Pharmacokinetic (PK) models have been used to estimate physiological parameters such as permeability [1] and dispersion [2] of the contrast agent from the temporal changes in gadolinium concentration. The contrast agent concentration can be estimated using the RF-spoiled gradient echo signal, pre-contrast T₁₀, and the acquisition flip angle. However, many datasets are acquired without T₁₀ and B₁ map due to longer acquisition duration. Several simulation studies [3] have shown significant errors in K^trans and v_e values of Tofts model due to their dependence on T₁₀ and B₁, assuming that the model perfectly describes the acquired data. The purpose of this study is to determine the dependence of the dispersion models’ [2] and Tofts models’ PK parameters on T₁₀ and B₁ values, as well as the errors introduced by using constant T₁₀ and B₁ values using acquired patient data.

Figure 1 shows the variation in concentration-time curves introduced by different choice of T₁₀ and B₁ for the same signal-time curve. The effect of errors in T₁₀ and B₁ values on the PK parameters was studied in 6 patients with 11 biopsy-proven tumors (7 malignant, 6 in the right breast). 3D RF-spoiled gradient echo fat-water separated DCE images were acquired using DISCO [4], a pseudorandom ky-kz sampling scheme enabling a favorable tradeoff between temporal and spatial resolution, on a 3T scanner (GE Healthcare, Waukesha, WI). One pre-contrast and four post-contrast images were acquired with high spatial resolution of 0.5×0.6×1.0 mm and low temporal resolution of 2 min. Fourteen images were acquired during the wash-in period with high temporal resolution of 13s and lower spatial resolution of 0.5×1.2×2.0 mm. Prior to the acquisition of pre-contrast DCE images (FA=12°), 3D variable flip angle (FA=2°, 5° and 8°) images with identical imaging parameters were acquired to estimate the water-only T₁₀ map [5]. A 2D multi-slice Bloch-Siegart B₁ map [6] was also acquired with a low spatial resolution of 5×5×5 mm and was also used for correcting the T₁₀ map. The DCE images, T₁₀ and B₁ maps were subsequently reconstructed to identical spatial resolution of 0.5×1.2×2.0 mm.

Voxel-by-voxel PK mapping was performed using a standard Tofts model [1] with modified Fritz-Hansen arterial input function as well as modified local density random walk (mLDRW) Dispersion model [2]. The PK parameters were estimated for 11 tumors using the following combinations of T₁₀ and B₁: (1) T₁₀ map, B₁ map, (2) T₁₀ map, FA=[0.6 to 1.4]×12°, (3) B₁ map, T₁₀=[1000 to 2000] ms, (4) T₁₀=1500ms, FA=[0.6 to 1.4]×12°, and (5) FA=12°, T₁₀=[1000 to 2000] ms. The PK parameters estimated over the tumor ROI using the T₁₀ and B₁ maps was considered as the standard. Every other PK parameter value was compared to the standard using the concordance correlation coefficient (ρ_c).

The median of the B₁-corrected T₁₀ within the tumor ROI varied between 1116 ms and 1821 ms and the median relative FA varied between 0.7 and 1.3. Figure 2 shows the box plot of ρ_c for different combinations of T₁₀ and B₁ values. Both kep of Tofts model and kappa of mLDRW dispersion model have a higher ρc and lower relative variation. The median and the range of ρ_c for each of the PK parameters for few combinations of T₁₀ and B₁ are tabulated in Figure 3. Parameters such as beta and mu have a lower ρc as well as huge variation indicating their sensitivity to T₁₀ and B₁ map. These results show that it may be possible to create PK parameter maps without acquiring T₁₀ and B₁ maps and using an average value instead. However only few parameters such as k_ep and kappa will have relatively high accuracy and precision, and parameters such as beta will have lower precision.The data analysis assumed that the acquired T₁₀ and B₁ maps were accurate and the ρ_c was calculated with the maps derived PK values as the standard. However, both T₁ and B₁ mapping introduces errors. The results also show that ρ_c is high when the average value of T₁ and B₁ maps are used and this, or the use of low-pass-filtered maps, may reduce error propagation. Pharmacokinetic parameters such as k_ep of Tofts model and kappa of mLDRW dispersion model are less dependent on T₁₀ and B₁ and hence these PK maps could potentially be used clinically with higher accuracy and precision even when T₁₀ and B₁ maps are not acquired.