Quantitative dynamic contrast-enhanced MRI (DCE-MRI) has shown great promise for detection and grading of prostate cancer. Pharmacokinetic (PK) analysis is a powerful tool that provides quantitative assessment for contrast uptake in DCE-MRI, however, B₁⁺ inhomogeneity, leading to flip angle (FA) variation, can introduce considerable errors into quantification, especially at 3.0T ¹. It is shown that B₁⁺ variation in the prostate is around 10-15% at 3.0T ², and several studies showed the influence of B₁⁺ inhomogeneity on PK parameters, such as K^trans, v_e and k_ep ¹. However, the conventional B₁⁺ correction approach typically includes complex mathematical calculation and modeling, limiting its practical application. In this work, we present a simplified and practical approach that corrects B₁⁺ errors in quantitative DCE-MRI. We investigate the error propagation from FA variation to the PK analysis using numerical simulation and evaluate the correction of B₁⁺-induced PK estimation errors in a total of 63 suspicious lesions of prostate cancer across two different MRI systems.

As demonstrated in Fig. 1, conventional B₁⁺ correction requires a series of quantification steps with updated parameters based on FA variation. This B₁⁺ correction approach can be non-trivial particularly when the entire PK modeling processing is not fully accessible (e.g, using a commercialized CAD software), limiting the practical application of B₁⁺ correction for various DCE-MRI analysis.

In standard Tofts modeling³ with a population-averaged arterial input function (AIF)⁴, the B₁⁺ correction can be simplified using Taylor series approximations under certain conditions: 1) small FA, 2) small TR/T₁₀ ,and 3) k ≈ 1, where T₁₀ is pre-contrast T₁ and k reflects B₁ inhomogeneity calculated by FA'/FA. Provided these conditions are satisfied, we can express the B₁⁺ correction process as 1) K^trans'/K^trans ≈ k², 2) v_e'/v_e ≈ k², and 3) k_ep'/k_ep ≈ 1, where FA, K^trans, v_e and k_ep are original values and FA’, K^trans’, v_e’ and k_ep’ are B₁⁺ corrected values. Note that the proposed model now becomes independent of T₁₀, K^trans, v_e, and k_ep, enabling the direct B₁⁺ correction of PK parameters without re-initiating pixel-by-pixel PK analysis.

We first evaluated the proposed correction model by measuring differences between conventional and proposed B₁⁺ correction using numerical simulation. The simulation was performed with 100 k values (0.7-1.3) for 27 combinations of representative K^trans, v_e and T₁₀ values (K^trans=0.5, 1.2, 2.5 min^-1, v_e=0.3, 0.5, 0.7 and T₁₀=1500, 2000, 2500ms)⁵. Imaging Parameters are assumed following clinical protocols (FA_VFA = 2°, 5°, 10°, 15°, FA_DCE = 12°, TR = 4ms).

With IRB approval, the proposed correction model was retrospectively applied to 63 suspicious lesions from 43 clinically-indicated prostate MRI exams to investigate the B₁⁺ influence in K^trans across two 3.0T MRI scanners (Skyra and Trio, Siemens). A sub-cohort of nine cases were also used for further evaluation of the proposed correction model. B₁⁺ maps were measured using reference region variable flip angle (RR-VFA) method^6,7, and regions of interest (ROIs) were manually drawn on both prostate and suspicious lesions according to radiology reports (Fig. 2). RF transmission modes differed between two scanners: Skyra was operated with “TrueForm” RF transmission (n=51) and Trio was operated with circular polarization (n=12)⁸. T-tests were performed to evaluate the difference.

The simulation results (Fig. 3) show that conventional and proposed methods are close to identical, indicating that the difference between the two procedures is minimal. Within a range of k between 0.7-1.3, the maximum relative error was 0.61% for K^trans'/K^trans and 0.64% for v_e'/v_e, negligible compared to error introduced by B₁⁺ inhomogeneity. With nine DCE-MRI cases, the in-vivo results also confirm the approximation error of the proposed model is negligible (0.87±0.08 % in the prostate and 0.95±0.07 % in suspicious lesions), as shown in Fig 2F.

The B₁⁺, T₁₀ and ΔK^trans (defined as original K^trans - corrected K^trans) in suspicious lesions were compared between two MRI scanners (Fig. 4). Due to the different B₁⁺ inhomogeneity patterns, both T₁₀ and ΔK^trans show different distributions across two MRI scanners. T₁₀ inconsistency between two systems is effectively reduced after the B₁⁺ correction (p_uncorrected =2.88×10^-6, p_corrected=0.81). B₁⁺-induced K^trans errors are also distinctively different (p = 2.21×10^-4) between two systems, which could be a critical problem when comparing parameters between systems and suggests that B₁⁺ correction is essential for quantitative DCE-MRI analysis.

A simple approximation method is proposed to provide practical solutions for B₁⁺ correction in quantitative DCE-MRI. The proposed model was evaluated by simulation and in-vivo data, and the approximation-induced error was shown to be negligible relative to the conventional method. Inconsistent B₁⁺-induced K^trans error distributions between systems were observed, indicating the necessity of B₁⁺ correction for PK analysis.