦       ¦   °--Pallidum, medial region                                                      0.115419422  0.5376634888 -0.578061712
330  ¦   ¦       ¦       °--Medial septal complex                                                    0.115419422  0.5376634888 -0.578061712
331  ¦   ¦       ¦           ¦--left Medial septal complex                                           0.432026010  0.4309149169 -1.264453550
332  ¦   ¦       ¦           °--right Medial septal complex                                         -0.180618679  0.4622388827  0.088268352
333  ¦   ¦       °--Striatum                                                                         1.658324800  2.3476741475 -0.310959991
334  ¦   ¦           ¦--Striatum ventral region                                                      1.550801178  2.5284638109 -1.199768683
335  ¦   ¦           ¦   ¦--Fundus of striatum                                                       1.999496426  0.5509667863  0.373314141
336  ¦   ¦           ¦   ¦   ¦--left Fundus of striatum                                              2.133218451  1.1596409853 -0.013727666
337  ¦   ¦           ¦   ¦   °--right Fundus of striatum                                             1.247320254 -0.2841634658  0.709236200
338  ¦   ¦           ¦   ¦--Nucleus accumbens                                                        1.469336962  1.5145326125 -2.151443289
339  ¦   ¦           ¦   ¦   ¦--left Nucleus accumbens                                               0.801725834  0.2394113252 -2.607528113
340  ¦   ¦           ¦   ¦   °--right Nucleus accumbens                                              2.111625081  2.6812467121 -1.451190941
341  ¦   ¦           ¦   °--Olfactory tubercle                                                       1.057643079  3.2735226328  1.065170532
342  ¦   ¦           ¦       ¦--left Olfactory tubercle                                              0.555636823  2.9916767168  0.704118992
343  ¦   ¦           ¦       °--right Olfactory tubercle                                             1.267182981  2.6988547116  1.077402071
344  ¦   ¦           ¦--Lateral septal complex                                                       1.446454993  1.4781951604  1.473681274
345  ¦   ¦           ¦   ¦--left Lateral septal complex                                              1.074719238  1.0223619814  0.962971948
346  ¦   ¦           ¦   °--right Lateral septal complex                                             1.699527025  1.7861313406  1.714832149
347  ¦   ¦           ¦--Striatum dorsal region                                                       1.596214410  2.0963519874 -0.519293268
348  ¦   ¦           ¦   °--Caudoputamen                                                             1.596214410  2.0963519874 -0.519293268
349  ¦   ¦           ¦       ¦--left Caudoputamen                                                    1.859464728  1.8487116380 -0.997631349
350  ¦   ¦           ¦       °--right Caudoputamen                                                   1.218261587  2.1706703309  0.012502435
351  ¦   ¦           °--Striatum-like amygdalar nuclei                                               1.832375976  4.2888005058  5.115183773
352  ¦   ¦               °--Medial amygdalar nucleus                                                 1.832375976  4.2888005058  5.115183773
353  ¦   ¦                   ¦--left Medial amygdalar nucleus                                        1.649454649  3.5027350393  6.015841462
354  ¦   ¦                   °--right Medial amygdalar nucleus                                       1.554653462  3.8495315817  3.322121641
355  ¦   ¦--Brain stem                                                                               1.583745611  0.8978202235  0.576741749
356  ¦   ¦   ¦--Midbrain                                                                             1.482751375  0.9233334208  0.727623017
357  ¦   ¦   ¦   ¦--Midbrain, sensory related                                                        1.733646988  1.1961440601  0.347272679
358  ¦   ¦   ¦   ¦   ¦--Inferior colliculus                                                          1.250658425  1.3021845449 -0.148862380
359  ¦   ¦   ¦   ¦   ¦   ¦--left Inferior colliculus                                                 1.506755316  1.2707578657  0.457813517
360  ¦   ¦   ¦   ¦   ¦   °--right Inferior colliculus                                                0.821472903  1.1574903177 -0.758326787
361  ¦   ¦   ¦   ¦   °--Superior colliculus, sensory related                                         1.851520639  1.0296901114  0.588342503
362  ¦   ¦   ¦   ¦       ¦--left Superior colliculus, sensory related                                1.568261327  0.6019098874  0.028568932
363  ¦   ¦   ¦   ¦       °--right Superior colliculus, sensory related                               1.989721569  1.3889997221  1.122791601
364  ¦   ¦   ¦   ¦--Midbrain, behavioral state related                                               1.278044402  0.7432672631  1.451893855
365  ¦   ¦   ¦   ¦   °--Midbrain raphe nuclei                                                        1.278044402  0.7432672631  1.451893855
366  ¦   ¦   ¦   ¦       °--Interpeduncular nucleus                                                  1.278044402  0.7432672631  1.451893855
367  ¦   ¦   ¦   ¦--Midbrain-other                                                                   0.713449487  0.2704957670  1.182176940
368  ¦   ¦   ¦   °--Midbrain, motor related                                                          1.801368507  1.2065084148  0.211349087
369  ¦   ¦   ¦       °--Periaqueductal gray                                                          1.801368507  1.2065084148  0.211349087
370  ¦   ¦   ¦--Hindbrain                                                                            1.502526079  0.3902447922  0.678674793
371  ¦   ¦   ¦   ¦--Medulla                                                                          1.520506068  0.7138915757  0.300797562
372  ¦   ¦   ¦   ¦   ¦--Medulla, sensory related                                                     1.203877836 -0.1769130118  1.027243978
373  ¦   ¦   ¦   ¦   ¦   °--Dorsal column nuclei                                                     1.203877836 -0.1769130118  1.027243978
374  ¦   ¦   ¦   ¦   ¦       °--Cuneate nucleus                                                      1.203877836 -0.1769130118  1.027243978
375  ¦   ¦   ¦   ¦   ¦           ¦--left Cuneate nucleus                                             1.211001095  0.3179974616  0.949499726
376  ¦   ¦   ¦   ¦   ¦           °--right Cuneate nucleus                                            1.006793033 -0.7204058499  0.988621354
377  ¦   ¦   ¦   ¦   ¦--Medulla, motor related                                                       1.279329514  0.9707679775  1.637193692
378  ¦   ¦   ¦   ¦   ¦   °--Inferior olivary complex                                                 1.279329514  0.9707679775  1.637193692
379  ¦   ¦   ¦   ¦   ¦       ¦--left Inferior olivary complex                                        0.931041802  0.4623712411  1.727648012
380  ¦   ¦   ¦   ¦   ¦       °--right Inferior olivary complex                                       1.328041302  1.2169292721  1.258835212
381  ¦   ¦   ¦   ¦   °--Medulla-other                                                                1.484132700  0.7003718159  0.207497745
382  ¦   ¦   ¦   °--Pons                                                                             1.271767625 -0.1426195782  1.099266121
383  ¦   ¦   ¦       ¦--Pons-other                                                                   1.402357708 -0.0404359668  1.023249227
384  ¦   ¦   ¦       ¦--Pons, behavioral state related                                              -0.094085620 -0.8919233340  0.665545743
385  ¦   ¦   ¦       ¦   °--Pontine reticular nucleus                                               -0.094085620 -0.8919233340  0.665545743
386  ¦   ¦   ¦       ¦       ¦--left Pontine reticular nucleus                                      -0.331832615 -1.3175088826  0.125943921
387  ¦   ¦   ¦       ¦       °--right Pontine reticular nucleus                                      0.109344029 -0.3031140761  1.174943388
388  ¦   ¦   ¦       °--Pons, sensory related                                                        0.250991887 -0.3573696516  1.528633935
389  ¦   ¦   ¦           °--Superior olivary complex                                                 0.250991887 -0.3573696516  1.528633935
390  ¦   ¦   ¦               ¦--left Superior olivary complex                                        0.431360482 -0.5298923233  0.783028129
391  ¦   ¦   ¦               °--right Superior olivary complex                                       0.055312375 -0.1543088009  1.989820764
392  ¦   ¦   °--Interbrain                                                                           1.345339267  1.2994805619  0.019566080
393  ¦   ¦       ¦--Hypothalamus                                                                     1.418759060  2.0242632847  0.848691833
394  ¦   ¦       ¦   ¦--Hypothalamus-other                                                           1.357096394  2.0966765525  0.920693158
395  ¦   ¦       ¦   ¦   ¦--left Hypothalamus-other                                                  1.265870260  1.7940052242  0.822054183
396  ¦   ¦       ¦   ¦   °--right Hypothalamus-other                                                 1.372199328  2.2958977861  0.952024045
397  ¦   ¦       ¦   °--Hypothalamic medial zone                                                     1.449062322  0.2632578814 -0.271838080
398  ¦   ¦       ¦       ¦--Mammillary body                                                          0.443426530 -1.3947075634 -0.682353284
399  ¦   ¦       ¦       ¦   ¦--left Mammillary body                                                 0.682257775 -0.8752146465 -0.961445428
400  ¦   ¦       ¦       ¦   °--right Mammillary body                                                0.140787394 -1.6124337031 -0.187841285
401  ¦   ¦       ¦       °--Medial preoptic nucleus                                                  2.637240476  3.7478657724  0.838867361
402  ¦   ¦       ¦           ¦--left Medial preoptic nucleus                                         2.059649279  3.2038641503  0.548685232
403  ¦   ¦       ¦           °--right Medial preoptic nucleus                                        2.805616094  3.4255477121  1.047550133
404  ¦   ¦       °--Thalamus                                                                         1.202231368  0.7961218736 -0.480196354
405  ¦   ¦           ¦--left Thalamus                                                                1.307001845  0.7493200649 -0.521925866
406  ¦   ¦           °--right Thalamus                                                               1.015141090  0.8055468306 -0.399629234
407  ¦   °--Cerebellum                                                                               0.789121694  0.0780332366  0.480722971
408  ¦       ¦--Cerebellar cortex                                                                    0.774967117  0.0878456635  0.450146071
409  ¦       ¦   ¦--Vermal regions                                                                   0.801116563  0.3918820972  0.286450835
410  ¦       ¦   ¦   ¦--Lingula (I)                                                                  0.835571369  0.7164572699  0.163602922
411  ¦       ¦   ¦   ¦--Central lobule                                                               0.632440227  0.1854723654  0.797477359
412  ¦       ¦   ¦   ¦--Culmen                                                                       0.700756176  0.5677158333  0.332873446
413  ¦       ¦   ¦   ¦   ¦--Culmen-other                                                             0.558685423  0.3052354569 -0.238726464
414  ¦       ¦   ¦   ¦   °--Lobules IV-V                                                             0.969705069  1.3881158298  2.212732445
415  ¦       ¦   ¦   ¦       ¦--left Lobules IV-V                                                    1.012207933  2.1533675403  2.198941501
