Interstitial Pressure Gradients in Tissue-isolated and Subcutaneous Tumors:Implications for Therapy1
Yves Boucher,2 Laurence T. Baxter,1 and Rakesh K. Jain4
Tumor Microcirculation Laboratory; Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
ABSTRACT
High interstitial fluid pressure (IFF) in solid tumors is associated withreduced blood flow as well as inadequate delivery of therapeutic agentssuch as monoclonal antibodies. In the present study, IFF was measuredas a function of radial position within two rat tissue-isolated tumors(mammary adenocarcinoma R3230AC, 0.4-1.9 g, n = 9, and Walker 256carcinoma, (1.5 5.0 g, n = 6) and a s.c. tumor (mammary adenocarcinomaR3230AC, 0.6-20.0 g, n = 7). Micropipettes (tip diameters 2 to 4 ^m)connected to a servo-null pressure-monitoring system were introduced todepths of 2.5 to 3.5 mm from the tumor surface and IFF was measuredwhile the micropipettes were retrieved to the surface. The majority (86%)of the pressure profiles demonstrated a large gradient in the peripheryleading to a plateau of almost uniform pressure in the deeper layers ofthe tumors. Within isolated tumors, pressures reached plateau values ata distance of 0.2 to I.I mm from the surface. In s.c. tumors the sharpincrease began in skin and levelled off at the skin-tumor interface. Theseresults demonstrate for the first time that the IFF is elevated throughoutthe tumor and drops precipitously to normal values in the tumor's
periphery or in the immediately surrounding tissue. These results confirmthe predictions of our recently published mathematical model of interstitial fluid transport in tumors (Jain and Baxter, Cancer Res., 48: 7022-7032, 1988), offer novel insight into the etiology of interstitial hypertension, and suggest possible strategies for improved delivery of therapeuticagents.
INTRODUCTION
The therapeutic efficacy of systemically administered anti-neoplastic agents ranging from chemotherapeutic drugs to biological response modifiers such as monoclonal antibodies andcytokines depends upon the ability of these molecules to reachtheir target in adequate quantities. The limited therapeuticsuccess of current systemic antineoplastic regimens may beattributed to their inability to reach all regions of a solid tumorin optimal quantities. For example, monoclonal antibodies havebeen demonstrated to accumulate mainly in the perivascularregions and in the peripheral regions of several solid tumors.In addition to heterogeneous blood supply, we have recentlyproposed another mechanism for the nonuniform delivery oftherapeutic agents: high IFF5 in tumors (1-3). The elevated
Received 12/12/89; revised 4/2/90.The costs of publication of this article were defrayed in part by the payment
of page charges. This article must therefore be hereby marked advertisement inaccordance with 18 U.S.C. Section 1734 solely to indicate this fact.
1Supported by the NCI (CA-36902) and NSF (CBT-88-16062). This work
3 Recipient of NSF Predoctoral Fellowship (1986-1989).4To whom requests for reprints should be addressed.5The abbreviations used are: IFF, interstitial fluid pressure; t.i., tissue isolated;
P,, effective vascular pressure, P, —a A ir; P,, vascular pressure; a A *•,osmoticreflection coefficient x osmotic pressure difference between blood vessel andinterstitium;
where S/Kis exchange vessel surface area per unit volume, ¿pis vascular hydraulicconductivity, K is interstitial hydraulic conductivity, and R is tumor radius.
IFF restricts the access of therapeutic agents to neoplastic cellsby (a) reducing the driving forces for extravasation of fluid andmacromolecules and (b) generating a convective flux of fluidand solute towards the periphery of tumors. For a tumor of 1-cm radius (4.2 g), the value of the radially outward fluid velocityat the tumor periphery is on the order of 0.1 ^m/s (2).
Since the original work of Young et al. (4) in 1950 it hasbeen known that IFF is significantly higher in tumors comparedto normal tissues. Generally, in normal tissues IFPs are subat-mospheric or just above atmospheric values (5), whereas intumors the upper range of pressure is between 10 and 30 mmHg (1). Several studies have also demonstrated that intratumorpressure increases as a tumor grows (4, 6-9). Intratumor pressure gradients have been evaluated by Wiig et al. (6). Themicropuncture technique was used to measure IFF in the superficial layers and the wick-in-needle technique was used formeasurements in the deeper regions. IFF was found to decreasegradually from the center to the periphery of the tumor. Similarresults were also obtained in our laboratory by Misiewicz (9).Recently, we have developed a mathematical model to describethe interstitial pressure as a function of depth in a tumor (3,10). The results of this model suggest that the pressure iselevated throughout the tumor, except for a sharp drop in theperiphery of tissue-isolated tumors (Fig. 1) and at the tumor-normal tissue interface in tumors embedded in normal tissue.While these predictions are plausible, there are no data onprecise spatial distribution of IFF in isolated or embeddedtumors to test this model. Therefore, the goal of this work wasto measure IFF as a function of depth in tumors.
