The LEGATOS technique: A new tissue‐validated dynamic contrast‐enhanced MRI method for whole‐brain, high‐spatial resolution parametric mapping

A DCE‐MRI technique that can provide both high spatiotemporal resolution and whole‐brain coverage for quantitative microvascular analysis is highly desirable but currently challenging to achieve. In this study, we sought to develop and validate a novel dual‐temporal resolution (DTR) DCE‐MRI‐based methodology for deriving accurate, whole‐brain high‐spatial resolution microvascular parameters.


| INTRODUCTION
Kinetic parameters derived from DCE-MRI are increasingly used in the study of tumors, both within and outside the brain, for assessment of tumor microenvironment and microvasculature. They have demonstrable value as predictive, prognostic, and treatment response biomarkers and are of increasing importance with the growing use of anti-angiogenic therapies. [1][2][3][4][5][6][7] Key limitations in current DCE-MRI techniques include the volume coverage, spatial resolution and accuracy of derived kinetic parameters, and the requirement for full-dose gadolinium-based-contrast agent (GBCA) administration during data acquisition. [8][9][10][11][12][13] Whereas whole-brain coverage and high-spatial (HS) resolution are essential where lesions are widespread, small, or exhibit significant microvascular heterogeneity, high-temporal (HT) resolution is required for accurate quantification of kinetic parameters such as cerebral blood flow, fractional plasma volume (v p ), transfer constant (K trans ), and the fractional volume of extravascular extracellular space (v e ). [14][15][16] Traditional Cartesian MRI has limitations in achieving simultaneous HS and HT resolution so that a compromise must be made in the protocol design. Dual-temporal resolution (DTR) techniques incorporating a staged dual-bolus of GBCA have been developed to address this limitation. 17 Li and colleagues measured plasma concentration curves from an initial low-dose high-temporal (LDHT) resolution acquisition to reconstruct a HT resolution vascular input function (VIF). 18 This accurate VIF was then used for subsequent kinetic analysis of a second full-dose HS resolution (FDHS) data set. This approach, termed the dual injection contrast enhanced (DICE)-FDHS method, generated HS resolution parametric maps, however, the low-temporal resolution (frame duration ∆t = 10 s) of the GBCA uptake curves in tissue resulted in covariate errors during kinetic fitting, observable as large vessel and vascular leakage contamination within the derived K trans and v p maps, respectively. 17 DTR DCE-MRI methods that can provide accurate pharmacokinetic estimates with high spatiotemporal resolution are, therefore, needed. Both dual injection and a single lowdose injection DTR DCE-MRI have shown the potential to provide high spatiotemporal resolution and whole-brain coverage for quantitative microvascular analysis. [19][20][21] This paper focuses on the dual injection technique. The aims of this feasibility study are therefore (1) to develop a new analysis technique, the level and rescale the gadolinium contrast concentration curves of high-temporal to high-spatial (LEGATOS) method, for deriving accurate, whole-brain high-spatial resolution microvascular parameters from dual injection DTR DCE-MRI data, and (2) to validate parameter estimates derived using the LEGATOS method using both computer simulation and an in vivo study incorporating correlation with histopathological data.

| Patients
For this feasibility study, we investigated previously acquired dual injection DTR DCE-MRI data in 13 patients with glioblastoma (GBM) and 17 patients with vestibular schwannoma (VS) (including 1 patient with bilateral neurofibromatosis type 2 [NF2]-related VS). Although GBM are the most common malignant brain tumor in adults, VS were also chosen as a disease model because they are not influenced by brain microenvironment and its vasculature because of their extra-axial location. In addition, smaller tumors can be resected whole permitting more robust comparisons between imaging and tissue data. The study obtained ethical approval (NHS Health Research Authority; NRES committee North West 13/NW/0131 and 13/NW/0247), and all participants provided informed consent.

| MR imaging
Imaging was performed on 2 Philips Achieva whole body scanners (Philips, Best, Netherlands) with most patients scanned at 1.5T (1 patient with a sporadic VS was scanned at 3.0T). For all studie, a macrocyclic GBCA (gadoterate meglumine; Dotarem, Guerbet S.A.) was administered by power injector as an intravenous bolus at a rate of 3 mL/s, followed by a chaser of 20 mL of 0.9% saline administered at the same effects compared to other high-spatial resolution approaches, and correlated with tissue markers of vascularity (P ≤ 0.003) and cell density (P ≤ 0.006). Conclusion: The LEGATOS method can be used to generate accurate, high-spatial resolution microvascular parameter estimates from DCE-MRI.

