#### Theory

Spatial normalisation expands and contracts some brain regions. Modulation involves scaling by the amount of contraction, so that the total amount of grey matter in the modulated GM remains the same as it would be in the original images.

This step is recommended if you are more interested in volume changes than differences in concentration (or density). Nevertheless, this post-processing step is optional and you can try both, with and without modulation to test your hypothesis. The use of this step depends on your data and what are you interested in. If you decide to use modulation both images will be saved: non-modulated and modulated images (indicated by a leading “m” or “m0” for non-linear terms only).

#### Interpretation

If we follow the commonly used terms “volume” for modulated data and “density” (or concentration) for unmodulated data and concentrate on GM there are many possible ways to correct or not correct for different brain size:

**No modulation:**

Correction |
Interpretation |

nothing | relative density |

globals | “localised” relative density after correcting for total GM or TIV (multiplicative effects) |

AnCova | “localised” relative density that can not be explained by total GM or TIV (additive effects) |

**Modulation:**

Correction |
Interpretation |

nothing | absolute volume |

globals | relative volume after correcting for total GM or TIV (multiplicative effects) |

AnCova | relative volume that can not be explained by total GM or TIV (additive effects) |

Total intracranial volume (TIV) can be approximated by calculating the sum of GM and WM, although sometimes additionally CSF is used or manually derived TIV values are used.

#### Optional modulation of non-linear effects only (VBM5.1)

These many options are confusing and it is difficult to find the best way which fits to your hypothesis. Thus, I have tried to find an easier solution which might be appropriate for most hypotheses. Modulated images can be optionally saved by correcting for non-linear warping only. Volume changes due to affine normalisation will be not considered and this equals the use of default modulation and globally scaling data according to the inverse scaling factor due to affine normalisation. I recommend this option if your hypothesis is about effects of relative volumes which are corrected for different brain sizes. This is a widely used hypothesis and should fit to most data. The idea behind this option is that scaling of affine normalisation is indeed a multiplicative (gain) effect and we rather apply this correction to our data and not to our statistical model. These modulated images are indicated by “m0” instead of “m” using the VBM5.1 toolbox. If you decide for this option there is no further need to correct for different brain size in the statistical model.

**Modulation of non-linear effects only:**

Correction |
Interpretation |

nothing | relative volume after correcting for different brain size |

#### Impact on smoothness

Another issue to consider is that modulation will additionally smooth your images and the resulting smoothness will be therefore increased. Hence, it is recommend to use a lower FWHM to smooth your modulated images. As rule of thumb: if you have used the default cutoff for spatial normalization (25 mm) you should lower the FWHM to around 70-80% for SPM2. For example, if you have smoothed non-modulated images with FWHM of 12 mm you can smooth modulated images with 8-9 mm to obtain approximately the same resulting smoothness.

The normalization in SPM5 is of much higher accuracy because a canonical registration of the GM/WM/CSF segmentations is iteratively used. In this case the increase of the smoothness for modulated images is smaller and you should lower the FWHM to around 80-90%.

#### Illustration