Diffusion‐derived intravoxel‐incoherent motion anisotropy relates to CSF and blood flow

Purpose

This study investigates the feasibility of multi‐b‐value, multi‐directional diffusion MRI for assessing the anisotropy of the cerebral pseudo‐diffusion (D*)‐tensor. We examine D*‐tensor's potential to (1) reflect CSF and blood flow, and (2) detect microvascular architectural alterations in cerebral small vessel disease (cSVD) and aging.

Methods

Multi‐b‐value diffusion MRI was acquired in 32 gradient directions for 11 healthy volunteers, and in six directions for 29 patients with cSVD and 14 controls at 3 T. A physics‐informed neural network was used to estimate intravoxel incoherent motion (IVIM)–DTI model parameters, including the parenchymal slow diffusion (D‐)tensor and the pseudo‐diffusion (D*)‐tensor, from which the fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were derived. Comparisons of D*‐tensor metrics were made between lateral, third, and fourth ventricles and between the middle cerebral arteries and superior sagittal sinus. Group differences in D*‐tensor metrics in normal‐appearing white matter were analyzed using multivariable linear regression, correcting for age and sex.

Results

D*‐anisotropy aligned well with CSF flow and arterial blood flow. FA(D*), MD(D*), AD(D*), and RD(D*) were highest in the third, moderate in the fourth, and lowest in the lateral ventricles. The arteries showed higher MD(D*), AD(D*), and RD(D*) than the sagittal sinus. Higher FA(D*) in the normal‐appearing white matter was related to cSVD diagnosis and older age, suggesting microvascular architecture alterations.

Conclusion

Multi‐b‐value, multi‐directional diffusion analysis using the IVIM–DTI model enables assessment of the cerebral microstructure, fluid flow, and microvascular architecture, providing information on neurodegeneration, glymphatic waste clearance, and the vasculature in one measurement.

1. INTRODUCTION

Diffusion‐weighted MRI has emerged as a powerful and versatile technique in clinical research. By measuring the motion of water molecules in organs, it offers a unique perspective on physiological processes and pathological conditions. One of the most used diffusion‐weighted MRI techniques is DTI, where diffusion‐sensitizing gradients are applied in multiple directions. Using DTI, the anisotropy of diffusing water molecules can be characterized, for instance, to measure the general direction of large axon bundles in the white matter (WM) using the D‐tensor for the brain parenchyma. ¹

Variants of diffusion‐weighted MRI further extend its applications. One such variant is the intravoxel incoherent motion (IVIM) model, which aims to distinguish slow diffusion (D) in the parenchyma from fast microcirculatory pseudo‐diffusion (D*) in the capillary network by sampling multiple b‐values. ² The IVIM model assumes that perfusion through randomly oriented capillaries mimics a pseudo‐diffusion effect. This technique is promising for research on pathologies in which both the microstructural integrity of the parenchyma and capillary network are altered, such as in brain tumors and brain tissue in cerebral small vessel disease (cSVD). ³ , ⁴

Besides randomly oriented capillaries, other forms of incoherent motion, such as blood flow in larger vessels, may also cause diffusion signal attenuation at low b‐values. ⁵ This signal attenuation depends on the orientation of the large vessels with respect to the diffusion gradient direction and the spatial dispersion of velocities, resulting in an anisotropic D*. Building upon the DTI model, a similar IVIM‐DTI model can describe the normalized signal (S(b,$\widehat{g}$)/S ₀) as:

$$\frac{S(b,\widehat{g})}{S_0}=f{e}^{-b{\widehat{g}}^T{\mathbf{D}}^{\mathbf{*}}\widehat{g}}+(1-f)e^{-b{\widehat{g}}^T\mathbf{D}\widehat{g}}.$$ (1)

Here, $\widehat{g}$ is the diffusion‐sensitizing direction, f is a scalar representing the signal fraction of the pseudo‐diffusion component, and D* and D are the pseudo‐diffusion and parenchymal diffusion tensors, respectively. ⁶

In addition to blood flow, a previous study ⁷ showed anisotropic signal attenuation of CSF flow in a variety of regions by performing DTI using only one low b‐value of 100 s/mm². CSF plays a crucial role in maintaining the brain's homeostasis and is involved in the brain clearance system (also coined glymphatic or intramural periarterial drainage system). ⁸ , ⁹ Alterations in CSF flow dynamics can be indicative of various neurological conditions, such as Alzheimer's disease. ⁷ , ⁸ , ¹⁰

In classical DTI, typically, multiple diffusion directions are acquired only for high (order of 1000 s/mm²) b‐values. However, by additionally acquiring a combination of low (<200 s/mm²) b‐values in multiple diffusion‐sensitizing directions, the D*‐tensor may also be estimated, providing information on the fast pseudo‐diffusion component pertaining to directional CSF or blood flow velocities. When the D*‐tensor is assessed in tissue, it is considered to reflect information on the microvascular architecture. ⁴ , ⁶ However, due to the relatively small signal effect of D* and substantial image noise, obtaining orientational information with conventional fitting techniques, such as least‐squares, is challenging. ⁶ Moreover, although several studies show the feasibility of IVIM‐DTI in the brain, ⁴ , ⁶ , ¹¹ the added clinical potential of IVIM‐DTI models has not been shown in the brain due to the poor signal.

