Integrated intravoxel incoherent motion tensor and diffusion tensor brain MRI in a single fast acquisition

The acquisition of intravoxel incoherent motion (IVIM) data and diffusion tensor imaging (DTI) data from the brain can be integrated into a single measurement, which offers the possibility to determine orientation‐dependent (tensorial) perfusion parameters in addition to established IVIM and DTI parameters. The purpose of this study was to evaluate the feasibility of such a protocol with a clinically feasible scan time below 6 min and to use a model‐selection approach to find a set of DTI and IVIM tensor parameters that most adequately describes the acquired data. Diffusion‐weighted images of the brain were acquired at 3 T in 20 elderly participants with cerebral small vessel disease using a multiband echoplanar imaging sequence with 15 b‐values between 0 and 1000 s/mm2 and six non‐collinear diffusion gradient directions for each b‐value. Seven different IVIM‐diffusion models with 4 to 14 parameters were implemented, which modeled diffusion and pseudo‐diffusion as scalar or tensor quantities. The models were compared with respect to their fitting performance based on the goodness of fit (sum of squared fit residuals, chi2) and their Akaike weights (calculated from the corrected Akaike information criterion). Lowest chi2 values were found using the model with the largest number of model parameters. However, significantly highest Akaike weights indicating the most appropriate models for the acquired data were found with a nine‐parameter IVIM–DTI model (with isotropic perfusion modeling) in normal‐appearing white matter (NAWM), and with an 11‐parameter model (IVIM–DTI with additional pseudo‐diffusion anisotropy) in white matter with hyperintensities (WMH) and in gray matter (GM). The latter model allowed for the additional calculation of the fractional anisotropy of the pseudo‐diffusion tensor (with a median value of 0.45 in NAWM, 0.23 in WMH, and 0.36 in GM), which is not accessible with the usually performed IVIM acquisitions based on three orthogonal diffusion‐gradient directions.


| INTRODUCTION
Diffusion-weighted MRI is a well established imaging technique that is sensitive to incoherent motion of spins caused by their thermal energy ("Brownian motion") and, in vivo, also to incoherent motion caused by pseudo-random flow. 1,2 A particularly important variant of diffusionweighted MRI in the brain is diffusion tensor imaging (DTI), which can quantify the mobility of water molecules along different spatial orientations, thus detecting the geometry and integrity of white-matter fiber bundles. 3,4 DTI requires the acquisition of a number of diffusion-weighted images (at least six, but frequently many more) with different spatial diffusion-gradient orientations. 5,6 Typically, for the brain parenchyma, intermediate to high diffusion weightings (b ≳ 1000 s/mm 2 ) are used. The diffusion tensor calculated from these data is a symmetric 3 Â 3 matrix with six independent entries that describe the orientation-dependent diffusion properties.
A different, emerging application of diffusion-weighted MRI exploits the aforementioned sensitivity of the diffusion-weighted signal to pseudo-random microscopic flow ("pseudo-diffusion"), which is mainly associated with capillary blood flow (i.e., perfusion), but can also be caused by other physiological processes. 7 This contrast mechanism is today referred to as the intravoxel incoherent motion (IVIM) effect. The IVIM contrast has been used in recent years for an increasing number of applications, predominantly in oncological studies. [8][9][10] IVIM MRI is based on the acquisition of additional diffusion-weighted images at relatively low b-values (between 0 and about 200 s/mm 2 ) to capture the comparably fast pseudo-diffusion of circulating blood water. 11,12 Typically, any orientation dependence is removed by averaging the signal over three orthogonal orientations, i.e., by acquiring so-called trace images. The different diffusion components can be determined using a biexponential model function for IVIM data analysis, from which two additional parameters (perfusion volume fraction, f, and pseudo-diffusion coefficient, D*) are calculated, complementing the conventional diffusion coefficient (parenchymal diffusivity of water, D). 1 Since bi-exponential analysis is generally very sensitive to noise, 13 multiple repetitions of these acquisitions are typically averaged to obtain sufficiently large signal-to-noise ratios and parameter fitting is frequently performed in a two-step approach. 14 Typically, diffusion-weighted MRI protocols are optimized for a single application, either to distinguish the small IVIM effect from the parenchymal diffusion signal or to quantify the anisotropic properties of parenchymal diffusion with DTI. However, it is also possible (but rarely done) to combine IVIM and DTI acquisitions, which requires the acquisition of multiple different b-values (including several low b-values) each acquired with at least six non-collinear diffusion-gradient orientations. Only such a dataset allows for a combined IVIM tensor/diffusion tensor evaluation, which can take into account orientation dependence not only in the conventional DTI analysis, but also in the (now tensor-aware) IVIM analysis. [15][16][17] The latter strategy allows for a multitude of different signal models, in which, e.g., the pseudo-diffusion coefficient can be described as a tensor resulting in a large number of free model parameters (e.g., 14 parameters for two tensors, the perfusion fraction, and the signal scaling). It depends on the underlying microstructure and physiology of the tissue, but also on the signal-to-noise ratio of the acquired data if fitting such a large number of parameters is feasible and results in biologically meaningful parameter maps.