K E Y W O R D S
accurate kinetic parameter mapping, dual-temporal resolution DCE-MRI, perfusion and permeability, spatial and temporal resolution rate. High-resolution 3D T 1 -weighted (T 1 W) gradient echo sequence with whole-brain coverage (TE = 3.2 ms, TR = 8.6 ms, slice thickness = 1.2 mm) both before and after contrast were obtained for tumor delineation.
Data were acquired using a previously described DTR, DICE technique. 17 For the first part of this DTR technique, a low-dose fixed-volume of GBCA was administered during acquisition of a HT resolution sequence using a 3D gradient echo sequence with a flip angle of 20°, TR/TE of 2.5 ms/0.696 ms, SENSE acceleration factor of 1.8, reconstructed matrix size of 96 × 96 × 22, voxel size of 2.5 × 2.5 × 6.35 mm 3 , pixel bandwidth of 700 Hz, and frame duration (Δt) of 1.0 s (n = 300). This was followed by a full-dose of GBCA (dose = 0.2 mL/kg × weight − dose of prebolus) administered during acquisition of a HS resolution sequence with a flip angle of 20°, TR/TE of 3.7 ms/0.93 ms, SENSE acceleration factor of 2.8, reconstructed matrix size of 240 × 240 × 70, reconstructed voxel size of 1 × 1 × 2 mm 3 , pixel bandwidth of 700 Hz, and frame duration (Δt) of 10.7 s (n = 60). For both the LDHT and FDHS acquisition, 0 padding was used for FFT reconstruction in the z-direction, which doubles the number of slices. For baseline longitudinal relaxation rate (R1 0 ) mapping, variable flip-angle (VFA; α = 2°, 8°, 15°, and 20°) acquisitions were undertaken before both the LDHT and FDHS DCE series. The spatial resolution of each VFA acquisition series was chosen to match the LDHT (2.5 × 2.5 × 6.35 mm 3 ) and FDHS (1 × 1 × 2 mm 3 ) DCE series, respectively.

