MRI Measurement of Change in Vascular Parameters in the 9L Rat Cerebral Tumor After Dexamethasone Administration

Abstract

Purpose

To demonstrate in the rat 9L cerebral tumor model that repeated MRI measurements can quantitate acute changes in the blood-brain distribution of Gadomer after dexamethasone administration.

Materials and Methods

A total of 16 Fischer 344 rats were studied at 7T, 15 days after cerebral implantation of a 9L tumor. MRI procedures employed a T-One by Multiple Read Out Pulses (TOMROP) sequence to estimate R₁ (R₁ = 1/T₁) at 145-second intervals before and after administration of Gadomer (Bayer), a macromolecular contrast agent (CA). Two baseline studies preceded Gadomer administration and 10 subsequent R₁ maps tracked CA concentration in blood and brain for 25 minutes. Thereafter, either dexamethasone (N = 10) or normal saline (N = 6) was administered intravenously. A total of 90 minutes later a second series of 12 TOMROP measurements of Gadomer distribution was performed. The influx constant, K₁, plasma distribution volume, v_D, backflux constant, k_b, and interstitial space, v_e, were determined, and the test-retest differences of each of four vascular parameters were calculated.

Results

Dexamethasone decreased K₁ approximately 60% (P = 0.02), lowered k_b and v_D (P = 0.03 and P < 0.01, respectively), and marginally but insignificantly decreased v_e.

Conclusion

This noninvasive MRI technique can detect drug effects on blood-brain transfer constants of CAs within two hours of administration.

THE PURPOSE OF THIS STUDY was to develop an MRI technique for evaluating acute drug action (i.e., within one to two hours of administration) upon blood-brain exchange in an experimental cerebral tumor. To accomplish this, a standard cerebral tumor model, the 9L gliosarcoma in Fischer 344 rats (1,2), was employed, and the blood-brain distribution of the macromolecular magnetic resonance contrast agent (MRCA), Gadomer, was assessed quantitatively by MRI both before (test data) and shortly after (retest data) drug administration. Of importance in the selection of this MRCA and the development of this technique, Gadomer is relatively rapidly cleared from the blood (half-life ≈ 30 minutes (3)). To produce an in vivo change in the blood-brain distribution system and test the sensitivity in time of this MRI procedure, dexamethasone was administered to the experimental animals after test data acquisition. Postprocessing analyses yielded sets of blood-brain transfer constants—flux rates and distribution spaces—appropriate to one of three models (4). The test-retest differences in the four transfer constants were calculated and used for statistical analysis of drug effects.

As to the choice of drug, the effects of dexamethasone on blood-brain tumor exchange of radioiodinated serum albumin (RISA) has been previously imaged by quantitative autoradiography of a different rat cerebral tumor model, the RG2 glioma (5): The effect of dexamethasone on tumor vascular permeability in another brain tumor model has been previously studied using RISA (5): in that experiment, dexamethasone lowered the transvascular transfer constant and the extravascular distribution space of RISA in the RG2 glioma model, but did not produce a significant change in the tumor plasma volume. Therefore, it was assumed that dexamethasone would have similar effects on the blood-brain distribution of Gadomer in the rat 9L model and this combination of MRCA and tumor would serve as a good proving ground of the test-retest MRI technique for assessing acute drug action.

THEORY OF INDICATOR EXCHANGE

The operating characteristics of the measurement under the conditions of our experiment—Gadomer in a 9L tumor—have been studied (4). In that work, it was determined that, for the case of blood-brain exchange in an ROI selected in the core of the 9L tumor, a full two-compartment model with both influx and efflux across the blood-brain barrier (BBB) was needed. The theory of two-compartment exchange was first stated in its integral form by Patlak and Blasberg (6), and later by Tofts et al (7), in the “consensus” model. The differential equation of the system is the same as that of a low-pass filter, which is to say that the system responds to most strongly to input functions with time constants that are longer than its transfer constant. In the Patlak integral formulation:

$$C_t\left(t\right)=K_1{\int }_0^t{e}^{-k_b(t-\tau )}{C}_p\left(\tau \right)d\tau +v_D{C}_p\left(t\right),$$ [1]

