Tumors residing in the central nervous system (CNS) compromise the blood–brain barrier (BBB) via increased vascular permeability, with the magnitude of changes dependent on the tumor type and location. Current studies determine penetrability of a cancer therapeutic by administering progressively larger molecules until cutoff is observed where little to no tumor accumulation occurs. However, decades-old experimental work and mathematical modeling document methods to calculate both the size of the vascular opening (pore) with solute permeability values. In this study, we updated this classic mathematical modeling approach with quantitative fluorescence microscopy in two preclinical tumor models, allowing simultaneous administration of multiple sized tracers to determine vascular permeability at a resolution of nearly one micron. We observed that three molecules ranging from 100 Da to 70 kDa permeated into a preclinical glioblastoma model at rates proportional to their diffusion in water. This suggests the solutes freely diffused from blood to glioma across vascular pores without steric restriction, which calculates to a pore size of >140 nm in diameter. In contrast, the calculated pore size of a brain metastasis of breast cancer was approximately 10-fold smaller than glioma vasculature. This difference explains why antibodies are effective against glioblastoma but generally fail in brain metastases of breast cancer. On the basis of our observations, we hypothesize that trastuzumab most likely fails in the treatment of brain metastases of breast cancer because of poor CNS penetration, while the similar sized antibody bevacizumab is effective in the same tumor type not because it penetrates the CNS degree better, but because it scavenges VEGF in the vascular compartment, which reduces edema and permeation. Cancer Res; 77(2); 238–46. ©2016 AACR.

Major Findings
  1. There is negligible postmortem diffusion of tracer in brain given removal and freezing in isopentane occurs in less than 60 seconds.

  2. Solute uptake is unidirectional over the time period sampled.

  3. The permeability surface area product (PS) can be substituted for Kin from eq. E, as the measured Kin for all tracers are permeability limited with values that are significantly lower than 20% of cerebral vascular blood flow.

  4. That a (solute radius) is at least 6-fold smaller than p (vascular pore radius).

The incidence of brain metastasis has substantially increased and represents approximately 50% of intracranial lesions observed in humans (1, 2). Yet the literature on permeability of the blood–tumor barrier stands in opposition with >90% of the work being performed in primary tumor models. This discrepancy must be addressed as it has recently been shown that permeability of brain metastases of breast cancer in two experimental metastasis model systems is highly heterogeneous, ranging nearly 30-fold between lesions and does not directly reflect what is observed in primary tumors (3). Therefore, this study evaluates two critical permeability parameters in metastatic lesions; (i) size-dependent permeability, (ii) size of pores in tumor vasculature, as both are critical to the understanding of the size of chemotherapeutics, which can diffuse into metastatic lesions and potentially have therapeutic benefit.

Quick Guide to Equations and Assumptions

The unidirectional blood-to-brain tumor transfer constant Kin is calculated for fluorescent marker distribution according to established QAR methodology using a multiple-time uptake approach (4). Briefly, to determine the apparent terminal volume of brain and tumor distribution [Vd(app)] of the tracer at the time of sacrifice we used the following relationship:

formula

where Cbr is concentration of tracer in brain, Cbl is concentration of tracer in blood, and t is sampling time. To measure the change of tracer concentration in brain over time in terms of uptake, and as Cbl is not constant with time, we used the following relationship:

formula

where Kin is the unidirectional brain uptake coefficient of the tracer. We solved for the integral of fluorophores or 14C-AIB plasma concentrations over time by sampling the concentration in blood in experimental animals by the equation:

formula

where Cbl is concentration of tracer in blood, n is the number of blood concentrations sampled in each experiment, which varied depending on size of the tracer, and t is time.

Finally, multiple-time uptake analysis allowed us to use the tracer to serve simultaneously as the permeability and vascular marker and by definition accounts for differing times of exposure, and therefore we divided Eq. D by the terminal blood concentration as described previously (5):

formula

where Vi is the total vascular space or initial equilibrating space of the tracer in the brain vasculature (or bound to vascular endothelium) at the time of sacrifice.

Given the heterogeneity in metastatic tumors, a single-time uptake was used to measure Kin in individual animals with MDA-MB-231BR-Her2 tumors, using the following equation (6, 7)

formula

where Cbr is the amount of the compound in the lesion per unit mass of the tissue (less than a 0.5% vascular correction; ref. 7) at time T, and Cbl is the blood concentration of the compound.

To provide an estimation of the pore diffusivity of the water-soluble tracers and the number of cylindrical pores in tumor vasculature (per unit of mass of tissue), we used the following relationship (8):

formula

where δ is the mean thickness of the endothelial wall (∼10 nm), a is the approximate radius of the tracer in aqueous solution (AIB: ∼2.8A0; TX Red 625 Da: ∼7 A0; TX Red 3 kDa dextran: ∼15.9 A0 and TX Red 70 kDa dextran: ∼60 A0; refs. 9, 10), p is the approximate radius of the vascular pore, and N is the number of pores per unit of mass of tissue. Dw is the aqueous diffusion coefficient at 37°C and was estimated if not known from the following relationship:

formula

where Dw in cm2/s × 10−7 was approximately equal to AIB: ∼98; TX Red 625 Da: 40; TX Red 3 kDa dextran: 15; and TX Red 70 kDa dextran: 3.8; refs. 11, 12. To calculate the total pore area per gram (At) of tissue, we rearranged Eq. E (8):

formula

Within the normal brain vasculature, endothelial cells are sealed together by tight-junction protein complexes. This unique structure coupled with pericytes, astrocytes, and neuronal input creates a barrier that significantly restricts para-cellular diffusion of polar and or large molecules between the blood and brain (blood-brain barrier; BBB). However, the vasculature within a brain tumor is both anatomically and functionally different. Anatomically, tumors as small as 0.5 mm in diameter can promote the formation of new vessels that lack the classic BBB tight junction structure (13), have lost astrocytic contact, and have both increased vesicular density (14) and fenestrations or pores, which allow the free para-cellular passage of molecules from blood into brain (15). These anatomic changes functionally result in the brain tumor vasculature (blood–tumor barrier, BTB) having an increased permeability (16–18), which is size dependent (19, 20). For example, small molecules (<500 Da) have substantially increased diffusion rates (up to 30-fold) and larger molecules (>5,000 Da) have only an approximately 2- to 3-fold increase (21–23).

