# Bayesian Pharmacokinetic Modeling of Dynamic Contrast-Enhanced Magnetic Resonance Imaging: Validation and Application

## TL;DR

This paper introduces a Bayesian probabilistic approach for analyzing dynamic contrast-enhanced MRI data, providing detailed uncertainty estimates of perfusion parameters and demonstrating its effectiveness in phantom validation and treatment response assessment.

## Contribution

The paper presents a novel Bayesian Tofts model that offers a robust, probabilistic alternative to traditional NLLS methods for tracer-kinetic analysis in DCE-MRI.

## Key findings

- Bayesian model yields accurate posterior distributions comparable to NLLS.
- Posterior distributions effectively assess treatment response with uncertainty quantification.
- Method provides a single-step approach for parameter estimation and uncertainty analysis.

## 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.