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Am J Physiol Heart Circ Physiol 281: H715-H721, 2001;
0363-6135/01 $5.00
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Vol. 281, Issue 2, H715-H721, August 2001

Quantitative analysis of intratumoral infusion of color molecules

Sarah McGuire and Fan Yuan

Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Intratumoral infusion has a potential for improving distribution of drugs. To optimize the infusion, we developed a novel technique to quantify the distribution volume of color molecules (Vd) in solid tumors. Evans blue-labeled albumin was infused locally with the use of a needle into a rat fibrosarcoma ex vivo under different pressures. After the infusion, tumor tissues were sectioned serially into thin slices. The blue area in each slice was quantified with the use of the newly developed technique. The Vd was calculated based on the blue area and the slice thickness. Our data showed that infusion pressure and volume (Vi) had significant effects on Vd. The median of Vd/Vi decreased from 2.99 to 1.79 when infusion pressure was increased from 50 to 163 cmH2O, presumably due to retardation of convective transport. In addition, the coefficient of variation in Vd/Vi was increased from 0.13 at 50 cmH2O to 0.64 at 163 cmH2O. The dependence of Vd/Vi and its variation on infusion pressure suggests that 1) infusion-induced tissue deformation is unpredictable and 2) both the unpredictability and the interstitial retardation of convective transport increase with infusion pressure.

distribution volume; drug delivery; convective transport


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

WITH THE ADVANCES in molecular medicine and drug discovery, more large therapeutic agents such as antibodies, liposomes, and genes will be used in cancer treatment. Thus drug delivery in solid tumors has become an important concern (13). Systemic delivery alone may not be adequate to distribute large molecules throughout tumor tissues due to heterogeneous vasculature, stagnant blood flow, and high interstitial fluid pressure (IFP) commonly found in solid tumors (13, 14, 23, 32), whereas local delivery of large therapeutic agents based on polymeric devices is also hampered by various interstitial barriers (9, 12, 30). A practical approach to enhancing delivery of macromolecules or nanoparticles in solid tumors is via convection (13). However, the driving force for convection, i.e., the IFP gradient, is minimal in the center of solid tumors due to the elevated pressure (13). Hence, the key to improve interstitial transport of macromolecules is to enhance the pressure gradient, which can be achieved and optimized through intratumoral infusion (5, 18). Infusion may symmetrically distribute therapeutic agents to a large region in tumor tissues and thus enhance the therapeutic efficacy of drugs (5, 10). Furthermore, direct infusion will reduce systemic toxicity because localized delivery will significantly decrease the plasma concentration of drugs (18).

The success of intratumoral infusion depends largely on the ability to reach the tumor with a needle and the transport parameters determined by interstitial structures, cell density, and molecular properties of drugs (7, 24, 34). Brain tumors are an ideal case for direct infusion because they are generally accessible to needle insertion, and the blood-brain barrier acts to limit the entrance of infused drugs into systemic circulation (4, 18, 21, 24). Other solid tumors accessible to needle insertion may also be candidates for this method (26). The question then becomes how to overcome the resistance to convective transport of drugs in the interstitial space, which consists of interstitial fluid and extracellular matrix (e.g., glycosaminoglycans and collagen) (20). Convection depends on fluid velocity and interstitial retardation of drugs by the extracellular matrix and cells. The retardation is most significant when the molecule size approaches the cutoff size of the spacing between fibers or between cells (19). On the other hand, the fluid velocity depends on the hydraulic conductivity. The hydraulic conductivity of a tissue is not constant but changes with tissue deformation. The tissue deformation can be induced by the pressure gradient needed to drive molecules through tissues during infusion (1, 10, 17, 29, 33, 34). Zhang et al. (34) demonstrated that the infusion pressure may alter the hydraulic conductivity by up to several orders of magnitude. The mechanism of alteration is related with the changes in the size and the connectivity of fluid channels in tissues. An increase in the size and improvement in the connectivity will enhance both fluid and solute transport. The pressure gradient may either expand or compress the tissue, depending on how it is applied. Tissue compression may close and/or disconnect fluid channels and thus lead to a significant increase in the interstitial resistance to convective transport. To understand how infusion pressure will affect the convective transport of drugs, we developed a new technique to quantify the distribution volume of infused color molecules in solid tumors. Using this technique, we found that the distribution of infused tracers depended on the infusion volume and pressure.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Tumors. Pieces (~1 mm in diameter) of a rat fibrosarcoma were transplanted subcutaneously into the right hindlimb of 2-mo-old female Fischer rats (~150 g). When tumors reached ~2-3 cm in diameter, rats were anesthetized with an intraperitoneal injection of pentobarbital (50 mg/kg body wt). Tumor tissues were then removed and put immediately into cold DMEM contained in a centrifuge tube in ice.

