The direct infusion of an agent into a solid tumor, modeled as a spherical poroelastic material with anisotropic dependence of the tumor hydraulic conductivity upon the tissue deformation, is treated both by solving the coupled fluid/elastic equations, and by expressing the solution as an asymptotic expansion in terms of a small parameter, ratio between the driving pressure force in the fluid system, and the elastic properties of the solid. Results at order one match almost perfectly the solutions of the full system over a large range of infusion pressures. Comparison with experimental results is acceptable after the hydraulic conductivity of the medium is properly calibrated. Given the uncertain estimates of some model constants, the order zero solution of the expansion, for which fluid and porous matrix are decoupled, yields acceptable values and trends for all the physical fields of interest, rendering the coupled analysis (in the limit of small displacements) of little use. When the deformation of the tissue becomes large nonlinear elasticity theory must be resorted to.

References

References
1.
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
.
2.
Boucher
,
Y. J.
,
Kirkwood
,
M.
,
Opacic
,
D.
,
Desantis
,
M.
, and
Jain
,
R. K.
, 1991, “
Interstitial Hypertension in Superficial Metastatic Melanomas in Patients
,”
Cancer Res.
,
51
, pp.
6691
6694
.
3.
Roh
,
H. D.
,
Boucher
,
Y.
,
Kalnicki
,
S.
,
Buchsbaum
,
R.
,
Bloomer
,
W. D.
, and
Jain
,
R. K.
, 1991, “
Interstitial Hypertension in Carcinoma of Uterine Cervix in Patients: Possible Correlation With Tumor Oxygenation and Radiation Response
,”
Cancer Res.
,
51
, pp.
6695
6698
.
4.
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
.
5.
Shipley
,
R. J.
, and
Chapman
,
S. J.
, 2010, “
Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours
,”
Bull. Math. Biol.
,
72
, pp.
1464
1491
.
6.
Smith
,
J. H.
, and
Humphrey
,
J. A. C.
, 2007, “
Interstitial Transport and Transvascular Fluid Exchange During Infusion Into Brain and Tumor Tissue
,”
Microvascular Res.
,
73
, pp.
58
73
.
7.
Zhang
,
X.-Y.
,
Luck
,
J.
,
Dewhirst
,
W. M.
, and
Yuan
,
F.
, 2000, “
Interstitial Hydraulic Conductivity in a Fibrosarcoma
,”
Am. J. Physiol.
,
279
, pp.
H2726
H2734
.
8.
Netti
,
P. A.
,
Baxter
,
L. T.
,
Boucher
,
Y.
,
Skalak
,
R. K.
, and
Jain
,
R. K.
, 1995, “
A Poroelastic Model for Interstitial Pressure in Tumors
,”
Biorheology
,
32
, p.
346
.
9.
Sarntinoranont
,
M.
,
Rooney
,
F.
, and
Ferrari
,
M.
, 2003, “
Interstitial Stress and Fluid Pressure Within a Growing Tumor
,”
Ann. Biomed. Eng.
,
31
, pp.
327
335
.
10.
Lai
,
W. M.
, and
Mow
,
V. C.
, 1980, “
Drag-Induced Compression of Articular Cartilage During a Permeation Experiment
,”
Biorheology
,
17
, pp.
111
123
.
11.
Barry
,
S. I.
, and
Aldis
,
G. K.
, 1990, “
Comparison of Models for Flow Induced Deformation of Soft Biological Tissues
,”
J. Biomech.
,
23
, pp.
647
654
.
12.
McGuire
,
S.
,
Zaharoff
,
D.
, and
Yuan
,
F.
, 2006, “
Nonlinear Dependence of Hydraulic Conductivity on Tissue Deformation During Intratumoral Infusion
,”
Ann. Biomed. Eng.
,
34
, pp.
1173
1181
.
13.
Basser
,
P. J.
,. 1992, “
Interstitial Pressure, Volume, and Flow During Infusion Into Brain Tissue
,”
Microvasc. Res.
,
44
, pp.
143
165
.
14.
Pries
,
A. R.
,
Cornelissen
,
A. J. M.
,
Sloot
,
A. A.
,
Hinkeldey
,
M.
,
Dreher
,
M. R.
,
Höpfner
,
M.
,
Dewhirst
,
M. W.
, and
Secomb
,
T. W.
, 2009, “
Structural Adaptation and Heterogeneity of Normal and Tumor Microvascular Networks
,”
PLoS Comput. Biol.
,
5
(
5
), pp.
e1000394
.
15.
Truskey
,
G. A.
,
Yuan
,
F.
, and
Katz
,
D. F.
, 2009,
Transport Phenomena in Biological Systems
,
2nd ed.
,
Pearson Prentice Hall Bioengineering
,
Upper Saddle River, NJ
.
16.
Baxter
,
L. T.
, and
Jain
,
R. K.
, 1990, “
Transport of Fluid and Macromolecules in Tumors. II. Role of Heterogeneous Perfusion and Lymphatics
,”
Microvasc. Res.
,
40
, pp.
246
263
.
17.
Bonfiglio
,
A.
,
Leungchavaphongse
,
K.
,
Repetto
,
R.
, and
Siggers
,
J. H.
, 2010, “
Mathematical Modeling of the Circulation in the Liver Lobule
,”
ASME J. Biomech. Eng.
,
132
, p.
111011
.
18.
Swabb
,
E. A.
,
Wei
,
J.
, and
Gullino
,
P. M.
, 1974, “
Diffusion and Convection in Normal and Neoplastic Tissues
,”
Cancer Res.
,
34
, pp.
2814
2822
.
19.
McGuire
,
S.
, and
Yuan
,
F.
, 2001, “
Quantitative Analysis of Intratumoral Infusion of Color Molecules
,”
Am. J. Physiol.
,
281
, pp.
H715
H721
.
20.
Jain
,
R. K.
, 1987, “
Transport of Molecules in the Tumor Interstitium: A Review
,”
Cancer Res.
,
47
, pp.
3039
3051
.
21.
Fung
,
Y. C.
, 1993,
Biomechanics. Mechanical Properties of Living Tissues
.
Springer
,
Berlin
.
22.
Sun
,
W.
, and
Sacks
,
M. S.
, 2005, “
Finite Element Implementation of a Generalized Fung-Elastic Constitutive Model for Planar Soft Tissues
,”
Biomech. Model Mechanobiol.
,
4
, pp.
190
199
.
23.
Wu
,
J.
,
Long
,
Q.
,
Xu
,
S.
, and
Padhani
,
A. R.
, 2009, “
Study of Tumor Blood Perfusion and its Variation Due to Vascular Normalization by Anti-Angiogenic Therapy Based on 3D Angiogenic Microvasculature
,”
J. Biomech.
,
42
, pp.
712
721
.
24.
Wu
,
J.
,
Xu
,
S.
,
Long
,
Q.
,
Collins
,
M. W.
,
König
,
C. S.
,
Zhao
,
G.
,
Jiang
,
Y.
, and
Padhani
,
A. R.
, 2008, “
Coupled Modeling of Blood Perfusion in Intravascular, Interstitial Spaces in Tumor Microvasculature
,
J. Biomech.
,
41
, pp.
996
1004
.
25.
Yuan
,
F.
, 2011, personal communication.
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