
[Cancer Research 60, 2497-2503, May 1, 2000]
© 2000 American Association for Cancer Research
Role of Extracellular Matrix Assembly in Interstitial Transport in Solid Tumors1
Paolo A. Netti2,
David A. Berk3,
Melody A. Swartz4,
Alan J. Grodzinsky and
Rakesh K. Jain5
Steele Laboratory for Tumor Biology, Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 [P. A. N., D. A. B., M. A. S., R. K. J.], and Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 [A. J. G.]
 |
ABSTRACT
|
|---|
The extracellular matrix (ECM) may contribute to the drug resistance of
a solid tumor by preventing the penetration of therapeutic agents. We
measured differences in interstitial resistance to macromolecule (IgG)
motion in four tumor types and found an unexpected correspondence
between transport resistance and the mechanical stiffness. The
interstitial diffusion coefficient of IgG was measured in
situ by fluorescence redistribution after photobleaching.
Tissue elastic modulus and hydraulic conductivity were measured
by confined compression of excised tissue. In apparent contradiction to
an existing paradigm, these functional properties are correlated with
total tissue content of collagen, not glycosaminoglycan. An extended
collagen network was observed in the more penetration-resistant tumors.
Collagenase treatment of the more penetration-resistant tumors
significantly increased the IgG interstitial diffusion rate. We
conclude that collagen influences the tissue resistance to
macromolecule transport, possibly by binding and stabilizing the
glycosaminoglycan component of the ECM. These findings suggest a new
method to screen tumors for potential resistance to macromolecule-based
therapy. Moreover, collagen and collagen-proteoglycan bonds are
identified as potential targets of treatment to improve macromolecule
delivery.
 |
INTRODUCTION
|
|---|
Solid tumors may evince "physiological resistance" to
treatment, partly by preventing the delivery of blood-borne drugs to
cancer cells (1, 2, 3)
. The tumor
ECM6
is one source of such resistance; tumor and stromal cells produce and
assemble a matrix of collagens, proteoglycans, and other molecules that
hinder the transport of macromolecules. A potentially serious flaw of
novel anticancer strategies such as gene and immune therapies is their
reliance on high molecular weight agents that could fail to penetrate
the tumor interstitium. Although the importance of this type of
physiological resistance is recognized (4
, 5)
, no method
has yet been devised to identify penetration-resistant tumors or to
modify the permeability of the tumor ECM.
In mature tissues, resistance to water and solute transport is
generally attributed to the amount of so-called hydrophilic ground
substance, predominately GAG (6, 7, 8, 9)
. However, it is now
appreciated that GAG content alone does not fully account for the high
transport resistance presented by many soft tissues
(10, 11, 12)
. Tumor tissue may possess unique characteristics,
attributable in part to an embryonic-like stage of development with
extensive synthesis of ECM (13, 14, 15)
, which leads to
substantial differences in composition and assembly compared with the
host tissue (16, 17, 18, 19)
. These differences may have important
functional consequences. This study explored whether resistance to
macromolecule transport in a range of tumors is related to gross
differences in tumor ECM composition.
We postulated that anomalous assembly of the collagen network component
and its interaction with the proteoglycan component of the tumor ECM
could greatly influence the physiological barrier to macromolecule
motion posed by healthy tissue ECM. To test this hypothesis, we
evaluated the interstitial transport of the proteins IgG and BSA in
four different tumor lines and correlated the resistance with ECM
structure and composition. As a corollary to this hypothesis, we also
tested whether resistance to macromolecule penetration is correlated
with the mechanical stiffness of tissue, a property that is also
dependent on the fibrillar collagen network and its interaction with
the proteoglycans.
 |
Materials and Methods
|
|---|
Tumor Preparation
Four different tumor lines were used in this study: human colon
adenocarcinoma (LS174T); human glioblastoma (U87); human soft tissue
sarcoma (HSTS 26T), all of which were xenografted in athymic
NCr/Sed-nu/nu mice; and murine mammary carcinoma (MCaIV)
grown in C3H mice. Tumors used for determination of mechanical and
fluid transport properties, biochemical assays, and histological
staining were grown s.c. in the leg. The tumors used for interstitial
diffusion measurements were implanted in the s.c. region of the dorsal
skin within a window chamber preparation described previously
(20)
. All procedures were performed in accordance with the
animal care guidelines of the Massachusetts General Hospital.
Mechanical and Fluid Transport Properties
The mechanical and fluid transport parameters of tumor
interstitium were determined by confined compression tests following
the same procedures adopted previously for cartilage (21
, 22)
. The diameter of s.c. tumors used for these measurements
ranged from 7 to 10 mm (1520 days postimplantation). Slices of
freshly excised tissue, 6 mm in diameter and 0.81.6-mm thick, were
placed in a poly(methyl methacrylate) cylindrical confining chamber. A
fitted porous polyethylene platen was placed above to maintain chemical
equilibrium with the physiological saline and to allow interstitial
fluid to flow freely between the tissue and the saline reservoir during
the experiment. The chamber was mounted in an ultrasensitive
servo-controlled materials tester (Dynastat Mechanical Spectrometer;
IMASS, Hingham, MA) as described by Frank and Grodzinsky
(22)
. Each specimen was compressed 25 µm in ramps of
15 s and allowed to relax for 20 min. Ten successive measurements
were performed on each tissue slice. At each step of tissue
compression, the hydraulic conductivity K was estimated from
the transient stress relaxation rate by using a poroviscoelastic model
(see Appendix I) . Fig. 1
shows typical stress relaxation curves obtained for the four different
tumors analyzed. The solid lines are the data fitting obtained with the
model.

