The concept of Intravoxel Incoherent Motion (IVIM) (1) for perfusion measurement in the heart has gained significant interest in recent years (2), (3). However, low signal-to-noise ratio, partial voluming, cardiac and respiratory motion render IVIM acquisitions and parameter mapping of the heart very challenging. The objective of the present work was to implement cardiac IVIM using a second-order motion compensated diffusion weighted spin-echo approach in conjunction with Bayesian processing to permit perfusion and diffusion parameter mapping of the heart during cardiac contraction.

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 mm², slice thickness: 8 mm, reduced field-of-view (FOV): 230×100 mm², 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/mm²) (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 S₀, 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 2·10⁴ samples for a burn-in phase and 10⁴ 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.

Systolic IVIM data were successfully acquired in all subjects (Figure 2). BSP processing (Table 1) resulted in reduced fluctuation of D and f maps across the myocardium when compared to the LSQ results (Figure 3). The intra-slice variation of D, f and D* was 0.02·10^-3 mm²/s, 0.026, 3.19·10^-2 mm²/s for BSP versus 0.03·10^-3 mm²/s, 0.041, 2.32·10^-2 mm²/s for LSQ (Figure 4). Mean values per sector and slice across the myocardium were comparable (1.33·10^-3 mm²/s, 0.095, 5.99·10^-2 mm²/s (BSP) vs. 1.27·10^-3 mm²/s, 0.114, 4.18·10^-2 mm²/s (LSQ)). Comparing mean values of the mid-ventricular and apical slices a difference of 0.01·10^-3 mm²/s, 0.018, 1.19·10^-2 mm²/s for D, f, and D* was found across volunteers. The overall mean and standard deviation of the perfusion fraction across all volunteers was 0.104±0.064 and 0.086±0.049 for the mid-ventricular and apical slice, respectively.Second-order motion compensated diffusion-weighted imaging in combination with Bayesian shrinkage prior inference allows to map the perfusion fraction of the human heart during systolic contraction. Imaging in systole reduces partial volume effects due to a more favorable ratio of voxel size to myocardial thickness when compared to imaging in diastole. In addition, systolic time points are more reproducible in the presence of heart rate variations thereby improving the consistency of the data. In combination with Bayesian processing perfusion maps with reduced noise are obtained when compared to standard segmented least squares fitting.Bayesian Intravoxel Incoherent Motion mapping is considered a promising approach to map myocardial perfusion fractions without the need for contrast agent administration. Further work is warranted to study local perfusion changes during both rest and pharmacologically induced stress in ischemic patients.