Reliable estimation of Diffusional kurtosis in the skeletal muscle needs perfusion correction.
Alberto De Luca1,2,3, Alessandra Bertoldo1, and Martijn Froeling3

1Department of Information Engineering, University of Padova, Padova, Italy, 2Neuroimaging Lab, Scientific Institute IRCCS Eugenio Medea, Bosisio Parini (LC), Italy, 3Department of Radiology, University Medical Center, Utrecht, Netherlands

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 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.

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 K), f f) 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 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.

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

1. Oudeman, J. et al. Techniques and applications of skeletal muscle diffusion tensor imaging: A review. J. Magn. Reson. Imaging n/a–n/a (2015). doi:10.1002/jmri.25016

2. Le Bihan, D. et al. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology 161, 401–7 (1986).

3. Jensen, J. H., Helpern, J. a, Ramani, A., Lu, H. & Kaczynski, K. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn. Reson. Med. 53, 1432–40 (2005).

4. Klein, S., Staring, M., Murphy, K., Viergever, M. A. & Pluim, J. P. W. elastix: a toolbox for intensity-based medical image registration. IEEE Trans. Med. Imaging 29, 196–205 (2010).

5. Filli, L. et al. Dynamic intravoxel incoherent motion imaging of skeletal muscle at rest and after exercise. NMR Biomed. 28, 240–246 (2015).

Figures

Figure 1 – 25,50 and 75 percentile of A)results of simulations(4 biologically feasible f,K settings, 3 SNR levels) and B)results on real-data for each ROI and time-point. Effects of perfusion are more evident on A)[M1A] and [M1B] estimations and B)muscles SOL and GAS. Dashed black line are imposed values.

Table 1 - Relative errors at SNR=30 for the 4 considered simulations. Model [M2], that includes IVIM correction, resulted in the lowest relative errors for all simulations. Errors increase with perfusion fraction (I-III f=5%, II-IV f=15%).

Figure 2 – Example slice of A) non-weighted diffusion data and B-F) maps obtained with model [M2]. Panels A-B and D-E-F share the same color bar. Panel B is the estimated non-weighted image, Panel E is the blood signal fraction, F the kurtosis map.

Table 2 - Relative difference (%) between estimations of KK), ff), and MD (δMD) over two time-points. Last column is the mean of the increments across subjects and ROIs. NA value for TA of S1 is due to signal drop-out in the second time-point.

Figure 3 - Left panel shows correlations between δf (computed with [M2]) and δK. Pearson correlation was significant and high for both [M1A] and [M1B], but not for [M2]. Right panel shows correlations between δf and inter-scan variations of MD (δMD), none of which significant.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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