View larger version (22K):
[in this window]
[in a new window]
|
Fig. 1. Stress relaxation in confined compression for four tumor
types. Typical stress relaxation curves obtained by compressing tumor
tissue in a confined chamber. The HSTS 26T sarcoma (D)
and U87 glioblastoma (C) tissues present a sequential
increase of stress with strain, whereas for the LS174T
(A) and MCaIV (B) carcinomas, the stress
relaxes almost to the initial value.
|
|
Diffusion Coefficient Measurements.
The interstitial diffusion rate of tracer macromolecules was determined
by FRAP with spatial Fourier analysis as described previously
(23)
. This implementation of the FRAP method measures the
mobility of fluorescently labeled molecules over a length scale of
10100 µm. Fluorescent molecules are introduced into the
interstitial space of tissue and allowed to reach a quasi-steady-state
distribution (no measurable change in local concentration over a time
scale of minutes). The tissue is irradiated for a duration of 50100
ms with blue light (wavelength, 488 nm) from an argon ion laser (model
2020; Spectra-Physics, Mountain View, CA) focused to a spot size of
40 µm diameter with an incident power of
30 mW. This pulse
of light creates a darkened photobleached region that subsequently
dissipates as nonfluorescent and fluorescent tracer molecules mix
because of diffusion. The rate of spot dissipation is quantified by
image analysis, and as described previously (23)
, is fit
to a two-component model that assumes a freely diffusing fraction of
fluorescent molecules and an immobile nonspecifically bound fraction.
The diffusion coefficients were measured in tumors implanted in dorsal
skinfold chambers, 1517 days postimplantation, when each tumor had
reached approximately 34 mm in diameter. The probe molecules (500
µg of BSA or 300 µg of IgG in 0.15 ml of sterile PBS) were
administered systemically via tail vein. The IgG was a nonbinding
monoclonal antibody, S1, of type IgG subclass 1. It was supplied as a
gift from Hybritech (San Diego, CA) and prepared by filtration
in a size exclusion chromatography column, eluted with isotonic PBS and
filter-sterilized. The FRAP measurements for BSA and IgG were performed
at 8 and 24 h after injection, respectively. In a different group
of HSTS 26T and U87 tumors, diffusion coefficients were determined
before and after collagenase treatment. Tumors were treated immediately
after the initial determination of IgG mobility. Treatment consisted of
a local injection of 0.3 ml of 10% collagenase (from
Clostridium, obtained from United States Biochemical Corp.,
Cleveland, OH) in PBS or, for the control groups, 0.3 ml of saline
alone. The diffusion coefficient was measured again 24 h after
treatment, and statistical significance of the change was assessed by a
two-tailed paired t test.
Determination of the Composition and Structure of Tumor
Interstitial Matrix.
The biochemical analysis for GAG, HA, and collagen content was
performed on s.c. tumors of 78 mm diameter. Tumor tissues were
surgically excised from the s.c. tissue of the hind limb, cut in three
pieces, rapidly frozen in liquid nitrogen, and stored at -70°C. Each
piece (4050 mg) was then used for one of the three analyses. GAG
content was determined by the method described previously
(24)
. Tissues were finely dispersed with a homogenizer
(Polytron; Brinkmann Instrument, Westbury, NY), solubilized in 1 ml of
digest buffer (125 µg/ml papain in 0.1 M sodium
phosphate, 5 mM Na2 EDTA, and 5
mM cysteine-HCl, pH 6.0), and incubated for 18 h at
60°C. Sulfated GAG content was determined with the Blyscan
Proteoglycan and Glycosaminoglycan assay (Biocolor Ltd., Belfast,
Ireland). The total amount of GAG was determined by acids-carbazole
reaction (25)
. The results of both measurements were
expressed as equivalent mass of hexuronic acid. The amount of HA was
estimated as the difference between the total and sulfated GAG
measurements.
To measure total collagen content, 100 ml of papain digest were
hydrolyzed in 6 N HCl at 110°C for 18 h. The
hydroxyproline content of the hydrolysate was then assessed by
colorimetry (26)
. Results are expressed as mg of collagen
by reference to a standard solution of purified collagen type I
(Vitrogen 100; Collagen Corp., Palo Alto, CA) in which a
hydroxyproline:collagen ratio of 6.8 was measured.
Three tumors of each group were processed for histological staining.
The tissue was embedded in paraffin, and 5-µm sections were cut from
the fixed tissue and stained with Massons trichrome for collagen or
PAS for proteoglycans. The stained sections were observed by
transmitted light microscopy with a x40 objective, and images were
recorded on color photographic film and subsequently digitized on a
flatbed color scanner. The collagen stain images shown here were
produced by subtracting the red from the blue channel of the digitized
image (Adobe Photoshop software) so that the regions of greatest
collagen staining (red absorbance) appear blue.
 |
RESULTS
|
|---|
Penetrability of tumors to macromolecules correlates with tissue
elasticity and hydraulic conductivity.
