Volumetric, large field-of-view contrast enhanced MRI typically involves only two MR measurements: One before contrast administration, S1, and another, S2, at some time $$$t$$$ when equilibrium of contrast is expected. To provide quantification of tissue enhancement in these cases, it is common to calculate the relative enhancement, $$$\epsilon_{R}$$$, at each voxel location: $$ \epsilon_{R} = \frac{S_{2} - S_{1}}{S_{1}}$$ Another possibility is to compute the fractional enhancement, $$$\epsilon_{F}$$$: $$ \epsilon_{R} = \frac{S_{2} - S_{1}}{S_{1} + S_{2}}$$

It can be shown that both quantitative parameters are monotonically increasing with increasing contrast agent concentration. Furthermore, both parameters are independent of T2*-weighting, proton density and coil sensitivity, improving their performance as quantitative metrics. However, little work has been done to investigate the statistical properties of these parameters and how this may affect clinical interpretation of contrast enhancement studies.

In this article we investigate the contrast-to-noise properties of both the relative and fractional enhancement indices. We demonstrate preliminary evidence that $$$\epsilon_{F}$$$ outperforms $$$\epsilon_{F}$$$ in terms of signal-to-noise ratio (SNR) through numerical simulation, and improves clinical visualization of retroperitoneal sarcoma.

Patients: Twenty-five patients with retroperitoneal sarcoma were imaged as part of a prospective single-centre study including: 21 well-differentiated/dedifferentiated liposarcomas, 3 leiomyosarcomas and 1 lipoma. All patients provided written consent prior to their involvement in this study.

Imaging: T1-weighted imaging was acquired before and 4 minutes after the administration of gadolinium-based contrast (Dotarem, 0.2 ml/kg boy weight administered at 2 ml/s using a power injector) ensuring that the field of view covered the entire tumour in each patient. We used a 3D FLASH sequence with 17° flip angle ($$$\alpha$$$), repetition time (TR) = 3.8ms and echo time (TE) = 1.06ms on a 1.5T machine (Aera, Siemens Healthcare, Germany).

Simulations: We investigated the response of enhancement parameters, $$$\epsilon_{R}$$$ and $$$\epsilon_{F}$$$, by calculating the expected values as a function of contrast agent, [CA], over the range 0-5 mM in the absence of noise. We use the standard formulae for T1w signal intensity:

$$ \text{S}_{1}(\text{TR}, \alpha) = \text{S}_{0}\sin (\alpha)\frac{1 - \text{E}_{1}}{1-\cos (\alpha)\text{E}_{1}}, \quad \text{E}_{1} = \exp \left\{-\text{TR}\cdot\text{R}_{1}\right\}$$

$$ \text{S}_{2}(\text{TR}, \alpha) = \text{S}_{0}\sin (\alpha)\frac{1 - \text{E}_{1}\text{E}^{\Delta}_{1}}{1-\cos (\alpha)\text{E}_{1}\text{E}^{\Delta}_{1}}, \quad \text{E}^{\Delta}_{1} = \exp \left\{-\text{TR}\cdot\Delta\text{R}_{1}\right\}, \quad\Delta\text{R}_{1} = r_{1}\text{[CA]}$$

We matched all parameters in these simulations with those used for clinical imaging, matching the relaxivity of the contrast agent used ($$$r_{1} = 3.6 \text{ L mmol}^{-1}\text{ s}^{-1}$$$ [1]), over a range of plausible tissue T1-values (0.1-1.5 ms). We repeated these calculations but with the inclusion of Rician noise [2] at different SNRs ($$$\sigma_{0}$$$ = 20, 50, 80, 110, 140 and 170) for the base signal intensity, $$$\text{S}_{0}$$$. This simulation was repeated 105 times so that estimates of SNR for each of the enhancement parameters, $$$\epsilon_{R}$$$ and $$$\epsilon_{F}$$$, could be calculated over a range of T1 and [CA] values.

Image analysis: A clinical radiologist with 15 years experience in MR-imaging compared volumetric datasets of calculated enhancement parameters, $$$\epsilon_{R}$$$ and $$$\epsilon_{F}$$$, in all 25 patients. Images were viewed side-by-side on a multi-planar-reformat workstation (OsiriX, Switzerland); the radiologist was blinded to the method used ($$$\epsilon_{R}$$$ or $$$\epsilon_{F}$$$). For each of the following subjective criteria: (i) Overall contrast-to-noise, (ii) signal-to-noise, (iii) detection of disease, (iv) image artefacts and (v) within-lesion contrast, the radiologist decided whether one method was preferred over the other, or whether they tied.

Figure 1 presents the results from simulations in the absence of noise. It clearly depicts the positive monotonicity of both enhancement parameters as a function of contrast agent concentration. Figure 2 presents the same data but in the presence of Rician noise added to the S0 term, and Figure 3 depicts the SNR of $$$\epsilon_{R}$$$ and $$$\epsilon_{F}$$$ over repeated simulations of Figure 2. Both figures demonstrate that the theoretical noise properties of fractional enhancement $$$\epsilon_{F}$$$ are superior to relative enhancement $$$\epsilon_{R}$$$. Results from the radiological assessment are presented in Figure 4, where it is demonstrated that $$$\epsilon_{F}$$$ outperforms $$$\epsilon_{R}$$$ for all criteria (examples shown in Figure 5). We have investigated the effects of image noise on two possible quantification methods for two-point dynamic contrast enhanced MR measurements, the relative enhancement and fractional enhancement ($$$\epsilon_{R}$$$ and $$$\epsilon_{F}$$$ respectively). Through numerical simulations we have demonstrated that $$$\epsilon_{R}$$$ provides more uniform variation as a function of intrinsic tissue T1 and contrast agent concentration but $$$\epsilon_{F}$$$ outperforms in the presence of image noise. This was validated in a clinical setting of 25 patients with retroperitoneal sarcoma where $$$\epsilon_{F}$$$ was statistically superior in terms of image quality and tumour detection. We thus conclude that $$$\epsilon_{F}$$$ provides a more robust measurement for two-point dynamic MR studies.