© The Author 2006. Published by Oxford University Press.
ARTICLE |
Use of Three-Dimensional Tissue Cultures to Model Extravascular Transport and Predict In Vivo Activity of Hypoxia-Targeted Anticancer Drugs
Affiliations of authors: Auckland Cancer Society Research Centre, The University of Auckland, Auckland, New Zealand (KOH, FBP, MPH, WAD, WRW); Department of Physiology, University of Arizona, Tucson, AZ (TWS, RH); Department of Radiation Oncology, Stanford University School of Medicine, Stanford, CA (JMB); Department of Radiation Oncology, Duke University Medical Center, Durham, NC (MWD)
Correspondence to: Kevin O. Hicks, PhD, Auckland Cancer Society Research Centre, The University of Auckland, Private Bag 92019, Auckland, New Zealand (e-mail: k.hicks{at}auckland.ac.nz).
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ABSTRACT |
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 TopNotes Abstract IntroductionMaterials and methodsResultsDiscussionReferences |
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Background: Because of the inefficient vasculature of solid tumors, anticancer drugs must penetrate relatively long distances through the extravascular compartment. The requirement for such diffusion may limit their activity, especially that of hypoxia-targeted drugs. We tested whether a three-dimensional pharmacokinetic/pharmacodynamic (PK/PD) model based on a representative mapped tumor microvascular network could predict the therapeutic activity of anticancer drugs in mouse xenograft tumors. Methods: Diffusion coefficients of the hypoxia-activated anticancer drug tirapazamine (TPZ) and of 15 TPZ analogs were estimated by measuring their transport through HT29 colon cancer multicellular layers (MCLs). Anoxic cytotoxic potency (by clonogenic assay) and metabolism of the TPZ analogs were measured in HT29 cell suspensions, and their plasma pharmacokinetics was measured in CD-1 nude mice. This information was used to create a spatially resolved PK/PD model for the tumor microvascular network. Model predictions were compared with actual hypoxic cell kill as measured by clonogenic assays on HT29 xenograft tumors 18 hours after treatment with each TPZ analog. Results: Modeling TPZ transport in the tumor microvascular network showed substantial drug depletion in the most hypoxic regions, with predicted maximum cell kill of only 3 logs, compared with more than 10 logs if there were no transport impediment. A large range of tissue diffusion coefficients (0.027 x 10–6–1.87 x 10–6 cm2/s) was observed for the TPZ analogs. There was a strong correlation between model-predicted and measured hypoxic cell kill (R2 = 0.89) but a poor correlation when the model did not include extravascular transport (R2 = 0.32). Conclusions: Extravascular transport in tumors, and its consequences for tumor cell killing, can be predicted by measuring drug penetration through MCLs in vitro and modeling pharmacokinetics at each position in three-dimensional microvascular networks.
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INTRODUCTION |
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TopNotesAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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In therapeutic drug monitoring, measurement of drug concentration is usually confined to the plasma, with the assumption that plasma concentrations accurately reflect concentration at the site of action. A central problem in cancer pharmacology is that this assumption may often be invalid (1,2) because of inefficient blood supply in tumors, although there is little information on the magnitude of this problem for small-molecule drugs. It is well known that the microvascular system in many tumors is functionally inadequate, as demonstrated by the widespread occurrence of hypoxia and necrosis (3,4). Tumors typically contain irregular, tortuous networks of leaky microvessels with heterogeneous blood flow and large intervessel distances (5). These features, together with the lack of functional lymphatic drainage and high interstitial pressures, make diffusion, rather than convection, the dominant mechanism of extravascular transport of nutrients and drugs in tumors (6). Because many cancer cells are at greater distances from capillaries than are cells in normal tissues, inadequate penetration of antitumor agents into the extravascular compartment is considered a limitation in cancer therapy (7,8). However, the lack of suitable experimental models has made it difficult to address the issue of drug penetration in tumors explicitly during drug discovery and development. The purpose of this study was to develop a theoretical framework for understanding small-molecule drug distribution at the microregional level in tumors and to validate this approach for one class of anticancer agents.
To develop a model of drug distribution in tumors, information on parameters affecting extravascular transport properties of drugs (including diffusion coefficients and kinetics of reaction in tissues) is needed. One way to obtain such information is from drug transport studies using multicellular layer (MCL) cultures of human tumor cells in vitro (2,9–11). MCLs, which are grown by seeding tumor cells on a permeable support membrane, form diffusion-limited structures (typically 10–20 cells in thickness) at tissue-like cell densities. Unlike other three-dimensional tissue culture models, MCLs provide the opportunity to use compound-specific analytic techniques, such as high-performance liquid chromatography (HPLC), that distinguish parent drug from drug metabolites. To measure the kinetics of drug penetration, MCLs are placed between two compartments of a diffusion chamber (Fig. 1), and the time course of disappearance of drug from one compartment (donor) and its appearance in the other (receiver) is measured. However, to understand the pharmacologic significance of MCL penetration kinetics, it is essential to fit these data to diffusion–reaction models and thus determine the parameters that control these extravascular transport properties. These parameters can then be used to model the pharmacokinetics and pharmacodynamics of the drugs in tumors under the constraints imposed by plasma pharmacokinetics and microvascular geometry.
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Here we have developed a pharmacokinetic/pharmacodynamic (PK/PD) model to predict cell kill within tumors. We focused on analogs of tirapazamine (TPZ). This small-molecule drug, which is currently in phase III clinical trials (12), is selectively toxic to hypoxic cells (13) because it undergoes enzymatic reduction to a DNA-damaging free radical under hypoxic conditions (14,15) but is back oxidized to the nontoxic parent under aerobic conditions (16). Hypoxic cells are important targets in cancer therapy because they are more resistant than well-oxygenated cells to radiotherapy and many forms of chemotherapy (17). A series of TPZ analogs provides a useful test of the model because the target (i.e., hypoxic) cells are those that are most distant from the functional vasculature, suggesting that efficient extravascular transport will be essential for optimal activity. Indeed, TPZ shows lower selectivity for hypoxic cells in tumor xenografts than in single-cell cultures (18), and studies with multicellular spheroids (19) and MCLs (9,11) suggest that reductive metabolism of TPZ is fast enough to compromise its penetration, leading to lower drug exposure in hypoxic tissue. The TPZ analogs (Supplementary Table 1) were selected to span a range of physicochemical properties expected to influence extravascular transport. In particular, their measured octanol–water partition coefficients at pH 7.4 (P7.4), a major determinant of diffusion coefficients of TPZ analogs in MCLs of HT29 colon cancer cells (20), spanned nearly three orders of magnitude (log P7.4 ranges from –1.15 for compound 4 to 1.70 for 15). In addition, four compounds (12–15) contained an acridine (DNA intercalating) moiety, which is expected to increase cytotoxic potency (21) but impede extravascular transport (2,10).
