Processing pipeline details¶

tedana works by decomposing multi-echo BOLD data via PCA and ICA. These components are then analyzed to determine whether they are TE-dependent or -independent. TE-dependent components are classified as BOLD, while TE-independent components are classified as non-BOLD, and are discarded as part of data cleaning.

In tedana, we take the time series from all the collected TEs, combine them, and decompose the resulting data into components that can be classified as BOLD or non-BOLD. This is performed in a series of steps, including:

Principal components analysis
Independent components analysis
Component classification

Multi-echo data¶

Here are the echo-specific time series for a single voxel in an example resting-state scan with 5 echoes.

The values across volumes for this voxel scale with echo time in a predictable manner.

Adaptive mask generation¶

Longer echo times are more susceptible to signal dropout, which means that certain brain regions (e.g., orbitofrontal cortex, temporal poles) will only have good signal for some echoes. In order to avoid using bad signal from affected echoes in calculating $T_{2}^*$ and $S_{0}$ for a given voxel, tedana generates an adaptive mask, where the value for each voxel is the number of echoes with “good” signal. When $T_{2}^*$ and $S_{0}$ are calculated below, each voxel’s values are only calculated from the first $n$ echoes, where $n$ is the value for that voxel in the adaptive mask.

Monoexponential decay model fit¶

The next step is to fit a monoexponential decay model to the data in order to estimate voxel-wise $T_{2}^*$ and $S_0$ .

In order to make it easier to fit the decay model to the data, tedana transforms the data. The BOLD data are transformed as $log(|S|+1)$ , where $S$ is the BOLD signal. The echo times are also multiplied by -1.

_images/04_echo_log_value_distributions.png

A simple line can then be fit to the transformed data with linear regression. For the sake of this introduction, we can assume that the example voxel has good signal in all five echoes (i.e., the adaptive mask has a value of 5 at this voxel), so the line is fit to all available data.

Note

tedana actually performs and uses two sets of $T_{2}^*$ / $S_0$ model fits. In one case, tedana estimates $T_{2}^*$ and $S_0$ for voxels with good signal in at least two echoes. The resulting “limited” $T_{2}^*$ and $S_0$ maps are used throughout most of the pipeline. In the other case, tedana estimates $T_{2}^*$ and $S_0$ for voxels with good data in only one echo as well, but uses the first two echoes for those voxels. The resulting “full” $T_{2}^*$ and $S_0$ maps are used to generate the optimally combined data.

The values of interest for the decay model, $S_0$ and $T_{2}^*$ , are then simple transformations of the line’s intercept ( $B_{0}$ ) and slope ( $B_{1}$ ), respectively:

$S_{0} = e^{B_{0}}$

$T_{2}^{*} = \frac{1}{B_{1}}$

The resulting values can be used to show the fitted monoexponential decay model on the original data.

_images/06_monoexponential_decay_model.png

We can also see where $T_{2}^*$ lands on this curve.

_images/07_monoexponential_decay_model_with_t2.png

Optimal combination¶

Using the $T_{2}^*$ estimates, tedana combines signal across echoes using a weighted average. The echoes are weighted according to the formula

$w_{TE} = TE * e^{\frac{-TE}{T_{2}^*}}$

The weights are then normalized across echoes. For the example voxel, the resulting weights are:

_images/08_optimal_combination_echo_weights.png

The distribution of values for the optimally combined data lands somewhere between the distributions for other echoes.

_images/09_optimal_combination_value_distributions.png

The time series for the optimally combined data also looks like a combination of the other echoes (which it is).

_images/10_optimal_combination_timeseries.png

TEDPCA¶

The next step is to identify and temporarily remove Gaussian (thermal) noise with TE-dependent principal components analysis (PCA). TEDPCA applies PCA to the optimally combined data in order to decompose it into component maps and time series. Here we can see time series for some example components (we don’t really care about the maps):

These components are subjected to component selection, the specifics of which vary according to algorithm.

In the simplest approach, tedana uses Minka’s MLE to estimate the dimensionality of the data, which disregards low-variance components.

A more complicated approach involves applying a decision tree to identify and discard PCA components which, in addition to not explaining much variance, are also not significantly TE-dependent (i.e., have low Kappa) or TE-independent (i.e., have low Rho).

After component selection is performed, the retained components and their associated betas are used to reconstruct the optimally combined data, resulting in a dimensionally reduced (i.e., whitened) version of the dataset.

TEDICA¶

Next, tedana applies TE-dependent independent components analysis (ICA) in order to identify and remove TE-independent (i.e., non-BOLD noise) components. The dimensionally reduced optimally combined data are first subjected to ICA in order to fit a mixing matrix to the whitened data.

Linear regression is used to fit the component time series to each voxel in each echo from the original, echo-specific data. This way, the thermal noise is retained in the data, but is ignored by the TEDICA process. This results in echo- and voxel-specific betas for each of the components.

TE-dependence ( $R_2$ ) and TE-independence ( $S_0$ ) models can then be fit to these betas. These models allow calculation of F-statistics for the $R_2$ and $S_0$ models (referred to as $\kappa$ and $\rho$ , respectively).

_images/14_te_dependence_models_component_0.png

_images/14_te_dependence_models_component_1.png

_images/14_te_dependence_models_component_2.png

A decision tree is applied to $\kappa$ , $\rho$ , and other metrics in order to classify ICA components as TE-dependent (BOLD signal), TE-independent (non-BOLD noise), or neither (to be ignored). The actual decision tree is dependent on the component selection algorithm employed. tedana includes two options: kundu_v2_5 (which uses hardcoded thresholds applied to each of the metrics) and kundu_v3_2 (which trains a classifier to select components).

Removal of spatially diffuse noise (optional)¶

Due to the constraints of ICA, MEICA is able to identify and remove spatially localized noise components, but it cannot identify components that are spread out throughout the whole brain. See Power et al. (2018) for more information about this issue. One of several post-processing strategies may be applied to the ME-DN or ME-HK datasets in order to remove spatially diffuse (ostensibly respiration-related) noise. Methods which have been employed in the past include global signal regression (GSR), T1c-GSR, anatomical CompCor, Go Decomposition (GODEC), and robust PCA.