Animals and Tumors. Walker 256 carcinoma and mammary adenocarcinoma R3230AC were transplanted in female Sprague-Dawley andFisher 344 rats, respectively. The two tumors were grown as ovariant.i. preparations with a single artery and vein, following the procedureof Cullino and Grantham (11) as adapted by Sevick and Jain (12). Inbrief, the ovary was removed and tumor slurry was injected in the fatpad which is linked to the rest of the body by the ovarian artery andvein. The preparation was enclosed in a Parafilm bag and when thetumor reached the desired size it was exteriorized for pressure measurements. Subcutaneous tumors were prepared by injecting tumorslurry from the mammary adenocarcinoma R3230AC line in the flankof Fisher 344 rats.
Pressure Measurement. Systemic arterial pressure was measured bya pressure transducer (model P23Gb; Gould Inc., Pittsburgh, PA) filledwith heparinized saline, connected to a preamplifier (model 11-4113-
Fig. 1. The pressure profiles generated with the mathematical model for a t.i.tumor are shown here as normalized pressure as a function of normalized depth(where 0 = tumor surface, 1 = tumor center, and r/R = depth/tumor radius).Profiles are shown for different values of the parameter a2, which is the dimen-
sionless hydraulic conductivity ratio. For physiological parameters within atumor. «2is approximately 1350 (3, 10). Adapted from (Ref. 3). The profiles fora tumor grown s.c. are given in Ref. 10.
TUMOR
MICROMAMPIXATOR
Fig. 2. A diagram of the major components of the experimental system. Amicropipette (length, ~5 cm; tapered portion. 5-mm long; with a tip diameter of2-4 HU) is positioned with a micromanipulator inside the tumor. A servo-nullsystem is used to counterbalance the tissue pressure with an external motor (14).This counter-pressure is then measured with a pressure transducer, and theamplified output is sent to a chart recorder.
01; Gould Inc., Cleveland, OH). Interstitial pressure measurementswere performed using micropipettes and a servo-null device (model 5;
Instrumentation for Physiology and Medicine, Inc., San Diego, CA)(13, 14). The counter-pressure generated by this system was sent to anamplifier (model 13-4615-50; Gould Electronics, Cleveland. OH). Theamplified signals from both pressure-measurement devices were sent toa dual-channel chart recorder (model 595; Omega Engineering, Stamford, CT). This type of active system was required due to the extremelyslow response time of a passive system for a tip diameter of 2 ^m. Thesystem was calibrated by determining the linear relationship betweenimposed pressure and measured pressure in a saline test chamber. Fig.2 shows a schematic diagram of the experimental setup.
A graded micromanipulator was used to maneuver the micropipetteand to measure the depth of insertion. The micropipette, in parallelwith the micromanipulator, was positioned to penetrate the tumorperpendicularly. Pipette insertion was aided by the use of a stereomi-croscope (Nikon SMZ-1; Charles Seifert Associates, Carnegie, PA). Amagnification of X20-45 was used to determine tissue distortion. Thetissue was illuminated by a fiberoptic light source (Nikon MKII fiberoptic light source and bifurcated light guide: Charles Seifert Associates,Carnegie, PA).
Micropipette Preparation. A thick-walled capillary tubing was used(0.86-mm o.d. x 0.38-mm i.d., 0.24-mm wall thickness) to make micro-pipettes with a horizontal pipette puller (Narishege PN-3; MedicalSystems, Corp., Great Neck, NY). The micropipettes were filled with1 M NaCl solution prepared from twice filtered, twice distilled, deion-ized water. The tip diameter ranged from 2 to 4 ^m; the diameter at 1,2, and 3 mm from the tip was 30-35, 75-85, and 150-225 urn,respectively.