where C_p(t) and C_t(t) are the plasma and tissue concentrations of the indicator at time t, K₁ is the unidirectional transfer or influx constant of that material from plasma across the barrier into the interstitial fluid, k_b is the rate constant for efflux across the BBB, v_D is the fractional distribution volume of the indicator in the “fast” mixing compartments on the blood side of the BBB (always plasma water but in various cases includes plasma proteins and red cells) as detailed in the compartmental analysis in Patlak and Blasberg (6) and Patlak et al (8); in the case of Gadomer, v_D is indistinguishable from the plasma volume (4). This presentation will follow “MRI conventions,” in which concentrations are in units of mL indicator/mL tissue, flow rates and transfer constants are in units of minute⁻¹, etc. This is in distinction to the “radiological conventions,” in which concentrations are in units of mL indicator/g tissue, and K_i and k_b are in units of mL.g⁻¹·minute⁻¹. Numerically, since the density of brain tissue is very close to 1 g/mL, the two unit systems produce estimates of transfer constant and distribution volume that differ by much less than the variability of the measurements.

The change in the longitudinal relaxation rate, ΔR₁, in both tissue and blood was taken as a measure of the indicator concentration, and the R₁ relaxivity of contrast agent (CA) was assumed to be equal for both tissue and blood. We will consider these assumptions in the Discussion. A point in the sagittal venous sinus was taken for a measure of blood concentration vs. time, a procedure previously validated (9) by direct comparison with arterial samples.

The equivalence between variables of the consensus model (7) and the variables above has been described (4), along with the observation equation equivalent to Eq. [1] and the nested model systems available for the analysis of data. These models, numbered according to the number of parameters are as follows:

• Model 1. The no-leakage condition, in which K₁ = k_b = 0, and only v_D is nonzero. This is the model that identifies normal BBB function and is observed in the majority of the brain pixels in most studies including the present one.

• Model 2. Leakage across the BBB with no efflux from the tissue: k_b = 0, K₁ and v_D nonzero. This model, corresponding to the original Patlak model (8), considers the efflux of extravascular CA to be negligible for the duration of the analysis. This model has proven useful in conditions of very low influx and permeability and/or low S/N (9) as well as for a marker that is trapped in the tissue (7).

• Model 3. This is the full model of Eq. [1]. Under the conditions of this experiment, this model has proved useful in the core region of the cerebral tumor (4).

It should be emphasized that each of these models can be appropriate to a given volume of tissue in a given experiment, and thus the model choice must be determined pixel-by-pixel. An F-test comparing Model 1 to Model 2, and Model 2 to Model 3, is available (4), and was employed in the selection of regions of interest (ROIs).

MATERIALS AND METHODS

Animal Preparation: 9L Tumors in Fischer 344 Rats

A total of 16 male Fischer 344 rats (weight = 220−300 g) were studied in a protocol approved by the institution's animal care committee.

The 9L tumor is a well-characterized rat brain tumor model (10,11). Following standard methods (1,4), 10,000 9L rat cells were injected into a location 2.5 mm anterior to the bregma, 2.0 mm to the right of the midline, and at a depth of 3.0 mm. Following implantation, the animals were returned to their cages. Untreated 9L brain tumors were typically 2 to 3 mm in diameter on day 14 and 5 to 6 mm in diameter on day 18 (2).

About 15 days after cell implantation, each rat was anesthetized with 3.0% halothane for induction, and then spontaneously respired with 1.0% to 2.0% halothane in a 2:1 N₂O:O₂ mixture using a face mask during the MRI measurement period. Body temperature was maintained constant (37°C) with a recirculating water pad monitored via an intrarectal type T thermocouple. A tail vein cannula was placed for the administration of CA and dexamethasone. Arterial blood pressure and gases were not measured because such determinations involve a femoral cut down (incision), femoral artery isolation and cannulation, and heparinization of the animal. These procedures can lead to arterial bleeding, death in the magnet, and termination of the experiment. In the past it has been reported for the rat RG-2 glioma model that arterial blood pressure and gases were unaffected by dexamethasone in experiments that lasted up to four hours and were comparable to those of untreated controls (5). These matters led us to not risk arterial bleeding and to assume that blood pressure and gases were similar and normal in both groups of rats.

