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pharmacodynamic modeling
Journal of Controlled Release 61 (1999) 93–106
Optimization of antitumor effect of liposomally encapsulated doxorubicin based on simulations by pharmacokinetic / pharmacodynamic modeling Hideyoshi Harashima*, Shinya Iida, Yumiko Urakami 1 , Mari Tsuchihashi, Hiroshi Kiwada Faculty of Pharmaceutical Sciences, The University of Tokushima, 1 -78 -1 Shomachi, Tokushima City, Tokushima 770 -8505, Japan Received 11 July 1998; received in revised form 5 March 1999; accepted 17 April 1999
Abstract It has been reported that long circulating liposomes enhanced the antitumor effect of doxorubicin (DOX) by increasing delivery of DOX to tumor tissues. However, there is no quantitative information on the relationship between the antitumor effect and liposomal characteristics governing the release rate of entrapped drugs, although the importance of drug release-rate control from liposomes has been pointed out. Here, we developed a physiological model for free and liposomal DOX to calculate the time course of free DOX in the extracellular space and linked this with a cell kill kinetic model to quantify the antitumor effect of DOX. Simulations were performed to clarify the relationship between antitumor effect and pharmacokinetic or physicochemical parameters of liposomes, as well as pharmacological or physiological parameters of tumor tissues. The importance of long circulation time of liposomes was confirmed. The optimum rate of drug release from long circulating liposomes was found at the release rate constant of around 0.06 h 21 . This optimum value was not dependent on the tumor proliferation time, sensitivity of tumor cells to DOX, or the tumor blood flow-rate. This simulation indicated that the optimization of the delivery to tumor tissue by long circulating liposomes could be possible by changing the release rate of DOX for the maximum antitumor effect. 1999 Elsevier Science B.V. All rights reserved. Keywords: Drug delivery system; Simulation; Liposomes; Doxorubicin; Optimization
1. Introduction The development of long circulating liposomes
*Corresponding author. Tel.: 181-886-33-7260; fax: 181-88633-9506. E-mail address: [email protected] (H. Harashima) 1 Present address: Department of Pharmacy, Kyoto University Hospital, Faculty of Medicine, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan.
(LCL) remarkably increased the usefulness of liposomes as drug carriers and enhanced the therapeutic index of doxorubicin (DOX) [1,2]. The enhanced antitumor effects of DOX after its encapsulation into LCL have been examined in mice against many kinds of murine [3–6] and human [7,8] tumors. The enhanced antitumor effect of DOX in LCL has been shown in every study compared to that in free form or conventional liposomes. There is also increasing evidence of the successful clinical results of DOX in LCL against AIDS-related Kaposi’s sarcoma [9–12].
0168-3659 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 99 )00110-8
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Phase II study revealed that 192 (80.7%) out of 238 patients achieved a complete (6.3%) or partial (74.4%) response [10]. This result is quite different from the clinical study using conventional liposomes, where among 50 patients available for efficacy, none had a complete response, five (10%) had a partial response, 32 (64%) had a minor response, 12 (24%) no change and one (2%) progression as their best response [9]. These experimental evidence show the importance of the long circulation property in the tumor delivery of liposomal DOX. Although the long circulating property is essential in enhancing the antitumor properties of DOX, there is no clear explanation about the optimum release rate of DOX from liposomes and how long LCL should remain in the blood circulation. There is no theoretical base to predict the optimum condition of liposomes for DOX in humans, although clinical trials have already started [9–12]. We are also not certain whether the optimum condition of LCL for
DOX determined in experimental animals directly applies to humans. The optimum condition in humans could be different from that in animals. In this report, we have developed the pharmacokinetic and pharmacodynamic model of DOX in LCL to examine the importance of each parameter on the antitumor effect, in the hope of optimizing the antitumor effect. A physiological model of tumor tissue was developed [13–15] to calculate the concentration of free DOX in the extracellular compartment, the concentration that was linked with the cell kill kinetic model [16,17] to quantify the antitumor effect of DOX. Based on this model, the effect of liposomalization on the local pharmacokinetics of DOX was quantitatively explained and the antitumor effect of DOX in LCL was also evaluated quantitatively by the change in tumor cell number. This simulation examined the importance of each parameter in determining the antitumor effect of DOX, and the optimum rate of drug release from liposomes for
Fig. 1. Pharmacokinetic model for free and liposomal DOX. Global pharmacokinetics was described by a compartment model and intra-tumor disposition was described by a flow model with tumor blood flow-rate (Q). Tumor tissue was divided into three compartments, capillary (CAP), interstitial (INT) and TUMOR CELL. Open and closed circles represent free and liposomal DOX, respectively. DOX in liposomes was released according to the first order rate constant (k rel ) in BLOOD, CAP and INT. Liposomal DOX in CAP was transported into INT unidirectionally (k tu ). Liposomal DOX was taken up by RES (k RES ) and efflux of DOX was neglected. Rapid equilibrium was assumed between CAP and INT for free DOX and Cecs was defined for free DOX in the extracellular compartment (ECS) as described in Methods. Distribution of free DOX to tumor cells was described with k et and k te . The k 12 , k 21 and k 10 represent the micro pharmacokinetic constants for free DOX. Each parameter used in the simulation was summarized in Table 1.
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DOX was shown to exist independent of the circulation time of liposomes, sensitivity of tumor cells to DOX, or tumor blood flow-rate.
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the disposition of free DOX, which was released from liposomal DOX in blood and tumor compartments. The first order rate process was assumed for this process and described by k rel in both blood and capillary compartments.
2. Materials and methods
2.1. Pharmacokinetic modeling of free and liposomal DOX A kinetic model was developed for free and liposomally encapsulated DOX in rats. All tissue except tumor was described by the hybrid model and tumor tissue was linked to blood compartment with tumor blood flow as shown in Fig. 1.
2.1.1. Free DOX A two-compartment model was applied to describe
2.1.2. Liposomal DOX A one-compartment model was applied for liposomal DOX and the elimination of liposomal DOX was described by k RES which represents the liposomal uptake by reticuloendothelial system (RES) without efflux of DOX [18]. 2.1.3. Tumor distribution The tumor tissue was divided into three compartments namely capillary (Vcap ), interstitial (Vint ) and tumor cell (Vtu ) where the capillary compartment was linked to the blood compartment with the tumor
Table 1 Kinetic parameters for free and liposomal DOX anatomical / physiological / pharmacological parameters for tumor tissue a Fixed Parameters (1) Kinetic parameters for free DOX Vc k 12 (ml / 250 g) (h 21 ) 515 5.13
k 21 (h 21 ) 0.927
k el (h 21 ) 1.56
k et (h 21 ) 2.27
k te (h 21 ) 0.0485
fb (h 21 ) 0.20
(2) Kinetic parameters for liposomal DOX Vc lipo k tu (ml / 250g) (h 21 ) 16.7 7.17 (3) Anatomical parameters for tumor tissue Vcap Vint (ml / g) (ml / g) 0.0285 0.323
Vtu (ml / g) 0.648
Altered parameters in simulations (1) Kinetic parameters for liposomal DOX k RES k rel (h 21 ) (h 21 ) 0.6 / 0.06 / 0.006 0.6 / 0.06 / 0.006 (2) Physiological / pharmacological parameters for tumor Q k (ml / h / g) [h 21 /(mg / ml)] 41.2 / 9.69 16.2 / 10.8 / 5.40 / 1.69
ks (h 21 ) 0.173 / 0.0578 / 0.0193
a Each fixed parameter was referred from literatures as explained in Determination of parameters for simulations. The k RES , k rel , Q, k and k s were altered in simulations as described in Materials and methods. Values in bold were used in simulations if conditions were not specified.
