For DSC imaging, a ‘byproduct' of the contrast agent leakage correction method proposed by Weisskoff et al (1994) and Boxerman et al (2006) is the ‘K₂' term reflecting the estimated contrast agent extravasation into the interstitial space. Under the assumption that the K₂ parameter reflects tumor permeability (i.e., something similar to K^trans), a single DSC-MRI acquisition could potentially provide estimates of both CBV and permeability for use in an alternative VNI parameter except the collagen blood parameter. One limitation to this approach, however, is that the contrast agent leakage correction model assumes that the contrast agent bolus arrives at the same time in tumor and normal-appearing tissue and that tumoral and nontumor tissue have equal mean transit times (MTTs). Given the irregularity of tumor vasculature (Bastin et al, 2006; Jain et al, 2007), this assumption seems tenuous. Consequently, alternative MTT insensitive correction methods have been proposed that might provide better estimates of tumor permeability (Quarles and Schmainda, 2007; Quarles et al, 2009). We recently described the theoretical basis for an alternative technique where the leakage value is determined by incorporating a contrast agent leakage term in the tissue-specific residue function R(t), which then accounts for leakage-induced variations in the first-pass curve (Bjornerud et al, 2011). First, our results suggested that there was a significant linear correlation between the residual error term of K₂ and MTT for both T₁- and T₂^*-dominant extravasation, indicating an increasing error in K₂ for increasing tumoral MTT deviations from reference tissue MTT. Second, our results suggested that contrast agent leakage correction assessment directly from the tissue residue function might provide a more accurate estimate of the underlying capillary permeability independent of tumoral MTTs.

From this, as explained in Part I, equation (1) can be written in matrix notation in terms of the measured changes in T₂^* relaxation rates: where Y is a matrix describing the apparent change in the transverse relaxation rate (R2^*) in tissue in the presence of T₁ effects and extravasation, A is a matrix describing the corresponding change in R2^* in blood, and h is the apparent residue function in the presence of contrast agent leakage. Following standard arterial input function (AIF) deconvolution, h is given by: where K_a is the apparent transfer constant between plasma and extravascular, extracellular space, N is the number of data points, Δt is the sampling interval, and t_c is the time index corresponding to T_c. If the total measurement time is much greater than T_c, then for t T_c, H(t) is dominated by the leakage term. By further assuming negligible reflux, that is exp(−K^transt/v_e) approaching unity because K^transNΔt/v_e1, we get:

Results of the K_a and K^trans comparisons are shown in Figure 2. For the patients as a group, the linear mixed model showed a significant relationship between increasing median K_a values and increasing K^trans cohorts (P<0.01). Conforming to the simulations in Part I, a borderline significantly higher goodness of fit (F-test; P=0.05) was observed when fitting a quadratic polynomial curve to the data (smoothened) compared to using a linear fit; adjusted R²=0.95 (P=0.001) versus adjusted r²=0.87 (P=0.001), respectively. In 10 of 30 patient curves, a negative ‘dip' was seen in the K_a values at low K^trans values.

For method II, compared with baseline values, higher normalized CBV values were seen at day +1 in patients with increased PFS (Spearman's rank: ρ=−0.54, P=0.002) and increased OS (ρ=−0.46, P=0.010). For K_a, borderline significantly higher histogram peak K_a values were observed at day +1 in patients with increased PFS (ρ=−0.36, P=0.053). For OS, higher K_a values were seen in patients with increased OS at day +1 (ρ=−0.49, P=0.006). The median CBV and K_a values at the two time points are shown in Figure 3, separated into three groups according to median PFS and OS. For method I, higher normalized CBV values were seen at day +1 in patients with increased PFS (Spearman's rank: ρ=−0.50, P=0.005) and OS (ρ=−0.53, P=0.003). For K₂, there was no correlation between changes in K₂ from baseline to day +1 and PFS (ρ=−0.014) or OS (ρ=−0.092).

Figure 4 shows scatter plots of the relationship between logarithmic differences in patient-specific tumoral mean K_a and K₂ values and quantitative mean MTT values at the baseline MR examination for T₁- and T₂^*-dominant contrast agent extravasation, separately. For both T₁- and T₂^*-dominant contrast agent extravasation, significantly larger discrepancies between the K_a and K₂ values were observed for larger values of MTT (Spearman's rank: ρ=0.47, P=0.01 and ρ=0.46, P=0.01, respectively). There was no significant correlation between the logarithmic differences in CBV (SE images) for the two methods at baseline and MTT in tumor areas with T₁- or T₂^*-dominant contrast agent extravasation.