A cerebral pathology that appears highly suitable for the evaluation of the combined IVIM-DTI analysis is cerebral small vessel disease (cSVD). 18,19 cSVD is characterized by alterations in brain parenchyma such as white matter with hyperintensities (WMH), lacunes, and microbleeds. [20][21][22] An increasing number of studies suggest that chronic cerebral hypoperfusion is involved in the etiology of cSVD, 23-26 while evidence from DTI-based studies demonstrates loss of microstructural integrity of the WM in cSVD. 27 Therefore, cSVD can serve as a suitable disorder for the simultaneous assessment of perfusion and diffusion changes by an integrated IVIM-DTI acquisition. Previous studies using scalar IVIM models have already shown distinct pathophysiological effects in patients with cSVD and neurodegenerative Alzheimer's disease. 28,29 The purpose of this study was to evaluate such an integrated IVIM-DTI acquisition of the brain with a clinically feasible scan time below 6 min and to use a model-selection approach to find a set of DTI and IVIM tensor parameters that most adequately describes the acquired data.  30,31 IVIM data (n = 231) were available in the follow-up scans in 2020. To evaluate the potential of an integrated IVIM-DTI acquisition in normal-appearing tissue and in microstructural abnormalities, we randomly selected 20 participants with a wide range of WMH burden (median [interquartile range] 20.29 mL [14.70 mL, 30.40 mL], range 0.75-66.9 mL). The mean age was 77.0 years (standard deviation 7.96 years), and 13 participants (65%) were males. The Arnhem-Nijmegen Region Medical Review Ethics Committee approved the study and all participants provided written informed consent.

| Data processing and segmentation
MP2RAGE images were post-processed to obtain high-contrast 3D T 1 -weighted (so-called regularized UNI) images exhibiting the best compromise between a significant decrease in noise levels in regions of low or no signal (near air or skull) and a small increase in image intensity bias 35 using freely available code (https://github.com/JosePMarques/MP2RAGE-related-scripts). WMH was segmented from coregistered and bias-corrected T 1 -weighted and FLAIR images by using a variant of the 3D U-net deep learning algorithm. 36 All WMH segmentations were then manually edited and cleaned from misclassified artifacts using a custom 3D editing tool written in MATLAB (R2018a, MathWorks, Natick, MA, USA).
Gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF) probability maps were segmented from T 1 -weighted images using SPM12 (http://www.fil.ion.ucl.ac.uk/spm/). Additionally, we used manually corrected WMH masks to refine the initial, automatically segmented probability maps 21 and to obtain normal-appearing white matter (NAWM) masks (by removing the WMH voxels from the original WM mask). To restrict the subsequent analysis to the cerebrum, we excluded the cerebellum and brain stem from all masks. This was done by, first, calculating cerebellum and brain stem masks with Sequence Adaptive Multimodal Segmentation (SAMSEG) 37 and then removing all cerebellum and brain stem voxels from the GM, WM, and CSF probability maps. Finally, we registered the obtained GM, WM, and CSF probability maps into IVIM space using ANTs 38 and minimized the influence of partial-volume effects by choosing only voxels for each mask with tissue probabilities greater than 0.99. Examples of the resulting masks for one participant are shown in Figure 1.
