Noninvasive Magnetic Resonance Imaging of Transport and Interstitial Fluid Pressure in Ectopic Human Lung Tumors

Introduction

Tumor angiogenesis facilitates blood supply and perfusion, leading to enhanced tumor growth and formation of metastasis ( 1). However, the newly formed capillaries in malignant tumors usually exhibit complex and tortuous architecture and function which may elevate the interstitial fluid pressure (IFP; refs. 2– 8). The increase in IFP is mainly due to increased water permeability of the tumor microvasculature and the lack of functioning lymphatic vessels, and hence water accumulation ( 9– 11). Additionally, intratumoral elevated IFP levels were attributed to molecular modulations in the composition and elasticity of the tumor interstitium ( 12). The increase in IFP leads to a positive pressure gradient, which is a driving force for a convective transport back into the capillaries or to adjacent regions with low IFP. Such convective forces inhibit the transfer of drugs to the tumor interstitium and facilitate tumor cell intravasation into the vascular or lymphatic circulation, and hence promote metastasis ( 13). In regions with high IFP, the delivery of drugs may be impaired, resulting in failure of therapy ( 14). Determining IFP, and particularly the spatial distribution of the net tracer transfer to the tumor interstitium, may predict the efficiency of drug delivery and help design improved drug administration protocols. Moreover, it can help design new protocols that specifically decrease IFP or result in normalization of the vascular function ( 12, 15, 16).

Thus far, assessment of tumor IFP has been done by methods such as the wick-in-needle and the micropancture technique ( 12, 14). These methods are invasive and limited to measurements in few locations. It would therefore be highly useful to develop a noninvasive imaging method that would map the spatial distribution of IFP and the net transfer into the tumor interstitium. An early attempt to use magnetic resonance imaging (MRI) for mapping IFP was based on correlating proton relaxation rates with IFP values obtained by the wick-in-needle technique ( 17). However, the results showed that both T₁ and T₂ relaxation rates did not correlate with the measured IFP ( 17). Subsequent dynamic contrast-enhanced MRI studies, using a bolus injection of gadolinium-diethylenetriaminepentaacetic acid (GdDTPA), indicated the presence of disparities between the influx and outflux transcapillary transfer constants in breast tumors ( 18). This disparity with the outflux exceeding the influx constant increased from the tumor rim to the center. This distribution is in accord with the profile of IFP distribution in tumors as was previously shown ( 13, 19). Recently, dynamic contrast-enhanced MRI studies of fibrosarcoma mouse model showed that a decline in IFP, induced by thalidomide, was accompanied by increased plasma volume fraction and fractional efflux rate from the interstitial space to the plasma ( 20).

Here we present an alternative contrast-enhanced MRI method that reveals the distribution of the contrast material due to the net effect of extravasation, diffusion, and convection in ectopic NCI-H460 non–small-cell lung cancer tumors implanted in immunodeficient mice, which exhibit high IFP values (∼28 mm Hg). For comparison, we also applied this method to investigate orthotopic MCF7 human breast tumors which exhibit a significantly lower IFP (∼14 mm Hg). The contrast agent was continuously administered by slow infusion into the blood circulation, raising its blood level to a steady-state concentration. The MRI recordings monitored T₁ relaxation rates and signal intensity before the start of the infusion and during the infusion, including at blood and tumor steady-state concentrations. Analysis of the changes in T₁ relaxation rates yielded steady-state tissue GdDTPA concentration (mmol/tissue volume) maps of the tumors and their surrounding. These maps reflected inhibition of transfer due to elevated tumor IFP and transfer by convection in the tumor surrounding.

Materials and Methods

Animals and tumors. Human NCI-H460 non–small-cell lung cancer cells were obtained from the American Type Culture Collection (Rockville, MD) and were cultured as recommended by the supplier. Cells (8 × 10⁶), suspended in 0.5 mL PBS, were implanted s.c. into the flank of 6-week-old female CD1-NU mice. Cultivation of MCF7 cells and implantation of orthotopic MCF7 tumors were previously described ( 21, 22).

During the experiments, mice were anesthetized by inhalation of 1% isoflurane (Medeva Pharmaceuticals, Inc., Rochester, NY) in an O₂/N₂O (3:7) mixture applied through a nose cone. All the protocols were approved by the Weizmann Institute Animal Care and Use Committee.