The tumors can be classified, according to their mechanical behavior in
confined compression, into "rigid" and "soft" groups. Fig. 2
shows composite equilibrium stress-strain curves for the four different
tumor lines. The elastic moduli shown in Table 1
are calculated from the stress-strain curve at strains <10%
(inset of Fig. 2
). The sarcoma (HSTS 26T) and glioblastoma
(U87) display sequential increases of stress with strain, as is typical
of normal soft tissues (21
, 22)
. The two carcinomas, in
contrast, exhibit viscous behavior typical of a macromolecular solution
rather than a well-structured solid matrix. This is also evident by the
data of Fig. 1
. After each successive compression, the stress measured
in the two carcinomas relaxed down to the initial value, whereas for
the sarcoma and glioblastoma, the stress decayed to a plateau value
higher than the initial value. Fig. 2
indicates that at strains <5%,
the two carcinomas show a virtually infinite compliance (zero slope of
the stress-strain curve), indicating an absence of structural integrity
(Fig. 1
, inset). The hydraulic conductivity of the tumor
tissues was evaluated by fitting the data for stress relaxation after
confined compression (Fig. 1)
. Fig. 3
shows the tissue hydraulic conductivity for the four tumors as a
function of tissue deformation (i.e., hydration). As
expected, the hydraulic conductivity is a strong function of tissue
hydration, according to data reported for other soft tissues
(27)
. The dependence of K on tissue hydration
is well described by an exponential law, in agreement to that suggested
in the literature for soft tissues (28)
and hydrogels
(29)
. To compare our results with those published for
normal tissues, we obtained the hydraulic conductivity of tumor tissues
by extrapolating the data of Fig. 3
to zero deformation. This value
represents the hydraulic conductivity of unstrained tissue. By
comparing our values with a compilation of published values for normal
tissue (27)
, we found that the resistance to water flow in
all but one of the tumors was lower than that of normal tissues of
comparable GAG content.
View this table:
[in this window]
[in a new window]
|
Table 1 Mechanical and transport properties of four tumor types
Elasticity and water flow are assessed by confined compression. Elastic
moduli are obtained by a linear least-squares fit of the equilibrium
stress-strain data for strains <0.1. The hydraulic conductivity
K0 of the unstressed tissue is estimated from the
transient stress relaxation at each compression step.
K0 is significantly higher in HSTS 26T
(P < 0.05; ANOVA), whereas the variation in
K0 among the other three tumor lines is not
statistically significant. Data are the mean and SE of at least five
tumor samples. The diffusion coefficient of IgG is measured by FRAP.
Values in parentheses indicate the range of ±1 SD about the mean of at
least five tumors, based on a log-normal distribution. A statistically
significant dependence on tumor type is found for IgG mobility; IgG
diffusivity is >2-fold higher in the two carcinomas (MCaIV and LS174T)
compared with the glioblastoma (U87) and sarcoma (HSTS 26T).
|
|
We used the FRAP technique to measure the interstitial mobility of
tracer proteins in vivo (30
, 31)
. This
technique measures protein mobility at the microscopic level so that
transport in the bulk interstitial matrix is assessed separately from
transvascular transport (extravasation across endothelial cells and
associated perivascular matrix). In all tumors, a significant fraction
(2040%) of the macromolecules was immobile over the time-scale of
100 s; this fraction was attributed to nonspecific binding.
Comparison among the tumor groups revealed no significant difference in
the nonspecific binding. The diffusion rate of the remaining unbound
fraction was observed to depend on the molecule and tumor type. Fig. 4
shows the mean diffusivity of macromolecules in the four different
tumor tissues. The diffusion coefficients in buffered saline solution
alone (+) were also determined. The lines shown in the plot indicate
the power law dependence of diffusion coefficient on macromolecule
radius (D
R-n) over a limited range:
the free-solution data fit the Stokes-Einstein hydrodynamic model of
mobility (n = 1); the glioblastoma/sarcoma
group exhibits a much stronger dependence (n = 3) than the carcinoma group (n = 1.5).
Consistent with previous studies, BSA diffused at a modestly hindered
rate that did not differ significantly among tumor types. Although the
mean BSA mobility in the MCaIV and LS174T groups are
10% greater
than in the U87 and HSTS 26T groups, the difference is not significant
given the variance in the data (ANOVA test). However, as indicated in
Table 1
, the diffusion coefficient of the larger IgG molecule is
significantly greater in the two carcinomas (MCaIV and LS174T) compared
with the glioblastoma (U87) and sarcoma (HSTS 26T). The statistical
comparison between tumor types (two-tailed unpaired t test)
is as follows: no significant difference between LS174T
versus MCaIV (P = 0.88) or between
HSTS 26T versus U87 (P = 0.76);
significant differences between LS174T versus HSTS 26T
(P = 0.0027), MCaIV versus HSTS
26T (P = 0.0023), LS174T versus
U87 (P = 0.00044), and MCaIV
versus U87 (P = 0.0002). These
results indicate a correlation between mechanical stiffness and
resistance to movement of macromolecules of tumor tissues.
Interstitial movement of macromolecules does not correlate with GAG
content.
