52 consecutive patients with different, newly diagnosed brain tumors were included in the study (25 glioblastoma, 12 meningioma, 12 metastasis, 3 lymphoma patients). For 21 patients, MRI examination was performed twice with a time interval of 1 to 4 days. 18 patients received preoperatively dexamethasone (10 glioblastoma, 2 meningeoma, 5 metastasis, 1 lymphoma patients). We excluded five patients who received an MRI examination twice and eight patients with single-time MRI examinations from further analysis due to non-plausible vascular input functions or movement artifacts.

MRI was performed on a 3 Tesla MR scanner (Siemens Magnetom Verio). In addition to the standard tumor protocol, a dynamic 10 echo FLASH sequence (T_R = 44 ms, α = 70˚, T_E = 1.2, 2.2, 3.1, 4.1, 5.5, 6.4, 8.0, 10.0, 12.0 and 13.0 ms, matrix 256 × 208 (acquisition matrix: 128 × 73), GRAPPA acceleration factor = 3) with a temporal resolution of 2 seconds was run during the application of CM (0.1 ml/kg body weight of Gadovist, (Bayer Schering) at a flow of 4 ml/s followed by 10 ml of saline). The sequence includes 3 slices of each 5 mm thickness. One slice was positioned in the neck region for measurement of an Arterial Input Function (AIF), two others were placed in the tumor region, identified with native T₁ and T₂ weighted images. After 10 of 60 dynamic scans, the CM was administered.

For calculation of and S₀, different procedures were applied (see appendix). The calculations were based on the first and last echo only (i.e., conventional dual-echo approach), as linear fit on the logarithmic signal intensities, as monoexponential fit on the signal intensities themselves or as fit of two complex intensities of components with different Larmor frequencies (i.e., a multi-echo Dixon approach). Calculations based on first and second echo only were also performed as negative control.

The quality of the multi-echo corrections (i.e., the determination of S₀ and maps) was evaluated by calculation of CNR ratios for the time curves of and S₀ for the AIF, VOF and tumor ROIs. For this purpose, the difference of the curve maximum and the baseline value was divided by the standard deviation along the baseline. For plausibility control, modified Euclidean distances between glioblastoma, meningioma, metastasis and lymphoma were calculated based on K^trans and rBV (both calculated with the VOF, see Table 1). For reasons of non-symmetric parameter distributions and noisy data, medians instead of mean values were used. Taking into account the asymmetric parameter distribution, the normalization was done with the mean difference of the 75 and 25 percentiles of the two classes being compared. As an overall quality parameter, we used the sum of these distances normalized to the size of the smaller class.

For estimation of the vascular input function, we implemented several time courses: S₀(t) and of a ROI in a neck artery (AIF) and in a venous sinus (mostly superior sagittal sinus―VOF) and in the tumor ROI. Manual drawing of vascular ROIs was supported by pixel exclusion based on lower and upper thresholds for maximum change and time of maximum in S₀(t) and respectively. During the definition of the ROIs, both S₀(t) and were checked for plausibility control. In case of non-plausible curve shapes, other vessels or other vessel segments were selected. Baseline subtraction was performed after manual selection of a baseline range, mostly including the 4^th to 22^th scan. For the use of a S₀(t) curve in based models, the curve was normalized to the maximum of and vice versa (in the case of from the tumor ROI the corresponding maxima from the healthy tissue ROI were used in order to minimize the influence of the non-linearity of the dependence of S₀ from the CM concentration). As a preprocessing step, the vascular input functions were shifted in time (except for in the tumor ROI). For that reason, positions of the maxima of the curves were determined by Gaussian fits to the data points exceeding 60.6% of the maximum (for normal distributions, this is equivalent to the position range of mean ± standard deviation). The VIFs were shifted so that their maximum position became equal to that of the curve measured in the tumor ROI. When applying in the tumor ROI as vascular input function, rBV and K^trans estimations are biased by the “real rBV” multiplicatively. Therefore, appropriate rescaling has to be done, preferable with rBV determined on the base of another vascular input function in order to avoid errors.

The degree of nonlinearity in S₀(CM concentration) was qualitatively eva- luated by comparing the curve shape of S₀(t) with that of.

The following models were combined with the above-described vascular input functions:

For S_0,Tumor(t) we applied the Patlak and Extended Tofts models [10] [11] [12] [13] to calculate K^trans, rBV and v_e. The curve fits were performed with precalculated rBV as well as with rBV as free parameter.

For we used the Indicator Dilution Theory (IDT) to determine rBV, regional blood flow (rBV) and mean transit time (MTT) [14] [15] [16] . For that, Gaussian and Gama Variate peaks were fitted to curves.

Additionally, we evaluated simple empiric parameters like maximum relative and maximum absolute enhancement in S_0,Tumor(t) and maximum temporal increase of. Each parameter was examined before as well as after normalization to the corresponding value from a ROI in contralateral healthy tissue.

Based on the perfusion parametric images, lacunarity parameters were calculated as published elsewhere [17] .