Most nonbiological chemotherapeutics (e.g., paclitaxel and doxorubicin) are typically less than 1,500 Da in size and accordingly tend to penetrate tumors through angiogenic vascular BTB pores to a significantly greater degree than in normal brain (12). Recently, numerous mAbs have been approved for the treatment of breast, colon, squamous cell carcinomas, glioma, and lymphomas/leukemias (24–26). These antibodies are approximately 100-fold larger in size than chemotherapeutics and, if they are able to cross the BTB, may have efficacy in treating both primary and metastatic tumors. Determining the size of molecules that can diffuse across the BTB is technically difficult but has been shown preclinically in models that have homogenous permeability from tumor to tumor (e.g., gliomas). In this report, we describe novel imaging methodology that allows for the simultaneous measurement of size-dependent permeability and prediction of vascular pore sizes in metastases that have heterogeneous permeability. These data are then directly compared with a primary tumor model as control, because, to the best of our knowledge, this is the first report that calculates pore size in metastatic lesions and/or any tumor in the brain that has substantial variability in permeability among different tumors.

Chemicals

Sulpho-rhodamine 101 (MW 625 Da), TX Red 3 kDa dextran lysine fixable, TX Red 70 kDa dextran lysine fixable were purchased from Molecular Probes and Invitrogen. 14C-AIB (specific activity: 55 mCi/mmole) was purchased from American Radiolabeled Chemicals. All other chemicals are of analytic grade and were purchased from Sigma.

In vivo tumor animals

Craniotomy and RG-2 tumor implantation.

All animal experiments were conducted in accordance with Institutional Animal Care and Use Committee and NIH guidelines. Intraperitoneal injections of ketamine (100–200 mg/kg) and xylazine (5–10 mg/kg) were used for anesthesia in all experiments. Human glioblastoma multiforme does not have a circumscribed border and as such we utilized the rat glioma (RG-2; obtained from ATCC in 2010 and in passage less than 6 months at the time of the experiment) tumor cell line as this model also displays an infiltrative growth pattern and is representative of human glioblastoma multiforme (27). Briefly, male Fischer-344 rats (Charles River Laboratories) were implanted stereotactically with approximately 100,000 stably eGFP-transfected RG-2 cells in 5 μL (28) at coordinates of 4.5 mm lateral to bregma and 5 mm deep.

Seven days after implantation, one of the three fluorescent markers (6 mg/kg body weight) was injected intravenously; TX Red 625 Da (0–5 minute circulation), TX Red 3 kDa dextran (0- to 20-minute circulation), or TX Red 70 kDa dextran (0- to 60-minute circulation). Six blood samples were collected throughout each experimental time period (see Fig. 1) and after collecting the final blood sample, animals were sacrificed and brain tissue was removed rapidly (<60 seconds) from the skull and flash frozen in isopentane (−50°C). Brains were then sectioned (20 μm) using a cryostat (Shandon Cryotome) at −23°C and sections were mounted on glass slides and air dried. Concentrations of the fluorophores in blood and brain were determined using fluorescent microscopy using matching tissue standards (as described previously; ref. 12). In a separate set of tumor-bearing animals, we injected 14C-AIB (100 μCi/Kg) along with a fluorophore to compare permeability differences of these tracers. After tissue preparation, fluorescence images were taken to analyze the TX Red 3-kDa dextran permeability, and autoradiograms were generated by coexposing the sections on Fujifilm FLA 7000 with tissue-calibrated 14C-standards for 4 days. The regional radioactivity was measured in tumor, contralateral regions. Quantitative analysis of the regional radioactivity was performed using MCID program (Interfocus Imaging).

Figure 1.

A, The peripheral blood concentration of the three fluorescent dyes (TX Red 625 Da, TX Red 3 kDa, and TX Red 70 kDa) at various sampling times after an intravenous injection. Data are mean ± SEM (n = 5–6). B, The relationship between clearance and molecular weight of the fluorescent marker (r2 = 0.993).

Figure 1.

A, The peripheral blood concentration of the three fluorescent dyes (TX Red 625 Da, TX Red 3 kDa, and TX Red 70 kDa) at various sampling times after an intravenous injection. Data are mean ± SEM (n = 5–6). B, The relationship between clearance and molecular weight of the fluorescent marker (r2 = 0.993).

Close modal

Metastatic tumor development

Immunocompromised female NuNu mice (Charles River Laboratories) were inoculated with 175,000 eGFP-transfected MDA-MB-231BR-Her2 cells (obtained as a gift from Pat Steeg, NIH, Womens Malignancies Branch, Bethesda, MD, in 2007 and passaged less than 6 months at the time of the experiments; were authenticated with STR profiling) via left cardiac ventricle in serum-free media. Tumors seeded the brain and were allowed to grow for 4–6 weeks. After tumor development, animals were anesthetized and administered and 14C-AIB and TX Red 625 Da or TX Red 70 kDa dextran into femoral vein and allowed to circulate for 5 to 60 minutes. At the end of the circulation period, the animals were euthanized by severing the cardiac ventricles and the brain was rapidly removed from the skull and flash frozen in isopentane (−50°C), cut coronally (20 μm), placed on slides and air dried.

Fluorescence imaging and defining tumor regions

Fluorescence was observed with an Olympus MVX-10 stereo microscope using a 2× objective (numerical aperture; 0.5) and an optical zoom of 0.63 to 6.3×. The excitation and emission of TX Red and or the TX Red dextrans was accomplished using a chroma filter (Chroma Technology Corp.) with an excitation filter of 560 ± 55 nm and an emission filter of 645 ± 75 nm. The dichromatic mirror inhibited the capture of emission wavelengths of light below 595 nm (Olympus America Inc.). Tumor-bearing brain slices were analyzed using a binary mask methodology (i.e., voxel-defined regions of interest) based upon eGFP fluorescence to define the tumor (Slidebook 4.2). Briefly, binary masking consisted of defining the tumor based upon the presence of eGFP fluorescence on a voxel-by-voxel basis. If eGFP fluorescence was present (approximately >3-fold above background), it was considered to be tumor, which was further confirmed by cresyl violet staining.

