Validation of Dynamic Contrast-Enhanced Magnetic Resonance Imaging-Derived Vascular Permeability Measurements Using Quantitative Autoradiography in the RG2 Rat Brain Tumor Model

Abstract

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is widely used to evaluate tumor permeability, yet measurements have not been directly validated in brain tumors. Our purpose was to compare estimates of forward leakage K^trans derived from DCE-MRI to the estimates K obtained using [¹⁴C]aminoisobutyric acid quantitative autoradiography ([¹⁴C]AIB QAR), an established method of evaluating blood-tumor barrier permeability. Both DCE-MRI and [¹⁴C]AIB QAR were performed in five rats 9 to 11 days following tumor implantation. K^trans in the tumor was estimated from DCE-MRI using the threeparameter general kinetic model and a measured vascular input function. K_i was estimated from QAR data using regions of interest (ROI) closely corresponding to those used to estimate K^trans. K^trans and K_i correlated with each other for two independent sets of central tumor ROI (R = 0.905, P = .035; R = 0.933, P = .021). In an additional six rats, K^trans was estimated on two occasions to show reproducibility (intraclass coefficient = 0.9993; coefficient of variance = 6.07%). In vivo blood-tumor permeability parameters derived from DCE-MRI are reproducible and correlate with the gold standard for quantifying blood tumor barrier permeability, [¹⁴C]AIB QAR.

Introduction

Tumor angiogenic vessels are larger, are more tortuous, and have large endothelial fenestrations and caveoli that make them more permeable than normal vessels. Such vessels are thought to promote tumor growth by increasing blood flow and nutrient delivery and are, therefore, a target for cancer therapies. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is currently in wide use as a method for monitoring vascular permeability within tumors, as a means of assessing early response to antiangiogenic therapy in clinical trials [1–3].

Despite its widespread use, there is controversy over the physiological meaning of parameters derived from DCE-MRI, as well as concerns over the reproducibility of such measurements. To date, the only attempts to validate DCE-MRI have been either reproducibility studies, simulations, or qualitative comparisons to histology and immunohistochemical markers of tumor angiogenesis such as CD31 and microvascular density measurements [4]. Although measures of reproducibility and qualitative comparisons to immunohistochemistry are helpful, they are not physiologically based and, therefore, do not directly assess vascular permeability. Indeed, there is concern that DCE-MRI-derived parameters are more dependent on tumor blood flow than on vascular permeability. Others have raised concerns that an assumption of slow water exchange between intracellular and extracellular compartments may be incorrect and may lead to gross errors in permeability measurements [5]. Studies using DCE-MRI to monitor tumor response to vascular-disrupting agents have raised concerns about the utility of DCE-MRI biomarkers [6]. Without comparison studies with “true” functional measures of permeability, the validity of DCE-MRI as an index of vascular permeability is unclear, and the true physiological meaning of the influx rate constant (K^trans) remains unknown.

In this study, we directly compare the DCE-MRI index of vascular permeability (K^trans) to a standard experimental method of measuring the influx rate constant (K_i) of small molecules leaking from vascular space into extravascular-extracellular space by [¹⁴C]aminoisobutyric acid quantitative autoradiography ([¹⁴C]AIB QAR) in the RG2 rat brain tumor model [7,8]. K^trans and K_i are both measures of the permeability-surface area product per unit volume in the RG2 tumor and, thus, should correlate with each other; yet these measures are obtained through markedly divergent techniques [2,8,9]. K^trans is derived from a two-compartment pharmacokinetic model based on the curve fitting of the time-gadolinium concentration curve in the tumor. K_i is derived from the unique characteristics of AIB, which leaks unidirectionally from the blood into tissue and is then trapped at the site of leakage. K_i can thus be determined from [¹⁴C]AIB QAR data with very high spatial resolution using a “unidirectional model” and simple calculation [7]. In addition to examining correlations to this “gold standard” measure, the reproducibility of DCE-MRI K^trans estimates is examined for repeated RG2 tumor DCE-MRI estimates.

Materials and Methods

Animal Preparation

All studies were performed after obtaining the approval of the institutional Animal Care and Use Committee. The maintenance and care of animals were in compliance with National Institutes of Health guidelines. RG2 tumor cells were grown in culture and implanted (1 x 10⁵ cells in 5 µl of phosphate-buffered saline) into the caudate-putamen of five adult male Fischer-344 rats (weight range, 250–300 g; Harlan Laboratories, Indianapolis, IN) using previously described techniques [10]. Cells were grown in vivo for 9 to 11 days before injection. On the day of implantation, animals were anesthetized with isoflurane, and one venous and two arterial polyethylene microtubing cannulations (PE-50; Becton Dickinson, Franklin Lakes, NJ) were placed for venous gadolinium diethylenetriamine pentaacetic acid (Gd- DTPA) infusion, venous [¹⁴C]AIB injection, arterial [¹⁴C]AIB plasma concentration sampling, and arterial blood pressure monitoring.