Experimental Procedure. The rats were anesthetized with sodiumpentobarbital (40-50 mg/kg). For subsequent injections of anesthetic,an i.p. line was installed. To monitor systemic pressure, the left carotid
artery was cannulated and the rats were placed on a temperature-regulated heating pad. Following a small skin incision, the Parafilmbag enclosing the isolated tumor was removed. To minimize tumormovements due to respiration, two 23-gauge needles were passed
through the skin on opposite sides of the tumor pedicle. The needleswere fixed to a cork which was taped to the heating pad. Subcutaneoustumors were immobilized in a similar way after shaving the fur overlyingthe tumor mass. During the measurement of IFP with the micropunc-ture technique, warm isotonic saline was dripped continuously onisolated tumors and the intact skin overlying s.c. tumors.
After zero pressure was recorded in the saline film covering thetumor, the micropipettes were introduced perpendicularly to the surfaceto depths of 2.5 to 3.5 mm and then retracted to the surface. Individualpressure measurements between 3.5 and 1.5 mm and from 1.5 mm tothe surface were made at intervals of 0.1 to 0.3 mm and 0.05 to 0.15mm, respectively. Each pressure measurement was monitored for atleast 10 s. The IFP measurements were accepted when (a) no visibledistortion of the tumor or skin surface was observed, (h) the fluidcommunication between the micropipette and the interstitial spacecould be demonstrated electrically, and (c) the zero pressure in thesaline at the surface was not modified during the insertion and withdrawal of the micropipette (15). Micropipettes were advanced to fulldepth and retrieved to the surface, since repeated insertion and withdrawal to a given depth led to frequent pipette breakage and clogging.At least two good tracks were required in an animal to validate theresults. Generally, IFP measurements were restricted to one or twosmall (5-mm x 5-mm) regions/tumor.
After the animals were sacrificed, s.c. tumors were removed and themean skin thickness was measured. For skin measurements two smallskin incisions were made in the same region where IFP was estimated.Under a stereomicroscope, the distance between the surface of the skinand the tumor was measured with a micropipette and the gradedmicromanipulator. The mean skin thickness was obtained from at leastfive measurements/tumor.
Control Experiments. To validate the present experimental approach,the following control studies were performed.
(a) The influence of tissue compression and penetration depth ofmicropipettes was evaluated in the thigh muscle of anesthetized ratsand in dead tumor tissue. After the removal of the overlying skin,micropipettes were introduced up to depths of 3.0 to 5.0 mm from thesurface of the muscle. Pressure measurements were obtained at intervalsof 0.2 mm as the micropipettes were withdrawn.
(¿>)IFP stability in the plateau and in the region of a steep pressuregradient was tested by continuously monitoring pressure in each regionfor 5 to 10 min.
(c) To test if the micropipette could create a "tunnel effect," whereby
the IFP could equilibrate, IFP measurements obtained as describedabove were compared to measurements taken up to 200, 400, 800,1200, and 1600 Mm from the surface after the micropipettes wereinserted, respectively, to 350. 600, 1000, !400, and 1800 ^m. After onemeasurement was obtained at each depth, the micropipette was retrieved to the surface. These control measurements were compared todeeper measurements in the same region of the tumor.
(d) To evaluate if the IFP measured in the superficial layers (1-2.5mm from the surface) of tumors is similar to or different from that ofthe central regions, micropuncture and micropore chamber pressuremeasurements were compared simultaneously. Micropore chamberssurrounded by mammary adenocarcinoma R3230AC were preparedfollowing the procedure of Butler et al. (16). In brief, the microporechambers were coated with tumor slurry and installed under the skin.Fluid communication between the chamber and the pressure-measuringdevice was established by PESO tubing ( 16). The pressure was measuredwhen the chamber was surrounded completely by tumor tissue. Withthe rats prepared as described previously, the chambers were connectedto a pressure transducer, amplifier, and chart recording system. Micro-pipettes were introduced to the depth of 2.5 mm from the surface. Asthe micropipettes were retrieved, IFP measurements obtained with thetwo techniques were compared.