Statistical analysis

Kin was determined with linear regression using least squares analysis. One-way ANOVA analysis followed by a Bonferroni multiple comparison test was used for the evaluation of regional brain uptake data. All data represent mean ± SD unless otherwise indicated. Differences were considered significant at the P < 0.05 level. (Graphpad Prism version 5.00 for Windows, GraphPad Software).

Method development for quantitative permeability measurements

To determine permeability changes, we developed a quantitative fluorescence microscopy technique coupled to autoradiography that provides approximately 1-μm spatial resolution to evaluate permeability. Briefly, in the first set of experiments, we ascertained the terminal concentrations of the permeability markers in blood, brain, and RG-2 tumors using fluorescent standards to confirm previous results obtained with autoradiography and chromatography methods. As concentration of the marker changed with time, we determined the blood–concentration time profiles at varying times from one to 60 minutes after injection (Fig. 1A). A significant correlation (r2 = 0.99) was observed between the molecular weight of the fluorescent marker and clearance (Fig. 1B), agreeing with previous literature showing dextran conjugates undergo renal elimination with filtration rates being dependent on size (29).

Tumor-bearing brain slices were analyzed using a binary mask region-of-interest methodology based upon eGFP fluorescence to define the tumor (Fig. 2A–D). Binary masking consisted of defining the tumor based upon the presence of eGFP fluorescence on a voxel-by-voxel basis. If eGFP fluorescence was present (approximately >3-fold above background), it was considered to be tumor. Once blood and tumor concentrations of the permeability markers were determined, we utilized an intravenous multiple uptake time approach to determine the transfer coefficient (Kin) in normal brain and tumor (Fig. 2E and F; refs. 1, 2). The control Kin obtained from similar plots for all the molecules are shown in the first column of Fig. 2G. The ordinate intercept for the TX Red 625 Da and AIB was approximately 0.003 ± 0.008 mL/g (Fig. 2E) and approximately 0.004 ± 0.009 mL/g (Fig. 2F), respectively, which represents the vascular space (Vv) within brain. Similarly, the Vv was determined using similar plots for TX Red 3-kDa dextran (0.0054 ± 0.0014 mL/g) and TX Red 70-kDa dextran (0.0013 ± 0.0004). These data are consistent with the previous work (30, 31).

Figure 2.

Representative images from the simultaneous injection of 14C-AIB with TX Red 625 Da are shown. A, eGFP RG-2 tumor. B, The terminal accumulation of TX Red 625 Da. C, The accumulation of dye was then converted to an intensity image, where red is the highest area of dye accumulation and blue is the lowest. These data were then directly compared with the 14C-AIB autoradiogram (D), which shows similar degrees of accumulation of tracer. This experiment provided concurrent QAR and fluorescent data that allow a direct comparison of permeability variances. E and F, Multiple time point graphical analysis of individual experiments to calculate the transfer constant Kin in normal brain (open circles) and tumor (filled circles) for TX Red 625 Da (red dots) and 14C-AIB (blue dots) are shown, respectively. The slope of the regressed line is equivalent to Kin and the ordinate intercept is equivalent to the vascular volume of the tracer, Vi. A linear regressed line was the best fit for the data (goodness of fit; quantification of sum of squares). Scale bar, 1 mm. G, Blood-to-brain transfer coefficients for AIB, TX Red 625 Da, TX Red 3 kDa, and TX Red 70 kDa in brain and the tumor. The Kin values were obtained from individual multiple time point graphical analysis plots in each respective regions of interest. **, P < 0.01; ***, P < 0.001, respectively. Data are mean ± SD; n = 3–6 for all data points.

Figure 2.

Representative images from the simultaneous injection of 14C-AIB with TX Red 625 Da are shown. A, eGFP RG-2 tumor. B, The terminal accumulation of TX Red 625 Da. C, The accumulation of dye was then converted to an intensity image, where red is the highest area of dye accumulation and blue is the lowest. These data were then directly compared with the 14C-AIB autoradiogram (D), which shows similar degrees of accumulation of tracer. This experiment provided concurrent QAR and fluorescent data that allow a direct comparison of permeability variances. E and F, Multiple time point graphical analysis of individual experiments to calculate the transfer constant Kin in normal brain (open circles) and tumor (filled circles) for TX Red 625 Da (red dots) and 14C-AIB (blue dots) are shown, respectively. The slope of the regressed line is equivalent to Kin and the ordinate intercept is equivalent to the vascular volume of the tracer, Vi. A linear regressed line was the best fit for the data (goodness of fit; quantification of sum of squares). Scale bar, 1 mm. G, Blood-to-brain transfer coefficients for AIB, TX Red 625 Da, TX Red 3 kDa, and TX Red 70 kDa in brain and the tumor. The Kin values were obtained from individual multiple time point graphical analysis plots in each respective regions of interest. **, P < 0.01; ***, P < 0.001, respectively. Data are mean ± SD; n = 3–6 for all data points.

Close modal

Determining the size pores in a single RG-2 tumor

One significant advantage of this method is that simultaneous permeability measurements of different sized markers can be done in the same tumor, where in previous studies multiple tumors in different animals were needed to determine whether there were differences in size-dependent permeability (3, 17). As an example in this set of experiments, we injected both 14C-AIB and TX Red 625 Da in the same animal (Fig. 2). At the time of sacrifice, both brain and tumor (Fig. 2A) concentrations of the fluorophores were determined using microscopy (representative raw image data shown in Fig. 2B and C) and 14C-AIB concentrations were determined using QAR (representative raw image data shown in Fig. 2D). The transfer coefficient Kin for 14C-AIB and TX Red 625 Da in the tumor were 42 ± 1 × 10−5 mL/s/g and approximately 12 ± 0.2 × 10−5 mL/s/g. The magnitude of permeability changes (Fig. 2E) compared with normal brain (14C-AIB: 2.9 ± 1.1 × 10−5 mL/s/g; TX Red 625 Da: ∼1.3 ± 0.1 × 10−4 mL/s/g) agreed with previously reported values. Similar to the control permeability data, linkage of the dye to a progressively larger dextran reduced vascular permeability changes in the tumor. For example, the Kin for TX Red 3 kDa in tumor was only increased 5-fold in the tumor and the larger TX Red 70 kDa had only a 2-fold increase (control: 0.63 ± 0.26 × 10−5 mL/s/g; tumor: 1.8 ± 0.3 × 10−5 mL/s/g; Fig. 2E). Importantly, the ratio of unidirectional uptake of TX Red 625 Da, TX Red 70 kDa, and 14C-AIB were nearly equal to the ratio of the tracers respective aqueous diffusion constant; Dw (Table 1). These data suggest all three sized molecules can freely diffuse from blood to the glioma across vascular pores without steric restriction suggesting a pore size in the glioma model of >140 nm in diameter. These data, while obtained simultaneously in a single tumor, are consistent with the previous literature evaluating pore sizes in the vasculature of multiple gliomas (5).