DCE-MRI Scanning

Animals were placed on a Philips Intera 3.0-T MR scanner (Philips Medical Systems, Andover, MA) with a dedicated 7-cm rat solenoid radiofrequency coil (Philips Research Laboratories, Hamburg, Germany) with maintenance isoflurane anesthesia from 9 to 11 days following tumor implantation. Scout images were obtained to define a coronal plane perpendicular to the dorsum of the rat brain for subsequent imaging. For anatomic imaging, 32 two-dimensional fast spin-echo T₂ slices were acquired. For T₁ mapping, a low-flip-angle (FA = 3°) three-dimensional fast field echo (FFE) sequence with parameters otherwise matching the DCE-MRI scan sequence was performed immediately before dynamic scans.

DCE-MRI

Thirty DCE-MRI three-dimensional T₁ FFE sequence volumes were obtained over 10 minutes at a temporal resolution of 20 sec/vol.

Geometric parameters were as follows: slice thickness = 1 mm; slice gap = -0.5 mm (oversampled); slices = 16 (32); field of view (FOV) = 76.8 mm; matrix = 256 x 244–resulting in an interpolated in-plane resolution of 0.33 mm.

Contrast parameters were: T_R = 8.1 milliseconds; T_E = 2.3 milliseconds; FA = 12°. Following five baseline scans, 0.5 ml/kg Gd-DTPA (Magnevist; Bayer HealthCare Pharmaceuticals, Wayne, NJ) was injected through the femoral vein using a Hamilton syringe (Hamilton Co., Reno, NV) connected to a polyethylene microtubing (PE-50; Becton Dickinson) at a constant rate of 0.5 ml/kg per minute over 1 minute, with a 2-minute saline flush using a microinfusion pump (PHD 2000; Harvard Apparatus, Holliston, MA).

[¹⁴C]AIB QAR

[¹⁴C]AIB QAR was performed within 30 minutes of MR scanning. Animals were transferred to a radiation-secure facility, placed under maintenance anesthesia, and prepared for constant-withdraw plasma sampling similar to that described in Asotra et al. [11]. A saline-filled PE-90 tubing was attached to the femoral artery line, and a saline-filled (1.0 ml) Hamilton syringe (Hamilton Co.) in a Harvard pump (PHD 22/2000; Harvard Apparatus) was set to constant withdrawal (33 µl/min). A 0.5-ml bolus of 100 µCi (n = 6) or 33 µCi (n = 2) of [¹⁴C]AIB was manually injected into the femoral vein over 15 seconds, 1 minute after starting the pump. After approximately 20 minutes, the pump was stopped, PE-90 blood sample was collected, and time at the experimental end point was documented (T_e). Blood samples were collected at the time of sacrifice. The animal was immediately guillotined, and the brain was rapidly removed (∼ 5 minutes) and frozen in 2-methylbutane. Guillotining was required in the experimental design to rapidly freeze the brain and to prevent significant diffusion of [¹⁴C]AIB away from the initial site of leakage, and was approved as an exception by the institutional Animal Care and Use Committee.

Arterial blood samples were immediately spun, plasma samples were collected, and plasma concentrations for the PE-90 tubing ($\overline{C_{\text{p}}(t)}$) and the femoral line (C_p(T_e)) were measured. At an angle approximating the MR slice plane, frozen brains were sectioned in a cryomicrotome into 40-µm sections per 200-µm interval and photographed. Sections were exposed on film (Fuji Photo Film, Inc., Greenwood, SC) for 3 to 4.5 days for 100-µCi infusions (n = 6), or for 10.5 to 12 days for 33-µCi infusions (n = 2), with 40 µmm [¹⁴C]AIB standards (0–35 µCi; American Radiolabeled Chemicals, Inc., St. Louis, MO). The use of standards allowed for changes in the specific radioactivity of [¹⁴C]AIB infusions to speed up film development without affecting the accuracy of tissue [¹⁴C]AIB concentration determinations or the calculation of K_i. Films were scanned using a BAS-5000 Bio-Imaging Analyzer (Fuji Medical Systems, Stamford, CT).