After the first MRI estimate of permeability (described below), dexamethasone was administered in an intravascular dose of 8 mg/kg in 0.8 mL over a period of three minutes to 10 of the 16 animals studied. The remaining six animals received normal saline in the same volume. The dexamethasone dose was chosen on the basis of previous work in animal cerebral tumor models (12,13), in which between 3 and 30 mg/kg of dexamethasone was shown to be effective in reducing interstitial tumor pressures and relieving edema. A total of 90 minutes after the administration of dexamethasone a second permeability study was performed.

MRI Imaging

A 7-T, 12-cm (clear bore) Magnex (Yarnton, UK) magnet with actively shielded gradients of 25 Gauss/cm and 100 μsec rise times was employed for MRI imaging. The magnet was interfaced with a Bruker (Billerica, MA, USA) Avance console running Paravision V2.1.1. The radio frequency (RF) coils were a Bruker volume resonator for transmission and an actively-decoupled 2-cm Bruker surface coil for reception. The volume resonator, animal holder, and surface coil formed an imaging unit that was inserted in the magnet. After animal location in the holder, the surface coil was centered over the brain, the holder was located in the volume coil, and the imaging apparatus and animal were located in the magnet. Using a three-plane sequence, the central imaging slice was placed to view the largest lateral extent of the tumor.

As noted, the change in the measured longitudinal relaxation rate, R₁ (R₁ = 1/T₁) is assumed to be linear in concentration of MRCA. T-One by Multiple Read Out Pulses (TOMROP) (14), an imaging variant of the Look-Locker sequence (15), was used to estimate R₁. At least one dummy cycle (N pulses followed by T_relax) was applied before the start of data acquisition. Inversion of the longitudinal magnetization was accomplished using a nonselective hyperbolic secant adiabatic pulse of duration 12 msec. One phase-encode line of 24 small-tip-angle (∼18°) gradient-echo images (TE = 4 msec) was acquired after each such adiabatic inversion, at 50-msec intervals, for a total recovery time of 1200 msec with a 2.22-second interval between each adiabatic inversion. Matrix size = 128 × 64, FOV = 32 mm, and three 2-mm slices. Total imaging time per TOMROP set was approximately 145 seconds.

All images were obtained with 32-mm FOV. Prior to the first administration of the MRCA, a single-slice arterial spin labeling (ASL) perfusion(16,17) study (matrix size = 64 × 64) was run to determine cerebral blood flow (CBF) in the central slice of the data set. Additionally, a high-resolution T2-weighted image set (TR/TE = 2000 msec/10 msec, Carr-Purcell-Meiboom-Gill (CPMG) echoes = 3, matrix size = 256 × 192, 17 0.5-mm slices, accumulations = 4), a T₁-weighted high-resolution image set (TR/TE = 1000 msec/7.5 msec, matrix size = 256 × 192, 27 0.5-mm slices, accumulations = 4), and two baseline TOMROP studies were obtained. Two further baseline TOMROP studies were obtained, after which another TOMROP sequence was started and Gadomer was administered by a slow infusion (250 mmol/kg in a 0.3-mL volume in about one minute). During and after the administration of Gadomer, 10 iterations of TOMROP were run to follow the tissue concentration of MRCA across a 25-minute period. Intravascular dexamethasone was administered and, after an interval of about 90 minutes, a second determination of vascular permeability was performed, namely two TOMROP sets, Gadomer infusion followed by 10 TOMROP sets, and a postcontrast T₁-weighted image.

Using the postcontrast T₁-weighted image, each slice was examined for the presence of tumor; if leakage was seen, the area of leakage was outlined manually, filled, and the volume of tumor in the slice calculated by multiplying the area of leakage by the slice thickness. All such volumes were summed, thus yielding an estimate of the volume of tumor with leaky microvessels.