| The new DTR DCE-MRI processing method
Our new DTR-based mapping technique relied on 2 key steps, which can be summarized as follows: Key step I: combination of the HT and HS resolution series to construct a 4D GBCA concentration volume (HTHS-merged) with a HT arterial phase followed by a HS parenchymal tissue phase.
A 2-part 4D GBCA concentration volume, termed HTHSmerged, was constructed from the HT (high-temporal, lowspatial) and HS (high-spatial, low-temporal) resolution dynamic series. The native 4D HT dynamic images (voxel size = 2.5 × 2.5 × 6.35 mm 3 ) were first co-registered and resliced to a HS baseline image frame (voxel size = 1 × 1 × 2 mm 3 ) using a 4th degree B-spline interpolation within statistical parametric mapping 22 to obtain a 4D HT aligned volume (voxel size = 1 × 1 × 2 mm 3 ). The signal intensity-time curves from this 4D HT aligned and the 4D HS dynamic image volumes were then converted to GBCA concentration-time curves using their respective baselines and R1 0 derived from the pre-injection VFA acquisitions.
The constructed DTR 4D GBCA concentration volume (HTHS-merged) must retain an HT arterial phase to enable accurate discrimination between plasma volume and vascular leakage effects. The initial 40 s of the HT aligned concentration-time course was, therefore, concatenated with later concentration-time points obtained from the FDHS series. The time point for this adjoining (t adj ) was selected to be just after the recirculation phase to limit the effects of rapid systemic contrast agent leakage and fluctuations because of recirculation. Because of the differences in administered dose and time of GBCA administration between the LDHT and FDHS DCE series, the later phase of the HS concentration curves also needed to be cross-calibrated with the HT curves for both bolus arrival time (BAT) and GBCA dose before concatenation. 19 The major steps in the construction of the DTR 4D concentration volume from the dual injection DTR data are illustrated in Figure 1.
Key step II: pixel-by-pixel rescaling the concatenated HT arterial phase to resemble the supposed "true" HS resolution arterial phase using LEGATOS.
Through containing an initial HT arterial phase (HT aligned ) followed by a HS parenchymal tissue phase, the HTHSmerged volume maintains the temporal fidelity of the arterial phase of the LDHT series. Despite the HT data set being resampled/interpolated in image space to higher spatial resolution, however, the observed HT aligned data (voxel size = 1 × 1 × 2 mm 3 ) still primarily reflects the arterial phase of the acquired low-spatial resolution pixel GBCA concentration curve and must be replaced with a reconstructed HS arterial phase. Without this reconstruction step parameter maps (in particular v p ) derived from kinetic fitting of the 4D HTHS-merged concentration volume generated in key step I would still closely resemble those obtained from the native low-spatial resolution LDHT DCE data set.
In key step II, LEGATOS was therefore used for pixelby-pixel reconstruction of the concatenated low-spatial resolution HT arterial phase of the HTHS-merged concentration volume to reflect the supposed "true" HS resolution one. This pixel-wise reconstruction method was based on the fact that the GBCA concentration value is not affected by the imaging parameters. Rather, the observed difference in the GBCA concentration between the concatenated HT aligned and doseadjusted HS concentration curves in each pixel of the HTHSmerged 4D concentration volume ( Figure 2, left column, voxel size = 1 × 1 × 2 mm 3 ) reflects the difference in the native spatial resolution during data acquisition and any possible effects of the statistical parametric mapping interpolation of the native HT arterial phase; assuming there is no dominant noise process affecting estimated GBCA concentration. In addition, the LEGATOS method assumes that in each tissue pixel of the HTHS-merged 4D concentration volume generated in key step I, the supposed "true" HS resolution arterial phase has the same shape as the observed HT aligned arterial phase, so it can be obtained by re-scaling the HT aligned arterial phase using a calibration ratio, ratio calib . Therefore, where C t-HT (t) is the observed HT aligned arterial phase concentration-time curve, C t-HS (t) is the supposed "true" HS arterial phase concentration-time curve, and The calibration ratio was calculated from the concatenated HTHS-merged concentration-time curve by taking the ratio of the mean concentration of 5 HS frames following the concatenation time point, t adj , over the mean concentration of 4 final frames of the HT aligned arterial phase series before t adj . This calibration ratio was then used to rescale the initial HT aligned arterial phase of each pixel concentrationtime curve to achieve a smooth concatenation with the later HS parenchymal phase before kinetic fitting ( Figure 2). The LEGATOS method will automatically adjust this calibration ratio and scaling procedure to achieve a smooth concatenation between the HT aligned and HS concentration-time curves. As such, although the first-pass bolus shape of the HT aligned curve is propagated through to the reconstructed arterial phase of the HS curve, any scale change (eg, because of statistical parametric mapping interpolation) of the HT aligned arterial phase will not be propagated through to the final concentration-time curve.