DCE-MRI Analysis

All DCE-MRI data were processed using an investigational pharmacokinetic analysis package (KinMod plug-in to CINEtool; GE Healthcare, Waukesha, WI) based on IDL (Research Systems, Inc., Boulder, CO). Precontrast T₁ maps were generated from data obtained at 3° and 12° flip angles [12,13]. DCE-MRI signal was converted into Gd-DTPA concentration.

A region(s) of interest (ROI) for vascular input function (VIF) selection was drawn around the confluence of dural sinuses, taking care to exclude regions with time-of-flight inflow artifacts. Using the CINEtool program, a semiautomated algorithm based on variance thresholding was used to select an ROI, from which the VIF was calculated. Signals were converted to Gd-DTPA concentration, assuming a normal blood T₁ of 1320 milliseconds.

The VIF was convolved with general kinetic model (GKM) transfer function using a first approximation of the three free parameters to each C_t(t) curve according to:

$$C_{\text{t}}(t)=(1-f_{\text{bv}})/(1-\text{Hct})K^{\text{trans}}[C_{\text{b}}(t)\otimes {\text{e}}^{-K^{\text{trans}}/V_{e}t}]+f_{\text{bv}}{C}_{\text{b}}(t)$$

where C_b(t) ibr time data and Hct is the hematocrit of Fischer-344 male rats (0.50). This equation is identical to the bidirectional GKM model equation of Iannotti et al. [14] with a conversion from plasma concentration and fractional plasma volume to blood concentration and fractional blood volume, respectively (Appendix A). The three free parameters (K^trans, f_bv, and v_e) were iteratively adjusted to find a best-fit solution that minimized variance between modeled and measured C_t(t) curves using the Levenberg-Marquardt method. Estimates of K^trans, v_e, and f_bv were made both on a voxelwise basis and by using ROI in which signal was averaged within the ROI.

Three ROI were hand-drawn on T₁-weighted images at peak contrast enhancement, approximately 5 minutes after the injection of contrast media. The mean value of the three regions for contrast-enhancement ratio (CER_c), the ratio of enhancement signal to baseline signal, was measured. A CINEtool function automatically generated ROI with boundaries equal to 25%, 50%, and 75% of the CER_c for each animal.

[¹⁴C]AIB QAR Analysis

Optical density measurements of autoradiographs were converted to tissue concentration using 40-µCi standards and a polynomial fit of the curve of optical density versus tissue radioactivity per volume using MATLAB (MathWorks, Natick, MA). Autoradiograph pixelwise concentration and K_i maps were generated according to:

$$K_{\text{i}}=(C_{\text{t}}-f_{\text{pv}}{C}_{\text{p}}(T_{\text{e}}))/\int C_{\text{p}}(t)dt$$

$$\int C_{\text{p}}(t)dt=\overline{C_{\text{p}}(t)T}$$

where C_t is the pixel tissue concentration; the fractional plasma volume (f_pv) is assumed to be 2.2% based on prior studies [15]; T is the time of actual sample withdrawal during total experimental time (T_e); C_p(T_e) is the plasma concentration at T_e; and $\overline{C_{\text{p}}(t)}$ is the concentration of radioactive plasma collected during T. Using a constant rate of sample withdrawal, the integral ∫ C_p(t) dt solves to $\overline{C_{\text{p}}(t)}$ T.

A radiologist blinded to the study results analyzed anatomic landmarks in gross brain photographs, T₂ images, and postcontrast T₁ images to select three [¹⁴C]AIB QAR section autoradiographs to match MR sections. [¹⁴C]AIB QAR ROI were semiautomatically generated using the image processing software MIPAV (http://mipav.cit.nih.gov; National Institutes of Health, Bethesda, MD). The [¹⁴C]AIB QAR tumor ROI aimed to match the 25% DCE-MRI ROI were first generated. For each [¹⁴C]AIB concentration map, ROI were drawn in the brain region contralateral to the tumor to plot the mean and distribution of normal tissue “background” concentration values, and the value at 3 SD above the mean background value (BG_3SD) was recorded. A mask over each tumor section was then created with edges at each individually determined BG_3SD threshold. This mask was then used to generate the QAR ROI at the tumor edge, approximating the volume of the 25% DCE-MRI ROI. To generate the QAR ROI matching the 50% and 75% threshold DCE-MRI ROI, concentration threshold values were increased until the volume of the generated QAR mask approximated the volume of the corresponding 50% or 75% DCE-MRI ROI. The final [¹⁴C]AIB QAR ROI were then copied and pasted to [¹⁴C]AIB QAR pixelwise influx rate constant (K_i) maps. The mean K_i value, standard deviation, and volume were recorded for each QAR K_i map. A final [¹⁴C]AIB QAR K_i value corresponding to each DCE-MRI slice was determined as the mean measure of the three selected [¹⁴C]AIB QAR sections.