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concentration in Cecs and cell density (Cs ) under the assumption that the cell population is kinetically homogeneous for DOX and the volume of tumor tissue is 1 gram: dCs / dt 5 2 kfb Cecs Cs 1 k s Cs
Fig. 2. Pharmacodynamic model for DOX. A cell kill kinetic model was applied to quantify the antitumor effect of DOX. This pharmacodynamic model was linked with unbound concentration of free DOX in the ECS of tumor tissue ( fb ?Cecs ). The proliferation of tumor cells was represented by k s . Cell killing action was described by the bimolecular reaction of cell density (Cs ) and fb Cecs with the proportional rate constant k as described by Eq. (1).
blood flow-rate (Q) [13–15]. Recent studies clarified that liposomes escape the tumor capillary space into the interstitial space slowly, however, there was little uptake by tumor cells [3,19,20]. Based on this reported evidence, we assumed that liposomes were transported from the capillary space to the interstitial space without uptake by tumor cells. Rapid equilibrium was assumed between capillary and interstitial compartment for free DOX and the extracellular concentration of free DOX was defined as Cecs . The Cecs corresponds to the medium concentration of DOX in the in vitro experiments and it is an important variable for the simulation of the antitumor effect of DOX. The uptake of DOX by tumor cells was described by k et and k te .
2.2. Pharmacodynamic modeling of free DOX The antitumor effect of DOX was quantified by introducing the cell kill kinetic model as shown in Fig. 2, which was developed by Ozawa et al. [16,17]. The antitumor effect of type-I classified antitumor agents depended on the area under the concentration–time curve (AUC) and this kinetic characteristic was explained well by this cell kill kinetic model [16]. In brief, the cell killing action of cell cycle phase-nonspecific agents (type-I) occurs as a bimolecular reaction depending on the unbound drug
(1)
where k s and k represent the cell proliferation rate constant and drug-induced irreversible cell death rate constant, respectively. The k s was fixed at 0.0578 (h 21 ). The fb represents the unbound fraction of DOX in ECS [21]. The effect of the alteration of k, which represents the sensitivity of tumor cells to DOX, on the time course of tumor cell number was simulated by linking the cell kill kinetic model with Cecs in the physiological model of liposomal DOX as described above. In this simulation, the following criteria were applied in determining the order of antitumor effect of liposomal DOX. • Criteria 1: Lower number of antitumor cells at the bottom. When the antitumor cells decreased to one from 10 10 , the liposomes which achieve this point faster, the better. When the tumor cells reached the bottom and the recovering phase started, liposomes with the lower bottom are more effective. • Criteria 2: When a significant decrease in the number of tumor cells was not observed and only a decreased rate of tumor proliferation was observed, liposomes which show the higher growth inhibition at exponential growth phase are more effective.
2.3. Determination of parameters for simulations Pharmacokinetic parameters (k 12 , k 21 , k el , Vc ) for free doxorubicin were estimated by the nonlinear least squares’ method (MULTI) [22] using the reported time course of plasma concentration of free DOX in rats [23]. The rate constants of DOX for tumor distribution (k et and k te ) were estimated by nonlinear least squares’ method (RUNGE(MULTI)) [24] using the reported time courses of plasma and tumor concentration curve [25]. The volume of distribution for liposomes was fixed at the value reported previously [26]. The tumor uptake of liposomal DOX was approximated by the first order
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106
rate constant k tu , which was calculated as follows (See Appendix C). k tu 5 Q ? CLtu /(Q 2 CLtu ) /Vcap
(2)
where CLtu represents the uptake clearance of liposomes by tumors based on the blood concentration of liposomes. The Vcap and Vint were obtained by taking the average from the reported values [27–29]. The Vtu was calculated by 1 2 (Vcap 1Vint ), since we assumed the total volume of tumor tissue to be 1 ml. The reported values [30–32] on tumor blood flowrate ranged from 3.3 to 52 (ml / h / g) and there was two peaks with the averaged values, 9.69 and 41.2 (ml / h / g). Since the lower peak represented the major values, we fixed Q at 9.69 in the following simulations. The effect of altering Q was also examined.
2.4. Simulation of drug concentrations and antitumor effect by altering KRES and k rel To clarify the optimum condition of k RES and k rel for antitumor effect of DOX, k RES and k rel were altered and the antitumor effect as well as DOX concentration in each compartment was simulated based on the pharmacokinetic / pharmacodynamic model described above. The k RES principally determines the circulation times of liposomes in blood and was altered from 0.6 to 0.006 (h 21 ). The range of release rate used in our simulations mostly reflects the actual values which are commonly observed in the animal experiments of liposomes. The value of 0.6 (h 21 ) corresponds to the rate constant for conventional liposomes and the value of 0.06 (h 21 ) corresponds to that for long circulating liposomes in rodents [1]. There seems no report showing 0.006 (h 21 ) in rodents. Therefore this value is the lower limit at this stage. The k rel was assumed to be equal for blood, tumor capillary, and tumor interstitial compartments and was altered from 0.6 to 0.006 (h 21 ), which also corresponds to experimental values for the release rate of DOX in our laboratory (data not shown).
2.4.1. Alteration of tumor proliferation time on the antitumor effect of liposomal DOX It is difficult to fix the proliferation time of tumor
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cells at a certain value, since the proliferation time varies depending on the type of tumor cells as well as experimental conditions. Thus, the effect of the proliferation rate constant, k s was examined by altering its value from 0.173 to 0.0193 (h 21 ) under the condition of long circulation liposomes (k RES 5 0.06 h 21 ). In other simulations, 0.0578 (h 21 ) was used for k s .
2.4.2. Alteration of tumor sensitivity on the antitumor effect of liposomal DOX Sensitivity of tumor cells to DOX has been reported to vary depending on the time of incubation [16,33] as well as tumor type [33,34]. Time dependent IC 50 of DOX can be explained well with the cell kill kinetic model introduced in this simulation [16]. There exists a huge variation in IC 50 even for the same incubation time: 0.2 mM for ovarian carcinoma OV-1063 [34] vs. 0.01 mM for breast cancer T47D [33] under 72-h incubation. To examine this wide range of sensitivity to DOX depending on the tumor type, simulations were performed by altering k from 1.69 / 5.40 / 10.8 / 16.2 [(h?mg / ml)21 ] under the condition of long circulating liposomes (k RES 50.06 h 21 ). In other simulations, 16.2 [(h?mg / ml 21 ] was used for k. 2.4.3. Effect of physiological alteration on the antitumor effect of DOX The blood flow-rate to tumor tissue is also an important factor influencing the antitumor effect of liposomal DOX. Since tumor tissue is heterogeneous and reported values for tumor blood flow-rate varied from 3.3 to 52 [30–32], Q was increased from 9.69 to 41.2 (ml / min / g) under fixed conditions for other parameters. In other simulations, 9.69 (ml / h) was used for Q.
