FA, mean diffusivity (MD), axial diffusivity (AD, eigenvector L1), and L2 and L3 maps were created using DTIFIT by applying a diffusion tensor model to each voxel.
By applying a diffusion gradient field of high b values, the biexponential model can differentiate the diffusion in extracellular from that in intracellular, which are defined as fast diffusion coefficient D∗ and slow diffusion coefficient D, respectively.
Fractional anisotropy, mean diffusivity, axial diffusivity (eigenvector L1) and L2 and L3 maps were created using DTIFIT by applying a diffusion tensor model to each voxel (Behrens et al., 2003).
Diffusion-weighted images are generated by applying a diffusion-sensitizing gradient, the strength of this gradient can be altered by changing the b value on the scanner.
The tumors were positioned in the isocenter of the magnet and were imaged axially in a single section through the tumor center by applying a diffusion-weighted single-shot fast spin echo sequence with ETL = 84 and TR = 5002 ms.
DW-MRI was carried out by applying a diffusion-weighted single-shot fast spin echo pulse sequence (RARE) with a TR of 1300 ms, a TE of 26 ms, an image matrix of 64 × 64, a FOV of 3 × 3 cm, a slice thickness of 0.7 mm, and a slice gap of 0.3 mm.
The Ge diffusion coefficients were estimated by applying a linear diffusion equation to the fitting curves, and they indicated a rapid diffusion to the surface side rather than the interface side.
DW functions are computed by sequentially applying a diffusion operator (for instance, the transition matrix P) at the current scale k, compressing the range via a local orthonormalization procedure, representing the operator in the compressed range and computing the P2k on this range.
The proposed method shortens the diffusion time by applying a single refocused bipolar diffusion gradient on one side of a refocusing RF pulse, instead of a set of diffusion sensitizing gradients, separated by a refocusing RF pulse, while reducing the impact of magnetic field inhomogeneity by using a spin echo sequence.
These problems can in part be mitigated by applying a proper degree of diffusion weighting: if DWI is used with the aim to detect liver lesions, it is highly recommended to apply a lower b-value (e.g. a b-value between 10 and 50 s/mm) instead of a b-value of 500 s/mm.
By applying a mathematical model of diffusion and reaction solved at steady-state conditions (Yarmush et al., 1992) to PHH MPCCs (Fig. 3A; supplementary material Fig. S3), it was estimated that the typical cell surface pO2 when cultures are incubated at normoxia ranges from 110 to 130 mmHg (Table 1).