Using equation 8, the VNI parameter correlated significantly with PFS using both methods I (Spearman's rank: ρ=0.50, P=0.005) and II (ρ=0.61, P<0.001). A higher (positive) VNI value indicated prolonged PFS, whereas a lower (negative) VNI value indicated shorter PFS. The VNI parameters also correlated significantly with OS using method I (ρ=0.55, P=0.002) and II (ρ=0.64, P<0.001). Similar to PFS, a higher (positive) VNI value indicated prolonged OS, whereas a lower (negative) VNI value indicated shorter OS. Scatter plots of the VNI parameter as a function of PFS and OS are shown for both methods in Figure 5. Conforming to the reference study (Sorensen et al, 2009), including values for circulating collagen IV levels in the VNI analysis, the correlation to PFS was improved for both methods (method I: ρ=0.63 and method II: ρ=0.67), whereas no improvement was observed for OS for either method.

K^trans from DCE imaging is extensively used as an imaging marker for the characterization of glioma type and treatment effect (Tofts and Kermode, 1991; Roberts et al, 2000; Batchelor et al, 2007; Sorensen et al, 2009; Beaumont et al, 2009; Lacerda and Law, 2009). Furthermore, it has also been shown that cerebral perfusion, blood volume, and permeability can be simultaneously acquired from the DCE first-pass response and used to characterize gliomas (Li et al, 2003; Larsson et al, 2009). In one study (Li et al, 2003), this was performed by iterative separation of the intravascular and extravascular components of the contrast agent concentration contribution to the first-pass curves. In our study using a fully automated approach, DSC imaging was selected over DCE because optimal assessment of brain tissue hemodynamics from DCE imaging is dependent on correct estimates of T₁ and reduction of T₂^* effects on the AIFs. Also, compared with DSC, DCE usually suffers from lower temporal resolution and spatial coverage. Nevertheless, contrary to DCE imaging, DSC-based measures of permeability have not received as much attention for tumor classification. Reasons for this might be the complexity of the analysis and that DSC-based permeability values are hard to quantify. Consequently, permeability estimates using DSC in the literature vary. One study reported differences in a K^trans parameter between glioblastomas, meningiomas, and lymphomas by using first-pass pharmacokinetic modeling on the DSC images (Johnson et al, 2004). Using the same method, a second study reported good correlation between K^trans from DCE and DSC in gliomas, whereas a third study reported poor correlation between K^trans and glioma grade (Law et al, 2004; Cha et al, 2006). When comparing K^trans from DCE and DSC in meningiomas, the correlation was poor (Cha et al, 2006). Furthermore, another study used the same method to successfully predict high glioma grade based on a combination of K^trans and CBV (Law et al, 2006). Using method I, one study showed that the DSC-based K₂ parameter could successfully differentiate between high- and low-grade gliomas, whereas another study did not observe this effect (Donahue et al, 2000; Provenzale et al, 2002). Also, similar to our study, K₂ has been shown to be unsuccessful in predicting response (time to progression) of antiangiogenetic therapy in glioblastomas (Sawlani et al, 2010).

Results from the simulations in Part I and the patient data in Part II suggest a similar relationship between the DSC-derived K_a permeability parameter and K^trans from DCE imaging. Using linear mixed model analysis on the patient data, median K_a values were found to increase significantly for increasing K^trans cohorts. Furthermore, our results showed the K_a data tended to converge at higher values of K^trans, resulting in a borderline significantly higher goodness of fit when using a quadratic polynomial function compared with that of a linear function. Thus, although the assumption of a linear relationship to K^trans will be valid for most K_a values, care should be taken with high K_a values as our proposed DSC leakage correction model assumes a negligible reflux (K^transt_N−1/v_e1), which is not reasonable for high values of permeability. As discussed in more detail in Part I, this leads to an underestimation of K_a. Our group is currently working on a method that will assess and correct for this effect by applying a second linear fit to the tail of the residue function. Furthermore, even with the use of a 0.1-mmol/kg predose to minimize T₁-dominant extravasation effects (Paulson and Schmainda, 2008; Hu et al, 2010), 10 of 30 patients showed a negative ‘dip' in the K_a values at low K^trans. As discussed in Part I, this might be explained by the predose not being able to remove all T₁ effects in the MR signal in all patients. Here, it has been previously shown that the size of the loading dose needs to be sufficiently high (0.1mmol/kg) for optimal tissue saturation (Donahue et al, 2000). Consequently, for the range of K_a (K₂) values reported in our study, care should be taken when evaluating values close to zero. Potentially, at the cost of lower SNR, using a lower flip angle in the DSC imaging protocol should minimize this effect.