Statistics

Regression statistics were generated for K^trans versus K_i for each ROI pair of central tumor slices (SPSS, Chicago, IL).

Reproducibility Studies

In a separate set of experiments on a separate population of six Fischer-344 rats, test-retest repeat DCE-MRI studies were performed between 14 and 24 hours after the first injection of Gd-DTPA. DCE-MRI ROI for each experiment were obtained using hand-drawn ROI to be consistent with commonly used techniques. A user was instructed to select a central slice and to draw ROI (n = 5) within but closely approximating tumor edges to exclude a boundary of approximately 0.5 mm from the tumor edge for all scan MR central slice data. VIFs were then chosen, and parameter estimates were generated as described previously. To reduce variance due to hand-drawn ROI, the value for test-retest scans was calculated as the mean of five K^trans estimates for five tumor ROI.

Reproducibility Statistics

Reproducibility statistics included the intraclass correlation coefficient (ICC), coefficient of variation (CoV), and within-subject standard deviation (wSD). (Microsoft Excel, Redmond, WA) [16–20].

Results

Tumors were successfully implanted and grown in 11 Fischer-344 rats. [¹⁴C]AIB autoradiography and DCE-MRI data were completed and analyzed on five of these animals, whereas repeat DCE-MRI test-retest studies were completed on the remaining six animals.

DCE-MRI K^trans versus [¹⁴C]AIB QAR K_i

K_i maps generated from [¹⁴C]AIB QAR autoradiographs and K^trans maps generated from DCE-MRI voxelwise data for the central tumor slice of each animal are shown (Figure 1). Similarities in the topographies of K^trans and K_i maps can be appreciated, with higher influx rate constants in the central tumor and lower influx rate constants peripherally in both K^trans and K_i maps. Note that distortions from tissue “chatter” caused by displacement during cryomicrotome tissue slicing in [¹⁴C]AIB QAR K_i maps are not present in in vivo DCE-MRI K^trans parameter maps.

Figure 1.

(A) [¹⁴C]AIB QAR K_i maps. (B) DCE-MRI K^trans parameter maps for central tumor slices for each animal. DCE-MRI K^trans parameter maps are displayed within the 25% threshold ROI.

Tumor ROI, autoradiography K_i measures, and DCE-MRI measures of K^trans, k_ep, v_e, and f_bv are listed for each tumor ROI for each animal (Table 1). The mean percentile differences in transfer constants between autoradiography and DCE-MRI (mean ± SD) were -2.88 ± 9.51%, -1.33 ± 2.28%, and -5.98 ± 26.2% for the 75%, 50%, and 25% thresholds, respectively.

Table 1.

[¹⁴C]AIB QAR Influx Rate Constant (K_i) Measures and DCE-MRI Parameter Estimates of the Influx Rate Constant (K^trans), Efflux Rate Constant (k_ep), Fractional Leakage Space Volume (v_e), and Fractional Blood Volume (f_bv) for 75%, 50%, and 25% Threshold ROI and ROI Areas for Central Tumor Slices.

Animal	Tumor Days	Threshold (%)	Ki (min-1)	Area (mm2)	Ktrans (min-1)	Area (mm2)	Differential Ratio of Tumor Area	kep (min-1)	ve	fbv
1	9	25	0.0272	9.1	0.0420	9.9	0.088	0.443	0.096	0.03
		50	0.0306	7.3	0.0660	7.2	-0.014	0.546	0.123	0.02
		75	0.0346	5.4	0.0900	5.4	0.000	0.641	0.141	0.01
2	11	25	0.0208	24.3	0.0480	20.3	-0.165	0.321	0.150	0.04
		50	0.0254	15.6	0.0690	15.6	0.000	0.387	0.174	0.03
		75	0.0273	11.3	0.0900	11.2	-0.009	0.459	0.198	0.02
3	10	25	0.0126	11.6	0.0180	7.2	-0.379	0.174	0.096	0.03
		50	0.0172	3.8	0.0360	3.6	-0.053	0.268	0.132	0.04
		75	0.0185	2.6	0.0420	2.1	-0.192	0.283	0.144	0.04
4	10	25	0.0121	13.0	0.0240	11.1	-0.146	0.192	0.126	0.04
		50	0.0160	6.2	0.0420	6.2	0.000	0.249	0.168	0.03
		75	0.0171	3.9	0.0540	3.9	0.000	0.254	0.210	0.03
5	11	25	0.0055	9.9	0.0180	12.9	0.303	0.146	0.126	0.04
		50	0.0060	7.1	0.0270	7.1	0.000	0.168	0.162	0.05
		75	0.0072	3.5	0.0390	3.7	0.057	0.209	0.186	0.04