Selection of ROIs

In other work (4), tumor ROIs were selected by manually outlining the region of enhancement in a postcontrast T₁-weighted image. The subsequent time–concentration analysis used the mean ΔR₁ in the ROI as an estimate of MRCA concentration in the ROI, and a single Patlak graphical analysis to estimate the mean vascular parameters in the ROI. In distinction, the work herein utilizes a pixel-by-pixel estimate of ΔR₁ as a local measure of MRCA concentration and the F-test of Model 2 vs. Model 3 is used as a statistic for the selection of an ROI.

In other work, three models for concentration-time data have been described, and an objective statistical test (an F-test) constructed so that a preferred model can be selected (4). When the concentration–time data from one ROI was used for this selection, it was found that for this MRCA in this tumor, three model parameters were required to account for the time variation of the MRCA concentration. However, when the concentration–time data is considered pixel-by-pixel, model selection is not as well defined, since rather than one F-test per model comparison, there are numerous F-tests per ROI, thus increasing the probability that accidental failures of the null hypothesis will occur. In order to address the problem of multiple sampling, the threshold for windowing the F-test was iteratively Bonferroni-corrected by the approximate number of pixels in the ROI (18). That is to say, the F-test threshold was adjusted to a P value of 0.05 divided by the approximate number of pixels in the ROI. Small, “accidental” ROIs of less than four pixels were eliminated by erosion, leaving a connected region of typically several hundred pixels. For instance, Fig. 1 shows the T₁-weighted image taken immediately after the first permeability study, and the map of the F-test for Model 2 vs. Model 3, along with the ROI selected by the procedure just described. Shown in Fig. 2 are concentration-time (i.e., ΔR₁ vs. time) curves for the venous sinus and the tumor ROI, along with the corresponding Model 2 and Model 3 Patlak plots (4). In all cases, the pretreatment studies were used to define the ROI, which was then used to summarize both pre- and posttreatment results.

Figure 1.

Left: Postcontrast T₁-weighted image, 2-mm slice thickness. Right: Map of F-test comparison of Model 2 vs. Model 3, and ROI chosen by thresholding the F-test map at a value of 70.

Figure 2.

Left: Concentration–time curves for blood (circles) and tissue (squares), as measured by the change in R₁. Tissue concentrations are scaled upward by a factor of 5, in order for the time behavior to be better visualized. The first (precontrast) point of the next blood curve, taken at about 110 minutes after the first injection of contrast, is plotted as a triangle. Note the near-total clearance of CA from blood in this time. Right: Patlak concentration–time plots for Model 2 (circles) and Model 3 (squares). Curvature in the Model 2 plots signals the presence of significant efflux from the extracellular space back to vascular space. The superiority of Model 3 as a straight-line fit is evident.

Data Analysis

A total of three 2-mm-thick slices of data on 2-mm centers were available. Using TOMROP image sets taken at intervals of 145 seconds, pixel-by-pixel R₁ maps were constructed using a maximum-likelihood procedure constrained to yield nonnegative estimates of the model parameters (19). Pixel-by-pixel maps of the parameters of the three possible models were constructed, as were maps of the F-statistic for comparison of Model 1 to Model 2 and Model 2 to Model 3. When Model 3 holds, then the K₁/k_b ratio approximates the extravascular distribution volume of Gadomer, v_e.

For each of the three available slices, if a connected region with a significantly high F-test could be identified, an ROI was formed by thresholding the F-test map in the manner described. For each animal, parameter values contained in each slice's ROI were summarized as a mean ± sample SD and were averaged across all slices from that animal. This mean was taken as the final summary parameter for each study. Pretreatment minus posttreatment differences of each of the four summary parameters were computed. The same procedure was employed to obtain pre-saline minus post-saline differences for the controls. The mean of the pre-minus posttreatment sample differences were compared to the mean of the control differences, with the null hypothesis that all differences were selected from the same pool. A failure of the null hypothesis implied that there was a measurable effect due to the administration of dexamethasone.