IVIM-DTI data were pre-processed before further evaluation with a standard pipeline including MRtrix dwidenoise, MRtrix mrdegibbs, 39 and FSL TOPUP distortion correction, 40 as well as eddy-current and motion correction (FSL eddy_correct). 41

| IVIM and DTI evaluation
For model comparison and quantitative evaluation, we considered seven different IVIM-DTI models with varying numbers of free parameters that can all be considered as special cases of the following, most general model used in our study: This model is based on a symmetric 3 Â 3 diffusion tensor, D (in equations, vectors and tensors are denoted by bold letters), describing anisotropic parenchymal water diffusion, a symmetric 3 Â 3 pseudo-diffusion tensor, D*, describing anisotropic capillary flow, and a scalar perfusion signal fraction, f. Each of the tensors has six free parameters (D xx , D yy , D zz , D xy , D xz , D yz ; D xx *, D yy *, D zz *, D xy *, D xz *, D yz *), so together with the signal scaling, S 0 , and the perfusion fraction, f, this model has p = 14 free fit parameters. When naming specific models, we denote the above-mentioned tensors by "D 6 " and "D 6 *" to differentiate from the scalar parameters "D" and "D*". So, the model in Equation (1) is referred to as "D 6 *-f-D 6 " (p = 14). In contrast, the usually used (scalar) IVIM model 1 has p = 4 parameters and is denoted by "D*-f-D". The standard (non-IVIM) DTI model with p = 7 parameters is denoted by "D 6 " (p = 7). All investigated tensor models (i.e., all models except D*-f-D, Equation 2) included a tensor description (D 6 ) of the parenchymal diffusion, as the pertaining signal decay is much stronger than for the IVIM part.
The simplest combination of D*-f-D and D 6 is the IVIM model D*-f-D 6 with scalar IVIM parameters, D* and f, and a diffusion tensor, D, resulting in p = 9 free parameters, given by All other evaluated models were derived from Equation (1) by restricting the tensorial properties of D* to reduce the number of IVIM parameters from six (full tensor, D*), while retaining the seven parameters of S 0 and D. This approach was motivated by the higher robustness of the measured diffusion-tensor parameters compared with pseudo-diffusion tensor components, and is independent of any biological assumptions about the underlying tissue structure.
The strongest applied restriction of the general 14-parameter model D 6 *-f-D 6 is to assume that D* is a tensor proportional to the D tensor, thus having the same anisotropy and orientation as D. Hence, instead of fitting D* based on six free parameters as in Equation (1), it can be defined as a scaled normalized D tensor. To do this, we first determine the normalized D tensor with trace 3: D with the scalar scaling factors D*. This perfusion-signal model is denoted "D 6 *s" (letter "s" for "scaled") and can be integrated into the IVIM model D*-f-D 6 , yielding "D 6 *s-f-D 6 ". This model has p = 9 parameters (the same number of parameters as the D*-f-D 6 model with isotropic IVIM properties).
In a next step, to allow for different degrees of anisotropy, D* can be defined as a linear combination of a normalized isotropic tensor, 1, and the normalized tensor b D from above. The weighting of these two components is given by the "anisotropy" coefficients (1 À a) and a: if D* is , the anisotropy of D* can be varied by a, between 0 (for a = 0) and the anisotropy of D (for a = 1). We denote this perfusion-signal model by "D 6 *a" (the letter "a" indicating the anisotropy parameter) and define the model "D 6 *a-f-D 6 " with 10 free parameters.
F I G U R E 1 Brain segmentations determined from tissue probability maps: from left to right, b 0 images, NAWM region (yellow), WMH region (magenta), GM region (cyan), and CSF region (green). To minimize partial-volume effects, the threshold for tissue selection was set to a probability of 99%, which mostly excluded voxels with contributions from more than one tissue (and resulted in relatively sparse voxel masks).
Finally, as a last modeling approach with complexity between D 6 *a on the one hand and the full D 6 * model on the other hand, it is possible to allow for arbitrary tensor eigenvalues, while keeping the eigenvectors fixed as taken from the diffusion tensor, D. These models can exhibit arbitrary anisotropy values and tensor shapes (e.g., cylindrical or flat), but the spatial orientation of the tensor ellipsoid is the same as the one of the D tensor in each voxel. Mathematically, this model can be described using the (orthogonal) eigenvector matrix E and the diagonal eigenvalue matrix Δ = diag(λ 1 ,λ 2 ,λ 3 ) of the diffusion tensor D, which can, thus, be expressed as D = EΔE T . We can now define D* = E diag(D 1 *,D 2 *,D 3 *)E T with three independent eigenvalues but the same eigenvectors as D. We denote this perfusion-signal model by "D 6 *e" (with the letter "e" for eigenvalues) and define the model "D 6 *e-f-D 6 " with 11 free parameters. An overview over all seven models is presented in Table 1; only the last model in this table allows for fully independent IVIM tensor orientations. (10 more IVIM-DTI models that allow for a tensor-valued perfusion fraction f are presented and evaluated in Supporting Information 3.) For all models with pseudo-diffusion parameters (i.e., all models except D 6 ), step-wise ("segmented") fitting was used. 14  Non-linear data fitting (monoexponential model and tensor models) was performed with the non-linear least-squares fit routine "kmpfit" from the Kapteyn package, Version 3.0. 42 The signal models were implemented in Python 3.7.