The accuracy and precision of IVIM‐DTI may be improved by using physics‐informed deep learning. Previously, physics‐informed neural networks have been shown to outperform conventional fitting methods with regard to accuracy, repeatability, and parameter map quality for multiple IVIM models. ¹² , ¹³ , ¹⁴ However, thus far deep learning has not been employed to optimize the parameter estimation of the IVIM‐DTI model from multi‐b‐value, multi‐directional diffusion MRI.

In the current study, we aim to demonstrate the feasibility of IVIM‐DTI using multi‐b‐value, multi‐directional diffusion MRI. To this end, we utilize a physics‐informed neural network to address the challenges in the parameter estimation process. To show feasibility, we assess the anisotropy of the D*‐tensor and provide a proxy for CSF and blood flow in the brain. For this, we analyze the D*‐tensor in two evident macroscopic structures being large intracranial blood vessels and the CSF‐filled cavities of the ventricular system. Second, we aim to investigate the alterations in microvascular architecture due to cSVD and aging to explore the clinical potential of the D*‐tensor. In cSVD and aging, the average microvessel diameter and flow velocities increase, leading to inefficient oxygen extraction. ¹⁵ , ¹⁶ , ¹⁷ These alterations in microvascular architecture are expected to affect the anisotropy of the D*‐tensor in tissue. Altogether, assessing the IVIM‐DTI model parameters can offer insights into the cerebral microstructure, fluid dynamics, and microvascular architecture simultaneously, providing comprehensive information for various neurological diseases.

2. METHODS

2.1. Study populations and MRI acquisition

2.1.1. Proof‐of‐principle study for measuring CSF and blood flow

To demonstrate the principle of multi‐b‐value, multi‐directional diffusion MRI to capture the anisotropy of IVIM, we included 11 healthy subjects (age range: 22–59 years, seven females). ¹⁸ These subjects were scanned on a 3 T MRI system (Philips, Ingenia CX, Best, The Netherlands) equipped with a 32‐channel head coil. An extensive diffusion MRI scan was acquired with 15 b‐values in 32 noncollinear gradient directions (single‐shot spin‐echo EPI, TR/TE = 2279/79 ms, b‐values = 0, 10, 20, 30, 40, 50, 60, 100, 200, 300, 400, 500, 600, 800, and 1000 s/mm², multi‐band factor = 3, bandwidth phase‐encoding/frequency direction = 24.4/2128 Hz, acquisition time = 17:08 min:s, in‐plane resolution = 2.4 × 2.4 mm, acquisition matrix = 92 × 110, slice thickness = 2.4 mm, slice gap = 0.48 mm, 57 transverse slices). An additional image without diffusion‐weighting (b = 0 s/mm²) was acquired with opposite phase‐encoding direction to correct for EPI distortions. The study protocol also included T₁‐weighted images with two different TIs for anatomical reference and a time‐of‐flight to visualize the arteries (Table 1). Ethical approval for this substudy was waived by the medical ethics committee of Maastricht University Medical Center+ (Maastricht, The Netherlands). All participants gave written informed consent prior to inclusion.

TABLE 1.

Overview of the acquisition settings.

	T1‐weighted imaging	Time of flight (TOF)	T2‐weighted fluid‐ attenuated inversion recovery (FLAIR)	Multi‐b‐value multi‐directional diffusion MRI
TR [ms]	2900	25	4800	2279
TE [ms]	3.7	5.8	289	79
TI [ms]	650 and 2100	–	1650	–
Flip angles [degrees]	6 and 6	20	90	90
FOV [mm]	240 × 240 × 180	200 × 200 × 74	256 × 256 × 180	221 × 269 × 155
Slice gap [mm]	–	–	–	0.48
Acquired voxel size [mm]	1 × 1 × 1	0.25 × 0.49 × 1	1 × 1 × 1	In‐plane: 2.4 × 2.4; Slice thickness: 2.4
Acquisition time [min:s]	4:35	4:30	6:14	6 directions, 3:08; 32 directions, 17:08

2.1.2. Case–control study for investigation of microvascular architecture

We investigated the cerebral microvascular architecture using a shorter diffusion MRI protocol in a subset of 29 patients with cSVD and 14 elderly controls from the prospective, observational CRUCIAL‐VCI study (registration: NL72696.068.20). This study was part of the CRUCIAL study, a multicenter research program on the role of microvascular rarefaction in vascular dementia and heart failure (trial registration: ISRCTN22301128). ¹⁹ For more details on in‐ and exclusion criteria, see van Dinther et al. ¹⁹ Similar to the proof‐of‐principle study, the subjects were scanned on a 3 T MRI system (Philips, Ingenia CX) equipped with a 32‐channel head coil. The acquisition parameters of the diffusion MRI scan were also kept similar, except for the number of noncollinear gradient directions. Only six directions were acquired to decrease the acquisition time for this clinical study (3:08 min:s). As before, an image without diffusion‐weighting (b = 0 s/mm²) was acquired with opposite phase‐encoding direction to correct for EPI distortions. The study protocol also included T₂‐weighted fluid‐attenuated inversion recovery images and T₁‐weighted images with two different TIs for anatomical reference (Table 1). The CRUCIAL‐VCI study was approved by the medical ethics committee of Maastricht University Medical Center+, and informed consent was obtained from all participants prior to inclusion.