As just noted, the statistic employed for testing was the pre- minus postadministration parameter difference for each of the measured parameters. This allowed the use of the animal as its own control, and considerably lowered the variance of the measurements due to interanimal differences. The normality of each statistic was checked using a Shapiro-Wilk test. A two-sample t-test was used to test the treatment effect on MRI parameter changes if the differences were normally distributed. If otherwise, a nonparametric Wilcoxon rank-sum test was employed.

For reporting and comparing these and other parameters, sample values are taken as mean ± SD, and standard statistical tests are reported when used.

RESULTS

Tumor age was 14.6 ± 0.7 days for all 16 animals, 14.9 ± 0.7 days for the 10 treated animals, and 14.2 ± 0.7 days for the six controls. Leakage of Gadomer was noted in the tumors of all 16 animals. The mean volume of the blood–tissue distribution of Gadomer was 53.5 ± 40.2 mm³ (range = 12.3−140.6 mm³) for all 16 rats, 59.3 ± 46.3 for the 10 treated animals, and 42.7 ± 27.9 mm³ for the six controls. Of the 16 animals, nine had a CBF map corresponding to at least one of the slices selected for study (five studies in the dexamethasone group, four in the control group). In these nine instances, the tumor mass was, in general, well-perfused (overall mean = 1.56 ± 0.91 minutes⁻¹), and tumor perfusion did not differ between the treatment group (1.75 ± 1.04 minutes⁻¹) and the controls (1.33 ± 0.77 minutes⁻¹).

Figure 3, continuing with the animal study shown in Fig. 1, displays maps of estimates of vascular parameters pre- and post-dexamethasone treatment, along with a map of the F-test for Model 2 vs. Model 3, and the ROI chosen. The changes, which are most clearly visible in the map of K₁, do not appear to be uniform; the pathophysiological correlates of this inhomogeneity are a subject of further study.

Figure 3.

Vascular parameters pre- (left) and post-dexamethasone (right) administration. a: Vascular volume v_D. b: Transfer constant K₁ (minute⁻¹). c: Efflux constant k_b (minute⁻¹). d: F-test for Model 3 vs. Model 2, with a high value resulting in rejection of Model 2. Only those regions in (c) with high F-test values have valid results for the estimate of k_b. A widespread decrease in K₁ and k_b are easily visualized. Less visible is a moderate decrease in v_D. Bright spots in the maps of v_D correspond to vascular pools. Note the decrease in the F-test from pre- to post-dexamethasone studies.

Reiterating that the statistic studied was the difference between the first and second study for each of the model parameters, Table 1 summarizes the grouped data taken from the ROIs. In the control group, the mean differences of all parameters were not significantly nonzero. However, a trend toward an increasing post-saline estimate of v_D, K₁, and k_b was apparent. Accordingly, as noted in Materials and Methods the test-retest differences in the parameters were employed as a statistic, and the means of these differences were compared as a test for drug effect. Note that the difference trends in the control population are opposite to those in the dexamethasone-treated population.

Table 1.

Vascular Parameters Pre- and Post-Injection: Dexamethasone or Saline.

	vD(mL/mL) x 10−2			K1 (minute−1) x 10−3			kb (minute−1) x 10−2			ve (mL/mL) x 10−2
	Pre	Post	Diff	Pre	Post	Diff	Pre	Post	Diff	Pre	Post	Diff
Dexamethasone (N = 10)
Means	1.86	1.58	0.28	7.52	4.64	2.89	7.56	5.57	1.98	9.48	8.17	1.30
SD	1.13	1.09	0.30	4.90	2.91	2.47	3.71	1.70	2.40	2.74	4.02	2.56
Paired t			2.83*			3.51**			2.48*			1.53
Saline (N = 6)
Means	1.41	3.24	−1.83	0.72	0.82	−0.10	7.38	8.13	−0.75	10.01	11.35	−1.35
SD	1.09	2.16	2.43	0.29	0.15	0.21	2.91	3.92	1.70	3.09	3.54	3.49
Paired t			−1.69			−1.06			−0.99			−0.86

^*P < 0.025.

^**P < 0.005.

Diff = difference.