(e) Finally, IFP decay after death was studied in t.i. tumors. Systemicand tumor interstitial pressures were recorded simultaneously before
and after the animals were sacrificed with ether or a Nembutal overdose.Data Analysis. The experimental results were compared with our
mathematical model (3, 10). An important feature of this model is thatthe pressure profile in a uniformly perfused tumor depends on twoparameters: P,, the effective vascular pressure, and a, the dimensionlessparameter which incorporates the ratio of vascular to interstitial hydraulic conductivities and the blood vessel surface area/unit tissuevolume. Statistical analysis of the data was performed with a one-tailedStudent t test. The mathematical model was tested by fitting the datato the model to yield these two parameters, using nonlinear least squaresregression. The resulting parameters were compared with literaturevalues.
RESULTS
In the majority of tumors studied (86% of pressure profiles),IFF rose rapidly in the tumor periphery in t.i. tumors (Fig. 3A)and within the skin or in the skin-tumor interface in s.c. tumors(Fig. 35). In both cases the pressure reached a maximum andremained relatively uniform throughout the tumor. To characterize the IFF profiles as a function of depth, the depth at whichthe pressure was 90% or more of the mean plateau pressurewas considered as the end point of the sharp rise. In isolatedtumors the increase in pressure ended at a distance of 0.15 to1.2 mm from the surface. The relative frequency of the endpoint of the pressure rise versus the radial position is illustratedin Fig. 4. The steepness of the increase in IFF was variable. Int.i. Walker 256 carcinoma and mammary adenocarcinoma3230AC the profiles rose, respectively, from atmospheric pressure to 90% of maximum pressures within 0.1 to 0.3 mm and
Fig. 3. Typical experimental pressure profiles for mammary adenocarcinomatumors. A, t.i. tumor (tumor 10, 0.4 g). Maximum pressures between 10 and 15mm Hg were found between 0.15 and 2.0 mm from the tumor surface. The sharprise occurred between 0.2 and 0.8 mm from the surface. B, s.c. tumor (tumor 6.2.6 g), with a mean skin thickness of 300 firn, represented by the vertical line. Intracks 2 and 3 the sharp rise in pressure occurs in skin. The steep rise in pressureseems to occur completely in the tumor for track 4.
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Fig. 4. Histograms representing the relative frequency (number of pressureprofiles) of the distance from the tumor surface to the beginning of the IFFplateau in Walker 256 t.i. tumors, mammary adenocarcinoma R3230AC t.i.. andR3230AC s.c.
Table 1 Types of interstitial pressure profilesShapes of the pressure profiles are described in the text.
No. of profiles
Plateau and Doublesteep gradient U shape plateau
Gradualincrease
Mammary adenocarcinoma(t.i.)
Mammary adenocarcinoma(S.C.)
Walker 256 carcinoma (t.i.)
Total
29(87.9%) 3(9.1%) 1(3.0%) 0
18 (94.7%) 1 (5.3%) O O
15(75.0%) 0 2(10.0%) 3(15.0%)
62(86.0%) 4(6.4%) 3(4.8%) 3(4.8%)
0.1 to 0.8 mm. Within s.c. tumors (mammary adenocarcinomaR3230AC) plateau pressures were reached at 0.1 to 0.8 mmfrom the skin surface.
The mean skin thickness was 0.3 mm (n = 7), with a rangeof 0.12 to 0.55 mm. The minimum and maximum skin thickness values overlying a given tumor could vary by more than100% in some cases. Because of this large variation in skinthickness, it was not possible to determine the exact locationof the pressure increase for the different pressure profiles obtained. However, to obtain a relative estimate, the pressureprofiles were divided into three categories: those starting theirrise at depths smaller than the minimum skin thickness, thoserising at a depth between the minimum and maximum skinthickness, and those rising at a depth greater than the maximumskin thickness. Based on these criteria, 29% of the pressureprofiles started their rise in the skin, 54% at the skin-tumorinterface, and 17% in the tumor.
Three types of atypical pressure profiles were also seen: (a)a U shape formed by high pressures followed by a sharp dropand a rapid increase; (b) a gradual decrease in pressure fromthe deeper to the peripheral regions of the tumor; and (c) aprofile formed by two rapid increases and two plateaus. The Ushapes had a width of 300 to 700 urn and were observed withina distance of 200 to 1400 ^m from the surface. Table 1 showsthe relative frequency of occurrence of the pressure profiles.