We have previously shown that measurements of the metabolism and diffusion of TPZ in MCLs can be incorporated in a one-dimensional spatially resolved PK/PD model to explain the reduced cell killing by TPZ in anoxic HT29 MCLs relative to single-cell suspensions (22). We now extend this PK/PD model to three-dimensional tumors using rates of drug metabolism from stirred cell cultures and diffusion coefficients measured in MCLs to assess extravascular transport and plasma pharmacokinetics measured in nude mice to determine drug concentrations in the vascular compartment. We modeled tumor pharmacokinetics of TPZ and its analogs using a real microvascular network whose structure had been derived from confocal microscopic observations of a tumor growing in a window chamber (Fig. 2, A) (23). We then added a cellular pharmacodynamic model based on stirred cell cultures and tested the ability of the three-dimensional PK/PD model to predict the activity of the TPZ analogs against hypoxic cells in HT29 human tumor xenografts in mice. Hypoxic cell killing was assessed specifically by exploiting the selectivity of ionizing radiation for aerobic cells in tumors (24). Because of this selectivity, the increased cell kill caused by the combined effect of radiation and drug over that caused by radiation provides a measure of the ability of the drugs to kill the radioresistant hypoxic cells.
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MATERIALS AND METHODS |
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TopNotesAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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Compound Formulation and Physicochemical Parameters
The syntheses of TPZ and compounds 1–4 (25), 7, 9 (26), 10, 11 (27), 12 (28), and 13, 14 (21) have been previously reported. Synthesis of compounds 5, 6, 8, and 15 are described in the Supplementary Methods (available at: http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16). In vitro experiments used frozen (–80 °C) DMSO stock solutions of the compounds diluted at least 100-fold into culture medium. For in vivo studies, DMSO solutions were diluted 20-fold into saline or lactic acid buffer. Concentrations of all solutions were determined by absorbance spectrophotometry. Octanol/aqueous buffer (pH 7.4) partition coefficients were determined at room temperature using the shake flask method (29) (0.5 mL in each phase) with drug concentrations in both the octanol and buffer phases analyzed by HPLC (20,22).
Cell Culture
HT29 human colon carcinoma cells from American Type Culture Collection (Manassas, VA) were cultured as monolayers in 
minimal essential medium (MEM, Gibco, Invitrogen Corporation, Carlsbad, CA) with 5% heat-inactivated fetal bovine serum (FBS, Gibco). Cultures were used within 12 passages from frozen stocks, which were confirmed free of Mycoplasma. Cells were prepared for studies of drug metabolism and clonogenicity and for inoculation into mice by growing them as multicellular spheroids in spinner flasks (22,30). The spheroids were enzymatically dissociated using 0.05% trypsin/EDTA (Gibco), with magnetic stirring for 10 minutes to prepare single-cell suspensions.
Drug Metabolism and Cytotoxicity
TPZ analogs that were selective for hypoxic cells were chosen by evaluation of the antiproliferative potencies (IC50) of analogs in 96-well plates under both aerobic and anoxic conditions, as described (25). The hypoxic–cytotoxic ratio was calculated as the ratio of the aerobic IC50 to the anoxic IC50 from a given experiment. The cytotoxic potency of TPZ analogs in anoxic HT29 cell suspensions was also assessed by clonogenic assays (loss of colony forming potential), and metabolic consumption of the compounds was measured in the same experiments as described previously for TPZ (22). Briefly, suspensions of HT29 cells (10 mL at 1 or 2 x 106 cells/mL) were incubated in MEM without serum in magnetically stirred 20-mL bottles under flowing 5% CO2/95% N2 for 90 minutes. Drugs were then introduced using deoxygenated DMSO stock solutions to give initial concentrations (C0) in the medium that permitted approximately 10% cell survival after 1 hour. DMSO-only controls were included in each experiment. Samples (0.5 mL) were removed at intervals (typically 5 and 30 minutes and 1, 2, and 3 hours), quickly equilibrated with air to prevent further drug metabolism, and centrifuged at 16 000g for 1 minute. The supernatant was stored at –80 °C for subsequent HPLC analysis, and the cell pellet was resuspended in fresh MEM with 10% FBS. Serial dilutions were plated into 5 mL of this medium in 60-mm cell culture dishes. The plates were incubated at 37 °C for 14 days and stained with methylene blue, and colonies (>50 cells) were counted to determine the plating efficiency (PE). Surviving fraction (SF) was calculated at each time as PE(treated)/PE(controls). The percentage of viable cells at the end of drug exposure was determined by analyzing the exclusion of 0.4% trypan blue using a hemocytometer; more than 85% of cells were viable in all experiments. Oxygen in solution was measured using an OxyLite 2000 O2 luminescent fiber optic probe (Oxford Optronix Ltd, Oxford, UK) as previously described (30); oxygen concentrations were <0.1 µM O2 in all cases. An internal reference (TPZ at 30 µM) was included in all experiments for quality control. Metabolic consumption of the compounds was assessed using HPLC of the thawed supernatants (see below) to measure extracellular drug concentrations (C) as a function of time (t). For each compound, the rate of drug metabolism was fitted by regression as a first-order process to determine the rate constant for metabolism (kmet) under anoxia for that compound.