3. Results
3.1. Simulation of drug concentrations by altering k RES and k rel The concentration of free and liposomal DOX in each compartment is shown in Fig. 3. Since the free concentration of DOX in the ECS compartment is a
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Fig. 3. Time course of free and liposomal DOX concentration in each compartment. Time courses of free and liposomal DOX concentration were simulated by altering k RES and k rel as shown in Table 2. Cb : free DOX in BLOOD. Cb lipo : liposomal DOX in BLOOD. Cint lipo : liposomal DOX in INT. Cecs : free DOX in ECS. Ctu : tumor concentration of DOX. The dose of DOX was fixed at 6 mg / kg.
key concentration in determining the antitumor effect of DOX, the effect of k RES and k rel on the time courses of Cecs should be focused. At a high k rel 21 value (0.6 h ) as shown in Fig. 1C, F and I, there was little difference between Cecs and Cb , which indicates that there is little benefit to be gained by liposomal encapsulation. As k rel decreases from 0.6 to 0.06 (h 21 ), the difference between Cecs and Cb became significant, which enhances the antitumor effect of DOX by limiting the distribution of free DOX to whole body. Further decrease in k rel from 0.06 to 0.006 (h 21 ) remarkably influenced the disappearance rate of DOX in the ECS, INT and TUMOR compartments (B → A, E → D, and H → G). Although the level of free DOX in the ECS is low in the lowest k rel (0.006), the half-life of DOX in ECS, INT and TUMOR CELL increased. The
peak concentration of free DOX in ECS and liposomal DOX in INT are principally determined by both k RES and k rel as shown in Table 2. The smaller the k RES and k rel , the higher the peak concentration of Cint lip and Cecs . This result clearly indicated that a smaller k RES and / or k rel increased the delivery of DOX to INT compartment in liposomal form and increased the released amounts of free DOX in ECS. The slowest combination of k rel and k RES has the highest AUC of free DOX in the ECS compartment, although the peak concentration of DOX in the ECS compartment is higher in the higher k rel at the same k RES . Thus, the peak concentration in the ECS compartment is principally determined by k rel , however, AUC in ECS compartment is principally governed by both k RES /k rel . The peak concentration of DOX in TUMOR CELL did not correlate with the
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106 Table 2 Peak concentration of DOX in Cint
lip
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, Cecs and Ctu in each combination of k RES and k rel a
(A) k RES 50.006 /k rel 50.006 Cint lip (77, 1460) Cecs (76, 0.158) Ctu (103, 3.86)
(B) k RES 50.006 /k rel 50.06 Cint lip (15, 297) Cecs (13, 0.358) Ctu (32, 5.84)
(C) k RES 50.006 /k rel 50.6 Cint lip (1.6, 33) Cecs (1.4, 0.598) Ctu (8.4, 2.85)
(D) k RES 50.06 /k rel 50.006 Cint lip (36, 576) Cecs (66, 0.062) Ctu (34, 1.41)
(E) k RES 50.06 /k rel 50.06 Cint lip (11, 218) Cecs (10, 0.266) Ctu (27, 3.84)
(F) k RES 50.006 /k rel 50.6 Cint lip (1.6, 32) Cecs (1.4, 0.573) Ctu (8.2, 2.63)
(G) k RES 50.6 /k rel 50.006 Cint lip (7.6, 86.0) Cecs (4.8, 0.010) Ctu (50, 0.184)
(H) k RES 50.6 /k rel 50.06 Cint lip (4.0, 65.3) Cecs (3.2, 0.084) Ctu (19, 0.829)
(I) k RES 50.006 /k rel 50.6 Cint lip (1.2, 23.0) Cecs (0.8, 0.420) Ctu (7.0, 1.49)
a Time to peak concentration (h) and the peak concentration (mg / ml) of DOX in Cint combination of k RES and k rel as (time, concentration).
peak concentration of Cecs and the highest Ctu was observed in B (k RES 50.006 /k rel 50.06).
3.2. Simulation of antitumor effect by altering pharmacokinetic and pharmacodynamic parameters 3.2.1. Alteration of kRES and k rel An antitumor effect simulated by the cell kill kinetic model linked with Cecs is shown in Fig. 4. There is a general tendency for the antitumor effect to be increased by decreasing the k RES . This result
lip
, Cecs and Ctu were summarized for each
confirmed the requirement of long circulating time of liposomes as a superior drug carrier. There was little effect of liposomal encapsulation under the rapid RES uptake of liposomal DOX as shown in Fig. 4C, however the antitumor effect of liposomal DOX increased remarkably by lowering the k rel in the case of the long circulating liposomes as shown in Fig. 4B. The killing effect continued for a longer time and decreased the number of tumor cells almost completely by reducing k rel from 0.6 to 0.06 (h 21 ). Further decrease of k rel from 0.06 to 0.006 (h 21 )
Fig. 4. Effect of k RES and k rel on the antitumor effect of liposomal DOX. Antitumor effects of liposomal DOX were simulated based on the pharmacodynamic model of DOX, which was linked with Cecs in the physiological model described in Figs. 1 and 2. (A) k RES 50.006 h 21 , (B) k RES 50.06 h 21 , (C) k RES 50.6 h 21 . Lines: ——: control, ? ? ? ? ? ?: free, - - - - -: k rel 50.6 h 21 , - ? - ? -: k rel 50.06 h 21 , ------: k rel 50.006 h 21 .
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Fig. 5. Effect of tumor proliferation time on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor proliferation time which was represented by k s in the pharmacodynamic model in Fig. 2. The k RES was fixed at 0.06 h 21 . (A) k s 50.173, (B) k s 50.0578, (C) k s 50.0193 (h 21 ). Lines: ——: control, - - - - - -: k rel 50.6 h 21 , - ? - ? -: k rel 50.06 h 21 , – – – –: k rel 50.006 h 21 .
increased the duration of tumor killing time, however the rate of killing tumor cells decreased compared to k rel at 0.06 (h 21 ). In case of super-long circulating liposomes as shown in Fig. 4A, the antitumor effect
was enhanced for the corresponding case at the same k rel , and the same order of antitumor effect was seen between Fig. 4A and B. It was shown by this simulation that the most effective rate of drug release
Fig. 6. Effect of tumor sensitivity on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor sensitivity which was represented by k in the pharmacodynamic model in Fig. 2. The k RES was fixed at 0.06 h 21 . (A) k51.69, (B) k55.40, (C) k510.8, (D) k516.2 [(h?mg / ml)21 ]. Lines: ——: control, ? ? ? ? ? ?: free, - - - -: k rel 50.6 h 21 , 2 ? - ? - ? -: k rel 50.06 h 21 : ------: k rel 50.006 h 21 .
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Fig. 7. Effect of tumor blood flow-rate on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor blood flow-rate (Q) in the flow model for tumor tissue. The k RES was fixed at 0.06 h 21 . (A) Q59.69, (B) Q541.2 (ml / h / g). Lines: ——: control, ? ? ? ? ? ?: free, - - - -: k rel 50.6 h 21 , - ? - ? - ? -: k rel 50.06 h 21 : ------: k rel 50.006 h 21 .
was at 0.06 (h 21 ) for long circulating liposomes (Fig. 4A and B). As to conventional liposomes which are represented by k RES 50.6 (Fig. 4C), there was no benefit of liposomal encapsulation and the administration of free DOX showed the highest antitumor effect.
3.2.2. Alteration of ks The effect of tumor proliferation time on the antitumor effect of liposomal DOX is shown in Fig. 5 by changing k rel under the long circulating liposomes. The effect of k s on the absolute number of tumor cells is significant, however the pattern of change in the tumor cells is similar for each k s . The order of effective liposomes is independent of k s : k rel 50.06.k rel 50.006.k rel 50.6. In the following simulations, k s was fixed at 0.0578 (h 21 ). 3.2.3. Alteration of k The effect of tumor sensitivity on the antitumor effect of liposomal DOX was also examined by changing the k from 16.2 to 1.69 [(h?mg / ml)21 ] as shown in Fig. 6. By decreasing the k, the extent of antitumor effect was decreased, however the pattern of time course of tumor cells was similar for each k. Therefore the optimum rate of drug release was always observed at k rel 50.06 (h 21 ). 3.2.4. Alteration of Q The antitumor effect of liposomal DOX was
simulated by altering tumor blood flow-rate for each k rel at a fixed k RES of 0.06 (h 21 ). As shown in Fig. 7, tumor blood flow-rate is also a critical factor in determining the antitumor effect of liposomal DOX. Under the high tumor blood flow-rate (Q541.2 ml / h / g), the antitumor effect was reduced remarkably compared to the low tumor blood flow-rate (Q59.69 ml / h / g). Although the enhanced effect by liposomal encapsulation is slight in the case of higher tumor blood flow-rate, the order of antitumor effect among each liposomes with different k rel is still the same with the low tumor blood flow-rate.