Having observed a link between tissue mechanical rigidity and
resistance to the transport of the macromolecule IgG, we sought to
identify a corresponding link to ECM composition. Fig. 5A
shows the total GAG, sulfated GAG, and HA contents of each
tumor. We detected no significant differences in sulfated GAG content
among the tumors. However, HSTS 26T and MCaIV had a higher content of
total GAG and, by inference, HA compared with both U87 and LS174T. When
HA content is calculated as the difference between total and sulfated
GAG, the
2-fold greater value measured for MCaIV and HSTS 26T
compared with LS174T and U87 is statistically significant
(P < 0.05). The significant differences in
HA content, however, are not consistent with the differences seen in
the functional parameters. Altogether, there is poor correlation
between functional properties (resistance to transport or compression;
Table 1
) and GAG or HA content. On the other hand, the total collagen
content of each tissue (Fig. 5B)
does appear to mirror the
measurements of elasticity and IgG mobility. The "rigid" U87 and
HSTS tumors have significantly higher collagen levels compared with the
"soft" carcinoma group.
Role of collagen organization on interstitial transport of
macromolecules.
To better understand the role of collagen on the transport resistance,
we also sought to identify differences in collagen distribution among
the different tumor tissues. Fig. 6
shows typical cross-sections of each tumor type stained for collagen.
The U87 and HSTS 26T tumors show more intense staining for collagen
compared with the two carcinomas, consistent with the biochemical data
from Fig. 5
. In addition, it is remarkable to note the apparent absence
of any collagen organization in the two carcinomas, whereas the sarcoma
and glioblastoma instead show apparently well-organized collagen
lattices. A relatively collagen-rich area was evident at the border
between the carcinomas and the host tissue; this "capsule" probably
constitutes the major portion of collagen detected by chemical assay
(Fig. 5B)
in the carcinomas.

View larger version (140K):
[in this window]
[in a new window]
|
Fig. 6. Histological staining of collagen in the four different
tumors. The collagen staining is weak and diffuse in the MCaIV
(A) and LS174T (B) compared with U87
(C) and HSTS 26T (D). The most important
feature to note is the lack of an interconnected collagen network in
the two carcinomas; collagen is associated with blood vessels. Compared
with the carcinoma tissues, the U87 and HSTS 26T sections show
well-organized interconnected collagen lattices surrounding cell
clusters. The HSTS 26T sarcoma has a finer network structure compared
with the U87 tissue.
|
|
The histological data suggest that the organization of collagen, in
addition to the absolute concentration, may be important in controlling
transport. To test this hypothesis, we treated tumors of the
"rigid" type with collagenase to enzymatically degrade collagen
network. After collagenase treatment, the diffusivity of IgG in these
low-mobility groups increased by
2-fold (Fig. 7)
to the same level observed in the two (untreated) carcinomas (values
shown in Table 1
). Collagenase treatment induced increases in the IgG
interstitial diffusion coefficient by 100% in HSTS 26T
(P < 0.0001) and 80% in U87
(P < 0.05), whereas the control saline
treatment had no significant effect. This observation supports the
hypothesis that an intact collagen network is required for tissue to
effectively resist penetration by macromolecules.

View larger version (51K):
[in this window]
[in a new window]
|
Fig. 7. Effect of collagenase treatment on IgG mobility in U87 and
HSTS 26T. Measurements were performed 24 h (pretreatment diffusion
coefficient) and 48 h (24 h after treatment) after i.v.
administration of fluorescein-labeled IgG. There were four tumors in
each collagenase-treated group and three tumors in each saline-treated
control group. At least 10 FRAP measurements were performed in each
tumor. Bars, SD.
|
|
 |
DISCUSSION
|
|---|
The ECM acts as a dispersive filter, controlling the
composition of extracellular fluid and the rate of molecular
trafficking. This control is mediated by a synergistic interaction
among ECM constituents. Although proteoglycans are essential to the
physiological functions of the ECM, our data support the view that
proteoglycans require a stabilizing solid matrix to exert their full
transport-limiting effect. It is widely accepted that in mature normal
tissues, the collagen network provides the structural and mechanical
integrity of the ECM (12
, 32)
, whereas proteoglycans
anchored to the network regulate the movement of fluid and solute
(12
, 27)
and provide resistance to compressive forces
(12
, 33)
. Indeed, the importance of a structural matrix is
made evident by the observation that macromolecular solutions of GAG
offer transport resistance orders of magnitude lower than most tissues
with equal proteoglycan content (27)
. Interestingly, the
hydraulic conductivities of LS174T and MCaIV tumors are comparable with
those of GAG solution of the same concentration, whereas the hydraulic
conductivity of HSTS tumor is comparable with that of soft tissue with
the same GAG content (27)
. Hence, this suggests that
tumors rich in HA are not necessarily resistant to fluid and
macromolecule penetration unless the HA is stabilized by a collagen
matrix.
Tissue collagen composition alone is unlikely to completely control the
resistance to transport of macromolecules. It has been reported that
collagen gels in vitro exhibit resistances to transport of
fluid (34)
and macromolecules (35)
, which are
significantly less than that shown by tissues having the same collagen
composition. Our results suggest that the organization of the collagen
and the combination of collagen and proteoglycans contribute
significantly to the interstitial transport resistance. This hypothesis
is also supported by in vitro data showing that composite
gels of collagen and hyaluronic acid have a higher resistance to
macromolecular transport than gels of collagen or hyaluronic acid alone
(36)
.