Intratumoral infusion. The tumor tissue (~2 cm in size) was immersed in 1% albumin solution maintained at 4°C in a container mounted on a stage. The tumor was perfused with a solution of Evans blue-labeled albumin (prepared by mixing 0.04% Evans blue and 0.1% albumin in 0.9% saline) via a 21-gauge needle inserted into the center of the tumor. The needle was modified by creating a slot 2 mm in length along the shaft ~1-2 mm above the tip. This was done to ensure unimpeded flow through the needle. The needle was connected to a reservoir of Evans blue-labeled albumin solution via 0.52-mm diameter tubing. The infusion pressure was defined as the height of the reservoir relative to the tip of the needle. The flow rate was determined by measuring the velocity of a bubble introduced into the tubing. The total infusion time was also recorded to determine the average flow rate. Additionally, periodic flow rate measurements were made throughout the infusion to determine the time dependence of the flow rate. The infusion volume was approximately the same for all pressures. The exact volume of infusion was quantified in each experiment based on the measurement of the total distance of bubble movement and the diameter of the tubing. We found that the average infusion volumes were 30.2 ± 3.0, 32.4 ± 0.8, 43.4 ± 7.7, and 36.1 ± 5.3 µl, and the average flow rates were 1.4 ± 1.5, 19.5 ± 12.4, 16.3 ± 15.1, and 51.3 ± 44.0 µl/min for pressures of 36, 50, 94, and 163 cmH2O, respectively.

Microwave fixation of tumor tissues. After infusion, the tumor was removed from the stage and immediately transferred into 50 ml of physiological saline and fixed by a Panasonic microwave (model no. NN-5548BA) at full power for ~90 s.

Tumor volume measurement. The tumor volume was measured before and after microwave fixation by water volume displacement. A container consisting of a 5-ml pipette and a 50-ml conical centrifuge tube was used in the measurement. The pointed end of the tube was cut open and attached to the pipette with an inner diameter of 6.3 mm. A fresh tumor and a fixed amount of saline were added to the container. The level of saline in the pipette was recorded. The container was then emptied and saline was added back to the container until it reached the same level in the pipette. The difference in the amount of saline added to the container was used as a measure of the total tumor volume. The same procedure was repeated after microwave fixation of tumors. The amount of saline added to the container with fixed tumor tissues was the same as that when the volume of fresh tumor tissues was measured. The difference in tumor volume induced by fixation was determined by measuring the distance between the saline levels in the pipette before and after fixation, respectively.

Sectioning and imaging of tissue. The fixed tissue was cooled in fresh saline at 4°C for ~1 min. The tissue around the dyed volume was then carefully removed with a scalpel so that it would fit on the stage of the Vibratome (model 3000, Technical Products International; St. Louis, MO) maintained at 4°C. Sections of 200 µm thickness were sliced from the tumor tissue and immobilized on microscope slides. Color images of tissue sections were then scanned into a personal computer using a Plustek Optic Pro document scanner (model 12000P).

Image analysis. The color images were analyzed using Image Pro software (Media Cybernetics; Silver Spring, MD). These images can be described in a red, green, blue color scheme, in which each image pixel contains three values ranging from 0 to 255 that represent the intensity of red, green, and blue. A criterion was established for extracting the blue area in each image based on the selection of those pixels that contained more blue than red or green (22). The extraction was accomplished by separating each color image into red, green, and blue images and dividing the blue image by the sum of red, green, and blue images. After this operation, any pixel value greater than or equal to one-third would have a dominant blue component. These fractional pixel values were then multiplied by 255. A threshold value of 88 was chosen to select the dyed area. This value includes a ~3% cushion to eliminate those pixels that may have a slight blue tint, due to variations in the light source of the scanner, but are not contained in the dyed region. Pixels with intensity >88 were assigned to white while the rest of the pixels became black. A second criterion for selecting image pixels was that the blue component be greater than both the red and green components. Those pixels that fit this criterion were also assigned to white and combined with the previous criterion pixels using a logical AND function to produce a single image. The area of the white region (i.e., blue region) in the binary image was then calculated based on a scaling factor of 144 pixels per squared millimeter, which was determined through image calibration.