Table 1.

Blood-to-brain transfer and aqueous diffusion constants for glioma

KinDw
(mL/s/g × 105)(cm2/s × 107)
TX Red 70 kDa 1.8 3.8 
TX Red 625 Da 12 40 
AIB 42 98 
AIB/TX Red 70-kDa Ratio 23.4 25.7 
AIB/TX Red 625-Da Ratio 3.5 2.5 
KinDw
(mL/s/g × 105)(cm2/s × 107)
TX Red 70 kDa 1.8 3.8 
TX Red 625 Da 12 40 
AIB 42 98 
AIB/TX Red 70-kDa Ratio 23.4 25.7 
AIB/TX Red 625-Da Ratio 3.5 2.5 

NOTE: The ratio of the unidirectional uptake of the water-soluble tracers should be nearly equal to the ratio of the tracers respective aqueous diffusion constant, Dw. This ratio has >70% equality for TX Red 625 Da, TX Red 70 kDa dextran, and 14C-AIB. The data suggest the vascular pores in glioma allow unrestricted diffusion of molecules greater than the size of IgG.

Furthermore, using data from simultaneous injections, and from all three fluorescent tracers, we were able to calculate the surface area of the pores (Eq. H) present in the glioma vasculature. Briefly, the total surface area of the pores, which allow water soluble tracers to diffuse into tumor tissue, was approximately 4.3 × 10−5 cm2/g. These data are consistent with previous work in RG-2 tumor models showing a calculated pore surface area of approximately 6.2 × 10−5 cm2/g (5). While our value is slightly lower, it may represent the difference between tumor stages; where 10 days of RG-2 tumor growth can increase vascular pore permeability by approximately 20%–30% (32), ours were implanted for 7 days to minimize peripheral pathophysiologic changes and to keep tumor and tumor vasculature normalized between animals.

Heterogenous permeability of metastatic MDA-MB-231BR-Her2 tumors

Once we had determined that our method was in general agreement for primary gliomas both in terms of regional permeability changes and in pore sizes/surface area, we applied the method to study brain metastases of breast cancer. We observed that changes in permeability from normal brain differed broadly among individual metastasis; representative images are shown in Fig. 3A–D. As can be seen qualitatively in Fig. 3, lesions one and two have an increased permeability compared with normal brain, yet are substantially less than lesion five. Of interest the mid-line lesion in Fig. 3 had the highest permeability in this sample. We have recently shown that increased expression of a desmin+ subpopulation of pericytes and reduced CD13+ pericytes and laminin α2 correlates with increased permeability (33). The heterogeneous brain metastases of breast cancer model data are in sharp contrast to the relatively homogenous glioma to glioma permeability observed in different animals. On the basis of historical reports (18), it is important to note that the BTB permeability had only a weak correlation with metastasis size (Fig. 3E and F). Quantitatively, of 174 MDA-MB-231BR-Her2 metastases, approximately 9% showed no statistical difference in permeability form normal brain, whereas approximately 75% showed relatively modest permeability increases. Only approximately 15% of the metastases demonstrated TX Red 625 Da permeability changes that were greater than 5-fold.

Figure 3.

Representative fluorescence and bright-field images of metastases developed after left cardiac injection of MDA-MB-231Br-Her2 cells. Images of the same brain sections showing eGFP tumors (A), Cresyl violet stain (B), brain accumulation of TX Red 625 Da (C), and 14C-AIB accumulation (D). Heterogenous permeability is evident in this image (A–D), where metastases 1 and 2 have relatively low tracer accumulation, lesion 3 and 4 have intermediate accumulation, and lesion 5 has a relative high accumulation. A correlation of permeability between 14C-AIB and TX Red 625 Da, TX Red 70 kDa is shown in E and F. The red line in E and F is the predicted line of permeability for each tracer, assuming there is no steric restriction in vascular pores for the water-soluble molecules to enter into tumor tissue.

Figure 3.

Representative fluorescence and bright-field images of metastases developed after left cardiac injection of MDA-MB-231Br-Her2 cells. Images of the same brain sections showing eGFP tumors (A), Cresyl violet stain (B), brain accumulation of TX Red 625 Da (C), and 14C-AIB accumulation (D). Heterogenous permeability is evident in this image (A–D), where metastases 1 and 2 have relatively low tracer accumulation, lesion 3 and 4 have intermediate accumulation, and lesion 5 has a relative high accumulation. A correlation of permeability between 14C-AIB and TX Red 625 Da, TX Red 70 kDa is shown in E and F. The red line in E and F is the predicted line of permeability for each tracer, assuming there is no steric restriction in vascular pores for the water-soluble molecules to enter into tumor tissue.

Close modal

While there were significant permeability changes in most metastatic lesions in both models, the changes were much less on average compared with the glioma model. Therefore, we set out to determine whether there were differences in the size of the pores in the metastatic vasculature that would limit accumulation of the tracer. In our analysis of the data, we observed a highly significant correlation (r2 = 0.81) between the uptake of 14C-AIB and TX Red 625 Da measured in the same metastases (Fig. 3E). However, the observed diffusion rate for TX Red 625 Da was only approximately 50% of what would be predicted (Table 2, Fig. 3E red line) if the molecule was able to freely diffuse across vascular pores without steric hindrance. To verify this in a second set of experiments, we simultaneously injected the larger TX Red 70-kDa dextran with 14C-AIB in animal that had metastatic lesions. Evaluation of this data showed no correlation of uptake with 14C-AIB (Fig. 3F) and the uptake of the larger dextran was also not consistent with pore diffusivity parameters predicted by 14C-AIB (Table 2; Fig. 3F, red line). Using these data, we then calculated the pore size present in the metastatic lesions to be approximately 10-fold smaller than what was observed in the glioma vasculature. These data strongly suggest that the metastatic vasculature is not near as porous or leaky as what is found in the primary glioma model. The implication is that chemotherapeutic uptake in metastases will be significantly restricted in comparison with gliomas.

