Synopsis
Perfusion is
known to affect the estimation of Diffusion Tensor Imaging (DTI) measures on
the skeletal muscle. However, no previous works evaluated its effects on kurtosis
estimation. Therefore, in this study we investigated the influence of perfusion
on kurtosis. Synthetic signals for different perfusion levels with and without isotropic
kurtosis were generated and then fitted with and without taking IVIM into consideration.
Results showed that IVIM correction was essential to estimate non-biased values
of kurtosis in case of increased perfusion. Real data showed that the
simultaneous estimation of kurtosis and IVIM is robust and feasible.Purpose
Blood
perfusion is known to affect the estimation of Diffusion Tensor Imaging (DTI)
measures on the skeletal muscle
1. 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.
Methods
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.
Results
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.
Discussion
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 exercise
5. 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 δ
f, therefore perfusion effects appear to be collected by
K when IVIM correction is not included.
Conclusion
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.
Acknowledgements
No acknowledgement found.References
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