Prostate DCE-MRI with B1+ correction using an approximated analytical approach

Purpose: To develop and evaluate a practical (Formula presented.) correction method for prostate dynamic contrast-enhanced (DCE) MRI analysis. Theory: We proposed a simple analytical (Formula presented.) correction method using a Taylor series approximation to the steady-state spoiled gradient echo signal equation. This approach only requires (Formula presented.) maps and uncorrected pharmacokinetic (PK) parameters as input to estimate the corrected PK parameters. Methods: The proposed method was evaluated using a prostate digital reference object (DRO), and 82 in vivo prostate DCE-MRI cases. The approximated analytical correction was compared with the ground truth PK parameters in simulation, and compared with the reference numerical correction in in vivo experiments, using percentage error as the metric. Results: The prostate DRO results showed that our approximated analytical approach provided residual error less than 0.4% for both K^trans and v_e, compared to the ground truth. This noise-free residual error was smaller than the noise-induced error using the reference numerical correction, which had a minimum error of 2.1+4.3% with baseline signal-to-noise ratio of 234.5. For the 82 in vivo cases, K^trans and v_e percentage error compared to the reference numerical correction method had a mean of 0.1% (95% central range of [0.0%, 0.2%]) across the prostate volume. Conclusion: The approximated analytical (Formula presented.) correction method provides comparable results with less than 0.2% error within 95% central range, compared to reference numerical (Formula presented.) correction. The proposed method is a practical solution for (Formula presented.) correction in prostate DCE-MRI because of its simple implementation.