Bayesian Intravoxel Incoherent Motion Imaging to Map Perfusion in the Human Heart

Georg Spinner^{1}, Constantin von Deuster^{1,2}, Christian Torben Stoeck^{1}, and Sebastian Kozerke^{1}

A second-order motion compensated diffusion-weighted spin-echo EPI
sequence (Figure 1) (4) was implemented on a a 1.5T
Philips Achieva system (Philips Healthcare, Best, The Netherlands) equipped
with a 5-channel cardiac receiver coil array and a gradient system delivering
80 mT/m at 100 mT/m/ms. Data from four healthy volunteers (3 female, 1 male,
age: 23.5±3.0 years, weight 63.3±8.3 kg, heart rate 69±5 beats/min) were
acquired. Two short-axis slices at mid-ventricular and apical level were
prescribed and diffusion images were obtained with following parameters:
spatial resolution: 2.5×2.5 mm^{2}, slice thickness: 8 mm, reduced
field-of-view (FOV): 230×100 mm^{2}, TR/TE: 2R-R/85ms, 7 signal
averages, spectral-spatial water-only excitation. Diffusion encoding was
performed using 16 optimized b-values (range: 0-880 s/mm^{2}) (5) acquired along three
orthogonal diffusion encoding directions during cardiac contraction (50% end systole).
Each diffusion direction and b-value was acquired during respiratory navigated breath holding (acceptance
window: 5 mm).

In post-processing, affine image registration of diffusion weighted images and averages was performed using elastix (6) to correct for residual respiratory motion induced geometrical inconsistency. In addition, image intensities were corrected to account for variations of the effective repetition time TR as a result of varying heart rate. Thereupon, the signal S(b) was fitted using the IVIM model (Equation 1):

$$S(b)=S_{0} \left[ (1-f) e^{-bD} + f e^{-bD^{*}}\right] \quad (1),$$

with reference intensity S_{0}, diffusion encoding
strength b, diffusion coefficient D, perfusion
fraction f and pseudo-diffusion coefficient D*. For model
fitting, a Bayesian shrinkage prior (BSP) inference approach (7) was implemented to estimate
the parameters of the IVIM model. The shrinkage prior was a multivariate
Gaussian distribution of the log-transformed parameters with a Jeffrey's
hyper-prior (8) on the parameter
region-of-interest (ROI) mean μ and covariance matrix Σ_{μ}:

$$p \left( \mu, \Sigma_{\mu} \right) = |\Sigma_{\mu}|^{-1/2} \quad (2)$$

The Markov Chain
Monte Carlo implementation of Equation 2 used 2·10^{4} samples for a burn-in phase
and 10^{4} for the actual sampling. For comparison, a standard segmented
least squares (LSQ) fit (9) was used. Both the LSQ and the
BSP method were implemented in Matlab (The Mathworks, Natick, MA) as part of
the overall processing chain. In data analysis, the variance of D, f and D*
across the myocardium and slices was compared for BSP vs. LSQ in each subject
according to the AHA segmentation scheme (10). Mean values and ranges are
reported for the study population.

1. Le Bihan D, Breton E, Lallemand D, Aubin ML, Vignaud J, Laval-Jeantet M. Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging. Radiology 1988;168:497–505. doi: 10.1148/radiology.168.2.3393671.

2. Moulin K, Croisille P, Feiweier T, Delattre BM a, Wei H, Robert B, Beuf O, Viallon M. In-vivo free-breathing DTI & IVIM of the whole human heart using a real-time slice-followed SE-EPI navigator-based sequence: a reproducibility study in healthy volunteers. 23rd Annu. Meet. ISMRM 2015;3:5220.

3. Delattre BM a, Viallon M, Wei H, Zhu YM, Feiweier T, Pai VM, Wen H, Croisille P. In vivo cardiac diffusion-weighted magnetic resonance imaging: quantification of normal perfusion and diffusion coefficients with intravoxel incoherent motion imaging. Invest. Radiol. 2012;47:662–70. doi: 10.1097/RLI.0b013e31826ef901.

4. Stoeck CT, von Deuster C, Genet M, Atkinson D, Kozerke S. Second-order motion-compensated spin echo diffusion tensor imaging of the human heart. Magn. Reson. Med. 2015: doi: 10.1002/mrm.25784.

5. Lemke A, Stieltjes B, Schad LR, Laun FB. Toward an optimal distribution of b values for intravoxel incoherent motion imaging. Magn. Reson. Imaging 2011;29:766–76. doi: 10.1016/j.mri.2011.03.004.

6. Klein S, Staring M, Murphy K, Viergever M a., Pluim JPW. Elastix: A toolbox for intensity-based medical image registration. IEEE Trans. Med. Imaging 2010;29:196–205. doi: 10.1109/TMI.2009.2035616.

7. Orton MR, Collins DJ, Koh D-M, Leach MO. Improved intravoxel incoherent motion analysis of diffusion weighted imaging by data driven Bayesian modeling. Magn. Reson. Med. 2014;71:411–20. doi: 10.1002/mrm.24649.

8. Jeffreys H. An Invariant Form for the Prior Probability in Estimation Problems. Proc. R. Soc. London A Math. Phys. Eng. Sci. 1946;186:453–461.

9. Notohamiprodjo M, Chandarana H, Mikheev A, Rusinek H, Grinstead J, Feiweier T, Raya JG, Lee VS, Sigmund EE. Combined intravoxel incoherent motion and diffusion tensor imaging of renal diffusion and flow anisotropy. Magn. Reson. Med. 2014;00:1–7. doi: 10.1002/mrm.25245.

10. Cerqueira MD, Weissman NJ, Dilsizian V, Jacobs AK, Kaul S, Laskey WK, Pennell DJ, Rumberger J a., Ryan TJ, Verani MS. Standardized Myocardial Segmentation and Nomenclature for Tomographic Imaging of the Heart. J. Cardiovasc. Magn. Reson. 2002;4:203–210. doi: 10.1081/JCMR-120003946.

Figure 1: Second order motion compensated diffusion weighted
imaging sequence. Dashed lines indicate the variation of gradients to achieve
different diffusion encoding strengths (b-values) whilst keeping the duration
of the gradients constant.

Figure 2: Example trace images obtained for an apical
and mid-ventricular slice for all recorded b-values (0-880 s/mm^{2}).

Figure 3: Example IVIM parameter maps comparing
least squares (LSQ) and Bayesian shrinkage prior (BSP) based results.

Figure 4: Boxplots of IVIM parameters for least squares
(LSQ) and Bayesian shrinkage prior (BSP) based inference fitting in a single
subject.

Table 1:
Mean IVIM parameters for all volunteers and slices after TR correction and
using Bayesian shrinkage prior (BSP) inference.

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

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