The mean test-retest differences of the parametric estimates in the saline group were compared to the mean differences in the treatment group. All three parameters showed significantly larger differences (i.e., the parameter decreased in the retest study) in the dexamethasone-treated vs. control groups. The parameter v_D decreased by 15% (P < 0.01, Wilcoxon rank-sum test), K₁ by nearly 40% (P = 0.02, Wilcoxon rank-sum test), and k_b by 26% (P = 0.03, t-test). On the other hand, v_e, calculated as a ratio of k_b/K₁ showed a nonsignificant (P = 0.1) trend downward. In 10 of 10 studies, K₁ decreased after dexamethasone treatment, whereas K₁ increased in four of six after saline administration (Fig. 4b). This pattern was echoed in the estimate of k_b. It appeared that v_e was relatively unchanged by dexamethasone because the downward change in k_b induced by the drug was tracked by a similar downward change in K₁.

Figure 4.

v_D, K₁, k_b, and v_e changes in the test-retest experiment. Values from individual studies are plotted as pre- vs. posttreatment points, with dexamethasone points as open circles and saline groups as solid circles. Group trends are clear, particularly in K₁ changes.

Since the trends in the control population were opposite to those of the dexamethasone group, an examination of the paired t-test results of the latter group was of interest. Dexamethasone treatment strongly and significantly lowered v_D, K₁, and k_b (Table 1), whereas v_e again showed a nonsignificant decrease. These outcomes are of interest because in clinical settings it may be more important that a change in vascular parameters can be observed than that an unbiased estimate of the change can be made. It appears that, particularly for K₁, a robust, noninvasive measure of changes in microvascular permeability by contrast-enhanced MRI is at hand.

The model-derived parameters from the individual experiments are presented in Fig. 4 as plots of the posttreatment (either saline or dexamethasone) value of each vs. the pretreatment value. A line of identity (slope = 1.0, intercept = 0.0) is included on each graph. Generally, an examination of these plots confirms the findings of the summary statistics of Table 1, and moreover gives a visual sense of the variability typical of the measurement of each of the parameters. For instance, in the control group, v_D demonstrates 6 of 6 studies with points above the line of identity (LOI), and nine of 10 treatment studies with points below the LOI. Thus, a decrease in v_D in these tests appears to discriminate between treated and untreated animals. The test-retest trend upward in v_D is probably a methodological problem, due to the incomplete clearance of Gadomer in the interval between the two tests.

As for the transfer constant K₁ (Fig. 4b), for the dexamethasone group, the slope of a least-squares fit line (forced through the origin) was 0.66. Since points for the saline-infused group tended to cluster above the line of identity, dexamethasone appeared to lower the influx of Gadomer in 10 tumors of the treated group by about one-third. In the control group, there is no strong trend in K₁, thus allowing the inference that a persistent level of CA influences mainly the estimate of vascular volume, rather that the rate constant K₁. In the dexamethasone group the test-retest K₁ lay below the line in 10 of 10 studies, showing a sensitive measure of change in vascular permeability.

DISCUSSION

Nakagawa et al (5) used RISA and quantitative autoradiography (QAR) to measure changes in v_D, K₁, and v_e in the RG-2 rat brain tumor model after dexamethasone administration (1.5 mg/kg intramuscularly [i.m.] twice a day for 48 hours before testing). In a total of 72 animals implanted with RG-2 tumors, dexamethasone produced a significant decrease in v_e, and a trend toward lowered K₁ and v_D. The results of the present study are in essential agreement, with dexamethasone treatment yielding significant drops in K₁, k_b, and v_D and a downward trend in v_e.

