Abstract

The presence of a capsule around a tumor is known to be correlated with benign status, and the absence of a capsule often has negative implications for patient prognosis. A mechanical description is presented of the growth of a tumor and the resulting deformations of surrounding normal tissue. A mathematical model of the mechanics is analyzed using physical parameters measured in vivo and in vitro. The model has only three dimensionless parameters, and its results are very robust with respect to parameter variation. We show that the presence of contractility in the surrounding tissue, corresponding to a host defense, can make an existing capsule denser and constrain the tumor better, but cannot be responsible for the observed pressure gradients in encapsulated tumors. Some implications for treatment are discussed.

References

1.
Vaage
,
J.
,
1992
, “
Fibrosis in Immune Control of Mammary-Tumor Growth
Int. J. Cancer
,
51
, pp.
325
328
.
2.
Robbins, S. L., Cotran, R. S., and Kumar, V., 1984, “Neoplasia,” Pathologic Basis of Disease, 3 Edition, W. B. Saunders, pp. 214–253.
3.
Ng
,
I. O. L.
,
Lai
,
E. C. S.
,
Lai
,
M. M. T.
, and
Fan
,
S. T.
,
1992
, “
Tumor Encapsulation in Hepatocellular Carcinoma: a Pathological Study of 198 Cases
,”
Cancer (N.Y.)
,
70
(
1
), pp.
45
49
.
4.
Barr
,
L. C.
,
1989
, “
The Encapsulation of Tumours
,”
Clin. Expl. Metastasis
,
7
(
3
), pp.
277
282
.
5.
Barr, L. C., Carter, R. L., and Davies, A. J. S., 1988, “Encapsulation of Tumours as a Modified Wound Healing Response,” Lancet, ii, pp. 135–137.
6.
Helmlinger
,
G.
,
Netti
,
P. A.
,
Lichtenbeld
,
H. C.
,
Melder
,
R. J.
, and
Jain
,
R. K.
,
1997
, “
Solid Stress Inhibits the Growth of Multicellular Tumor Spheroids
,”
Nature Biotech
,
15
, pp.
778
783
.
7.
Skalak
,
R.
,
Zargaryan
,
S.
,
Jain
,
R. K.
,
Netti
,
P. A.
, and
Hoger
,
A.
,
1996
, “
Compatibility and the Genesis of Residual Stress by Volumetric Growth
,”
J. Math. Biol.
,
34
, pp.
889
914
.
8.
Ritchie, A. C., 1970, “The Classification Morphology and Behavior of Tumours,” General Pathology, 4th Edition, H. E. W. Florey, ed., Lloyd-Luke, p. 668.
9.
Berenblum, L., 1970, “The Nature of Tumour Growth,” General Pathology, 4th Edition, H. E. W. Florey, ed., Lloyd-Luke, pp. 645–667.
10.
Jain
,
R. K.
,
1988
, “
Determinants of Tumor Blood Flow: a Review
,”
Cancer Res.
,
48
, pp.
2641
2658
.
11.
Netti
,
P. A.
,
Baxter
,
L. T.
,
Boucher
,
Y.
,
Skalak
,
R.
, and
Jain
,
R. K.
,
1997
, “
Macro- and Microscopic Fluid Transport in Living Tissues: Application to Solid Tumors
,”
AIChE J.
,
43
(
3
), pp.
818
834
.
12.
Mow
,
V. C.
,
Kuei
,
S. C.
,
Lai
,
W. M.
, and
Armstrong
,
C. G.
,
1980
, “
Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments
,”
ASME J. Biomech. Eng.
,
102
, pp.
73
84
.
13.
Simon
,
B. R.
,
Liable
,
J. P.
,
Pflaster
,
D.
,
Yuan
,
Y.
, and
Krag
,
M. H.
,
1996
, “
A Poroelastic Finite Element Formulation Including Transport and Swelling in Soft Tissue Structures
,”
ASME J. Biomech. Eng.
,
118
, pp.
1
9
.
14.
Joseph, D. D., 1990, Fluid Dynamics of Viscoelastic Liquids, Springer-Verlag, New York, NY.
15.
Drew
,
D. A.
,
1971
, “
Averaged Field Equations for Two-Phase Media
,”
Stud. Appl. Math.
,
L
(
2
), pp.
133
166
.
16.
Drew
,
D. A.
,
1983
, “
Mathematical Modeling of Two-Phase Flow
,”
Annu. Rev. Fluid Mech.
,
15