Measurements of IFP. IFP was measured in H460 tumors (n = 7) 13 days after their implantation and in MCF7 tumors (n = 9) ∼5 weeks after their implantation using the wick-in-needle apparatus ( 23). Briefly, a 23-gauge needle with a side hole located at ∼3 mm from the needle tip was connected to a pressure monitor system (model 295-1 Pressure, Stryker, Kalamazoo, MI) especially designed for measuring tissue fluid pressures. The system was filled with saline. The needle was inserted into a central part of the tumor or into the flank muscle (n = 20) for reference, and 50 μL of 0.9% sodium chloride were injected to ensure fluid communication between the tissue and the pressure monitor system.

Histology. At the end of the MRI experiments, tumors were dissected free from s.c. tissue and cut in the middle in a plane parallel to that of the magnetic resonance images. Tumors were fixed in 2.5% paraformaldehyde for H&E staining or in 4% zinc solution (0.5% zinc chloride and zinc acetate, 0.05% calcium acetate in 0.1 mol/L tris buffer, pH 7.4) for CD31 immunofluorescence staining. Seven-micrometer-thick paraffin-embedded sections were prepared.

For endothelial staining, the sections were deparaffinized in xylene, hydrated in series of graded ethanol, and rinsed in double-distilled water. Sections immersed in cold acetone (−20°C, 7 minutes) and rinsed in double-distilled water were then blocked with 20% normal rabbit serum and incubated overnight with primary rat anti-mouse CD31 (platelet/endothelial cell adhesion molecule 1, monoclonal rat anti-mouse, 1:100; PharMingen, San Diego, CA), which is constitutively expressed on the surface of mature endothelial cells. Next, sections were incubated for 1 hour in biotinylated antirat CD31 (1:100; Vector Lab, Burlingame, CA). Antibody distribution was visualized using a fluorescence streptavidin-Cy3 conjugated complex (Jackson ImmunoResearch Laboratories, Inc., Baltimore, MD). Nuclear staining was done using Hoechst solution (Molecular Probes, Eugene, OR) diluted 1:2,000.

Stained sections were examined by fluorescence microscope (E600, Nikon, Toyo, Japan) equipped with Plan Fluor objective connected to a CCD camera (DMX1200F, Nikon). Digital images (3.2 mm²) of all the tumor area were collected and analyzed using the Image-Pro plus 4.1 software. Quantification of endothelial staining was done by measuring the percentage of area with positive staining for CD31.

MRI studies. MRI scans were acquired with a 4.7-T Biospec spectrometer (Bruker Biospin, Rheinstetten, Germany). Fourteen H460 tumors and nine MCF7 tumors were scanned using a protocol that included an initial two-dimensional T₂-weighted spin echo sequence with echo time = 68 ms; repetition time = 2,500 ms; 128 × 128 matrix; 1-mm slice thickness; an interslice distance of 1.1; and 3 × 3 cm² field of view. The tumor region of interest in each slice was traced on the T₂-weighted images and this trace was then used for localizing the tumor in the various subsequent images obtained at the same spatial resolution. The size of the tumors was determined from the area of the region of interest and the slice thickness, taking into account the inter-slice distance ( 24). T₁ measurements were then done using two-dimensional sequential inversion recovery snapshot fast low-angle shot imaging with 11 inversion times ranging from 10 ms to 10 seconds; echo time = 3.5 ms; repetition time = 15 ms; flip angle = 10 degrees; and the same matrix size and field of view as the T₂-weighted images. Two-dimensional T₁-weighted gradient echo images were also scanned using echo time/repetition time = 2.73/35.8 ms; flip angle = 60 degrees; and the same spatial resolution as the T₂-weighted images acquiring four scans within 18 seconds. Following these measurements, slow infusion was initiated with 0.05 mol/L GdDTPA solution (gadopentate-dimeglumine, Schering, Berlin, Germany) at a rate of 0.66 mmol/h/kg wt for 2 hours. Sequential images were scanned during the slow infusion using the three-dimensional T₁-weighted gradient echo sequence described above. At 90 minutes after the start of infusion, T₁ relaxation rates were measured again using the inversion recovery snapshot fast low-angle shot sequence described above.

Separate experiments were done to monitor the GdDTPA enhancement in the carotid arteries and determine the time needed to reach steady-state in the blood during the slow infusion (n = 3). In these experiments, inversion recovery fast low-angle shot sequence was applied using a fixed inversion time of 120 ms; echo time = 3.5 ms; repetition time = 15 ms; flip angle = 10 degrees; 128 × 128 matrix; 1-mm slice thickness; and 3 × 3 cm² field of view at a temporal resolution of 6 s.