Fluorescence-image analysis. Fluorescent images of tumor tissues were obtained using a ×10 objective of a fluorescence microscope (Axiovert 100TV, Zeiss), a MTI CCD-72 camera, and NIH Image software. The excitation and emission wavelengths of Evans blue are 550 and 610 nm, respectively. Although it was not optimized, we used a rhodamine filter set to detect fluorescence from Evans blue molecules in tissues. The total fluorescence area was much larger than the field of view of the ×10 lens, so images of smaller areas of the fluorescence were saved sequentially and reassembled into the complete image using the montage command in NIH Image. A 3% threshold value was then applied to create a binary image where those pixels above the cutoff were assigned to white. The area of the white region (i.e., fluorescent region) was calculated using a 7343.7 pixels/mm2 scale factor.

Measurement of distribution volume. The blue area calculated for each section was multiplied by the section thickness (200 µm) and summed to obtain the distribution volume of color molecules in a tumor.

Measurement of interstitial pressure. The IFP was measured in five tumors ex vivo using a differential pressure transducer (model PK 8862 1, 180PC Pressure Sensor, Micro Switch; Freeport, IL). The wet port was connected to a needle with polyethylene tubing filled with 0.9% saline. After the sensor was calibrated and it was verified that there were no bubbles in the system, the needle was inserted into the center of the tumor to obtain a voltage reading. This voltage was then converted to a pressure reading based on the calibration factor.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The distribution of color molecules in tissue slices is not a step function. Numerical simulation indicates that the distribution is relatively uniform in the center and decreases to zero within a short distance (24). Therefore, the size of distribution area depends on the sensitivity of detection systems to tracers. To demonstrate the dependence, we compared the sizes of the same area determined by the color- and the fluorescence-image analysis techniques, respectively. The comparison is shown in Fig. 1. The shapes of distribution in both true color and fluorescence images were similar, but the blue area (10.3 mm2) in Fig. 1A was ~50% of the fluorescence area (20.9 mm2) in Fig. 1B. The color technique underestimated the area of the dye because it was less sensitive than the fluorescence technique to the periphery of the dyed region where the blue coloring was faint. The underestimation by the color technique will not affect the conclusions in this study because all were based on the relative changes between different groups. The error in the area measurement translates directly to the distribution volume measurement, because the thickness of blue regions was determined by the slice thickness.


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  		Fig. 1.   Distribution of Evans blue-labeled albumin in a tumor section immediately after infusion. A, left: true color image; right, binary image based on the color image on the left and a 3% cutoff threshold. B, left: fluorescence image; right, binary image based on the fluorescence on the left and a 3% cutoff threshold.

Examples of color images of a solid tumor from serial sections after intratumoral infusion at the pressure of 94 cmH2O are shown in Fig. 2A. For the purpose of demonstration, only the images of sections with odd index numbers are shown in Fig. 2. The blue areas can be easily visualized at the center of each section (Fig. 2A). These areas were extracted through the color-image analysis. The resulting images were converted into binary representations with the extracted areas shown in white (Fig. 2B). The binary images were used to determine the distribution volume of Evans blue-labeled albumin as described in METHODS.


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  		Fig. 2.   Serial sections of tumors immediately after infusion of Evans blue-labeled albumin. A: true color images of the sections. B: binary images showing the extracted blue areas from those images shown in A.

The distribution volume of Evans blue-labeled albumin (Vd) depended on the infusion volume (Vi), and the ratio of Vd/Vi could be influenced by tissue hydration and deformation as well as interstitial retardation of convective transport during intratumoral infusion. We quantified the ratio of Vd/Vi at four different infusion pressures: 36, 50, 94, and 163 cmH2O, and the results are shown in Fig. 3.


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  		Fig. 3.   Volume fraction as a function of pressure. Ratios of volume distribution to volume infusion (Vd/Vi) were quantified at infusion pressures of 36, 50, 94, and 163 in cmH2O, respectively. Symbols represent data from individual experiments; n = 2 for pressure of 36 cmH2O and n = 5 for other pressures.

We found that Vd/Vi was pressure and tumor dependent. At the pressure of 36 cmH2O (26.5 mmHg), we could quantify the volume distribution in only 2 of 18 tumors (Fig. 3). The high failure rate was caused by either no flow in tumors (n = 8) or insertion of the needle into large blood cavities (n = 8). The cavities were likely formed through necrosis and hemorrhage during tumor growth. The flow problem at low infusion pressure could be caused by the high IFP that is a characteristic of most solid tumors (13) and the disconnection of interstitial fluid channels in tumor tissues (34). To quantify its contribution to the flow resistance at low infusion pressures, we measured IFP in five different tumors ex vivo. The results were 3.6, 2.9, 3.4, 2.6, and 2.0 mmHg, respectively, with an average of 2.9 mmHg. When the tumor was cut in half, the pressure was reduced to approximately zero. These data indicated that the infusion pressure was much higher than the residual IFP after tumors were removed from animals and that a threshold pressure of ~24 mmHg must be exceeded to open and connect fluid channels in the interstitium to allow fluid flow.

