## 2 Materials and Methods
### MRI Data Acquisition and Evaluation
#### 2.3.2 Functional MRI Data Acquisition, Processing and Evaluation  
The bh-fMRI data were measured by means of T2*-weighted echo-planar imaging (EPI) sequences with the following parameters: TR = 3000 ms, TE = 36 ms, matrix 96 \(\times\) 96, 3 mm slice thickness, 34 slices in interleaved ascending order, FOV = 245 mm, resolution 2.6 \(\times\) 2.6 \(\times\) 3.0 mm, echo spacing 0.58 ms, TA 6:53 min, 135 measurements.  
The breath-hold task consisted of 60 s of regular breathing, followed by five repetitive cycles, each consisting of 9 s end-expiratory breath-hold periods and 60 s of normal breathing. The respiratory instructions were presented visually by means of a wall-mounted display and a mirror fixed to the head coil. Presentation V20.1 (Neurobehavioral Systems, Berkeley, CA, USA) was used to present the scanner-triggered stimuli.  
The MRI data preprocessing was performed in Statistical Parameter Mapping (SPM12) ([[https://www.Fil.Ion.Ucl.Ac.UK/spm/](https://www.Fil.Ion.Ucl.Ac.UK/spm/)]([https://www.Fil.Ion.Ucl.Ac.UK/spm/](https://www.Fil.Ion.Ucl.Ac.UK/spm/)) URL (accessed on 10 June 2024) running on MATLAB (R2018b (The MathWorks, Inc., Natick, MA, USA; [[http://www.mathworks.com](http://www.mathworks.com)]([http://www.mathworks.com](http://www.mathworks.com)))). The DICOM images were converted to NifTI slice timing corrected to equalize the time of image acquisition, realigned to correct for patients' head movement, normalized to the standard MNI space and segmented with the use of binary masks (vascular territories of the ACA, MCA and cerebellum) [19; 20]. Further processing of the data was performed by using in-house scripts programmed in MATLAB. As the cerebellum represents a region  
Figure 1: Exemplary MRI and [15]Water PET data evaluation of one patient. Each territory of the anterior cerebral artery and the middle cerebral artery (MCA) was evaluated with respect to postischemic FLAIR lesions > 4 mm (**(a)**, see arrow), Ivy sign on axial FLAIR images (**(b)**, see arrows), arterial vessel wall contrast enhancement (**c**) and >50% reduced breath-hold fMRI cerebrovascular reactivity (bh-fMRI CVR) response compared to the cerebellar bh-fMRI CVR response (**(d)**, see the right MCA territory (MCA-r)), as well as at least a severely reduced cerebral perfusion reserve capacity after acetazolamide administration (**(e)**, see right MCA territory).  
where a physiological hemodynamic response is expected in patients with MMA [10; 15; 21], the mean cerebellar signal time course of each of the five repetitive cycles was calculated to verify patients' compliance in performing the breath-hold task. In the case of the incorrect execution of the breath-hold paradigm, individual cycles could be excluded from further evaluation [10; 15; 21; 22]. For a more detailed description, we refer to the study of [PERSON] et al. [10]. Next, the signal time courses of all included breath-hold cycles were averaged and the VOI mean signal time course of the above-mentioned masks was calculated. The relative BOLD signal change was calculated to adjust for variability in the baseline signal intensity of the EPI sequence. The relative reduction [%] (in steps of 10% from 0% to 100% and steal phenomenon) of the BOLD signal peak in comparison to the cerebellar BOLD signal peak was analyzed in the ACA and the MCA territories (see Figure 1). The value with the lower CVR was considered the CVR value for the respective ICA territory.