Processing and analysis. T₁ relaxation rates were calculated at pixel resolution applying a nonlinear least square fit of the intensity I per pixel at varying inversion times. The curves obtained from measurements before administration of the contrast agent and at steady-state infusion conditions exhibited a single decay time constant according to the following equation: I = I_inf [1 − A exp(−TI / T₁)], with I_inf [maximum intensity at a long inversion time (TI)], A (maximum value 2), and T₁ as the free variables in this fit with R² of the fit ranging from 0.9 to ∼1. At steady-state concentration of the contrast agent in the tissues, the intracellular and extracellular T₁ water relaxation rates differ due to the sole presence of GdDTPA in the extracellular compartment. At a maximum concentration in the extracellular compartment of ∼1 mmol/L, the upper limit for this difference is ∼4 s⁻¹ whereas the effective intracellular-extracellular water exchange rate is more than an order of magnitude higher, 50 s⁻¹ (based on intracellular lifetime of ∼100 ms and an intracellular to extracellular volume ratio of 4). Hence, water exchange between the intracellular and extracellular compartments is at the fast exchange limit ( 25) and the T₁ relaxation rate at steady state is decaying uniexponentially as was indeed found in the T₁ measurements. Furthermore, under this fast exchange condition, tissue GdDTPA concentration (C_Gd), defined as the amount of GdDTPA in millimoles per tissue volume at GdDTPA steady-state concentration, is obtained from the measured relaxation rates according to the equation C_Gd = (1/T_1ss − 1/T₁₀) / r₁, where r₁ is the water relaxivity of GdDTPA in solution, 4.2 s⁻¹ × (mmol/L)⁻¹ ( 26), and 1/T_1ss and 1/T₁₀ are the relaxation rates at steady-state concentration and before the infusion, respectively.

Maps of the actual GdDTPA concentration in the extracellular volume fraction of H460 tumors were calculated estimating an extracellular volume fraction of 0.2 ( 14). The extracellular volume fraction of MCF7 tumors was determined by applying a method based on diffusion MRI ( 22). Further estimation of IFP in the H460 tumors was obtained by assuming a linear relation between IFP and the calculated GdDTPA concentration in the extracellular volume at steady state using an approximate scale of IFP between 0 mm Hg at the rim and 28 mm Hg at the center.

An attempt was made to analyze the enhancement curves during the first 30 minutes of the infusion using the kinetic model described by Tofts and Berkowitz ( 27) and a nonlinear least square fit program previously developed in our laboratory ( 28). The output of this analysis yielded the influx and efflux transcapillary transfer rate constants.

Results

Solid tumors of H460 non–small-cell lung cancer cells rapidly developed within a week after cell inoculation. Measurements of tumor size, obtained by analyzing the T₂-weighted images, showed continuous fast growth from an average size (± SD) of 110 ± 20 mm³ (n = 7) 9 days after implantation to 510 ± 150 cm³ (n = 7) a week later.

The IFP of the tumors was determined by the wick-in-needle method. Attempts were made to measure the pressure close to the center of the tumors. H460 tumors exhibited high IFP values, ranging from 18 to 45 mm Hg with a mean ± SD of 28 ± 8 mm Hg (n = 7). The IFP values of MCF7 tumors were lower and more diverse, ranging from 4 to 32 mm Hg with a mean of 14 ± 10 mm Hg (n = 9). Measurement in the flank muscle opposite to the tumor site and of control mice showed IFP values ranging from 0 to 5 mm Hg.

The analysis of histologic sections of H460 tumors revealed their structural and morphologic features. Sections stained with H&E showed well-delineated, but nonencapsulated, tumors composed of cohesive, densely cellular, and disorganized sheets of pleomorphic cells, exhibiting occasional invasion into the surrounding connective tissue. The tumors predominantly consisted of viable, cellular regions with occasionally small localized regions of necrosis spread homogeneously over the entire tumor section ( Fig. 1A and B ). Specific immunostaining of endothelial cells with CD31 monoclonal antibody traced the capillary distribution in the tumors ( Fig. 1C-F). The density of the capillaries varied both at the boundaries and in central regions; part of the regions exhibited high density ( Fig. 1C and F) and others had low density ( Fig. 1D and E). Thus, the heterogeneous distribution of the capillaries was similar in the centers and rims of the tumors with an average CD31 stained area of 1.1 ± 0.4% [7 tumors, in each 4 to 10 fields of 3.2 mm² (2 × 1.6 mm)]. The histologic features of the orthotopic MCF7 tumors were similar to those previously described ( 22) and revealed the presence of a larger extracellular volume fraction and a more heterogeneous distribution of the cells than in the H460 tumors. Staining of the capillaries indicated an average stained area similar to that of H460 tumors of 1.3 ± 0.6%.

