T1-weighted dynamic contrast-enhanced (DCE) MRI enables quantitative measurement of tissue microenvironment by means of contrast kinetic analysis with signal-to-concentration conversion that requires pre-contrast T1 value of the tissue.¹ Despite recent development of T1 mapping methods, it remains challenging to perform accurate T1 mapping in a relatively short time, so most routine clinical DCE-MRI exams do not include T1 measurements. In the absence of measured pre-contrast T1 values, signal-to-concentration conversion is often carried out using an assumed T1 with (i) the assumption of a linear relationship between the contrast enhancement and contrast agent concentration (i.e. LC, linear conversion), or (ii) the non-linear signal equation for steady state gradient echo sequence (i.e. NLC, nonlinear conversion). A recent study with 17 patients has shown that linear conversion may be acceptable for quantification of model-free hepatic perfusion parameters.² However, it has not been shown how these two conversion methods may affect the contrast kinetic analysis in a wide range of kinetic parameters. The purpose of this study was to evaluate the effect of LC and NLC methods on the estimation of contrast kinetic parameters using a simulation model.

The simulation study was conducted using the most commonly used generalized kinetic model (GKM)³ and a population based arterial input function (AIF).⁴ For a given set of transfer rate (K^trans) and extracellular extravascular space volume fraction (v_e) values, a time concentration curve (TCC) was generated using the GKM model, and was converted to the spoiled gradient recalled echo (SPGR) signal (TE= 1.27ms, TR = 6.8ms).⁵ A flip angle (FA) of 45° was used based on reports that the LC method works better with a higher FA, ideally at 90°.⁶ The temporal resolution was assumed to be 1sec and the total scan time was 8.3min with 1.3min of pre-contrast scan. We also assumed that the T2* effect is negligible; the contrast agent T1 relaxivity (r₁) was 6.5 L/s∙mM; and the longitudinal relaxation rate $$$R_{1}(t) =R_{10}+r_{1}C(t)$$$ where R₁₀ is the pre-contrast (1/T1) and C(t) is the contrast agent concentration. Rician noise was added to the generated time-intensity curve (TIC) by adding Gaussian noise, to both real and imaginary data, with a standard deviation corresponding to 10% of the average precontrast signals (Figure 1A). Prior to applying the GKM model analysis, the noisy TIC, S(t), was converted to TCC, C(t), using either the NLC method with the SPGR signal equation or the LC method: $$$ C(t) = \frac{S(t)/S_{0}-1}{r_{1} T_{10}} $$$ where S₀ is the pre-contrast average signal and T₁₀ is the assumed precontrast T1 value (Figure 1B). T₁₀ was assumed to be 1500ms for the artery and 700ms for the tissue.^2,7 The simulation study was carried out to investigate the following three questions:

(1) Uncertainty in contrast kinetic parameter estimation: K^trans was varied from 0.1 to 0.9min^-1 while v_e was fixed to 0.3. v_e was then varied from 0.1 to 0.7 while keeping K^trans constant at 0.5 min^-1. For each pair of K^trans and v_e values, noise TIC was generated 20 times and parameter estimation was performed with random initial values in all cases unless specified otherwise. The assumed T₁₀ values were used for this case.

(2) Effect of assumed T₁₀: The effect of assuming a wrong T₁₀ was investigated for a representative case of K^trans = 0.5 min^-1 and v_e=0.3. T₁₀ was varied from 500ms to 900ms.

(3) Effect of FA: The effect of FA was investigated for a representative case of K^trans = 0.5 min^-1 and v_e=0.3. FA was varied from 15° to 65°.

Fig.2A shows that the LC method leads to 3.1-54.8% over-estimation of K^trans while the NLC method had 0.1-1.3% error. In the LC method, the increase in K^trans from 0.1 to 0.9 min^-1 resulted in a 1.3-3.0% change in v_e (Fig.2B). Fig.2C and 2D show varying v_e with a fixed Ktrans, where ve was over-estimated by 0.4-3.8% and 0-2.2% in LC and NLC methods, respectively (Fig. 2D). Note that the NLC K^trans did not show a noticeable change with the v_e increase, whereas the LC K^trans was overestimated by 21.4-33.6% (Fig. 2C). The error in the assumed T₁₀ resulted in monotonical changes in the estimated K^trans and v_e using both methods (Fig.3). The parameter accuracy of the LC method decreased dramatically as the FA decreases (Fig.4).

Our study demonstrates that a simulation study can provide useful insights on the uncertainty in the contrast kinetic parameters estimated using the LC and NLC methods. Further study is warranted to investigate this effect in different pathological conditions.