At higher infusion pressures, fluid flow could be easily established in tumors, presumably due to an increase in the interstitial pressure gradient and opening of fluid channels through pressure-induced tissue deformation (34). However, there was a large variation in the shape of the distribution volume of Evans blue-labeled albumin in tumor tissues. These shapes could be classified into four different categories: 1) approximately spherical inside the tumor, 2) irregular inside the tumor, 3) irregular along the needle track, and 4) irregular inside blood cavities. The percentages of these categories in 48 experiments pooled from the data at pressures of 50, 94, and 163 cmH2O were 31%, 21%, 17%, and 31%, respectively. There was no correlation between the infusion pressure and the percentages of these categories, except for the percentage of the third category. It was only 6% at 50 cmH2O, but increased to 30% and 20% at 94 and 163 cmH2O, respectively. These data were consistent qualitatively with the results observed in the intrabrain infusion of [14C]albumin (7). The shape of distribution volume in the last three categories was random and could not be controlled through infusion conditions. Therefore, we quantified the distribution volume only in tissues with approximately spherical distribution of blue molecules as shown in Fig. 3.

The ratio of Vd/Vi was heterogeneous even when the infusion pressure was maintained at a constant level. The heterogeneity was relatively low at the infusion pressure of 50 cmH2O (coefficient of variation = 0.13) and increased with the infusion pressure (Fig. 3). The coefficients of variation for 94 and 163 cmH2O were 0.32 and 0.46 respectively. The median of Vd/Vi decreased from 2.99 to 1.79 when the infusion pressure was increased from 50 to 163 cmH2O, but the decrease was statistically insignificant (P > 0.05, Kruskal-Wallis test). In addition, we found that Vd/Vi was inversely correlated with the infusion rate (Fig. 4). In general, Vd/Vi should be independent of the infusion pressure or infusion rate if tissue deformation does not occur. Therefore, data shown in Figs. 3 and 4 suggested that 1) tissue deformation was unpredictable and 2) the unpredictability increased with the infusion pressure.


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  		Fig. 4.   Volume ratio (Vd/Vi) as a function of infusion rate (Q). Data points for different pressures are presented with different symbols.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

We developed a new technique to quantitatively analyze intratumoral infusion of color molecules. Evans blue-labeled albumin was infused into a rat fibrosarcoma at pressures of 36, 50, 94, and 163 cmH2O, respectively, and the distribution volume of albumin was quantified based on a novel color-image analysis technique. The distribution volume with irregular shapes was random and could not be controlled through infusion conditions. Therefore, data shown in Figs. 3 and 4 were obtained only in tumors with approximately spherical distribution of tracers. The spherical distribution volume varied among different tumors even when the infusion pressure was fixed, and the variation increased with the infusion pressure. Furthermore, the distribution volume was inversely correlated with the infusion rate. These data indicate that infusion-induced changes in tissue structures and interstitial retardation of convective transport play important roles in infusion-mediated drug delivery in solid tumors.

Volume distributions in tumors. The distribution volume of infused molecules depends on not only transport parameters but also mechanical properties of tissues. This is because the pressure gradient established during infusion may cause tissue deformation (10, 34), which in turn will affect both convection and diffusion. Tissue deformation also results in a nonlinear relationship between the flow rate and the infusion pressure (34). The coupling between tissue deformation and molecular transport makes it difficult to predict how the distribution volume depends on infusion conditions (4, 16).

Distribution volume has been studied predominately in brain tissues (4, 7, 16, 21), although quantitative measurement of the distribution volume is inconsistent among different studies. Bobo et al. (4) demonstrated that the distribution volume is a linear function of the infusion volume and decreases with the size of infused molecules. The molecular size dependence suggests that convective transport of larger molecules is retarded more significantly by interstitial structures and cells than that of smaller molecules, presumably due to stronger interactions between tissues and molecules. However, there is no correlation between the distribution volume in the brain and the size of molecules when data from different studies are compared (4, 7, 16, 21). Other factors that may affect infusion-mediated delivery of therapeutic agents include the dose and the infusion rate. Kroll et al. (16) investigated effects of these factors on the distribution volume of monocrystalline iron oxide nanocompounds in the brain. These authors demonstrate that the distribution volume may increase with the dose of monocrystalline iron oxide nanocompounds and decrease with the infusion rate if other infusion parameters are fixed, and that the infusion rate dependence of the distribution volume is more significant at a high dose than at a low one (16). However, the data discussed above cannot be confirmed by Chen et al. (7), who show that the flow rate and the dose have no effect on the distribution volume of [14C]albumin when the flow rate is increased from 0.1 to 5 ml/min or the concentration of [14C]albumin is diluted up to fourfold. The discrepancy between these studies suggests that further investigation is required for understanding mechanisms of flow rate and dose dependences of the distribution volume.

