  Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance
imaging data is commonly performed with the well-known Tofts model and
nonlinear least squares (NLLS) regression. This approach yields point estimates
of model parameters, uncertainty of these estimates can be assessed e.g. by an
additional bootstrapping analysis. Here, we present a Bayesian probabilistic
modeling approach for tracer-kinetic analysis with a Tofts model, which yields
posterior probability distributions of perfusion parameters and therefore
promises a robust and information-enriched alternative based on a framework of
probability distributions. In this manuscript, we use the Quantitative Imaging
Biomarkers Alliance (QIBA) Tofts phantom to evaluate the Bayesian Tofts Model
(BTM) against a bootstrapped NLLS approach. Furthermore, we demonstrate how
Bayesian posterior probability distributions can be employed to assess
treatment response in a breast cancer DCE-MRI dataset using Cohen's d. Accuracy
and precision of the BTM posterior distributions were validated and found to be
in good agreement with the NLLS approaches, and assessment of therapy response
with respect to uncertainty in parameter estimates was found to be excellent.
In conclusion, the Bayesian modeling approach provides an elegant means to
determine uncertainty via posterior distributions within a single step and
provides honest information about changes in parameter estimates.