For the central tumor 75% threshold, K^trans (mean ± SD) measured with DCE-MRI was 0.0630 ± 0.0253, and the corresponding [¹⁴C]AIB autoradiography K_i measure (mean ± SD) was 0.0209 ± 0.0104. The fractional extravascular-extracellular space v_e (mean ± SD) was 17.6 ± 3.2%. The fractional blood volume (mean ± SD) was 2.80 ± 1.3%. Mean DCE-MRI parameter estimates were comparable to published measures for central tumor regions obtained using radiolabeled serum albumin for v_e and f_bv (7.5% and 3.2%, respectively) [15,21]. DCE-MRI experimental measures of ve were 2.3-fold higher than published measures for RG2 tumors. For fractional blood volume (f_bv), the percentile difference between experimental measures and published measures in RG2 tumors was only 12.5%.

DCE-MRI K^trans and [¹⁴C]AIB QAR K_i maps display the variation and range of influx rate constants measured across the tumors (Figure 1). K^trans and K_i heterogeneity varied together on a pixel-by-pixel basis. DCE-MRI K^trans versus [¹⁴C]AIB QAR K_i were plotted for the 75%, 50%, and 25% threshold ROI for central tumor slices (Figure 2). For the central 75% threshold, K^trans and K_i influx rate constants were positively correlated (slope ± SEM = 2.190 ± 0.594; R = 0.905; R² = 0.819; adjusted R² = 0.759; F = 13.6; P = .034). For the central 50% threshold, the slope decreased, but R increased (slope ± SEM = 1.838 ± 0.411; R = 0.933; R₂ = 0.870; adjusted R₂ = 0.826; F = 20.0; P = .021).

Figure 2.

DCE-MRI K^trans versus [¹⁴C]AIB QAR K_i for central tumor slices for the (A) 75%, (B) 50%, and (C) 25% threshold ROI.

Tumor ROI incorporating increasing proportions of the tumor edge were analyzed to study the impact of tumor periphery on DCE-MRI parameter estimates. Examples of ROI and corresponding histograms of K^trans voxelwise data and K_i pixelwise data are shown for animal 1 (Figure 3). Despite distortions related to tissue sectioning, the strategy employed for ROI selection was qualitatively accurate in selecting the same tumor tissue in both [¹⁴C]AIB QAR autoradiographs and DCE-MRI maps. Lowering the ROI threshold resulted in larger ROI with more tumor periphery. Histograms of K_i from QAR data were unimodal for all three ROI thresholds. Histograms of K^trans from DCE-MRI data were unimodal for the central tumor 75% threshold, but were bimodal for the 25% and 50% thresholds with more tumor periphery. This “noise,” which is seen as a secondary high-amplitude peak of low K^trans on histograms of DCE-MRI voxelwise data, can be qualitatively appreciated as a rim of low K^trans values at tumor edges in K^trans maps (Figure 1).

Figure 3.

Sample images of tumor ROI and corresponding histograms for animal 1. (A) Images of DCE-MRI ROI (white) for the 25%, 50%, and 75% thresholds. (B) Images of corresponding [¹⁴C]AIB QAR ROI (white). (C) Histograms of DCE-MRI K^trans voxelwise data for the corresponding DCE-MRI ROI threshold with polynomial fit trendlines. (D) Histograms of [¹⁴C]AIB QAR K_i pixelwise data for the corresponding [¹⁴C]AIB QAR ROI threshold.

A comparison of influx rate constants derived from DCE-MRI and QAR using different ROI demonstrated a systematic decrease in K^trans relative to K_i as more of the tumor periphery was included in tumor ROI. The slope of regression line (slope ± SEM) for K^trans versus K_i decreased systematically from 2.190 ± 0.594, to 1.838 ± 0.411, to 1.443 ± 0.483 for the 75%, 50%, and 25% threshold ROI, respectively. For the 25% threshold ROI that included the highest proportion of tumor periphery, the correlation between K^trans and K_i measures was not statistically significant (R = 0.865; R² = 0.749; adjusted R² = 0.665; F = 8.94; P = .058).

DCE-MRI K^trans Reproducibility

There was positive reproducibility of K^trans estimates for repeat DCE-MRI experiments on a separate population of animals with implanted RG2 tumors (n = 6) (Figure 4). The mean (± SD) K^trans for the first test was 0.0759 ± 0.130, and the mean (± SD) K^trans for the second test was 0.0798 ± 0.139. Test-retest K^trans estimates had an ICC of 0.9993 and a regression coefficient (R) of 0.9997 (P < .001). The CoV was 10.2%, and the wSD was 0.00323. The 95% confidence interval for measurement error was ± 20.1% or ± 0.00633.