The transport barrier posed by the ECM is particularly important in
tumor because it may prevent the penetration of therapeutic agents. To
assess the role of ECM composition and organization on the penetration
of high molecular weight therapeutic agents, we evaluated the diffusion
hindrance of probe macromolecules (BSA and nonspecific IgG) within the
tumor interstitium in vivo. The data show that resistance to
IgG penetration is related to tumor rigidity and to collagen
organization, as suggested by histology (Fig. 6)
and tested by
collagenase treatment (Fig. 7)
. In contrast, total tissue content of
proteoglycans did not vary substantially among the four tumor types,
and modest differences in HA and total GAG did not correspond to the
observed differences in the tissue functional properties. This result
is supported by published observations of direct intratumoral infusion
of macromolecular solutions in the two of the same tumor types used for
the present study. Boucher et. al (37)
reported
that when a solution of Evans-blue-stained albumin was infused into the
center of LS174T tumors at flow rates of 0.1 µl/min for 90 min, the
dye flowed radially outward from the needle tip into a spherical volume
of 2.54.0 mm diameter. In contrast, using the same infusion protocol
in HSTS 26T tumors, they observed a greater resistance to flow,
indicated by a nonuniform distribution of the dye and significant
accumulation in a narrow region around the infusion needle. These data
show that tumors with a well-defined collagen network are more
resistant to penetration by macromolecular drugs compared with tumors
that exhibit a loose collagen network. We propose that macromolecule
access to tumor tissue is dominated by deficiencies in collagen
assembly and relatively insensitive to variations in GAG content.
Degeneration of the collagen network and a resulting compromised
physiological function may be general features of tumors. Proteolytic
remodeling of the ECM may be a requirement for tumor angiogenesis,
growth, invasion, and metastasis (38)
. Moreover, molecular
defects in the assembly process may be associated with the loss of
normal cellular growth regulation mechanisms. For example,
ß1 integrin fibronectin receptor expression
such as
5ß1 affects
ECM organization and is altered in neoplastic cells
(39, 40, 41, 42)
. Regardless of the reason, ECM organization is
often abnormal in tumors (16
, 17
, 19)
.
The results identify measurable tumor characteristics that could
be useful in predicting penetration by therapeutic macromolecules. We
suggest that simple histological staining of tumor tissue biopsies can
be used to assess the feasibility of therapeutic approaches requiring
macromolecule penetration. Delivery of high molecular weight agents
should be facilitated in tumors with poorly organized and loosely
interconnected collagen networks. In this study, both types of
carcinoma exhibit deficient collagen assembly, but in general this
trait is probably determined by the interaction of both neoplastic and
host cells. Particularly in tumors of epithelial origin, host stromal
cells are involved in the production and organization of matrix
molecules (43)
. Hence, the transport properties of the
tumor interstitial matrix likely depend on the site of tumor growth as
well as the tumor type.
If "molecular medicine" is to have an impact on cancer treatment,
it will be necessary to confront and overcome the delivery problems
affecting these novel agents. Modification of the tumor ECM is one
strategy that could promote better delivery. Hyaluronidase treatment
reportedly enhances chemotherapy of some tumors. However, this approach
may not be applicable in systemic treatments, and it is possible that
the chemosensitizing effect occurs by mechanisms other than enhanced
permeability of the ECM (44)
. This study points to
collagen as a likely target for modification. A tumor with a
well-developed collagen network could be considered "physiologically
resistant" to macromolecule-based therapies, but this resistance
could be reduced by treatments that reverse or inhibit collagen
production and assembly.
 |
Appendix 1
|
|---|
The proviscoelastic model used to describe the fluid transport
and the mechanical properties of tumor tissue is similar to that
proposed by Mak (45) but with a more suitable constitutive equation.
Following the approach largely used to describe the biomechanics of
cartilage (22
, 28)
, we consider the tumor tissue as a
biphasic medium composed of a solid viscoelastic matrix (ECM) and a
fluid phase (interstitial fluid; Refs. 46
and
47
). The theory assumes that the total stress acting on
the tissue is the sum of the stress acting on the solid matrix and the
stress acting on the interstitial fluid:
The momentum balance for the tissue under the hypothesis of
negligible inertial forces is:
 | (A1) |
For the momentum balance of the fluid phase, it is assumed that
the divergence of the fluid stress is balanced by the fractional drag
force, i.e.:
where
is the drag coefficient;
u
is the displacement of the solid phase;
vf and
u/
t
are the local velocities of the fluid
and solid phase, respectively. This equation can also be written as:
 | (A2) |
where
is the tissue volume fraction and K (=
2/
) is the tissue hydraulic conductivity (a
measure of the resistance to water flow). Eq. A2 represents a
generalized Darcys law, where the hydrostatic pressure gradient acts
on the relative velocity between the solid and liquid phases, and it
expresses the basic concept of the biphasic theory, i.e.,
the coupling between stress and fluid movement. Indeed, if the
divergence of the solid stress tensor
(
·
s) is not zero, then a
hydrostatic pressure gradient arises, leading to a relative motion
between the solid and fluid phase.
