A theoretical model for intraperitoneal delivery of cisplatin and the effect of hyperthermia on drug penetration distance

Abstract

A theoretical model for the intraperitoneal (i.p.) delivery of cisplatin and heat to tumor metastases in tissues adjacent to the peritoneal cavity is presented. The penetration distance (the depth to which drug diffuses directly from the cavity into tissues) is predicted to be on the order of 0.5 mm. The model shows that exchange with the microvasculature has more effect than cellular uptake in limiting the penetration distance. Possible effects of hyperthermia are simulated, including increased cell uptake of drug, increased cell kill at a given level of intracellular drug, and decreased microvascular density. The model suggests that the experimental finding of elevated intracellular platinum levels up to a depth of 3 to 5 mm when drug is delivered i.p. by a heated infusion solution is due to penetration of heat to this distance, causing increased cell uptake of drug. Beyond a depth of about 0.5 mm, the drug is delivered mainly through the circulation. Use of sodium thiosulfate to deactivate systemic cisplatin may therefore be counterproductive when heat is delivered locally. The model suggests that i.p. delivery of heat, combined with systemic delivery of drug, may be as effective as i.p. delivery of heat and drug.

Figure 1

Plasma concentration of (ultrafilterable) platinum after i.p. infusion. Line: theoretical model for ovarian carcinoma cells. Filled circles: experimental data for rat from Ref. [40].

Figure 2

Predictions of the mathematical model for rat, with ovarian carcinoma cells, without hyperthermia. Solid lines: normal tumor perfusion (vessel surface density S_v = 70 cm^-1). Dashed lines: low tumor perfusion, represented by reduced surface density (S_v = 7 cm^-1). Dashed-dotted lines: zero tumor perfusion. Dotted lines: with sodium thiosulfate administered intravenously, assumed to deactivate all circulating cisplatin. (A) Peak extracellular concentration in tumor as a function of position. The peak value is reached at different times at different points, so this curve is not a concentration profile at one instant in time. (B) Peak intracellular concentration in tumor as a function of position. (C) Survival fraction of cancer cells.

Figure 3

Predictions of mathematical model as in Figure 2, but with regional hyperthermia (i.e., all tissues adjacent to the peritoneal cavity heated to a uniform 43 C). Solid lines: normal tumor perfusion. Dashed lines: low tumor perfusion. Dashed-dotted lines: zero tumor perfusion. Dotted lines: normal tumor perfusion without heating, as shown in Figure 2.

Figure 4

Predictions of theoretical model for penetration of heat into the tumor tissues adjacent to the peritoneal cavity. The cavity is assumed to be at a constant temperature of either 42°C or 43°C for 90 minutes, after which it returns to 37°C. The cases of normal, low, and zero tumor perfusion are shown. Except for the case of w_b = 0, all profiles are steady state reached after approximately 5 to 10 minutes.

Figure 5

Predictions of mathematical model as in Figure 2, but with i.p. hyperthermia, achieved by infusing the peritoneal cavity with a solution at 43°C. Solid lines: normal tumor perfusion. Dashed lines: low tumor perfusion. Dashed-dotted lines: zero tumor perfusion. Dotted lines: normal tumor perfusion without heating, as shown in Figure 2.