Figure 4.

Test-retest K^trans estimates from repeat DCE-MRI experiments for all subjects and excluding the highest K^trans data point (inset).

Given that there was systematic offset in the data, it was alternately analyzed to more closely approximate “true” measurement error. The second K^trans estimate was consistently higher than the first estimate (mean ± SEM = 0.00385 ± 0.0011). Closely timed studies were required in these fast-growing tumors, and this systematic offset was likely due to the effects of residual contrast in tumors on the second day of Gd-DTPA injection, but could have been caused also by tumor changes. According to accepted statistical methods, systematic changes between scans can be accounted for by subtracting the mean difference between subjects' scans from the second scan values [18]. After adjusting for systematic offset, the CoV was 6.07%, and the wSD was 0.00174. The 95% confidence interval for a given measurement was ± 11.9% or ± 0.00341. The repeatability (r) was 16.8% or 0.00482. Therefore, a difference of 16.8% or 0.00482 in two independent tumor measurements using this method in a single tumor represents a true tumor change in K^trans.

Reproducibility results were similar for the analysis of data from five animals and excluding the high K^trans value. The data, excluding this high value, (Figure 4, inset) are on virtually the same line as the data for all six animals. The ICC is lower due to the decreased range in data, with a value of 0.9152. After adjusting for systematic offset, however, the CoV and wSD for five animals were very similar to the results for the six animals. The CoV was 6.63%, and the wSD was 0.00135. The 95% confidence interval for a given measurement was ± 13.0% or ± 0.00265. The repeatability (r) was 18.4% or 0.00374.

Discussion

DCE-MRI is in wide clinical use and has proven useful in detecting early changes in vascularity after angiogenic inhibitor treatment. Wedam et al. [22] used methods similar to this DCE-MRI method, with Gd-DTPA and the same IDL software package, to demonstrate changes in K^trans in breast cancer patients during treatment with bevacizumab, a vascular endothelial growth factor inhibitor. However, in spite of its wide use, the interpretation of K^trans values is still uncertain. The results of the current study demonstrate a significant correlation between DCE-MRI-derived K^trans and [¹⁴C]AIB QAR-derived K_i in the RG2 tumor model. [¹⁴C]AIB QAR is a long-established quantitative method of measuring vascular leakage for small molecules, and this result is therefore useful in confirming that K^trans is highly related to vascular permeability, at least in some animal tumor models. Thus, although offset by a factor of roughly 2 in absolute value, DCE-MRI estimates are predictors of “gold standard” measurements of vascular permeability. Differences in the biophysical properties of AIB and DTPA likely account for these small differences. Permeability is a function of the characteristics of the molecule transiting the membrane, such as surface charge, molecular weight, ionization, lipophilicity, and shape. Gd- DTPA (547 Da) is a charged and extremely hydrophilic molecule, whereas AIB (102 Da) is a synthetic amino acid that is neutral and hydrophilic [7,23]. Thus, within practical experimental limits, these two agents produced remarkably similar results.

Although there was a strong correlation between K^trans and K_i in central tumor regions, the correlation was weaker when the periphery of the tumor was included. There was a measured decrease in [¹⁴C]AIB QAR K_i values at RG2 tumor edges consistent with prior results for the RG2 model, and partial volume effects of normal and tumor tissues near the edge are expected to lower DCE-MRI K^trans [24]. The low K^trans values seen at the tumor edge were thus likely due to partial volume effects. RG2 tumors are also known to be edematous [25], and it is possible that this effect contributed to the lowering of K^trans values at tumor edges. The effect of variance in K^trans relative to K_i as more of the periphery is included in the measurement is reflected in the change in slope in the line of regression (Figure 2). The two-fold decrease in K^trans values between the 75% threshold and the 25% threshold demonstrates the impact of tumor edge “noise” and the need for strategies of ROI selection that avoid these edge effects. The impact of partial volume effects on tumor edges and necrotic regions, however, is expected to be lower in human studies, which generally include tumors larger than those evaluated in this model.