2.2. Image analysis

2.2.1. Diffusion data and tensor modeling

Standard preprocessing was performed for the diffusion images, that is, correction for geometric EPI distortion (topup, FMRIB Software Library (FSL) ²⁰ v6.0.4), and for eddy currents and head displacement (ExploreDTI ²¹ v4.8.6). The signals were normalized to the measured signal at b = 0 s/mm² (S ₀). Subsequently, the IVIM‐DTI model ⁶ (Equation (1)) was fitted to the diffusion data in a voxel‐wise manner. To ensure D and D* are positive definite matrices, we applied the Cholesky decomposition (D = V ^T V and D* = U ^T U), where the Cholesky components V_1–6 and U_1–6 are the parameters to be estimated. ⁶

We used a self‐supervised physics‐informed neural network called IVIM‐DTI‐NET to estimate the IVIM‐DTI model parameters from the diffusion data. As a comparison to IVIM‐DTI‐NET, we also fitted this model using the one‐step least‐squares and the segmented (two‐step) least‐squares methods. ⁶

Hereafter, eigenvectors and eigenvalues were derived from D and D*, from which the fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) (i.e., largest eigenvalue), and radial diffusivity (RD) (i.e., average of the two lowest eigenvalues) were calculated. ²² Furthermore, the eigenvalues and eigenvectors of D and D* were visualized using ellipsoids (fanDTasia ²³ ).

IVIM‐DTI‐NET

Our self‐supervised physics‐informed neural network (IVIM‐DTI‐NET), depicted in Figure 1, learns the IVIM‐DTI model by incorporating it into the loss function. IVIM‐DTI‐NET was implemented in Python (v3.10.9) using PyTorch (v1.12.1) and can be found on GitHub (https://github.com/paulienvoorter/IVIM‐DTI‐NET). We copied most of the network hyperparameters from IVIM‐NET by Kaandorp et al. ¹⁴ but adjusted the neural network to handle multi‐b‐value, multi‐directional diffusion data. The network contained three parallel blocks (one for D* prediction, one for D prediction, and one for f prediction) of two fully connected hidden layers. Both layers contained 15 neurons with an exponential linear unit activation function and batch normalization, and a 10% dropout was used after the first layer. The input of IVIM‐DTI‐NET was the normalized multi‐b‐value, multi‐directional signal. After the second hidden layer, the Cholesky components U_1–6 and V_1–6 (of D*‐tensor and D‐tensor, respectively) were predicted and constrained with sigmoid functions needed for network convergence. The f was predicted and constrained by an absolute value function. The predicted D*‐tensor, D‐tensor, and f‐scalar in the output layer were then used to predict the signal decay curve using the IVIM‐DTI model (Equation (1)) and the corresponding loss, which was needed in the training process.

FIGURE 1.

Physics‐informed neural network architecture (IVIM‐DTI‐NET) for IVIM‐DTI parameter estimation, adapted from Kaandorp et al. ¹⁴ The hyperparameters and training strategy were taken from Kaandorp et al, ¹⁴ including a learning rate of 3 × 10⁻⁵ (Adam optimizer). To ensure D and D* to be a positive definite matrix, we used its Cholesky factorization. An absolute constraint was applied to f, and sigmoid constraints were applied to V_1–6 and U_1–6. The lower and upper values for the sigmoid constraints were based on previous research ⁶ : 0.011 ≤ V_1–3 ≤ 0.041, −0.015 ≤ V_4–6 ≤ 0.015, −0.129 ≤ U_1–3 ≤ 0.297, and −0.213 ≤ U_4–6 ≤ 0.213

D, tensor of the tissue diffusion; D*, tensor of the pseudo‐diffusion.

Using Equation (1), the IVIM‐DTI input signal can be calculated for any given parameter combination. During the training process, the network was optimized by minimizing the mean of the square of the error between the measured signal and this predicted signal. The multi‐b‐value, multi‐directional diffusion in vivo voxel data available was split into training data (90%) and validation data (10%). We used a batch size of 128 and 500 iterations per epoch. The training process stopped after no decrease in validation loss for 10 consecutive epochs (early stopping). Separate neural networks were trained for the volunteer and CRUCIAL‐VCI datasets because the number of gradient directions differed between these datasets. As an additional analysis, we trained IVIM‐DTI‐NET and predicted the parameters using a subset of six directions from the volunteer dataset to see whether the results are comparable with those obtained from the full 32‐direction dataset. For this, we selected the six gradient directions that were most similar to the gradient directions scanned in the CRUCIAL‐VCI dataset.

Least‐squares estimation

The least‐squares fit was carried out in MatLab (R2023b; MathWorks, Natick, MA). We evaluated both the one‐step least‐squares, fitting all parameters simultaneously, and the segmented least‐squares, fitting the D‐tensor first. We used the function lsqcurvefit with the Levenberg–Marquardt algorithm to estimate f, U_1–6, and V_1–6. For the segmented least‐squares fit, the signals at b ≥ 200 s/mm² were used in the first step to estimate V_1–6 (Cholesky components of the D‐tensor). The following initial guesses for the parameters were used: f = 0.1, V_1–3 = $\sqrt{0.0007{\mathrm{mm}}^2/\mathrm{s}}$, V_4–6 = 0, U_1–3 = $\sqrt{0.01{\mathrm{mm}}^2/\mathrm{s}}$, and U_4–6 = 0. ⁶

2.2.2. Regions of interest (ROIs)

CSF flow

The CSF in the lateral, third, and fourth ventricles was automatically segmented from the T₁‐weighted images (samseg v7.1.0 ²⁴ ). We expect the magnitude variation of uni‐directional CSF flow velocities (laminar flow) to be highest in the third ventricle, moderate in the fourth ventricle, and lowest in the lateral ventricles, based on previous literature. ²⁵ , ²⁶ All ROIs were transformed into the diffusion image space (FSL FMRIB linear image registration tool [flirt] v6.0.4 ²⁷ ).

