INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

INTERSTITIAL TRANSPORT of large therapeutic agents is one of the major problems for drug and gene delivery in solid tumors (19). These agents accumulate only in perivascular regions when delivered systemically (19, 21, 31, 44, 46). The penetration depth of liposomes, for example, is ~30 µm at 52 h after intravenous injection (46). In the case of local drug delivery using controlled release devices, large therapeutic agents accumulate only in the vicinity of devices even a few days after device implantation (12, 39). The limited interstitial penetration in solid tumors is caused by slow diffusion and inadequate convective transport due to elevated interstitial fluid pressure (19). Diffusion of molecules cannot be changed significantly unless chemical structures of therapeutic agents or tissues are modified substantially, whereas convection can be enhanced through either elevation of systemic blood pressure (17, 35) or intratumoral infusion of therapeutic agents (10, 27, 43). Convection may improve drug delivery by up to 40% in the systemic approach and by several orders of magnitude in the case of intratumoral infusion. Bobo et al. (5) demonstrated that the distribution volume of ¹¹¹In-labeled transferrin infused directly into the brain at 4.0 µl/min is ~20 times larger than the distribution volume of the same molecule through pure diffusion. Intratumoral infusion of therapeutic agents has shown promising results in the treatment of nonresectable tumors in the brain and the pancreas (27, 43). The treatment of brain tumor patients has achieved >50% response rate without causing severe systemic toxicity (27). However, the efficiency of intratumoral infusion of therapeutic agents remains to be improved.

The efficiency depends on several transport mechanisms (5, 8, 25, 32, 34) that are related to 1) hydraulic conductivity, 2) tissue deformation, 3) retardation of convective transport, and 4) gradient of interstitial fluid pressure established during the infusion. The pressure gradient is a driving force for convective transport, but an increase in the gradient does not necessarily improve the distribution of therapeutic agents in tissues (25). This is because biological tissues are viscoelastic materials (13). The increase in the pressure gradient may cause tissue compression that will lead to a significant increase in the interstitial resistance to convective transport through a decrease in the hydraulic conductivity (K). Therefore, it is important to quantify how tissue deformation affects K to improve the efficiency of intratumoral infusion of therapeutic agents. However, most techniques for K measurement will cause tissue deformation by themselves. Consequently, only the apparent hydraulic conductivity (K_app) has been determined experimentally in normal and tumor tissues as well as in polymer gels (1, 2, 9, 15, 18, 20, 22, 23, 26, 37, 40, 41, 47, 48). K_app is defined by Darcy's law, assuming that tissue deformation is negligible in deriving the relationship between perfusion pressure and flow rate. K_app has been used to determine K as a function of tissue deformation through mathematical models (2, 18, 23, 26, 37). K_app can be altered significantly during interstitial perfusion in normal tissues and polymer gels (2, 15, 18, 20, 22, 23, 26, 37, 41, 47), but perfusion-induced changes in K_app in tumor tissues are still unknown. To this end, K_app in fibrosarcoma tissues was quantified in this study using two ex vivo perfusion systems. We found that variation in perfusion conditions could alter K_app in solid tumors by several orders of magnitude and that the changes in K_app might be explained by perfusion pressure-induced tissue deformation.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Tumors