4. Discussion It is essential to apply a physiologically-based pharmacokinetic model to describe the drug disposition in tumor tissue and to evaluate the effect of each parameter of liposomes as well as anatomical and / or physiological parameter of tumor tissue on the antitumor effect of liposomal DOX. A three compartment–flow model was applied to tumor tissue to calculate the Cecs , which corresponds to the medium concentration in the in vitro antitumor experiments. This model is not a conceptual model but is based on the real parameters such as Cecs , Q, Vint , Vcap , etc., which has the advantage of being able to extrapolate from experimental animals to humans [35,36]. In this paper, this model was first applied to examine the
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effect of each parameter on the alteration of Cecs and to understand the mechanism of enhanced antitumor effect of DOX in LCL. Pharmacodynamic modeling is required to evaluate the antitumor effect of liposomal DOX quantitatively. In these simulations, a cell kill kinetic model was introduced to describe the antitumor effect of DOX in terms of number of viable tumor cells which was originally developed by Jusko [37] to evaluate the pharmacodynamics of the antitumor effect of phase-nonspecific chemotherapeutic agents and further developed by Ozawa et al. [16] to explain the AUC-dependency in the antitumor effect of phasenonspecific agents. This model assumes the bi-molecular reaction between drug concentration at the site of action and tumor cell to describe the cell killing effect of antitumor agent. In general, the medium concentration is used as the drug concentration, because the medium concentration is usually proportional to the concentration at the site of action, and because of the difficulty in measuring the drug concentration at the site of action. This pharmacodynamic model can explain the time-dependent decrease of IC 50 observed in the antitumor effect of these agents [16,38]. Simulations in Fig. 4 showed the tendency that the longer the circulation time of liposomes, the higher the antitumor effect. This result confirmed the reported experiments on the enhanced antitumor effect of DOX in LCL against mouse colon carcinoma (C-26) [31, mammary carcinomas MC2, MC19 and MC65 [5], T-cell lymphoma (J6456) [6] and human lung tumor (TL-1) [8,39]. The long circulation time of liposomal DOX can be achieved by lowering both k RES and k rel as shown in Table 2. To increase the tumor delivery of liposomal DOX, the smaller k rel is more efficient, however the Cecs also decreases with the decrease of k rel . As shown in Fig. 3, when the k RES was fixed at 0.06 (h 21 ), the highest AUC ecs was achieved in the lowest k rel (50.006 h 21 ), however the rate of tumor cell killing was much higher at k rel 50.06 (h 21 ) as shown in Fig. 4B. Since AUC determines the antitumor effect of type-I drugs [16,17,40], the AUC of Cecs (AUC ecs ) is expected as an index of antitumor effect of DOX. However, we regarded the condition at k rel 50.06 (h 1 ) better than that at k rel 50.006 (h 21 ) according to the criteria
described above. This criteria includes not only the extent of bioavailability of DOX but also the rate of bioavailability of DOX from LCL in terms of antitumor effect of DOX. In the clinical situation, the rate of tumor cell killing is one of the most important factors for the antitumor drugs classified into type-I. Under such circumstances, this simulation clearly shows the existence of the optimum rate of drug release around 0.06 (h 21 ) in this condition. This result may depend upon the conditions of other parameters such as physiological / anatomical parameters of tumor cells. Therefore, we have performed simulations by altering tumor proliferation time which was represented by k s in the pharmacodynamic model in Fig. 2. As shown in Fig. 6, it was found that liposomes with k rel 50.06 (h 21 ) always exert highest antitumor effect and the pattern of time courses of tumor cells were similar for each k s . The tumor sensitivity to DOX which was represented by k is one of the most important parameters in performing simulations, however, it is difficult to assume a certain value for k, because tumor sensitivity can vary depending on the type of tumor, and heterogeneity of tumor cells. Therefore simulations in a wide range of tumor sensitivity should be required to evaluate the characteristics of liposomes. As shown in Fig. 6, there is a tendency that the rate of tumor cell killing decreased with the decrease of k, however, there is still the same order of efficiency of liposomes among different k rel in each k. This simulation confirmed that the optimum rate of drug release from liposomes is independent on the tumor sensitivity to antitumor drug. The effect of tumor blood flow-rate on the antitumor effect was also examined as an important physiological parameter of tumor tissues. As shown in Fig. 7, the antitumor effect of liposomal DOX was compared between normal blood flow-rate (A) and higher blood flow-rate (B). The antitumor effect decreased after increasing the Q, which may be different from the expectation that antitumor effect will increase in higher tumor blood flow-rate due to increased delivery of liposomal DOX to tumor tissue. This result can principally be explained by the wash-out effect of free DOX in ECS by the blood flow. The delivery of liposomal DOX is not increased by increasing tumor blood flow because the
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rate of liposomal delivery from capillary to interstitial compartment is limited by the CLup , not by tumor blood flow-rate [18]. The order of antitumor efficiency was still the same between these conditions. These simulations confirmed the superiority of k rel 50.06 (h 21 ) to exert highest antitumor effect in every condition examined above. In this simulation, we did not include tumor heterogeneity which has been known as an anatomical as well as physiological parameter of tumor tissue [28]. Vascular space in tumor varies from 1% to 28% depending on the tumor type, tumor size and tumor growth rate [28]. A two-compartment model has also been postulated for the pharmacokinetic analysis of drug disposition after intratumoral injection in a tissue isolated tumor perfusion system [30,41]. These studies indicated that a homogenous one-compartment model is not enough to analyze the intratumor disposition of drugs accurately. Therefore the physiological model composed of vascular space, interstitial space and tumor cell should be altered for further precise prediction of drug disposition in tumor tissue. The effect of the efflux of DOX from RES on the antitumor effect should also be evaluated. In the case of conventional liposomes (k RES 50.6), the effluxed DOX from RES can contribute to increase the antitumor effect, however little effect was observed in the case of LCL (k RES 50.06,0.006), where increase of Cecs in the LCL is generally negligible in any efflux rate of DOX from RES (data not shown). LCL has been shown to extravasate into the interstitial space from the tumor capillary, but usually not to be taken up by tumor cells in the C-26 colon carcinoma [3,19], rat mammary adenocarcinoma [42] and human colon adenocarcinoma LS174T cells [20]. The optimum diameter was shown to exist around 100 nm in Yoshida sarcoma [18]. The underlying mechanism of this transport process is not understood well, however tumor vessels are permeable presumably due to large pores in the vessel wall — the cutoff size of the pores seems to be between 400 and 600 (nm) [43]. Based on these experimental evidences, DOX in LCL is considered to be delivered into the interstitial space slowly and then encapsulated DOX is released into the interstitial compartment. The local sustained
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release of DOX from liposomes can elevate the extracellular concentration of free DOX which is the driving force for the antitumor effect of DOX and DOX in LCL are not necessarily endocytosed by the tumor cell for its antitumor activity [44–46]. Horowitz et al. showed no evidence for direct cellular uptake of liposome-entrapped DOX by human ovarian cancer cells for liposomes with various compositions [44]. On the other hand, Forsen et al. have shown the smaller IC 50 of DaunoXome (SUV) than that of free daunorubicin in the in vitro experiment at longer incubation period [47]. This result suggested the contribution of intracellular action of liposomal daunorubicin to the antitumor effect as well as local sustained release effect [47]. Therefore, the antitumor effect of liposomal DOX after endocytosis should also be included especially in the case of SUV as drug carrier. One of the principal toxicities of DOX is a cardiotoxicity, which limits the total cumulative dose of 550 mg / m 2 in humans associated with the development of congestive heart failure [48]. This toxicity can be reduced by modification of the administration schedule [49] or liposomal encapsulation [50–52], through reducing the peak plasma concentration of DOX. Myelosuppression is also a major toxicity for DOX [9]. Remarkable efficacy and safety of DOX in LCL has been shown in clinical studies of AIDS-related Kaposi’s sarcoma [12], where appearance of myelosuppressive toxicity was greatly decreased compared to conventional liposomes [12]. The reduced toxicity of DOX in LCL is also an advantage of this carrier system by limiting the distribution of free drug to normal tissue. Quantitative evaluation of both antitumor effect and toxicity of DOX in LCL is a further subject to be solved.
