Parametric maps of spatial two-tissue compartment model for prostate dynamic contrast enhanced MRI - comparison with the standard Tofts model in the diagnosis of prostate cancer

The spatial two-tissue compartment model (2TCM) was used to analyze prostate dynamic contrast enhanced (DCE) MRI data and compared with the standard Tofts model. A total of 29 patients with biopsy-confirmed prostate cancer were included in this IRB-approved study. MRI data were acquired on a Philips Achieva 3T-TX scanner. After T2-weighted and diffusion-weighted imaging, DCE data using 3D T1-FFE mDIXON sequence were acquired pre- and post-contrast media injection (0.1 mmol/kg Multihance) for 60 dynamic scans with temporal resolution of 8.3 s/image. The 2TCM has one fast (K1trans and k1ep) and one slow (K2trans and k2ep) exchanging compartment, compared with the standard Tofts model parameters (Ktrans and kep). On average, prostate cancer had significantly higher values (p < 0.007) than normal prostate tissue for all calculated parameters. There was a strong correlation (r = 0.94, p < 0.0001) between Ktrans and K1trans for cancer, but weak correlation (r = 0.28, p < 0.05) between kep and k1ep. Average root-mean-square error (RMSE) in fits from the 2TCM was significantly smaller (p < 0.001) than the RMSE in fits from the Tofts model. Receiver operating characteristic (ROC) analysis showed that fast K1trans had the highest area under the curve (AUC) than any other individual parameter. The combined four parameters from the 2TCM had a considerably higher AUC value than the combined two parameters from the Tofts model. The 2TCM may be useful for quantitative analysis of prostate DCE-MRI data and may provide new information in the diagnosis of prostate cancer.


Introduction
Multi-parametric MRI (mpMRI) plays an important role in detection and grading of prostate cancer (PCa) [1][2][3]. Although T2-weighted (T2W) imaging and diffusion-weighted imaging (DWI) are the two main components of prostate mpMRI, dynamic contrast enhanced (DCE) MRI assists in the interpretation of T2W imaging and DWI in detection of high-risk PCa, and in surveillance status post prostatectomy, radiotherapy or focal ablation [4][5][6][7][8][9]. However, compared to T2W imaging and DWI, qualitative analysis of DCE-MRI is the least standardized [10]. There are often overlap enhancement patterns between benign and malignant tissues in prostate peripheral and transition zones. Some benign lesions, such as benign prostatic hyperplasia (BPH) nodules, show strong early enhancement, while some malignant lesions do not show early enhancement or washout [11]. Therefore, there are often false positives in diagnosis of PCa by using DCE-MRI [12].
Prostate DCE-MRI data is also often analyzed quantitatively using pharmacokinetic models, such as the standard Tofts model, to extract the volume transfer rate constant (K trans ) (exchange between blood plasma and the extravascular extracellular space (EES)) and fractional volume of EES (v e ) [13,14].
However, the standard Tofts model may not be compatible with the heterogeneous characteristics of the tumor micro-environment that results in an initial rapid uptake of contrast agent followed by a less rapid, but prolonged, uptake of the contrast agent [15,16]. As a result, tumor heterogeneity at the microscopic level could cause poor ts to DCE-MRI data for the standard Tofts model and errors in extracting K trans and v e . This would limit the diagnostic accuracy when using the standard Tofts model to analyze DCE-MRI data. Therefore, more complex models should be used to analyze DCE-MRI data, such as the multicompetent models [17], "shutter-speed" model [18], two-compartment exchange model 2CXM [19,20], and spatial two-tissue compartment model (2TCM) [21].
In contrast to the standard Tofts model with only one tissue compartment, the 2TCM has one slow and one fast exchanging tissue compartment. Previous study demonstrated that MRI contrast agent distributions in heterogeneous tissue could be more adequately accessible with 2TCM, especially at tumor margins [21]. In this study, the 2TCM was used to analyze prostate DCE-MRI data and prove the hypothesis that diagnostic accuracy could be improved for DCE-MRI. The results obtained from 2TCM were compared with those from the standard Tofts model as a DCE model evaluation.