| Model comparison and statistical analysis
The fitting performances of the seven different IVIM-DTI signal models (S m ,m ¼ 1…7) listed above were compared using the residual sum of squared fit errors (chi 2 ).
where S n are the measured signal intensities for all N = 90 b-values and gradient directions, and S 0,mean is the (voxelwise) mean value of the signal over the six b = 0 s/mm 2 measurements (the model parameter S 0 from Equation (1) is still fitted and not assumed to be exactly S 0 = 1). Then the (corrected) Akaike information criterion (for a model with p parameters) was evaluated for each voxel. [43][44][45] For each participant, the median values of chi 2 and the AICc were calculated separately for voxels of NAWM, WMH, and GM. Median values were used because of the asymmetric (non-normal) statistical distribution of chi 2 and AICc values. From these individual median values, the corresponding Akaike weights w(m) were calculated as

| Quantitative IVIM-DTI evaluation
Using the AICc-optimal IVIM-DTI models (models with the highest Akaike weights), the quantitative fit parameters (e.g., trace of the diffusion   The models D*-f-D 6 (p = 9) and D 6 *e-f-D 6 (p = 11), favored by the Akaike criterion, were then used to derive quantitative diffusion and perfusion (IVIM) parameters from all 20 participants and to compare these results with parameters from the traditional non-tensor IVIM analysis (D*-f-D) with p = 4 free parameters. The results are summarized as boxplots in Figure 5; the corresponding median values and interquartile ranges are given in Table 2. These three models provided highly consistent diffusion coefficients of approximately 0.75 Â 10 À3 mm 2 /s in NAWM,

| DISCUSSION
In this study, we have demonstrated that data from a single time-efficient integrated IVIM-DTI measurement with a cubic voxel size of 2 Â 2 Â 2 mm 3 and a scan time below 6 min was most adequately described (in terms of the AICc) by extended IVIM models with a tensor description of parenchymal diffusion. As expected, it was shown that such a model with a tensor description of the parenchymal diffusion describes the diffusion decay curves substantially better than tensor-free (scalar) models. In addition, models that allow for carefully restricted pseudo-diffusion (D* tensor) anisotropy were most adequate in WMH and GM. A more general IVIM model with a full pseudo-diffusion tensor was disfavored by the AICc analysis. These results were obtained from an integrated IVIM-DTI brain MRI protocol with 15 b-values and six diffusion directions for each b-value and comparative computational analyses of, in total, seven different IVIM-DTI models with varying tensor contributions to the IVIM component.   While it is well known that anisotropic diffusion tensors are required to adequately capture water diffusion in the brain, the relevance of tensor-aware IVIM models in the brain (or in most other biological tissues) is less clear. Only a few studies have demonstrated evidence for anisotropic blood flow properties (e.g., in the renal medulla 15,16 or in the liver 7 ), and first preliminary evaluations have been published for the human brain. 17,47 A major challenge in the combined evaluation of conventional diffusion tensors and IVIM-related tensors is the large number of free parameters that must be fitted by such models. Each tensor has six free parameters, so combining a conventional tensor, D, and a pseudo-diffusion tensor, D*, requires the fit of 12 tensor parameters plus a weighting factor (namely, the perfusion fraction f ). Allowing both the pseudo-diffusion coefficient and the perfusion fraction to be described by tensors as proposed by some authors 16,47 would increase this to 18 free tensor parameters (cf. Supporting Information 3 for the evaluation of models with perfusion fraction tensor). In contrast to established two-tensor (or multi-tensor) models that are commonly used to resolve WM fiber crossings, 48 the calculation of additional tensors from the IVIM signal at low b-values is compromised by the inherent general difficulty of biexponential (or multiexponential) fitting in the presence of noise, 13 and by the fact that the IVIM signal effect is relatively small compared with the contribution of the parenchymal diffusion signal. Thus, it is necessary to verify carefully and quantitatively whether the improved fit of IVIM-DTI models with more free parameters can really be attributed to a model that better describes the data, or is only due to noise (over-)fitting.
