Comparison of tri‐exponential decay versus bi‐exponential decay and full fitting versus segmented fitting for modeling liver intravoxel incoherent motion diffusion MRI

Abstract

Objectives To determine whether bi‐ or tri‐exponential models, and full or segmented fittings, better fit the intravoxel incoherent motion (IVIM) imaging signal of healthy livers. Methods Diffusion‐weighted images were acquired with a 3 T scanner using a respiratory‐triggered echo‐planar sequence and 16 b‐values (0–800 s/mm2). Eighteen healthy volunteers had their livers scanned twice in the same session, and then once in another session. Liver parenchyma region‐of‐interest‐based measurements were processed with bi‐exponential and tri‐exponential models, with both full fitting and segmented fitting (threshold b‐value = 200 s/mm2). Results With the signal of all scans averaged, bi‐exponential model full fitting showed Dslow = 1.14 × 10−3 mm2/s, Dfast = 193.6 × 10−3 mm2/s, and perfusion fraction (PF) = 16.9%, and segmented fitting showed Dslow = 0.98 × 10−3 mm2/s, Dfast = 42.2 × 10−3 mm2/s, and PF = 23.3%. IVIM parameters derived from the tri‐exponential model were similar for full fitting and segmented fitting, with slow (D'slow = 0.98 × 10−3 mm2/s; F'slow = 76.4 or 76.6%), fast (D'fast = 15.1 or 15.4 × 10−3 mm2/s; F'fast = 11.8 or 11.7%) and very fast (D'Vfast = 445.0 or 448.8 × 10−3 mm2/s; F'Vfast = 11.8 or 11.7%) diffusion compartments. The tri‐exponential model provided an overall better fit than the bi‐exponential model. For the bi‐exponential model, full fitting provided a better fit at very low and low b‐values compared with segmented fitting, with the latter tending to underestimate Dfast; however, the segmented method demonstrated lower error in signal prediction for high b‐values. Compared with full fitting, tri‐exponential segmented fitting offered better scan‐rescan reproducibility. Conclusion For healthy liver, tri‐exponential modeling is preferred to bi‐exponential modeling. For the bi‐exponential model, segmented fitting underestimates Dfast, but offers a more accurate estimation of Dslow.

Age and gender dependence of liver diffusion parameters and the possibility that intravoxel incoherent motion modeling of the perfusion component is constrained by the diffusion component

“…Until now there has been no consensus regarding the best threshold b ‐value 3,19,32 . It has been estimated that the perfusion‐related compartment contributes ~17% of the total signal at b = 0 s/mm 2 , then decreases to become negligible at b ≥ 25 s/mm 2 8 . Thus, the commonly used threshold b ‐value of 200 s/mm 2 may be too high 3 .…”

“…Images with 16 b ‐values of 0, 2, 4, 7, 10, 15, 20, 30, 46, 60, 72, 100, 150, 200, 400 and 600 s/mm 2 were acquired. The b ‐values selection was based on our own experience with the following considerations 5,8,19,24 : (1) in most clinical scanners, the maximum b ‐value number allowed is 16; (2) images with b ‐value greater than 600 s/mm 2 tend to have too much noise; (3) to densely sample images with b ‐values of less than 10 s/mm 2 to model the initial fast signal decay; and (4) to relatively densely sample images with b ‐values around ~60 s/mm 2 , which is the critical point to separate fast and slow components. Three‐motion probing gradient directions were applied for each b‐value.…”

“…The signal value at each b ‐value was normalized by attributing a value of 100 at b = 2 s/mm 2 (S norm = (SI/SI (2) ) × 100, where S norm is the normalized signal, SI = signal at a given b ‐value, and SI (2) = signal at b = 2 s/mm 2 ). Both full fitting and segmented fitting were performed, 1,8,12 and for segmented fitting, the threshold b ‐value to separate the fast and slow components was 60 or 200 s/mm 2 3,17–19 For the bi‐compartmental model, the signal attenuation was modeled according to Equation 2: where SI( b ) and SI (2) denote the signal intensity acquired with the b ‐factor value of b and b = 2 s/mm 2 , respectively.…”

“…Recently, it was demonstrated that, with careful selection of b ‐values and improved image postprocessing, PF and D slow measurement can be quite reproducible, and D fast can be moderately reproducible 3–5 . There is also strong evidence that the relationship between liver DWI signal and b ‐value does not follow bi‐exponential decay; instead, it can be better fitted by the addition of a very fast component with a tri‐exponential decay model 5–12 . However, the fitting of a tri‐exponential decay model can be quite instable at the level of an individual study subject 6,8,13 .…”

Evidence of Tri-Exponential Decay for Liver Intravoxel Incoherent Motion MRI: A Review of Published Results and Limitations

“…Since flowing or moving spins are present in these compartments, which are directly or indirectly connected together, it can be hypothesized that more than two compartments of diffusion exist in the liver and could be analyzed through the recorded DWI signal decay. Recently, evidence of the existence of an additional very fast component of diffusion in the liver has been published [ 20 , 22 , 23 , 24 , 25 , 26 ]. Therefore, a tri-exponential decay model has been proposed.…”