Patients
This retrospective study was approved by the Ethics Committee of the University of Chicago, Institutional Review Boards (IRB), with the approval number IRB13-0756. Informed patient consent was compliant with the Health Insurance Portability and Accountability Act (HIPAA). The patients imaged and followed by subsequent radical prostatectomy were recruited for this study between March 2014 and May 2015.
Twenty-nine patients (mean age 57 years, range 40-70 years; and mean PSA 7.4 ng/lm, range 1.8-26.1 ng/lm) with biopsy-con rmed prostate cancer were included in this study. Patients who received prior radiation or hormonal therapy were excluded.
In order to obtain unique results for tting C(t) using MATLAB, Eq. 2 was written in an asymmetric form as follows: where and . Please note that for different pixels either or could be large or small depending on whether ε is smaller or larger than 1.0. In order to consistently compare calculated parameters, we selected as the larger one of them (= ) with its corresponding or as . Therefore, for each pixel is always larger than in our study.  It can be seen that the 2TCM ts are much better than those of the standard Tofts model. On average (± standard deviation), the RMSE (= 0.013 ± 0.009) obtained 2TCM was signi cantly smaller (p < 0.001) than the RMSE (= 0.022 ± 0.024) obtained from the Tofts model, which shows the better tting for the data using 2TCM.  There are strong correlations (r = 0.82 to 0.94, p < 0.0001) between K trans and K i trans (i = 1, 2) for cancer ( Fig. 4 (a)), and moderate to strong correlations (r = 0.69 to 0.93, p < 0.0001) for normal tissue (Fig. 4 (b)). There was weak correlation (r = 0.28, p < 0.05) between k ep and k 1 ep , but strong correlation (r = 0.83, p < 0.0001) between k ep and k 2 ep for cancer (Fig. 4 (c)). There were moderate correlations (0.67 < r < 0.77 p < 0.0001) between k ep and k i ep (i = 1, 2) for normal tissue (Fig. 4(d)). This indicates more useful parameters could be obtained and suggesting advantages for the 2TCM. Finally, Table 1 shows ROC analysis results for all individual parameters and combined parameters obtained from the Tofts model and 2TCM when differentiating between cancer and normal tissue. It shows that the parameter K 1 trans has the highest AUC of 0.787, which is at least ~ 7% higher than any other individual parameter. The combined four parameters obtained from the 2TCM have a much higher AUC value of 0.800 than the combined two parameters obtained from the Tofts model (0.742).

Discussion
The 2TCM was compared with the Tofts model by using prostate DCE-MRI data. For all calculated parameters, PCa had signi cantly higher values than normal tissue. Our results also demonstrated that prostate cancer is heterogeneous, involving both the fast (K 1 trans ) and the slow (K 2 trans ) exchange compartments. Mathematically, when k 1 ep and k 2 ep are the same, two additive exponential terms can be combined as one exponential term, which is used in the Tofts model. However, Fig. 4

(c) and (d) clearly
showed that k 1 ep and k 2 ep are very different. Therefore, it is necessary to have the 2TCM to t PCa contrast agent concentration curve accurately. The strong correlation between K trans and K 1 trans but weak correlation between k ep and k 1 ep in cancer tissue suggests that the 2TCM is needed in diagnostic PCa. The fast K 1 trans obtained from the 2TCM showed better separation between cancer and normal tissue than K trans obtained from the Tofts model. Combined 2TCM parameters had much a higher AUC value than combined Tofts model parameters, suggesting potential advantages for diagnosis of PCa.
PIRADS version 2.1 favors qualitative analysis of DCE-MRI data, which is the least standardized compared to T2W imaging and DWI [10]. On the other hand, the two-compartment (i.e. blood plasma and EES) pharmacokinetic Tofts model is the most commonly used quantitative analysis technique in clinic for diagnosis of PCa. However, the standard Tofts model often could not t cancer contrast agent concentration curve accurately and there were false positives when using calculated parameters to detect cancer. Our results demonstrate that the 2TCM could further improve accuracy in diagnosing PCa compared with the Tofts model. This improvement in quantitative analysis of DCE-MRI data would enhance the role of DCE-MRI in prostate mpMRI.
Our results showed that PCa had much higher K trans and k ep than normal prostate tissue, which was consistent with previous studies [24,14]. Similarly, all the parameters calculated from the 2TCM were also much higher in cancer than normal tissue. The fast K 1 trans is similar to K trans in the diagnosis of cancer, but K 1 trans has much lower values at selected false positive regions where K trans is higher.
As we demonstrated in this study, using the 2TCM is just as simple as using the Tofts model. But the results obtained from the 2TCM were much richer than the Tofts model. There were several limitations to this study. First, our sample size was relatively small. The 2TCM should be tested in a much larger and more diverse group of patients. Second, there was no reliable analysis for the drawn ROIs. Since both Tofts model and 2TCM shared the same ROIs, the result of comparisons between two models should be valid. Third, the 2TCM was only compared with the Tofts model. In the future, more models should be compared with 2TCM. Finally, we did not follow the contrast agent for a longer period of time (≤ 8 minutes). If DCE-MRI data were acquired for a longer period, we believe the advantage of the 2TCM would be more apparent obvious, as the errors in tting curves using the Tofts model would be higher.
Nevertheless, more studies are needed to further explore the 2TCM in analysis of prostate DCE-MRI data.

Conclusion
Our study demonstrated that the 2TCM of DCE-MRI may be useful for quantitative analysis of prostate DCE-MRI. We compared the 2TCM with the standard Tofts model to demonstrate an advantage using the 2TCM. The Tofts model often does not t contrast agent concentration curves accurately and the 2TCM may provide new diagnostic information in prostate cancer.

Statements & Declarations
Funding This research was supported by National Institutes of Health (R01CA218700, U01CA142565, R01CA172801 and S10OD018448).  Figure 1 Plot of AIF (purple line) traced over iliac artery (purple dot on image) is shown below DCE image. Plots of measured C(t) (black dots) at selected three pixels in tumor (a, b, and c) and one pixel in normal tissue (d) indicated by red arrows on DCE-MRI, and as well as corresponding ts of C(t) by the Tofts model (red line) and the 2TCM (green line). The extracted parameters are also given within the gure.   Scatter plots of physiological parameters (K trans and k ep ) obtained from Tofts model vs. parameters (K i trans and k i ep , i=1, 2) calculated from 2TCM for all ROIs of cancer and normal prostate tissue. The colored lines show linear correlations.