Mathematical modeling of intraperitoneal drug delivery: simulation of drug distribution in a single tumor nodule

Figures & data

Figure 1. Visualization of the six used geometries in our model. (a and d) Geometries of spherical tumor shape comprising two different zones: a necrotic center of radius r_n (darker gray area) and the viable tumor zone. A concentration and pressure boundary condition are applied at the outer edge of the tumor. (b and e) Geometries of an ellipsoid tumor shape. (c and f) Geometries of the peritoneal tumor shape.

Table 1. Parameters used for baseline simulations.

Parameter	Unit	Value	Reference
r	m	0.01	–
rn	m	0.005	–
ρ	kg/m^3	1000	Teo et al. (2005)
Lp	m/Pa s	2.10 × 10^−11	Baxter & Jain (1989)
K	m^2/Pa s	3.10 × 10^−14	Baxter & Jain (1989)
μ	Pa s	1.00 × 10^−3	Teo et al. (2005)
K	m^2	3.10 × 10^−17	Baxter & Jain (1989)
S/V	m^−1	2.00 × 10^4	Baxter & Jain (1989)
Pv	Pa	2.08 × 10^3	Baxter & Jain (1989)
πb	Pa	2.67 × 10^3	Baxter & Jain (1989)
πi	Pa	2.00 × 10^3	Baxter & Jain (1989)
c		0.82	Baxter & Jain (1989)
MW	g/mol	300	Shah et al. (2009)
D	m^2/s	2.5 × 10^−10	Shah et al. (2009)
Β	s^−1	7.32 × 10^−4	Shah et al. (2009)
σ		8.17 × 10^−5	–
Pc	cm/s	1.43 × 10^−4	Shah et al. (2009)

Table 2. Parameter values used to study the influence of several transport-related parameters.

	S/V (m^−1)	Lp (m/Pa s)	C (–)	Reference
Vascular normalization simulations
Baseline values	2.00 × 10^4	2.10 × 10^−11	0.82	Baxter & Jain (1989)
50% Vascular normalization	1.35 × 10^4	1.19 × 10^−11	0.865	–
100%Vascular normalization	7.00 × 10^3	2.70 × 10^−12	0.91	Baxter & Jain (1989)
	Diffusion coefficient (m^2/s)	Reference	IC50 [mol/m^3]
Drug diffusion simulations
Cisplatin	2.5 × 10^−10	Shah et al. (2009)	6.2 × 10^−3	De Vlieghere et al. (2016)
Paclitaxel	0.77 × 10^−10	Winner et al. (2016)	1.4 × 10^−6	Smith et al. (2005)
		Intrinsic permeability (m^2)
Permeability simulations
Normal tissue		6.4 × 10^−18		Baxter & Jain (1989)
Commonly used value		3.1 × 10^−17		Baxter & Jain (1989)
Lower limit of the range		6.4 × 10^−17		–

All parameters that are not listed in this table are kept at their baseline value (Table 1) for each simulation.

Figure 2. Summary of model output and analyzed variables. (a and b) Three-dimensional pressure and concentration distributions in the small spherical geometry (SS). (c and d) Two-dimensional pressure and concentration distributions in the xy-plane of the SS geometry. The x-axis is plotted on the figures in black. (e and f) One-dimensional pressure and concentration profiles along the x-axis in the SS geometry. All analyzed variables as discussed in the “Analyzed variables” section are presented in the figure.

Figure 3. (a–c) Interstitial fluid pressure (IFP) distribution profiles of the six baseline cases. Both length along the axis and IFP are normalized; the former with respect to the maximal length along the axis, the latter with respect to the overall maximal pressure (IFP_max = 1533.88 Pa). The figures (d–f) show a comparison between the resulting concentration profiles after IP chemotherapy in which cisplatin or paclitaxel is used. Concentrations are normalized with respect to the boundary concentration (C₀=0.8 mol/m³).

Figure 4. Normalized concentration profiles in which both length along the axis and concentration are normalized; the former with respect to the maximal length along the axis, the latter with respect to the boundary concentration (C₀=0.8 mol/m³). The figures (a–f) show the resulting concentration profiles after vascular normalization therapy for all geometries.

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