The clonogenicity data for each compound were fitted to one of three cellular PK/PD models in which surviving fraction is related to cumulative drug metabolism (M):
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 | [1b] |
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where , 
, and 
are proportionality constants. M is calculated as
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where 
is the HT29 cell volume fraction (intracellular volume divided by total culture volume) determined previously (22), and C0 is the drug concentration at time zero (see supplementary information for further details; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16). The proportionality constant for each one-parameter model was fitted to the clonogenicity data by regression, and the model with the best fit (i.e., with the highest R2) was used for predicting in vivo activity.
Multicellular Layer Diffusion Studies
MCL cultures of HT29 cells were grown in MEM with 10% FBS as described (20,22). TPZ analogs were added to the donor compartments of diffusion chambers (Fig. 1) at 10–50 µM along with approximately 1 µM 14C-urea (2.11 GBq/mmol, Amersham, Sydney, Australia) for determination of MCL thickness by using the known diffusion coefficient of 14C-urea in HT29 MCLs (10). The cultures were kept in 95% O2 (to suppress bioreductive drug metabolism) and 5% CO2 (to maintain pH at 7.4), and 100 µL of medium was sampled from each compartment every hour for 5 hours. In each sample, concentrations of 14C-urea were determined by liquid scintillation counting and of TPZ analogs were determined by HPLC, as described below. Diffusion coefficients of each compound were calculated by fitting data to a transport model for MCL based on Fick's second law (Equation 11 in Supplementary Methods; http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16) as previously described (2,9,20).
Animals, Dosing, and Determination of Maximum Tolerated Dose
All animal experiments followed protocols approved by The University of Auckland Animal Ethics Committee, using specific pathogen–free male CD-1 homozygous nude mice (approximately 25 g body weight) derived from breeding mice supplied by Charles River Laboratories (Wilmington, MA). Varying doses of compounds were administered intraperitoneally at 20 µL/g body weight in 5% DMSO/saline or, in the case of some of the weak bases (compounds 5, 13–15), lactic acid buffer (100 mM lactic acid titrated to pH 4.0 with sodium hydroxide). Dose escalation was based on an eight-step logarithmic dose scale (101/8-fold = 1.33-fold increments). The observation time was 28 days. The maximum tolerated dose (MTD) was determined as the highest dose that caused no drug-related deaths, body weight loss of more than 15% relative to the pretreatment value, or severe morbidity in a group of three to six mice.
Plasma Pharmacokinetics
CD-1 nude mice (typically three per drug) were injected intraperitoneally with each drug at the MTD. Mice were bled by cardiac puncture under terminal anesthesia (compounds 1–4, 8, 10–12, 14) into heparinized plasma separator tubes (Microtainer Brand Tubes, Becton and Dickinson and Co, Franklin Lakes, NJ). Alternatively, small (20–40 µl) blood samples were obtained serially by puncturing the lateral tail vein of unanaesthetized restrained animals (typically at 15 minutes, 30 minutes, 1 hour, and 2 hours) and collecting a droplet of blood with heparinized haematocrit tubes (compounds 5–7, 9, 13, 15). TPZ at a dose of 270 mmol/kg gave similar results using either the terminal or serial sampling methods (Supplementary Fig. 2; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16); this finding was confirmed by comparison of the two methods at a dose of 133 µmol/kg (data not shown). Blood was centrifuged immediately to separate plasma, which was frozen for subsequent HPLC analysis (see below). The area under the drug concentration–time curve extrapolated to infinite time (AUC
) and the maximum concentration (Cmax) and terminal half-life (t1/2) of the drug were calculated by noncompartmental analysis using WinNonLin v 4.01 (Pharsight Corp, Mountain View, CA). Drug plasma protein binding was determined by equilibrium dialysis in 50% mouse plasma buffered with 10 mM phosphate pH 7.4 in 0.85% saline and extrapolated to give the concentration of unbound drug in 100% mouse plasma.
High-Performance Liquid Chromatography
HPLC with photodiode array detection was performed to determine drug concentrations as described (22). For in vitro studies, samples of culture medium were analyzed directly; plasma samples were treated with three volumes of ice-cold acetonitrile to precipitate proteins before analysis. Calibration curves and stability were determined for each compound in each experiment under the same sample-handling conditions.
Activity Against Hypoxic Cells in HT29 Human Tumor Xenografts by Excision Assay
HT29 tumors were grown subcutaneously on the backs of nude mice by injecting 107 cells. When tumors reached a volume of approximately 300 mm3 (average of two largest diameters 7–10 mm by calipers), mice were randomly assigned to five treatment groups for each TPZ analog and treated with vehicle control (i.e., DMSO with saline or lactate; group A), test drug (group B), gamma radiation (20 Gy; group C), TPZ given 5 minutes after radiation (group D), and test drug given 5 minutes after radiation (group E). Drugs were administered as single intraperitoneal doses at the same dose levels as used for the pharmacokinetics studies (i.e., at the MTD). Tumors were excised 18 hours after treatment, and tumor cells were dissociated enzymatically and plated to determine the number of surviving (clonogenic) cells per gram of tumor tissue, as described (31). Because hypoxic cells are resistant to radiation, drug-induced hypoxic cell kill could be calculated as the difference between group C and group D or E. Surviving fractions (SF) were calculated as the ratio of clonogens per gram of tumor in the treated group versus the control group, and drug-induced hypoxic cell kill was calculated as
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Calculation of Oxygen Distribution in the Three-Dimensional Microvascular Network Model
We simulated oxygen transport in tumors as previously reported (23), using a microvascular network in a representative region of a rat mammary carcinoma (R3230Ac) within a window chamber (Fig. 2, A). The microvascular geometry of this region had been mapped in three dimensions using confocal microscopy, and the direction and velocity of blood flow had been measured for most of the vascular segments by intravital fluorescence microscopy (23). Perivascular pO2 of this tumor had been previously well characterized by Eppendorf electrodes (32). Oxygen transport was simulated in this tumor microregion using a Green's function method (23,33) to estimate steady-state blood and tissue oxygen distributions. Each blood vessel is represented in the tumor microvascular network as a set of short cylindrical elements, with the surface of each element acting as a discrete oxygen source. The surrounding tissue is subdivided into many small volume elements, each of which acts as a discrete oxygen sink. The tissue distribution of oxygen is represented mathematically as the sum of oxygen fields corresponding to the sources and sinks. The strengths of the sources and sinks were computed by matching oxygen levels and fluxes at the vessel walls, taking into account the longitudinal decline of oxygen content along vessels. For further details, see the supplementary information and (23,33,34). A FORTRAN implementation of the method is available for download at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16. Oxygen transport parameter values and resulting morphological and oxygen transport characteristics of this network are shown in Supplementary Table 2 and Supplementary Fig. 1 (http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16).
