Reliability of dynamic contrast-enhanced magnetic resonance imaging data in primary brain tumours: a comparison of Tofts and shutter speed models

Fourteen patients (7 male, 7 female; aged 23–73 years, mean 40 years) with primary brain tumours were recruited to this study. Ethical approval was given by the local ethics committee and informed consent was obtained from all patients. Patients had an MRI at diagnosis, prior to receiving any treatment. Following surgery, histopathological data showed three patients with WHO grade IV glioblastoma, two patients with WHO grade III astrocytoma, two patients with WHO grade III oligodendroglioma, three patients with WHO grade II astrocytoma, three patients with WHO grade II oligodendroglioma and one patient with a WHO grade I dysembryoplastic neuroepithelial tumour.

MR images were acquired on a 3-T Siemens Verio MRI system using a 32 channel head coil; including pre- and post-contrast T₁-weighted images, T₂-FLAIR images and a DCE sequence with a variable flip angle pre-contrast T₁ map acquisition. The DCE-MRI protocol included five pre-contrast spoiled gradient recalled echo (SPGRE) 3D vibe sequences at five different flip angles (2, 8, 12, 15, 20, 26), and a dynamic 3D vibe sequence (TR = 3.34 ms, TE = 0.99 ms, flip angle = 26, FOV 240 × 240 mm, acquisition matrix 128 × 128, slice thickness 5 mm, slice gap 1 mm, 80 volumes). To obtain acquisitions before, during and after the injection of the CA, 0.1 mmol/kg body-weight gadolinium-diethylene triaminepentacetate (Gd-DTPA, Gadovist) was injected using a power injector on the fifth acquisition using a flow rate of 3 ml/s immediately followed by 20 ml saline solution. The 3D acquisition allowed us to cover the entire brain; 80 time points were acquired with an average temporal resolution of 2.89 s and a total acquisition time of ≈ 4 min.

Volumes of interest (VOIs) were drawn by a Radiologist and confirmed by a Consultant Neuroradiologist for each patient around T₂-FLAIR hyperintense regions and on a 2-cm-diameter circular region in normal-appearing contra-lateral white matter. DCE-MRI data were analysed using a semi-automated in-house software written in MATLAB (Mathworks, R2017a). Before the application of any of the aforementioned pharmacokinetic models, we calculated the relaxation rate at baseline (R₁₀) and relaxed signal (M₀) as 3D maps, with the Ernst formula (assuming TE < <T₂*) using the set of SPGRE pre-contrast images acquired at different flip angles [21]:where α is the flip angle having values [(2, 8, 12, 15, 20, 26]) and TR is 3.34 ms. Reformulating Eq. 1 as a linear regression system (y = cx + d) following the method described by Liberman et al. in [22], gives:where \( E={e}^{-{R}_{10} TR} \).

The slope c = E and intercept d = M₀ (1 − E) can thus be estimated and continuing from [22], R₁₀ and M₀ can then be obtained through:

Then, 4D (x, y, z, t) post-injection longitudinal relaxation rate R₁(t) maps for each dynamic phase are calculated using signal intensity data from the post-contrast dynamic series:where α = 26, A = S(t) − S(0)/M₀ sin(α), B = (1 − E)/1 − E · cos(α). S(0) and S(t) are the pre-contrast injection signal intensity and the signal at the dynamic phase t, respectively [23].

The longitudinal relaxation rate is determined in order to calculate the concentration of the CA. This is done through a calibration between the concentration of CA [CA] and the measured H₂O MR signal. This can be modelled by either a linear or nonlinear relationship as described below.

An additional ROI was drawn around the external carotid artery for the calculation of the image-derived AIF [34] (Fig. 2). Signal intensity curves were converted to R₁-time curves by using the baseline signal intensity before the first pass of the CA as a reference, setting the haematocrit in the blood to 0.45, and getting the baseline blood T₁ from the T₁₀ map (Eq. 8).