The expected behavior is that models with more fit parameters show improved goodness of fit, i.e., a reduced sum of squared fit errors (chi 2 ). This is reflected by our results, which exhibit the smallest chi 2 values (median over all GM or WM voxels) with the most extensive model, (Figure 2), which has p = 14 free parameters, followed by the model D 6 *e-f-D 6 with p = 11 free parameters. However, the large number of free parameters can result in problems related to overfitting.
The AICc and the derived Akaike weight compensate for the overfitting effect seen with models with many fit parameters and are established metrics to decide if a model really fits better or not. 44 By balancing the goodness of fit (chi 2 ) and the number of free parameters (p), the highest F I G U R E 6 FA(D) and FA(D*) in NAWM, WMH, and GM obtained with the (optimal) model D 6 *e-f-D 6 . The boxplots show the statistical distribution over 20 participants using the individual median values in each brain region.
Akaike weight points to the most adequate model (which, of course, may be different for different tissues or different voxels). In our results, the significantly highest Akaike weights were found for the nine-parameter model D*-f-D 6 in NAWM and for the 11-parameter model D 6 *e-f-D 6 in WMH and GM (Figure 3). These are biexponential models with a diffusion tensor describing the restricted water diffusion at high b-values (between about 400 and 1000 s/mm 2 ) and IVIM components describing fast pseudo-diffusion at low b-values (below 400 s/mm 2 ). This IVIM part is modeled with two scalar parameters in the nine-parameter model D*-f-D 6 , but tensorial in the 11-parameter model D 6 *e-f-D 6 . The latter model uses the same eigenvectors for water diffusion (D 6 ) and pseudo-diffusion (D 6 *), but allows fitting of three optimal eigenvalues for pseudodiffusion. Thus, the principal axes of the pseudo-diffusion ellipsoid are the same as for tissue diffusion, but the shape and thus anisotropy of this F I G U R E 7 FA(D*) maps (Rows 1 and 4) with corresponding FA(D) maps (Rows 2 and 5) and diffusivity maps (Rows 3 and 6) from two representative participants (A, 77 years old, male; B, 70 years old, male). Shown are four slices (from left to right) of each map; the CSF region has been set to 0. All maps were calculated with the (GM and WMH optimal) model D 6 *e-f-D 6 . Areas with hyperintense lesions and low FA(D*) are indicated by arrows, areas with smoothly distributed FA(D*) values by arrow heads. (Additional data pre-processing only for this visualization: to increase the SNR and obtain smoother visualizations, the diffusion-weighted signal of each voxel was replaced by the mean value of an approximately spherical region around this voxel consisting of a total of 19 voxels (a 3 Â 3 Â 3 cube without the eight corner voxels); only voxels belonging to the same tissue mask were averaged.) ellipsoid can be different, which allows for the calculation of the FA of the pseudo-diffusion tensor as a perfusion-related parameter in addition to the magnitude of pseudo-diffusion (D*). In other words, with the imaging data obtained by the current fast scan protocol we found no evidence for independent orientations of the parenchymal diffusion and the pseudo-diffusion due to the blood microcirculation. This missing evidence, however, is of course no proof or indication that diffusion and pseudo-diffusion tensors are oriented along the same axis. Longer protocols with higher signal-to-noise ratio and/or increased angular resolution might be required to resolve information of the spatial orientation of the blood microcirculation that is independent of the fiber orientation. Generally, very complex models with fully tensorial perfusion properties of the pseudo-diffusion (such as D 6 *-f-D 6 ) can consistently improve the chi 2 values, but not as much as would be required to clearly favor these models in terms of the AICc and Akaike weight.
