Background
Cardiovascular magnetic resonance (CMR) diffusion weighted imaging relies on signal attenuation due to random motion of water molecules in the presence of diffusion encoding gradients. Additionally, microvascular perfusion can contribute to the signal loss as described by the intravoxel incoherent motion (IVIM) model [
1,
2]. According to Le Bihan et al. [
3,
4], perfusion can be modeled as pseudo diffusion on a macroscopic scale, assuming random orientation of microvasculature in the capillary network. Consequently, the signal intensity can be described by a bi-exponential signal decay as a function of the diffusion encoding strength (b-value). As the IVIM method is an endogenous contrast technique, its application is particularly suited to obtain a tissue perfusion surrogate where contrast agent administration is contraindicated. In recent years, this technique has gained significant momentum with successful applications in various body parts [
5‐
9]. Beyond body and brain applications, IVIM of the in-vivo human heart has also been demonstrated [
10,
11].
Cardiac IVIM may allow to delineate infarcted and ischemic areas showing good agreement with late-gadolinium enhanced imaging [
12,
13]. Moreover, IVIM may enable the assessment of chronic and acute ischemia [
14] as well as conditions related to microvascular obstruction of the myocardium [
15].
Despite recent progress, in-vivo cardiac diffusion weighted imaging still remains challenging due to cardiac and respiratory motion. Additionally, low signal-to-noise ratio (SNR) and long scan times are major impediments to a wider acceptance in a clinical setting. Motion induced signal loss in spin-echo (SE) based cardiac diffusion weighted imaging has been addressed by first-order motion-compensated diffusion gradient designs in conjunction with careful cardiac trigger delay selection [
16] and more recently by second-order motion compensation [
17‐
19]. Initial results of the application of second-order motion compensation for IVIM acquisitions during systole have previously been presented in a porcine model [
14]. For diastolic imaging, time-shifted triggering and dedicated post processing using principal component analysis (PCA) filtering in combination with temporal maximum intensity projection (PCATMIP) has been proposed [
20‐
23].
Experimentally, cardiac IVIM parameters were initially reported for the in-vivo canine heart by Callot et al. [
24]. The measured diffusion weighted signal agreed well with the bi-exponential IVIM model with reduced signal decay in the absence of perfusion post-mortem [
14].
IVIM parameter maps of various organs such as brain or heart [
20,
25] are typically of noisy appearance. Due to the non-linearity and bad conditioning of the regression problem, the perfusion related parameters are estimated with considerable error at typical SNR values as shown in [
26,
27]. Besides modifying the data acquisition protocol to obtain higher SNR at the expense of lower spatial resolution and/or longer scan time, group analysis of longitudinal data of individuals incorporating both intra- and inter-subject variations [
28] or regional smoothing [
29] have been proposed. These approaches are, however, limited by the necessity of repeated measurements across multiple independent subjects or loss of spatial resolution and increased partial-voluming, respectively.
To address the SNR limitation of IVIM analysis, a hierarchical Bayesian data analysis framework has been presented by Orton et al. [
30] and demonstrated for liver application. Using this approach, information across the region-of-interest is taken into account for voxelwise parameter inference. Parameter estimation is performed using a posterior distribution combining data likelihood and a hierarchical prior. This combination enables effective denoising of parameter maps with reduced parameter estimation error.
The objective of the present work was to implement and assess Bayesian shrinkage prior (BSP) inference for IVIM parameter mapping of the in-vivo human heart and compare its performance to segmented least-squares (LSQ) fitting.
Discussion
In the present work, Bayesian shrinkage prior inference has been implemented and compared to segmented least-squares fitting for IVIM parameter mapping in the in-vivo human heart.
Robust data acquisition was possible using a second-order motion-compensated diffusion weighted spin-echo sequence [
17] triggered to early systole. Using a trigger delay of 25% peak systole is advantageous because of increased coronary flow compared to peak contraction. Moreover, a large part of systole is potentially available for IVIM acquisitions as shown in [
17]: trigger delays in the range of 15–77/79% peak systole at the apex/base allow for robust diffusion data acquisition. In addition, imaging in systole has the advantage of a relatively thick myocardium compared to the voxel size.
Using motion-compensated diffusion gradients may lead to a reduced sensitivity to blood circulation and myocardial perfusion [
41]. However, deviations from a mono-exponential diffusion model at lower b-values due to perfusion were observed in all measurements indicating sufficient sensitivity to microcirculation and perfusion. Balancing motion-induced signal loss due to cardiac bulk motion while achieving optimal sensitivity to perfusion is however a subject deserving further attention.
Computer simulations revealed minimum SNR thresholds of 30–60 for relative errors in terms of bias and variation of 20% each, depending on the perfusion regime for BSP while the LSQ method required a minimum SNR of at least 200. The increase in bias in
F for the SNR range of 125–175 using LSQ is suspected to be an artefact of the segmented fit, which leads to an error propagation of
D and
S
int
into the estimation of the perfusion parameters. Furthermore, we note that Federau and colleagues also reported a similar increase in bias in
F in Fig.