416  ¦       ¦   ¦   ¦       °--right Lobules IV-V                                                   0.709134990  0.2063080784  1.712499931
417  ¦       ¦   ¦   ¦--Declive (VI)                                                                 0.538867752  0.3363799464 -0.396026491
418  ¦       ¦   ¦   ¦--Folium-tuber vermis (VII)                                                    0.310555219 -0.6572257309  0.553620973
419  ¦       ¦   ¦   ¦--Pyramus (VIII)                                                               0.114361408 -1.1716348134 -0.122503664
420  ¦       ¦   ¦   ¦--Uvula (IX)                                                                   1.019650002  0.9698165209  0.641931425
421  ¦       ¦   ¦   °--Nodulus (X)                                                                  0.852089619  0.5041327130  0.060295162
422  ¦       ¦   °--Hemispheric regions                                                              0.740404315 -0.1100928419  0.542077894
423  ¦       ¦       ¦--Simple lobule                                                                0.900318043  0.4845938688  0.442729274
424  ¦       ¦       ¦   ¦--left Simple lobule                                                       0.740724793  0.0557133492  0.070811795
425  ¦       ¦       ¦   °--right Simple lobule                                                      0.971511765  0.8711357579  0.760311345
426  ¦       ¦       ¦--Ansiform lobule                                                              0.695379345 -0.2945121278  0.393489469
427  ¦       ¦       ¦   ¦--Crus 1                                                                   0.775500852  0.3335302291  0.504764362
428  ¦       ¦       ¦   ¦   ¦--left Crus 1                                                          0.626610038  0.4164899736  0.674526227
429  ¦       ¦       ¦   ¦   °--right Crus 1                                                         0.863471558  0.2297919683  0.308812003
430  ¦       ¦       ¦   °--Crus 2                                                                   0.563105459 -0.9098253097  0.258296292
431  ¦       ¦       ¦       ¦--left Crus 2                                                          0.681574599 -0.5778621749 -0.036099323
432  ¦       ¦       ¦       °--right Crus 2                                                         0.376586435 -1.0943085453  0.501502624
433  ¦       ¦       ¦--Paramedian lobule                                                            0.221167753 -1.3170558868 -0.053565310
434  ¦       ¦       ¦   ¦--left Paramedian lobule                                                   0.190444580 -1.7082841875 -0.344471521
435  ¦       ¦       ¦   °--right Paramedian lobule                                                  0.222154418 -0.8188742857  0.199316719
436  ¦       ¦       ¦--Copula pyramidis                                                             0.416609360 -1.0115321434 -0.304311750
437  ¦       ¦       ¦   ¦--left Copula pyramidis                                                    0.166374682 -1.4857198575 -0.674838933
438  ¦       ¦       ¦   °--right Copula pyramidis                                                   0.530527957 -0.4204030855  0.077564560
439  ¦       ¦       ¦--Flocculus                                                                    0.488078962 -1.1438444537  0.257545757
440  ¦       ¦       ¦   ¦--left Flocculus                                                           1.049352906 -0.5861831277  0.260688356
441  ¦       ¦       ¦   °--right Flocculus                                                         -0.107017991 -1.3451407656  0.168840643
442  ¦       ¦       °--Paraflocculus                                                                0.909416937  1.5056060358  1.563757517
443  ¦       ¦           ¦--left Paraflocculus                                                       0.782402133  1.2518022140  1.442429259
444  ¦       ¦           °--right Paraflocculus                                                      0.686995593  1.1372114672  1.116192357
445  ¦       °--Cerebellar nuclei                                                                    0.829252808 -0.2546533292  1.226981208
446  ¦           ¦--Dentate nucleus                                                                  0.963358523  0.3058957215  1.212591790
447  ¦           ¦   ¦--left Dentate nucleus                                                         0.621170196  0.4307961881  1.118666891
448  ¦           ¦   °--right Dentate nucleus                                                        1.118211787  0.1519825399  1.120227551
449  ¦           ¦--Interposed nucleus                                                               0.845796001 -0.3631800998  1.542033080
450  ¦           ¦   ¦--left Interposed nucleus                                                      0.752363498 -0.6311195267  1.027591631
451  ¦           ¦   °--right Interposed nucleus                                                     0.797680118 -0.0773013413  1.826239737
452  ¦           °--Fastigial nucleus                                                                0.414000235 -0.4622907284  0.549607657
453  ¦               ¦--left Fastigial nucleus                                                       0.874949110 -0.1867597282  1.242790928
454  ¦               °--right Fastigial nucleus                                                     -0.130652157 -0.6892240159 -0.257294658
455  ¦--fiber tracts                                                                                 2.150477239  1.3231353253  1.608474260
456  ¦   ¦--cranial nerves                                                                           2.148484410  1.0541548229  2.514324494
457  ¦   ¦   ¦--olfactory nerve                                                                      1.591407390  1.2030042728  3.026495691
458  ¦   ¦   ¦   ¦--anterior commissure, olfactory limb                                              2.310598198  1.9274689705  1.732266470
459  ¦   ¦   ¦   ¦   ¦--left anterior commissure, olfactory limb                                     2.319491611  1.8137283093  1.643635625
460  ¦   ¦   ¦   ¦   °--right anterior commissure, olfactory limb                                    2.066020981  1.8378206625  1.621930698
461  ¦   ¦   ¦   °--lateral olfactory tract, general                                                 0.560458007  0.3760334461  3.282104518
462  ¦   ¦   ¦       ¦--left lateral olfactory tract, general                                        0.318417989  0.4751561287  2.949569318
463  ¦   ¦   ¦       °--right lateral olfactory tract, general                                       0.753672180  0.2624337931  3.393751832
464  ¦   ¦   ¦--facial nerve                                                                         0.503628736  0.2010688712  1.324505547
465  ¦   ¦   ¦   ¦--left facial nerve                                                                0.071789234  0.0899680474  2.601573574
466  ¦   ¦   ¦   °--right facial nerve                                                               0.728209962  0.2495366002  0.293914638
467  ¦   ¦   ¦--dorsal roots                                                                         1.729110189  0.0210856043  1.325992275
468  ¦   ¦   ¦   °--cervicothalamic tract                                                            1.729110189  0.0210856043  1.325992275
469  ¦   ¦   ¦       °--medial lemniscus                                                             1.729110189  0.0210856043  1.325992275
470  ¦   ¦   ¦           ¦--left medial lemniscus                                                    1.796439057 -0.3198919903  1.148365047
471  ¦   ¦   ¦           °--right medial lemniscus                                                   1.554010561  0.3248174502  1.397105277
472  ¦   ¦   ¦--optic nerve                                                                          2.319380924  2.2051152882  2.171375255
473  ¦   ¦   ¦   °--optic tract                                                                      2.319380924  2.2051152882  2.171375255
474  ¦   ¦   ¦       ¦--left optic tract                                                             2.433546979  2.3582389248  1.939141665
475  ¦   ¦   ¦       °--right optic tract                                                            1.799122864  1.6720875557  1.982864258
476  ¦   ¦   °--oculomotor nerve                                                                     1.694038184  1.1240515001 -1.543441559
477  ¦   ¦       °--posterior commissure                                                             1.694038184  1.1240515001 -1.543441559
478  ¦   ¦--medial forebrain bundle system                                                           1.540475526  2.0017675507  0.820057396
479  ¦   ¦   ¦--cerebrum related                                                                     1.423348074  1.9732838642  1.145093345
480  ¦   ¦   ¦   ¦--anterior commissure, temporal limb                                               2.470733784  0.2908251710 -0.340182774
481  ¦   ¦   ¦   ¦   ¦--left anterior commissure, temporal limb                                      2.987143019 -0.0310075142 -0.635956949
482  ¦   ¦   ¦   ¦   °--right anterior commissure, temporal limb                                     1.211486500  0.5191781773  0.079016248
483  ¦   ¦   ¦   ¦--fornix system                                                                    1.276863711  2.0244522916  1.008159964
484  ¦   ¦   ¦   ¦   ¦--fimbria                                                                      1.197368804  1.9241690259  1.122456161
485  ¦   ¦   ¦   ¦   ¦   ¦--left fimbria                                                             1.149926424  1.3194997807  0.659880189
486  ¦   ¦   ¦   ¦   ¦   °--right fimbria                                                            1.134706437  2.5033318604  1.567066898
487  ¦   ¦   ¦   ¦   °--dorsal fornix                                                                1.305478532  1.9034242474  0.139303618
488  ¦   ¦   ¦   ¦       ¦--left dorsal fornix                                                       1.200454919  1.9478101720  0.829696211
489  ¦   ¦   ¦   ¦       °--right dorsal fornix                                                      1.145516293  1.4308040610 -0.685742635
490  ¦   ¦   ¦   ¦--stria terminalis                                                                 0.875916484  0.8485722236  1.207521008
491  ¦   ¦   ¦   ¦   ¦--left stria terminalis                                                        1.176326201  0.8926954223  2.195529588
492  ¦   ¦   ¦   ¦   °--right stria terminalis                                                       0.404096537  0.6556549639 -0.095721630
493  ¦   ¦   ¦   °--cingulum bundle                                                                  0.934204359  1.9919773639  1.197684218
494  ¦   ¦   ¦       ¦--left cingulum bundle                                                         0.866906432  1.5950795248  0.745933895
495  ¦   ¦   ¦       °--right cingulum bundle                                                        0.827003715  2.1282876111  1.555308756
496  ¦   ¦   °--hypothalamus related                                                                 2.105240176  1.8750241211 -1.005769668
497  ¦   ¦       ¦--epithalamus related                                                              1.678513311  2.2881400844 -0.947293349
498  ¦   ¦       ¦   ¦--fasciculus retroflexus                                                       0.477564308  1.2195420930  0.079626463
499  ¦   ¦       ¦   ¦   ¦--left fasciculus retroflexus                                              0.103645074  1.5692283258 -0.264877770
500  ¦   ¦       ¦   ¦   °--right fasciculus retroflexus                                             0.793723964  0.8444637880  0.388089940
501  ¦   ¦       ¦   ¦--habenular commissure                                                        -0.480412326  0.1016967594 -3.155430400
502  ¦   ¦       ¦   ¦   ¦--left habenular commissure                                                0.369251851  0.7809603568 -3.899862835
503  ¦   ¦       ¦   ¦   °--right habenular commissure                                              -0.762855815 -0.2286317318 -2.102189266