Acknowledgements This study was partly supported by a Grant-in-Aid for Scientific Research provided by the Ministry of Education, Science and Culture of Japan (09557197) and the Takeda Science Foundation. The authors would also like to thank Mr. Rick Cogley for his helpful advice in writing the English manuscript.
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Appendix A. Nomenclature AUC BLOOD CAP Cb Cb
lipo
Cint
lipo
Ccap
lipo
Cecs Cs Ctu CLtu CLup DOX ECS INT k k 10 k 12 k 21 k et k rel k RES ks k te k tu Q RES Vc
Area under the concentration–time curve (mg h / ml) Blood compartment Capillary compartment Concentration of free DOX in BLOOD (mg / ml) Concentration of liposomal DOX in BLOOD (mg / ml) Concentration of liposomal DOX in INT (mg / ml) Concentration of liposomal DOX in CAP (mg / ml) Concentration of free DOX in ECS (mg / ml) Density of tumor cell (number / ml) Concentration of free DOX in TUMOR (mg / ml) Tumor uptake clearance of liposomal DOX (ml / h) Intrinsic tumor uptake clearance of liposomal DOX (ml / h) Doxorubicin Extracellular compartment Interstitial compartment Drug-induced irreversible cell death rate constant [(h?mg / ml)21 ] Elimination rate constant of free DOX from BLOOD (h 21 ) Rate constant for DOX from BLOOD to TISSUE (h 21 ) Rate constant for DOX from TISSUE to BLOOD (h 21 ) Rate constant for DOX from ECS to TUMOR CELL (h 21 ) Rate constant for release rate of DOX from liposomes (h 21 ) Rate constant for liposomal uptake by RES (h 21 ) Cell proliferation rate constant (h 21 ) Rate constant for DOX from TUMOR CELL to ECS (h 21 ) Rate constant for liposomal DOX from CAP to INT (h 21 ) Tumor blood flow-rate (ml / h / g) Reticuloendothelial system Central volume of distribution for free DOX (ml)
Vcap Vint Vtu
Capillary space in tumor tissue (ml) Interstitial space in tumor tissue (ml) Cellular space in tumor tissue (ml)
Appendix B. Mass balance equations in the pharmacokinetic model The mass balance equations for the free and liposomal DOX in the model (Fig. 1) are described as follows.
5.1. Free DOX (a) BLOOD Vc dCb / dt 5 k relVc lipo Cb lipo 2 k 12 Vc Cb 1 k 21 X 1 Q ? Cecs 2 QCb
(B.1)
(b) TISSUE dX / dt 5 k 12Vc Cb 2 k 21 X
(B.2)
(c) ECS Vecs dCecs / dt 5 Q ? Cb 1 k teVtu Ctu 2 Q ? Cecs 2 k etVecs Cecs 1 k rel (Vcap Ccap lipo 1Vint Cint lipo )
(B.3)
(d) TUMOR CELL Vtu dCtu / dt 5 k et Vecs Cecs 2 k teVtu Ctu
(B.4)
5.2. Liposomal DOX (a) BLOOD Vc lipo dCb lipo / dt 5 Q ? Ccap lipo 2 Q ? Cb lipo 2 (k RES 1 k rel )Vc lipo Cb lipo
(B.5)
(b) RES dXRES / dt 5 k RESVc lipo Cb lipo
(B.6)
(c) CAP Vcap dCcap lipo / dt 5 Q ? Cb lipo 2 Q ? Ccap lipo 2 (k rel 1 k tu )Vcap Ccap lipo
(B.7)
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106
(d) INT Vint dCint lipo / dt 5 k tu Vcap Ccap lipo 2 k relVint Cint lipo (B.8)
Appendix C. Calculation of k tu from CLtu The tumor uptake of liposomal DOX was approximated by the first order rate constant k tu , calculated according to the following equations: CLtu 5 Q ? CLup /(Q 1 CLup )
(C.1)
k tu 5 CLup /Vcap
(C.2)
k tu 5 Q ? CLtu /(Q 2 CLtu ) /Vcap
(C.3)
where CLup represents the intrinsic uptake clearance of liposomes by the tumor based on the capillary concentration of liposomes.
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Optimization of antitumor effect of liposomally encapsulated doxorubicin based on simulations by pharmacokinetic / pharmacodynamic modeling Hideyoshi Harashima*, Shinya Iida, Yumiko Urakami 1 , Mari Tsuchihashi, Hiroshi Kiwada Faculty of Pharmaceutical Sciences, The University of Tokushima, 1 -78 -1 Shomachi, Tokushima City, Tokushima 770 -8505, Japan Received 11 July 1998; received in revised form 5 March 1999; accepted 17 April 1999
Abstract It has been reported that long circulating liposomes enhanced the antitumor effect of doxorubicin (DOX) by increasing delivery of DOX to tumor tissues. However, there is no quantitative information on the relationship between the antitumor effect and liposomal characteristics governing the release rate of entrapped drugs, although the importance of drug release-rate control from liposomes has been pointed out. Here, we developed a physiological model for free and liposomal DOX to calculate the time course of free DOX in the extracellular space and linked this with a cell kill kinetic model to quantify the antitumor effect of DOX. Simulations were performed to clarify the relationship between antitumor effect and pharmacokinetic or physicochemical parameters of liposomes, as well as pharmacological or physiological parameters of tumor tissues. The importance of long circulation time of liposomes was confirmed. The optimum rate of drug release from long circulating liposomes was found at the release rate constant of around 0.06 h 21 . This optimum value was not dependent on the tumor proliferation time, sensitivity of tumor cells to DOX, or the tumor blood flow-rate. This simulation indicated that the optimization of the delivery to tumor tissue by long circulating liposomes could be possible by changing the release rate of DOX for the maximum antitumor effect. 1999 Elsevier Science B.V. All rights reserved. Keywords: Drug delivery system; Simulation; Liposomes; Doxorubicin; Optimization
1. Introduction The development of long circulating liposomes
*Corresponding author. Tel.: 181-886-33-7260; fax: 181-88633-9506. E-mail address: [email protected] (H. Harashima) 1 Present address: Department of Pharmacy, Kyoto University Hospital, Faculty of Medicine, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan.
(LCL) remarkably increased the usefulness of liposomes as drug carriers and enhanced the therapeutic index of doxorubicin (DOX) [1,2]. The enhanced antitumor effects of DOX after its encapsulation into LCL have been examined in mice against many kinds of murine [3–6] and human [7,8] tumors. The enhanced antitumor effect of DOX in LCL has been shown in every study compared to that in free form or conventional liposomes. There is also increasing evidence of the successful clinical results of DOX in LCL against AIDS-related Kaposi’s sarcoma [9–12].