, pp.
261
291
.
17.
Fung, Y. C., 1990, Biomechanics: Motion, Flow, Stress, and Growth, Springer-Verlag, New York, NY.
18.
Dembo
,
M.
, and
Harlow
,
F.
,
1986
, “
Cell Motion, Contractile Networks, and the Physics of Interpenetrating Reactive Flow
,”
Biophys. J.
,
50
(
1
), pp.
109
121
.
19.
Doi, M., and Edwards, S. F., 1986, The Theory of Polymer Dynamics, Oxford University Press, Oxford, UK.
20.
Swabb
,
E. A.
,
Wei
,
J.
, and
Gullino
,
P. M.
,
1974
, “
Diffusion and Convection in Normal and Neoplastic Tissues
,”
Cancer Res.
,
34
, pp.
2814
2822
.
21.
Boucher
,
Y.
,
Brekken
,
C.
,
Netti
,
P. A.
,
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1998
, “
Intratumoral Infusion of Fluid: Estimation of Hydraulic Conductivity and Implications for the Delivery of Therapeutic Agents
,”
Br. J. Cancer
,
78
(
11
), pp.
1442
1448
.
22.
Barocas
,
V. H.
,
Moon
,
A. G.
, and
Tranquillo
,
R. T.
,
1995
, “
The Fibroblast-Populated Collagen Microsphere Assay of Cell Traction Force—Part 2: Measurement of the Cell Traction Parameter
,”
ASME J. Biomech. Eng.
,
117
, pp.
161
170
.
23.
Forgacs
,
G.
,
Foty
,
R. A.
,
Shafrir
,
Y.
, and
Steinberg
,
M. S.
,
1998
, “
Viscoelastic Properties of Living Embryonic Tissues: a Quantitative Study
,”
Biophys. J.
,
74
(
5
), pp.
2227
2234
.
24.
Jain
,
R. K.
,
1996
, “
1995 Whitaker Lecture: Delivery of Molecules, Particles, and Cells to Solid Tumors
,”
Ann. Biomed. Eng.
,
24
, pp.
457
473
.
25.
Higton
,
D. I. R.
, and
James
,
D. W.
,
1964
, “
The Force of Contraction of Full-Thickness Wounds of Rabbit Skin
,”
Brit. J. Surg.
,
51
, pp.
462
466
.
26.
Kolodney
,
M. S.
, and
Wysolmerski
,
R. B.
,
1992
, “
Isometric Contraction by Fibroblasts and Endothelial Cells in Tissue Culture: a Quantitative Study
,”
J. Cell Biol.
,
117
(
1
), pp.
73
82
.
27.
Kim, S., and Karrila, S. J., 1991, Microhydrodynamics: Principles and Selected Applications, Butterworth-Heinemann, Boston, MA.
28.
Fung, Y. C., 1993, Biomechanics: Mechanical Properties of Living Tissues, 2nd Edition, Springer-Verlag, New York, NY.
29.
Gullino
,
P. M.
,
Clark
,
S. H.
, and
Grantham
,
F. H.
,
1964
, “
The Interstitial Fluid of Solid Tumors
,”
Cancer Res.
,
24
, pp.
780
797
.
30.
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1989
, “
Transport of Fluid and Macromolecules in Tumors I. Role of Interstitial Pressure and Convection
,”
Microvasc. Res.
,
37
, pp.
77
104
.
31.
Boucher
,
Y.
,
Baxter
,
L. T.
, and
Jain
,
R. K.
,
1990
, “
Interstitial Pressure Gradients in Tissue-Isolated and Subcutaneous Tumors: Implications for Therapy
,”
Cancer Res.
,
50
, pp.
4478
4484
.
32.
Boucher
,
Y.
,
Kirkwood
,
J. M.
,
Opacic
,
D.
,
Desantis
,
M.
, and
Jain
,
R. K.
,
1991
, “
Interstitial Hypertension in Superficial Metastatic Melanomas in Humans
,”
Cancer Res.
,
51
, pp.
6691
6694
.
33.
Gutmann
,
R.
,
Leunig
,
M.
,
Feyh
,
J.
,
Goetz
,
A. E.
,
Messmer
,
K.
,
Kastenbauer
,
E.
, and
Jain
,
R. K.
,
1992
, “
Interstitial Hypertension in Head and Neck Tumors in Patients: Correlation with Tumor Size
,”
Cancer Res.
,
52
, pp.
1993
1995
.
34.
Wang
,
H.-B.
,
Dembo
,
M.
, and
Wang
,
Y. -L.
,
2000
, “
Substrate Flexibility Regulates Growth and Apoptosis of Normal but not Transformed Cells
,”
Am. J. Physiol. Cell Physiol.
,
279
, pp.
C1345–C1350
C1345–C1350
.
You do not currently have access to this content.