Measurement of K_app

Perfusion of tumor slices. A piece of tumor tissue was glued onto a specimen block and transferred to the stage of a Vibratome (model 3000, Technical Products International, St. Louis, MO) maintained at 4°C. The tissue was sectioned into 900-µm slices by the Vibratome, and the slices were cut into 5-mm disks using a skin biopsy punch. The disks were then mounted in a perfusion chamber modified from the original design by Swabb et al. (40). The procedure of preparation is as follows. A tumor disk was sandwiched between two nylon meshes with the thickness of 200 µm, average pore size of 300 µm, and 50% open area. The nylon meshes were supported by polyethylene frits (average pore size of 70 µm), which were clamped together by a Delrin chamber with the spacing controlled by two rubber O-rings. The whole perfusion chamber was immersed in 0.1% albumin solution and ~1 cm below the surface. One end of the chamber was open to the solution, and the other end was connected to a reservoir of the same albumin solution. The height of reservoir relative to the chamber level was defined as the perfusion pressure (cmH₂O). The volume of infused fluid varied between 0.5 and 6 µl, depending on the infusion pressure and the time period of infusion. Effect of the infusion volume on the infusion pressure was negligible, because the diameter of the reservoir was ~1 cm. A small air bubble was introduced into the tubing connecting the chamber and the reservoir, and the product of bubble velocity and cross-sectional area of tubing was used to quantify the perfusion rate. The entire perfusion system was maintained at 4°C. At each setting of the reservoir height, the perfusion rate was monitored as a function of time. We found that it reached steady state within 200 min, and the steady state could be maintained for at least 17 h. The rate of flow at steady state (Q) was used to calculate K_app in all experiments based on Darcy's law: K_app = (Qh₀)/(Sp), where p was the pressure difference, S was the cross-sectional area of the chamber, and h₀ was the slice thickness before perfusion (i.e., 900 µm).

6

Intratumoral infusion using a 23-gauge needle. A tumor chunk (~1.5 cm in size) was immersed in physiological saline maintained at 4°C in a container mounted on a stage. The center of the chunk was <1 cm below the surface of saline. The tumor was perfused with the solution of 0.1% Evans blue-labeled albumin via a 23-gauge needle inserted into the center of the chunk. The needle was connected to an albumin solution reservoir via tubing. Again, the perfusion pressure was defined as the relative height of the reservoir, and the flow rate was determined by the velocity of a bubble introduced into the tubing. During the perfusion of tumor chunks, the flow rates at pressures of 94 and 163 cmH₂O were so high that the entire tumors became blue within 10 min before the perfusion reached the steady state. To circumvent this problem, we quantified the flow rate every 20 s until its variation was <10% between two adjacent measurements. The perfusion was then stopped, and the last measurement of flow rate was used to determine K_app. The measurements of K_app at 20 and 36 cmH₂O were performed at the steady state of perfusion. The perfusion was nearly spherically symmetric, and the size of tumors was much larger than the needle diameter. Therefore, K_app was calculated based on Darcy's law for unidirectional flow in an infinite region around a spherical fluid cavity: K_app = Q/(4a₀p₀), where Q is the flow rate, P_o is the perfusion pressure, and a₀ is the initial radius of fluid cavity. We assumed that a₀ was equal to the radius of needle tip. The radius of cavity may increase with time. The increase will affect K but not K_app measurement.

Estimation of the Distribution Volume

Viability and Total Number of Cells

Mathematical Model

(1)

(2)

(3)

(4)

Statistical Analysis

	RESULTS

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1-D Perfusion of Tumor Slices

View larger version (16K): [in this window] [in a new window]   Fig. 1.   A: effect of perfusion pressure on the apparent hydraulic conductivity (Kapp) in a rat fibrosarcoma. The symbols and error bars represent means and SD (n = 5), respectively. The arrows indicate the direction of pressure change. Temperature is 4°C. B: effect of tissue temperature on Kapp. The perfusion pressures (cmH2O) were 94 (open bars), 139 (filled bars), and 163 (stippled bars). The columns and error bars represent mean and SD (n = 6), respectively.

Tumor tissues are heterogeneous. To reduce the heterogeneity in our experiments, K_app was measured using the same tumor slice when the pressure difference was changed in a cycle (Fig. 1A), i.e., seven data points were obtained from each slice. It took 3-4 h to obtain one data point (see METHODS). Therefore, each slice had to be perfused for ~24 h. During this long period of perfusion, tissue temperature needed to be maintained at 4°C to minimize cell damage. However, the temperature in solid tumors in vivo ranges between 32 and 37°C, depending on the site of tumor growth. Therefore, we investigated the effect of tissue temperature on interstitial fluid flow and K_app.