Blood flow

After coregistration of the time‐of‐flight images and the T₁‐weighted images to the diffusion image space (FSL flirt v6.0.4 ²⁷ ), ROIs were manually drawn in the middle cerebral arteries (the M1 segment) using the time‐of‐flight image and in the superior sagittal sinus using the T₁‐weighted image (p. v.). For the blood vessels, we expect the middle cerebral arteries to have a higher flow velocity and a higher variation in flow velocities due to laminar flow compared to the superior sagittal sinus.

Microvascular architecture

We assessed the IVIM‐DTI–related parameters in the normal‐appearing WM (NAWM), meaning outside of the WM hyperintensities because previous studies have demonstrated early pathophysiological changes in the NAWM of patients with cSVD. ³ , ²⁸ , ²⁹ The NAWM was automatically segmented from the T₁‐weighted and the fluid‐attenuated inversion recovery images (samseg v7.1.0 ²⁴ ). Any vascular lesions, such as infarcts, hemorrhages, developmental venous anomalies, cavernomas, and residual WM hyperintensities, were manually removed from the NAWM mask (p. v., m.v.d.). The NAWM mask was transformed to the diffusion image space (FSL flirt v6.0.4 ²⁷ ).

2.3. Statistical analysis

2.3.1. Proof‐of‐principle study

We used repeated‐measures analysis of variance with post hoc analyses to compare FA(D*), MD(D*), AD(D*), and RD(D*) between the lateral, third, and fourth ventricles. Furthermore, we compared FA(D*), MD(D*), AD(D*), and RD(D*) between the middle cerebral arteries and the superior sagittal sinus using paired t‐tests.

As an additional analyses, we performed paired t‐tests to compare FA(D*) and its within‐subject SD in NAWM derived using IVIM‐DTI‐NET with those obtained using the segmented least‐squares method. We hypothesize that fewer noise‐induced outliers would result in a lower FA(D*) and a lower SD(FA(D*)).

2.3.2. Case–control study

The study population's characteristics were reported as either mean ± SD, median [interquartile range], or number (percentages). To create an overview of any differences in general and health characteristics between patients with cSVD and controls, we conducted independent samples t‐tests or Pearson's X ² tests, where appropriate. Differences in NAWM‐derived FA(D*), MD(D*), AD(D*), and RD(D*) between patients and controls were investigated using linear regression analyses, with age and sex as covariates. We considered a p‐value below 0.05 as statistically significant.

3. RESULTS

During the training process of IVIM‐DTI‐NET, the minimum validation loss was reached at 20 epochs and 37 epochs for the volunteer data and CRUCIAL‐VCI data, respectively. Figure S1 compares the D*‐ and D‐tensor maps obtained by IVIM‐DTI‐NET and the least‐squares methods. Both the segmented least‐squares and IVIM‐DTI‐NET fitting methods seem to estimate the D‐tensor well, whereas the one‐step least‐squares method appears more susceptible to image noise. Both the one‐step and segmented least‐squares–derived D*‐tensor maps contained a substantial number of outliers, whereas the IVIM‐DTI‐NET–derived D*‐tensor map was able to avoid them. Accordingly, IVIM‐DTI‐NET has a lower FA(D*) in the NAWM compared to the segmented least‐squares method (0.54 ± 0.02 vs. 0.65 ± 0.03; p < 0.001). IVIM‐DTI‐NET also has a lower within‐subject SD(FA(D*)) compared to the segmented least‐squares method (0.14 ± 0.01 vs. 0.24 ± 0.01; p < 0.001). Therefore, we only consider the results derived using IVIM‐DTI‐NET in the following sections.

3.1. CSF and blood flow

Figure 2 shows example ellipsoidal representations of the D*‐ and D‐tensor within the brain's ventricular system. Likewise, Figure 3 visualizes example ellipsoidal representations of the D* and D‐tensor for the middle cerebral arteries and the sagittal sinus. As can be observed in these figures, the anisotropic D* ellipsoids align well with the CSF and arterial blood flow, whereas D ellipsoids are more isotropic at these locations. In addition to Figures 2 and 3, Figure S1 presents the results obtained using only a subset of six directions, compared to the full 32‐directional diffusion data.

FIGURE 2.

An example of a T₁‐weighted image with corresponding (three color‐coded) ventricular segmentation (A), D* ellipsoids (B), and D ellipsoids (C) for a sagittal slice containing the lateral, third, and fourth ventricles for a representative subject (healthy volunteer). The red‐green‐blue colors show the main diffusion direction and FA‐weighting (i.e., black color represents isotropic diffusion). In line with expectations, the D* ellipsoids seem to indicate higher CSF flow velocities in the narrower cavity regions (third ventricle, foramen of Monro, and aqueduct of Sylvius) and lower CSF flow velocities in larger cavities (lateral and fourth ventricles). The D ellipsoids are more or less isotropic at the locations where substantial CSF flow would be expected and have a ˜25 times smaller magnitude than the D* ellipsoids.

