  Purpose: Tracer-kinetic models can be used for the quantitative assessment of
contrast-enhanced MRI data. However, the model-fitting can produce unreliable
results due to the limited data acquired and the high noise levels. Such
problems are especially prevalent in myocardial perfusion MRI leading to the
compromise of constrained numerical deconvolutions and segmental signal
averaging being commonly used as alternatives to the more complex
tracer-kinetic models. Methods: In this work, the use of hierarchical Bayesian
inference for the parameter estimation is explored. It is shown that with
Bayesian inference it is possible to reliably fit the two-compartment exchange
model to perfusion data. The use of prior knowledge on the ranges of kinetic
parameters and the fact that neighbouring voxels are likely to have similar
kinetic properties combined with a Markov chain Monte Carlo based fitting
procedure significantly improves the reliability of the perfusion estimates
with compared to the traditional least-squares approach. The method is assessed
using both simulated and patient data. Results: The average (standard
deviation) normalised mean square error for the distinct noise realisations of
a simulation phantom falls from 0.32 (0.55) with the least-squares fitting to
0.13 (0.2) using Bayesian inference. The assessment of the presence of coronary
artery disease based purely on the quantitative MBF maps obtained using
Bayesian inference matches the visual assessment in all 24 slices. When using
the maps obtained by the least-squares fitting, a corresponding assessment is
only achieved in 16/24 slices. Conclusion: Bayesian inference allows a
reliable, fully automated and user-independent assessment of myocardial
perfusion on a voxel-wise level using the two-compartment exchange model.
