Diffusion-weighted magnetic resonance imaging (DW-MRI) allows for the quantification of the self-diffusion of water molecules in biological tissue by calculating the apparent diffusion coefficient (ADC). In perfused tissue, the intravoxel incoherent motion (IVIM) model proposed by Le Bihan et al.¹ more accurately describes the signal attenuation as a function of the diffusion weighting. By introducing a second, faster decaying exponential IVIM accommodates for molecular motion caused by perfusory effects. While several in vivo studies already suggest the feasibility of IVIM as a diagnostic tool, efforts are still made to realistically model microvasculature for a controlled and detailed analysis of influence factors on the IVIM signal characteristics. In previous studies, IVIM effects were simulated via spongy and porous structures, which produce incoherent motion merely indirectly^1–3. The purpose of this project was to demonstrate IVIM measurements in a phantom which realistically models a 3-dimensional capillary network.

A 3-dimensional capillary network was formed using melt-spun sugar fibers embedded into synthetic resin as proposed by Bellan et al⁴. Sugar fibers were produced with a modified cotton candy machine (Candyland, Klarstein, Berlin, Germany), which was optimized in terms of rotational speed and heating temperature to adjust the diameter of the sugar filaments. Subsequently, the fiber balls were placed in a PET mold (5×3×2cm³), covered with a two-component resin (E45GB, Breddermann Kunstharze, Schapen, Germany) and provided with an inlet and an outlet. After curing, the phantom was placed in a bath of water and ethanol for several days to dissolve the sugar fiber network embedded in the resin. Once dissolved, controlled water flow through the phantom was induced via a Harvard Apparatus (PHD 2000, Harvard Bioscience Inc., Holliston, Massachusetts, United States) at varying flow rates (0-0.5ml/min). Extensive IVIM measurements were performed on a 3 T whole-body MRI system (Skyra, Siemens Healthcare, Erlangen, Germany) using a wrist coil and a single-shot EPI sequence (TR/TE=4000ms/53ms; b-values=0,10,20,30,40,50,60,80,100,150,200,300,400,500,600 s/mm²; matrix=64x64; FoV=320x320mm²; slice thickness=5mm; 10 averages, PAT 2 (GRAPPA), acquisition time 29 min). Signal intensities were averaged over a region of interest covering the capillary network but excluding the inlet and outlet. IVIM parameters (slow diffusion D, pseudodiffusion D* and perfusion fraction f) were estimated using a non-linear least-squares fit.
Furthermore, to assess the fractional anisotropy (FA), a DTI sequence was employed with 64 averages at b=0 s/mm² and 30 diffusion gradient directions at b=600 s/mm² (10 averages each); TR/TE=1000/52ms; spatial resolution as above; acquisition time 24 min.

Figure 1 shows the manufactured flow phantom after the sugar fibers were dissolved with the capillary network clearly visible in the lower part of the mold. IVIM parameters determined at different flow rates are summarized in Table 1. Measured signal intensities and the fitted IVIM curves as well as parameter estimates plotted versus the flow rates are displayed in Figure 2. Figure 3 shows images of the capillary network taken with an optical microscope (Leica DM 2500); spot tests of capillary diameters yielded a range of 4 to 40 µm. The voxel-wise calculated FA was determined to be 0.12±0.04 inside the capillary network.Our study represents the first attempt at performing IVIM measurements in a phantom that realistically mimics blood flow in a capillary bed. Capillary diameters of 4 to 40 µm suggest the dissolved sugar fiber network closely approximates the geometry of in vivo capillaries5. A quasi isotropic alignment of the capillary fibers within the imaging voxels was confirmed by a low fractional anisotropy of 0.12, giving rise to the applicability of the IVIM model to our phantom. The self-diffusion of water molecules is clearly restricted inside the capillaries, as the diffusion coefficient determined without flow is considerably less than what is expected from free diffusing water at room temperature (~2×10^-3mm²/s). The presence of two compartments and of a perfusion fraction f<1 can be explained by fluid-filled dead ends and microspheres (inherent to the molding process), numerous of which were observed by light microscopy. In accordance with the IVIM theory, the pseudodiffusion D*, which can be associated with the flow velocity inside the capillaries6, as well as the product D*×f, constituting a measure of flow6, show proportionality to the applied flow rate. These results demonstrate that the presented flow phantom is ideal to assess the applicability of IVIM measurements and influence factors such as flow rates, fiber density, fiber diameter, or acquisition parameters (field strength, gradient schemes, b-values, etc).