D*, tensor of the pseudo‐diffusion; D, tensor of the tissue diffusion; FA, fractional anisotropy.

FIGURE 3.

An example of a maximum‐intensity–projection time‐of‐flight angiogram (A), along with D* ellipsoids (B) and D ellipsoids (C) overlayed on the angiogram for an axial slice at the level of the circle of Willis in the same subject as Figure 2. The D* ellipsoids are also shown for a midsagittal T₁‐weighted slice containing the sagittal sinus (yellow) (D). The red‐green‐blue colors show the main diffusion direction and FA‐weighting (i.e., black color represents isotropic diffusion). This figure shows that the direction of the D* ellipsoids overlaps well with the middle cerebral arteries, and as expected, no anisotropy was observed in the D‐tensor inside the arteries. CSF flow also has anisotropic D* ellipsoids (e.g., the suprasellar cistern, see arrows). The magnitude of D* in the sagittal sinus appears ˜3 times smaller than in the middle cerebral arteries. Few sagittal sinus voxels even have a D* magnitude which is too small to be visualized using the current scale.

The quantitative values of the D*‐tensor in the ventricles and blood vessels are summarized in Table 2 and were found to be significantly different between the ventricles (p < 0.001). Post hoc analyses revealed that FA(D*), MD(D*), AD(D*), and RD(D*) in the third ventricle were higher than in the fourth ventricle (p < 0.001, p = 0.002, p < 0.001, and p = 0.02, respectively); and FA(D*), MD(D*), AD(D*), and RD(D*) in the fourth ventricle were higher than in the lateral ventricles (p < 0.001, p < 0.001, p < 0.001 and p = 0.001, respectively). The results for the D*‐tensor in the ventricles and blood vessels using a subset of six directions are reported in Table S1.

TABLE 2.

Pseudo‐diffusion–related measures in ventricles and blood vessels (volunteer data, n = 11).

Region	FA(D*)	MD(D*) [10−2 mm2/s]	AD(D*) [10−2 mm2/s]	RD(D*) [10−2 mm2/s]	f
CSF a
Lateral ventricles	0.43 (0.04)	0.8 (0.1)	1.3 (0.2)	0.6 (0.2)	0.46 (0.02)
Third ventricle	0.67 (0.04)	2.9 (0.8)	5.5 (1.1)	1.7 (0.6)	0.52 (0.07)
Fourth ventricle	0.59 (0.03)	1.0 (0.5)	3.4 (0.1)	1.1 (0.3)	0.47 (0.03)
Blood vessels b
Middle cerebral arteries	0.55 (0.11)	2.9 (1.2)	4.5 (1.7)	2.1 (1.0)	0.37 (0.03)
Superior sagittal sinus	0.48 (0.05)	0.8 (0.2)	1.2 (0.4)	0.6 (0.2)	0.25 (0.07)

Notation: Mean (SD).

^a Lateral ventricles vs. Third ventricle: ∆FA(D*): p < 0.001, ∆MD(D*): p < 0.001, ∆AD(D*): p < 0.001, ∆RD(D*): p < 0.001, ∆f: p = 0.005.

Third ventricle vs. Fourth ventricle: ∆FA(D*): p < 0.001, ∆MD(D*): p = 0.002, ∆AD(D*): p < 0.001, ∆RD(D*): p = 0.02, ∆f: p = 0.03.

Lateral ventricles vs. Fourth ventricle: ∆FA(D*): p < 0.001, ∆MD(D*): p < 0.001, ∆AD(D*): p < 0.001, ∆RD(D*): p = 0.001, ∆f: p = 0.41.

^b Middle cerebral arteries vs. Superior sagittal sinus: ∆FA(D*): p = 0.11, ∆MD(D*): p < 0.001, ∆AD(D*): p < 0.001, ∆RD(D*): p = 0.001, ∆f: p = 0.01.

AD, axial diffusivity; D*, tensor of the pseudo‐diffusion; f, signal fraction of the pseudo‐diffusion component; FA, fractional anisotropy; MD, mean diffusivity; RD, radial diffusivity.

The middle cerebral arteries had a higher MD(D*), AD(D*), and RD(D*) compared to the superior sagittal sinus (p < 0.001, p < 0.001, and p = 0.001), whereas the FA(D*) did not differ between arterial and venous blood vessels (p = 0.11).

3.2. Microvascular architecture

Table S2 summarizes the study population's characteristics. Patients more often had a history of hypercholesterolemia, stroke, and transient ischemic attack, as well as a higher WM hyperintensity volume compared to controls.

An overview of the NAWM‐averaged IVIM‐DTI–related measures in patients with cSVD and controls is presented in Table 3. Note that the f values in tissue are considerably lower than the f values in CSF cavities and large blood vessels because f in tissue is dominated by a relatively small blood signal fraction.

TABLE 3.

IVIM‐DTI–related measures in the normal‐appearing white matter for patients with cSVD (n = 29) and controls (n = 14).