| Kinetic analysis
The extended Tofts model (ETM) was fitted to the tissue GBCA concentration-time curves of the 4D HTHS-merged concentration volume from each patient. 23,24 This fitting was F I G U R E 1 Combination of the low-dose high-temporal (LDHT) and full-dose high-spatial (FDHS) data from dual injection DTR MRI. Combination of the low-dose high-temporal (LDHT) and full-dose high-spatial (FDHS) GBCA concentration-time curves from dual injection dualtemporal resolution DCE MRI data are shown. The LDHT data are first co-registered to a HS baseline image frame and interpolated to generate a 4D HT aligned DCE data set with the same x, y, and z dimensions (1 × 1 × 2 mm 3 ) as each HS image frame. To allow for timing cross-calibration in the subsequent merge process, the arterial input function bolus arrival time (BAT AIF ) and the time point for adjoining the HT aligned and FDHS concentration-time curves (t adj ) are derived for the LDHT and FDHS data sets, respectively. The 4D HT aligned and FDHS signal intensity (SI) DCE volumes are then converted to 4D GBCA concentration volumes. For the merge process the later parenchymal phase of the FDHS concentrationtime curves are cross-calibrated with the LDHT curves for both timing and GBCA dose and are then concatenated to the arterial phase of the lowdose HT aligned data set to generate a HTHS-merged 4D concentration volume. GBCA = gadolinium-based-contrast agent Baseline 1. Co-register/reslice 4D low dose high temporal, low spatial resolution (LDHT) DCE SI volume to a high spatial resolution (HS) baseline image frame to produce 4D HT aligned data. performed either immediately following key step I (HTHSmerged method), or following both key steps I and II above (the LEGATOS method). In both cases the final spatial resolution of derived kinetic parameter maps was 1 × 1 × 2 mm. Kinetic analysis was also performed using the LDHT or FDHS tissue GBCA concentration-time curves alone as a comparative measure. The dynamic MR signal measured from voxels in the vertical part of superior sagittal sinus was used as an indirect estimate of the arterial input function as described previously 25,26 (Supporting information Figure  S1). As part of the fitting procedure the BAT for each tissue voxel is estimated and the C p (t) measured from the superior sagittal sinus time-shifted to align with the BAT of each tissue GBCA concentration-time curve. A map of scaled fitting error (SFE) 27 was generated as an integral part of each fitting procedure to assess the discrepancy between the derived curve and the original data and tumor voxels with an SFE value above 50% were excluded from the statistics. In all cases to confirm the acceptance of the use of SFE > 50% for excluding outlier tumor voxels, visual inspection of derived SFE and kinetic parameter maps (before and after exclusion of voxels with SFE > 50%) was performed.

LEGATOS method
Dual injection DTR MRI data obtained from a patient with a sporadic VS imaged at 3T was used as the base for the computer simulation. 20 HS resolution parameter estimates for K trans , v p , v e, and bolus arrival time (t0), derived from the LEGATOS analysis were used as the "true" values for simulation of a 4D FDHS GBCA concentration volume. The combined low-dose C p (t) curve used as a VIF for the in vivo LEGATOS analysis ( Figure 3A) was time-shifted and summed to generate a full-dose, HT resolution VIF for use in the simulation of tissue enhancement curves ( Figure 3B). The simulated tissue voxel concentration-time curves were then F I G U R E 2 Pixel-by-pixel rescaling of the HT arterial-phase of the HTHS-merged concentration-time curve to resemble the supposed "true" high-spatial resolution one. Panels (A) and (B) show 2 representative pixels from the tissue GBCA concentration-time curve in a VS imaged at 3T. The left column represents the HTHS-merged concentration-time curve in each pixel and the right column shows the rescaling of the HT arterialphase to achieve a smooth concatenation with the later parenchymal HS phase. Ratio calib is used to rescale the initial C t-HT (t) for each pixel, so that the C t-HT (t) and C t-HS (t) are concatenated, although maintaining the shape of the first-pass C t-HT (t) curve. resampled with a temporal interval of 10-s to resemble the in vivo acquired FDHS-DCE data set. Quantitative image comparisons between the in vivo acquired and the simulated 4D FDHS concentration volumes were performed using the structural similarity index. 28 The mean structural similarity index values between 2 images were calculated using the same slice level within the 2 volumes. The simulated FDHS-DCE data set was then combined with the in vivo LDHT data set to construct a HTHS-merged 4D concentration volume as described in key step I. The ETM was then either directly fitted to the tissue GBCA concentrationtime curves of this 4D HTHS-merged concentration volume (HTHS-merged method), or undertaken following initial HT concentration-time curve rescaling (the LEGATOS method), yielding "measured" K trans , v p , v e, and t0 maps.