Table 2.

Blood-to-brain transfer and aqueous diffusion constants for brain metastases

Mean Kin (mL/s/g × 105)Dw (cm2/s × 107)
TX Red 625 Da 40 
AIB 19.4 98 
AIB/TX Red 625 Da Ratio 6.3 2.5 
TX Red 70 kDa 0.8 3.8 
AIB 34.2 98 
AIB/TX Red 70 kDa Ratio 42.8 25.7 
Mean Kin (mL/s/g × 105)Dw (cm2/s × 107)
TX Red 625 Da 40 
AIB 19.4 98 
AIB/TX Red 625 Da Ratio 6.3 2.5 
TX Red 70 kDa 0.8 3.8 
AIB 34.2 98 
AIB/TX Red 70 kDa Ratio 42.8 25.7 

NOTE: The ratio of the unidirectional uptake of the water-soluble tracers should be nearly equal to the ratio of the tracers respective aqueous diffusion constant, Dw. This ratio has <70% equality for TX Red 625 Da, TX Red 70 kDa dextran, and 14C-AIB. The data suggest that the vascular pores in brain metastases restrict molecules the size of larger chemotherapeutics (∼1,000 Da) and biologic therapeutics (>100 kDa).

Surprisingly, while metastases are the most common intracranial lesion (34), there has been very little quantitative data on permeability changes in metastases, especially compared with the primary tumor literature. Most information on brain metastasis permeability in humans is qualitatively based upon CT or MRI enhancement (34) and there are only a few preclinical datasets that have used a physiologic model of brain metastasis where the hematologic transfer, implantation, and lesion growth in brain is preserved (4, 18, 35, 36). The permeability data presented herein is consistent with our previous report showing there is substantial variability between lesions (12), which differs from primary tumors (see Supplementary Figs. S1–S3 for images showing variability in tumor permeability to the different dyes).

In this work, we have examined the tumor vascular permeability using quantitative fluorescence microscopy. Crucial to the development of this methodology was the ability to quantify fluorescent dye concentration in tissue similar to what has been documented for radioisotopes in QAR studies. Briefly, this was accomplished by summing the fluorescence intensity of each fluorophore in each pixel in a defined region of interest (e.g., brain homogenates, brain, tumor, etc…). Then all images (standards and experimental) were captured using the same settings for gain, exposure, optical zoom, on naïve samples (focus was obtained in the eGFP channel) to maintain consistency of fluorescence emission (37). Using this method, the brain homogenates and blood standards had a range of linearity between fluorescence intensity and dye concentrations of approximately 3 log units, which is consistent with most QAR standards (12). This range was large enough for us to give peripheral doses of dyes that produced, at the time of sacrifice, brain and tumor dye concentrations that fell within the midpoint of the standards.

One limitation in these studies that had to be overcome was that the standard curves of fluorescence intensity versus concentration had different slopes in blood and brain. These data, similar to previous work (38), suggested that tissue matrices can alter fluorescence emission. Attenuation of fluorescence signal by blood is a well-documented phenomenon where the emitted photons of fluorescence can be transferred to the heme moieties present in the red blood cell (39). The consequences of quenching the TX Red signal in our study had the possibility of altering two pieces of critical data. First, quenching could change the accuracy of our peripheral pharmacokinetics, by not allowing an accurate determination of dye concentration in blood. However, our pharmacokinetic parameters (Fig. 1A; Table 3) are in close agreement with the two previous studies that used radiolabeled dextrans and scintillation counting (31). Furthermore, the relationship between clearance and the molecular weight of the dextran shown in Fig. 1B is consistent with the clearance of fluorescein-labeled dextrans in rats using high-performance liquid chromatography for analysis (29, 40).

Table 3.

Peripheral pharmacokinetic parameters of TX Red and TX Red Dextran conjugates

T1/2 (min)AUC (mg·min/mL)Clearance (mL/min/kg)
TX Red 625 Da 1.3 ± 0.1 0.07 ± 0.01 42.1 ± 2.7 
TX Red 3 kDa 8.4 ± 0.2 0.7 ± 0.1 8.4 ± 0.8 
TX Red 70 kDa 29.2 ± 0.5 12.4 ± 0.7 0.49 ± 0.03 
T1/2 (min)AUC (mg·min/mL)Clearance (mL/min/kg)
TX Red 625 Da 1.3 ± 0.1 0.07 ± 0.01 42.1 ± 2.7 
TX Red 3 kDa 8.4 ± 0.2 0.7 ± 0.1 8.4 ± 0.8 
TX Red 70 kDa 29.2 ± 0.5 12.4 ± 0.7 0.49 ± 0.03 

NOTE: Pharmacokinetic parameters of the fluorophores used were calculated by sampling blood at various intervals and determining concentrations from the standard curve. Values represent mean ± SD.

The second concern that fluorescence quenching in blood created in this study was a potential misrepresentation of dye concentration for the end distribution volume of in brain. This could be compounded by differences in tissue accumulation in the active growing regions of the tumor versus a necrotic core. While some necrosis is evident in an RG-2 model, consistent with our previous work, the brain metastases of breast cancer model shows little evidence of necrosis (12, 21). While this cannot be easily rectified, we believe that the small volume of blood per mass of tissue (assumed to be ∼1% in normal brain and possibly as high as 4% in tumor or tumor core) did not significantly affect the calculated permeability value. For example, TX Red 3-kDa dextran has a molecular radius in fluid of approximately 15.9 A° (41, 42), for which we obtained a mean Kin value of approximately 4.0 × 10−6 mL/s/g in normal brain (Fig. 3). In comparison, 14C-inulin (MW 5.5 kDa) has a similar radius of approximately 15 A° (31), for which a permeability value of approximately 2.2 × 10−6 mL/s/g was observed using radiolabeled isotopes and similar mathematical modeling (43). The observed permeability changes (fold increase) in tumor, which is based upon size, is consistent with the magnitude of change observed in prior literature.

