**11. Quantitative Maps**

Broadly speaking, MR contrasts are driven by how much T1 or T2 signal contributes to the image. These T1w or T2w images are qualitative in nature and fail to accurately assess tissue parameters such as recovery or relaxation time. However, certain sequences allow for parametric mapping (quantitative MRI or qMRI), where the intensities within each pixel are proportional to the T1 or T2. These values can be used to quantify intrinsic, biologically meaningful tissue information [202]. Additionally, qMRI allows for direct comparison across time, across subjects, and across scanners or sites, which is essential for the development of neuroscientific research and its application to the clinical situation [203]. Moreover, quantitative measures can aid identification and visualization of target structures with an objective approach and can minimize human error resulting from subjective interpretation. qMRI can only be made from specific sequences that comply with the principles of di fferential weightings, which incorporate an inversion or saturation recovery parameter with multiple inversion times or spoiled gradient echo sequences with variable flip angles [204]. However, in our experience, quantitative sequences at 3 T take at least twice as long as weighted MRI sequences used in clinical settings.

As mentioned, quantitative maps are used to index anatomical composition. For instance, the observed relaxation of T1 is extremely fast in myelinated white matter. The inverse of longitudinal relaxation rates, known as R1 [205], is thought to be linearly related to myelin concentrations [206,207]. T1 maps have been utilized clinically, for example, with quantifying perfusion; imaging hemorrhages and infarctions; evaluating contrast uptake; monitoring of tumors, gliosis, and multiple sclerosis

lesions [205,208,209]. Quantitative T1 maps will usually require post-processing, most commonly achieved with the look-up table method, which functions to relate pixelwise T1 values within the native map with predefined and validated intensity values [159]. The automated creation of these T1 parametric maps can be built into the sequence at a cost of both time and capacity. Further post-processing is often required and relies on expertise that is again typically not available within a standard clinical setting [160,210].

For DBS of the STN, T2\* maps can be used to improve visualization of the STN because iron content causes the T2\* relaxation time to shorten, which for the STN at 7 T is around 15 ms [61,211]. A frequently used method to create T2\* maps is done by fitting an exponential decay curve to the signal intensities per pixel from each of the multiple echoes obtained from a GRE sequence [212]. Moreover, the pixel intensities of reciprocal T2\* maps (R2\*) are proportional to iron load, with STN R2\* values hovering around 67 s<sup>−</sup><sup>1</sup> (1/15 ms) at 7 T [155,213–216]. Alternatively, T2\* images can be post-processed to create quantitative susceptibility maps (QSM), which quantify a tissue's magnetic susceptibility distribution on the basis of its perturbation of the magnetic field [213]. They are similar to SWI in that they are made from the separate magnitude and phase images of a GRE sequence, but they comprise multiple echoes and allow for quantitative measures rather than weightings. QSM requires initial phase unwrapping, background field extraction, and calculation of locally generated phase o ffsets, which refer to the fact that the phase of a single voxel can be expressed as either positive of negative, depending on its orientation relative to the magnetic field [214]. These phase-o ffsets are then deconvolved, typically with a dipole kernel, from which the underlying tissue susceptibility can be extracted per voxel, independently of surrounding voxels [215]. Moreover, QSMs are preferred over SWI, as SWI is limited by the non-local orientation-dependent e ffects of phase, which means that the same tissues can appear with di fferent intensities on the basis of their location, whereas QSM solves this problem by convolving dipole fields [216,217]. Background removal methods based on principles of sophisticated harmonic artifact reduction for phase data (SHARP, also known as spherical mean value (SMV) filtering) and projection onto dipole fields (PDF) are commonly employed. SHARP is based on a theory similar to shimming, in that static magnetic fields and the corresponding phase maps are represented by harmonic functions. In regions of inhomogeneous susceptibility, the field will be non-harmonic, and background fields that are harmonic are eliminated from the phase data by subtraction [213,218]. The PDF method removes background fields by comparing the magnetic fields of dipoles inside a region of interest with those directly outside [219,220]. Alternatively, Laplacian boundary values can be used, which are based on a finite di fference scheme [221]. However, quantifying an arbitrary distribution of susceptibility from the phase signal is challenging and poses an inverse problem whereby e ffects are first calculated from which parameters or causes are then determined, resulting in a noise amplification of the ensuing signal. The inversion problem can be solved with calculation of susceptibility through multiple orientation sampling (COSMOS). However, this method requires the acquisition of multiple head orientations, which is time-consuming and impractical for clinical use [222,223]. Morphology-enabled dipole inversion, or MEDI, will match the boundaries of each dipole with those observed in the T2\*-weighted magnitude images [222]. Quantitative susceptibility and residual mapping (QUASAR) accounts for biophysical frequency contributions, which acknowledges that the notion that the local Larmor frequency is a ffected by the static field perturbations related to tissue susceptibility, as well as the magnetic field, chemical shifts, directional alignment of axons, and energy exchange between water and macromolecules [224]. Alternatively, some algorithms solve the entire equation within a single step by incorporating SHARP principles with simultaneous total generalized variation (TGV)-regularized dipole inversion [225,226]. Similarly phase removal using the Laplacian operator (HARPERELLA) simultaneously combines phase unwrapping and background removal [227]. These methods comprise tool boxes that are largely available in Matlab or Python (see [228] and the references therein).

The clinical potential of QSM lies in its sensitivity to variations in iron stored in ferritin and hemosiderin, lipids and calcium, levels of di fferential oxygenation-saturation present in venous blood, and identification of sub millimeter white matter microstructure [229–231]. Further, QSM has been shown to be superior to T2\* in parcellations of the STN, which could translate into better visualization and targeting for DBS [223,228,232]. T2 relaxometry has been shown to predict motor outcome in some PD patients with STN DBS, where patients who have low T2 values may fail to show a clinical benefit [233]. It is possible that this can be explained by the fact that patients with low T2 relaxometry will have less contrast between the STN and the surrounding tissue, hindering the accurate visualization and targeting of the structure, which could be solved by employing QSM. However, QSM obtained during a scanning session is still experimental and under development. Further, there are many competing post-processing methods for creating QSM images, which makes translation challenging.

### **12. Complications Unrelated to Pre-Operative Planning**

Lastly, we would like to mention that while this paper specifically refers to suboptimal placement of DBS leads due to the limitations of neuroimaging, negative outcomes of DBS application can arise independently of planning procedures and surgical expertise. For example, neurosurgery has been linked to brain deformation and shift, changes in cerebral spinal fluid volume, and intracranial pressure, which may induce spatial variability both during the surgery and cause a shift in the implanted lead location during recovery [27,234]. Similarly, DBS surgeries are associated with infection (mostly found in the chest and connector) [235]; reactive gliosis and gliotic scarring [236]; hemorrhage either during the surgery or delayed (in less than 5%) [237]; and, although rare, cerebral pneumocephalus [238]. In all these cases, the DBS system may require reimplantation, replacement, or removal.