0168-3659 / 99 / $ – see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 99 )00110-8
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Phase II study revealed that 192 (80.7%) out of 238 patients achieved a complete (6.3%) or partial (74.4%) response [10]. This result is quite different from the clinical study using conventional liposomes, where among 50 patients available for efficacy, none had a complete response, five (10%) had a partial response, 32 (64%) had a minor response, 12 (24%) no change and one (2%) progression as their best response [9]. These experimental evidence show the importance of the long circulation property in the tumor delivery of liposomal DOX. Although the long circulating property is essential in enhancing the antitumor properties of DOX, there is no clear explanation about the optimum release rate of DOX from liposomes and how long LCL should remain in the blood circulation. There is no theoretical base to predict the optimum condition of liposomes for DOX in humans, although clinical trials have already started [9–12]. We are also not certain whether the optimum condition of LCL for
DOX determined in experimental animals directly applies to humans. The optimum condition in humans could be different from that in animals. In this report, we have developed the pharmacokinetic and pharmacodynamic model of DOX in LCL to examine the importance of each parameter on the antitumor effect, in the hope of optimizing the antitumor effect. A physiological model of tumor tissue was developed [13–15] to calculate the concentration of free DOX in the extracellular compartment, the concentration that was linked with the cell kill kinetic model [16,17] to quantify the antitumor effect of DOX. Based on this model, the effect of liposomalization on the local pharmacokinetics of DOX was quantitatively explained and the antitumor effect of DOX in LCL was also evaluated quantitatively by the change in tumor cell number. This simulation examined the importance of each parameter in determining the antitumor effect of DOX, and the optimum rate of drug release from liposomes for
Fig. 1. Pharmacokinetic model for free and liposomal DOX. Global pharmacokinetics was described by a compartment model and intra-tumor disposition was described by a flow model with tumor blood flow-rate (Q). Tumor tissue was divided into three compartments, capillary (CAP), interstitial (INT) and TUMOR CELL. Open and closed circles represent free and liposomal DOX, respectively. DOX in liposomes was released according to the first order rate constant (k rel ) in BLOOD, CAP and INT. Liposomal DOX in CAP was transported into INT unidirectionally (k tu ). Liposomal DOX was taken up by RES (k RES ) and efflux of DOX was neglected. Rapid equilibrium was assumed between CAP and INT for free DOX and Cecs was defined for free DOX in the extracellular compartment (ECS) as described in Methods. Distribution of free DOX to tumor cells was described with k et and k te . The k 12 , k 21 and k 10 represent the micro pharmacokinetic constants for free DOX. Each parameter used in the simulation was summarized in Table 1.
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DOX was shown to exist independent of the circulation time of liposomes, sensitivity of tumor cells to DOX, or tumor blood flow-rate.
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the disposition of free DOX, which was released from liposomal DOX in blood and tumor compartments. The first order rate process was assumed for this process and described by k rel in both blood and capillary compartments.
2. Materials and methods
2.1. Pharmacokinetic modeling of free and liposomal DOX A kinetic model was developed for free and liposomally encapsulated DOX in rats. All tissue except tumor was described by the hybrid model and tumor tissue was linked to blood compartment with tumor blood flow as shown in Fig. 1.
2.1.1. Free DOX A two-compartment model was applied to describe
2.1.2. Liposomal DOX A one-compartment model was applied for liposomal DOX and the elimination of liposomal DOX was described by k RES which represents the liposomal uptake by reticuloendothelial system (RES) without efflux of DOX [18]. 2.1.3. Tumor distribution The tumor tissue was divided into three compartments namely capillary (Vcap ), interstitial (Vint ) and tumor cell (Vtu ) where the capillary compartment was linked to the blood compartment with the tumor
Table 1 Kinetic parameters for free and liposomal DOX anatomical / physiological / pharmacological parameters for tumor tissue a Fixed Parameters (1) Kinetic parameters for free DOX Vc k 12 (ml / 250 g) (h 21 ) 515 5.13
k 21 (h 21 ) 0.927
k el (h 21 ) 1.56
k et (h 21 ) 2.27
k te (h 21 ) 0.0485
fb (h 21 ) 0.20
(2) Kinetic parameters for liposomal DOX Vc lipo k tu (ml / 250g) (h 21 ) 16.7 7.17 (3) Anatomical parameters for tumor tissue Vcap Vint (ml / g) (ml / g) 0.0285 0.323
Vtu (ml / g) 0.648
Altered parameters in simulations (1) Kinetic parameters for liposomal DOX k RES k rel (h 21 ) (h 21 ) 0.6 / 0.06 / 0.006 0.6 / 0.06 / 0.006 (2) Physiological / pharmacological parameters for tumor Q k (ml / h / g) [h 21 /(mg / ml)] 41.2 / 9.69 16.2 / 10.8 / 5.40 / 1.69
ks (h 21 ) 0.173 / 0.0578 / 0.0193
a Each fixed parameter was referred from literatures as explained in Determination of parameters for simulations. The k RES , k rel , Q, k and k s were altered in simulations as described in Materials and methods. Values in bold were used in simulations if conditions were not specified.
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concentration in Cecs and cell density (Cs ) under the assumption that the cell population is kinetically homogeneous for DOX and the volume of tumor tissue is 1 gram: dCs / dt 5 2 kfb Cecs Cs 1 k s Cs
Fig. 2. Pharmacodynamic model for DOX. A cell kill kinetic model was applied to quantify the antitumor effect of DOX. This pharmacodynamic model was linked with unbound concentration of free DOX in the ECS of tumor tissue ( fb ?Cecs ). The proliferation of tumor cells was represented by k s . Cell killing action was described by the bimolecular reaction of cell density (Cs ) and fb Cecs with the proportional rate constant k as described by Eq. (1).
blood flow-rate (Q) [13–15]. Recent studies clarified that liposomes escape the tumor capillary space into the interstitial space slowly, however, there was little uptake by tumor cells [3,19,20]. Based on this reported evidence, we assumed that liposomes were transported from the capillary space to the interstitial space without uptake by tumor cells. Rapid equilibrium was assumed between capillary and interstitial compartment for free DOX and the extracellular concentration of free DOX was defined as Cecs . The Cecs corresponds to the medium concentration of DOX in the in vitro experiments and it is an important variable for the simulation of the antitumor effect of DOX. The uptake of DOX by tumor cells was described by k et and k te .
2.2. Pharmacodynamic modeling of free DOX The antitumor effect of DOX was quantified by introducing the cell kill kinetic model as shown in Fig. 2, which was developed by Ozawa et al. [16,17]. The antitumor effect of type-I classified antitumor agents depended on the area under the concentration–time curve (AUC) and this kinetic characteristic was explained well by this cell kill kinetic model [16]. In brief, the cell killing action of cell cycle phase-nonspecific agents (type-I) occurs as a bimolecular reaction depending on the unbound drug
(1)
where k s and k represent the cell proliferation rate constant and drug-induced irreversible cell death rate constant, respectively. The k s was fixed at 0.0578 (h 21 ). The fb represents the unbound fraction of DOX in ECS [21]. The effect of the alteration of k, which represents the sensitivity of tumor cells to DOX, on the time course of tumor cell number was simulated by linking the cell kill kinetic model with Cecs in the physiological model of liposomal DOX as described above. In this simulation, the following criteria were applied in determining the order of antitumor effect of liposomal DOX. • Criteria 1: Lower number of antitumor cells at the bottom. When the antitumor cells decreased to one from 10 10 , the liposomes which achieve this point faster, the better. When the tumor cells reached the bottom and the recovering phase started, liposomes with the lower bottom are more effective. • Criteria 2: When a significant decrease in the number of tumor cells was not observed and only a decreased rate of tumor proliferation was observed, liposomes which show the higher growth inhibition at exponential growth phase are more effective.