| Tissue analysis
Tissues from 15 sporadic VS were analyzed. Ethical approval was obtained for tissue analyses (REC reference 15/ NW/0429 and 19/NS/0167). Serial 5-µm sections were cut from each paraffin block and stained with hematoxylin and eosin (H&E) and immunoperoxidase immunohistochemistry (IHC). Tissue sections were assessed for cell density (H&E), microvessel surface area (CD31) and vascular permeability (fibrinogen) using immunoperoxidase IHC. Detailed protocols are described in Supporting Information Methods.

| Statistical analysis
Results from the computer simulation were used to quantitatively evaluate the LEGATOS method. The percentage deviation (PD) of the "measured" values from the "true" values were calculated, where PD = (measured − true)/true. Pixel-bypixel calculation of PD within the 3D tumor region-of-interest for the patient was applied onto each of the 4 parametric maps derived using either the LEGATOS or the HTHS-merged method. Tumor mean and SD of the PD values were generated and compared between the 2 analysis approaches. For the in vivo study, mean tumor K trans and v p estimates derived from the 13 patients with GBM using either the LEGATOS approach or native LDHT data sets alone were compared using linear regression. For the 15 resected sporadic VS the inter-tumor correlation between DCE-MRI derived parameter estimates (K trans , v p, and v e ) and tissuederived metrics (H&E cell density and CD31 microvessel surface area) are reported as Pearson's product moment correlation coefficient (r) or Spearman's ρ in the case of nonlinear associations.

| Computer simulation
The combined low-dose VIF used for the in vivo LEGATOS analysis and the reconstructed full-dose VIF used for the FDHS 4D DCE volume simulations are shown in Figure  3A,B, respectively. A close similarity between the parenchymal tissue phase (t > 40 s) of the simulated low-dose GBCA concentration-time curves and the parenchymal phase of the simulated full-dose curves rescaled by the dose ratio was demonstrated ( Figure 3C). This result supported the assumption that the LDHT and FDHS 4D concentration volumes can be merged through concatenation of the LDHT initial phase with later phases of the dose-calibrated FDHS 4D concentration volumes. A high similarity between the simulated and the in vivo acquired 4D FDHS DCE dynamic images was seen ( Figure 3D) and the mean structural similarity index between the in vivo and the simulated 4D FDHS concentration volume was 0.998 ± 0.001 (n = 35 slices, range = 0.996-0.999).
Representative voxel fits of the in vivo acquired LDHT DCE-MRI data obtained from the patient imaged at 3T are shown in Supporting Information Figure S2 and demonstrate that when using the ETM, there is a good fit between the F I G U R E 4 Comparison of kinetic parameter maps derived from computer-simulated dual injection DCE (DICE) data with the "true" in vivo parameter maps. The left-hand column (in vivo-LEGATOS) displays the LEGATOS-derived kinetic parameter maps (K trans , v p , and v e ) from the sporadic vestibular schwannoma (VS) patient DCE data displayed in Figure 3D, which were used as the "true" parameter values for DCE data simulation. The middle and right-hand column display the "measured" kinetic maps derived from analysis of the computer-simulated DICE data with either the LEGATOS (Simu-LEGATOS) or the HTHS-merged method (Simu-merge), respectively. Direct fitting of the simulated HTHSmerged data, without prior LEGATOS reconstruction produced a v p map with comparatively less spatial detail (short arrow). K trans and v e maps derived directly from the simulated DICE data with the HTHS-merged method also demonstrated vessel contamination adjacent to the vestibular schwannoma on the left side (long arrow), an effect not seen in the LEGATOS derived images scaled VIF and the early phase data of both tumor and normal appearing grey and white matter voxels. LEGATOS analysis of both the in vivo acquired and the computer simulated data produced highly comparable kinetic parameter maps ( Figure  4). Tumoral vascular heterogeneity was clearly evident on the LEGATOS v p maps derived using both the in vivo acquired and the computer simulated data but direct fitting of the simulated HTHS-merged data without prior LEGATOS reconstruction produced a v p map with comparatively less spatial detail. The accuracy of kinetic parameter estimates was improved through use of the LEGATOS method compared to direct fitting of the simulated HTHS-merged data (v p : mean PD −1.4% ± 29.8% vs. 13.9% ± 180%, P = .05; v e : mean PD 0.8% ± 13.5% vs. 11.7% ± 23.8%, P < .001; K trans ; mean PD 7.2% ± 12.3% vs. 8.8% ± 78.4%, P > .05).

