`permuco4brain`

The threshold-free cluster-enhancement (Smith and Nichols 2009) (or TFCE) is a transformation of the statistical signal or map. After running the test for all voxels (samples \(\times\) channels), the TFCE transforms the observed statistic \(T_i\) for the voxel \(i\) using:

\[ \text{TFCE}(i) = \int_{h=0}^{T_i} e_i(h)^E h^H \text{d} h. \]

The TFCE does an integral over all the thresholds \(h\). The function \(e_i(h)\) is called the *extend* of the cluster created by the threshold \(h\) and represents the number of test/voxel in that cluster. In addition, the parameters \(E\) and \(H\) are set *a priori* and controls the influence of the extend and height on the TFCE. The \(p\)-value for the voxel \(i\) is computed by comparing its \(\text{TFCE}(i)\) with the null distribution of the TFCE. For each permuted signal \(T_i^\ast\), we keep the maximal value over the whole signal \(\max_i\left[\text{TFCE}^*(i) \right]\) for the null distribution of the TFCE.

In `permuco4brain`

, we implement the suggestion from Pernet et al. (2015) and Smith and Nichols (2009) to use \(E<1\). Hence, the default values are \(E = 0.5\) and, for a F statistic, \(H = 1\) and, for a \(t\) statistic, \(H = 2\).

Moreover, by default in `permuco4brain`

, the integral is estimated using `ndh = 500`

steps. More precisely, the maximal over all statistics, ( all samples and all permutations) is equally divided into `ndh = 500`

values for the \(h\)’s. All the default arguments for the TFCE can be changed by adding the arguments `E = ...`

, `H = ...`

or `ndh = ...`

in the `brainperm()`

function.

Finally, the threshold-free cluster-enhancement (Smith and Nichols 2009) (or TFCE) is performed simply by specifying the argument `multcomp = "tfce`

in the `brainperm()`

. However, the TFCE uses more computational resources than the default cluster-mass test (Maris and Oostenveld 2007) and it must be consider before running the function.

First, we activate the package `permuco4brain`

and `future`

(Bengtsson 2020)

Following the vignette, you may have saved the data (`signal`

: a 3D array, `graph`

: an `igraph`

defining the adjacency of the channel and design: a `data.frame`

). We load it using:

`load("signal_design_graph.RData")`

Using `future`

for parallelization, we set \(2000\)M RAM per workers by changing the options:

`options(future.globals.maxSize = 2000 * 1024^2)`

This value should mainly depends on the number of tests/voxels (here \(64\) channels \(\times\) \(411\) times-points \(26304\)) and the number of steps in the approximation of the integral (here \(500\)). Moreover, the RAM per worker \(\times\) the number of worker should not exceed the total RAM of your computer.

Using the `plan()`

function, we parallelize the computation using 6 `workers`

and run the TFCE by simply specifying `multcomp = "tfce"`

.

```
plan(multisession, workers = 6)
tfce <- brainperm(signal ~ action*stimuli*mvpa_c + Error(participant/(action*stimuli)),
data = design, graph = graph, multcomp = "tfce")
```

It should run for 30-40 minutes per effect. Using this formula, there is a total of 7 effects including 3 main effects, 3 double interactions and 1 triple interaction.

Similarly to the cluster-mass test, we produce a heat-map using the `image()`

function:

`image(tfce, effect = 2)`

Or showing the results distributed in space:

And, we extract the results for all effects, all time-points, all channels, using the `summary()`

function.

`tfce_full_table <- summary(tfce, table_type = "full")`

Finally, the vignette `Figure using ggplot2`

shows more examples for figures that can be customize for publication.

Bengtsson, Henrik. 2020. *A Unifying Framework for Parallel and Distributed Processing in R Using Futures*. https://arxiv.org/abs/2008.00553.

Maris, Eric, and Robert Oostenveld. 2007. “Nonparametric Statistical Testing of EEG- and MEG-Data.” *Journal of Neuroscience Methods* 164 (1): 177–90. https://doi.org/10.1016/j.jneumeth.2007.03.024.

Pernet, C. R., M. Latinus, T. E. Nichols, and G. A. Rousselet. 2015. “Cluster-Based Computational Methods for Mass Univariate Analyses of Event-Related Brain Potentials/Fields: A Simulation Study.” *Journal of Neuroscience Methods* 250: 85–93. https://doi.org/10.1016/j.jneumeth.2014.08.003.

Smith, S, and T Nichols. 2009. “Threshold-Free Cluster Enhancement: Addressing Problems of Smoothing, Threshold Dependence and Localisation in Cluster Inference.” *NeuroImage* 44 (1): 83–98. https://doi.org/10.1016/j.neuroimage.2008.03.061.