# A correction for modeling radial, spiral, and PROPELLER dynamic contrast‐enhanced data: Time‐averaged extended Tofts

## TL;DR

This paper introduces a corrected model for dynamic contrast-enhanced MRI to improve pharmacokinetic accuracy when using time-averaged signals from non-Cartesian sampling.

## Contribution

A modified extended Tofts model that accounts for time-averaged signals in non-Cartesian MRI acquisitions.

## Key findings

- The modified model provides more accurate and precise results than conventional models for time-averaged acquisitions.
- At long acquisition times (15 s/frame), the modified model outperformed conventional discrete sampling.
- In vivo experiments showed more consistent parameter estimates with the corrected model.

## Abstract

Dynamic contrast‐enhanced sequences (e.g. spiral, radial, PROPELLER MRI) often rely on oversampling the center of k‐space. Instead of the discrete snapshots obtained by Cartesian sampling, oversampling the k‐space center results in time‐averaging of the signal. We hypothesize that these time‐averaged signals decrease the accuracy of pharmacokinetic modeling and propose a model that accounts for this effect.

To test our hypothesis, a modified extended Tofts model tailored to accommodate time‐averaged signals is proposed. Simulated Monte Carlo experiments were conducted to compare the performance of the modified model with the conventional model. Additionally, to validate the findings in vivo, models were fitted to pseudo‐spiral variable‐density dynamic contrast‐enhanced MRI scans of pancreatic cancer patients reconstructed at 4, 8, 10, and 15 s/frame.

The simulations demonstrated that for time‐averaged acquisitions, our modified extended Tofts model provided more accurate and precise results than conventional models. Additionally, by integrating signals, some information on high temporal behavior was recovered. Particularly, at long acquisitions (15 s/frame), variable‐density sampling with the modified model outperformed conventional discrete sampling. In vivo experiments confirmed these findings, as the corrected model showed more consistent estimates of parameters vp and ve over the tested sampling frequencies, highlighting its potential to improve accuracy in clinical settings.

Our study demonstrates that time‐averaged signals lead to decreased accuracy and precision in pharmacokinetic modeling when ignored. We suggest using our corrected pharmacokinetic model when performing dynamic contrast‐enhanced with variable‐density acquisitions, especially for dynamic scan times that are 8 s and longer.