A model comparison was carried out using the AIC to test for the best model in a given voxel. In particular, in the presence of exchange (where the NEM fails in the description of data), a voxel-wise comparison between models was carried out (with ETM and SSM being an extension of the TM, and the ESSM an extension of the SSM) to indicate which model provided the best fit using the AIC in each voxel. The selection method is shown in the flowchart in Fig. 3. The choice was expressed with a value of 1, 2, 3, 4 or 5 for the TM, ETM, SSM, ESSM and NEM, respectively, in a volumetric mask (same dimensions of the original tumour volume mask). The percentage of 1 s, 2 s, 3 s, 4 s and 5 s in each mask was evaluated to quantify the frequency of model choice. The model selection map was used to build final pharmacokinetic maps for the K^trans, k_ep and v_e, where, for each voxel, the value is the result of the fitting of the model of choice (lowest AIC).

The behaviour of each model was assessed by studying the quality of fit for each of the models. The input data, together with the fitted curves were normalized by the maximum value of the input data in order to compare results from the different fits. An example of a comparison of fit is shown in Fig. 4. For each tumour, a map with the result of the statistical comparison among models was built (Fig. 5). In this map, each colour represents the model for which the voxel-wise AIC value was lowest: The selected model of choice representing majority of low AIC was NEM (35.5% of voxels), followed by the ETM (32%), TM (28.2%), SSM (4.3%) and ESSM (< 0.1%). Fig. 5 shows the model selection map evaluated for two different lesions. Furthermore, final pharmacokinetic maps, for the K^trans, k_ep and v_e, were built considering the model selection procedure. Within the final pharmacokinetic maps, each voxel was represented by the model with the best fit (lowest AIC) within that voxel. For each of these maps, the stability of each parameter and for each lesion was presented in terms of CV maps. Table 1 shows the results of the stability test on the final K^trans map. The total number of voxel of the lesion, for each patient, together with the average K^trans value evaluated over the whole tumour, is shown. Furthermore, the map was thresholded with a CV lower than 10, 20 and 50%, and the resultant percentage of preserved voxels (and their average value) is shown. Fig. 6 shows two final K^trans maps with their CV map overlaid on them (A and D).

MR scanners usually employ post processing perfusion tools which fit DCE data with the TM. This model (together with its extended version [32]) considers the system in a fast exchange limit [36, 37], assuming an infinitely fast transcytolemmal water exchange between the EES and the intracellular space, which does not affect the overall signal decrease [36, 37]. Therefore, many studies on the cell membrane water permeability coefficient have shown FXL to be physiologically unreasonable and inconsistent [38]. The shutter speed model was introduced to reflect a more realistic tissue environment. The model accounts for the intercompartmental water exchange effect, modelling this non-infinitely-fast exchange with the mean intracellular water molecule lifetime τ_i. In 2005, Li et al. introduced a second generation of the shutter speed model which considers also a non-infinitely fast equilibrium transendothelial water exchange.

The heterogeneity that exists in brain tumours means that one model is insufficient in explaining the different biologies that exist in different tumour regions. Multiple pharmacokinetic models are required for a complete description of the tissue. This variability is testified by the model selection procedure which showed how, in a single slice of one tumour, multiple models perform better. This result confirms the study of Bagher-Ebadian where they implemented a selection method based on nested models [3]. They found that in the necrotic core of the tumour, models describing vascular filling with no microvascular leakage (similar to the TM) and leakage without vascular reabsorption were selected because of the lack of blood flow. They also hypothesised that the model describing leakage with reabsorption (similar to the ETM) would be selected in the fast growing rims of the lesion. Our results show that there are a number of regions in the tumour where the CA exudation is prevented by the BBB and where the concentration of CA is so low that the evidence of perfusion is missing. In this case, the use of the NEM is recommended as the use of different models could result only in overfitting the data. In fact, our results showed that no leakage of the CA into the interstitium and the lack of flow of the CA through the tissue made the NEM the model of choice for the majority of regions, particularly in the non-enhancing lesions (37.5% of voxels). The result is very close to the ETM (32%), which was the model of choice in the enhancing lesions (54.8%). This suggests that, in areas where there is enhancement, a model with three parameters performs better and that the choice is dependent on the underlying state of the tissue. In fact, both the ETM and SSM are fitted by three parameters but the third parameter is very different between the two models (v_p for the ETM describing a vascular component in the tissue, and τ_i for the SSM describing the transcytolemmal water exchange). Furthermore, with the implementation of the ESSM, we saw that the transendothelial water exchange did not have any impact on the signal (compared with parameters derived by the fitting of simpler models). It is necessary to consider that the ESSM required nine parameters to be fitted and that the cost of fitting extra parameters is often contrary to the principle of parsimony. In fact, in fitting data to a noise-limited dataset, the estimation could be very poor and dependent on the optimization procedure itself (the initial conditions, for example) [3]. We compared the AIC values from the different fitting procedures to check whether a model with more parameters is more appropriate than a simple one. The ESSM was selected as the model of choice by < 0.1% of voxels, indicating that a model with three parameters performed better in the description of brain tumours and further confirming the poor quality of fit observed for the ESSM model. Our outcome agreed with the results of Duan et al. [39]. Using representative in silico and clinical (cervical cancer) DCE-MRI data, they demonstrated the sensitivity of complicated models (parameters > 3) to noise and their decreasing probability of being selected in low signal-to-noise data [39].