The mass balance equations for the fluid and solid phase,
respectively, are:
 | (A3) |
and
 | (A4) |
To complete the description, the constitutive equations for the
fluid and solid phases are needed. Because the average fluid velocity
field (
) is
irrotational (46), it can be described as a perfect fluid,
i.e.:
For the solid matrix, we assume a viscoelastic behavior that,
under the hypothesis of small strain, can be described in general terms
as:
 | (A5) |
where
is the deformation tensor,
e is the dilatation of the tissue
), µ
and
are the Lamé constant, m(t) is the
memory function of the material, and c is a material
constant. The first term is the Laplacian multipliers to take into
account the effect of hydrostatic pressure on the solid matrix; the
second and third terms represent the elastic components of the
mechanical response of the material; and the fourth term takes into
account the effects of viscoelasticity of the matrix. The memory
function can be expressed in terms of the spectrum of relaxation times
of the material [H]:
We assumed the ECM to be a linear viscoelastic solid with a
spectrum of relaxation times:
 | (A6) |
where
-
and
+
are the
shortest and the longest relaxation times, respectively. The parameter
is a measure of the range of the relaxation times. Similar forms of
the relaxation spectrum have been used to describe the viscoelasticity
of soft tissues such as ligaments and skin (48)
.
Combining equations A1
A4 with the constitutive equations of
the fluid and solid phases, the governing equation in the Laplace space
for a uniaxial geometry results:
 | (A7) |
where
 | (A8) |
The boundary equations are:
 | (A9) |
where
is compression displacement at each step (
25
µm), t0 is the time required for the
compression step (15 s), and h is the thickness of the
specimen.
Eq. A8
with the boundary conditions (A9) is integrated in the Laplace
space and then numerically converted in the time domain to fit the
experimental data and estimate the parameters K, H, c, and
.
 |
Appendix 2
|
|---|
 |
ACKNOWLEDGMENTS
|
|---|
We thank Drs. Yves Boucher, Alain Pluen, and Saroja Ramanujan
for many helpful discussions.
 |
FOOTNOTES
|
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
1 Supported by Outstanding Investigator Grant
R35-CA56591 from the National Cancer Institute (to R. K. J.). 
2 Present address: Department of Material and
Production Engineering, University of Naples Federico II, Piazzale
Tecchio, 80, 80125 Napoli, Italy. 
3 Present address: School of Pharmacy and
Pharmaceutical Sciences, University of Manchester, Oxford Road,
Manchester M13 9PL, United Kingdom. 
4 Present address: Department of Chemical
Engineering, Northwestern University, Evanston, IL 60208. 
5 To whom requests for reprints should be
addressed. Phone: (617) 726-4083; Fax: (617) 726-4172; E-mail: jain{at}steele.mgh.harvard.edu 
6 The abbreviations used are: ECM, extracellular
matrix; GAG, glycosamingoglycan; FRAP, fluorescence recovery after
photobleaching; HA, hyaluronan; PAS, periodic acid Schiff. 
Received 8/26/99.
Accepted 3/ 1/00.
 |
REFERENCES
|
|---|
-
Jain R. K. Delivery of molecular medicine to solid tumors. Science (Washington DC), 271: 1079-1080, 1996.[Medline]
-
Jain R. K. The next frontier of molecular medicine: delivery of therapeutics. Nat. Med., 4: 655-657, 1998.[Medline]
-
Jain R. K. 1995 Whitaker Lecture: Delivery of molecules, particles and cells to solid tumors. Ann. Biomed. Eng., 24: 457-473, 1996.[Medline]
-
Swabb E. A., Wei J., Gullino P. M. Diffusion and convection in normal and neoplastic tissues. Cancer Res., 34: 2814-2822, 1974.[Abstract/Free Full Text]
-
Dedrick R. L., Flessner M. F. Pharmacokinetic problems in peritoneal drug administration: tissue penetration and surface exposure. J. Natl. Cancer Inst., 89: 480-487, 1997.[Abstract/Free Full Text]
-
Mow V. C., Mak A. F., Lai W. M., Rosenberg L. C., Tang L. H. Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations. J. Biomech., 17: 325-338, 1984.[Medline]
-
Ogston A. G., Sherman T. F. Effect of hyaluronic acid upon diffusion of solutes and flow of solvent. J. Physiol., 156: 67-74, 1961.
-
Auckland K., Nicolaysen G. Interstitial fluid volume: local regulatory mechanisms. Physiol. Rev., 61: 556-643, 1981.[Free Full Text]
-
Comper W. D., Laurent T. C. Physiological function of connective tissue polysaccharides. Physiol. Rev., 58: 255-315, 1978.[Free Full Text]
-
Jackson G. W., James D. F. The hydrodynamic resistance of hyaluronic acid and its contribution to tissue permeability. Biorheology, 19: 317-330, 1982.[Medline]
-
Levick J. R. Relation between hydraulic resistance and composition of the interstitium Staub N. C. Hogg J. C. Hargens A. R. eds. . Interstitial-Lymphatic Liquid and Solute Movement, 13: 124-133, Karger Basel 1987.
-
Winlove C. P., Parker K. H. The physiological function of the extracellular matrix Reed R. K. Laine G. A. Bert J. L. Winlove C. P. McHale N. eds. . Interstitium, Connective Tissue and Lymphatics, : 137-165, Portland Press London 1995.
-
Iozzo R. V. Biology of a diseaseproteoglycans: structure, function, and role in neoplasia. Lab. Investig., 53: 373-396, 1985.[Medline]
-
Sakamoto S., Sakamoto M. Degradative processes of connective tissue proteins with special emphasis on collagenolysis and bone resorption. Mol. Aspects Med., 10: 301-428, 1988.