| In vivo evaluation
For the 17 patients with VS and 13 patients with GBM native tumor R1 0 estimates obtained from the VFA acquisitions before the LDHT DCE series are given in Table 1.
Comparative kinetic parameter maps from a patient with NF2 and bilateral VS imaged using the dual injection DTR protocol are shown in Figure 5A alongside fits of representative vessel voxel GBCA concentration-time curves obtained using each method. Compared to the use of native LDHT data sets the LEGATOS method offered superior visualization of small lesions and intratumoral heterogeneity in derived K trans and v p maps. The DICE-FDHS method also offered superior spatial resolution but because of undersampling of the firstpass bolus in each pixel-enhancing curve, derived K trans and v p maps suffered from large vessel contamination and lack of vessel contrast, respectively, features not seen in the LDHTor LEGATOS-derived maps. As shown in Figure 5B, whereas the DICE-FDHS method demonstrates poor discrimination between plasma volume and vascular leakage effects giving a very high value of K trans (=1.1 min −1 ) and low value of v p (=0.04) within the vessel, voxel fits of the native LDHT, HTHS-merged, and LEGATOS concentration-time curves produced lower K trans and higher v p values, respectively.
Representative tumor maps of K trans and v p in 2 patients with glioblastoma are shown in Figure 6 and Supporting Information Figure S3. Similar to the findings in VS, LEGATOS permitted superior visualization of microvascular heterogeneity in the contrast enhancing tumor edge compared to maps derived from the LDHT data sets alone. Estimates of mean tumor K trans and v p derived from the contrast enhancing tumor region of the 13 imaged glioblastoma are shown in Figure 6C and demonstrate the strong correlation between K trans (R 2 = 0.88, P < .0001) and v p estimates (R 2 = 0.79, P < .0001) derived using either the LEGATOS approach or native LDHT data sets alone.

| Imaging and pathology analysis
The inter-tumor correlation between LEGATOS derived kinetic parameter estimates and tissue metrics in the 15 sporadic VS that underwent the dual injection DTR protocol are shown in Figure 7. There was a significant inverse correlation between cell density and mean tumor v e (ρ = −0.69, P = .006, Figure 7A) and a significant positive correlation between CD31 % microvessel surface area with both mean tumor v p (r = 0.85, P = .001, Figure 7B) and mean tumor K trans (r = 0.71, P = .003, Figure 7C).
Representative imaging and tissue from a patient with a sporadic VS imaged at 1.5T is shown in Figure 8. Compared to use of the native LDHT data sets, the LEGATOS reconstruction method permitted better characterization of spatial heterogeneity in cell density and microvascular metrics across the tumor volume.

