Fig 1.
The enhanced permeation and retention (EPR) effect.
(A) Schematic illustration of a tumor vessel illustrating loss of smooth muscle cells, local degradation of the extracellular matrix, and increased permeability of the endothelium. (B) Illustration of the pharmacokinetic model taking into account the EPR effect. The rate constants kp and kd describe exchange with the peripheral volume. The rate constants kepr and kb describe extravasation from circulation into the tumor, and intravasation back into the circulation, respectively. The rate constant kel represents clearance by the kidneys, MPS, and any other non-tumor elimination processes, such that when kb = 0, k10 = kepr + kel where kel is the elimination rate constant. (C) Standard two compartment model with central and peripheral compartments. c1 and c2 represent the drug concentration in blood (central compartment) and normal tissue (peripheral compartment), respectively. The first order rate constant k10 describes all elimination pathways, including clearance by the kidneys, uptake by the MPS, and tumor accumulation. The first order rate constants k12 and k21 describe exchange between the two compartments. Note that kp = k12, kd = k21. (D) Two compartment model defined in terms of the drug amount, where Nbl is the amount of drug in blood (mg), and Np is the amount in peripheral tissue (mg). (E) Three compartment model with the addition of a tumor “compartment” where Nt is the amount of drug in the tumor. Exchange with the tumor is described by the rate constants kepr and kb, respectively. The rate constant kel describes elimination pathways including clearance by the kidneys and uptake by the MPS, but does not include tumor accumulation.
Table 1.
Pharmacokinetic data for Doxil and doxorubicin obtained from a human clinical trial [12].
Fig 2.
The influence of the EPR effect on the rate of tumor uptake of Doxil for an administered dose of 100 mg (50 mg m-2).
(A) Pharmacokinetics for Doxil. Symbols are data from a clinical trial reported by Gabizon et al. [12]. The solid red line is obtained from our model using values for kp, kd, and kel derived from median values of A, B, α, and β reported by Gabizon et al. (Table 1) [12], where kel ~ k10 when kel >> kepr. The dotted lines represent the pharmacokinetics for the minimum and maximum values of A, B, α, and β. (B) Simulations of the pharmacokinetics for Doxil with kepr/kel = 0, 10–1, 10–2, and 10–3, and kb = 0. (C) Amount of Doxil in tumor for kepr/kel = 10–1, 10–2, 10–3, and 10–4, and kb = 0. (D) Amount of Doxil in tumor for kepr/kel = 10–3 and kb/kepr = 0, 10, 100, 1000. The amount of Doxil in tumor represents the total amount of doxorubicin.
Fig 3.
The influence of the EPR effect on the rate of tumor uptake of doxorubicin for an administered dose of 100 mg (50 mg m-2).
(A) Pharmacokinetics for doxorubicin. Symbols are data from a clinical trial reported by Gabizon et al. [12]. The solid red line is obtained from our model using values for kp, kd, and kel derived from median values of A, B, α, and β reported by Gabizon et al. [12] (Table 1), where kel ~ k10 when kel >> kepr. The dotted lines represents the pharmacokinetics for the minimum and maximum values of A, B, α, and β. (B) Simulations of the pharmacokinetics for doxorubicin with kepr/kel = 0, 10–1, 10–2, and 10–3, and kb = 0. (C) Amount of doxorubicin in tumor for kepr/kel = 10–1, 10–2, 10–3, and 10–4, and kb = 0. (D) Amount of doxorubicin in tumor for kepr/kel = 10–3 and kb/kepr = 0, 10, 100, 1000.
Fig 4.
Drug accumulation rate in the tumor per 100 μm vessel length assuming a 1 cm3 tumor with 150 m of vessels (150 mm mm-3).
(A) Doxil and (B) Doxorubicin. Values for kp, kd, and kel are given in Table 1, where kel ~ k10 when kel >> kepr. In both cases kepr/kel = 10–3.