In addition to the infusion rate and the dose, the distribution volume depends on the size of interstitial fluid space. The average ratio of Vd/Vi shown in Fig. 4 was 2.7, which is about one-half of that in the brain (7). The difference in the volume ratio could be caused by the size of the interstitial space and the technique of measurement. The color-image analysis technique used in our study is less sensitive to tracers than the autoradiography method used by Chen et al. (7), in detecting regions with low concentration of infused albumin. Therefore, the color-image analysis technique underestimated the ratio of Vd/Vi. On the other hand, the interstitial space is ~50% of the total tissue volume in the fibrosarcoma (15) and ~16% in the brain (6). Although the volume ratio may not be proportional to the size of the interstitial space, it is likely that the former is inversely correlated with the latter. Thus the Vd/Vi in the brain should be greater than that in the fibrosarcoma.

The Vd discussed above is valid only for spherical distribution of tracers in solid tumors, which accounted for 31% of the experiments in our study. In other experiments, the shape of distribution was irregular. The irregular distribution has been observed in previous studies of intratumoral infusion and the results are tumor-line dependent (5, 10). For example, the distribution of Evans blue-labeled albumin is approximately spherical in a human colon adenocarcinoma LS174T but irregular in a human sarcoma HSTS26T under the same experimental conditions (5). However, the irregular distribution has not been found in the study of intrabrain infusion (4, 21). The difference between tumor and brain studies could be caused by infusion-induced mechanical stresses and tissue structures.

Tumor tissues in a spherical shell surrounding the injection site are stretched during the infusion in both longitudinal and latitudinal directions and are compressed in the radial direction (1, 2, 34). Tissue stretch may open and connect a network of transport channels formed within the interstitial space, and the degree of opening and connection of these channels depends on mechanical properties of tumor tissues (34). Mechanical properties are likely heterogeneous in solid tumors. The heterogeneity can be caused by necrotic regions and blood pools as well as abnormal assembly of extracellular matrix (25). These defects form weak structures at both macroscopic (e.g., necrotic regions and blood pools) and microscopic (e.g., abnormal assembly of extracellular matrix) levels in tumor tissues. The weak structures can be ruptured in a random manner by infusion-induced mechanical stresses if the local strain energy release rate is greater than the critical value for fracture formation (31). The rupture of tissues may cause the irregular distribution of infused molecules.

The defects in tissues may also explain the intertumoral variation in distribution volume and flow rate shown in Figs. 3 and 4. The heterogeneity was likely caused by microscopic defects in tumors that were not large enough to create the irregular distribution of infused molecules but could significantly enlarge fluid channels and thus decrease the resistance to convective transport of tracers. Consequently, the heterogeneity in the distribution volume shown in Fig. 3 increased with the infusion pressure.

The distribution volume has been visualized but has not been quantified in previous studies of intratumoral infusion (5, 10). To make a comparison, we estimated the range of the distribution volume based on the information provided in the paper of Boucher et al. (5). Although the infusion rate is either 0.10 or 0.14 µl/min, which is lower than those shown in Fig. 4, the ratio of Vd/Vi in a human colon adenocarcinoma LS174T is between 0.6 and 3.7, which is within the same range as that shown in Figs. 3 and 4.

Interstitial resistance to convective transport. The contribution of diffusion is negligible during high-flow infusion (24). Therefore, the transport of Evans blue-labeled albumin in tumors was dominated by convection. Convection is determined by the convective velocity and the concentration of solutes. In general, convective velocity is slower than fluid velocity due to interactions between solutes and tissue structures. The ratio of the velocities is defined as the retardation coefficient (f) (11, 19). For convective transport through a membrane, f is equivalent to 1 - sigma , where sigma  is the filtration reflection coefficient.

The retardation coefficient is a phenomenological parameter and depends on infusion conditions, tissue structures, and molecular properties of solutes. It has been poorly quantified in the literature (19). Parameswaran et al. examined sigma  of albumin in membrane-like structures, such as pig mediastinal pleura (27) and rabbit mesentery (28) during tissue perfusion. These authors found that sigma  of albumin in these tissues increased with the perfusion rate. For tissue pieces, it is more appropriate to use f than sigma  to quantify the interstitial retardation of convective transport. This is because the definition of f is more physically meaningful and straightforward than sigma . There are no data of f in solid tumors. The value of f depends on the volume ratio of Vd/Vi and the interstitial fluid volume fraction (phi ). The ratio of Vd/Vi, pooled from different groups, was inversely correlated with the infusion rate (Fig. 4). The phi  might be increased near the infusion site during intratumoral infusion. However, the change in phi  should be small, because the cavity size was much smaller than that of the blue region. Therefore, the data shown in Fig. 4 suggest that f decreases or interstitial retardation increases with the infusion rate. The inverse correlation is consistent with the data in the literature (16, 27, 28).