Measure	Patients with cSVD	Controls
FA(D*)	0.344 (0.030)	0.327 (0.013)
MD(D*)	0.730 (0.046)	0.761 (0.043)
AD(D*)	0.995 (0.059)	1.022 (0.060)
RD(D*)	0.596 (0.046)	0.631 (0.034)
f	0.124 (0.015)	0.113 (0.010)
FA(D)	0.369 (0.020)	0.388 (0.020)
MD(D)	6.81 (0.41)	6.42 (0.23)

Note: Mean (SD), units: MD(D*) 10⁻² mm²/s, AD(D*) 10⁻² mm²/s, RD(D*) 10⁻² mm²/s, MD(D) 10⁻⁴ mm²/s.

cSVD, cerebral small vessel disease; D*, tensor of the pseudo‐diffusion; D, tensor of the tissue diffusion; IVIM‐DTI, intravoxel incoherent motion diffusion tensor imaging.

The patients had a higher FA(D*) in NAWM compared to controls (β = 0.016 [95% confidence interval (CI) 0.000–0.031], p = 0.048). Figure 4 demonstrates that FA(D*) increases with older age (β = 0.001 per year [95% CI 0.001–0.002], p = 0.002) and shows representative examples of the FA(D*) maps for a patient with cSVD and a control subject. Sex did not affect FA(D*) (p = 0.22). Furthermore, no significant effect of cSVD, age, or sex was observed on MD(D*), AD(D*), and RD(D*), except for a lower AD(D*) in females (β = −0.049 [95% CI −0.090 to −0.009], p = 0.02). Further details of the linear regression analyses' results, including the effect of cSVD, age, and sex on the other IVIM‐DTI parameters, are reported in Table S3.

FIGURE 4.

Scatterplot illustrating the relationship between the D* fractional anisotropy in normal‐appearing white matter and age. A fitted line for the patients and controls combined is shown with a 95% mean confidence interval. Fractional anisotropy of D* increases with older age (β = 0.001, p = 0.002). Examples of FA(D*) maps are shown for a patient with cSVD (A: 83 years) and a control (B: 52 years).

cSVD, cerebral small vessel disease; D*, tensor of the pseudo‐diffusion.

4. DISCUSSION

This study provides evidence for the feasibility and utility of assessing the anisotropy of the D*‐tensor from multi‐b‐value, multi‐directional diffusion MRI in the brain using a dedicated physics‐informed neural network. First, we demonstrated the applicability of this method to simultaneously assess CSF and blood flow by showing that anisotropic D* ellipsoids align with the direction of ventricular CSF flow pathways as well as arterial blood flow. Second, we revealed that the fractional anisotropy of D* in normal‐appearing WM is higher in patients with cSVD and older age, suggesting alterations in the microvascular architecture.

4.1. CSF and blood flow

Investigating neurofluids noninvasively is an emerging field of research due to the important role of the brain waste clearance system in several neurodegenerative diseases. ³⁰ CSF is considered the first component of the waste clearance system, with subsequent fluid movement in and out of the parenchyma through perivascular spaces, driving metabolic waste clearance. ³¹ In the last couple of years, several studies have performed low b‐value diffusion MRI to evaluate whole‐brain CSF flow within the ventricular system and paravascular spaces. ³² , ³³ , ³⁴ , ³⁵ , ³⁶ , ³⁷ Our observed differences in FA(D*) and MD(D*) among the lateral, third, and fourth ventricles align with findings from previous studies measuring the CSF pseudo‐diffusivity in the brain's ventricular system. ²⁵ , ³² , ³³ Previous studies found a low MD(D*) in the lateral ventricles about 3 × 10⁻³ mm²/s (our study: 8 × 10⁻³ mm²/s) and a high MD(D*) in the third and fourth ventricles about 8–13 × 10⁻³ mm²/s (our study: 10 and 29 × 10⁻³ mm²/s for fourth and third ventricle, respectively). ²⁵ , ³³ Likewise, our study found higher MD(D*) and AD(D*) in the middle cerebral arteries compared to the superior sagittal sinus, which are qualitatively in line with the expected differences in maximal blood flow velocities inside these vessels (mean blood velocity middle cerebral artery is 61 to 65 cm/s vs. peak sagittal sinus velocity of 20 to 25 cm/s). ³⁸ It is important to note that the spatial variance in flow velocities increases with higher mean flow velocities when assuming laminar flow, hence resulting in a higher D*. Of note, whereas the blood flow velocities in the middle cerebral arteries are higher than those in the CSF, the flow incoherency in the CSF may contribute significantly to IVIM, resulting in CSF D* values in the same order as those in the middle cerebral arteries.

Besides the higher blood flow velocities, the higher CSF flow velocities within the subarachnoid space around the middle cerebral arteries likely also contributed to AD(D*) due to partial volume effects. ⁷ , ²⁵ , ³³ , ³⁴ Additionally, when assuming the intramural periarterial drainage theory, ⁹ the fluid efflux through the smooth muscle cells occurs in the opposite direction (but parallel) to the CSF inflow in the subarachnoid space, which might also contribute to AD(D*). The periarterial CSF movement is primarily driven by arterial pulsatility, contrasting with the slow CSF movement around the superior sagittal sinus due to the absence of pulsations. ³² Vessel wall movement during the cardiac cycle and subsequent fluid movement perpendicular to the vessel direction might be reflected by RD(D*), which was found to be higher for the arteries (21 × 10⁻³ mm²/s) than for the vein (6 × 10⁻³ mm²/s).