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Figure 1.

Histopathology and vascular distribution of ectopic human H460 non–small-cell lung cancer tumors in immunodeficient mice. A, a macroscopic view of H&E-stained section of a tumor exhibiting dense cellular distribution with localized small necrotic regions (arrows) homogeneously dispersed between the cellular regions throughout the whole tumor section. B, a microscopic view of a region in this tumor exhibiting homogeneous, dense packing of the cells. C to F, microscopic views of tumor regions immunostained for the endothelial cell marker CD31 (red fluorescence) and with Hoechst solution (blue fluorescence) for nuclear counter staining. C and D, inner tumor regions; E and F, regions at the boundaries.

The MRI experiments were designed to characterize the capability of the microcapillary network to transfer the contrast agent into the tumor tissue and explore the influences of high IFP on this transfer. To that end, we employed a slow contrast agent infusion into the blood circulation monitoring the concomitant changes in signal enhancement. The arterial input function of this infusion protocol was determined by monitoring the enhancement in the carotid arteries ( Fig. 2A ). At ∼20 minutes after the start of the infusion, the concentration of the contrast agent in the blood circulation reached a steady state (of ∼0.9 mmol/L); i.e., the rate of infusion was equal to the rate of clearance from the blood through the kidneys into the urine. Following blood steady state, other parts in the mouse body also reached steady-state concentration ( Fig. 2B and C).

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Figure 2.

Dynamic profiles of the change in the concentration of GdDTPA in the plasma and of tissue GdDTPA concentration in muscle tissues during GdDTPA slow infusion. A, obtained from dynamic contrast-enhanced images of the carotid artery as described in Materials and Methods. The time points were fitted to the equation Cp = [D(a(1 − exp(−mt)) / m)] / (1 − Ht) with D = 0.011 mmol/kg/min, Ht = 0.45 yielding a = 9.0 kg/L, and m = 0.16 min⁻¹. Steady-state GdDTPA concentration in the blood was reached after ∼20 minutes of infusion. B and C, tissue GdDTPA concentration in the neck and foreleg muscles, respectively. Steady-state GdDTPA concentration was reached after ∼30 minutes of infusion. The infusion protocol and monitoring of changes in GdDTPA concentration are described in Materials and Methods.

Monitoring of H460 tumors by MRI before and during slow infusion of the contrast material revealed heterogeneous enhancement patterns with distinct high enhancement in the surrounding regions outside the tumor boundaries ( Fig. 3A and B ). Two different signal enhancement patterns were observed: (a) In predominant intratumoral regions, signal enhancement increased slowly and reached a steady enhancement ( Fig. 3C). This indicated that tumor GdDTPA concentration reached a steady state. (b) In regions surrounding the tumors, signal enhancement increased steadily for 90 minutes, suggesting transfer of GdDTPA due to an outward convection ( Fig. 3D). In addition, some internal regions exhibited null enhancement even after 90 minutes of slow infusion, suggesting a substantial increase in IFP that completely inhibited transcapillary transfer or transport through the interstitium from adjacent regions.

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Figure 3.

GdDTPA contrast enhancement in ectopic H460 tumor during slow infusion. A and B, T₁-weighted gradient echo images acquired after 10 and 60 minutes of GdDTPA slow infusion, respectively. Tumor region of interest was delineated on the corresponding T₂-weighted image and duplicated to the corresponding contrast-enhanced images. The acquisition variables are described in Materials and Methods. Note an outward enhancement in the boundary regions of the tumor indicating convection in that direction. C, an enhancement curve inside the tumor (labeled 1 in B) reaching a steady state after 30 minutes of infusion. D, an enhancement curve in the tumor surrounding (labeled 2 in B) showing continuous contrast agent accumulation.