Measures of K^trans obtained using DCE-MRI proved highly reproducible in this study. A high correlation was observed with two independent repeated measurements. This has implications for the magnitude of the therapeutic effect required to be measurable by DCE-MRI. Galbraith et al. demonstrated that “failed” pixel data had to be removed to reduce interscan variability and that a relatively large variance was required to show statistical changes in human tumors even after data exclusion. Changes of -45% to 83% were needed to overcome the CoV of 24% to 29% in conventional studies [19]. Liu et al. [26] thus used a decrease of > 50% in K^trans to detect a real change in advanced tumors treated with the angiogenic inhibitor AG-013736. Recent studies of reproducibility in human abdominal tumors, gliomas, and prostate malignancies using an assumed VIF showed similar results requiring changes of > 31% to > 44% (CoV = 11–16%) in one study and a measurement error of > 16% (CoV = 8.2%) in another [20,27]. The ICC, CoV, and 95% confidence interval for measurement error in this study compared favorably to prior results. The improved reproducibility in our model can be traced to improved VIFs, reliable pulse sequences, and a two-compartment model with a sufficient number of parameters to fit most of the pixels within the tumor. Reproducibility results from clinical and preclinical DCE-MRI are, however, highly variable. Such studies often reported pixel “failures” (i.e., inability to fit the data to the model) and reported pixel exclusion ranging between 13% and 74% [19,28]. However, the DCE-MRI method used in this study required no filtering or removal of pixel data within the ROI. This is likely because the modeling allowed better fitting of measured data and because tightly controlled experimental conditions led to robust data sets. Although one study reported a CoV of 7.7% after significant pixel data exclusion (mean = 39%) [28], we were able to achieve a 95% confidence interval of an individual K^trans measure of ± 0.00341 (± 11.9%) (ICC = 0.9993; CoV = 6.07%) with no pixel data exclusion. The precision of DCE-MRI was predictable from strong correlation results with [¹⁴C]AIB QAR K_i measures because the ability to detect a correlation is related to the precision of independent measures. Although a correlation is possible with “noisy” data using a large number of experiments, statistical correlation was demonstrated in this study using only a small number of animals suggesting a relatively high precision of the DCE-MRI method.

The successful use of a VIF certainly contributed to the robustness of this technique. Direct measurement of arterial blood was not possible in this model given the small size of vessels in small animals, and the VIF was instead measured from venous sinus blood. A similar technique using measurements of VIF from the sagittal sinus has been used in human DCE-MRI studies [28]. Although several groups have used slow injections in pharmacokinetic modeling [29], it is argued that a bolus injection is needed for accurate mathematical modeling of Gd-DTPA kinetics [5,28,30]. The results of this study suggest that a slow bolus allows for accurate and precise parameter estimates. Furthermore, a fast bolus requires rapid data acquisition with reduced signal-to-noise ratios to accurately measure the VIF. Finally, a longer acquisition interval allows for higher-resolution images, which are advantageous for clinical studies. Recent simulations and experimental data using this DCE-MRI method suggest that there is no significant difference in K^trans estimates using a slow injection versus a bolus injection in patient studies (unpublished observations). If correct, a slow injection may be more satisfactory for DCE-MRI in the clinical setting than was originally thought because high resolution is often needed.

In this experiment, it was not possible to correlate other DCE-MRI parameters, such as k_ep, with [¹⁴C]AIB QAR because the latter only measures the forward leakage rate. Two other free parameters were estimated from the best-fit solution of the GKM: f_bv and v_e. Although parameter estimates of fractional blood (f_bv) and leakage space volumes (v_e) were comparable to published measures using other techniques for RG2 tumors, leakage space estimates showed greater variation from prior published values. Zhou et al. [31] have shown that measures of v_e obtained using a method similar to that used in this study can vary based on the dosing of Gd-DTPA when corrections are not made to account for the effects of transcytolemmal water exchange on tissue relaxivity. Based on these results, the values of v_e obtained in this study would be expected to have varied for different doses of Gd-DTPA. It may, therefore, be necessary to make such corrections to obtain accurate DCE-MRI v_e measures.

This study has a number of limitations. We cannot discount the possibility that the good correlation between K^trans and K_i may be related to the nature of the RG2 model. In vessels where flow is high relative to permeability, such as in the RG2 model, the rate of influx of AIB and Gd-DTPA from the vessel to the tumor is a function of vascular permeability [2,8,9]. In tumor regions with lower blood flow, K^trans may be more dependent on flow than on permeability and, therefore, may not accurately depict vascular permeability. A broader range of tumor models is needed to confirm the validity of DCE-MRI parameters for predicting vascular permeability across a range of tumor blood flow rates. By examining K^trans estimates in a permeability-limited high-flow tumor model, this study allowed K^trans estimates to be simplified to indices of permeability—the parameter that is potentially most valuable for monitoring treatment effects on angiogenic tumor vasculature.