| DISCUSSION
We have described LEGATOS: a novel DTR DCE-MRI processing approach for deriving accurate, HS resolution, and whole-brain coverage kinetic parameter maps. Data from computer simulations and in vivo imaging demonstrated that kinetic parameters derived using LEGATOS provided superior discrimination of plasma volume and vascular leakage effects compared to other HS resolution approaches. Comparison with matched tumor tissue demonstrated that LEGATOS derived microvascular parameters accurately differentiated inter-tumor differences in microvessel surface area and cell density and permitted better evaluation of intratumoral heterogeneity in these tissue metrics compared to HT data alone. Previous attempts to derive HS kinetic parameters from DTR DCE-MRI such as the DICE-FDHS method 17 showed significant covariate fitting errors in derived parameter maps because of the low-temporal resolution of the sampled tissue uptake curves. Our strategy overcomes this limitation by first merging the separately acquired HT (low-spatial) and HS (low-temporal) DCE-MRI data sets into a merged 4D GBCA concentration-time course, and second rescaling the HT arterial phase of this HTHS-merged concentrationtime course to match the "true" HS one, before subsequent kinetic analysis. We hypothesized that HT sampling of the initial part of the tissue uptake curves would address fitting errors induced by temporal jitter uncertainty (uncertainty in time alignment of the arterial input function and tissue uptake curves) 29 and undersampling at the bolus peak. Our acquired data supported this with the LEGATOS derived parameter maps demonstrating superior separation of plasma volume and vascular leakage-based changes in the tissue GBCA concentration-time course. F I G U R E 5 Kinetic parameter maps from a neurofibromatosis type-2 patient imaged using a dual injection, dual-temporal resolution protocol. (A) K trans and v p maps obtained from dual injection DCE (DICE) MRI at 1.5T are shown. Note the large right-sided VS and multiple supra-and infra-tentorial meningiomas in this patient. Maps derived using the native low-dose high-temporal resolution tissue concentration-time curves (LDHT), the native full-dose high-spatial resolution tissue concentration-time curves (DICE-FDHS method), the HTHS-merged data and the LEGATOS reconstructed data are shown. Although the LDHT derived K trans map appears free of large vessel contamination, the small tuberculum sellae meningioma (long arrow) is difficult to visualize. The DICE-FDHS derived maps better demonstrate this meningioma and intratumoral heterogeneity within the VS but show considerable large vessel contamination (short arrow). The degree of large vessel contamination is reduced in the HTHS-merged data and almost absent in the LEGATOS derived K trans map. Relative to the HTHS-merged data, the LEGATOS map displayed greater spatial detail in the derived v p map. (B) Fits of representative vessel voxel GBCA concentration-time curves with the ETM. Fits obtained using each method shown. The DICE-FDHS method demonstrate poor discrimination of plasma volume and vascular leakage effects in the vessel GBCA concentration-time curve giving a high value of K trans (=1.1 min −1 ) and low value of v p (=0.04) within the vessel. Voxel fits of the native LDHT, HTHS-merged, and LEGATOS concentration-time curves produced lower K trans and higher v p values, respectively Previous in vivo studies in sporadic VS have demonstrated that kinetic parameter estimates derived through use of the ETM with low-spatial, HT resolution DCE-MRI accurately reflect inter-tumor differences in tissue vascularity metrics and correlate with differences in macrophage content and tumor growth rate. 5,30 However, the inherent low-spatial resolution in derived parameter maps limited accurate assessment of intratumoral heterogeneity, especially within smaller lesions. In the present study we demonstrated that HS resolution LEGATOS derived microvascular parameters permitted better evaluation of intratumoral heterogeneity in microvessel area and cell density compared to HT data alone and accurately differentiated inter-tumor differences in these tissue parameters. The LEGATOS-derived mean tumor v e showed an inverse correlation with cell density, and both the mean tumor v p and mean tumor K trans showed a positive correlation with CD31 % microvessel surface area. Although a limitation of any non-invasive imaging technique such as DCE-MRI is that the true in vivo tissue perfusion parameters are unknown and can only be extrapolated from architectural features detectable on ex vivo tissue specimens such as microvessel density and microvessel surface area, the correlation between CD31 and both DCE-MRI derived v p and K trans has been previously reported in human vessel wall studies. [31][32][33] Previous authors have attempted to achieve high spatiotemporal resolution in DCE-MRI through the use of advanced time resolved or "keyhole" imaging techniques 34 such as Siemens TWIST, 35 Phillips 4D-TRAK 36 (left) and v p (right) estimates derived from the contrast enhancing tumor region of the 13 imaged GBM using the LDHT and LEGATOS methods. The left panel demonstrates the strong correlation between K trans estimates derived using the LEGATOS approach and estimates derived from the native LDHT data sets alone (R 2 = 0.88, P < .0001). The right panel demonstrates the strong correlation between v p estimates derived using the LEGATOS approach and estimates derived from the native LDHT data sets alone (R 2 = 0.79, P < .0001) TRICKS, 37 and DISCO. 