Once we had determined that our method was general validity in measuring the permeability alterations in tumor vasculature, we determined the size of pores in the tumors. Our data suggest that there is substantial discrepancy between the size of the molecule that can freely diffuse into gliomas and metastatic lesions. To make this comparison mathematically, we calculated the size of the vascular pores based upon theories of pore diffusivity. The pore theory model postulates water-soluble tracers that are trapped to a large degree in the normal brain vasculature will enter into tumor tissue through “cylindrical pores” or channels in the newly formed vasculature. Furthermore, if the pores are large enough, the molecules should enter into the tumor tissue at a transfer rate that is proportionately similar to their diffusion rates in water. For the glioma model, the largest Dextran tested (70 kDa) diffused across the tumor vasculature at approximately the same ratio rate (compared with 14C-AIB) as it would in water. This suggests that the 70-kDa dextran (∼12 nm in diameter) is able to freely diffuse from blood through angiogenic vascular pores into tumor. In order for this free diffusion to occur, the diameter of the vascular pore must be at least 12 times greater than the diameter of the largest molecule for which the diffusion constant remained proportionately constant (5), and accordingly the diameter of the vascular pore in the RG-2 tumor is ≥ 140 nm. These calculations assume that molecules with similar hydrodynamic radii have similar rates of permeability across a vascular pore. However, there are data demonstrating that nanorods have increased permeability rates across a tumor vessel compared with a similar hydrodynamic-sized nanosphere. It is thought that the nanorod may have reduced steric hindrance and viscous drag during vascular flow and as it inters the vascular pore (44).

While tertiary and quaternary structured proteins are different in shape to an aqueous dextran, in theory, the pore size of the glioblastoma vasculature is sufficiently large to allow the 149-kDa mAb (∼10 nm in size (45) to freely accumulate into tumor tissue, and may be a reason bevacizumab and other mAbs are showing promise in the treatment of gliomas (46). It can also be reasoned that VEGF (∼3 nm) can exit from the tumor into the circulation through these vascular pores. As the VEGR-2 is expressed approximately symmetrically on the luminal and abluminal side of the blood (47), we propose bevacizumab may pharmacologically act in the circulation as well to reduce effects of VEGF on the vasculature. This hypothesis is consistent and builds upon previous work that suggests normalization of the vasculature by blockade of the VEGFR-2 allows the permeability of smaller nanometer molecules (<12 nm) across the tumor vasculature (48). This may be a primary reason there are concerns that bevacizumab may normalize the BTB and limit chemotherapeutic efficacy and allow tumor growth (49, 50).

In contrast to the glioma model in which the pores were large enough to allow unrestricted passive diffusion of TX Red 70 kDa, in the brain metastases of breast cancer model, passive diffusion rates of the solutes across the BTB were observed to be approximately 40%–60% less than predicted unrestricted values based off of proportionate diffusion rates in water. This degree of restriction suggests that there is steric hindrance in the pore for free diffusion of large molecules (5). Using similar calculations from the glioma model the pore size may be only approximately 9 nm in diameter and may be as small as approximately 5 nm based upon the size of free TX Red. Although these are average measurements and the spread of the actual pore sizes in the vasculature is most likely very heterogeneous. Importantly, if the free dye and the 70-kDa dextran demonstrated significantly restricted permeability then trastuzumab at an approximate size of 5.5–6 nm will be restricted from diffusing across vascular pores into the metastatic lesion as well. However, we propose similar to gliomas, VEGF may be able to cross the vascular pores (though in a more restricted fashion) from the tumor into the circulation and this may be a factor in how bevacizumab is able to demonstrate antiangiogenic effects in brain metastases.

In summary, the data presented herein have shown in preclinical models that: (i) permeability of brain metastases is highly heterogenous and significantly reduced compared with gliomas; (ii) there are pore size restrictions that may limit the use of mAbs in metastatic lesions; and (iii) the location for the action for bevacizumab in brain metastases may be limited to the luminal side of the vasculature.

No potential conflicts of interest were disclosed.

Conception and design: R.K. Mittapalli, P.R. Lockman

Development of methodology: R.K. Mittapalli, C.E. Adkins, P.R. Lockman

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): C.E. Adkins, A.S. Mohammad, J.A. Lockman, P.R. Lockman

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): R.K. Mittapalli, C.E. Adkins, K.A. Bohn, A.S. Mohammad, P.R. Lockman

Writing, review, and/or revision of the manuscript: R.K. Mittapalli, C.E. Adkins, K.A. Bohn, A.S. Mohammad, J.A. Lockman, P.R. Lockman

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): C.E. Adkins, A.S. Mohammad, J.A. Lockman, P.R. Lockman

Study supervision: A.S. Mohammad, P.R. Lockman

We thank Robert Thorne, PhD, for his valuable input into the manuscript.

This research was supported by grants from the National Cancer Institute (R01CA166067-01A1) and Department of Defense Breast Cancer Research Program (W81XWH-062-0033; awarded to P.R. Lockman). Additional support for this research was provided by WVCTSI through the National Institute of General Medical Sciences of the NIH (U54GM104942).