2.3. Determination of parameters for simulations Pharmacokinetic parameters (k 12 , k 21 , k el , Vc ) for free doxorubicin were estimated by the nonlinear least squares’ method (MULTI) [22] using the reported time course of plasma concentration of free DOX in rats [23]. The rate constants of DOX for tumor distribution (k et and k te ) were estimated by nonlinear least squares’ method (RUNGE(MULTI)) [24] using the reported time courses of plasma and tumor concentration curve [25]. The volume of distribution for liposomes was fixed at the value reported previously [26]. The tumor uptake of liposomal DOX was approximated by the first order
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106
rate constant k tu , which was calculated as follows (See Appendix C). k tu 5 Q ? CLtu /(Q 2 CLtu ) /Vcap
(2)
where CLtu represents the uptake clearance of liposomes by tumors based on the blood concentration of liposomes. The Vcap and Vint were obtained by taking the average from the reported values [27–29]. The Vtu was calculated by 1 2 (Vcap 1Vint ), since we assumed the total volume of tumor tissue to be 1 ml. The reported values [30–32] on tumor blood flowrate ranged from 3.3 to 52 (ml / h / g) and there was two peaks with the averaged values, 9.69 and 41.2 (ml / h / g). Since the lower peak represented the major values, we fixed Q at 9.69 in the following simulations. The effect of altering Q was also examined.
2.4. Simulation of drug concentrations and antitumor effect by altering KRES and k rel To clarify the optimum condition of k RES and k rel for antitumor effect of DOX, k RES and k rel were altered and the antitumor effect as well as DOX concentration in each compartment was simulated based on the pharmacokinetic / pharmacodynamic model described above. The k RES principally determines the circulation times of liposomes in blood and was altered from 0.6 to 0.006 (h 21 ). The range of release rate used in our simulations mostly reflects the actual values which are commonly observed in the animal experiments of liposomes. The value of 0.6 (h 21 ) corresponds to the rate constant for conventional liposomes and the value of 0.06 (h 21 ) corresponds to that for long circulating liposomes in rodents [1]. There seems no report showing 0.006 (h 21 ) in rodents. Therefore this value is the lower limit at this stage. The k rel was assumed to be equal for blood, tumor capillary, and tumor interstitial compartments and was altered from 0.6 to 0.006 (h 21 ), which also corresponds to experimental values for the release rate of DOX in our laboratory (data not shown).
2.4.1. Alteration of tumor proliferation time on the antitumor effect of liposomal DOX It is difficult to fix the proliferation time of tumor
97
cells at a certain value, since the proliferation time varies depending on the type of tumor cells as well as experimental conditions. Thus, the effect of the proliferation rate constant, k s was examined by altering its value from 0.173 to 0.0193 (h 21 ) under the condition of long circulation liposomes (k RES 5 0.06 h 21 ). In other simulations, 0.0578 (h 21 ) was used for k s .
2.4.2. Alteration of tumor sensitivity on the antitumor effect of liposomal DOX Sensitivity of tumor cells to DOX has been reported to vary depending on the time of incubation [16,33] as well as tumor type [33,34]. Time dependent IC 50 of DOX can be explained well with the cell kill kinetic model introduced in this simulation [16]. There exists a huge variation in IC 50 even for the same incubation time: 0.2 mM for ovarian carcinoma OV-1063 [34] vs. 0.01 mM for breast cancer T47D [33] under 72-h incubation. To examine this wide range of sensitivity to DOX depending on the tumor type, simulations were performed by altering k from 1.69 / 5.40 / 10.8 / 16.2 [(h?mg / ml)21 ] under the condition of long circulating liposomes (k RES 50.06 h 21 ). In other simulations, 16.2 [(h?mg / ml 21 ] was used for k. 2.4.3. Effect of physiological alteration on the antitumor effect of DOX The blood flow-rate to tumor tissue is also an important factor influencing the antitumor effect of liposomal DOX. Since tumor tissue is heterogeneous and reported values for tumor blood flow-rate varied from 3.3 to 52 [30–32], Q was increased from 9.69 to 41.2 (ml / min / g) under fixed conditions for other parameters. In other simulations, 9.69 (ml / h) was used for Q.
3. Results
3.1. Simulation of drug concentrations by altering k RES and k rel The concentration of free and liposomal DOX in each compartment is shown in Fig. 3. Since the free concentration of DOX in the ECS compartment is a
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Fig. 3. Time course of free and liposomal DOX concentration in each compartment. Time courses of free and liposomal DOX concentration were simulated by altering k RES and k rel as shown in Table 2. Cb : free DOX in BLOOD. Cb lipo : liposomal DOX in BLOOD. Cint lipo : liposomal DOX in INT. Cecs : free DOX in ECS. Ctu : tumor concentration of DOX. The dose of DOX was fixed at 6 mg / kg.
key concentration in determining the antitumor effect of DOX, the effect of k RES and k rel on the time courses of Cecs should be focused. At a high k rel 21 value (0.6 h ) as shown in Fig. 1C, F and I, there was little difference between Cecs and Cb , which indicates that there is little benefit to be gained by liposomal encapsulation. As k rel decreases from 0.6 to 0.06 (h 21 ), the difference between Cecs and Cb became significant, which enhances the antitumor effect of DOX by limiting the distribution of free DOX to whole body. Further decrease in k rel from 0.06 to 0.006 (h 21 ) remarkably influenced the disappearance rate of DOX in the ECS, INT and TUMOR compartments (B → A, E → D, and H → G). Although the level of free DOX in the ECS is low in the lowest k rel (0.006), the half-life of DOX in ECS, INT and TUMOR CELL increased. The
peak concentration of free DOX in ECS and liposomal DOX in INT are principally determined by both k RES and k rel as shown in Table 2. The smaller the k RES and k rel , the higher the peak concentration of Cint lip and Cecs . This result clearly indicated that a smaller k RES and / or k rel increased the delivery of DOX to INT compartment in liposomal form and increased the released amounts of free DOX in ECS. The slowest combination of k rel and k RES has the highest AUC of free DOX in the ECS compartment, although the peak concentration of DOX in the ECS compartment is higher in the higher k rel at the same k RES . Thus, the peak concentration in the ECS compartment is principally determined by k rel , however, AUC in ECS compartment is principally governed by both k RES /k rel . The peak concentration of DOX in TUMOR CELL did not correlate with the
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106 Table 2 Peak concentration of DOX in Cint
lip
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, Cecs and Ctu in each combination of k RES and k rel a
(A) k RES 50.006 /k rel 50.006 Cint lip (77, 1460) Cecs (76, 0.158) Ctu (103, 3.86)
(B) k RES 50.006 /k rel 50.06 Cint lip (15, 297) Cecs (13, 0.358) Ctu (32, 5.84)
(C) k RES 50.006 /k rel 50.6 Cint lip (1.6, 33) Cecs (1.4, 0.598) Ctu (8.4, 2.85)
(D) k RES 50.06 /k rel 50.006 Cint lip (36, 576) Cecs (66, 0.062) Ctu (34, 1.41)
(E) k RES 50.06 /k rel 50.06 Cint lip (11, 218) Cecs (10, 0.266) Ctu (27, 3.84)
(F) k RES 50.006 /k rel 50.6 Cint lip (1.6, 32) Cecs (1.4, 0.573) Ctu (8.2, 2.63)
(G) k RES 50.6 /k rel 50.006 Cint lip (7.6, 86.0) Cecs (4.8, 0.010) Ctu (50, 0.184)
(H) k RES 50.6 /k rel 50.06 Cint lip (4.0, 65.3) Cecs (3.2, 0.084) Ctu (19, 0.829)
(I) k RES 50.006 /k rel 50.6 Cint lip (1.2, 23.0) Cecs (0.8, 0.420) Ctu (7.0, 1.49)
a Time to peak concentration (h) and the peak concentration (mg / ml) of DOX in Cint combination of k RES and k rel as (time, concentration).
peak concentration of Cecs and the highest Ctu was observed in B (k RES 50.006 /k rel 50.06).