1 of [
27] using a segmented approach; albeit in the SNR range of approx. 20–40 with simulated IVIM parameters which are commonly found in the brain (
D=0.7·10
−3mm
2s,
F=4% and
D
∗=17·10
−3mm
2s). Even though the relative bias in
F in the considered SNR range is below about 20%, the segmented fit might benefit from a joint parameter estimation (potentially using two regimes of mono- and bi-exponential decay) in this regard. While these simulation results are indicative, several factors confounding in-vivo measurements have not been taken into account in the simulations including residual motion artifacts and partial voluming with hyperintense blood signal and epicardial fat [
42]. These effects would lead to a broadening of the parameter histograms. Accordingly, the width of the prior is increased by the presence of a large number of affected voxels. The shrinking procedure in these cases is less effective.
In-vivo, BSP analysis resulted in IVIM parameter maps with considerably smaller intra-myocardial standard deviations relative to LSQ. Both variability and estimation uncertainty in terms of standard deviation under the posterior were greatly reduced with BSP compared to LSQ (Fig.
6), indicating the benefit of taking into account prior knowledge. The setting of arbitrary fit constraints was obsolete in the BSP procedure. In addition, BSP regression was aided by the prior which led to the elimination of outliers on or close to the fit boundaries.
An effective spatial denoising of the parameters can be achieved because the prior in BSP is chosen to be a unimodal distribution. This prior assumes a population mean of the IVIM parameters for the whole region-of-interest and hence assumes the myocardium of the left ventricle to have a rather homogenous spatial tissue characteristic. If local pathologies such as myocardial infarcts (as for example presented in
Appendix 2) and corresponding fibrous tissue with reduced perfusion [
14] are present, a different choice of priors such as a spatial homogeneous prior [
43] is deemed more appropriate [
42]. Alternatively, multimodal priors can be applied to distinguish among different tissue types while still retaining spatial information. Methods using mixture models [
44] of multivariate Gaussians could also be implemented to address this limitation. In contrast to the LSQ approach, which allows data processing on a pixel-by-pixel basis, the BSP method requires pre-segmentation of the data, which renders automation in a post-processing workflow more challenging.
Overall, the in-vivo IVIM parameters measured in this study are in good accordance with recent literature [
10,
20]. The diffusion coefficients
D found in this study using LSQ and BSP were within the range of the values found in [
10,
20]. A higher measured diffusivity is indicative of residual motion effects in the data [
45]. In addition, the mean diffusivity measured using spin-echo based diffusion tensor imaging (DTI) during early systole [
40] was within 14% and 6% of the mean measured diffusion coefficient of the present study for LSQ and BSP, respectively. The measured perfusion fraction
F was found to be lower compared to data reported in [
10]. The LSQ and BSP estimation of approx. 13% is close to the 12% found in [
20] during diastole. The pseudo-diffusion coefficients
D
∗ of 201.50 ± 313.20 mm
2/s (LSQ) and 13.11 ± 14.53 mm
2/s (BSP) as measured in the present study are different from previous data (52.68 ± 52.61·10
−3 mm
2/s [
10], 43.6 ± 9.2·10
−3 mm
2/s [
20]). However,
D
∗ usually contains the highest number of outliers and the mean across the region-of-interest is therefore prone to be heavily influenced by the choice of the actual value of the box-constraints. If the medians across the regions-of-interest are considered, it is shown that the majority of the LSQ estimates gather in the range of 20 to 50·10
−3 mm
2/s. Moreover, data in Fig.
6 indicates that mean estimates of
D
∗ are considerably influenced by outliers with median parameter values close to the ones found using the BSP method.
The IVIM perfusion parameters in an infarcted animal model (see also
Appendix 2) show good accordance with the perfusion defect visible in the contrast enhanced perfusion scan, especially considering the blood flow related [
25,
27] product of
F ×
D
∗ of the BSP derived estimates. However, the extension of the infarct indicated by IVIM appears smaller compared to the darkened area of the contrast enhanced perfusion scan. This might be due to residual motion and/or partial voluming which can yield elevated IVIM parameter estimates.
All SNR measurements were obtained from a single signal average. Thereby confounding factors due to image registration and phase correction for averaging of complex data were avoided. The in-vivo SNR was above the 20% parameter error threshold found in simulations. The scan time of ca. 18 min for a heart rate of 60 bpm for this study was in-between previous scanning times of 15 min [
10] and 20 min [
20]. Optimizations of the experiment design in terms of b-value distribution [
46], higher static field strength and improved gradient performance to reduce echo times may allow to reduce parameter estimation error and scan time.
By design, Bayesian approaches exploiting information across the region-of-interest can be used to examine distributed rather than focal pathologies of the myocardium. Accordingly, potential applications relate to microvascular obstruction and reduced and/or delayed perfusion of the myocardium in hypertrophic cardiomyopathy and diabetes [
15,
47].