The steady-state tissue GdDTPA concentration maps in both H460 and MCF7 tumors were determined from the T₁ relaxation rates measured before infusion and at steady-state tumor GdDTPA concentration (∼70 minutes after blood steady-state concentration was reached; Figs. 4A-C , 5A-C , and 6A-C ). The high tissue GdDTPA concentration outside the tumors (in the range 1-2 mmol/L) reflected transport via convection. The steep decrease from the tumor rim towards the center reflected the increase in IFP. Inner regions of part of the H460 tumors were completely void of GdDTPA despite the long duration of infusion, indicating the presence of high IFP and convective flow outwards ( Figs. 4C and 5C). This concentration distribution was in contrast to the homogeneous morphology of the tumors as was indicated by histologic sections in planes similar to those of the images ( Fig. 1A). It was also in contrast to the distribution of capillaries that did not show large differences in the microvascular density between the rim and the center ( Fig. 1).

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Figure 4.

Parametric images of T₁ relaxation times and calculated tissue GdDTPA concentration at steady state of ectopic H460 tumor. A and B, pre-contrast T₁ map and steady-state T₁ map 90 minutes after the start of slow infusion, respectively. Tumor region of interest was delineated on the corresponding T₂-weighted image and duplicated on the T₁ maps. C, steady-state tissue GdDTPA concentration map 90 minutes after the start of infusion. Note the heterogeneous distribution of the contrast agent in the tumor and the high tissue GdDTPA concentration outside the tumor due to outward convection. D, histologic, H&E-stained central section approximately sliced in parallel to the imaging plane.

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Figure 5.

Parametric images of T₁ relaxation times and calculated GdDTPA concentration maps and profiles at steady state of ectopic H460 tumor. A and B, pre-contrast T₁ map and T₁ map 90 minutes after the start of slow infusion, respectively. Tumor region of interest was delineated on the corresponding T₂-weighted image and duplicated on the T₁ maps. C, map of steady-state tissue GdDTPA concentration 90 minutes after the start of infusion. D, map of steady-state GdDTPA concentration in the extracellular volume 90 minutes after the start of infusion. The map was derived from (C) assuming an extracellular volume fraction of ∼0.2 (14). E and F, two GdDTPA concentration profiles in the extracellular volume along the lines drawn in (D). Note the steep decrease in the concentration from the tumor rim to its center.

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Figure 6.

Parametric images of T₁ relaxation times and calculated GdDTPA concentration maps and profiles at steady state of orthotopic MCF7 tumor. A and B, pre-contrast T₁ map and T₁ map 90 minutes after the start of slow infusion, respectively. Tumor region of interest was delineated on the corresponding T₂-weighted image and duplicated on the T₁ maps. C, map of steady-state tissue GdDTPA concentration 90 minutes after the start of infusion. D, map of steady-state GdDTPA concentration in the extracellular volume 90 minutes after the start of infusion. The map was derived from (C) measuring a mean extracellular volume fraction of 0.4 in this tumor. E and F, two GdDTPA concentration profiles in the extracellular volume along the lines drawn in (D). The IFP of this tumor was 10 mm Hg, in accord with the presence of contrast material throughout the tumor, including the center; however, there is still a descending concentration gradient from the periphery to the center.

The cells in the H460 tumors were distributed homogeneously and were densely packed as was revealed in the histologic slices ( Fig. 1A and B). We estimated an extracellular volume fraction of 0.2, which is close to the low limit of this variable as was shown in previous measurements ( 14). MCF7 tumors revealed less dense cellular packing than that found in H460 tumors. The extracellular volume fraction of these cells was estimated to be 0.4 using diffusion MRI studies as was previously described ( 22). This enabled us to calculate maps of GdDTPA concentration in the extracellular volume of H460 and MCF7 tumors ( Figs. 5D and 6D, respectively). The profiles of this distribution from one side of the tumor to the opposite side ( Figs. 5E and F and 6E and F) show that in the rim, GdDTPA concentration is similar to that found in the blood as expected for a low, or null, IFP. However, towards the tumor center, GdDTPA concentration decreases, reaching very low or null concentrations in the inner parts in accord with the presence of high IFP. A linkage between steady-state GdDTPA concentration and IFP was also found for the two types of tumors; GdDTPA concentration in central parts of MCF7 tumors was consistently higher than that found in H460 tumors, in accord with their lower IFP.