Calculation of Pharmacokinetics/Pharmacodynamics in the Three-Dimensional Microvascular Network Model
The Green's function transport model for the tumor microregion was modified to include drug diffusion and metabolism information by introducing reaction–diffusion equations for drug concentration in addition to those for pO2. The equations were solved numerically using the plasma pharmacokinetics as measured in nude mice to define the input drug concentration in blood flowing into the region (as described in the supplementary information section 11). The drug concentration and amount of drug metabolized at each point in the tumor microregion were calculated using the diffusion coefficients measured in HT29 MCL and the rate constants for drug metabolism measured in HT29 cell suspensions. Drug-induced cell kill at each point in the tumor microregion was then calculated from the drug concentration and amount of metabolized drug at that point by using the appropriate cellular PK/PD model (Equations 1a–1c) as determined in cell suspensions.
Calculation of Cell Kill in the Tumor Microregion Due to Radiation
Radiation-induced cell kill at each tissue point in the tumor microregion was also calculated using the linear quadratic model and oxygen dependence for HT29 cell radiosensitivity as described previously (30). This model, applied to the three-dimensional tumor region in Fig. 2, A at the dose used in the excision assay (20 Gy), predicted 1.63 logs of radiation-induced cell kill, similar to the measured value of 1.79 ± 0.11 (mean ± 95% confidence interval) for the 137 HT29 tumors assayed during the course of this study.
Pharmacokinetic/Pharmacodynamic Model Prediction of Overall Hypoxic Cell Kill
The predicted SF for drug and radiation at each point within the 3D tumor microregion (calculated as described above using HT29 PK/PD parameters) was averaged to calculate the overall cell kill for the entire tumor microregion. The difference between this SF (drug + radiation) and the corresponding SF value for radiation alone gave the predicted average drug-induced cell kill in the hypoxic (i.e., radiation-resistant) subpopulation of cells.
Statistical Methods
Data from the excision assay were compared among groups using one-way analysis of variance with Dunnett's test. Compounds were considered to be active if the cell kill for the combination of drug plus radiation (i.e., treatment groups D or E) was statistically significantly (two-sided P<.05) higher than cell kill with radiation alone (i.e., treatment group C). PK/PD models for single-cell suspensions and diffusion coefficients in MCL were estimated by linear and nonlinear regression (further details are available in the Supplemental Methods at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16).
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RESULTS |
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Three-Dimensional Simulation of Tirapazamine Transport in a Representative Tumor Microregion
We first simulated TPZ transport by building on a previously reported (23) oxygen transport model for the R3230Ac tumor microregion shown in Fig. 2, A. The oxygen distribution predicted by this model is shown in Fig. 2, B. The predicted radiobiological hypoxic fraction (i.e., the fraction of cells at [O2] < 4 µM [3 mm Hg]; shaded bars in Fig. 2, B), which is considered to be resistant to radiotherapy, was 28%—within the typical range for human tumor xenografts (35). The transport model was extended by incorporating terms for TPZ diffusion to calculate the steady-state TPZ concentrations at each point in the microregion. This three-dimensional PK model used the measured HT29 MCL transport parameters for TPZ, the plasma PK for TPZ in nude mice, and the hyperbolic dependence of TPZ metabolism on oxygen concentration (30) (parameters are listed in Supplementary Table 2 at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16). The model predicted substantial decreases in TPZ exposure (of 30%–60% as compared with plasma values) in hypoxic (
4 µM O2) tumor regions (Fig. 3, A). The variation in TPZ exposure at the same pO2 value reflects differences in the transport properties of TPZ and O2, combined with the heterogeneity in intercapillary distances and blood flow rates in the three-dimensional tumor microregion. For example, the high diffusion coefficient and consumption rate of oxygen compared with TPZ gives rise to greater extraction of oxygen than TPZ from vessels, and thus steeper longitudinal concentration gradients, such that some hypoxic tissue is close to vessels that contain high concentrations of TPZ.
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Pharmacodynamic predictions at each point in the three-dimensional tumor microregion were based on a model in which the rate of cell killing is a function of the concentration of TPZ and the rate of its intracellular metabolism (Equation 1c) (22). As shown in Fig. 3, B, if the sensitivity of cells in the tumor microregion were equivalent to that of HT29 cells in culture, TPZ would be predicted to provide an overall cell kill (–log10 SF) of 1.58 logs in the radiobiologically hypoxic zones in this region, with a maximum of approximately 3 logs of kill for the most hypoxic cells. If there were no extravascular transport limitation (i.e., if TPZ concentrations in tumor tissue and plasma were equal), approximately 13 logs of kill would be predicted in the most severely hypoxic cells (solid line in Fig. 3, B), with 4.23 logs overall in the radiobiologically hypoxic zone (i.e.,
4 µM O2). Thus, on the basis of the transport parameters of TPZ as measured in MCLs, this model indicates that the activity of TPZ in tumors is compromised by its inefficient penetration into hypoxic tissue. Validation of the Spatially Resolved Pharmacokinetic/Pharmacodynamic Model
We next tested the ability of this spatially resolved PK/PD model to predict cell killing by TPZ and 15 structurally diverse analogs of TPZ (Supplementary Table 1; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16) in HT29 tumor xenografts in mice. Antiproliferative (IC50) assays showed that the compounds all had TPZ-like hypoxia-selective cytotoxicity in vitro (with potencies against anoxic HT29 cells at least 10-fold greater than at 20% O2; Supplementary Table 1 at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16).
