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On the Infusion of a Therapeutic Agent Into a Solid Tumor Modeled as a Poroelastic Medium

[+] Author and Article Information
Alessandro Bottaro1

Research Center for Materials Science and Technology,  Università di Genova, 1, via Montallegro, 16145 Genova, Italyalessandro.bottaro@unige.it

Tobias Ansaldi

Research Center for Materials Science and Technology,  Università di Genova, 1, via Montallegro, 16145 Genova, Italy

1

Corresponding author.

J Biomech Eng 134(8), 084501 (Aug 06, 2012) (6 pages) doi:10.1115/1.4007174 History: Received December 09, 2011; Revised July 06, 2012; Posted July 18, 2012; Published August 06, 2012; Online August 06, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of the section of a solid tumor of spherical shape. The magnified view on the right shows a detail of the porous interstitium, with the micro-vasculature created around the tumor cells.

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Figure 2

Shape of the dimensionless function f(r) (representing the hydraulic conductivity coefficient, Lp , of the capillary walls) for cases 1–3, as reported in the text. Case 1: solid line; case 2: dashed line; case 3: dotted line.

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Figure 7

Exact (thick solid lines), order zero (thin solid lines) and order one asymptotic results (dashed lines) in dimensionless form for pinfusion  = 108.75 mmHg (δ = 0.3) and K0  = 3 × 10−6  cm2 /(mmHg s). The horizontal line in the frame with the IFP denotes the effective vascular pressure.

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Figure 6

Exact (thick solid lines), order zero (thin solid lines) and order one asymptotic results (dashed lines) in dimensionless form for pinfusion  = 43.75 mmHg (δ = 0.1) and K0  = 3 × 10−6  cm2 /(mmHg s). The leading order value of u is zero and K0  = 1 (not drawn). The horizontal line in the frame with the IFP denotes the effective vascular pressure.

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Figure 5

Inflow rate at r = a′ as function of the infusion pressure (both variables are in dimensional form). Symbols are used to denote the experimental data points by McGuire [12]. The three cases of Fig. 2 are plotted with the same line style used previously. The top curves refer to K0  = 3 × 10−5  cm2 /(mmHg s); the bottom curves, closer to the experimental data, are for K0  = 3 × 10−6  cm2 /(mmHg s). The order zero results of the asymptotic model in the Lp  = Lp0 limit are also displayed, with thin solid lines; when Lp varies (as in Fig. 2) the leading order results are but mildly affected.

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Figure 4

Solution of the full model (in dimensionless form) for δ = 0.2. From top left frame, and clockwise: radial distribution of the displacement u, of the hydraulic conductivity K of the tissue, of the flow rate Q through any given spherical surface at radius r (including transvascular fluid exchange), and of the IFP. Cases 1–3 with line styles as in Fig. 2 The thin horizontal line in the figure with the IFP denotes the dimensionless value of the effective vascular pressure.

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Figure 3

Solution of the full model (in dimensionless form) for δ = 0.05. From top left frame, and clockwise: radial distribution of the displacement u, of the hydraulic conductivity K of the tissue, of the flow rate Q through any given spherical surface at radius r (including transvascular fluid exchange), and of the IFP. Cases 1–3 with line styles as in Fig. 2 The thin horizontal line in the figure with the IFP denotes the dimensionless value of the effective vascular pressure.

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