Temperature may affect K_app through both fluid viscosity and tissue structures. To minimize tissue damage induced by long-term perfusion at high temperatures mentioned above, each tumor slice was perfused at a fixed pressure and temperature. When the pressure or the temperature had to be changed, a new tissue slice was perfused in the study. We found that K_app was temperature dependent at the perfusion pressures of 139 and 163 cmH₂O, respectively (P < 0.01) (Fig. 1B). At 94 cmH₂O, the temperature dependence was not statistically significant (P = 0.068). The insignificance was caused by one data point at 4°C that was much larger than the rest five data points in the same group, presumably due to tumor heterogeneity. Removal of that data point made the temperature dependence of K_app at 94 cmH₂O significant as well. The temperature dependence in all pressure groups became insignificant when the data were normalized by the viscosity of solutions at the corresponding temperatures (P > 0.5). These results were consistent with those in the literature (40), suggesting that the temperature dependence of K_app is caused by changes in fluid viscosity. Meanwhile, we also found that temperature could significantly affect the barrier function of tissue slices. When a slice was perfused ex vivo at 4°C and the perfusion pressure was maintained at a constant level, the perfusion rate decreased gradually with time and eventually reached the steady state within 200 min. However, we found that in some experiments at 37 or 41°C, the perfusion rate decreased gradually with time only for a certain period and then increased suddenly by a factor of >10 within a few seconds before reaching the steady state. The sudden increase in the perfusion rate suggested that the tumor slice was ruptured. The percentage of ruptured slices was both temperature and pressure dependent (Table 1). At low temperature (4°C) or pressure (94 cmH₂O), no rupture was observed, presumably due to minimal cell damage and inactivation of proteases in tissues. When both temperature and pressure were increased, the percentage of ruptured slices was increased as well (Table 1). When rupture happened, we immediately stopped experiments and discarded data.

To understand mechanisms underlying the tissue rupture, we quantified cell viability in tissues perfused or incubated without perfusion for 3 h at different temperatures. We found that cell viability was independent of the perfusion pressure but was affected by temperature. The viability ranged from 86 to 95% at 4°C, from 67 to 85% at 37°C, and from 40 to 60% at 41°C (n = 4). In addition, the cell density was between 3.7 and 6.2 × 10⁵ in four tumors incubated at 4°C. As the incubation temperature was increased, the average decrease in cell density was 9% at 37°C and 28% at 41°C. These data suggested that the rupture of slices was partly caused by cell death and loss in tumors. However, cell death and loss do not necessarily lead to tissue rupture, because only a fraction of slices was ruptured during the perfusion (see Table 1). This apparent contradiction could be explained by the distribution of cell damage. If the damage was concentrated in a few spots, then the rupture was more likely to occur in the weakened regions. On the other hand, tissue rupture did not have to occur if the same amount of damaged cells were distributed uniformly throughout multiple layers of cells in a slice. Another important factor that may cause tissue rupture is the pressure gradient across tumor slices. Cell damage may destroy cell-ECM or cell-cell adhesions. Loosened cells, subcellular components, or ECM could be pushed through weakened regions in tissues by the pressure gradient and then cause tissue rupture. This mechanism might explain why the percentage of ruptured slices was pressure dependent (Table 1). Taken together, the rupture of tumor slices was likely caused by cell death and loss as well as the pressure gradient across slices; the total number of damaged cells did not have to be correlated with the probability of tissue rupture.