The mean systemic pressure was 103 mm Hg (SD = 15.4).The maximum IFPs ranged from 2 mm Hg (Walker 256 t.i.)to 37 mm Hg (mammary adenocarcinoma R3230AC t.i.). Themagnitudes of the mean plateau pressures in tumors are givenin Table 2. A strong correlation was found between the meaninterstitial pressure and the mass of the tumor for Walker 256t.i. (Fig. 5); however, the mammary adenocarcinoma tumors(both s.c. and t.i.) did not show a significant correlation betweenthe mass and IFF. The mean pressure was almost equal in
°Mean ±SD of pressures at depths of 1.0, 1.2, and 1.4 mm.* Statistically significant difference in means (P < 0.05).
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Fig. 5. In A, the mean IFP is plotted versus the depth of the measurement forall Walker 256 t.i. tumors. •,large tumors, >1.2 g (n = 3); O, small tumors,<0.6 g (n = 3). Error bars, S.D. The difference in the mean plateau pressuresbetween large and small tumors is statistically significant (/' •0.05). In B, in theWalker carcinoma t.i. the mean central IFP (depth, >1.25 mm) was linearlyrelated to the tumor mass (r2 = 0.94; IFP = 3.05 x mass (g) + 3.02 mm Hg) for
weights up to 6 g. However, no such correlation was found for other tumorpreparations (see Table 2).
small and large s.c. mammary adenocarcinoma R3230AC tumors.
Control Studies
The measurement of IFP as a function of radial position inthe thigh muscle showed that IFP was not influenced by thedepth of penetration. IFP was found to vary between 0 and 0.4mm Hg. The pressure in dead tumor tissue was 0 mm Hg.
IFP measurements taken after the micropipettes were introduced no more than 0.2 mm past the desired depth showed thatmicropipettes introduced to greater depths (e.g., 2.0 to 3.5 mmfrom the surface) may underestimate the pressures at a distanceof 200 to 1000 urn from the tumor surface (Fig. 6). In somecases the controls showed that deep pressure measurementsshifted the profiles up to 400 /¿mtoward the center of thetumor.
The IFP was stable in both the flat and steep gradient regionsfor periods of up to 10 min. The simultaneous recording ofinterstitial pressure and systemic blood pressure showed that
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Fig. 6. Pressure profiles obtained in a mammary adenocarcinoma R3230ACt.i. tumor. Note that after a deep insertion of the micropipettes (tracks I to 4)the sharp drop occurs at a greater distance from the surface compared tomeasurements (Control) obtained following an insertion to a depth of 1 mm orless. Error bars, SD of four measurements for the control (see "Discussion" for
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Fig. 7. As a control experiment the interstitial (R3230AC t.i.) and systemicarterial pressures were monitored following death of the animal by an etheroverdose. Solid gray line, arterial pressure, ranging from 0 to 100 mm Hg; dashedblack line, interstitial pressure, ranging from 0 to 10 mm Hg. Note that the IFPdecreased in parallel with the systemic pressure.
the two pressures decayed in parallel after death (Fig. 7).The simultaneous measurement of IFP with two techniques
demonstrated that the pressure was very similar in central andsuperficial regions. Mean values of 8.7 and 8.8 mm Hg werefound, respectively, in the center of the tumor by microporechamber measurements and in the superficial regions of thetumor (1-1.5-mm deep) with micropipettes.
DISCUSSION
The objective of this study was to experimentally determinethe spatial distribution of interstitial pressure within solid tumors. These experiments were motivated by predictions of steeppressure gradients in the tumor periphery by our recent mathematical model (3, 10). The principal result of this study is thatIFP is elevated throughout the tumor and drops precipitouslyin the periphery of isolated tumors or at the skin-tumor interface in s.c. tumors. This finding is in general agreement withour model.
Two previous experimental studies showed that interstitialpressure was highest in the center of a tumor and decreasedtoward the periphery (6, 9). Wiig et al. (6) used a combinationof micropipette and wick-in-needle methods, while Misiewicz(9) used micropipettes for all measurements. In both studies,unlike the current study, a sharp pressure drop in the peripherywas not seen. In the study of Wiig et al. (6), mean IFP measurements were made at the "surface," "outer," "middle," and"center" of the tumor, as opposed to obtaining a precise radialdistribution. The "surface" measurements were obtained up to
a depth of 800 urn with micropipettes. No IFF measurementswere reported between 0.8 and 2.0 mm from the tumor surface,and in the deeper layers measurements were made with thewick-in-needle method. Because of the lack of spatial resolution
in the superficial layer, it was difficult to discern the flat andthe steep gradient regions of the pressure profiles. In the deeperlayers, no significant differences in pressure were found betweenthe central and middle layer; however, IFF was significantlyhigher in the center as compared to the outer region. While itis possible that the difference in pressure between outer andcentral regions represents a true biological phenomenon, technical artifacts might also explain the difference in IFF betweenthe two regions. Higher pressures in the center could be due tocompression caused by penetration of the needle. Alternatively,the lower pressure in the outer layer could be due to the "tunnel"
formed by the insertion of the needle used to measure pressure.The IFF in the tunnel could partially equilibrate with theatmospheric pressure or skin pressure, yielding a lower measurement. In addition, the 23-gauge needle (diameter, 0.63 mm)used by Wiig et al. (6) is of larger diameter than a micropipetteand could make a larger tunnel. This argument is supported byour current studies with the micropuncture technique.