Assuming a linear relation between GdDTPA concentration at steady state and IFP, and using an average scaling of the range of IFP from 0 to 28 mm Hg (based on the wick-in-needle measurements), yielded estimated IFP maps and profiles as shown in Fig. 7 for three H460 tumors. The linear relation was based on the assumption that the flux of GdDTPA is predominantly determined by the extravasation across the capillary walls and that the effect of transport in the interstitium is negligible.

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Figure 7.

Estimated IFP maps and profiles of typical ectopic H460 tumors. The IFP maps were derived as described in Materials and Methods. Tumor region of interest was delineated on the corresponding T₂-weighted image and duplicated on the maps. The IFP profiles were calculated along the lines drawn on the corresponding IFP maps.

Attempts were made to analyze the change in contrast enhancement in the dynamic phase, before reaching a steady state, according to the physiologic-model proposed by Tofts and Berkowitz ( 27). This model does not take into consideration fluxes due to differences in the hydrostatic pressure in the capillaries and the IFP, and therefore may fail to yield relevant results in tumors with high IFP. Indeed, analysis of the dynamic data in H460 tumors that exhibited high IFP yielded k_in values of (1.1 ± 0.43) × 10⁻² min⁻¹ and k_ep values of (0.96 ± 0.38) × 10⁻² min⁻¹, resulting in unrealistically high median k_in/k_ep values of ∼1.0, which, according to the model, estimate the extracellular volume fraction. In contrast, analysis of the dynamics in MCF7 tumors with a lower IFP yielded k_in values of (1.1 ± 0.2) × 10⁻² min⁻¹ and k_ep values of (3.0 ± 0.9) × 10⁻² min⁻¹, resulting in a median k_in/k_ep of 0.4 ± 0.1, which was similar to the extracellular volume fraction measured by the MRI diffusion method. We therefore conclude that it is important to include in the model of dynamic contrast enhancement terms that will account for pressure gradients, particularly in tumors with high IFP.

Discussion

The aim of this work was to estimate the in vivo distribution of IFP in tumors by a new MRI application that employs the most common contrast agent, GdDTPA. We found that human H460 non–small-cell lung cancer tumors implanted in nude mice exhibit rapid growth and elevated IFP values of ∼28 mm Hg and are therefore suitable as a tumor model in this study. For comparison, we also investigated orthotopic MCF7 human breast tumors that exhibited a lower IFP of ∼14 mm Hg and higher extracellular volume fraction but a similar distribution of blood vessels. In general, reported IFP values in tumors range between 10 and 50 mm Hg whereas IFP values in normal tissues, including the muscle tissue of nude mice, range between −2 and 0 mm Hg ( 29– 31).

In most previous dynamic contrast-enhanced MRI studies of tumors in rodents and humans, the contrast agent was administered by a bolus injection. Our initial attempts to monitor signal enhancement in H460 tumors after a bolus administration of the contrast agent showed that only a small fraction of the tumor pixels (7-25%) were enhanced (data not shown). These results suggested slow transcapillary transfer rates of GdDTPA through the microvascular network of the tumors. To improve detection of enhancement in regions with slow transfer rates, we applied a slow and long infusion protocol. Moreover, extending the infusion time to allow diffusion of GdDTPA in the interstitium (calculated tissue diffusion distance of GdDTPA is ∼2.4 mm during 90 minutes; refs. 18, 32) and reaching tumor steady-state conditions made it possible to accurately determine T₁ relaxation times at this stage. This further enabled us to map the tumor steady-state tissue GdDTPA concentration and estimate the IFP distribution.

In the absence of IFP, GdDTPA transfer from the plasma into the interstitial space and back is due to diffusion through the capillary walls and in the interstitial space in the direction of the concentration gradients. At blood and tumor steady state, the extracellular concentration throughout the tumor should be equal to the plasma concentration. Tissue GdDTPA concentration distribution under this condition would therefore be directly proportional to the extracellular volume fraction. Typically, the distribution of the steady-state tumor tissue GdDTPA concentration showed a steep decline from the rim towards the tumor center. Such a distribution was not found in the histologic sections for the cell density (and hence extracellular volume fraction), as well as for the capillary density. The observed steep decline in the tissue GdDTPA concentration, therefore, reflected an increase in IFP with regions void of GdDTPA exhibiting highest IFP.