The key parameters of the PK/PD model were determined experimentally for each TPZ analog (Table 1). Concentration–time data, measured in transport experiments with HT29 MCLs in diffusion chambers, are illustrated in Fig. 4, A. Fitting the simple Fick's Law diffusion model yielded effective tissue diffusion coefficients, D, that ranged from 2.7 x 10–8 cm2/s for compound 3 to 1.87 x 10–6 cm2/s for compound 10 (see Table 1 and Supplementary Table 3 at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16).
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; 1, 
; 2, +; 5, 
; 6, 
; 7, 
; 9, 
; 13, x. The resulting parameter estimates as shown in Rates of drug metabolism in anoxic HT29 cell suspensions also varied widely among TPZ analogs (Fig. 4, B), as did cell killing (Fig. 4, C). For 10 of the 15 analogs, the relationships between exposure, metabolism, and cell killing were similar to that for TPZ (Equation 1c). For these compounds, cell killing was proportional to C x M under conditions of constant drug concentration. Representative data for compounds with such a dependence are shown in Fig. 4, C; the log SF is plotted against the "exposure integral," the integrated form of Equation 1c. The potency parameter,
, estimated from the log SF data ranged from 0.56 µM–2 for the most potent DNA intercalator (compound 12) to 1.57 x 10–6 µM–2 (4; see Table 1). For two compounds, the log cell kill was better described by proportionality to M, and for three compounds killing was proportional to M2 (Table 1).
To apply the PK/PD model to tumors in mice, it was necessary to determine the concentration–time profile of each drug in plasma following a single intraperitoneal dose at the MTD (Fig. 4, D). AUC and Cmax values (Table 1) for total drug were converted to values for unbound drug using the free drug fraction, 
, measured in mouse plasma by equilibrium dialysis. The oxygen dependence of metabolic reduction of the analogs by HT29 tumor cells was assumed to be the same as for TPZ (30).
The HT29 transport and cytotoxicity parameters in Table 1 were used in the three-dimensional PK/PD model to predict drug concentrations and hypoxic cell killing throughout the tumor microregion for each compound in the same way as shown for TPZ in Fig. 3. These predictions were compared with measured hypoxic cell killing by each TPZ analog in HT29 tumor xenografts in mice. Clonogenic assays on the tumors are illustrated for three compounds (1, 6, and 9) in Fig. 5. The results of these assays indicated that two of the compounds (1 and 9) were active and one (6) was inactive. That is, compound 1 and 9 gave 2.17 ± 0.15 and 1.84 ± 0.16 logs of hypoxic cell kill, respectively, whereas cell kill by compound 6 was not statistically significantly greater than that produced by radiation alone.
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We next compared the measured values of hypoxic cell killing for each compound with those predicted by the PK/PD model in the whole tumor region (i.e., the additional killing compared to that for radiation alone) (Fig. 6, A). Of the six compounds (TPZ plus five analogs) predicted to provide more than 0.5 logs of killing (the approximate threshold for detection of a statistically significant increase in cell killing above with radiation alone), all showed statistically significant activity in the HT29 excision assay, whereas the 10 compounds predicted to give less than 0.5 logs of killing were all inactive in that assay. Linear regression of the observed versus predicted values (Fig. 6, A) demonstrated a strong and statistically significant relationship between these values (P = 1.53 x 10–7, R2 = 0.87). Moreover, the slope of the regression of the observed versus predicted response (0.93) was not significantly different from unity (P = .19). However, the relationship between observed and predicted values was much weaker when it was assumed that the drug pharmacokinetics in the target cells was the same as that in plasma (Fig. 6, B; R2 = 0.32, P = .023 for a nonzero slope), with a slope of only 0.29. This result indicates that the PK/PD model overpredicts activity when extravascular transport is not taken into account. Specifically, when the transport component was ignored, four compounds (5, 13, 14, and 15) were incorrectly predicted to be active (false positives). The overprediction of activity when extravascular transport is ignored clearly demonstrates that the ability of the compounds to penetrate to target cells in tumors is a critical determinant of their antitumor activity.
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Optimization of Extravascular Transport in Drug Design and Development
The PK/PD modeling approach also has potential application to drug design by allowing prediction of optimal extravascular transport parameters within a series of drugs. These parameters can be evaluated rapidly in vitro, for example by mass spectrometry in MCL studies (36), or predicted as illustrated by the dependence of D on log P7.4 (20). As an example of lead compound optimization, consider the parameters D and kmet for TPZ analogs assuming that all other parameters are as for TPZ (Fig. 7). Increasing D for this hypothetical analog sixfold (to 2.4 x 10–6 cm2/s) is predicted to markedly increase hypoxic cell killing in HT29 tumors (Fig. 7, A), reflecting the limitation to TPZ activity imposed by its slow diffusion. Increasing kmet by the same factor (to 6.7 min–1) would cause a dramatic loss of activity against the most hypoxic cells (Fig. 7, B) as a result of increased consumption before drug reaches hypoxic regions. Such metabolic activation in well-oxygenated tissues would defeat the therapeutic rationale for hypoxia-activated prodrugs.
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To illustrate the effects of varying both parameters simultaneously, drug-induced cell killing over the tumor region is shown in Fig. 7, C. For any given D, an optimal value for kmet is found. Metabolic reduction has opposing effects (9)—it interferes with drug transport but is required to form the active cytotoxic radical—so excessively high or low values compromise cell killing in the radiobiologically hypoxic region. The predicted optimal kmet increases with increasing D, reflecting the reduced impact of metabolic consumption on penetration at high D. For an analog with sixfold higher D, the predicted optimum value of kmet is 2.7 min–1 (versus 1.1 min–1 for TPZ), resulting in 3.7 logs of kill additional to radiation (versus 1.5 logs for TPZ). Analogs that have high kmet and low D values are activated to a greater extent in aerobic than hypoxic regions (i.e., they lack hypoxic selectivity in vivo). Figure 7, D shows the model prediction for the dependence on D and kmet of hypoxic selectivity, defined as log cell kill in the hypoxic region (<4 µM O2) minus log cell kill in the well-oxygenated region (>30 µM). For sixfold elevated D, the value of kmet that optimizes hypoxic selectivity is 1.9 min–1, and the selectivity is then 2.7-fold greater than for TPZ itself. These results show that in vivo hypoxic selectivity is a function of extravascular transport and that optimization of transport properties (such as maximizing lipophilicity and minimizing unproductive drug metabolism in the tumor) can provide major gains in the activity of hypoxia-activated prodrugs.