The retardation of convective transport is likely caused by extracellular matrix and cells in tumors. However, several other mechanisms exist that may reduce molecule distribution in solid tumors during infusion. First, the interstital fluid pressure is high and nearly uniform in solid tumors (13). The elevated IFP reduces the driving force for intratumoral infusion, which is the difference between the infusion pressure and the IFP. Second, fluid channels from the center to the periphery must be opened and/or connected to allow convective transport. The opening and the connection requires the pressure difference to be higher than a threshold value (see Fig. 3 and Ref. 34). Finally, blood-filled cavities and necrotic areas in solid tumors can act as sinks for the infused molecules and thus prevent a uniform distribution of drugs.

Error analysis. Microwave fixation might cause tissue swelling or shrinking. Thus we quantified changes in the volume of five tumors after fixation and found that they were 1.7%, 4.3%, 2.7%, -3.5%, and 1.6%, respectively, where the minus sign indicates a decrease in the volume. The average of the absolute changes was 2.8%. These data indicated that the effect of fixation on the Vd was smaller than that of diffusion as will be discussed later.

Although convection is the dominant mode of transport during intratumoral infusion, diffusion cannot be neglected near the edge of the distribution volume due to the large concentration gradient. The concentration profile of Evans blue-labeled albumin is nearly uniform in the center and drops quickly to zero within a boundary layer near the edge (24). This concentration profile indicates that the color-image analysis technique will underestimate the distribution volume because of its insensitivity to regions with low concentration of albumin. The underestimation depends on the thickness of the boundary layer (delta ), which can be estimated as 4pi a2D/Q, where a is the radius of distribution volume, D is the diffusion coefficient of albumin, and Q is the infusion rate. If a = 3 mm (see Fig. 1), D = 3 × 10-7 cm2/s (3), and Q = 10 µl/min (see Fig. 4), then the ratio of delta /a is ~10-5 (<<1). Therefore, the concentration profile is close to a step function immediately after infusion. However, diffusion of albumin during microwave fixation may enlarge the boundary layer. The enlargement can be estimated based on a mathematical model of one-dimensional diffusion of albumin (8). The details of the estimation are as follows.

The diffusion coefficient of albumin at room temperature (20°C) is ~3 × 10-7 cm2/s (3). The initial concentration of albumin (C0) was assumed to be uniform within the sphere and zero outside the sphere. During the fixation, the temperature in the tissue was assumed to be 100°C, which decreased the viscosity of the interstitial fluid by a factor of ~5 and increased the diffusion coefficient by a factor of 6.4 according to the Stokes-Einstein equation. During the microwave fixation (90 s), the concentration profile was changed from a step function of radial distance to a more spread form. If the initial radius of the distribution volume was 3 mm, the locations with the concentration of 97% and 3% of C0 would occur at 99% and 110% of the initial radius, respectively. We defined the distance between these locations as the thickness of the boundary layer. Thus the mathematical model predicted that the thickness of the boundary layer was increased from zero to 11% of the sphere radius during the fixation. The thickness increase may cause ~10% overestimation in Vd.

The image analysis techniques used in the study also introduced errors in the estimation of distribution volume. It was likely that the blue area determined by the color-image analysis technique underestimated the distribution area of the tracer. The underestimation was caused by the inability of the color technique to include faint blue areas in the periphery of the dye spot. The lack of sensitivity to the faint color was partly due to the need to eliminate the background blue tint caused by the variation in the light source of the scanner. On the other hand, the background problem made the color-image analysis technique insensitive to fixation-induced artifacts in the distribution area of Evans blue-labeled albumin as mentioned above. In contrast, the fluorescence-image analysis technique was more accurate to detect the distribution area of Evans blue-labeled albumin and thus more sensitive to fixation-induced artifacts. Consequently, it might overestimate the distribution volume by 10%. The overestimation could not explain the twofold difference in Vd/Vi quantified by two different techniques, which was likely caused by the insensitivity of the color technique to Evans blue-labeled albumin.