504  ¦   ¦       ¦   °--stria medullaris                                                             1.770971503  2.1143345661 -1.146700471
505  ¦   ¦       ¦       ¦--left stria medullaris                                                    2.023598396  2.1705796325 -1.332094318
506  ¦   ¦       ¦       °--right stria medullaris                                                   1.360911085  1.7452659007 -0.688963151
507  ¦   ¦       °--mammillary related                                                               2.423727063 -0.7550889250 -0.442895689
508  ¦   ¦           °--mammilothalmic tract                                                         2.423727063 -0.7550889250 -0.442895689
509  ¦   ¦               ¦--left mammilothalmic tract                                                1.659889378 -0.1171444058 -1.167462245
510  ¦   ¦               °--right mammilothalmic tract                                               2.292247664 -1.0425552677  0.280110962
511  ¦   ¦--cerebellum related fiber tracts                                                          1.207103685 -0.6731593860  1.109353572
512  ¦   ¦   ¦--cerebellar peduncles                                                                 1.333049122 -0.3940821783  0.937750668
513  ¦   ¦   ¦   ¦--inferior cerebellar peduncle                                                     1.846750581 -0.1742773605  1.683232687
514  ¦   ¦   ¦   ¦   ¦--left inferior cerebellar peduncle                                            1.650803111 -0.5274839821  0.966048330
515  ¦   ¦   ¦   ¦   °--right inferior cerebellar peduncle                                           1.833562764  0.2135018197  2.228914994
516  ¦   ¦   ¦   ¦--middle cerebellar peduncle                                                       0.078003411 -1.6841446020  0.821612995
517  ¦   ¦   ¦   ¦   ¦--left middle cerebellar peduncle                                              0.637041792 -1.0932816953  0.893183470
518  ¦   ¦   ¦   ¦   °--right middle cerebellar peduncle                                            -0.494995673 -2.0424804761  0.637186174
519  ¦   ¦   ¦   °--superior cerebelar peduncles                                                     1.866219901  1.4357060341 -0.207709260
520  ¦   ¦   ¦       ¦--left superior cerebelar peduncles                                            2.100065683  1.6014450846 -0.612786189
521  ¦   ¦   ¦       °--right superior cerebelar peduncles                                           1.197845389  0.8524755970  0.294398358
522  ¦   ¦   °--arbor vitae                                                                          1.094967161 -0.7264646370  1.095255893
523  ¦   ¦       ¦--trunk of arbor vita                                                              0.249376885 -1.3656898153 -0.215967253
524  ¦   ¦       ¦--lobule 1-2 white matter                                                          0.407272183 -0.6639925354  0.847822802
525  ¦   ¦       ¦--lobule 3 white matter                                                            0.575466592 -0.5843281885  0.181280028
526  ¦   ¦       ¦--trunk of lobules 1-3 white matter                                                0.357930485 -0.0643722805  3.165628427
527  ¦   ¦       ¦--lobules 4-5 white matter                                                         1.037605030  0.1173819511  1.964007469
528  ¦   ¦       ¦--lobules 6-7 white matter                                                         1.174431393  0.1190539616  1.095324172
529  ¦   ¦       ¦--lobule 8 white matter                                                            1.289973777 -0.8376652790  0.701796257
530  ¦   ¦       ¦--trunk of lobules 6-8 white matter                                                0.671687432 -0.2532454079  0.962830534
531  ¦   ¦       ¦--lobule 9 white matter                                                            1.700294505  0.2500978666  0.491521513
532  ¦   ¦       ¦--lobule 10 white matter                                                           1.040719048 -0.5444897316  0.076229029
533  ¦   ¦       ¦--anterior lobule white matter                                                     1.399211667 -0.2469755574  2.586161014
534  ¦   ¦       ¦   ¦--left anterior lobule white matter                                            1.039226709  0.6522929115  2.808271803
535  ¦   ¦       ¦   °--right anterior lobule white matter                                           1.385056985 -0.8948126256  1.902870981
536  ¦   ¦       ¦--simple lobule white matter                                                       0.786699517  0.0141732247  1.977775850
537  ¦   ¦       ¦   ¦--left simple lobule white matter                                              0.737959476 -0.0580944882  1.026267752
538  ¦   ¦       ¦   °--right simple lobule white matter                                             0.757017679  0.0998234391  3.154142792
539  ¦   ¦       ¦--crus 1 white matter                                                              0.907176864  0.1020015098  1.794245837
540  ¦   ¦       ¦   ¦--left crus 1 white matter                                                     1.327802377 -0.1954340956  0.969461132
541  ¦   ¦       ¦   °--right crus 1 white matter                                                    0.292667047  0.4425422351  2.619793847
542  ¦   ¦       ¦--trunk of simple and crus 1 white matter                                          0.683830254 -0.1543774100  0.492658497
543  ¦   ¦       ¦   ¦--left trunk of simple and crus 1 white matter                                 0.893765234 -0.4267375651  0.428809631
544  ¦   ¦       ¦   °--right trunk of simple and crus 1 white matter                                0.510425559  0.1635844086  0.501152327
545  ¦   ¦       ¦--crus 2 white matter                                                              0.827435967 -0.8433632144  1.218662999
546  ¦   ¦       ¦   ¦--left crus 2 white matter                                                     0.784499018 -0.4526559313  1.248883026
547  ¦   ¦       ¦   °--right crus 2 white matter                                                    0.824192047 -1.1504274752  1.089026499
548  ¦   ¦       ¦--paramedian lobule                                                                0.706120466 -0.7996922771 -1.107350935
549  ¦   ¦       ¦   ¦--left paramedian lobule                                                       0.498512486 -0.8856012367 -2.103030884
550  ¦   ¦       ¦   °--right paramedian lobule                                                      0.854524124 -0.6348662929  0.542589479
551  ¦   ¦       ¦--trunk of crus 2 and paramedian white matter                                      0.946628973 -0.3417484417  1.607024991
552  ¦   ¦       ¦   ¦--left trunk of crus 2 and paramedian white matter                             1.444188828  0.2303834938  1.378653266
553  ¦   ¦       ¦   °--right trunk of crus 2 and paramedian white matter                            0.313610219 -0.8638885906  1.599889860
554  ¦   ¦       ¦--copula white matter                                                              1.089207222 -0.7834367950  1.401930877
555  ¦   ¦       ¦   ¦--left copula white matter                                                     1.041275434 -0.4522357105  1.204110854
556  ¦   ¦       ¦   °--right copula white matter                                                    0.889458395 -1.2663285125  1.435711149
557  ¦   ¦       ¦--paraflocculus white matter                                                       1.131422271  0.6846374153  2.043332403
558  ¦   ¦       ¦   ¦--left paraflocculus white matter                                              0.859996453  0.3712204704  1.650531496
559  ¦   ¦       ¦   °--right paraflocculus white matter                                             1.169497933  0.8368621451  2.025063171
560  ¦   ¦       °--flocculus white matter                                                           0.791174388 -0.8967756918  0.606117586
561  ¦   ¦           ¦--left flocculus white matter                                                  0.092666179 -1.3235134590  0.215584691
562  ¦   ¦           °--right flocculus white matter                                                 1.017188613 -0.3354294177  0.715950199
563  ¦   ¦--lateral forebrain bundle system                                                          2.104832266  1.8986318303  1.178137677
564  ¦   ¦   ¦--corticospinal tract                                                                  1.868519930  1.3047556736  1.358881441
565  ¦   ¦   ¦   ¦--cerebal peduncle                                                                 0.518848970  1.5829092106  1.449517671
566  ¦   ¦   ¦   ¦   ¦--left cerebal peduncle                                                       -0.022906544  0.9255311505  1.313347214
567  ¦   ¦   ¦   ¦   °--right cerebal peduncle                                                       0.979645957  1.8029160375  1.153727811
568  ¦   ¦   ¦   ¦--corticospinal tract-other                                                        1.812661412  0.6419987117  2.273358956
569  ¦   ¦   ¦   ¦   ¦--left corticospinal tract-other                                               1.820304312  0.5898378727  1.955871467
570  ¦   ¦   ¦   ¦   °--right corticospinal tract-other                                              1.682481344  0.6505705925  2.430010308
571  ¦   ¦   ¦   °--internal capsule                                                                 1.384089563  0.8462189032 -0.521317360
572  ¦   ¦   ¦       ¦--left internal capsule                                                        1.772963036  0.7497751723 -0.498879786
573  ¦   ¦   ¦       °--right internal capsule                                                       0.865147263  0.8587314904 -0.476402980
574  ¦   ¦   °--corpus callosum                                                                      1.926965106  1.9028358220  0.852139296
575  ¦   ¦       ¦--left corpus callosum                                                             1.883981582  1.5349752033  0.340235630
576  ¦   ¦       °--right corpus callosum                                                            1.757950767  2.0729145388  1.203112858
577  ¦   °--extrapyramidal fiber systems                                                             1.610760837  0.2365229332 -1.362304225
578  ¦       °--rubrospinal tract                                                                    1.610760837  0.2365229332 -1.362304225
579  ¦           °--ventral tegmental decussation                                                    1.610760837  0.2365229332 -1.362304225
580  °--ventricular systems                                                                          0.404262804  1.1657903703  1.193909016
581      ¦--cerebral aqueduct                                                                       -0.344516501  0.5323949580  1.183060938
582      ¦--fourth ventricle                                                                         0.055648481 -0.2553900868  1.806931965
583      ¦--lateral ventricle                                                                        0.449174310  1.4187258536  1.679362553
584      ¦   ¦--lateral ventricle-other                                                              0.409779976  1.3975520934  1.619273577
585      ¦   ¦   ¦--left lateral ventricle-other                                                     0.333981058  0.9484254456  1.753957334
586      ¦   ¦   °--right lateral ventricle-other                                                    0.432140277  1.7406445621  1.274047799
587      ¦   °--subependymal zone                                                                    1.480314360  1.0229571330  2.351625594
588      ¦       ¦--left subependymal zone                                                           1.021510534  0.9138485774  2.279145619
589      ¦       °--right subependymal zone                                                          1.653206826  0.9836130165  2.088557892
590      °--third ventricle                                                                          0.293618011  0.6766126391 -1.680965321