All models were fitted in a step-wise ("segmented") approach, which required the definition of a threshold b-value b segm to differentiate the fast pseudo-diffusion regime from the slow tissue diffusion regime. The threshold was set to the relatively high value of b segm = 400 s/mm 2 in this study, since the pseudo-diffusion coefficients were rather low with values around 5 Â 10 À3 mm 2  The quantitative evaluation based on the optimal model yielded results ( healthy control group is required to analyze potential regional variations in patients relative to controls. The This study has some limitations. First, many more IVIM-DTI models could be considered for data analysis (e.g., using four-parameter instead of six-parameter tensors 55 ). In addition, we restricted IVIM fitting to a simple step-wise ("segmented") algorithm with a fixed threshold to differentiate between slow and fast diffusion components. Other approaches such as Bayesian fitting, full bi-exponential fitting, or deep-learning-based fitting [56][57][58] are available but are beyond the scope of this work. Furthermore, extensions of scalar models have also successfully been applied, in which the faster diffusion regime (i.e. lower b-values) is modeled by two (spectral) diffusion components in patients with cerebrovascular pathology, one for the blood microcirculation and one component thought to represent interstitial fluid. 29,59 Second, our model-selection results must be expected to depend strongly on the data quality, i.e. in particular on the signal-to-noise ratio and number of b-values and diffusion-gradient directions. With substantially higher SNR, more parameters (as in the D 6 *-f-D 6 model) might be accurately measurable; however, this would require much longer scan durations. The publications by Finkenstaedt et al. and Mozumder et al. 17,47 used substantially longer IVIM-DTI protocols with scan times of about 30 min to assess tensor properties of the pseudo-diffusion and of the perfusion fraction in the brain. They presented promising results, but did not perform any model selection analysis with statistical methods such as the Akaike or the Bayesian information criterion. In the present study, we used a protocol with a clinically feasible scan duration of 5 min 21 s. This had the advantage that scans could be performed in a large cohort of participants with clinically relevant pathologies. Any potential overfitting of our data with models with too many degrees of freedom was controlled by strict model selection based on the AICc. With respect to the available signal-to-noise ratio, it should also be noted that our protocol acquired relatively thin slices with cubic 2 Â 2 Â 2 mm 3 voxels, which is typical for DTI applications, while many (scalar) IVIM protocols acquire much thicker slices resulting in higher SNR, but anisotropic voxel dimensions and more severe partial volume effects.
Third, one could argue that a region-based, in contrast to a voxel-based, approach would be more adequate to tackle the relatively low signalto-noise ratio due to the small perfusion signal effect in the IVIM models. However, as the investigated patients displayed regional brain tissue inhomogeneities, for instance WMH, and region-based approaches generally average over a distribution of different tensor orientations, we feel that the voxel-based approach is well justified.
Finally, considering the quantitative IVIM and diffusion parameters obtained, we acknowledge that these values may be influenced by the presence of cSVD in the participants and are not necessarily identical to parameters in younger or age-matched healthy controls. However, analyzing data from this cohort had the advantage that the clinical feasibility of the acquisition protocol and influence of, e.g., motion artifacts are more realistically represented than in young healthy controls. By establishing the method in the target population, not in healthy volunteers, we ensure applicability for clinical use.
Currently, there is no effective treatment for cSVD and its progression over time is hard to predict. Clinical progress in this field relies on better understanding of the pathophysiological mechanisms underlying this disease. The clinical value of establishing such complex mathematical models for MRI in patients with cSVD is that we can capture both abnormalities of the parenchyma and blood microcirculation within one time-efficient MRI scan, and describe microstructural tissue and blood circulation parameters in a physiological/physical and quantitative way, more accurately than with purely scalar models. This is relevant from a logistic point of view, as most clinical research neuroimaging protocols are constituted of multiple sequences and often need to be integrated in clinical MRI slots with limited time. Finally, cSVD is a brain disorder in which cerebrovascular pathology interacts with the neural tissue, for which an integral approach of the brain parenchyma and microcirculation is most pathophysiologically adequate. Future studies need to show whether advanced tensor IVIM models can provide distinct parameters that discern normal from affected tissue parts and add to scalar models, which was beyond the current study scope.
In conclusion, using a short (5 min 21 s) integrated IVIM-DTI protocol with 15 b-values and six diffusion directions for each b-value we demonstrate that IVIM models with 9 and 11 parameters were most adequate to simultaneously determine parameters such as perfusion fraction, f, and pseudo-diffusion coefficient, D*, as well as DTI parameters. The (11-parameter) model with the highest Akaike weights in WMH and GM allowed for the additional calculation of the FA of the pseudo-diffusion tensor, which is not accessible with the usually performed IVIM acquisitions based on three orthogonal diffusion-gradient directions.