Furthermore, some methodological considerations regarding the CSF flow measurement should be discussed. In contrast to our study, previous studies ³² , ³³ , ³⁴ , ³⁵ , ³⁶ , ³⁷ completely focused on measuring CSF flow, employing a single low b‐value and a mono‐tensor model for the pseudo‐diffusivity. They often suppress the signal from blood and tissue using a long TE. ³⁴ , ³⁵ On the other hand, we incorporated a range of low b‐values and used the shortest TE possible. This multi‐b‐value diffusion technique is sensitive to both CSF and blood flow, and tissue diffusion simultaneously, and can isolate the fast and the slow diffusion components using a bi‐tensor model. An advantage of using multiple b‐values over a single low b‐value is that it can capture a range of CSF and blood pseudo‐diffusivities (i.e., a variety in velocities). ³⁹ However, a drawback of acquiring multiple b‐values is the increase in the acquisition time. Moreover, partial volume effects might occur for voxels containing both CSF and blood flow, and CSF cannot be discerned from blood with our currently used TE.

4.2. Microvascular architecture in cerebral small vessel disease and aging

We found that the FA(D*) in the NAWM of cSVD patients was 0.34 ± 0.03, which somewhat deviates from a previous study by Dietrich et al. ⁴ that reported a median FA(D*) of 0.45 (interquartile range: 0.05) in the NAWM of a cSVD population. This discrepancy can be explained by the different model fitting approaches, IVIM‐DTI models, and acquisition settings used, but also by their older cSVD population. ⁴ To our knowledge, it has thus far not been explored whether the D*‐tensor is able to discern normal tissue from tissue affected by microvascular pathology. The increase in NAWM‐averaged FA(D*) in cSVD and aging suggests more orientated (in contrast to random) blood flow in the microvasculature, potentially driven by factors such as capillary remodeling and vessel diameter changes. In aging, a shift from capillaries to arterioles has been reported in vivo using vessel architecture imaging. ¹⁵ Furthermore, the decrease in functional pericytes is believed to play a strong role in age‐ and cSVD‐related microvascular remodeling, such as vessel regression and vessel dilation. This would lead to a less homogenous microvascular bed, limiting the extraction efficacy of oxygen. ¹⁷ The increase in arterioles and dilated small vessels would add to anisotropic incoherent motion due to flow velocities in a specific direction, thus a higher FA(D*) in tissue. The dilated small vessels might also explain the higher f that we observed in cSVD and aging. Our study results imply that a higher FA(D*) is a proxy for the functional properties of the microvascular architecture potentially indicative of the microvascular condition.

Another explanation for the higher tissue‐derived FA(D*) observed in aging and cSVD could be a reduction in orthogonal interstitial fluid movement. This hypothesis is further supported by the observed trend of decreased tissue‐derived RD(D*) in both cSVD and aging. Such a reduction in orthogonal fluid movement may suggest a diminished exchange of fluid, and consequently waste products, between tissue and blood.

4.3. Parenchymal diffusion

In line with expectations, MD(D) was found to be increased with cSVD and aging, suggesting a loss of tissue integrity, and FA(D) was decreased in cSVD. ⁴⁰ Our MD(D) and FA(D) were within the ranges found in previous DTI research. ⁴¹ Furthermore, our observed color‐coded D‐tensor maps derived using IVIM‐DTI‐NET corresponded well with the D‐tensor maps derived using the segmented least‐squares method (Figure S1B), validating IVIM‐DTI‐NET's ability to accurately map the D‐tensor.

4.4. Methods for D*‐tensor estimation

To obtain these results from multi‐b‐value, multi‐directional diffusion data, a novel analysis method using IVIM‐DTI‐NET has been proposed. Mozumder et al. ⁶ have evaluated several approaches to fit the IVIM‐DTI model to multi‐b‐value, multi‐directional diffusion data because it is an ill‐conditioned problem. They recommended using a one‐step fitting approach based on a damped Gauss‐Newton and Gaussian prior for the model parameters, ⁶ which has yet to be compared to our IVIM‐DTI‐NET performance. In concordance with their results, we observed high estimation errors for the D*‐tensor using the one‐step and segmented least‐squares methods. ⁶ Previous studies have shown that least‐squares methods for IVIM parameter estimation result in more outliers. ¹² , ¹³ , ¹⁴ An outlier in a single direction can cause significant anisotropy bias, making least‐squares methods less desirable for IVIM‐DTI parameter estimation.