3-D Perfusion in Tumor Chunks

Again, we found that K_app was pressure dependent (P < 0.01) (Fig. 2). The threshold pressure required for starting the fluid flow was ~10 cmH₂O, which was lower than that in 1-D perfusion (see Fig. 1A). When the perfusion pressure was increased from 20 to 163 cmH₂O, K_app was increased 538-fold (Fig. 2). The amount of changes in K_app for the same pressure range was much higher than that observed in 1-D experiments (Fig. 2). The maximum difference in K_app between 1-D versus 3-D experiments was 80,260-fold (Fig. 2) and could be further increased by increasing the perfusion pressure. In addition to K_app, we estimated the ratio of distribution volume of Evans blue- labeled albumin in tissues (V_d) versus volume of infused solution (V_i). We found that V_d/V_i ranged between 0.63 and 1.25, depending on the perfusion pressure. The data of V_d/V_i are important in understanding mechanisms of the large increase in K_app shown in Fig. 2, which will be discussed later. In 3-D experiments, we found sometimes that the distribution volume of Evans blue in tumor tissues was irregular. In this case, the experimental data were discarded. The irregularity could have been caused by several possibilities. One was that the needle tip was inserted into a necrotic region or a large blood pool in solid tumors. Another was that tumor tissues were ruptured during infusion.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   The Kapp in fibrosarcomas at different perfusion pressures. The curve labeled with 1-D (1-dimensional) was copied from the data at 4°C shown in Fig. 1B. The curve labeled with 3-D (3-dimensional) was obtained from the infusion experiments in which 0.1% Evans blue-labeled albumin solution was infused into tumor chunks via a 23-gauge needle. The perfusion pressure varied between 20 and 163 cmH2O. The threshold pressures in 1-D and 3-D experiments are indicated by an arrowhead and arrow, respectively. The symbols and error bars represent mean and SD, respectively. The number of tumors was 6 in 1-D experiments and 3 or 4 in 3-D experiments. Temperature is 4°C.

Numerical Simulation of Fluid Transport in a Channel

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Simulation of the effective hydraulic conductivity in a slit channel (Kchannel) as a function of the relative channel height (h/h0, where h is the channel height and ho is the channel height before channel deformation) and k0, using Eqs. 1 through 4. (Kchannel)0 and k0 are Kchannel and the specific hydraulic permeability before channel deformation, respectively, and h2/12µ is the effective hydraulic conductivity in a channel without extracellular matrix. A: Kchannel is normalized by (Kchannel)0; B: Kchannel is normalized by h2/12µ. The value of k0 varied from 21 to 500 nm2.

The effective hydraulic conductivity depended on the specific hydraulic permeability in the interstitial space before channel deformation (k₀). The effect of k₀ on K_channel/(h²/12µ) was more significant than that on K_channel/(K_channel)₀ (Fig. 3). At h/h₀ = 100, K_channel/(K_channel)₀ and K_channel/(h²/12µ) were increased by factors of 4.9 and 13.0, respectively when k₀ increased from 21 to 500 nm². k₀ had minimal effect on the shapes of K_channel/(K_channel)₀ and K_channel/(h²/12µ) profiles (Fig. 3).

The results shown in Fig. 3A demonstrate that the hydraulic conductivity was very sensitive to the channel height. An increase in the channel height from 20 nm to 2 µm would lead to a 938-fold increase in K_channel in baseline simulations. Similar changes in h could also occur in tumor tissues when they were stretched in both longitudinal and latitudinal directions during 3-D infusion experiments. In the case of 1-D perfusion experiments, tissue slices were compressed in the direction of flow. The compression had a tendency to reduce the intercellular distance in both flow and lateral directions. In this case, both h/h₀ and K_channel/(K_channel)₀ were <1 (Fig. 3A). The simulation results shown in Fig. 3A were consistent qualitatively with our experimental data of K_app in tumor tissues shown in Fig. 2.

The ratio of K_channel and h²/12µ characterized the relative contribution of the channel wall to flow resistance. When h/h₀ was close to 1  ₀, ECM was densely packed and the space between fibers of ECM approached zero. When h/h₀ was large, i.e., > , interaction between the channel wall and fluid was negligible compared with that between ECM and fluid. In both extreme cases, the dominant resistance to fluid flow in the channel came from ECM. Therefore, the ratio of K_channel and h²/12µ had a bell-shaped curve when h/h₀ was increased from 1  ₀ to 100 and k₀ was fixed (Fig. 3B).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Pressure Dependence of K_app