Additional limitations of this study include technical challenges in comparing in vivo MRI and invasive QAR methods. There was considerable distortion of tissues using the [¹⁴C]AIB QAR technique due to shearing, warping, and tearing, and matching DCE-MRI and [¹⁴C]AIB autoradiograph tissue regions was technically difficult. The strategy employed, including the use of large computer-generated ROI and central tumor slices, reduced misregistration error.

In the future, macromolecular contrast agents may be better measures of permeability by separating flow effects from K^trans indices of permeability [32–34]. This effect would be most prominent in areas with a high permeability-to-flow ratio. Macromolecular agents have been used in preclinical DCE-MRI tumor studies, but these techniques are not yet ready for clinical studies because these macromolecular agents have not yet been approved by regulatory agencies for human use and because techniques used in these studies, such as ex vivo VIF measurements, are not easily applied to clinical studies [35]. QAR validation of macromolecular contrast agents will require a radioisotopically labeled macromolecule of similar hydrodynamic diameter, hydrophilicity, and surface charge as the MR-based macromolecular agent. The advantages of using low-molecular-weight Gd- DTPA versus higher-molecular-weight agents include the increased penetration of smaller compounds in areas of decreased permeability and the general availability and established safety of Gd-DTPA.

In summary, this study demonstrates a statistical correlation between direct measures of the influx (or forward leakage) rate constant obtained using DCE-MRI (K trans) and direct measures of the influx (or forward leakage) rate constant obtained using the “gold standard” method [¹⁴C]AIB QAR (K_i).

Abbreviations

K^trans

influx (or forward leakage) rate constant DCE-MRI-derived

K_i

influx (or forward leakage) rate constant, [¹⁴C]AIB QAR-derived

[¹⁴C]AIB QAR

[¹⁴C]aminoisobutyric acid quantitative autoradiography

f_bv

fractional blood volume

v_e

fractional leakage space (or fractional extravascular-extracellular space) volume

VIF

curve describing contrast concentration in large vessels as a function of time (or vascular input function)

Appendix

List of Terms

C_e(t)

Extravascular-extracellular space (or leakage space) tracer concentration

K^trans

DCE-MRI influx rate constant (or volume transfer constant)

C_p

Plasma tracer concentration

v_e

Fractional extravascular-extracellular space (or leakage space) volume

C_t

Tissue tracer concentration

⊗

Convolution

C_b(t)

Blood tracer concentration per time; VIF

f_bv

Fractional blood volume

f_pv

Fractional plasma volume

V_rbc

Red blood cell volume

V_roi

Volume of VIF

Derivation of GKM Bidirectional Pharmacokinetic Model

Convolution equation for bidirectional exchange between plasma and leakage space (extravascular-extracellular space)

$$C_{\text{e}}(t)v_{\text{e}}=K^{\text{trans}}{C}_{\text{p}}(t)\otimes {\text{e}}^{-K^{\text{trans}}}/v_{\text{e}}t$$ 1

$$C_{\text{t}}(t)=C_{\text{e}}(t)v_{\text{e}}$$ 2

$$C_{\text{t}}(t)=K^{\text{trans}}{C}_{\text{p}}(t)\otimes {\text{e}}^{-K^{\text{trans}}}/v_{\text{e}}t$$ 3

Plasma concentration as a function of blood concentration

$$C_{\text{p}}(t)=(C_{\text{b}}{V}_{\text{roi}})/(V_{\text{roi}}-V_{\text{rbc}})$$ 4

$$V_{rbc}=\text{Hct }{V}_{\text{roi}}$$ 5

$$C_{\text{p}}=C_{\text{b}}/(1-\text{Hct})$$ 6

Substitution of plasma concentration for blood concentration

$$C_{\text{t}}(t)=K^{\text{trans}}{C}_{\text{b}}(t)/(1-\text{Hct})\otimes {\text{e}}^{-K^{\text{trans}}/v_{\text{e}}t}$$ 7

Balanced equation for the total number of particles in tissue ROI or voxel

$$C_{\text{total}}(t)V_{\text{total}}=C_{\text{t}}(t)(1-f_{\text{bv}})V_{\text{total}}+C_{\text{b}}(t)f_{\text{bv}}{V}_{\text{total}}$$ 8

$$C_{\text{total}}(t)=C_{\text{t}}(t)(1-f_{\text{bv}})\text{ + }{C}_{\text{b}}(t)f_{\text{bv}}$$ 9

Therefore:

$$C_{\text{total}}=K^{\text{trans}}{C}_{\text{b}}(t)(1-f_{\text{bv}})/(1-\text{Hct})\otimes {\text{e}}^{-K^{\text{trans}}/v_{\text{e}}t}+C_{\text{b}}(t)f_{\text{bv}\text{.}}$$