For untreated tumor data, estimates of K₁ for albumin in Nakagawa et al (5) were larger (0.0236 ± 0.0089 minute⁻¹) than the group mean of K₁ for Gadomer (N = 14, 0.0074 ± 0.0044 minute⁻¹). This discrepancy in influx in untreated rats may be due to differences in the size and diffusivity of the two CAs, tumor type (RG-2 vs. 9L), and tumor size. Gadomer is about half the molecular weight of albumin but has a similar diffusion coefficient because of its shape. The RG-2 rat model is a transplanted glioma, whereas the 9L (also known as the RT-9) is a transplanted gliosarcoma. QAR studies with the capillary permeability marker, ¹⁴C-aminoisobutyric acid (AIB), have been conducted on five different rat brain tumor models (20), including the RG-2 and 9L/RT-9. The typical K₁ of AIB in the RG-2 tumors was around 0.03 mL g⁻¹ minute⁻¹; in addition, K₁ was found to be fairly uniform across the entire tumor and was relatively independent of tumor size (21). The AIB influx rate constant varied much more for the 9L/RT-9 tumors (22). In small tumors (area < 2.2 mm²), the average K₁ was around 0.003 mL g⁻¹ minute⁻¹, whereas in larger ones (area > 2.4 mm²), it was about 0.03 mL g⁻¹ minute⁻¹ and similar to that in the RG-2 tumors. In addition, influx rate varied considerably within the individual 9L/RT-9 tumors. The mean area of the 9L tumors in the current study was 2.3 mm², which means some were small and others were large according to the grading of Nakagawa et al (5). If microvessel permeability to Gadomer and albumin within the tumor parallels that of AIB, then it would be expected that Gadomer influx in the saline-treated 9L group (present study) would be less than that of albumin in the RG-2 tumors. Such a difference between these two studies is, of course, what was found.

In other, more recent work (23) in a 9L tumor model, a 40% decrease in tumor fractional blood volume (from 1.7 ± 0.4 to 1.0 ± 0.4) after dexamethasone treatment (3 mg/kg intraperitoneally [i.p.] for four days) was observed; this is in very good agreement with our observations. In a small study in humans, decreases in permeability of up to 73% were observed after dexamethasone administration, with accompanying decreases in tumor vascular volume (24). In general, then, the results of this investigation are consistent with earlier studies and support the validity of an MRI measurement of tumor microvascular fluxes and distribution volumes.

The theory of the two-compartment model of vascular exchange of an indicator using the uptake and clearance of MRI CAs is essentially complete (6–8). Given an established theory, the goal of any experimental procedure should be to provide an unbiased estimate of the vascular parameters of the model, i.e., of K₁, v_D, and k_b or v_e. A major problem in this effort is that of a reliable estimate of CA concentration vs. time using MRI imaging techniques. This problem arises because R₁, while linear in MRCA concentration in gels, is not linear in tissue, where the compartmentalization of water and/or CA becomes an important consideration (25–30). A second major problem is the identification of a reliable input function, from a source having the same relation between CA concentration and MR contrast as does the tissue. Both these problems become more difficult when the sampling times of the concentration–time experiment become short. In general then, our choice of CA–Gd-diethylene triamine pentaacetic acid (DTPA) in experimental reperfused ischemic infarction (9,31) and Gadomer (4) or Gd-albumin (32) in experimental cerebral tumor—have been driven by a wish to employ relatively slow sampling frequencies in concentration-time studies of vascular parameters.

Gadomer (Bayer) is a dendritic gadolinium chelate carrying 24 Gd atoms per molecule. The blood half-life is about 30 minutes in rats, and Gadomer is not metabolized or stored in any organ (3). Because of its weight—approximately 17 kD dry, but with an effective wet weight of about 30 kD—it is essentially an intravascular CA in most tissues. As we and others have noted, the compound does leak in aggressive tumors (33–35), but slowly enough so that many of the problems presented by rapid sampling can be avoided.

When considering sampling times in a concentration-time study, a certain amount of a priori information is necessary. As we have noted, the model equation is that of a low-pass filter. In this case, as a rule of thumb, concentration–time sampling intervals should be some small fraction (10ths) of the order of the characteristic time of the circuit. That is to say, sampling intervals should be some small fraction of the inverse of the transfer constant, K₁. Since for Gadomer in experimental cerebral tumor, $K_1^{-1}$ > 100 minute in all cases (4), sampling times on the order of a few minutes are acceptable for tissue sampling in an experimental tumor when Gadomer or Gd-albumin are used as a CA.