When tumor tissues were compressed in a confined space in 1-D perfusion experiments, the volume of tissue slices was reduced. There existed two competing forces in the lateral direction, which might affect interstitial water channels across tissues in the direction of perfusion. One was the fluid pressure established during the perfusion; another was the solid stress induced by tissue compression. The fluid stress, p, tended to enlarge water channels and reduce ECM density, whereas the solid stress in the direction perpendicular to the channel wall, _rr, had opposite effects on these channels and ECM density. Both stresses should increase with the perfusion pressure, because 1) cellular space was less compressible than interstitial space and 2) the diameter of tissue slices was fixed by the rubber O-rings mounted in the perfusion chamber. However, the stress difference, p  _rr, may not always increase monotonically with the perfusion pressure. When the perfusion pressure was low, tissue deformation was small and the compression-induced solid stress in the lateral direction was weak. Thus the stress difference might increase with the perfusion pressure. On the other hand, tissue deformation and the solid stress could be large when the perfusion pressure was high. Under this condition, the stress difference would decrease with the perfusion pressure. This behavior of stress difference provides a potential mechanism for explaining the K_app profile shown in Fig. 1A. During 3-D infusion experiments, tumor tissues were stretched in both longitudinal and latitudinal directions and compressed in the radial direction (3, 4). Thus the tissue volume was increased and the volume dilatation was positive everywhere in tissues (3, 4). In this case, both the solid and the fluid stresses in the circumferential direction would act together to open water channels across tissues in the radial direction. Therefore, K_app increased exponentially with the infusion pressure (Fig. 2).

One potential artifact that might cause the large increase in K_app observed in 3-D experiments was the backflow of infused fluid through the needle track (5, 8, 10). To estimate the effect of backflow on the experimental results shown in Fig. 2, tumor chunks were cut into four parts along the needle track immediately after infusion of Evans blue-labeled albumin solution. We found that there was always a blue spot at the center of each tumor chunk. No blue staining of needle tracks was observed in tumor chunks except for a few tumors perfused at 163 cmH₂O. All tumors with blue needle tracks were discarded. In addition to the examination of the needle track, we estimated the upper bound of the amount of fluid that could leak out along the needle track. The estimation was based on the measurement of V_d/V_i. If convection is the dominant mode of transport, this ratio should be close to /, where  is the fractional volume of interstitial fluid and  is the retardation coefficient of albumin. Therefore, the amount of fluid that could leak out along the needle track should be less than (V_i  V_d), because  < 1 (11, 28).  is ~50% in fibrosarcomas (24), and we found that V_d/V_i ranged between 0.63 and 1.25. Thus (V_i  V_d) was between 38 and 87% of the infused volume. These analyses suggested that the backflow accounted for at most a threefold overestimation of K_app, which was several orders of magnitude smaller than the increase in K_app shown in Fig. 2. Therefore, the large increase in K_app during 3-D experiments was mainly caused by tissue deformation-induced changes in interstitial structures.

Tissue deformation not only affected K_app but also likely caused the hysteresis in the K_app profile shown in Fig. 1A. This is because biological tissues are viscoelastic materials (13) and tissue deformation is irreversible.

The existence of the threshold pressure suggests that majority of the interstitial fluid in nonperfused tumor tissues is immobilized by ECM (15) and/or disconnected pores in the interstitial space. When the perfusion pressure is higher than the threshold level, it may open and/or connect water channels in the interstitial space and thus enable fluid flow in tissues (15). The differences in the threshold pressure between 1-D and 3-D experiments, shown in Figs. 1A and 2, could be explained by the fluid and solid stresses exerted on the wall of channels across tissues as discussed above. These stresses were in the opposite directions during 1-D experiments and the same direction during 3-D experiments. Thus the perfusion pressure required to start fluid flow in tissues was higher in tissue slices than in tissue chunks.

Comparison With Data in the Literature

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In addition to normal tissues mentioned above, the hydraulic conductivity in polymer gels has been investigated (20, 22, 37). Parker et al. (37) showed that K decreases exponentially as a function of square root of strain gradient when a column of polyurethane foam is compressed in the direction of flow. Similarly, K_app in Matrigel membrane is decreased by ~50% when the hydrostatic pressure difference across the membrane is increased from 6 to 78 cmH₂O (22). In agarose gels, K_app decreases as a linear function of the pressure difference across the gel membrane, and the amount of decrease depends on the concentration of agarose in gels (20). Comparing with K in biological tissues, K in gels is less affected by the pressure gradient or gel deformation, presumably due to the lack of cellular structures.