In the present study, in the majority (86%) of pressure tracksthe IFF rose rapidly from 0 mm Hg to its maximum value,ranging from 2 to 37 mm Hg, in less than 1 mm from thesurface. However, in many of the pressure tracks, zero pressurewas maintained for depths of 200 to 800 urn into the tumor.This may in part be a function of the insertion depth of themicropipette. The depth of micropipette insertion was found tobe important for the evaluation of IFF at 1 mm from thesurface. When micropipettes were inserted at distances of 1.0mm or less, pressures were higher in the periphery as comparedto deeper insertions (Fig. 6). This control shows that the pressure close to the surface may not be zero but, in fact, closer tothe maximum pressure seen in the center of the tumor. Sincethe measured pressure was non-zero when the pipette was beinginserted but near zero when withdrawn from a depth of 2.0 mmor more, it is probable that the zero pressure tail seen near thesurface might be due to a tunnel being produced by the thickerpart of the capillary tube away from the tip. This would resultin a region of zero pressure where the tissue fluid is in equilibrium with the pressure on the outside of the tumor. This resultsuggests that in reality the pressure gradient may be steeper inthe periphery of the tumor. Difference in the tissue compositionbetween the periphery and the more central parts of t.i. tumorscould also explain the variations in pressure observed at 1 mmfrom the surface. Histological examination of rapidly growingt.i. tumors has demonstrated that the surface may be coveredby a layer of fibrin of variable thickness.6 If the fibrin layer is
noncompliant, then the hole left by the micropipette will notclose, and the measured pressure will be zero. Further insidethe tumor there does not seem to be any error associated witha tunnel produced by the pipette. The pressure was recordedfor 10 min in areas of the tumor where the pressure waschanging with radial position. This pressure remained constantwith time, and high values were maintained.
The change in interstitial pressure due to a decrease in bloodpressure resulting from animal death was quite evident withinminutes after death. There was a rapid initial drop in the firstfew minutes to a few mm Hg, followed by a slower decaytowards zero pressure. These results suggest that the drivingforce for elevated IFF in tumors is the systemic pressure. The
decrease in IFF following animal death was also seen by Wiiget al. (6); however, they did not measure systemic pressuresimultaneously.
Limitations
Depth of penetration is the main limitation of the micro-puncture technique. In normal tissues this is not a majordrawback if one assumes that IFF is uniform throughout thetissue. Because of the presence of pressure gradients in tumors,IFPs have to be evaluated from the superficial to the centralregions. By comparing central (micropore chamber) and superficial (micropuncture) pressures, we found that IFF was similarin the two regions. This is additional evidence for relativelyuniform interstitial hypertension in the deeper layers of tumors.
Since it was practically impossible to relate the skin thicknessto the exact location where the micropipette was inserted,measurements of the mean skin thickness were made in theregion where two or more pressure profiles were obtained.However, due to the large variation of the skin thickness it wasnot possible to determine precisely the exact location of thepressure rise for the different pressure profiles. While it appearsthat, in some cases the pressure increase was in the skin or thetumor periphery, in other cases it was not possible to give adefinitive answer because of the proximity of the pressuregradient to the skin-tumor interface. The variations in skinthickness between the minimum and the maximum value wereoften 300 ¿¿m.The tunnel effect described previously could alsomodify the exact location of the pressure gradient. Although ofminor importance, the 50-100-^m intervals between pressuremeasurements could also be considered as a limiting factor.