To identify model/VIF-combinations allowing the most stable perfusion parameter estimation, the reliability and reproducibility of the calculated parameters were evaluated visually and quantitatively. For the visual evaluation of each parameter, the values of the first and second investigation were drawn on a patient-by-patient basis (see Figure 1). For the quantitative assessment, a normalized mean difference between the consecutive MRI sessions was calculated to be used as reproducibility parameter

(n = number of patients, x_1,i or x_2,i = parameter x for patient i at first or second measurement resp.). This parameter normalizes the mean of difference of measures between the two time points to the median of the corresponding parameter and defines in this way a relative measure of stability of that parameter. For plausibility reasons, was used to generate a list of the 30 best normalized and 30 best non-normalized parameters, from which the most plausible ones were selected on the basis of the diagrams mentioned above. This step was necessary due to the bias resulting from a few patients with unusual large deviations between the first and second measurements.

Statistical analysis was done using Excel with user functions written in VBA (Visual Basic for Applications, Microsoft Corporation). The image analysis was performed with a program written in IDL (“Interactive Data Language”, Exelis Visual Information Solutions Inc.).

The CNR values averaged over all measurements for as well as for S₀ curves are summarized in Table 1. The best overall CNR was achieved by the log-linear calculation according to Equation (5), followed by the 10 echo fit considering water and fat compartments. The CNR sum for the dual-echo correction was less precise with about 11% compared to the best value. In the normalized sum of Euclidean distances, the different methods appear in the same order, except for the calculation based on the first and second echoes only (see Table 1).

Most reliable pharmacokinetic parameters occurred to be K^trans and rBV. In Table 2, their reproducibility is shown depending on different models (Tofts, Patlak or fit to a Gaussian or Gama Variate peak) and VIF selected for calculation.

In general, the overall signal intensity in the slice aimed for the AIF estimation was significantly lower than in the tumor covering slice(s).

For all kinds of multi-echo correction, the CNR of the VOF was better than that of the AIF by a factor of 1.75 to 3.5, where the superior sagittal sinus allowed most plausible curves. For the preferred log-linear correction these factors amount to 2.96 for S₀ and 2.10 for resp. Perfusion evaluations using the VOF as vascular input function also result in the best reproducibility parameter (see next paragraph).

In addition, high reproducibility of perfusion parameters was achieved by using vascular input function from within the tumor ROI.

The frequency of occurrence of the different models and vascular input functions in the list of the 30 best model-VIF combinations is summarized in Table 3. In this summary, we excluded the lacunarity parameters for reasons of plausibility (Apparently good lacunarity parameters mostly were based on parameter images calculated with bad performing VIFs. Hence, their information content probably consists on the tumor shape rather than on the inhomogeneity

properties). The most reliable calculations are based on the Extended Toftsmodel, Gaussian fit and model-free calculations (like maximum enhancement e.g., which showed minimum of all parameters normalized to healthy tissue).

The results of IDT calculations are rather dissatisfactory. None of the IDT- based parameters was found either in the 30 best normalized or the best non- normalized parameters.

The lowest mean “fat-to-water” signal ratio was found for malignant glioma and the highest mean for meningioma. Besides this, higher “fat-to-water” signal ratios were detected in gliomas after dexamethasone application, compared to those without such medication. But due to the small sample size, these differences were not statistically significant.

In our study, the loglinear curve fit was found to suit best among all multi-echo correction algorithms tested. Remarkable, loglinear correction showed better results than the exponential one. From the physical point of view, however, the exponential fits correspond to the data more exactly than fits on logarithmized signal intensities (by taking the logarithms, the statistical uncertainty of higher values is compressed. Thus, linear fitting of logarithms overweighs the low-in- tensity data points corresponding to the late echoes). Otherwise, for numerical reasons, they are less stable compared to the linear fit on the logarithmized data. In other words, if the weighting of data points influences the curve fit to an important way, then the exponential fits should give better results than the loglinear ones. But, if numerical robustness is the essential objective of the multi- echo correction method, then the loglinear model should work better than the exponential ones. Therefore, in our data the stability aspect underwent more influence than the biased weighting of the data points.

We also found the biexponential fat-water models resulting in higher Euclidean distances between tumor entities and CNR―at least compared to the corresponding monoexponential models. But we want to stress, that models based on loglinear and monoexponential calculations are actually identical, the only differences are the different weighting of data points and the different numeric stability.

An extended discussion of the biexponential fat-water model can be found in the “signal decomposition” paragraph.

Testing simple dual-echo corrections, Euclidean distances between tumor entities based on K^trans and rBV, appeared to be surprisingly good for the first and second echo only ? in contrast to the CNR evaluation. This, however, seems to be a statistical artifact due to the high data noise and the small sample size. Obtained parameters were not significantly biased compared to the ones from the other correction methods, but they were noisier.

A prerequisite for quantitative perfusion measurements is the determination of VIF. Several approaches of manual, semi-automatic or automatic VIF determinations for brain perfusion measurements are available. There are for example measurements of a special slice caudal to the tumor for deriving of an AIF [22] , automatic selection of pixels within the brain with highest and/or fastest enhancement [23] or with clustering algorithms [24] , reference to the venous output function [25] or VIF estimation from averaging over several patients [13] [26] .