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DISCUSSION |
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TopNotesAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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Although poor drug penetration through tumor tissue has long been suspected to be an important limitation in anticancer drug development, there is little information on the magnitude of extravascular transport problems for small-molecule drugs. The purpose of this study was to develop a three-dimensional PK/PD model for small-molecule drug distribution in tumors and to validate this model for one class of compounds. We considered TPZ to be a good candidate for developing such a spatially resolved PK/PD model because of earlier studies demonstrating that the metabolism of this prodrug in hypoxic tissue can be rapid enough to interfere with its diffusion in three-dimensional cell culture models in vitro (9,11,19,22).
In the present study, we used PK/PD parameters determined in vitro to simulate transport of TPZ in a three-dimensional tumor microvascular network, using measured plasma pharmacokinetics as the input to the extravascular compartment. The drug transport model demonstrated that the most hypoxic cells in the mapped tumor region experience an exposure to drug (AUC) only 30%–60% of that in plasma (Fig. 3, A). Because cell killing is effectively a function of the square of the TPZ concentration (Equation 1c), the predicted pharmacodynamic deficit is even larger, with approximately 2–4 logs of kill in the most hypoxic cells compared with approximately 13 logs if the pharmacokinetics followed that in plasma. Averaging over the whole tumor region, the logs of hypoxic cell kill are lowered approximately threefold by the metabolic loss of TPZ during its diffusion. The model thus explains the observation that TPZ is much less selective for hypoxic cells in tumors than it is in low-cell density cultures (18,19). The loss of selectivity of TPZ in tumors is likely to compromise its therapeutic index because normal tissues are relatively well perfused and thus not protected by analogous pharmacokinetic barriers; i.e., although TPZ is a hypoxic cytotoxin it retains some cytotoxicity under aerobic conditions, and this will be relatively unaffected by penetration limitations. Given the low therapeutic ratio of TPZ (and of almost all cytotoxic drugs), such micropharmacokinetic problems would be expected to make a decisive difference to clinical outcome.
In this study, all of the PK/PD parameters for TPZ were determined with a single cell line (HT29), which made it possible to test the model against measured cell killing in tumors grown from that line. Clonogenic cell killing was chosen as the pharmacodynamic endpoint because this endpoint is the sum of all cell death pathways and is one of the few quantitative endpoints that can be used both in vitro and in vivo. Thus, we could test the PK/PD model without introducing additional assumptions. The model predicted that a single dose of TPZ at its MTD would kill 1.5 logs of radiation-resistant (i.e., hypoxic) cells in HT29 tumors, a finding that agreed well with measured cell killing in combination with radiation (Fig. 5). Importantly, when this three-dimensional model was extended to 15 TPZ analogs spanning a range of extravascular transport properties, it provided impressive prediction of measured activity, with an explained variability (R2) of 87%. The predictive power was greatly reduced, with an explained variability of only 32%, when the tissue pharmacokinetics was assumed to be the same as in plasma. Because this model validation study was undertaken using approximately equitoxic doses of the TPZ analogs, it provides a clear demonstration of the importance of extravascular transport as a determinant of therapeutic selectivity in this series of compounds.
The high predictive power of the model was achieved despite several limitations and approximations. One limitation was that the oxygen dependence of metabolic activation of the analogs was assumed to be the same as for TPZ. We made this assumption because experimental determination of activation/cytotoxicity at intermediate oxygen concentrations is technically challenging (30,37) and because the oxygen dependence is expected to be a function of the one-electron reduction potential, which, for these analogs, falls within a relatively small range (25). A second limitation was that each parameter was estimated based on sparse data sets (e.g., typically only three or four time points for the plasma PK analyses), and the estimates will thus be subject to substantial experimental error. However, because the predictions were so accurate the approach appears to be robust enough to be useful in a drug development/lead optimization setting in which limited screening data are obtained. A third limitation is that the microvascular network geometry is derived from an R3230Ac tumor growing in a window preparation in a rat, not a subcutaneous HT29 tumor in a mouse. The R3230Ac tumor region was chosen because, to our knowledge, it is the only three-dimensional tumor network for which vessel geometry, blood flow direction and velocities, and perivascular pO2 for many of the vascular segments have been measured accurately. A model of blood flow and oxygen transport for this region has already been developed (23,33). The R3230Ac tumor region can be considered representative in that its distribution of distances to the nearest capillary (Supplementary Fig. 1, A; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16), oxygen concentration distribution (Fig 1, B), and hypoxic fraction (28%) are similar to those in human tumors and xenografts (5,35,38,39) and give similar spatial patterns of oxygen distribution in relation to the capillaries (5,33,38). A sensitivity analysis comparing the predicted pharmacodynamics in this region to one-dimensional models (spheroids and tumor cords) indicates that the distribution of clonogenic cell kill is not highly sensitive to geometry (K.O.H., T.W.S., and W.R.W., manuscript in preparation). However, the mapped microvascular network has the advantages of representing heterogeneous tumor blood flows (Supplementary Fig. 1, C; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16), heterogeneous capillary diameters (Supplementry Fig. 1, B; available at http://jncicancerspectrum.oxfordjournals.org/jnci/content/vol98/issue16), and axial gradients of oxygen and drug concentration in the capillaries. Consequently, the PK/PD model developed here can be extended to other tumor microvascular networks as they become available, as well as to other drug series and intermediate pharmacodynamic endpoints with high spatial resolution, such as the presence of the DNA double-strand break marker H2AX (40).
The success of the spatially resolved PK/PD model for TPZ analogs validates MCLs for estimating diffusion coefficients of drugs in the extravascular compartment of tumors. The use of MCLs has the potential, in conjunction with three-dimensional PK/PD modeling, to reduce the number of animals required for testing of anticancer drugs because drug candidates with inadequate tumor penetration properties can be rejected on the basis of in vitro testing. MCL-guided PK/PD modeling also makes it possible to identify optimal rates of drug metabolism and diffusion in tissue during development of new anticancer drugs. This application is illustrated in Fig. 7, which demonstrates the large increase in therapeutic utility that can be achieved by optimizing the diffusion and metabolism rates of TPZ analogs. With increasing ability to predict such properties from drug physicochemical parameters (20), such modeling enhances the potential for in silico prediction of useful drugs during lead development.