Comparison with Mathematical Model
Fig. 8 shows the comparison of our mathematical model withexperimental data for one set of pressure readings. In thisexperiment there is excellent agreement between theory andexperiment. In addition, the best fit values for the parameters(a2 = 1210 ±420, Pc = 10.2 ±1.2 mm Hg) are in goodagreement with average values based on the literature («2=1356, Pe = 11.5; see Ref. 3). The fit was obtained by minimizingthe unweighted sum of squares between the model and data byvarying the two parameters. Table 3 gives the estimated parameters for a number of pressure profiles from different tumortypes. These profiles were selected to be fit by the model based
' P. M. Cullino, personal communication.
Depth (mm)
Fig. 8. This figure shows the comparison of theory to a typical pressure profile(tumor 7. mammary adenocarcinoma s.c.). •.data points; . theoretical profilefitted for two parameters: the effective vascular pressure. P., and the hydraulicconductivity ratio. <t2.Error bars, estimates of the precision of pressure and depthmeasurements. The error in depth measurements was obtained from the variationin the location of the surface between insertion and withdrawal. The error inpressure measurements was a result of the fluctuation of pressure due to animalrespiration. The estimated parameters are very close to the expected physiologicalvalues (see text).
L. Sa a /R = —•—= ratio of vascular to interstitial hydraulic conductivities XK V
surface area of exchange vessels per unit tissue volume.* The tracks from animals 12 and 13 were obtained by inserting the pipette
only 200 f<mpast the desired measurement depth, as opposed to over 2 mm deep.
on two criteria: (a) the region of near-zero pressure, if oneexisted, was less than 300 ¿itnand (b) there were at least fourdata points at or near the value of the plateau pressure.
As discussed in Ref. 10 there are slight differences in themathematical model for s.c. versus t.i. tumors. However, thes.c. and isolated tumor data were analyzed in the same way forthree reasons: (a) including a layer of skin in the theoreticalmodel requires four additional parameters: skin thickness, effective normal vascular pressure, and interstitial and vascularhydraulic conductivities in normal tissue; (b) the length overwhich the pressure drop occurred is greater than the uncertaintyin the measurement of pipette depth and skin thickness; and(c) the shape of the experimental profiles is qualitatively similar. The theory predicts that the pressure increase in a s.c.tumor occurs in the skin rather than in the tumor. In someexperiments the pressure did rise to a near maximum valuewithin the skin, in agreement with the model. However, in othertumors the uncertainties in skin thickness and depth measurements did not permit us to discern whether the pressure rosein the tumor or in surrounding tissue. Unlike model predictions,the IFF did not rise immediately in the periphery of someisolated tumors. As stated earlier, this apparent discrepancy isprobably due to the tunnel effect or a layer of fibrin on thetumor surface.
Another qualitative agreement between theory and experiment was the relationship between blood pressure and interstitial pressure. The decay of the interstitial pressure to 0 mm Hgwithin minutes after animal death and the correlation betweenreduced systemic pressure and reduced interstitial pressuresupport our model, in which a main determinant of tumorinterstitial pressure is the effective vascular pressure. Our mathematical model predicts that the IFF is directly related to theeffective vascular pressure (microvascular pressure minus on-cotic pressure contribution in the exchange microvessels; /•„—
o-ATT).These results also provide novel insights into the etiology
of interstitial hypertension in tumors, as discussed below.
Implications
The results obtained here have significant implications in twoareas: the etiology of interstitial hypertension and the deliveryof therapeutic agents.
Etiology of Interstitial Hypertension. As reviewed recently ( 1),at least three pathophysiological mechanisms have been associated with the elevated interstitial pressure in tumors: the lackof functioning lymphatics, high vascular permeability, and vascular collapse resulting from cells proliferating in a confinedspace. It is evident that the lack of functioning lymphatics isessential for interstitial hypertension. If the net fluid extrava-sating from the exchange vessels could be continuously removedby lymphatic vessels or some other mechanism, the interstitialpressure would not rise to the effective vascular pressure, Pf(=/", —a ATT).The next question is: what leads to values of P,
greater than 30 mm Hg in tumors? If the vessels were nothighly permeable, the osmotic term (a A TT)could be comparableto P„and hence the IFF would be much lower than Pv (or evenclose to zero). However, large vascular permeability would tendto reduce the osmotic pressure contribution and would make Pc(and hence the IFF) close to the hydrostatic pressure in exchange vessels A.