4.5. Study considerations

In the current study, we have extended IVIM‐NET ¹⁴ to IVIM‐DTI‐NET but did not explore any further improvement of the network for multi‐b‐value, multi‐directional diffusion data fitting. Optimizing IVIM‐DTI‐NET's hyperparameters (e.g., network size) and training strategies (e.g., learning rate and training length) for IVIM‐DTI parameter estimation presents a potential avenue for further improvement. Furthermore, it should be noted that re‐training IVIM‐DTI‐NET is required when using it for new datasets with different b‐values and gradient directions, which is a limitation that might be tackled in the future. ⁴²

Furthermore, validating the D*‐tensor as a proxy for microvascular architecture remains a challenge due to the difficulty in obtaining ground‐truth data. However, addressing this challenge is crucial for unlocking IVIM‐DTI's full clinical potential in conditions where abnormalities in the parenchyma, CSF flow, and/or blood circulation play a role, such as Alzheimer's disease and cSVD. ⁴ , ²⁵ As such, future studies should validate the in vivo FA(D*) measure, for example, with animal studies and histology focused on the architecture of the microvascular network. ⁴³

Moreover, though D* is not a measure for classical perfusion or flow, it would be interesting to compare D*‐tensor measures to existing techniques for flow measurement, such as phase‐contrast MRI. It is important to note that the D*‐tensor captures the incoherent motion, such as variation in flow velocities and turbulent flow, whereas phase‐contrast MRI captures the coherent motion, such as mean flow velocity, within a voxel. Hence, these techniques measure complementary information about the flow velocities assuming similar voxel sizes. However, a high‐resolution phase‐contrast MRI would be able to assess the variation in flow velocities within CSF cavities or large blood vessels, and therefore might be comparable with low‐resolution D*‐tensor values.

Lastly, for the clinical study the multi‐b‐value diffusion imaging was performed in only six gradient directions to keep the scan duration feasible for the patients with cSVD and controls. Ideally, one would measure more gradient directions, to increase the accuracy of the D*‐tensor. It remains to be investigated how the accuracy of the D*‐tensor improves when more than six gradient directions are used. Nevertheless, the conclusions drawn from the 32‐directional diffusion data remain valid when using only a subset of six directions, and it is remarkable that we were able to observe D*‐tensor differences between groups and with aging. This would suggest that our 3‐min diffusion scan is already valuable to assess the D*‐tensor in tissue as a proxy for the microvascular architecture.

4.6. Conclusion

Multi‐b‐value, multi‐directional diffusion data analysis using IVIM‐DTI‐NET holds the unique promise for simultaneous investigation of alterations in the cerebral microstructure, CSF dynamics, and microvascular architecture. Our study demonstrated a novel robust method to estimate the D*‐tensor. Direction‐sensitive CSF and blood flow characteristics were shown to be captured by the D*‐tensor. Furthermore, the microvascular architecture in the brain can be described by the FA(D*), whose increase was found to be related to cSVD and aging.

FUNDING INFORMATION

This work was supported by the European Union's Horizon 2020 project CRUCIAL (grant number 848109).

Supporting information

Figure S1. D*‐tensor as an overlay on the time‐of‐flight image showing the circle of Willis similar to Figure 3 (A1‐3) and D‐tensor maps (B1‐3) for different fitting algorithms: IVIM‐DTI‐NET (A1, B1), 1‐step least‐squares (A2, B2), and segmented least‐squares (A3, B3). The red‐green‐blue colors show the main diffusion direction and fractional anisotropy (FA)‐weighting (i.e., black color represents isotropic diffusion). The least‐squares‐derived D*‐tensor maps contain quite some outliers (i.e., at least one eigenvalue of D* > 0.5 mm²/s), which are excluded for visualization purposes. Although both the least‐squares‐derived and IVIM‐DTI‐NET‐derived D* ellipsoids seem to have the same direction as the middle cerebral arteries, this D* alignment is better visible for IVIM‐DTI‐NET, as it contains no noisy D* ellipsoids. The segmented least‐squares and IVIM‐DTI‐NET fitting methods seem to estimate the D‐tensor well, while the one‐step least‐squares method does not seem to be robust to image noise.

Figure S2. Results for a subset of the 32‐directional diffusion data. D*‐tensor ellipsoids are shown as an overlay on a T₁‐weighted image with corresponding (three color‐coded) ventricular segmentation (A + C, similar to Figure 2) and a time‐of‐flight image showing the circle of Willis (B + D, similar to Figure 3). (B2) The red‐green‐blue colors show the main diffusion direction and fractional anisotropy (FA)‐weighting (i.e., black color represents isotropic diffusion). A and B show the results when using the 32‐directional diffusion data and C and D show the results when using a subset of 6 directions. Though the D* ellipsoids slightly change when using 6 directions compared to 32 directions, it can be observed that they still align with the arterial blood flow and CSF flow pathways.

Table S1. Pseudo‐diffusion‐related measures in ventricles and blood vessels (volunteer data using a subset of 6 directions from the full 32‐directional data set, n = 11). Notation: mean (SD).

Table S2. Characteristics of a subset from the CRUCIAL‐VCI study population used in this study.

Table S3. Linear regression analyses' results of the IVIM‐DTI‐derived measures in normal‐appearing white matter in relation to cerebral small vessel disease diagnosis, age, and sex.

Voorter PHM, Jansen JFA, van der Thiel MM, et al. Diffusion‐derived intravoxel‐incoherent motion anisotropy relates to CSF and blood flow. Magn Reson Med. 2025;93(3):930‐941. doi: 10.1002/mrm.30294

DATA AVAILABILITY STATEMENT

The code for IVIM‐DTI‐NET has been made available on our open‐access GitHub repository (https://github.com/paulienvoorter/IVIM‐DTI‐NET). To facilitate the use of our code, we have also provided a sample multi‐b‐value, multi‐directional diffusion‐weighted imaging dataset of one volunteer (https://zenodo.org/records/12545278). The other datasets used in our study are available from the corresponding author upon reasonable request.