We can also make the tree visible graphically, using RMINC functions. This can only be done with one variable at a time, so we’ll use the stats at p65. Use the mouse to zoom and scroll.

hanatView(hvols, "statistic_65", low=2, high=6, symmetric=T)

And lastly, of course, we want to see it on the brain:

sliceSeries(nrow=6, ncol=1, begin=65, end=210) %>%
  anatomy(mritemplate, low=700, high=1400) %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvols, mrilabels, "statistic_21"), low=2, high=6, symmetric = T) %>%
  addtitle("P21") %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvols, mrilabels, "statistic_65"), low=2, high=6, symmetric = T) %>%
  addtitle("P65") %>%
  legend("t-statistics") %>%
  draw()

This is intriguing, but also somewhat ugly. Let’s lop off the bottom end of the tree so that we only visualize the symmetric ROIs. In other words, prune the tree to get rid of, for example, the left and right medial amygdala and keep just the bilateral medial amygdala.

# create a copy of the tree (since it modifies in place)
hvolsSym <- Clone(hvols)
# prune off ROIs whose names start with left or right
Prune(hvolsSym, function(x) !str_starts(x$name, "right") & !str_starts(x$name, "left"))

[1] 308

sliceSeries(nrow=6, ncol=1, begin=65, end=210) %>%
  anatomy(mritemplate, low=700, high=1400) %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvolsSym, mrilabels, "statistic_21"), low=2, high=6, symmetric = T) %>%
  addtitle("P21") %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvolsSym, mrilabels, "statistic_65"), low=2, high=6, symmetric = T) %>%
  addtitle("P65") %>%
  legend("t-statistics") %>%
  draw()

Prettier. But of course whether you want to keep things unilateral or bilateral is up to you. Equally you could restrict it to just bits of anatomy higher up the anatomical tree - that’s a big part of the benefit of working with trees.

Lastly, let’s create a table of the most significant structures:

ToDataFrameTree(hvols, "name", 
                "statistic_7", "p.value_7",
                "statistic_21", "p.value_21",
                "statistic_65", "p.value_65") %>%
  # keep any structure where the p value at any of the three ages is < 0.05
  filter(p.value_7 < 0.05 | p.value_21 < 0.05 | p.value_65 < 0.05) %>%
  # get rid of the 
  select(-levelName)

