# 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 cortical thickness (CT) data from a Hippunfold preprocessing directory of the Fink dataset (Fink et al. 2021).

The demo data (218 MB) required to run the package demos 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=1)
    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 -27.5 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=FALSE)

## 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)

    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)
    dev.off()

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.