Clinicians and MRI physicists interested in probing microvascular structure and diffusion MRI.

Diffusion imaging has been used to probe microstructure and, to a lesser degree, investigate perfusion. However, the contribution of microvasculature structure to the diffusion signal has largely been overlooked. LeBihan’s Intravoxel Incoherent Motion (IVIM) is perhaps the most well-known approach for modeling microvascular flow^[1]. Although its practical application has been encouraging, there is no clear link between IVIM measurements and microvascular structure^[2]. Velocity Autocorrelation Theory (VAT) presented by Kennan et al.^[3] shows promise for quantification of microvascular structure and function using diffusion-weighted images:

$$\frac{S}{S_0}=exp\Big(-\gamma^2 G^2 \frac{\langle \bar{v}^2\rangle}{3}T_0\Omega \Big)\quad\quad(1)$$

Where $$$S/S­0$$$ is the signal with/without diffusion weighting, $$$G$$$ is the gradient amplitude, γ is the gyromagnetic ratio, $$$v$$$ is blood velocity, and $$$T_0$$$ is the auto-correlation time. $$$Ω$$$ is a function of gradient pulse width $$$δ$$$, spacing $$$Δ$$$ and $$$T_0$$$.

By collecting a series of scans at varying diffusion times and gradient amplitudes one can estimate blood velocity ($$$v$$$) and velocity auto-correlation time ($$$T_0$$$) on a voxel-wise basis using equation (1). The mean segment length of the vascular system ($$$L$$$) can also be computed, as blood velocity ($$$v$$$) and velocity auto-correlation time ($$$T_0$$$) are related by equation (2):^[3]

$$L=2T_{0}v_{0}\quad\quad(2)$$

where $$$v_0$$$ is estimated as $$$\sqrt{\langle \bar{v}^2 \rangle}$$$ . The aim of our study was to test this model on diffusion MRI data in the human brain. The parameter estimates are compared to the known morphology of the microvasculature.

Two datasets were collected on a 3T Philips Achieva scanner using a SE-EPI sequence with 2.4mm isotropic resolution. Eddy current correction was done for all the scans using FSL.

Dataset 1: 3 Diffusion-Weighted MRI scans were collected at 3 different diffusion times (∆) from 23 healthy volunteers (25±6.0years) (Table 1a). Voxel-wise maps of $$$v$$$, $$$L$$$ and $$$T_0$$$ were generated for each subject by simultaneously least-squares fitting equations (1) and (2) across all images within MATLAB. Voxels with high sum-squared errors (mostly CSF) were set to zero. Paired t-tests were made across all subjects to investigate differences between calculated values of $$$v$$$ & $$$L$$$ in white and grey matter. SPM12 was used to normalise each subject’s $$$v$$$, $$$L$$$ and $$$T_0$$$ map to MNI space to create mean images.

Dataset 2: Diffusion-Weighted MRI scans were collected at 3 different diffusion times and 5 b-values from 1 participant (Table 1b). Voxel-wise maps of $$$v$$$, $$$L$$$ and $$$T_0$$$ were generated as in dataset 1.
In both datasets, the maximum b-value was 100 s/mm$$$^2$$$ in order to minimise the contribution of diffusion in the extravascular space.

SPM12 was used for both datasets to segment brain regions into white matter (WM), grey matter (GM) and CSF to investigate mean values and goodness of fit in each region.

Dataset 1: Across subjects WM had significantly slower (P<0.005) mean blood velocity and significantly shorter (P<0.0001) mean vessel segment length compared to GM. Figure 1 shows the mean capillary segment length image across all 23 subjects normalised to MNI space in dataset 1.

Dataset 2: Figure 2 shows the mean signal attenuation in WM, GM and CSF for a) ∆=18ms and b) b=100s/mm² – the lines indicate the best fits of equation (1). As CSF contains no vascular flow, the model should not fit well here, hence serving as a useful negative control. The plots demonstrate a good fit for WM and GM, but a poor fit in CSF – sum squared errors were 3.0x10^-4, 3.2x10^-4 and 0.02 for WM, GM and CSF respectively.

A summary of mean values for both datasets can be found in Table 2.

By collecting diffusion-weighted images at a range of b-values and diffusion times it is possible to obtain images of microvascular features: blood velocity, auto-correlation time and capillary segment length. Calculated capillary segment length values are in good agreement with literature: a confocal microscopy study measured the distribution of capillary segment lengths in human grey matter^[4] presented a mode of ~10µm, in good agreement with our mean capillary segment lengths in grey matter of 10.3±0.2µm and 8.89±5.10µm for datasets 1 and 2 respectively. Acquisition times for data presented here are fast with dataset 2 taking ~6 minutes to acquire. Quantification of microvascular properties could be important in diseases that affect vascular microstructure such as Alzheimer’s disease and cancer. Alzheimer’s disease has been linked to longer distances between branch points in capillary networks^[5] and tumours with greater microvascular proliferations and increased heterogeneity of microvascular structure and function^[6]. The imaging presented here may be sensitive to these changes.