Studies of interstitial fluid transport in tumor tissues have demonstrated that K_app is tumor dependent (6, 36, 40, 48). For example, K_app are 1.8 × 10⁷ cm² · cmH₂O¹ · s¹ in a human colon adenocarcinoma (LS174T) (48) and 3.1 × 10⁸ cm² · cmH₂O¹ · s¹ in Morris hepatoma (40). These data are two to three orders of magnitude higher than those shown in Fig. 1A. The discrepancy is not caused by experimental conditions, because tumor tissues in these studies are perfused using the same method as that in our 1-D experiments and the perfusion pressure is maintained at constant levels ranging from 4 to 85 cmH₂O. Thus other mechanisms need to be considered. In our 1-D experiments, we found that it was necessary to put two rubber O-rings in the perfusion chamber to prevent water leakiness through the junction of perfusion chambers. However, only one O-ring was used in previous studies (40, 48). In addition, K_app is tumor dependent. Netti et al. (36) quantified K_app in several tumors using a confined compression method. These authors have shown that K_app of a human soft tissue sarcoma (HSTS 26T) is 6.8 × 10⁸ cm² · cmH₂O¹ · s¹, which is 24 times lower than that of a mouse mammary carcinoma (MCaIV) under the same experimental conditions (36). The latter is found to be 1.8 × 10⁶ cm² · cmH₂O¹ · s¹.

In addition to the tumor dependence, Netti et al. (36) showed that K_app decreases exponentially as a function of compression strain in tumor tissues. At the strain of 0.2, K_app is about one order of magnitude smaller than that without deformation, which is similar to the data in a cartilage study mentioned above (26, 33). Boucher et al. (6) quantified K_app in vivo using a double-needle technique. They found that K_app is 1.3 × 10⁷ cm² · cmH₂O¹ · s¹ in LS174T tumors, which is close to those quantified ex vivo using either 1-D perfusion technique (48) or confined compression method (36).

Effects of ECM chemistry on K_app in solid tumors have been investigated in previous studies (36, 40). However, the results are still controversial. It is not clear if there exists a correlation between K_app and the concentration of glycosaminoglycans or other ECM components. Concentration of ECM components is just one variable that may affect K_app. Other variables include volume fraction of cells, arrangement of cells, ECM assembly, and cell-cell or cell-ECM adhesion. Unless these variables are well controlled in experiments, correlation between K_app and concentration of ECM components can be arbitrary.

Perfusion pressure-induced changes in K_app have not been considered in previous studies. However, this information is important in quantitative analysis of intratumoral infusion of drugs. Dillehay (10) investigated intratumoral infusion of blue dextran solution with fixed infusion rates. The author demonstrates that the infusion pressure increases initially and then slowly decreases with time during the infusion. Similar results have been found in the study of intrabrain infusion of sucrose and transferrin solutions (5). The slow pressure drop is likely caused by two mechanisms. One is the stretch of tumor tissues in both longitudinal and latitudinal directions as discussed above, which increases K and thus reduces the pressure. Another is stress relaxation in tissues during infusion, because biological tissues are viscoelastic materials (13). Stress relaxation reduces shear modulus and thus resistance to opening fluid channels. Consequently, more channels are opened, K is increased, and a lower interstitial fluid pressure gradient is required to maintain the same flow rate through tissues.

Implications for Drug and Gene Delivery

In conclusion, data in this study show that there exists a threshold infusion pressure below which intratumoral infusion cannot be achieved. Furthermore, the hydraulic conductivity is very sensitive to the infusion pressure and can be altered by several orders of magnitude, depending on how tissues are perfused. These experimental data suggest that 1) any change in tissue structures will alter the hydraulic conductivity and 2) it is very important to specify experimental conditions when comparing data of the hydraulic conductivity from different studies, even in the same tissue.