The measured value of /\ in tumor exchange vessels (<20-/jm diameter) is 10-15 mm Hg (17). Therefore, the maximumvalue of IFF in a tissue with highly permeable vessels andnonfunctional lymphatics would be 10-15 mm Hg, considerablyless than 30 mm Hg measured previously and in this investigation. As shown clearly in Fig. 7, the driving force for IFF isthe vascular pressure. Therefore, the vascular pressure in someexchange vessels in tumors has to be equal to or greater than30 mm Hg. Such large vascular pressures are only found inprecapillary arterioles in tumors (17). This observation leads totwo hypotheses: precapillary arterioles in tumors are themselvesfunctioning as exchange vessels (i.e., become permeable) orsomehow the pressure in the exchange vessels is being raisedto the arteriolar level. There is no direct evidence in the literature to date supporting the former hypothesis. There is, however, a plausible mechanism supporting the latter hypothesis.If proliferation of cancer cells in the proximity of an exchangevessel causes it to collapse, the pressure on the proximal sideof the vessel would go up to the level of its feeding arterioleand result in a proportionately higher interstitial pressure. Thishypothesis also explains the relationship between elevated interstitial pressure and vascular stasis and the correlation between IFF and growth in some tumors. At the periphery, theIFF must equilibrate with the surrounding pressure. The pressure drops over a small distance due to the rapid removal offluid from the periphery of the tumor.
Delivery of Therapeutic Agents. The results of the interstitialpressure experiments also have some important implicationsfor cancer detection and treatment. The results show a relativelyhigh and uniform pressure in the center of the tumor and asharp gradient of pressure in the periphery of the tumor. Thisleads to very little filtration of macromolecules from bloodvessels in the center, as well as a convective flow in the tumorperiphery which tends to push the solute towards the edge ofthe tumor (3). These conclusions are also supported by therecent data of Dvorak et al. (18), who have shown that smallmolecules can readily penetrate small tumors, whereas macro-molecules are limited primarily to the normal tissue-tumorinterface region. Considering these factors, novel approaches
to drug treatment using a low molecular weight agent in combination with antibodies have been suggested, e.g., bifunctionalantibody in conjunction with a low molecular weight chelateand antibody-directed catalysis in conjunction with prodrugs(19).
Another effect of the large pressure gradient at the peripheryof the tumor is that it leads to a large convective flow radiallyoutward near the periphery. Therefore, material that has extra-vasated in the periphery of the tumor will be washed out of thetumor as the solute is cleared from the bloodstream. It is alsoimportant to note that there is a large intertumor variation inpressure. Two tumors of the same type and mass, grown in thesame environment, may have greatly different IFPs. A typicalrange of variation is 10-40 mm Hg in large solid tumors. Theheterogeneities in blood flow and other physiological parameters may be much greater, ranging from a perfusion rate of zeroto perfusion rates greater than in the brain (20, 21). For thesereasons the response of tumors to therapeutic agents may varyconsiderably.
Although technically difficult, other approaches suggested bythe results of this study show that delivery could be enhancedby (a) decreasing the interstitial pressure in the center of thetumor by physical or enzymatic means, (b) increasing thediffusional permeability of the tumor blood vessels, allowing apathway for extravasation which does not depend on the difference between vascular and interstitial pressure, or (c) increasingthe dose of unlabeled antibody to increase concentration gradients to aid transcapillary and interstitial diffusion (19).
ACKNOWLEDGMENTS
We thank Brenda Bartel for her assistance in tumor implantationand Dr. Helge Wiig for his helpful comments on the manuscript.
ADDENDUM
Recently in collaboration with Drs. J. M. Kirkwood and W. D.Bloomer, we have measured interstitial hypertension in human tumors.In superficial melanomas the interstitial pressure varied between 39and 45 mm Hg [Y. Boucher, D. Opacic, J. M. Kirkwood, and R. K.Jain. Elevated interstitial fluid pressure in human melanomas (Abstract). 16th Gray Conference—Vasculature as a Target for Anti-Cancer Therapy, Manchester, England, September 17-21, 1990.) andin cervical carcinomas between 10 and 30 mm Hg [H. D. Roh, Y.Boucher, W. D. Bloomer, and R. K. Jain. Interstitial hypertension inhuman cervical carcinomas: Effect of radiation (Abstract). 16th Gray
Conference—Vascular as a Target for Anti-Cancer Therapy, Manchester, England, September 17-21, 1990.].
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