# Example analyses with VertexWiseR - Example 2

#### Charly Billaud, Junhong Yu

#### 2025-07-16

## Example 2: Mixed effect model of intervention-related changes on hippocampal thickness

Note: This is the most up-to-date demo. Its version published in Imaging Neuroscience (2024) 2: 1–14 no longer applies since the v1.3.0 fixes made to the TFCE_vertex_analysis_mixed() function (see our updates page for details).

The analysis will use surface data already extracted in R from a preprocessed subjects directory, which we make available so you do not need to preprocess a sample yourself. To obtain it, we had extracted thickness data from a Hippunfold preprocessing directory of the Fink dataset (Fink et al. 2021).

The demo data (~216 MB) required to run the example analysis, and can be downloaded from the package’s github repository with the following function:

    #This will save the demo_data directory in a temporary directory (tempdir(), but you can change it to your own path)
    demodata=VertexWiseR:::dl_demo(path=tempdir(), quiet=TRUE)

Here is the command line which was originally used to extract the surface:

    #HIPvextract(sdirpath = hippunfold_SUBJECTS_DIR, filename = "FINK_Tv", measure = "thickness", subj_ID = T)

To load the hippocampal thickness matrix:

    FINK_Tv_ses13 = readRDS(file=paste0(demodata,"/FINK_Tv_ses13.rds"))

To smooth the surface data:

    FINK_Tv_smoothed_ses13 = smooth_surf(FINK_Tv_ses13, 5)

To load the behavioural data (FINK_behdata_ses13.csv, which contains two rows per participant, for scanning sessions 1 and 3).

    dat_beh_ses13 = readRDS(paste0(demodata,"/FINK_behdata_ses13.rds"))

Here, we are interested in the interaction between session number (time) and group. To run the vertex-wise mixed model analysis with random field theory-based cluster correction, testing for the effect of session, group, session * group interaction, on hippocampal thickness, with subject ID as a random variable:

    model2_RFT=RFT_vertex_analysis(
      model = dat_beh_ses13[,c("session","group","session_x_group")],
      contrast = dat_beh_ses13[,"session_x_group"],
      surf_data=FINK_Tv_smoothed_ses13,
      random=dat_beh_ses13[,"participant_id"], p=0.05)

    model2_RFT$cluster_level_results

    ## $`Positive contrast`
    ##   clusid nverts     P     X    Y   Z tstat      region
    ## 1      1    974 0.041 -13.3 27.5 1.3  4.14 L Subiculum
    ##
    ## $`Negative contrast`
    ## [1] "No significant clusters"

To run the vertex-wise mixed model analysis with threshold-free cluster enhancement-based cluster correction, with 1000 permutations, testing for the effect of session, group, session * group interaction, on hippocampal thickness, with subject ID as a random variable:

    set.seed(123)
    model2_TFCE=TFCE_vertex_analysis_mixed(
      model = dat_beh_ses13[,c("session","group","session_x_group")],
      contrast = dat_beh_ses13[,"session_x_group"],
      surf_data= FINK_Tv_smoothed_ses13,
      nperm=1000,
      random = dat_beh_ses13[,"participant_id"],
      perm_type="within_between",
      nthread=4)
    TFCEoutput = TFCE_threshold(model2_TFCE, p=0.05)

    TFCEoutput$cluster_level_results

    ## $`Positive contrast`
    ##   clusid nverts     P     X    Y   Z tstat      region
    ## 1      1     73 0.033 -13.3 27.5 1.3  4.14 L Subiculum
    ##
    ## $`Negative contrasts`
    ## [1] "No significant clusters"

To plot the significant clusters from both models on the CITI168 hippocampal template surface:

    tmaps = rbind(model2_RFT$thresholded_tstat_map, TFCEoutput$thresholded_tstat_map)
    plot_surf(surf_data = tmaps,
              filename = 'FINK_tstatmaps.png',
              title=c('RFT-corrected\nclusters','TFCE-corrected\nclusters'),
              cmap='Reds',
              show.plot.window=TRUE)

## Example 2 follow-up: plotting and post-hoc analyses of hippocampal clusters across regression models

The code below was used in R (v.4.3.3) to plot the cluster-wise values from the RFT and TFCE corrected analyses and validate them with additional mixed linear models.

We produce a figure displaying the thickness of the hippocampal clusters in relation to the group and session variables, in RFT and TFCE models, demonstrating a steeper curve toward group 2:

    #We divide the cluster values by their sum to get the average thickness per vertex
    dat_beh_ses13$clustCTTFCE=(FINK_Tv_smoothed_ses13 %*% TFCEoutput$pos_mask)/sum(TFCEoutput$pos_mask>0)
    dat_beh_ses13$clustRFT=(FINK_Tv_smoothed_ses13 %*% model2_RFT$pos_mask)/sum(model2_RFT$pos_mask>0)

    library(ggplot2)
    library(ggbeeswarm)
    library(cowplot)

    a=ggplot(data=dat_beh_ses13,aes(y=clustCTTFCE,x=as.factor(session), color=as.factor(group)))+
      geom_quasirandom(dodge.width=0.5)+
      geom_line(aes(group=participant_id), alpha=0.2)+
      geom_smooth(aes(group=group), method="lm")+
      labs(y="Mean thickness (mm)", x="session", color="group")+
      guides(colour = "none")+
      ggtitle("Positive cluster\n (TFCE-corrected)")+
      ylim(1.1, 1.55)

    b=ggplot(data=dat_beh_ses13,aes(y=clustRFT,x=as.factor(session), color=as.factor(group)))+
      geom_quasirandom(dodge.width=0.5)+
      geom_line(aes(group=participant_id), alpha=0.2)+
      geom_smooth(aes(group=group), method="lm")+
      labs(y="Mean thickness (mm)", x="session", color="group")+
      ggtitle("Positive cluster\n(RFT-corrected)")+
      scale_color_discrete(name="Group",labels=c("group 1", "group 2"))+
      ylim(1.1, 1.55)

    #to write the image file
    #png(filename="traj.png", res=250, width=1400,height=604)

    plots=plot_grid(a,b, nrow=1,rel_widths=c(0.3,0.40))
    print(plots)

    ## null device
    ##           1

As an additional validation of these results, these significant clusters were extracted as regions-of-interests and fitted in a linear mixed effects model using another R package— lmerTest (Kuznetsova, Brockhoff, and Christensen 2017).

    library(lmerTest)

Linear mixed effect testing the effect of session, group, and session * group interaction on the positive RFT clusters’ average thickness value

    lme.RFT=lmer(clustRFT~session+group+session*group+(1|participant_id),data =dat_beh_ses13 )
    summary(lme.RFT)

    ## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
    ## lmerModLmerTest]
    ## Formula: clustRFT ~ session + group + session * group + (1 | participant_id)
    ##    Data: dat_beh_ses13
    ##
    ## REML criterion at convergence: -317.1
    ##
    ## Scaled residuals:
    ##      Min       1Q   Median       3Q      Max
    ## -2.69862 -0.43221 -0.04002  0.42291  2.57082
    ##
    ## Random effects:
    ##  Groups         Name        Variance Std.Dev.
    ##  participant_id (Intercept) 0.004837 0.06955
    ##  Residual                   0.000236 0.01536
    ## Number of obs: 96, groups:  participant_id, 48
    ##
    ## Fixed effects:
    ##                Estimate Std. Error        df t value Pr(>|t|)
    ## (Intercept)    1.326760   0.010717 54.685962 123.801  < 2e-16 ***
    ## session       -0.003450   0.001580 46.000000  -2.183   0.0342 *
    ## group         -0.006877   0.010717 54.685962  -0.642   0.5237
    ## session:group  0.007645   0.001580 46.000000   4.837 1.51e-05 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ##
    ## Correlation of Fixed Effects:
    ##             (Intr) sessin group
    ## session     -0.295
    ## group       -0.125  0.037
    ## session:grp  0.037 -0.125 -0.295

Linear mixed effect testing the effect of session, group, and session * group interaction on the positive TFCE clusters’ average thickness value

    lme.posTFCE=lmer(clustCTTFCE~session+group+session*group+(1|participant_id),data =dat_beh_ses13 )
    summary(lme.posTFCE)

    ## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
    ## lmerModLmerTest]
    ## Formula: clustCTTFCE ~ session + group + session * group + (1 | participant_id)
    ##    Data: dat_beh_ses13
    ##
    ## REML criterion at convergence: -272.9
    ##
    ## Scaled residuals:
    ##      Min       1Q   Median       3Q      Max
    ## -1.50112 -0.45415 -0.05631  0.49916  1.71410
    ##
    ## Random effects:
    ##  Groups         Name        Variance  Std.Dev.
    ##  participant_id (Intercept) 0.0048047 0.06932
    ##  Residual                   0.0005989 0.02447
    ## Number of obs: 96, groups:  participant_id, 48
    ##
    ## Fixed effects:
    ##                Estimate Std. Error        df t value Pr(>|t|)
    ## (Intercept)    1.134943   0.011549 66.462361  98.275  < 2e-16 ***
    ## session       -0.003589   0.002517 46.000000  -1.426 0.160692
    ## group         -0.009920   0.011549 66.462361  -0.859 0.393452
    ## session:group  0.010234   0.002517 46.000000   4.065 0.000186 ***
    ## ---
    ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    ##
    ## Correlation of Fixed Effects:
    ##             (Intr) sessin group
    ## session     -0.436
    ## group       -0.125  0.054
    ## session:grp  0.054 -0.125 -0.436

## References:

Fink, Andreas, Karl Koschutnig, Thomas Zussner, Corinna M. Perchtold-Stefan, Christian Rominger, Mathias Benedek, and Ilona Papousek. 2021. “A Two-Week Running Intervention Reduces Symptoms Related to Depression and Increases Hippocampal Volume in Young Adults.” Cortex 144 (November): 70–81. https://doi.org/10.1016/j.cortex.2021.08.010.
Kuznetsova, Alexandra, Per B. Brockhoff, and Rune H. B. Christensen. 2017. “lmerTest Package: Tests in Linear Mixed Effects Models.” Journal of Statistical Software 82 (December): 1–26. https://doi.org/10.18637/jss.v082.i13.