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1.
Leyland-Jones
B
. 
Human epidermal growth factor receptor 2-positive breast cancer and central nervous system metastases
.
J Clin Oncol
2009
;
27
:
5278
86
.
2.
Lin
NU
,
Winer
EP
. 
Brain metastases: the HER2 paradigm
.
Clin Cancer Res
2007
;
13
:
1648
55
.
3.
Lockman
PR
,
Mittapalli
RK
,
Taskar
KS
,
Rudraraju
V
,
Gril
B
,
Bohn
KA
, et al
Heterogeneous blood-tumor barrier permeability determines drug efficacy in experimental brain metastases of breast cancer
.
Clin Cancer Res
2010
;
16
:
5664
78
.
4.
Patlak
CS
,
Blasberg
RG
,
Fenstermacher
JD
. 
Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data
.
J Cereb Blood Flow Metab
1983
;
3
:
1
7
.
5.
Blasberg
RG
,
Fenstermacher
JD
,
Patlak
CS
. 
Transport of alpha-aminoisobutyric acid across brain capillary and cellular membranes
.
J Cereb Blood Flow Metab
1983
;
3
:
8
32
.
6.
Asotra
K
,
Ningaraj
N
,
Black
KL
. 
Measurement of blood-brain and blood-tumor barrier permeabilities with [14C]-labeled tracers
.
Methods Mol Med
2003
;
89
:
177
90
.
7.
Blasberg
RG
,
Shapiro
WR
,
Molnar
P
,
Patlak
CS
,
Fenstermacher
JD
. 
Local blood-to-tissue transport in Walker 256 metastatic brain tumors
.
J Neurooncol
1984
;
2
:
205
18
.
8.
Nakagawa
H
,
Groothuis
DR
,
Owens
ES
,
Fenstermacher
JD
,
Patlak
CS
,
Blasberg
RG
. 
Dexamethasone effects on [125I]albumin distribution in experimental RG-2 gliomas and adjacent brain
.
J Cereb Blood Flow Metab
1987
;
7
:
687
701
.
9.
Armstrong
JK
,
Wenby
RB
,
Meiselman
HJ
,
Fisher
TC
. 
The hydrodynamic radii of macromolecules and their effect on red blood cell aggregation
.
Biophys J
2004
;
87
:
4259
70
.
10.
Frigon
RP
,
Leypoldt
JK
,
Uyeji
S
,
Henderson
LW
. 
Disparity between Stokes radii of dextrans and proteins as determined by retention volume in gel permeation chromatography
.
Anal Chem
1983
;
55
:
1349
54
.
11.
Mastro
AM
,
Keith
AD
. 
Diffusion in the aqueous compartment
.
J Cell Biol
1984
;
99
:
180s
87s
.
12.
Sugaya
R
,
Wolf
BA
,
Kita
R
. 
Thermal diffusion of dextran in aqueous solutions in the absence and the presence of urea
.
Biomacromolecules
2006
;
7
:
435
40
.
13.
Front
D
,
Israel
O
,
Kohn
S
,
Nir
I
. 
The blood-tissue barrier of human brain tumors: correlation of scintigraphic and ultrastructural findings: concise communication
.
J Nucl Med
1984
;
25
:
461
5
.
14.
Bertossi
M
,
Virgintino
D
,
Maiorano
E
,
Occhiogrosso
M
,
Roncali
L
. 
Ultrastructural and morphometric investigation of human brain capillaries in normal and peritumoral tissues
.
Ultrastruct Pathol
1997
;
21
:
41
9
.
15.
Hirano
A
,
Matsui
T
. 
Vascular structures in brain tumors
.
Hum Pathol
1975
;
6
:
611
21
.
16.
Blasberg
RG
,
Gazendam
J
,
Patlak
CS
,
Shapiro
WS
,
Fenstermacher
JD
. 
Changes in blood-brain transfer parameters induced by hyperosmolar intracarotid infusion and by metastatic tumor growth
.
Adv Exp Med Biol
1980
;
131
:
307
19
.
17.
Groothuis
DR
,
Fischer
JM
,
Pasternak
JF
,
Blasberg
RG
,
Vick
NA
,
Bigner
DD
. 
Regional measurements of blood-to-tissue transport in experimental RG-2 rat gliomas
.
Cancer Res
1983
;
43
:
3368
73
.
18.
Hasegawa
H
,
Ushio
Y
,
Hayakawa
T
,
Yamada
K
,
Mogami
H
. 
Changes of the blood-brain barrier in experimental metastatic brain tumors
.
J Neurosurg
1983
;
59
:
304
10
.
19.
Black
KL
,
Chio
CC
. 
Increased opening of blood-tumour barrier by leukotriene C4 is dependent on size of molecules
.
Neurol Res
1992
;
14
:
402
4
.
20.
Nomura
T
,
Inamura
T
,
Black
KL
. 
Intracarotid infusion of bradykinin selectively increases blood-tumor permeability in 9L and C6 brain tumors
.
Brain Res
1994
;
659
:
62
6
.
21.
Adkins
CE
,
Mohammad
AS
,
Terrell-Hall
TB
,
Dolan
EL
,
Shah
N
,
Sechrest
E
, et al
Characterization of passive permeability at the blood-tumor barrier in five preclinical models of brain metastases of breast cancer
.
Clin Exp Metastasis
2016
;
33
:
373
83
.
22.
Adkins
CE
,
Nounou
MI
,
Hye
T
,
Mohammad
AS
,
Terrell-Hall
T
,
Mohan
NK
, et al
NKTR-102 Efficacy versus irinotecan in a mouse model of brain metastases of breast cancer
.
BMC Cancer
2015
;
15
:
685
.
23.
Mittapalli
RK
,
Liu
X
,
Adkins
CE
,
Nounou
MI
,
Bohn
KA
,
Terrell
TB
, et al
Paclitaxel-hyaluronic nanoconjugates prolong overall survival in a preclinical brain metastases of breast cancer model
.
Mol Cancer Ther
2013
;
12
:
2389
99
.
24.
Filipits
M
. 
Clinical relevance of monoclonal antibodies in non small cell lung cancer
.
J BUON
2009
;
14
Suppl 1
:
S147
52
.
25.
Eng
C
. 
The evolving role of monoclonal antibodies in colorectal cancer: early presumptions and impact on clinical trial development
.
Oncologist
2010
;
15
:
73
84
.
26.
Iwamoto
FM
,
Fine
HA
. 
Bevacizumab for malignant gliomas
.
Arch Neurol
2010
;
67
:
285
8
.
27.
Sibenaller
ZA
,
Etame
AB
,
Ali
MM
,
Barua
M
,
Braun
TA
,
Casavant
TL
, et al