                                                           name statistic_7    p.value_7 statistic_21   p.value_21 statistic_65   p.value_65
1                                               Claustrum-other  0.66355822 0.5086026242  -0.77538816 4.395259e-01  2.063137042 4.029563e-02
2                                         right Claustrum-other  1.08601453 0.2802465932  -0.09476306 9.246490e-01  3.718327788 2.556034e-04
3                                  left Claustrum: ventral part  0.66241155 0.5093717834   2.20032571 2.960843e-02  0.024642346 9.803630e-01
4            Intermediate nucleus of the endopiriform claustrum  2.35345052 0.0221337449   1.76907477 8.140516e-02  0.405583870 6.855362e-01
5       left Intermediate nucleus of the endopiriform claustrum  2.31301484 0.0244654275   1.65268003 1.031249e-01  1.114713001 2.665006e-01
6                                               Olfactory areas  1.05705001 0.2957630429   1.44562749 1.539279e-01  3.066738012 2.599887e-03
7                                                  Taenia tecta  0.13929334 0.8896651326   0.27995450 7.802533e-01 -3.570937775 4.476223e-04
8                                     Taenia tecta, dorsal part  0.05972928 0.9525575256   0.13708357 8.913086e-01 -3.727153054 2.525799e-04
9                                left Taenia tecta, dorsal part -0.10301294 0.9182575692  -0.22626351 8.215321e-01 -3.982354315 9.490486e-05
10                              right Taenia tecta, dorsal part  0.21157798 0.8331292080   0.48347036 6.301319e-01 -3.112188416 2.136721e-03
11                                      Cortical amygdalar area  0.42590961 0.6713255321   1.21225073 2.281128e-01  2.349771471 1.969870e-02
12                      Cortical amygdalar area, posterior part  0.42590961 0.6713255321   1.21225073 2.281128e-01  2.349771471 1.969870e-02
13  right Cortical amygdalar area, posterior part, lateral zone  0.62949149 0.5306604735   1.18978582 2.364804e-01  2.713181860 7.202958e-03
14                                      Piriform-amygdalar area  0.47455409 0.6364441146   0.87961960 3.811282e-01  2.820685973 5.246670e-03
15                                 left Piriform-amygdalar area -0.04023687 0.9680299193  -0.02075935 9.834894e-01  2.366453036 1.892470e-02
16                                right Piriform-amygdalar area  0.61685426 0.5388203695   1.22451576 2.229724e-01  2.122667779 3.492040e-02
17                                          Main olfactory bulb  1.08305318 0.2835784873   1.49807329 1.389888e-01  3.995371926 9.587945e-05
18                        Main olfactory bulb, glomerular layer  0.75445747 0.4533405421   0.84989070 3.979138e-01  4.000706834 8.912190e-05
19                   left Main olfactory bulb, glomerular layer  0.83932821 0.4043691191   0.70592297 4.822466e-01  4.145061245 5.017207e-05
20                  right Main olfactory bulb, glomerular layer  0.64471216 0.5214154427   0.95235460 3.437737e-01  3.719652908 2.596169e-04
21                   Main olfactory bulb, outer plexiform layer  0.27052966 0.7876657958   1.00630183 3.174905e-01  3.363204791 9.298018e-04
22              left Main olfactory bulb, outer plexiform layer  0.34753423 0.7294012793   1.35344065 1.800283e-01  3.261733045 1.312292e-03
23             right Main olfactory bulb, outer plexiform layer  0.18752772 0.8518500286   0.68395239 4.960192e-01  3.321958685 1.066005e-03
24                            Main olfactory bulb, mitral layer  0.86770684 0.3889166177   0.89737864 3.723329e-01  3.841059064 1.658985e-04
25                       left Main olfactory bulb, mitral layer  0.93004911 0.3559430760   0.81320042 4.186030e-01  3.879886238 1.429311e-04
26                      right Main olfactory bulb, mitral layer  0.74694151 0.4578757622   0.98381416 3.282236e-01  3.674016496 3.078499e-04
27                   Main olfactory bulb, inner plexiform layer  0.89497677 0.3741477061   1.05518383 2.945021e-01  3.941575362 1.121291e-04
28              left Main olfactory bulb, inner plexiform layer  0.78514758 0.4351056872   1.27233551 2.066698e-01  3.753259414 2.275460e-04
29             right Main olfactory bulb, inner plexiform layer  0.92604380 0.3578567019   0.83477035 4.062839e-01  3.947188325 1.095009e-04
30                           Main olfactory bulb, granule layer  1.76091574 0.0842571101   2.31149591 2.428824e-02  2.137291144 3.413842e-02
31                      left Main olfactory bulb, granule layer  1.83993486 0.0715233995   2.04604355 4.509538e-02  2.008888631 4.623745e-02
32                     right Main olfactory bulb, granule layer  1.56933273 0.1226471496   2.43826449 1.768667e-02  2.095090367 3.773361e-02
33                                     Accessory olfactory bulb  0.62497530 0.5346731678   0.98302402 3.293836e-01  3.027844995 2.858518e-03
34                   Accessory olfactory bulb, glomerular layer  0.66154132 0.5111876985   1.24188020 2.190283e-01  3.136957139 2.030710e-03
35              left Accessory olfactory bulb, glomerular layer  0.86727648 0.3896620427   1.59984992 1.145973e-01  3.077546089 2.438047e-03
36             right Accessory olfactory bulb, glomerular layer  0.40726913 0.6854575238   0.81143217 4.202058e-01  2.874803489 4.577300e-03
37                     Accessory olfactory bulb, granular layer  0.44260480 0.6595377469   0.48225407 6.309316e-01  2.277446150 2.382375e-02
38                left Accessory olfactory bulb, granular layer  0.82763716 0.4107053828   0.45727304 6.485833e-01  2.283772120 2.340339e-02
39                   left Dorsal intermediate entorhinal cortex  0.13796156 0.8906534529   2.90462092 4.580746e-03  1.805863904 7.237843e-02
40                       Ventral intermediate entorhinal cortex  0.14260186 0.8870408723   1.12386482 2.643080e-01  2.580144677 1.058807e-02
41                  left Ventral intermediate entorhinal cortex  0.55512661 0.5801408221   2.41836995 1.699507e-02  2.252376489 2.530432e-02
42                 right Ventral intermediate entorhinal cortex -0.26455688 0.7922954941  -0.22627045 8.216519e-01  2.225118794 2.729567e-02
43              left Entorhinal area, medial part, ventral zone  0.71249127 0.4786685244   2.00322015 4.839094e-02  2.022884019 4.440474e-02
44                                   Field CA1, pyramidal layer  1.04381684 0.2998619555  -0.01178439 9.906209e-01  2.081256723 3.861291e-02
45                                             left CA3Py Inner  2.13310567 0.0359664233   1.07334933 2.855173e-01  0.382301816 7.026177e-01
46                              left Field CA3, stratum lucidum  0.56562130 0.5732959058   0.89134829 3.748430e-01  2.491107528 1.350154e-02
47                                                Dentate gyrus  1.79397194 0.0786150983   2.23239929 2.924816e-02  0.717449838 4.741320e-01
48                               Dentate gyrus, molecular layer  1.69115148 0.0970295801   2.03473185 4.644921e-02  0.574504404 5.664836e-01
49                         right Dentate gyrus, molecular layer  1.59843853 0.1160794941   2.04555126 4.518122e-02 -0.145528216 8.844796e-01
50                            Dentate gyrus, granule cell layer  1.86031710 0.0669229798   2.48957847 1.455549e-02  0.893218815 3.727692e-01
51                                                         GrDG  1.84761452 0.0687634064   2.42251541 1.733923e-02  0.997684166 3.195882e-01
52                                                    left GrDG  2.05118091 0.0439434450   2.15321497 3.392520e-02  0.717370791 4.739516e-01
53                                                   right GrDG  1.22999524 0.2225206766   2.37204627 1.961839e-02  1.193153205 2.341483e-01
54                                                         PoDG  1.73397291 0.0867443002   2.44766457 1.599046e-02  0.568100465 5.705632e-01
55                                                    left PoDG  2.15662770 0.0335831228   2.04042669 4.333300e-02  0.478106514 6.330580e-01
56                                                   right PoDG  1.06193514 0.2918160254   2.43614484 1.674056e-02  0.528854900 5.974685e-01
57                                      Anterior cingulate area  2.89041508 0.0054666145   3.76649919 3.505578e-04 -0.092956490 9.260430e-01
58                        Anterior cingulate area, ventral part  2.81095197 0.0067881573   4.01505329 1.514331e-04  0.287881923 7.737716e-01
59                                   Cingulate cortex: area 24a  1.94990318 0.0557093705   3.22601044 1.843398e-03  0.495689971 6.206728e-01
60                              left Cingulate cortex: area 24a  1.72172185 0.0899576572   2.60219016 1.103268e-02 -0.146880923 8.833753e-01
61                             right Cingulate cortex: area 24a  1.96071742 0.0541003505   3.40376992 1.018842e-03  0.903126033 3.675325e-01
62                                  Cingulate cortex: area 24a'  3.62145879 0.0006053643   4.08238683 1.123576e-04 -0.482377653 6.300957e-01
63                             left Cingulate cortex: area 24a'  3.39065208 0.0011788097   3.74783699 3.264195e-04 -0.609395812 5.429467e-01
64                            right Cingulate cortex: area 24a'  3.18778802 0.0022346928   3.69818573 4.011053e-04 -0.236146429 8.135654e-01
65                         Anterior cingulate area, dorsal part  2.54791911 0.0134780545   2.89736778 4.990384e-03 -0.529072115 5.973861e-01
66                                   Cingulate cortex: area 24b  2.53120564 0.0138882710   3.14877364 2.322969e-03 -0.523440619 6.012595e-01
67                              left Cingulate cortex: area 24b  2.05525500 0.0443178927   2.35452236 2.129534e-02 -0.891604826 3.737567e-01
68                             right Cingulate cortex: area 24b  2.47763895 0.0157856008   3.25974019 1.612520e-03 -0.156533931 8.757686e-01
69                                           Retrosplenial area  2.04686285 0.0464736981   2.07377689 4.313839e-02  0.311427224 7.560106e-01
70                             Retrosplenial area, ventral part  2.45487020 0.0173984481   2.98196446 4.069894e-03  0.050104265 9.600994e-01
71                                   Cingulate cortex: area 29a  0.60869182 0.5441952216   2.04393674 4.297968e-02 -0.181179015 8.563970e-01
72                             right Cingulate cortex: area 29a  1.23878639 0.2190473756   2.52647726 1.298648e-02  0.004481050 9.964288e-01
73                                   Cingulate cortex: area 29c  2.60442964 0.0121297779   3.00309423 3.963946e-03  0.005246101 9.958214e-01
74                              left Cingulate cortex: area 29c  2.26627255 0.0277483037   2.23534580 2.920106e-02 -0.760420352 4.481708e-01
75                             right Cingulate cortex: area 29c  2.57758557 0.0126737048   3.31807905 1.484088e-03  0.663005258 5.082104e-01
76                                              Ectorhinal area -0.07621079 0.9395883641  -0.28216565 7.789645e-01 -2.620086064 9.941764e-03
77                                      right Ectorhinal cortex -0.12439314 0.9013876627  -1.12220904 2.650516e-01 -2.161095501 3.187571e-02
78                               Insular region: not subdivided -0.19258484 0.8480682738  -0.38576597 7.010893e-01 -2.393819072 1.791804e-02
79                         right Insular region: not subdivided -0.13033055 0.8967825861  -0.48275032 6.308853e-01 -2.546811622 1.174310e-02
80                                            Somatomotor areas  2.28246603 0.0266237956   2.24333530 2.855839e-02 -0.186638610 8.521829e-01
81                                           Primary motor area  2.14378680 0.0365063104   2.18624910 3.238118e-02 -0.416752777 6.773759e-01
82                                  left Frontal cortex: area 3  0.57290568 0.5683747565   0.53670373 5.926398e-01  2.729838053 6.868969e-03
83                                         Primary motor cortex  2.09939989 0.0404148379   2.19334018 3.185373e-02 -0.591792198 5.547645e-01
84                                   right Primary motor cortex  1.85990723 0.0677122064   2.06952805 4.191651e-02 -0.073733785 9.412988e-01
85                                         Secondary motor area  2.09690230 0.0409982950   1.83283465 7.184748e-02  0.384400838 7.012085e-01
86                                                 Orbital area  0.79197581 0.4314012828   2.24780070 2.746073e-02 -0.392504840 6.951159e-01
87                                   Orbital area, lateral part  0.82990598 0.4094046780   2.10563592 3.800542e-02 -0.649403540 5.167978e-01
88                             right Orbital area, lateral part  1.01490474 0.3135257102   2.21072636 2.947148e-02  0.124041205 9.014018e-01
89                             Orbital area, ventrolateral part  1.21844275 0.2277970946   2.41218048 1.832645e-02 -0.130135607 8.965964e-01
90                       right Orbital area, ventrolateral part  1.58469133 0.1186036375   2.74751526 7.670836e-03  0.598515679 5.502489e-01
91                         Posterior parietal association areas  2.29373983 0.0261473757   1.15091153 2.546325e-01  0.093526181 9.256158e-01
92                      left Medial parietal association cortex  2.00087236 0.0498773751   0.43731368 6.631407e-01  0.534527413 5.935963e-01
93                Parietal cortex: posterior area: rostral part  1.99876912 0.0485182444   0.22186624 8.247662e-01 -0.688751475 4.917189e-01
94                    Secondary visual cortex: mediomedial area  2.04075903 0.0463293986   1.57276974 1.208862e-01  0.313046815 7.546460e-01
95               left Secondary visual cortex: mediomedial area  2.25949199 0.0277367290   1.26045426 2.118176e-01 -0.061516255 9.510167e-01
96                             Primary somatosensory area-other  0.64431633 0.5219551585   2.11748339 3.782922e-02 -0.562347667 5.745749e-01
97                        left Primary somatosensory area-other  1.08118993 0.2839240117   2.48417509 1.524557e-02  0.022708242 9.819068e-01
98                       Primary somatosensory area, upper limb  1.79991104 0.0766385424   2.16653121 3.328038e-02 -0.458151461 6.473484e-01