In the present study, we drew the ROIs manually in order to control their influence on the time courses of S₀ and. In this way, we could avoid possible underestimation of peak changes due to partial volume and non-plausible curve shapes resulting from flow effects. It should be noted here, that the definition of an arterial ROI often was challenging. In some cases it was even not possible to obtain plausible time courses of S₀ and/or―possibly due to higher influence of turbulent flow on signal intensity at time with higher CM concentration. Another cause for implausible AIF curves in some cases was the bias of the mag- nitude of the signal intensity due to noise, especially for the late echoes leading to underestimation of during the bolus peak.

In our data, nonlinearity of S₀ (CM concentration) as well as biased curve shapes in the venous ROIs were less noticeable than in the arterial ones. This subjective impression was confirmed by CNR analysis as well as by rating of perfusion parameters with different vascular input functions. According to Yuan [25] , the advantage of venous time courses can be explained by lower flow velocity as well as more steady flow in veins compared to arteries. Additionally, in their work, VIFs derived from veins occurred to be less dependent on the selected slice than that derived from arteries.

Earlier studies [27] [28] demonstrated the crucial influence of the temporal shift of vascular input function on the estimation of perfusion parameters. Applying multi-echo sequences, this problem can be avoided by the measurement of in the tumor ROI. The peak position of can then be used for optimal time shift of a vascular input function measured elsewhere.

In addition to the correct position on the time axis, from the tumor ROI possesses the correct curve dispersion or peak broadening. This could be the reason for the quite good stability of perfusion parameters calculated with this VIF. These properties even overcompensates the worse signal-to-noise ratio compared to the vessel-based input functions.

However, due to downscaling by the volume fraction of capillaries in the tumor voxels, from the tumor ROI as vascular input function is nevertheless acceptable concerning position and peak width, but is not acceptable concerning the amplitude. Hence, perfusion parameters determined this way have to be corrected for this downscaling.¹

Although models with fewer numbers of free parameters like the Patlak approach are supposed to be more stable, we found better reproducibility with the Tofts model. This is a contradictory finding to previously published data [26] [29] . In [30] , owing to more fitting parameters, the two-compartment exchange model occurred to give less stable results at given acquisition duration compared to the Tofts and Extended Tofts models as well. The better reproducibility found in our data applying the Extended Tofts model might be explained by the fact, that in contrary to the Extended Tofts, in Patlak model one or two boundaries on the time axis (depending on the implementation) have to be chosen. The uncertainty during manual selection of these boundaries might overcompensate the a-priori better stability of fits to model functions with fewer degrees of freedom. It has to be evaluated, to what degree automatic determination of the upper (later) boundary based on statistical methods could reduce this uncertainty.

Calculations based on the Indicator Dilution Theory lead to quite instable results. This could be caused by the limited influence of smaller, even good vascularized tumors on the Mean Transit Time (MTT) of the CM bolus due to the comparatively short pathway of the blood through the tumor. Another reason could be the less stable rBV estimation by means of the fit of a Gamma Variate Function compared to the well performing Gaussian fit.

Diagnostics based on pharmacological parameters is one way to achieve comparability of results between different sites. Another way to reach this aim is standardization of measurement conditions allowing for comparison of simple model free parameters. In MR mammography, a qualitative description of the time course of contrast enhancement under mildly standardized measurement conditions occurred to meet the clinical needs [31] . In our data, among all parameters normalized to healthy tissue, the best reproducibility was obtained for the signal increase extrapolated to TE = 0, which is influenced by vessel permeability, perfusion and extravascular extracellular space.

The assumption for brain and tumor tissue to consist of two components with different Larmor frequency appears to improve the quality of curve fits of signal intensities such as a function of TE, compared to monoexponential fits without differentiation between fat and water signals. This is clearly seen in the evaluation of CNRs, but does not transfer to better accuracy of perfusion parameter based differentiation between tumor entities (Table 1). However, we demonstrated decreased lower-frequency-compartment (with a chemical shift in the range of fatty tissue) in gliomas after pretreating with dexamethasone compared to the untreated group (Table 4, Figure 2). Thus, the multi-echo perfusion approach has the potential to provide additional physiological information beyond the description of blood supply. The background of these findings has to be analyzed comparing such measurements with in-vivo MR spectroscopy.

Some limitations of this study are to be mentioned:

First of all, our data was not compared to any reference method. To our knowledge, no real “gold standard” for the perfusion measures exists. Hence, for the evaluation of the reliability of our data, we introduced the reproducibility parameter defined in Equation (1).

Second, evaluations were performed with in-house software. Although carefully tested during the development process, there remains a higher risk of incorrect calculations or numeric instabilities compared to commercial and/or widespread software solutions. No reference calculations with standard software were performed.

Finally, in the literature, DCE MR studies of brain tumors usually are performed for about 5 minutes at a temporal resolution of 5.3 s [32] resulting in about 55 time points. In our study, we needed a temporal resolution of 2 seconds or higher for the DSC evaluations. At the same time, this denser sampling of 60 time points within two minutes should at least partly compensate the lack of very late data points needed for determination of K^trans and v_e or k₂ resp.