Implications for drug delivery. Intratumoral infusion has the potential for controlled delivery of large therapeutic agents throughout tumor tissues. The results of this study indicate that a critical infusion pressure is required to overcome the IFP and induce tissue deformation that opens and connects transport channels within tumor tissues. However, a pressure gradient that is too large may rupture structures in tissues, causing a heterogeneous distribution or back flow of infusate through the needle track. Thus optimal control of intratumoral infusion is required for uniformly and reproducibly distributing large therapeutic agents throughout tumor tissues.

In summary, the distribution volume of color molecules in solid tumors can be quantified using the technique developed in our study. Both Vd and Vd/Vi were pressure or flow rate dependent. These data may provide important information on how to optimize intratumoral infusion of therapeutic agents in solid tumors.


    ACKNOWLEDGEMENTS

We thank Jennifer L. Lanzen for tumor preparations and Dr. Mark W. Dewhirst for scientific discussion.


    FOOTNOTES

The work is supported in part by the Whitaker Foundation Grant 97-0062 and the National Science Foundation Grant BES-9984062. S. McGuire is supported by a predoctoral fellowship from the Whitaker Foundation.

Address for reprint requests and other correspondence: F. Yuan, Dept. of Biomedical Engineering, Box 90281, Duke University, Durham, NC 27708 (E-mail: fyuan{at}acpub.duke.edu).

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

Received 17 October 2000; accepted in final form 13 April 2001.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

1.   Barry, SI, and Aldis GK. Flow-induced deformation from pressurized cavities in absorbing porous tissues. Bull Math Biol 54: 977-997, 1992[ISI][Medline].

2.   Basser, PJ. Interstitial pressure, volume, and flow during infusion into brain tissue. Microvasc Res 44: 143-165, 1992[ISI][Medline].

3.   Berk, DA, Yuan F, Leunig M, and Jain RK. Direct in vivo measurement of targeted binding in a human tumor xenograft. Proc Natl Acad Sci USA 94: 1785-1790, 1997[Abstract/Free Full Text].

4.   Bobo, RH, Laske DW, Akbasak A, Morrison PF, Dedrick RL, and Oldfield EH. Convection-enhanced delivery of macromolecules in the brain. Proc Natl Acad Sci USA 91: 2076-2080, 1994[Abstract/Free Full Text].

5.   Boucher, Y, Brekken C, Netti PA, Baxter LT, and Jain RK. Intratumoral infusion of fluid: estimation of hydraulic conductivity and implications for the delivery of therapeutic agents. Br J Cancer 78: 1442-1448, 1998[ISI][Medline].

6.   Cervos-Navarro, J, Turker T, and Worthmann F. Morphology of non-vascular intracerebral fluid spaces. Acta Neurochir Suppl (Wien) 60: 147-150, 1994[Medline].

7.   Chen, MY, Lonser RR, Morrison PF, Governale LS, and Oldfield EH. Variables affecting convection-enhanced delivery to the striatum: a systematic examination of rate of infusion, cannula size, infusate concentration, and tissue-cannula sealing time. J Neurosurg 90: 315-320, 1999[ISI][Medline].

8.   Crank, J. The Mathematics of Diffusion. Oxford: Clarendon, 1975.

9.   Dang, W, Colvin OM, Brem H, and Saltzman WM. Covalent coupling of methotrexate to dextran enhances the penetration of cytotoxicity into a tissue-like matrix. Cancer Res 54: 1729-1735, 1994[Abstract/Free Full Text].

10.   Dillehay, LE. Decreasing resistance during fast infusion of a subcutaneous tumor. Anticancer Res 17: 461-466, 1997[ISI][Medline].

11.   Fry, DL, Cornhill JF, Sharma H, Pap JM, and Mitschelen J. Uptake of low density lipoprotein, albumin, and water by deendothelialized in vitro minipig aorta. Arteriosclerosis 6: 475-490, 1986[Abstract/Free Full Text].

12.   Fung, LK, and Saltzman WM. Polymeric implants for cancer chemotherapy. Adv Drug Delivery Res 26: 209-230, 1997[ISI][Medline].

13.   Jain, RK. Delivery of molecular and cellular medicine to solid tumors. Microcirculation 4: 1-23, 1997[Medline].

14.   Juweid, M, Neumann R, Paik C, Perez-Bacete MJ, Sato J, van Osdol W, and Weinstein JN. Micropharmacology of monoclonal antibodies in solid tumors: direct experimental evidence for a binding site barrier. Cancer Res 52: 5144-5153, 1992[Abstract/Free Full Text].

15.   Krol, A, Maresca J, Dewhirst MW, and Yuan F. Available volume fraction of macromolecules in a fibrosarcoma: implications for drug delivery. Cancer Res 59: 4136-4141, 1999[Abstract/Free Full Text].

