Recent advances in the treatment of cancer involving therapeutic agents have shown promising results. However, treatment efficacy can be limited due to inadequate and uneven uptake in solid tumors, thereby making the prediction of drug transport important for developing effective therapeutic strategies. In this study, a patient-specific computational porous media model (voxelized model) was developed for predicting the interstitial flow field and distribution of a systemically delivered magnetic resonance (MR) visible tracer in a tumor. The benefits of a voxel approach include less labor and less computational time (approximately an order of magnitude reduction compared to the traditional computational fluid dynamics (CFD) approach developed earlier by our group). The model results were compared with that obtained from a previous approach based on unstructured meshes along with MR-measured tracer concentration data within tumors, using statistical analysis and qualitative representations. The statistical analysis indicated the similarity between the structured and unstructured models’ results with a low root mean square error (RMS) and a high correlation coefficient. The voxelized model captured features of the flow field and tracer distribution such as high interstitial fluid pressure inside the tumor and the heterogeneous distribution of the tracer. Predictions of tracer distribution by the voxelized approach also resulted in low RMS error when compared with MR-measured data over a 1 h time course. The similarity in the voxelized model results with experiment and the nonvoxelized model predictions were maintained across three different tumors. Overall, the voxelized model serves as a reliable and swift alternative to approaches using unstructured meshes in predicting extracellular transport within tumors.

References

References
1.
Jain
,
R. K.
, 1994, “
Barriers to Drug Delivery in Solid Tumors
,”
Sci. Am.
,
271
, pp.
58
65
.
2.
Jain
,
R. K.
, 1994, “
Transport Phenomena in Tumors
,”
Adv. Chem.Eng.
,
19
, pp.
130
200
.
3.
Baish
,
J. W.
,
Gazit
,
Y.
,
Berk
,
D. A.
,
Nozue
,
M.
,
Baxter
,
L. T.
, and
Jain
,
R. K.
, 1996, “
Role of Tumor Vascular Architecture in Nutrient and Drug Delivery: An Invasion Percolation-Based Network Model
,”
Microvasc. Res.
,
51
(
3
), pp.
327
346
.
4.
Ahlström
,
H.
,
Christofferson
,
R.
, and
Lörelius
,
L. E.
, 1988, “
Vascularization of the Continuous Human Colonic Cancer Cell Line LS 174 T Deposited Subcutaneously in Nude Rats
,”
APMIS
,
96
(
7–12
), pp.
701
710
.
5.
Hamberg
,
L. M.
,
Kristjansen
,
P. E. G.
,
Hunter
,
G. J.
,
Wolf
,
G. L.
, and
Jain
,
R. K.
, 1994, “
Spatial Heterogeneity in Tumor Perfusion Measured With Functional Computed Tomography at 0.05 μl Resolution
,”
Cancer Res.
,
54
(
23
), pp.
6032
6036
.
6.
Jain
,
R. K.
, 1988, “
Determinants of Tumor Blood Flow: A Review
,”
Cancer Res.
,
48
(
10
), pp.
2641
2658
.
7.
Konerding
,
M. A.
,
Steinberg
,
F.
, and
Budach
,
V.
, 1989, “
The Vascular System of Xenotransplanted Tumors–Scanning Electron and Light Microscopic Studies
,”
Scanning Microsc.
,
3
(
1
), pp.
327
335
.
8.
Less
,
J. R.
,
Skalak
,
T. C.
,
Sevick
,
E. M.
, and
Jain
,
R. K.
, 1991, “
Microvascular Architecture in a Mammary Carcinoma: Branching Patterns and Vessel Dimensions
,”
Cancer Res.
,
51
(
1
), pp.
265
273
.
9.
Jain
,
R. K.
, 1987, “
Transport of Molecules Across Tumor Vasculature
,”
Cancer and Metastasis Rev.
,
6
(
4
), pp.
559
593
.
10.
Bjørnaes
,
I.
, and
Rofstad
,
E. K.
, 2001, “
Microvascular Permeability to Macromolecules in Human Melanoma Xenografts Assessed by Contrast-Enhanced MRI—Intertumor and Intratumor Heterogeneity
,”
Magn.Reson. Imaging
,
19
(
5
), pp.
