Multicellular spheroids grown from epithelial cells can mimic the tumour microenvironment and provide a well-controlled environment for studying numerous tissue properties ¹. To our knowledge spheroids have not been used to investigate water diffusion dynamics. Recent reports demonstrate low-diffusivity epithelia in prostate ², breast ³, an esophagus tissue ⁴, unlinked to any differences in cell density relative to adjacent stroma ⁵. Spheroids demonstrate many of the physiological properties of glandular epithelia and provide an ideal experimental model for investigation of the distinctive structural properties that may contribute to low water mobility. The structural connections between adjacent cells in spheroids are very similar to those in intact tissue and thus they provide a more realistic model of tissue than previously investigated models based on pelleted cells. Here we report a pilot investigation of the correlation between known cell sizes in a spheroid culture and restriction radius estimated by a compartment model of diffusion MRI signals.

Spheroids were cultured from DLD-1 (human colorectal carcinoma) cell line using the liquid overlay method. Agar-coated wells were seeded with 1.8x10⁶ cells/ml and incubated under standard conditions for 4 days without motion (final spheroid diameter ~500 μm). Six spheroids were fixed with 4% paraformaldehyde for two hours, washed four times with PBS, and transferred to a 5-mm flat-bottom Shigemi NMR tube for imaging.

DWI. Imaging was performed at 25℃ in a 14T Bruker AV600 scanner. A 3D pulsed gradient spin echo sequence was applied with: Δ = 10, 20, 40 ms; δ = 2 ms; nominal b = 100, 311, 603, 965, 1391, 1873, 2411, 3000 s/mm²; voxel size 80×80×80 μm³; 3 orthogonal gradient directions; TE = 19, 26, 46 ms; TR = 400ms; SNR_b=0 ~17; FOV 5×5×1.6 mm; slice thickness = 80 μm; and matrix 62×62. A separate 6-direction DTI acquisition was performed with Δ = 10, 20 ms, δ = 2 ms, TE = 26 ms, TR = 400ms and nominal b = 1000 s/mm². The data were normalized to reduce T₂ dependence and contained 76 measurements. Four voxels from the center of each spheroid were selected (Fig 1).

Diffusion Models. Signal was modeled with one to two components representing non-exchanging spin pools. For each component, there were two candidate models ⁶: 1) a ‘Ball’ that is an isotropic tensor; and 2) a ‘Sphere’ describing diffusion inside an impermeable sphere of radius R. Diffusivities were constrained to be within biologically plausible limits so that 0<D<2.1 μm²/ms. For the ‘Sphere’ model, we constrained the radius to be 0.1<R<20 μm. Three models were fitted to the average signal from the combined data : Ball (equivalent to ADC); Bi-ball (conventional biexponential); and Ball-sphere. Anisotropic models were not tested.

Model fitting and ranking. Each model was fitted to the combined 6 and 3-direction data using the Levenberg-Marquardt minimization algorithm in the open source Camino toolkit ⁷. Akaike Information Criterion (AIC) was calculated to provide an objective comparison of the information content of different models.

Ranking of models by AIC indicated that the Ball-sphere had the highest information content. AIC = 46, 61, 105 for Ball-sphere, Bi-ball and Ball models respectively. Fig 2 illustrates the fit of the models to the average signal over the selected voxels. The sphere radius R from the Ball-sphere model was 8.5μm. For fits to the 24 individual voxels the mean sphere radius was 10.9±3.9 μm and the signal fraction of the sphere 0.68±0.15. The sphere and ball diffusivities were 0.93±0.77 and 1.5±0.9 µm²/ms respectively.Typical cell diameter for DLD-1 spheroids would be ~20-25 µm which is in good agreement with the mean restricted sphere radius of 10.9 μm and strongly suggests the restricted spin pool is primarily comprised of intracellular water. The sphere signal fraction of 0.68 is of particular interest as the intracellular volume fraction of pelleted single cells (eg. yeast or erythrocytes) does not normally exceed 0.5. The ball and sphere diffusivities are also consistent with previous estimated for extra and intracellular water respectively. In the spheroids the low extracellular volume fraction (the ball component of the Ball-sphere model) is consistent with the hypothesis that the presence of tight intercellular junctions in epithelia minimizes any signal from fast diffusing paracellular water, giving rise to the low diffusivity of epithelia observed in diffusion micro imaging ^2-4.Modelling of water diffusion in cultured epithelial cell spheroids returns structure-based parameters consistent with known cell properties. Cultured spheroids provide a highly controllable tissue model that will enhance our understanding of the tissue microstructure properties that affect diffusion contrast in clinical imaging.