99                 right Primary somatosensory area, upper limb  1.45325068 0.1512126574   2.37332813 2.013441e-02 -0.255831412 7.983521e-01
100                     right Primary somatosensory area, mouth -0.35368431 0.7243666184   0.81915561 4.141970e-01  2.082549849 3.846989e-02
101                             Supplemental somatosensory area  0.27393729 0.7850863297   0.05374051 9.572898e-01 -2.193598726 2.949333e-02
102                       right Supplemental somatosensory area  0.81308873 0.4191758410  -0.08250498 9.344502e-01 -2.481148664 1.392694e-02
103                            right Temporal association areas  0.84196550 0.4028433417   0.29474621 7.689178e-01 -2.141010829 3.347273e-02
104                                                Visual areas  1.62755273 0.1105684675   2.67963874 9.904321e-03 -0.232924936 8.162191e-01
105                                         Primary visual area  0.54444350 0.5882803837   2.82716725 6.161009e-03 -0.366128430 7.147011e-01
106                                    left Primary visual area  1.03833584 0.3031244166   2.49961834 1.454598e-02  0.168716196 8.661947e-01
107                                   right Primary visual area -0.20474541 0.8384342803   2.18006642 3.226467e-02 -0.804949551 4.218250e-01
108                                         Lateral visual area  1.37932670 0.1737291223   2.04751106 4.494255e-02  0.588044319 5.573340e-01
109                              left posteromedial visual area  1.53440489 0.1300323665   2.25328793 2.709939e-02 -0.093135073 9.258924e-01
110                                   Anterolateral visual area  1.49409073 0.1410430674   2.44257592 1.738979e-02 -0.875735807 3.824305e-01
111                              left Anterolateral visual area  1.85497638 0.0686827970   2.00640888 4.864694e-02 -1.920221055 5.637458e-02
112                             right Anterolateral visual area  0.90215195 0.3708664070   2.54430232 1.326990e-02  0.409875161 6.823953e-01
113                                    Anteromedial visual area  2.33925013 0.0230309425   1.64794332 1.042142e-01 -0.229944973 8.184092e-01
114                               left Anteromedial visual area  2.36060757 0.0217228601   1.79612790 7.691119e-02 -0.192907200 8.472501e-01
115                                             Cerebral nuclei  1.63147852 0.1092807178   2.15117690 3.581969e-02 -0.190005636 8.495780e-01
116                                     Pallidum, caudal region  1.52344843 0.1325999299   2.64911203 9.728901e-03  1.479175636 1.406851e-01
117                          Bed nuclei of the stria terminalis  1.52344843 0.1325999299   2.64911203 9.728901e-03  1.479175636 1.406851e-01
118                     left Bed nuclei of the stria terminalis  1.68710921 0.0963220316   2.97302617 3.857565e-03  1.602933125 1.105179e-01
119                                left Pallidum, dorsal region  2.05131978 0.0443853252   1.52745621 1.306455e-01  0.322436206 7.474645e-01
120                                                    Striatum  1.65832480 0.1038003652   2.34767415 2.253352e-02 -0.310959991 7.563029e-01
121                                     Striatum ventral region  1.55080118 0.1270250345   2.52846381 1.406037e-02 -1.199768683 2.319975e-01
122                                          Fundus of striatum  1.99949643 0.0490721918   0.55096679 5.828584e-01  0.373314141 7.092874e-01
123                                     left Fundus of striatum  2.13321845 0.0359793153   1.15964099 2.487870e-01 -0.013727666 9.890601e-01
124                                           Nucleus accumbens  1.46933696 0.1472129605   1.51453261 1.344342e-01 -2.151443289 3.275990e-02
125                                      left Nucleus accumbens  0.80172583 0.4259718411   0.23941133 8.114777e-01 -2.607528113 9.864867e-03
126                                     right Nucleus accumbens  2.11162508 0.0386463816   2.68124671 8.910977e-03 -1.451190941 1.483108e-01
127                                          Olfactory tubercle  1.05764308 0.2950764059   3.27352263 1.743996e-03  1.065170532 2.883791e-01
128                                     left Olfactory tubercle  0.55563682 0.5810390276   2.99167672 4.145212e-03  0.704118992 4.825402e-01
129                                    right Olfactory tubercle  1.26718298 0.2097004328   2.69885471 8.490021e-03  1.077402071 2.826126e-01
130                                      Striatum dorsal region  1.59621441 0.1167905721   2.09635199 4.046242e-02 -0.519293268 6.043303e-01
131                                                Caudoputamen  1.59621441 0.1167905721   2.09635199 4.046242e-02 -0.519293268 6.043303e-01
132                                          right Caudoputamen  1.21826159 0.2288407050   2.17067033 3.405644e-02  0.012502435 9.900413e-01
133                              Striatum-like amygdalar nuclei  1.83237598 0.0721813549   4.28880051 5.820549e-05  5.115183773 8.024375e-07
134                                    Medial amygdalar nucleus  1.83237598 0.0721813549   4.28880051 5.820549e-05  5.115183773 8.024375e-07
135                               left Medial amygdalar nucleus  1.64945465 0.1048898696   3.50273504 8.469651e-04  6.015841462 1.079239e-08
136                              right Medial amygdalar nucleus  1.55465346 0.1253935108   3.84953158 2.542587e-04  3.322121641 1.074963e-03
137                              right Superior olivary complex  0.05531238 0.9560068645  -0.15430880 8.776056e-01  1.989820764 4.787216e-02
138                                                Hypothalamus  1.41875906 0.1613389327   2.02426328 4.674921e-02  0.848691833 3.971582e-01
139                                          Hypothalamus-other  1.35709639 0.1800725820   2.09667655 3.966855e-02  0.920693158 3.584295e-01
140                                    right Hypothalamus-other  1.37219933 0.1752438842   2.29589779 2.462681e-02  0.952024045 3.423234e-01
141                                     Medial preoptic nucleus  2.63724048 0.0100175054   3.74786577 2.876162e-04  0.838867361 4.024806e-01
142                                left Medial preoptic nucleus  2.05964928 0.0423845059   3.20386415 1.736165e-03  0.548685232 5.837896e-01
143                               right Medial preoptic nucleus  2.80561609 0.0062241280   3.42554771 8.510278e-04  1.047550133 2.960226e-01
144                                                Lobules IV-V  0.96970507 0.3360978611   1.38811583 1.692986e-01  2.212732445 2.811182e-02
145                                           left Lobules IV-V  1.01220793 0.3155242173   2.15336754 3.458291e-02  2.198941501 2.909634e-02
146                                                fiber tracts  2.15047724 0.0365750013   1.32313533 1.912498e-01  1.608474260 1.100012e-01
147                                              cranial nerves  2.14848441 0.0355713497   1.05415482 2.950912e-01  2.514324494 1.273459e-02
148                                             olfactory nerve  1.59140739 0.1168527206   1.20300427 2.329001e-01  3.026495691 2.822097e-03
149                         anterior commissure, olfactory limb  2.31059820 0.0243423691   1.92746897 5.782111e-02  1.732266470 8.486384e-02
150                    left anterior commissure, olfactory limb  2.31949161 0.0236326136   1.81372831 7.355098e-02  1.643635625 1.018539e-01
151                   right anterior commissure, olfactory limb  2.06602098 0.0432829833   1.83782066 7.027689e-02  1.621930698 1.065218e-01
152                            lateral olfactory tract, general  0.56045801 0.5769417902   0.37603345 7.077661e-01  3.282104518 1.209066e-03
153                       left lateral olfactory tract, general  0.31841799 0.7511740960   0.47515613 6.359173e-01  2.949569318 3.558513e-03
154                      right lateral olfactory tract, general  0.75367218 0.4534626718   0.26243379 7.935520e-01  3.393751832 8.243206e-04
155                                           left facial nerve  0.07178923 0.9429219907   0.08996805 9.284511e-01  2.601573574 9.921604e-03
156                                                 optic nerve  2.31938092 0.0235569405   2.20511529 3.028513e-02  2.171375255 3.108564e-02
157                                                 optic tract  2.31938092 0.0235569405   2.20511529 3.028513e-02  2.171375255 3.108564e-02
158                                            left optic tract  2.43354698 0.0176991213   2.35823892 2.073433e-02  1.939141665 5.388782e-02
159                                           right optic tract  1.79912286 0.0764397294   1.67208756 9.811087e-02  1.982864258 4.872228e-02
160                              medial forebrain bundle system  1.54047553 0.1295956371   2.00176755 4.983811e-02  0.820057396 4.134250e-01
161                          anterior commissure, temporal limb  2.47073378 0.0157901158   0.29082517 7.718083e-01 -0.340182774 7.340588e-01
162                     left anterior commissure, temporal limb  2.98714302 0.0037180475  -0.03100751 9.753200e-01 -0.635956949 5.254840e-01
163                                               fornix system  1.27686371 0.2074412777   2.02445229 4.742052e-02  1.008159964 3.149437e-01
164                                               right fimbria  1.13470644 0.2615516035   2.50333186 1.488497e-02  1.567066898 1.189804e-01
165                                       left stria terminalis  1.17632620 0.2447710643   0.89269542 3.754781e-01  2.195529588 2.953636e-02
166                                             cingulum bundle  0.93420436 0.3535511579   1.99197736 4.957479e-02  1.197684218 2.324357e-01
167                                       right cingulum bundle  0.82700372 0.4110737821   2.12828761 3.607782e-02  1.555308756 1.214081e-01
168                                        hypothalamus related  2.10524018 0.0389756255   1.87502412 6.416111e-02 -1.005769668 3.157168e-01
169                                         epithalamus related  1.67851331 0.0977889412   2.28814008 2.452487e-02 -0.947293349 3.446032e-01
170                                        habenular commissure -0.48041233 0.6330947642   0.10169676 9.193621e-01 -3.155430400 1.958117e-03
171                                   left habenular commissure  0.36925185 0.7131234661   0.78096036 4.370375e-01 -3.899862835 1.310805e-04
172                                  right habenular commissure -0.76285581 0.4493484280  -0.22863173 8.200222e-01 -2.102189266 3.742223e-02
173                                            stria medullaris  1.77097150 0.0822404061   2.11433457 3.840288e-02 -1.146700471 2.531297e-01
174                                       left stria medullaris  2.02359840 0.0479164213   2.17057963 3.361202e-02 -1.332094318 1.845876e-01
175                                          mammillary related  2.42372706 0.0174874713  -0.75508893 4.517404e-01 -0.442895689 6.582867e-01
176                                        mammilothalmic tract  2.42372706 0.0174874713  -0.75508893 4.517404e-01 -0.442895689 6.582867e-01
177                                  right mammilothalmic tract  2.29224766 0.0241278951  -1.04255527 2.990973e-01  0.280110962 7.796605e-01
178                          right inferior cerebellar peduncle  1.83356276 0.0713658947   0.21350182 8.314767e-01  2.228914994 2.694144e-02
179                            right middle cerebellar peduncle -0.49499567 0.6222409196  -2.04248048 4.424289e-02  0.637186174 5.247251e-01
180                           left superior cerebelar peduncles  2.10006568 0.0383980504   1.60144508 1.117059e-01 -0.612786189 5.406625e-01
181                           trunk of lobules 1-3 white matter  0.35793049 0.7216886548  -0.06437228 9.488548e-01  3.165628427 1.809947e-03
182                                anterior lobule white matter  1.39921167 0.1654625266  -0.24697556 8.053778e-01  2.586161014 1.036662e-02
183                           left anterior lobule white matter  1.03922671 0.3023656928   0.65229291 5.159265e-01  2.808271803 5.462854e-03
184                                  simple lobule white matter  0.78669952 0.4337591405   0.01417322 9.887179e-01  1.977775850 4.923888e-02
185                            right simple lobule white matter  0.75701768 0.4515018762   0.09982344 9.206974e-01  3.154142792 1.846984e-03
186                                   right crus 1 white matter  0.29266705 0.7704954829   0.44254224 6.589346e-01  2.619793847 9.426042e-03
187                                      left paramedian lobule  0.49851249 0.6192860354  -0.88560124 3.774679e-01 -2.103030884 3.662099e-02
188                                  paraflocculus white matter  1.13142227 0.2627311766   0.68463742 4.959424e-01  2.043332403 4.250790e-02
189                            right paraflocculus white matter  1.16949793 0.2472015028   0.83686215 4.056647e-01  2.025063171 4.437365e-02
190                             lateral forebrain bundle system  2.10483227 0.0406985077   1.89863183 6.303237e-02  1.178137677 2.408808e-01
191                                   corticospinal tract-other  1.81266141 0.0743942481   0.64199871 5.226134e-01  2.273358956 2.405407e-02
192                             right corticospinal tract-other  1.68248134 0.0970751182   0.65057059 5.170479e-01  2.430010308 1.596292e-02
193                                       right corpus callosum  1.75795077 0.0844213461   2.07291454 4.219665e-02  1.203112858 2.306058e-01
194                                           subependymal zone  1.48031436 0.1424758663   1.02295713 3.084638e-01  2.351625594 1.959579e-02
195                                      left subependymal zone  1.02151053 0.3099360387   0.91384858 3.627250e-01  2.279145619 2.364119e-02
196                                     right subependymal zone  1.65320683 0.1017859992   0.98361302 3.272390e-01  2.088557892 3.792105e-02