16.   Kroll, RA, Pagel MA, Muldoon LL, Roman-Goldstein S, and Neuwelt EA. Increasing volume of distribution to the brain with interstitial infusion: dose, rather than convection, might be the most important factor. Neurosurgery 38: 746-752, 1996[ISI][Medline].

17.   Lai, WM, and Mow VC. Drag-induced compression of articular cartilage during a permeation experiment. Biorheology 17: 111-123, 1980[ISI][Medline].

18.   Laske, DW, Youle RJ, and Oldfield EH. Tumor regression with regional distribution of the targeted toxin TF-CRM107 in patients with malignant brain tumors. Nat Med 3: 1362-1368, 1997[ISI][Medline].

19.   Levick, JR. An analysis of the interaction between interstitial plasma protein, interstitial flow, and fenestral filtration and its application to synovium. Microvasc Res 47: 90-125, 1994[ISI][Medline].

20.   Levick, JR. Flow through interstitium and other fibrous matrices. Q J Exp Physiol 72: 409-438, 1987[Abstract/Free Full Text].

21.   Lieberman, DM, Laske DW, Morrison PF, Bankiewicz KS, and Oldfield EH. Convection-enhanced distribution of large molecules in gray matter during interstitial drug infusion. J Neurosurg 82: 1021-1029, 1995[ISI][Medline].

22.   Martin, I, Obradovic B, FL, and VNG Method for quantitative analysis of glycosaminoglycan distribution in cultured natural and engineered cartilage. Ann Biomed Eng 27: 656-662, 1999[ISI][Medline].

23.   Milenic, DE, Yokota T, Filpula DR, Finkelman MA, Dodd SW, Wood JF, Whitlow M, Snoy P, and Schlom J. Construction, binding properties, metabolism, and tumor targeting of a single-chain Fv derived from the pancarcinoma monoclonal antibody CC49. Cancer Res 51: 6363-6371, 1991[ISI][Medline].

24.   Morrison, PF, Laske DW, Bobo H, Oldfield EH, and Dedrick RL. High-flow microinfusion: tissue penetration and pharmacodynamics. Am J Physiol Regulatory Integrative Comp Physiol 266: R292-R305, 1994[Abstract/Free Full Text].

25.   Netti, PA, Berk DA, Swartz MA, Grodzinsky AJ, and Jain RK. Role of extracellular matrix assembly in interstitial transport in solid tumors. Cancer Res 60: 2497-2503, 2000[Abstract/Free Full Text].

26.   Order, SE, Siegel JA, Principato R, Zeiger LE, Johnson E, Lang P, Lustig R, and Wallner PE. Selective tumor irradiation by infusional brachytherapy in nonresectable pancreatic cancer: a phase I study. Int J Radiat Oncol Biol Phys 36: 1117-1126, 1996[ISI][Medline].

27.   Parameswaran, S, Brown LV, Ibbott GS, and Lai-Fook SJ. Hydraulic conductivity, albumin reflection and diffusion coefficients of pig mediastinal pleura. Microvasc Res 58: 114-127, 1999[ISI][Medline].

28.   Parameswaran, S, Brown LV, and Lai-Fook SJ. Effect of flow on hydraulic conductivity and reflection coefficient of rabbit mesentery. Microcirculation 5: 265-274, 1998[ISI][Medline].

29.   Parker, KH, Mehta RV, and Caro CG. Steady flow in porous, elastically deformable materials. J Appl Mech 54: 794-800, 1987.

30.   Shea, LD, Smiley E, Bonadio J, and Mooney DJ. DNA delivery from polymer matrices for tissue engineering. Nat Biotechnol 17: 551-554, 1999[ISI][Medline].

31.   Strobl, G. The Physics of Polymers. Berlin: Springer-Verlag, 1997.

32.   Yuan, F. Transvascular drug delivery in solid tumors. Semin Rad Oncol 8: 164-175, 1998[ISI][Medline].

33.   Zakaria, ER, Lofthouse J, and Flessner MF. In vivo hydraulic conductivity of muscle: effects of hydrostatic pressure. Am J Physiol Heart Circ Physiol 273: H2774-H2782, 1997[Abstract/Free Full Text].

34.   Zhang, XY, Luck J, Dewhirst MW, and Yuan F. Interstitial hydraulic conductivity in a fibrosarcoma. Am J Physiol Heart Circ Physiol 279: H2726-H2734, 2000[Abstract/Free Full Text].

Am J Physiol Heart Circ Physiol 281(2):H715-H721
0363-6135/01 $5.00 Copyright © 2001 the American Physiological Society


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