By using an approximate homogeneous interstitial volume fraction and scaling IFP according to the wick-in-needle results, we obtained an estimation of IFP distribution in the H460 tumors ( Fig. 7). We cannot exclude small local changes in the extracellular volume fraction which could affect the calculated extracellular GdDTPA concentrations and, hence, the calculated IFP values; however, these changes will not markedly modify the general profile across the tumor. This distribution is highly comparable to the IFP distribution measured previously by the wick-in-needle and micropuncture techniques and supports this approximation ( 13, 19, 33). Furthermore, the model of Baish et al. ( 34), which described the steady-state coupling between vascular and interstitial flows, predicted uniformly elevated IFP in the central region of tumors and a rapid decline to normal tissue values of 0 mm Hg at the periphery. However, independent measurements of the spatial variations in the extracellular volume fraction and comparison with invasive regional IFP measurements are necessary to verify and standardize this slow infusion MRI method.

We further assumed a linear relation between GdDTPA concentration in the extracellular volume fraction and the IFP. In general, the spatial distribution of GdDTPA concentration in the extracellular volume fraction is a result of the transcapillary extravasation flux and the interstitial transport flux ( 14, 35). The GdDTPA extravasation flux depends on the diffusion and the hydrostatic water pressure difference between the capillary pressure and IFP [e.g., see Eq. (F) in ref. 35]. The interstitial transport flux depends on the interstitial concentration gradient (diffusion component) and pressure gradient across the tumor interstitium − convection component [e.g., see Eq (G) in ref. 35]. We have assumed that in H460 tumors, with viable cells and blood vessels distributed throughout the whole tumor, the extravasation flux is dominant; therefore, under the steady-state condition, when GdDTPA flux is zero, the concentration gradient is linearly related to IFP. However, we cannot exclude the presence of an interstitial convective term which yields at steady state a logarithmic relation between the extracellular volume fraction concentration and IFP, and hence diverts the relation from linearity.

Efforts have previously been made to generally describe fluid flow and tracer transport in solid tumors. Specifically, the pathophysiologic effects of elevated IFP in tumors have been explored by using mathematical models developed by Jain and his group ( 34, 36– 38). Their model predicted a distribution of IFP with low IFP outside the tumor in the boundary with the normal tissue, which increases as the distance from the tumor edge towards the center increases depending on the ratio of the vascular to interstitial hydraulic conductivities ( 35, 36). Thus, for high values of this ratio, a plateau of high IFP is established in a large fraction of the inner tumor volume. Milosevic et al. ( 29) extended the mathematical modeling to investigate the relationship between elevated IFP and blood flow. Their model predicted elevated tumor IFP in the range of 0 to 56 mm Hg. Recently, a mathematical model was developed which included the microstructure of the vasculature allowing variations of vascular architecture, size, and conductivity ( 39). This model captured the strong coupling of the capillary and interstitial flow occurring for highly permeable vascular walls and showed that the assumption of uniform IFP is not generally appropriate. Beard and Bassingthwaighte ( 40) also extended the modeling to include convection and diffusion in three-dimensional complex physiologic geometries. Although these models are very useful to make new predictions, it is necessary to have new experimental methods that will provide data supporting or dismissing the theoretical predictions. Our method opens the way to obtain data for evaluating these theoretical predictions.

We examined here the use of a physiologic two-compartment exchange model that was adapted for a slow infusion protocol by Tofts ( 41). The mechanisms of transfer did not include the additional contribution of IFP, and the basic assumptions made in formulating this model were the same as those made for the bolus administration of the contrast agent ( 27, 41). In the MCF7 tumors that exhibited a low IFP, we obtained physiologic reasonable influx and efflux transfer constants as well as extracellular volume fractions. However, neglecting IFP and fluxes due to pressure gradients may have influenced the calculated values of the transcapillary transfer constants, particularly in the central regions. Analysis of the dynamic data of the H460 tumors that exhibited high IFP clearly showed the weakness of this model yielding underestimated efflux transfer constants and unrealistic extracellular volume fraction. This emphasizes the need to extend the physiologic model of dynamic contrast-enhanced MRI and explicitly add the influence of pressure gradients.

In summary, although transcapillary transfer and transport of low molecular weight substances are believed to be driven mainly by passive diffusion, our results indicate that transfer of the common gadolinium-based MRI contrast agents can be pressure-driven in the presence of elevated IFP. We also showed that the distribution of the most common MRI contrast agent under steady-state conditions can serve to map IFP and predict the presence of barriers to drug delivery.