38 Such techniques improved temporal resolution during data acquisition through undersampling of peripheral k-space. There has also been growing interest in estimating kinetic parameters directly from undersampled k-,t-space data without prior data reconstruction. 39,40 Our dual injection DTR DCE-MRI approach, however, offers greater temporal resolution during image acquisition (Δt < 1.5 s) compared to many of the above techniques, and a distinct advantage of the presented LEGATOS method is that it can be retrospectively acquired to dual injection DTR DCE-MRI data without the need for peripheral k-space undersampling.
In addition to its demonstrated application with full-dose DTR protocols, applicability of LEGATOS with a single injection low GBCA dose (fixed volume of 3 mL) interleaved HT and HS protocol has also been demonstrated in preliminary prospective unpublished studies at our institution. 21 Although the risk of gadolinium deposition in the brain following administration of macrocyclic GBCA such as gadoterate meglumine is thought to be lower than linear agents and the long-term clinical sequelae of such deposition is currently unknown 12,13 the ability to derive HS resolution kinetic parameter data following a low-dose administration may still have considerable clinical relevance, especially in patients  41 Further studies incorporating the LEGATOS technique and low GBCA dose acquisition protocols are, however, required to better evaluate the effect of this low-dose approach on image contrast-to-noise, and the accuracy of kinetic parameters derived using this technique. 21 The proposed LEGATOS method relies on the assumption that in each pixel of the HTHS-merged 4D concentration volume generated in key step I, the supposed "true" HS resolution arterial phase has the same shape as the observed HT aligned arterial phase, and therefore, can be obtained by rescaling the HT aligned arterial phase to achieve a smooth connection with the HS parenchymal phase. The ETM further assumes that the arterial phase of each enhanced tissue pixel curve is the initial plasma concentration curve scaled by v p . However, the above assumption may not be met if the HT aligned and "true" HS concentration curves display significant differences in the bolus mean transit time and/or in the amount of GBCA leakage. In this case, reconstruction of the initial HT contrast agent concentration curve using a single concentration ratio is not suitable and more complex adjustment may be required.
The ETM has been adopted in this study as previous application of this model with low-spatial resolution HT data sets derived from DTR DCE-MRI was found to give both tissue-validated and clinically relevant kinetic parameter estimates. 4,5,30 Recent studies have also shown through a model selection process using the Akaike information immunostains (middle, fibrinogen, brown; bottom, CD31, brown; immunoperoxidase-whole mount) from the tumor shown in panel A/B demonstrate heterogeneity in cell density (H&E), perivascular leak (fibrinogen) and microvessel density (CD31) across the tumor section. (D and E) Higher magnification images of the areas framed in the whole mount demonstrating regions of high (D) and low (E) cell density (HE, ×20 HPF), perivascular leak (fibrinogen, immunoperoxidase ×10 HPF) and microvessel density (CD31, immunoperoxidase × 10 HPF) criteria, that the ETM was one of the optimal models in pharmacokinetic analysis of DCE-MRI data in brain tumors 42 and papillary thyroid carcinoma. 43 One limitation of the ETM is that the derived parameter K trans is a hybrid parameter reflecting both capillary blood flow and permeability effects, 44,45 and future studies incorporating the high spatiotemporal resolution DCE data provided by the LEGATOS method and other DCE-MRI models, which seek to further separate out such effects should, therefore, be undertaken.

| CONCLUSION
We developed a novel DTR technique called LEGATOS to generate HS resolution kinetic parametric maps with an accuracy normally only obtainable with HT (Δt < 1.5 s), low-spatial resolution DCE-MRI. The accuracy of kinetic parameters estimated using this new technique outperformed previous DTR methods for deriving HS resolution parameter maps and analysis of tissue from VS investigated with LEGATOS validated our approach. Clinical application of this modality and its application with low GBCA dose DCE-MRI protocols require further studies.