Nevertheless, our results showed K_a to be sensitive to anti-VEGF treatment effects and predictive of both PFS and OS. Thus, the K_a values obtained in our patient data suggest that DSC imaging can form the basis for a pseudo-leakage parameter that scales with tumor permeability and consequently patient prognosis. Using a histogram-based method (Emblem et al, 2008), more homogenous distributions of K_a values (comparable to a greater reduction in mean values) were seen at day +1 in patients with increased PFS and OS. Compared to using mean values (assuming T₂^*-dominant leakage only), a higher correlation with PFS and OS was observed for both methods when using the histogram method (data not shown). Furthermore, compared to the reference study (Sorensen et al, 2009), a higher correlation with PFS and OS was observed for CBV using both methods. This is probably due to the use of a fully automated, user-independent analysis method including automatic AIF selection and partial volume correction (Bjornerud and Emblem, 2010). Interestingly, although the resulting CBV maps of the two methods can have clearly visible differences, our results suggest that the influence of the leakage correction method on predictive values of CBV to survival is relatively limited. Hence, when using CBV as the only parameter to assess tumor response to therapy, the choice of leakage correction method seems relatively unimportant. While this argument may not hold true for preoperative tumor grading, the high prognostic value of the CBV parameter to progression and survival during anti-VEGF treatment in our study seem to suggest that the dramatic changes in microvasculature blood volume reduce the influence of the leakage correction error. When including the K_a (K₂) parameter in the analysis, however, choosing an MTT insensitive correction method can prove important as studies have shown that MTT increases with the higher vascular complexity associated with tumor angiogenesis (Bastin et al, 2006; Jain et al, 2007). This may be especially critical when assessing therapy-induced vascular normalization properties as anti-VEGF therapy in combination with radiation and chemotherapy kills or suppress cancer cells thereby normalizing tumor vascularity and potentially restoring impaired blood flow (Griffon-Etienne et al, 1999; Batchelor et al, 2007; Sorensen et al, 2009; Jain et al, 2009). Furthermore, the Kaplan–Meier curves suggest that the VNI parameter derived using method II is able to consistently identify patients that respond to anti-VEGF therapy and subsequently have longer PFS and OS. Using method I, however, the survival distributions for OS were not different for the ‘poor responding' and ‘good responding' groups. Although these results should be used with care and there may be more than one choice of survival distribution groups, our results indicate that the VNI parameter of method II holds a higher sensitivity to potential treatment effects to that of method I.

Whether the higher predictive values of the K_a parameter over K₂ is because K_a is closer to a true measure of the permeability surface area product remains to be explored, but the correlation between the logarithmic differences in K_a and K₂ and MTT suggests that K₂ deviate from K_a at higher MTT values resulting in an overestimation of the K₂ leakage effect, an argument also supported by the results from Part I of our study. This effect was observed for both T₁- and T₂^*-dominant contrast agent extravasation. Contrary to Part I, however, there was no correlation between the logarithmic differences in CBV and MTT. This result is in line with the survival analysis discussed above, in that the K_a (K₂) seem to hold a higher sensitivity towards changes in MTT compared with CBV. A reason for this might be that relative changes in CBV are modest compared with relative changes in K_a (K₂). Nevertheless, it should be noted that this discrepancy between Parts I and II may in part also be explained by differences in sampling sizes between the two studies.

A potential limitation to method II is that an AIF needs to be identified. Although this is the focus of much research and debate (Rausch et al, 2000; Kiselev, 2001; Knutsson et al, 2004) selecting an optimal AIF with correct tissue density and large/small vessel hematocrit values can be difficult and further complicates the analysis compared with method I. However, to improve stability, we applied a recently published fully automatic method for AIF selection and partial volume correction (Bjornerud and Emblem, 2010). Furthermore, we minimized unwanted oscillations in the residue functions by employing a heavy computational iterative Tikhonov regularization-based SVD deconvolution method. Results from Part I of our study showed that the estimation of K_a is rather insensitive to oscillations and the use of a much faster truncated SVD approach should potentially have little influence on our results. Also, contrary to our simulations, an offset in K_a values for K^trans values equal to zero was observed in our patient data. This may be explained by an incorrect nonzero estimation of K_a for low leakage values due to noise limitations. Thus, a better estimation of the residue function by fitting a Lorentzian function and a linear component to the data may reduce this systematic error. This relatively small error, however, should be uniform across patients and have minimal influence on our results.

KEE received grant support from Norwegian Research Council, 191088/V50. AB is a consultant and on the advisory board of NordicNeuroLab AS, Bergen, Norway. RJHB received grant support from The Sigrid Juselius Foundation, the Instrumentarium Research Foundation, the Academy of Finland, the Paulo Foundation, and the Finnish Medical Foundation. TTB is a consultant and on the advisory boards of Vertex, Schering-Plough, Acceleron, Imclone, AstraZeneca, Roche/Genentech, and Amgen and received grant support from Takeda-Millennium, AstraZeneca, and Pfizer. RKJ received grant support from AstraZeneca, Dyax, and MedImmune and is a consultant and on the advisory boards of Astellas-Fibrogen, Dyax, Genzyme, Morphosys, AstraZeneca, Noxxon Pharma, Regeneron, and SynDevRx. AGS received grant support from National Cancer Institute and National Institutes of Health and is a consultant and on the advisory boards of ACR-Image Metrix, BayerScheringPharma, Bristol Meyers Squibb, BiogenIdec, Merrimack Pharmaceuticals, Olea Medical, Mitsubishi Pharma, GE Healthcare, Regeneron, Novartis, Roche, Siemens Medical, Takeda, AstraZeneca, National Institutes of Health, and Kit, Inc.