-
Ronnov-Jessen L., Petersen O. W., Bissell M. J. Cellular changes involved in conversion of normal to malignant breast: importance of the stromal reaction. Physiol. Rev., 76: 69-125, 1996.[Abstract/Free Full Text]
-
Liotta L. A., Rao C. N. Role of extracellular matrix in cancer. Ann. NY Acad. Sci., 460: 333-344, 1985.[Medline]
-
Dvorak H. F. Tumors. Wounds that do not heal. N. Engl. J. Med., 315: 1650-1659, 1986.[Medline]
-
Labat-Robert J., Robert L. Interaction between structural glycoproteins and collagens Nimmi M. E. eds. . Collagen, 1: 173-186, CRC Press Boca Raton, FL 1988.
-
Line S. R., Torloni H., Junqueira L. C. Diversity of collagen expression in the pleomorphic adenoma of parotid gland. Virchows Archiv. A Pathol. Anat. Histopathol., 414: 477-483, 1989.
-
Leunig M., Yuan F., Menger D. M., Boucher Y., Goetz A. F., Messmer K., Jain R. K. Angiogenesis, microvascular architecture, microhemodynamics, and interstitial fluid pressure during early growth of human adenocarcinoma LS174T in SCID mice. Cancer Res., 52: 6553-6560, 1992.[Abstract/Free Full Text]
-
Mow V. C., Kuei S. C., Lai W. M., Armstrong C. G. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J. Biomech. Eng., 102: 73-84, 1980.[Medline]
-
Frank E. H., Grodzinsky A. J. Cartilage electromechanics. I. Electrokinetic transduction and the effect of electrolyte pH and ionic strength. J. Biomech., 20: 615-627, 1987.[Medline]
-
Berk D. A., Yuan F., Leunig M., Jain R. K. Fluorescence photobleaching with spatial Fourier analysis: measurement of diffusion in light-scattering media. Biophys. J., 65: 2428-2436, 1993.[Abstract/Free Full Text]
-
Sah R. L., Kim Y-J., Doong J. H., Grodzinsky A. J., Plaas A. J. Biosynthetic response of cartilage explants to dynamic compression. J. Orthop. Res., 7: 619-636, 1989.[Medline]
-
Bitter T., Muir H. M. A modified uronic acid carbazole reaction. Anal. Biochem., 4: 330-334, 1962.[Medline]
-
Woessner J. F. The determination of hydroxyproline in tissue and protein samples containing small proportions of the imino acid. Arch. Biochem. Biophys., 93: 440-447, 1961.[Medline]
-
Levick J. R. Flow trough interstitium and other fibrous matrices. Q. J. Exp. Physiol., 72: 409-437, 1987.[Abstract/Free Full Text]
-
Mow V. C., Holmes M. H., Lai W. M. Fluid transport and mechanical properties of articular cartilage: a review. J. Biomech., 17: 377-394, 1984.[Medline]
-
Johnson E. M., Deen W. M. Hydraulic permeability of agarose gels. AlChE J., 42: 1220-1224, 1996.
-
Chary S. R., Jain R. K. Direct measurement of interstitial diffusion and convection of albumin in normal and neoplastic tissues using fluorescence photobleaching. Proc. Natl. Acad. Sci. USA, 86: 5385-5389, 1989.[Abstract/Free Full Text]
-
Berk D. A., Yuan F., Leunig M., Jain R. K. 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]
-
Barocas V. H., Tranquillo R. T. An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. J. Biomech. Eng., 119: 137-145, 1997.[Medline]
-
Silver, F. H. Biological Materials. Structure, Mechanical Properties, and Modelling of Soft Tissues. New York: New York University Press, 1987.
-
Jackson R. L., Bush S. J., Cardin A. D. Glycosaminoglycans: molecular properties, protein interactions, and role in neoplasia. Physiol. Rev., 71: 481-539, 1991.[Free Full Text]
-
Saltzman W. M., Radomsky M. L., Whaley K. J., Cone R. A. Antibody diffusion in human cervical mucus. Biophys. J., 66: 508-515, 1994.[Medline]
-
Shenoy V., Rosenblatt J. Diffusion of macromolecules in collagen and hyaluronic acid. Rigid-rod-flexible polymer, composite matrices. Macromolecules, 28: 8751-8758, 1995.
-
Boucher Y., Brekken C., Netti P. A., Jain R. K. Intratumoral infusion of fluid: estimation of hydraulic conductivity and implication for the delivery of therapeutic agents. Br. J. Cancer, 78: 1442-1448, 1998.[Medline]
-
Coussens L. M., Werb Z. Matrix metalloproteinases and the development of cancer. Chem. Biol., 3: 895-904, 1996.[Medline]
-
McDonald J. A. Extracellular matrix assembly. Annu. Rev. Cell Biol., 4: 183-207, 1988.
-
Plantefaber L. C., Hynes R. O. Changes in integrin receptors on oncogenically transformed cells. Cell, 56: 281-290, 1989.[Medline]
-
Juliano R. L. The role of ß1 integrins in tumors. Cancer Biol., 4: 277-283, 1993.