This table is neither visually appealing nor particularly parseable given the many many rows. We could reduce the number of rows by being stricter with our p value thresholds, and we could prune the anatomical tree to only look at some aspects. And lastly we can make the table prettier. We’ll do a bit of all of that, using the gt and gtExtras packages (see here for a nice intro).

First, let’s create our table, this time from the symmetric version of the atlas. Filter it to keep just the leaves - i.e. the bottom of our anatomical hierarchy.

#t_formatter <- 
#  formatter("span", 
#            style = x ~ style(
#              font.weight = "bold", 
#              color = ifelse(x > 0, "pink", ifelse(x < 0, "blue", "black"))))

resultsTable <- ToDataFrameTree(hvolsSym, "name", 
                "statistic_7", "p.value_7",
                "statistic_21", "p.value_21",
                "statistic_65", "p.value_65",
                filterFun = isLeaf) %>%
  # keep any structure where the p value at any of the three ages is < 0.05
  filter(p.value_7 < 0.05 | p.value_21 < 0.05 | p.value_65 < 0.05)

Next we round the t statistics since we don’t need so many significant digits. We also create a new trends column for plotting a trend-line (a bit superfluous, but hey). Lastly, a column to indicate where in the tree that node comes from.

resultsTable <- resultsTable %>%
  rowwise() %>%
  mutate(p7 = round(statistic_7, 2),
         p21 = round(statistic_21, 2), 
         p65 = round(statistic_65, 2),
         trend = list(c_across(p7:p65)),
         hierarchy = ifelse(any(FindNode(hvolsSym, name)$path == "Cortical plate"), 
                            FindNode(hvolsSym, name)$path[6], 
                            FindNode(hvolsSym, name)$path[3])) %>%
  select(hierarchy, name, p7, p21, p65, trend)

Finally we can turn it into a table, adding colours to the p values and a sparkline.

resultsTable %>%
  gt(groupname_col = 'hierarchy') %>%
  #cols_label(.list = desired_colnames) %>% 
  #spanners_and_header() %>%
  gt_color_rows(p7:p65, palette = colorRampPalette(c("blue", "white", "red"))(255), domain=c(-7,7)) %>%
  gt_plt_sparkline(trend) %>%
  tab_spanner(label=md("**Age (t-statistic)**"), columns=p7:p65) %>%
  tab_style(cell_text(weight = "bold"), cells_column_labels()) %>%
  tab_style(cell_text(indent = pct(3)), cells_body()) %>%
  tab_style(cell_text(weight = "bold", style = "italic"), 
            cells_row_groups()) %>%
  tab_header("Sex effects across age",
             subtitle = "Computed using estimated marginal means from a third order spline")

name	Age (t-statistic)			trend
Sex effects across age
Computed using estimated marginal means from a third order spline
name	p7	p21	p65	trend
Cerebrum
Claustrum-other	0.66	-0.78	2.06
Intermediate nucleus of the endopiriform claustrum	2.35	1.77	0.41
Bed nuclei of the stria terminalis	1.52	2.65	1.48
Fundus of striatum	2.00	0.55	0.37
Nucleus accumbens	1.47	1.51	-2.15
Olfactory tubercle	1.06	3.27	1.07
Caudoputamen	1.60	2.10	-0.52
Medial amygdalar nucleus	1.83	4.29	5.12
Olfactory areas
Taenia tecta, dorsal part	0.06	0.14	-3.73
Piriform-amygdalar area	0.47	0.88	2.82
Main olfactory bulb, glomerular layer	0.75	0.85	4.00
Main olfactory bulb, outer plexiform layer	0.27	1.01	3.36
Main olfactory bulb, mitral layer	0.87	0.90	3.84
Main olfactory bulb, inner plexiform layer	0.89	1.06	3.94
Main olfactory bulb, granule layer	1.76	2.31	2.14
Accessory olfactory bulb, glomerular layer	0.66	1.24	3.14
Accessory olfactory bulb, granular layer	0.44	0.48	2.28
Hippocampal formation
Ventral intermediate entorhinal cortex	0.14	1.12	2.58
Field CA1, pyramidal layer	1.04	-0.01	2.08
Dentate gyrus, molecular layer	1.69	2.03	0.57
GrDG	1.85	2.42	1.00
PoDG	1.73	2.45	0.57
Isocortex
Cingulate cortex: area 24a	1.95	3.23	0.50
Cingulate cortex: area 24a'	3.62	4.08	-0.48
Cingulate cortex: area 24b	2.53	3.15	-0.52
Cingulate cortex: area 29a	0.61	2.04	-0.18
Cingulate cortex: area 29c	2.60	3.00	0.01
Insular region: not subdivided	-0.19	-0.39	-2.39
Primary motor cortex	2.10	2.19	-0.59
Secondary motor area	2.10	1.83	0.38
Orbital area, lateral part	0.83	2.11	-0.65
Orbital area, ventrolateral part	1.22	2.41	-0.13
Parietal cortex: posterior area: rostral part	2.00	0.22	-0.69
Secondary visual cortex: mediomedial area	2.04	1.57	0.31
Primary somatosensory area-other	0.64	2.12	-0.56
Primary somatosensory area, upper limb	1.80	2.17	-0.46
Supplemental somatosensory area	0.27	0.05	-2.19
Primary visual area	0.54	2.83	-0.37
Lateral visual area	1.38	2.05	0.59
Anterolateral visual area	1.49	2.44	-0.88
Anteromedial visual area	2.34	1.65	-0.23
Brain stem
Hypothalamus-other	1.36	2.10	0.92
Medial preoptic nucleus	2.64	3.75	0.84
Cerebellum
Lobules IV-V	0.97	1.39	2.21
cranial nerves
anterior commissure, olfactory limb	2.31	1.93	1.73
lateral olfactory tract, general	0.56	0.38	3.28
optic tract	2.32	2.21	2.17
medial forebrain bundle system
anterior commissure, temporal limb	2.47	0.29	-0.34
cingulum bundle	0.93	1.99	1.20
habenular commissure	-0.48	0.10	-3.16
stria medullaris	1.77	2.11	-1.15
mammilothalmic tract	2.42	-0.76	-0.44
cerebellum related fiber tracts
trunk of lobules 1-3 white matter	0.36	-0.06	3.17
anterior lobule white matter	1.40	-0.25	2.59
simple lobule white matter	0.79	0.01	1.98
paraflocculus white matter	1.13	0.68	2.04
lateral forebrain bundle system
corticospinal tract-other	1.81	0.64	2.27
lateral ventricle
subependymal zone	1.48	1.02	2.35

Model comparisons

The approach so far is to examine sex differences at three somewhat arbitrary ages. Going back to part 1 of this series, we do better (or at least complement this approach) by comparing different models in order to ascertain where sex and age by sex interactions matter. Let’s test that approach out across all brain structures.