To our knowledge, this is the first use of a three-dimensional cell culture system to successfully predict therapeutic activity of a series of anticancer drugs in animal xenograft models. Given the highly inefficient microvascular supply in human tumors and the key importance of the least-accessible cancer cells in determining outcomes of chemotherapy, similar tissue penetration problems are likely to be important for many anticancer agents. Spatially resolved PK/PD models of the type developed here are potentially powerful adjuncts to other approaches, such as noninvasive imaging, for assessing the spatial heterogeneity of drug distribution and therapeutic response in tumors. Such models have the advantages of very high spatial resolution and applicability to endpoints (such as cell clonogenic death) that cannot be detected directly with current imaging modalities.
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TopNotesAbstractIntroductionMaterials and methodsResultsDiscussionReferences |
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This study was funded by a Program Project Grant (NIH/CA 82566) and grant number NIH/CA 40355 from the National Cancer Institute (NCI) and an NCI overseas investigator award (K. O. Hicks). The study sponsors had no role in the design, analysis, conduct, or writing of the study or the decision to submit it for publication. J. Martin Brown is conducting research funded by Sanofi-Aventis, which has licensed tirapazamine.
We thank Jane Botting, Rachel Chapman, Anna Chappell, Alfred Degenkolbe, Swarna Gamage, Sarath Liyanage, and Joanna Sturman for assistance with experimental determinations. HT29 radiosensitivity data were kindly provided by Dr Bronwyn Siim.
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(1) Minchinton AI, Tannock IF. Drug penetration in solid tumors. Nat Rev Cancer 2006;6:583–92.
(2) Hicks KO, Ohms SJ, van Zijl PL, Denny WA, Hunter PJ, Wilson WR. An experimental and mathematical model for the extravascular transport of a DNA intercalator in tumours. Br J Cancer 1997;76:894–903.[ISI][Medline]
(3) Vaupel P. Tumor microenvironmental physiology and its implications for radiation oncology. Semin Radiat Oncol 2004;14:198–206.[CrossRef][ISI][Medline]
(4) Dewhirst MW, Richardson R, Cardenas-Navia I, Cao Y. The relationship between the tumor physiologic microenvironment and angiogenesis. Hematol Oncol Clin North Am 2004;18:973–90.[CrossRef][ISI][Medline]
(5) Wijffels KI, Kaanders JH, Rijken PF, Bussink J, van den Hoogen FJ, Marres HA, et al. Vascular architecture and hypoxic profiles in human head and neck squamous cell carcinomas. Br J Cancer 2000;83:674–83.[CrossRef][ISI][Medline]
(6) Jain RK. Delivery of molecular and cellular medicine to solid tumors. Adv Drug Deliv Rev 2001;46:149–68.[CrossRef][ISI][Medline]
(7) Jain RK. The next frontier of molecular medicine: delivery of therapeutics. Nat Med 1998;4:655–7.[CrossRef][ISI][Medline]
(8) Tannock IF. Conventional cancer therapy: promise broken or promise delayed? Lancet 1998;351(Suppl 2):9–16.[CrossRef][ISI][Medline]
(9) Hicks KO, Fleming Y, Siim BG, Koch CJ, Wilson WR. Extravascular diffusion of tirapazamine: effect of metabolic consumption assessed using the multicellular layer model. Int J Radiat Oncol Biol Phys 1998;42:641–9.[CrossRef][ISI][Medline]
(10) Hicks KO, Pruijn FB, Baguley BC, Wilson WR. Extravascular transport of the DNA intercalator and topoisomerase poison N-[2-(dimethylamino)ethyl]acridine-4-carboxamide (DACA): diffusion and metabolism in multicellular layers of tumor cells. J Pharmacol Exp Ther 2001;297:1088–98.
(11) Kyle AH, Minchinton AI. Measurement of delivery and metabolism of tirapazamine to tumour tissue using the multilayered cell culture model. Cancer Chemother Pharmacol 1999;43:213–20.[CrossRef][ISI][Medline]
(12) Rischin D, Peters L, Fisher R, Macann A, Denham J, Poulsen M, et al. Tirapazamine, cisplatin, and radiation versus fluorouracil, cisplatin, and radiation in patients with locally advanced head and neck cancer: a randomized phase II trial of the Trans-Tasman Radiation Oncology Group (TROG 98.02). J Clin Oncol 2005;23:79–87.
(13) Zeman EM, Brown JM, Lemmon MJ, Hirst VK, Lee WW. SR-4233: a new bioreductive agent with high selective toxicity for hypoxic mammalian cells. Int J Radiat Oncol Biol Phys 1986;12:1239–42.[ISI][Medline]
(14) Daniels JS, Gates KS. DNA cleavage by the antitumor agent 3-amino-1,2,4-benzotriazine 1,4-dioxide (SR4233): evidence for involvement of hydroxyl radical. J Am Chem Soc 1996;118:3380–5.[CrossRef]
(15) Anderson RF, Shinde SS, Hay MP, Gamage SA, Denny WA. Activation of 3-amino-1,2,4-benzotriazine 1,4-dioxide antitumor agents to oxidizing species following their one-electron reduction. J Am Chem Soc 2003;125:748–56.[CrossRef][ISI][Medline]
(16) Baker MA, Zeman EM, Hirst VK, Brown JM. Metabolism of SR 4233 by Chinese hamster ovary cells: basis of selective hypoxic cytotoxicity. Cancer Res 1988;48:5947–52.