-
Ruoslahti E. Fibronectin and its
5ß1 integrin receptor in malignancy. Invasion Metastasis, 14: 87-97, 1994.[Medline]
-
Knudson W., Biswas C., Toole B. P. Interactions between human tumor cells and fibroblasts stimulate hyaluronate synthesis. Proc. Natl. Acad. Sci. USA, 81: 6767-6771, 1984.[Abstract/Free Full Text]
-
Croix B. S., Rak J. W., Kapitain S., Sheehan C., Graham C. H., Kerbel R. S. Reversal by hyaluronidase of adhesion-dependent multicellular drug resistance in mammary carcinoma cells. J. Natl. Cancer Inst., 88: 1285-1296, 1996.[Abstract/Free Full Text]
-
Mak A. F. The apparent viscoelastic behavior of articular cartilage. The contributions from the intrinsic matrix viscoelasticity and interstitial flows. J. Biomech. Eng., 108: 123-130, 1986.[Medline]
-
Netti P. A., Baxter L. T., Boucher Y., Skalak R., Jain R. K. Macro and microscopic fluid transport in living tissues: application to solid tumors. AlChE J., 43: 818-834, 1997.
-
Netti P. A., Baxter L. T., Boucher Y., Skalak R., Jain R. K. Time-dependent behavior of interstitial fluid pressure in solid tumors: implication for drug delivery. Cancer Res., 55: 5451-5458, 1995.[Abstract/Free Full Text]
-
Fung, Y. C. Biomechanics. Mechanical Properties of Living Tissues. New York: Springer-Verlag, 1993.
This article has been cited by other articles:

|
 |

|
 |
 
L. Hambach, M. Vermeij, A. Buser, Z. Aghai, T. van der Kwast, and E. Goulmy
Targeting a single mismatched minor histocompatibility antigen with tumor-restricted expression eradicates human solid tumors
Blood,
September 1, 2008;
112(5):
1844 - 1852.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
J. Henshaw, B. Mossop, and F. Yuan
Relaxin treatment of solid tumors: effects on electric field-mediated gene delivery
Mol. Cancer Ther.,
August 1, 2008;
7(8):
2566 - 2573.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
S. Nagano, J. Y. Perentes, R. K. Jain, and Y. Boucher
Cancer Cell Death Enhances the Penetration and Efficacy of Oncolytic Herpes Simplex Virus in Tumors
Cancer Res.,
May 15, 2008;
68(10):
3795 - 3802.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
J. H.E. Baker, K. E. Lindquist, L. A. Huxham, A. H. Kyle, J. T. Sy, and A. I. Minchinton
Direct Visualization of Heterogeneous Extravascular Distribution of Trastuzumab in Human Epidermal Growth Factor Receptor Type 2 Overexpressing Xenografts
Clin. Cancer Res.,
April 1, 2008;
14(7):
2171 - 2179.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
C. M. Ghajar, X. Chen, J. W. Harris, V. Suresh, C. C. W. Hughes, N. L. Jeon, A. J. Putnam, and S. C. George
The Effect of Matrix Density on the Regulation of 3-D Capillary Morphogenesis
Biophys. J.,
March 1, 2008;
94(5):
1930 - 1941.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
A. Khaibullina, B.-S. Jang, H. Sun, N. Le, S. Yu, V. Frenkel, J. A. Carrasquillo, I. Pastan, K. C.P. Li, and C. H. Paik
Pulsed High-Intensity Focused Ultrasound Enhances Uptake of Radiolabeled Monoclonal Antibody to Human Epidermoid Tumor in Nude Mice
J. Nucl. Med.,
February 1, 2008;
49(2):
295 - 302.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
M. Magzoub, S. Jin, and A. S. Verkman
Enhanced macromolecule diffusion deep in tumors after enzymatic digestion of extracellular matrix collagen and its associated proteoglycan decorin
FASEB J,
January 1, 2008;
22(1):
276 - 284.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
W. Mok, Y. Boucher, and R. K. Jain
Matrix Metalloproteinases-1 and -8 Improve the Distribution and Efficacy of an Oncolytic Virus
Cancer Res.,
November 15, 2007;
67(22):
10664 - 10668.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
Y. Zhang, L. Xiang, R. Hassan, and I. Pastan
Immunotoxin and Taxol synergy results from a decrease in shed mesothelin levels in the extracellular space of tumors
PNAS,
October 23, 2007;
104(43):
17099 - 17104.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
O. Tredan, C. M. Galmarini, K. Patel, and I. F. Tannock
Drug Resistance and the Solid Tumor Microenvironment
J Natl Cancer Inst,
October 3, 2007;
99(19):
1441 - 1454.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
A. Oldberg, S. Kalamajski, A. V. Salnikov, L. Stuhr, M. Morgelin, R. K. Reed, N.-E. Heldin, and K. Rubin
Collagen-binding proteoglycan fibromodulin can determine stroma matrix structure and fluid balance in experimental carcinoma
PNAS,
August 28, 2007;
104(35):
13966 - 13971.
[Abstract]
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
M. R. Dreher and A. Chilkoti
Toward a Systems Engineering Approach to Cancer Drug Delivery
J Natl Cancer Inst,
July 4, 2007;
99(13):
983 - 985.
[Full Text]
[PDF]
|
 |
|

|
 |

|
 |
 
S. Ganesh, M. Gonzalez Edick, N. Idamakanti, M. Abramova, M. VanRoey, M. Robinson, C.-O. Yun, and K. Jooss
Relaxin-Expressing, Fiber Chimeric Oncolytic Adenovirus Prolongs Survival of Tumor-Bearing Mice
Cancer Res.,
May 1, 2007;
67(9):
4399 - 4407.
[Abstract]
|