We propose a new multi-compartment model for the tissue signal in MRI and apply this to images of liver and placenta. Motivated by different flow characteristics in these organs, a three compartment model comprising fast and slowly circulating fluid pools and a tissue pool is fitted to overlapping multi-echo T2 relaxometry and an intra-voxel incoherent motion diffusion acquisition with low b-values. We compare and contrast parametric maps for regions of interest in liver and placenta.
We propose a general three-compartment model that distinguishes rapidly moving (perfusing) fluid with high pseudo-diffusivity; slowly-moving or static fluid with high T2; and otherwise static tissue with low-diffusivity and low T2. These are given respective volume fractions $$$f$$$ for moving fluid and $$$\nu$$$ for static fluid. The signal model for $$$S$$$, as a function of echo-time $$$t$$$ and diffusion weighting $$$b$$$, is represented by equation 1 combining the effects of T2 relaxation and diffusion-weighting. $$$S_0$$$ represents the initial signal magnitude. The diffusivities of these compartments are given by $$$d^*$$$ for moving fluid and $$$d$$$ for the remaining fluid and contribution of tissue since typically $$$d^*$$$ is much larger than $$$d$$$. We fix the relaxivities from literature values: $$$r_2^b=295ms$$$ for fluid and $$$r_2^t=60ms$$$ for tissue [6]. This is equivalent to the standard IVIM model if $$$r_2^b=r_2^t$$$ and $$$\nu=0$$$, although this changes the interpretation of the perfusion fraction $$$f$$$.
$$S(b,t)=S_{0}\bigl[ f e^{-\textbf{b}d^*-\textbf{t}r_2^b} + (1-f) e^{-\textbf{b}d} \bigl( \nu e^{-\textbf{t}r_2^b} + (1-\nu) e^{-\textbf{t}r_2^t} \bigr) \bigr]$$
We compare our proposed multi-compartment model with existing models. We evaluate the apparent diffusion coefficient (ADC), and the single-compartment T2 rate. Standard IVIM [2] simultaneously estimates the volume fraction of two compartments of diffusion, associating high-diffusivity regions with perfusing or moving fluid; thus we also evaluate the standard IVIM perfusion fraction. Results are presented as histograms over all voxels within manually segmented regions of interest.
Parametric maps for the liver are shown in Figure 1 for parameters drawn from standard IVIM (top row) and the three-compartment model (bottom row). Any contribution from static fluid, $$$\nu$$$ is minor. Figure 2 shows ROI histograms for six liver datasets for volume fractions and diffusivities. IVIM results are shown with orange bars, 3-compartment results with blue bars. There is little support across all datasets for a significant non-moving fluid compartment, consistent with known properties of the liver.
Placenta parameter histograms are shown in Figure 3 for single-compartment ADC and T2. Figure 4 compares histogram distributions of IVIM (orange) with the three-compartment model (blue). A significant non-zero volume fraction $$$\nu$$$ is seen for static/slowly moving fluid. Perfusion fractions remain comparable between the two models.
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