The reliability of DCE-MRI data is not only based on the goodness of fit of the chosen pharmacokinetic model, but also on the robustness of the extracted parameters. For this reason, we assessed, for each lesion and for each parameter, the coefficient of variation. We worked in a simulation environment where we added Gaussian noise to our signal and we fitted the noisy curves 500 times. This procedure resulted with a heterogeneous distribution of CVs that was not linked to contrast enhancement. In fact, Fig. 6 shows the plot of four different tissue activity curves together with the K^trans value and its CV in an enhancing and non-enhancing tumour. The curves in Fig. 6b, c belong to the same enhancing lesion and while they correspond to similar K^trans values of 0.81 and 0.52 [1/min], they varied by 12 and 128%, respectively. On the other hand, the curves in Fig. 6e, f belong to the same non-enhancing lesion and show regions with both a low (4%) and a high (97%) variability.

We set three different thresholds for the CV to evaluate the variability of the K^trans. Table 1 shows the percentage of voxels and their relative mean K^trans value at different CVs thresholds (10, 20 and 50%), for each lesion and for each patient. Higher grade glioma tend to have more voxels with a lower CV and also a more stable value of K^trans while, for some of the other patients, the mean value of K^trans is highly affected by the portion of voxels taken into consideration (P04, P07). This result confirmed the improper use of one average value in statistical comparisons of brain tumours. Not only because of the heterogeneity of the tissue under investigation but also, and more importantly, because it is affected by the reliability of fit within voxels.

Finally, Fig. 6 gives a graphical representation of this effect showing K^trans values under the 20% threshold of CV covering only 25% of voxels (an average percentage value evaluated among all patients). This result suggested that only this selection of voxels represents robust values, which can be used in the following statistical analyses, as, more importantly, in clinical evaluations. The selection of the threshold that makes DCE-MRI robust is, however, dependent on the effect size that is being measured and hence will vary across studies.

The main limitation of this study is the small size of the dataset. Furthermore, the sensitivity of DCE-MRI data to water exchange effect was reduced by the 26° flip angle acquisition (exchange-minimized approach) [40]. As a consequence, the precision of the τ_i parameter extracted might be low.

In conclusion, DCE-MRI methods hold great promise for quantitative in vivo evaluation of permeability and vascular properties under different pathophysiological conditions. It allows us to identify, and quantitatively measure, smaller changes in permeability for pathological conditions effecting the BBB, than would be observed through visuassessment of post-contrast T₁-weighted images. Different models yield different pharmacokinetic parameters and, for this reason, a model selection is critical for the appropriate analysis of DCE-MRI time courses based on the regional tissue biology, specifically permeability and vasculature. Future work needs to assess the physiological basis for each model in the reliable selection of DCE-MRI data. The applicability of each model depends on the physiology, anatomy and heterogeneity of the tumour and the tumour microenvironment. In addition, due to the noisy nature of DCE-MRI data, a model selection procedure alone is not enough: pharmacokinetic parameters need to be validated with a stability test in order to give only robust results for statistical analyses and clinical evaluation.