Genetic characterization of commonly used glioma cell lines in the rat animal model system
.
Neurosurg Focus
2005
;
19
:
E1
.
28.
Ningaraj
NS
,
Rao
MK
,
Black
KL
. 
Adenosine 5′-triphosphate-sensitive potassium channel-mediated blood-brain tumor barrier permeability increase in a rat brain tumor model
.
Cancer Res
2003
;
63
:
8899
911
.
29.
Mehvar
R
,
Robinson
MA
,
Reynolds
JM
. 
Dose dependency of the kinetics of dextrans in rats: effects of molecular weight
.
J Pharm Sci
1995
;
84
:
815
8
.
30.
Sisson
WB
,
Oldendorf
WH
. 
Brain distribution spaces of mannitol-3H, inulin-14C, and dextran-14C in the rat
.
Am J Physiol
1971
;
221
:
214
7
.
31.
Smith
QR
,
Ziylan
YZ
,
Robinson
PJ
,
Rapoport
SI
. 
Kinetics and distribution volumes for tracers of different sizes in the brain plasma space
.
Brain Res
1988
;
462
:
1
9
.
32.
Bartus
RT
,
Snodgrass
P
,
Dean
RL
,
Kordower
JH
,
Emerich
DF
. 
Evidence that Cereport's ability to increase permeability of rat gliomas is dependent upon extent of tumor growth: implications for treating newly emerging tumor colonies
.
Exp Neurol
2000
;
161
:
234
44
.
33.
Lyle
LT
,
Lockman
PR
,
Adkins
CE
,
Mohammad
AS
,
Sechrest
E
,
Hua
E
, et al
Alterations in pericyte subpopulations are associated with elevated blood-tumor barrier permeability in experimental brain metastasis of breast cancer
.
Clin Cancer Res
2016
;
22
:
5287
99
.
34.
Gerstner
ER
,
Fine
RL
. 
Increased permeability of the blood-brain barrier to chemotherapy in metastatic brain tumors: establishing a treatment paradigm
.
J Clin Oncol
2007
;
25
:
2306
12
.
35.
Zhang
RD
,
Price
JE
,
Fujimaki
T
,
Bucana
CD
,
Fidler
IJ
. 
Differential permeability of the blood-brain barrier in experimental brain metastases produced by human neoplasms implanted into nude mice
.
Am J Pathol
1992
;
141
:
1115
24
.
36.
Zhang
Z
,
Hatori
T
,
Nonaka
H
. 
An experimental model of brain metastasis of lung carcinoma
.
Neuropathology
2008
;
28
:
24
8
.
37.
Song
L
,
Varma
CA
,
Verhoeven
JW
,
Tanke
HJ
. 
Influence of the triplet excited state on the photobleaching kinetics of fluorescein in microscopy
.
Biophys J
1996
;
70
:
2959
68
.
38.
Welch
AJ
,
Gardner
C
,
Richards-Kortum
R
,
Chan
E
,
Criswell
G
,
Pfefer
J
, et al
Propagation of fluorescent light
.
Lasers Surg Med
1997
;
21
:
166
78
.
39.
Kim
J
,
Kim
J-M
. 
Fluorescence quenching of a partially conjugated polymer by hemoglobin
.
Macromol Res
2007
;
15
:
90
92
.
40.
Mehvar
R
,
Shepard
TL
. 
Molecular-weight-dependent pharmacokinetics of fluorescein-labeled dextrans in rats
.
J Pharm Sci
1992
;
81
:
908
12
.
41.
Ghandehari
H
,
Smith
PL
,
Ellens
H
,
Yeh
PY
,
Kopecek
J
. 
Size-dependent permeability of hydrophilic probes across rabbit colonic epithelium
.
J Pharmacol Exp Ther
1997
;
280
:
747
53
.
42.
Dreher
MR
,
Liu
W
,
Michelich
CR
,
Dewhirst
MW
,
Yuan
F
,
Chilkoti
A
. 
Tumor vascular permeability, accumulation, and penetration of macromolecular drug carriers
.
J Natl Cancer Inst
2006
;
98
:
335
44
.
43.
Lucchesi
KJ
,
Gosselin
RE
. 
Mechanism of L-glucose, raffinose, and inulin transport across intact blood-brain barriers
.
Am J Physiol
1990
;
258
:
H695
705
.
44.
Chauhan
VP
,
Popovic
Z
,
Chen
O
,
Cui
J
,
Fukumura
D
,
Bawendi
MG
, et al
Fluorescent nanorods and nanospheres for real-time in vivo probing of nanoparticle shape-dependent tumor penetration
.
Angew Chem Int Ed Engl
2011
;
50
:
11417
20
.
45.
Reth
M
. 
Matching cellular dimensions with molecular sizes
.
Nat Immunol
2013
;
14
:
765
7
.
46.
Zuniga
RM
,
Torcuator
R
,
Jain
R
,
Anderson
J
,
Doyle
T
,
Ellika
S
, et al
Efficacy, safety and patterns of response and recurrence in patients with recurrent high-grade gliomas treated with bevacizumab plus irinotecan
.
J Neurooncol
2009
;
91
:
329
36
.
47.
Feng
D
,
Nagy
JA
,
Brekken
RA
,
Pettersson
A
,
Manseau
EJ
,
Pyne
K
, et al
Ultrastructural localization of the vascular permeability factor/vascular endothelial growth factor (VPF/VEGF) receptor-2 (FLK-1, KDR) in normal mouse kidney and in the hyperpermeable vessels induced by VPF/VEGF-expressing tumors and adenoviral vectors
.
J Histochem Cytochem
2000
;
48
:
545
56
.
48.
Chauhan
VP
,
Stylianopoulos
T
,
Martin
JD
,
Popovic
Z
,
Chen
O
,
Kamoun
WS
, et al
Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner
.
Nat Nanotechnol
2012
;
7
:
383
8
.
49.
de Groot
JF
,
Fuller
G
,
Kumar
AJ
,
Piao
Y
,
Eterovic
K
,
Ji
Y
, et al
Tumor invasion after treatment of glioblastoma with bevacizumab: radiographic and pathologic correlation in humans and mice
.
Neuro Oncol
2010
;
12
:
233
42
.
50.
Pishko
GL
,
Muldoon
LL
,
Pagel
MA
,
Schwartz
DL
,
Neuwelt
EA
. 
Vascular endothelial growth factor blockade alters magnetic resonance imaging biomarkers of vascular function and decreases barrier permeability in a rat model of lung cancer brain metastasis
.
Fluids Barriers CNS
2015
;
12
:
5
.