Sampling times on the order of minutes also considerably simplify the problem of estimating blood concentration in the input function. We note that the transit time between the microvessels of the brain and the sagittal sinus is quite short—less than 10 seconds—compared to the sampling time of the experiment (145 seconds). If there is no significant extraction of the CA in any single pass, then the sagittal sinus can be used to form an estimate of the tissue input function, a conclusion that has been supported by direct comparison with arterial samples (9).

Noting again that typical transfer constants for this tissue and CA are small, one can conclude that inputs with short time-constants are essentially irrelevant—it is only the average long-term behavior of the input function that is sensed by the low-pass filter. This being so, the length of CA injection was increased from previous practice, with the injection starting with the beginning of the third Look-Locker experiment and proceeding over roughly one-half of the experiment. This was done with the idea that the MRI procedure would provide an estimate of the average concentration during the imaging interval. An examination of Fig. 2 appears to confirm this impression, with a smooth and apparently continuous input function producing a reasonable estimate of vascular volume in the tumor (4.5%) on the corresponding Patlak graphical plots.

We consider the question of the relation between CA concentration and a TOMROP estimate of R₁. Because T₁ is generally quite long compared to mean diffusion times over cellular distances, one would expect that most of the protons of water are equivalent in the absence of restriction, and therefore that T₁ decay is monoexponential. Techniques for estimating CA concentration via MRI contrast have, thus, generally utilized measures of T₁ and/or T₁-weighted images. For instance, a recent study of angiogenesis and permeability in tumor vascular beds (34) first determined R₁ maps by a progressive-saturation method. Following this determination, the uptake and clearance of a MRCA was followed with a saturation recovery (TR = 50 msec, tip-angle = 90°) sequence, in which the change in contrast was used to infer the change in MRCA concentration. This is common practice in MRI studies of MRCA concentration (26,27,33). These estimates of R₁ assume that the magnetization recovery remains monoexponential in tissue, independent of CA concentration. This has been shown to not be the case (25,29,30). The degree to which an estimate of MRCA concentration based on the linear assumption deviates from the true concentration depends on MRCA concentration, distribution space, the original relaxation rates in the compartments of distribution, plus tip-angle and repetition time of the MRI sequence (26,28,36). However, a slower multipoint estimate such as that produced by Look-Locker data may not show such dependencies: it is probable that the Look-Locker experiment, which in our procedures takes place over the space of 1200 msec, allows the intercompartmental exchange of protons for a long enough time that all tissue water protons become equivalent.

In focusing on validation of experimental design, the additional information available from these measures has not been considered. One interesting speculation is that an indirect measurement of the interstitial pressure in the tumor is available, in the form of a measure of bulk flow from the tumor. Consider Fig. 5, which is a map of the F-test comparison for Model 1 (no leakage) vs. Model 2 (leakage with no efflux). It has been determined that this tumor model using this CA generally requires Model 3 (leakage with backflux). In this F-test map, however, and in many of the other maps we have examined, there is a bright rim of highly significant “Model 2” pixels around the central tumor signaling that CA has entered the pixel and not returned to its vasculature. This suggests that CA has been transported across the leaky BBB by bulk flow-solvent drag, which then pushes plasma and Gadomer away from the site of leakage and further into the tissue. This suggestion is consistent with that of Nakagawa et al (5) who observed that radiolabeled albumin could be found at 30 minutes outside the tumor margin for a distance approaching 0.3 mm, which is approximately the pixel size of the MRI experiment. Research seeking a method that might quantitate the rate of bulk flow and the gradient of interstitial pressure within the tumor, both clinically significant parameters, is presently under investigation as an extension of the current study.

Figure 5.

The F-test map of the model comparison Model 1 (no leakage) to Model 2 (leakage without reflux) in the rat brain, prior to administration of dexamethasone. A bright rim signifies a region in which Model 2 is a strong choice, and may map the bulk flow of contrast agent out of the area of leaky vasculature (hence the lack of reflux).

In conclusion, we have demonstrated that a change in tumor vascular permeability, which was known to take place, could be sensitively, noninvasively, and efficiently measured by an MRI technique using a large CA and a relatively slow sampling time. This establishes the utility of the technique for measuring changes in tumor vascular permeability upon the administration of other agents with unknown effects.