Blood perfusion is known to affect the estimation of Diffusion Tensor Imaging (DTI) measures on the skeletal muscle¹. However, no previous works evaluated its effects on estimates of non-Gaussian diffusion using kurtosis. Therefore, the aim of this study was to investigate the relationship between models of perfusion and kurtosis through simulations and real data.

A) SIMULATIONS: Synthetic signals were generated (Matlab 2014b, The Mathworks) combining the signal equation of the IVIM model2 with that of isotropic kurtosis³:

$$S_{K}=S_{0}e^{-b\bar{D}+\frac{1}{6}b^2D^2K} [1]$$

$$S=fS_{K}+S_{0}(1-f)e^{-bD^*} [2]$$

with $$$f$$$ blood signal fraction, $$${\bar{D}}$$$ diffusion tensor, $$$D$$$ mean diffusivity (from $$${\bar{D}}$$$), $$$K$$$ isotropic kurtosis, $$${S_0}$$$ non-weighted signal, $$$D^{*}$$$ pseudo-diffusivity of blood and b diffusion vector weighting strength and direction. Simulations were performed using FA=0.34,MD=1.3µm²/s and 4 sets of biologically feasible f and K values: I) f=5% K=0, II) f=15% K=0, III) f=5% K=0.5 IV) f=15% and K=0.5. The simulated acquisition scheme comprised 12 b=0s/mm², 6 b=2,5,10,20,50,100,200s/mm², 10 b=400s/mm², 15 b=700s/mm², 25 b=1000s/mm² and 30 b=1300s/mm² which was identical to our in-vivo acquisition protocol. Signals were fitted using three methods:[M1A] linear least-squares fit of equation [1] excluding 0<b<400, [M1B] non-linear least-squares fit of equation [1] excluding 0<b<400, and [M2] and non-linear least-squares fit of equation [2] using all b-values. Simulations were repeated 5000 times with addition of Rician noise for SNR levels of 10, 30 and 100 of the non-weighted image. Bias of the estimates was computed as relative difference between median value of the estimated parameters and imposed values. B) REAL DATA: Three subjects (males, age: 27, 34 and 23 years) underwent MRI of the right calf twice, 7 days inter-scan time. Data was acquired on a 3T Philips Scanner using a 16 channel knee coil, and comprised a diffusion weighted (DW) EPI sequence (TE=55ms/TR=6500s, resolution 2.5x2.5x5mm³), and a DIXON sequence for anatomical reference (resolution 1x1x1mm³, 3 echoes). Regions of interest (ROIs) selecting the “Tibialis Anterior” (TA), “Soleus” (SOL) and “Gastrocnemius” (GAS) were manually drawn using the DIXON images. ROIs were moved to the diffusion space of each time point using a non-linear registration (Elastix⁴). Data was fitted with methods [M1A], [M1B] and [M2] identical to the simulations.

Figure 1A reports 25, 50 and 75 percentile of K, FA and MD for the 4 simulations. The relative errors for each simulation at SNR=30 are reported in Table 1. The simulations showed that for [M1A] and [M1B] in absence of kurtosis but with perfusion, K and MD were overestimated, while FA was underestimated even at SNR=100. Maximum relative errors were observed for f=15%, conversely the error of K was reduced when K>0 with f=5%.

Figure 2 shows an example slice of the computed parametric maps using real data with [M2] (SNR=37±5). 25, 50 75 percentile of K, FA and MD of each acquired time-point are shown in Figure 1B. Real data fitted with [M2] generally exhibited lower K and MD, and higher FA values than [M1A] and [M1B]. Table 2 reports inter-scan relative differences of K (δK), f (δf) and MD (δMD) for each ROI. Variation of K for models [M1A] and [M1B] ranged between 1.8% and 44%, with sign generally opposite to δf. Figure 3 shows that δK was significantly correlated to δf with [M1A] (77%) and [M1B] (90%), but not with [M2]. None of the models showed a significant correlation between δMD and δf.

Simulations showed that not accounting for IVIM leads to estimation errors of K up to 57% (Table 1) in the presence of high perfusion signal fractions. In-vivo this could occur near vessels or as result of muscle exercise⁵. Furthermore, adequate SNR is essential for estimation of K. At low SNR all methods showed biased and highly variable estimates (Figure 1A). Inter-scan variations of K with [M1A] and [M1B] (Table 2) were significantly correlated to variations of perfusion (Figure 3), as expected from simulations. Conversely, δMD was not significantly correlated to δf, therefore perfusion effects appear to be collected by K when IVIM correction is not included. In this study we show that, provided sufficient SNR, it is possible to simultaneously estimate perfusion, diffusion tensor and isotropic kurtosis. Effects of perfusion on kurtosis estimation were revealed on simulations and real data. Values of K and f of the SOL and GAS muscles were similar to those used in simulation III, which showed estimation of K is affected by f. Inter-scan Pearson’s correlations showed that IVIM correction is essential to disentangle effects of perfusion on Kurtosis, especially if K is used to evaluate disease or other transient effects.