The first step is to create a function that evaluates an arbitrary brain structure, runs our three statistical models, and computes the log-likelihood test. This function will take a single argument containing the dataframe to process, since when we iterate over our brain structures we first mutate our main dataframe to add the roi variable.

modelComp <- function(gf){
  # the default model - spline by age, no sex
  mSimple <- lmer(roi ~ ns(age, 3) + (1|subject_id), gf, REML = F)
  # different intercept but same slope by sex
  mIntercept <- lmer(roi ~ sex + ns(age, 3) + (1|subject_id), gf, REML=F)
  # different intercept and different slope by sex
  mInteraction <- lmer(roi ~ sex * ns(age, 3) + (1|subject_id), gf, REML=F)
  anova(mSimple, mIntercept, mInteraction) %>%
    # make output easier to parse
    tidy() %>%
    # keep just the most interesting variables
    select(term, AIC, BIC, logLik, p.value) %>%
    # and make it wider for easier looping
    pivot_wider(names_from = term, 
                values_from = c(AIC, BIC, logLik, p.value)) %>%
    # get rid of the one value that will always be NA
    select(-p.value_mSimple)
}

Let’s test that function out on a single brain structure to make sure it works and makes sense.

modelComp(gf %>% mutate(roi = FindNode(hvols, "Medial amygdalar nucleus")$volumes))

# A tibble: 1 × 11
  AIC_mSimple AIC_mIntercept AIC_mInteraction BIC_mSimple BIC_mIntercept BIC_mInteraction logLik_mSimple logLik_mIntercept logLik_mInteraction p.value_mIntercept p.value_mInteraction
        <dbl>          <dbl>            <dbl>       <dbl>          <dbl>            <dbl>          <dbl>             <dbl>               <dbl>              <dbl>                <dbl>
1       -690.          -702.            -718.       -670.          -678.            -684.           351.              358.                369.           0.000265            0.0000525

Now we are ready to iterate over our hierarchical tree

Traverse(hvols) %>% # start by traversing our hierarchy
  # run our modelComp function for every structure
  map_dfr(~ modelComp(gf %>% mutate(roi = .x$volumes))) %>%
  # and put it back into the tree
  do.call(hvols$Set, .)

boundary (singular) fit: see help('isSingular')
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This again gives us lots of those singular fit warnings, and again for the sake of this exercise we ignore them (we will come back to them in a future installment of this series). Let’s take a look by putting the results onto the brain.

# create a copy of the tree (since it modifies in place)
hvolsSym <- Clone(hvols)
# prune off ROIs whose names start with left or right
Prune(hvolsSym, function(x) !str_starts(x$name, "right") & !str_starts(x$name, "left"))

[1] 308

sliceSeries(nrow=6, ncol=1, begin=65, end=210) %>%
  anatomy(mritemplate, low=700, high=1400) %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvolsSym, mrilabels, "statistic_21"), low=2, high=6, symmetric = T) %>%
  addtitle("P21") %>%
  sliceSeries() %>% anatomy() %>%
  overlay(hanatToVolume(hvolsSym, mrilabels, "statistic_65"), low=2, high=6, symmetric = T) %>%
  addtitle("P65") %>%
  legend("t-statistics") %>%
  sliceSeries() %>% anatomy() %>%
  overlay(-log10(hanatToVolume(hvolsSym, mrilabels, "p.value_mIntercept"))*as.integer(mrilabels>0), low=1.3, high=6, symmetric = F) %>%
  addtitle("Intercept") %>%
  sliceSeries() %>% anatomy() %>%
  overlay(-log10(hanatToVolume(hvolsSym, mrilabels, "p.value_mInteraction"))*as.integer(mrilabels>0), low=1.3, high=6, symmetric = F) %>%
  addtitle("Interaction") %>%  
  legend("log10 p value") %>%
  draw()

One small trick to note in that bit of code:

This line, -log10(hanatToVolume(hvolsSym, mrilabels, "p.value_mIntercept"))*as.integer(mrilabels>0), looks a bit ungainly. What it does is to take the “p.value_mIntercept” column from our tree and turn it into a volume. Then, because p values are awkward to display, it computes the negative log10, so that 0.1 turns into 1, 0.01 turns into 2, etc. For visualization that looks a bit weird, since background voxels have a value of zero, and hence we add in *as.integer(mrilabels>0), which zeros the background out again again after the log10 computation.

Multiple comparisons

This brings us to the final bit of part 2 of this series: dealing with multiple comparisons. Since we are dealing with so many brain structures we have to adjust our p values to account for all these comparisons. We will do this via the false discovery rate-,The%20FDR%20is%20the%20rate%20that%20features%20called%20significant%20are,of%20these%20are%20truly%20null.). But there are three issues somewhat unique to working hierarchical anatomical trees to keep in mind:

The denominator matters: you thus have to make decisions about how to prune or otherwise adjust your anatomy tree before you adjust for multiple comparisons. For example, you might only care about bilateral structures and not look at unilateral (i.e. left and right) separately. In that case prune first, then apply FDR. Similarly, you might not care about the hierarchy and want to just examine the leaves. So extract them and then apply FDR.
If you are going to examine the full hierarchy you create some obvious dependence, since bottom level structures directly add up to top level structures (i.e. left hippocampus + right hippocampus = bilarateral hippocampus). This challenges the degree of dependence that the classical FDR method, by Benjamini and Hochberg, allows. There is an alternative, derived by Benjamini and Yekutieli, which is valid under arbitrary dependence assumption, but is also much more conservative (i.e. less likely to consider a particular test significant).
The last issue revolves around whether to pool your tests. For example, above we computed two log-likelihood tests when comparing our models. Do we want to adjust them separately or do we want to concatenate the p values and adjust them jointly?

The key message behind these points is that the choice of how to prune the tree and which FDR adjustment to employ has to be made before stats are computed and results examined. Which sucks, but thems the breaks.

Let’s implement them. First, let’s go for the symmetric tree and keeping the whole hierarchy, but not worrying too much about dependence and sticking with Benjamini and Hochberg:

pvalsIn <- hvolsSym$Get("p.value_mIntercept")
qvalsIn <- p.adjust(pvalsIn, method = "BH")
hvolsSym$Set(q.value_mIntercept = qvalsIn)

And if we wanted just the leaves:

pvalsIn <- hvolsSym$Get("p.value_mIntercept", filterFun = isLeaf)
qvalsIn <- p.adjust(pvalsIn, method = "BH")
hvolsSym$Set(q.value_mIntercept2 = qvalsIn, filterFun = isLeaf)

Let’s see if it makes a difference:

MeA <- FindNode(hvolsSym, "Medial amygdalar nucleus")
MeA$q.value_mIntercept

[1] 0.03732804

MeA$q.value_mIntercept2

[1] 0.04818229

It does, slightly.

And to finish, let’s stick with the first test (whole tree) and make a table of what survives a 10% FDR. First we also compute the different slope model q values

# onelinear for computing FDR
hvolsSym$Set(q.value_mInteraction = 
               p.adjust(hvolsSym$Get("p.value_mInteraction"), "BH"))

qTable <- ToDataFrameTree(hvolsSym, "name", 
                "statistic_7", 
                "statistic_21",
                "statistic_65",
                "q.value_mIntercept",
                "q.value_mInteraction") %>%
  # keep any structure where the p value at any of the three ages is < 0.05
  filter(q.value_mIntercept < 0.1 | q.value_mInteraction < 0.1)  %>%
  rowwise() %>%
  mutate(p7 = round(statistic_7, 2),
         p21 = round(statistic_21, 2), 
         p65 = round(statistic_65, 2),
         qIntercept = format.pval(q.value_mIntercept, digits=1),
         qInteract = format.pval(q.value_mInteraction, digits=1)) %>%
  select(name, p7, p21, p65, qIntercept, qInteract) 

qTable %>%
  gt() %>%
  gt_color_rows(p7:p65, palette = colorRampPalette(c("blue", "white", "red"))(255), domain=c(-7,7)) %>%
  tab_spanner(label=md("**Age (t-statistic)**"), columns=p7:p65) %>%
  tab_style(cell_text(weight = "bold"), cells_column_labels()) %>%
  tab_header("Sex effects across age",
             subtitle = "Computed using estimated marginal means from a third order spline")

name	Age (t-statistic)			qIntercept	qInteract
Sex effects across age
Computed using estimated marginal means from a third order spline
name	p7	p21	p65	qIntercept	qInteract
Anterior cingulate area, ventral part	2.81	4.02	0.29	0.09	0.6
Cingulate cortex: area 24a'	3.62	4.08	-0.48	0.09	0.2
Striatum-like amygdalar nuclei	1.83	4.29	5.12	0.04	0.007
Medial amygdalar nucleus	1.83	4.29	5.12	0.04	0.007
Medial preoptic nucleus	2.64	3.75	0.84	0.06	0.8

And there it is. That’s enough for part 2 - part 3 will get into general additive models so that we can be smarter than keeping third order splines throughout.