723
730
.
11.
Swartz
,
M. A.
, 2001, “
The Physiology of the Lymphatic System
,”
Adv. Drug Delivery Rev.
,
50
(
1–2
), pp.
3
20
.
12.
Butler
,
T. P.
,
Grantham
,
F. H.
, and
Gullino
,
P. M.
, 1975, “
Bulk Transfer of Fluid in the Interstitial Compartment of Mammary Tumors
,”
Cancer Res.
,
35
(
11
), pp.
3084
3088
.
13.
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
(
1
), pp.
77
104
.
14.
Young
,
J. S.
,
Llumsden
,
C. E.
, and
Stalker
,
A. L.
, 1950, “
The Significance of the Tissue Pressure of Normal Testicular and of Neoplastic (Brown-Pearce Carcinoma) Tissue in the Rabbit
,”
J. Pathol. Bacteriol.
,
62
(
3
), pp.
313
333
.
15.
Boucher
,
Y.
,
Baxter
,
L.
, and
Jain
,
R.
, 1990, “
Interstitial Pressure Gradients in Tissue-Isolated and Subcutaneous Tumors: Implications for Therapy
,”
Cancer Res.
,
50
(
15
), pp.
4478
4484
.
16.
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
(
24
), pp.
6691
6694
.
17.
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
(
7
), pp.
1993
1995
.
18.
Nathanson
,
S. D.
, and
Nelson
,
L.
, 1994, “
Interstitial Fluid Pressure in Breast Cancer, Benign Breast Conditions, and Breast Parenchyma
,”
Ann. Surg. Oncol.
,
1
(
4
), pp.
333
338
.
19.
DiResta
,
G. R.
,
Lee
,
J.
,
Larson
,
S. M.
, and
Arbit
,
E.
, 1993, “
Characterization of Neuroblastoma Xenograft in Rat Flank. I. Growth, Interstitial Fluid Pressure, and Interstitial Fluid Velocity Distribution Profiles
,”
Microvasc. Res.
,
46
(
2
), pp.
158
177
.
20.
Hassid
,
Y.
,
Furman-Haran
,
E.
,
Margalit
,
R.
,
Eilam
,
R.
, and
Degani
,
H.
, 2006, “
Noninvasive Magnetic Resonance Imaging of Transport and Interstitial Fluid Pressure in Ectopic Human Lung Tumors
,”
Cancer Res.
,
66
(
8
), pp.
4159
4166
.
21.
Milosevic
,
M. F.
,
Fyles
,
A. W.
, and
Hill
,
R. P.
, 1999, “
The Relationship Between Elevated Interstitial Fluid Pressure and Blood Flow in Tumors: A Bioengineering Analysis
,”
Int. J. Radiat. Oncol., Biol., Phys.
,
43
(
5
), pp.
1111
1123
.
22.
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
(
2
), pp.
246
263
.
23.
Tannock
,
I. F.
, 1968, “
The Relation Between Cell Proliferation and the Vascular System in a Transplanted Mouse Mammary Tumour
,.
Br. J. Cancer
,
22
(
2
), pp.
258
273
.
24.
Tannock
,
I. F.
, 1972, “
Oxygen Diffusion and the Distribution of Cellular Radiosensitivity in Tumours
,”
Br. J. Radiol.
,
45
(
535
), pp.
515
524
.
25.
Thomlinson
,
R. H.
, and
Gray
,
L. H.
, 1955, “
The Histological Structure of Some Human Lung Cancers and the Possible Implications for Radiotherapy
,”
Br. J. Cancer
,
9
(
4
), pp.
539
549
.
26.
Jain
,
R. K.
, and
Baxter
,
L. T.
, 1988, “
Mechanisms of Heterogeneous Distribution of Monoclonal Antibodies and Other Macromolecules in Tumors: Significance of Elevated Interstitial Pressure
,”
Cancer Res.
,
48
(
24
) (Part 1), pp.
7022
7032
.
27.
Pozrikidis
,
C.