(17) Brown JM, Wilson WR. Exploiting tumor hypoxia in cancer treatment. Nat Rev Cancer 2004;4:437–47.[CrossRef][ISI][Medline]
(18) Durand RE, Olive PL. Physiologic and cytotoxic effects of tirapazamine in tumor-bearing mice. Radiat Oncol Investig 1997;5:213–9.[CrossRef][Medline]
(19) Durand RE, Olive PL. Evaluation of bioreductive drugs in multicell spheroids. Int J Radiat Oncol Biol Phys 1992;22:689–92.[ISI][Medline]
(20) Pruijn FB, Sturman JR, Liyanage HDS, Hicks KO, Hay MP, Wilson WR. Extravascular transport of drugs in tumor tissue: effect of lipophilicity on diffusion of tirapazamine analogs in multicellular layer cultures. J Med Chem 2005;48:1079–87.[CrossRef][ISI][Medline]
(21) Hay MP, Pruijn FB, Gamage SA, Liyanage HD, Kovacs MS, Patterson AV, et al. DNA-targeted 1,2,4-benzotriazine 1,4-dioxides: potent analogues of the hypoxia-selective cytotoxin tirapazamine. J Med Chem 2004;47:475–88.[CrossRef][ISI][Medline]
(22) Hicks KO, Pruijn FB, Sturman JR, Denny WA, Wilson WR. Multicellular resistance to tirapazamine is due to restricted extravascular transport: a pharmacokinetic/pharmacodynamic study in HT29 multicellular layer cultures. Cancer Res 2003;63:5970–7.
(23) Secomb TW, Hsu R, Braun RD, Ross JR, Gross JF, Dewhirst MW. Theoretical simulation of oxygen transport to tumors by three-dimensional networks of microvessels. Adv Exp Med Biol 1998;454:629–34.[ISI][Medline]
(24) Hall EJ. Radiobiology for the radiologist. 5th ed. Philadelphia (PA): J.B. Lippincott Company; 2000.
(25) Hay MP, Gamage SA, Kovacs MS, Pruijn FB, Anderson RF, Patterson AV, et al. Structure-activity relationships of 1,2,4-benzotriazine 1,4-dioxides as hypoxia-selective analogues of tirapazamine. J Med Chem 2003;46:169–82.[CrossRef][ISI][Medline]
(26) Shinde SS, Anderson RF, Hay MP, Gamage SA, Denny WA. Oxidation of 2-deoxyribose by benzotriazinyl radicals of antitumor 3-amino-1,2,4-benzotriazine 1,4-dioxides. J Am Chem Soc 2004;126:7865–74.
(27) Hay MP, Denny WA. New and versatile synthesis of 3-alkyl- and 3-aryl-1,2,4-benzotriazine 1,4-dioxides: preparation of the bioreductive cytotoxins SR4895 and SR4941. Tetrahedron Lett 2002;43:9569–71.[CrossRef]
(28) Delahoussaye YM, Hay MP, Pruijn FB, Denny WA, Brown JM. Improved potency of the hypoxic cytotoxin tirapazamine by DNA-targeting. Biochem Pharmacol 2003;65:1807–15.[ISI][Medline]
(29) Siim BG, Hicks KO, Pullen SM, van Zijl PL, Denny WA, Wilson WR. Comparison of aromatic and tertiary amine N-oxides of acridine DNA intercalators as bioreductive drugs. Cytotoxicity, DNA binding, cellular uptake, and metabolism. Biochem Pharmacol 2000;60:969–78.[CrossRef][ISI][Medline]
(30) Hicks KO, Siim BG, Pruijn FB, Wilson WR. Oxygen dependence of the metabolic activation and cytotoxicity of tirapazamine: implications for extravascular transport and activity in tumors. Radiat Res 2004;161:656–66.[CrossRef][ISI][Medline]
(31) Wilson WR, Pullen SM, Hogg A, Hobbs SM, Pruijn FB, Hicks KO. In vitro and in vivo models for evaluation of GDEPT: quantifying bystander killing in cell cultures and tumors. In: Springer CJ, editor. Suicide gene therapy: methods and reviews. Totowa (NJ): Humana Press; 2003. p. 403–32.
(32) Dewhirst MW, Secomb TW, Ong ET, Hsu R, Gross JF. Determination of local oxygen consumption rates in tumors. Cancer Res 1994;54:3333–6.
(33) Secomb TW, Hsu R, Park EY, Dewhirst MW. Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann Biomed Eng 2004;32:1519–29.[CrossRef][ISI][Medline]
(34) Kavanagh BD, Secomb TW, Hsu R, Lin PS, Venitz J, Dewhirst MW. A theoretical model for the effects of reduced hemoglobin-oxygen affinity on tumor oxygenation. Int J Radiat Oncol Biol Phys 2002;53:172–9.[CrossRef][ISI][Medline]
(35) Moulder JE, Rockwell S. Hypoxic fractions of solid tumors: experimental techniques, methods of analysis, and a survey of existing data. Int J Radiat Oncol Biol Phys 1984;10:695–712.[ISI][Medline]
(36) Hicks KO, Patel K, Pruijn FB, Hay MP, Wilson WR. Effect of cell type and drug lipophilicity on the extravascular transport of small molecule anticancer drugs: tirapazamine analogs. Proc Am Assoc Cancer Res 2005;46:969.
(37) Koch CJ. Unusual oxygen concentration dependence of toxicity of SR-4233, a hypoxic cell toxin. Cancer Res 1993;53:3992–7.
(38) Bussink J, Kaanders JH, Rijken PF, Peters JP, Hodgkiss RJ, Marres HA, et al. Vascular architecture and microenvironmental parameters in human squamous cell carcinoma xenografts: effects of carbogen and nicotinamide. Radiother Oncol 1999;50:173–84.[CrossRef][ISI][Medline]
(39) Bussink J, Kaanders JH, Strik AM, Vojnovic B, Der Kogel AJ. Optical sensor-based oxygen tension measurements correspond with hypoxia marker binding in three human tumor xenograft lines. Radiat Res 2000;154:547–55.[CrossRef][ISI][Medline]
(40) Olive PL, Banath JP, Sinnott LT. Phosphorylated histone H2AX in spheroids, tumors, and tissues of mice exposed to etoposide and 3-amino-1,2,4-benzotriazine-1,3-dioxide. Cancer Res 2004;64:5363–9.
Manuscript received November 9, 2005; revised May 22, 2006; accepted June 16, 2006.
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