Abstract
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.
Highlights
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive imaging technique used to quantify microvascular tissue perfusion with the help of a contrast agent (CA) (Ingrisch and Sourbron 2013)
We assessed posterior probability distributions of tracer-kinetic parameters obtained with a Bayesian tofts model (BTM) against a standard nonlinear least squares (NLLS) approach.Validation with a digital reference objects (DRO) revealed high accuracy of BTM and NLLS approaches, indicated by strong similarity between estimated and ground truth maps
Analysis of the breast cancer DCE-MRI dataset with the BTM revealed that the degree of decrease in Ktrans gives information about the pathologic response to neoadjuvant chemotherapy (NACT)
Summary
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a noninvasive imaging technique used to quantify microvascular tissue perfusion with the help of a contrast agent (CA) (Ingrisch and Sourbron 2013). The CA increases T1 and T2 relaxation rates of surrounding water protons and causes signal enhancement in a T1-weighted acquisition. By measuring multiple T1-weighted images during the passage of the CA through the tissue of interest, a time-dependent CA concentration can be extracted from the signal-time course of each voxel. Besides determining semi-quantitative and descriptive parameters from the concentration curves, e.g. time to peak, area under curve, or maximum, quantitative perfusion parameters can be obtained by fitting pharmacokinetic (PK) models to the data (Roberts et al 2006, Sourbron and Buckley 2012, 2013). Popular PK models that characterize CA transport from DCE-MRI data are the classical Tofts model (TM) (Tofts 1997), the extended Tofts model and the two compartment exchange model (Sourbron and Buckley 2011)
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