, 2010, “
Numerical Simulation of Blood and Interstitial Flow Through a Solid Tumor
,”
J. Math. Biol.
,
60
(
1
), pp.
75
94
.
28.
Zhao
,
J.
,
Salmon
,
H.
, and
Sarntinoranont
,
M.
, 2007, “
Effect of Heterogeneous Vasculature on Interstitial Transport Within a Solid Tumor
,”
Microvasc. Res.
,
73
(
3
), pp.
224
236
.
29.
Tan
,
W. H. K.
,
Wang
,
F.
,
Lee
,
T.
, and
Wang
,
C. H.
, 2003, “
Computer Simulation of the Delivery of Etanidazole to Brain Tumor From PLGA Wafers: Comparison Between Linear and Double Burst Release Systems
,”
Biotechnol. Bioeng.
,
82
(
3
), pp.
278
288
.
30.
Pishko
,
G. L.
,
Astary
,
G. W.
,
Mareci
,
T. H.
, and
Sarntinoranont
,
M.
, 2011, “
Sensitivity Analysis of an Image-Based Solid Tumor Computational Model With Heterogeneous Vasculature and Porosity
,”
Annals of Biomedical Engineering
,
39
(
9
), pp.
2360
2373
.
31.
Kim
,
J. H.
,
Astary
,
G. W.
,
Chen
,
X.
,
Mareci
,
T. H.
, and
Sarntinoranont
,
M.
, 2009, “
Voxelized Model of Interstitial Transport in the Rat Spinal Cord Following Direct Infusion Into White Matter
,”
ASME J. Biomech. Eng.
,
131
, p.
071007
.
32.
Kim
,
J. H.
,
Mareci
,
T. H.
, and
Sarntinoranont
,
M.
, 2010, “
A Voxelized Model of Direct Infusion Into the Corpus Callosum and Hippocampus of the Rat Brain: Model Development and Parameter Analysis
,”
Med. Biol. Eng. Comput.
,
48
(
3
), pp.
203
214
.
33.
Chen
,
X.
,
Astary
,
G.
,
Sepulveda
,
H.
,
Mareci
,
T.
, and
Sarntinoranont
,
M.
, 2008, “
Quantitative Assessment of Macromolecular Concentration During Direct Infusion Into an Agarose Hydrogel Phantom Using Contrast-Enhanced MRI
,”
Magn. Reson. Imaging
,
26
(
10
), pp.
1433
1441
.
34.
Tofts
,
P. S.
, and
Kermode
,
A. G.
, 1991, “
Measurement of the Blood-Brain Barrier Permeability and Leakage Space Using Dynamic MR Imaging. 1. Fundamental Concepts
,”
Magn. Reson. Med.
,
17
(
2
), pp.
357
367
.
35.
Anderson
,
D. A.
,
Tannehill
,
J. C.
, and
Pletcher
,
R. H.
, 1984,
Computational Fluid Mechanics and Heat Transfer
,
Hemisphere
,
New York
, pp.
671
674
.
36.
El-Kareh
,
A. W.
, and
Secomb
,
T. W.
, 1995, “
Effect of Increasing Vascular Hydraulic Conductivity on Delivery of Macromolecular Drugs to Tumor Cells
,”
Int. J. Radiat. Oncol., Biol., Phys.
,
32
(
5
), pp.
1419
1423
.
37.
Sevick
,
E. M.
, and
Jain
,
R. K.
, 1989, “
Geometric Resistance to Blood Flow in Solid Tumors Perfused Ex Vivo: Effects of Tumor Size and Perfusion Pressure
,”
Cancer Res.
,
49
(
13
), pp.
3506
3512
.
38.
Geer
,
C.
, and
Grossman
,
S.
, 1997, “
Interstitial Fluid Flow Along White Matter Tracts: A Potentially Important Mechanism for the Dissemination of Primary Brain Tumors
,”
J. Neuro-Oncol.
,
32
(
3
), pp.
193
201
.
39.
Abbott
,
N.
, 2004, “
Evidence for Bulk Flow of Brain Interstitial Fluid: Significance for Physiology and Pathology
,”
Neurochem. Int.
,
45
(
4
), pp.
545
552
.
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