3.2. Simulation of antitumor effect by altering pharmacokinetic and pharmacodynamic parameters 3.2.1. Alteration of kRES and k rel An antitumor effect simulated by the cell kill kinetic model linked with Cecs is shown in Fig. 4. There is a general tendency for the antitumor effect to be increased by decreasing the k RES . This result
lip
, Cecs and Ctu were summarized for each
confirmed the requirement of long circulating time of liposomes as a superior drug carrier. There was little effect of liposomal encapsulation under the rapid RES uptake of liposomal DOX as shown in Fig. 4C, however the antitumor effect of liposomal DOX increased remarkably by lowering the k rel in the case of the long circulating liposomes as shown in Fig. 4B. The killing effect continued for a longer time and decreased the number of tumor cells almost completely by reducing k rel from 0.6 to 0.06 (h 21 ). Further decrease of k rel from 0.06 to 0.006 (h 21 )
Fig. 4. Effect of k RES and k rel on the antitumor effect of liposomal DOX. Antitumor effects of liposomal DOX were simulated based on the pharmacodynamic model of DOX, which was linked with Cecs in the physiological model described in Figs. 1 and 2. (A) k RES 50.006 h 21 , (B) k RES 50.06 h 21 , (C) k RES 50.6 h 21 . Lines: ——: control, ? ? ? ? ? ?: free, - - - - -: k rel 50.6 h 21 , - ? - ? -: k rel 50.06 h 21 , ------: k rel 50.006 h 21 .
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Fig. 5. Effect of tumor proliferation time on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor proliferation time which was represented by k s in the pharmacodynamic model in Fig. 2. The k RES was fixed at 0.06 h 21 . (A) k s 50.173, (B) k s 50.0578, (C) k s 50.0193 (h 21 ). Lines: ——: control, - - - - - -: k rel 50.6 h 21 , - ? - ? -: k rel 50.06 h 21 , – – – –: k rel 50.006 h 21 .
increased the duration of tumor killing time, however the rate of killing tumor cells decreased compared to k rel at 0.06 (h 21 ). In case of super-long circulating liposomes as shown in Fig. 4A, the antitumor effect
was enhanced for the corresponding case at the same k rel , and the same order of antitumor effect was seen between Fig. 4A and B. It was shown by this simulation that the most effective rate of drug release
Fig. 6. Effect of tumor sensitivity on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor sensitivity which was represented by k in the pharmacodynamic model in Fig. 2. The k RES was fixed at 0.06 h 21 . (A) k51.69, (B) k55.40, (C) k510.8, (D) k516.2 [(h?mg / ml)21 ]. Lines: ——: control, ? ? ? ? ? ?: free, - - - -: k rel 50.6 h 21 , 2 ? - ? - ? -: k rel 50.06 h 21 : ------: k rel 50.006 h 21 .
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Fig. 7. Effect of tumor blood flow-rate on the antitumor effect of liposomal DOX. Antitumor effects were simulated by altering the tumor blood flow-rate (Q) in the flow model for tumor tissue. The k RES was fixed at 0.06 h 21 . (A) Q59.69, (B) Q541.2 (ml / h / g). Lines: ——: control, ? ? ? ? ? ?: free, - - - -: k rel 50.6 h 21 , - ? - ? - ? -: k rel 50.06 h 21 : ------: k rel 50.006 h 21 .
was at 0.06 (h 21 ) for long circulating liposomes (Fig. 4A and B). As to conventional liposomes which are represented by k RES 50.6 (Fig. 4C), there was no benefit of liposomal encapsulation and the administration of free DOX showed the highest antitumor effect.
3.2.2. Alteration of ks The effect of tumor proliferation time on the antitumor effect of liposomal DOX is shown in Fig. 5 by changing k rel under the long circulating liposomes. The effect of k s on the absolute number of tumor cells is significant, however the pattern of change in the tumor cells is similar for each k s . The order of effective liposomes is independent of k s : k rel 50.06.k rel 50.006.k rel 50.6. In the following simulations, k s was fixed at 0.0578 (h 21 ). 3.2.3. Alteration of k The effect of tumor sensitivity on the antitumor effect of liposomal DOX was also examined by changing the k from 16.2 to 1.69 [(h?mg / ml)21 ] as shown in Fig. 6. By decreasing the k, the extent of antitumor effect was decreased, however the pattern of time course of tumor cells was similar for each k. Therefore the optimum rate of drug release was always observed at k rel 50.06 (h 21 ). 3.2.4. Alteration of Q The antitumor effect of liposomal DOX was
simulated by altering tumor blood flow-rate for each k rel at a fixed k RES of 0.06 (h 21 ). As shown in Fig. 7, tumor blood flow-rate is also a critical factor in determining the antitumor effect of liposomal DOX. Under the high tumor blood flow-rate (Q541.2 ml / h / g), the antitumor effect was reduced remarkably compared to the low tumor blood flow-rate (Q59.69 ml / h / g). Although the enhanced effect by liposomal encapsulation is slight in the case of higher tumor blood flow-rate, the order of antitumor effect among each liposomes with different k rel is still the same with the low tumor blood flow-rate.
4. Discussion It is essential to apply a physiologically-based pharmacokinetic model to describe the drug disposition in tumor tissue and to evaluate the effect of each parameter of liposomes as well as anatomical and / or physiological parameter of tumor tissue on the antitumor effect of liposomal DOX. A three compartment–flow model was applied to tumor tissue to calculate the Cecs , which corresponds to the medium concentration in the in vitro antitumor experiments. This model is not a conceptual model but is based on the real parameters such as Cecs , Q, Vint , Vcap , etc., which has the advantage of being able to extrapolate from experimental animals to humans [35,36]. In this paper, this model was first applied to examine the
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effect of each parameter on the alteration of Cecs and to understand the mechanism of enhanced antitumor effect of DOX in LCL. Pharmacodynamic modeling is required to evaluate the antitumor effect of liposomal DOX quantitatively. In these simulations, a cell kill kinetic model was introduced to describe the antitumor effect of DOX in terms of number of viable tumor cells which was originally developed by Jusko [37] to evaluate the pharmacodynamics of the antitumor effect of phase-nonspecific chemotherapeutic agents and further developed by Ozawa et al. [16] to explain the AUC-dependency in the antitumor effect of phasenonspecific agents. This model assumes the bi-molecular reaction between drug concentration at the site of action and tumor cell to describe the cell killing effect of antitumor agent. In general, the medium concentration is used as the drug concentration, because the medium concentration is usually proportional to the concentration at the site of action, and because of the difficulty in measuring the drug concentration at the site of action. This pharmacodynamic model can explain the time-dependent decrease of IC 50 observed in the antitumor effect of these agents [16,38]. Simulations in Fig. 4 showed the tendency that the longer the circulation time of liposomes, the higher the antitumor effect. This result confirmed the reported experiments on the enhanced antitumor effect of DOX in LCL against mouse colon carcinoma (C-26) [31, mammary carcinomas MC2, MC19 and MC65 [5], T-cell lymphoma (J6456) [6] and human lung tumor (TL-1) [8,39]. The long circulation time of liposomal DOX can be achieved by lowering both k RES and k rel as shown in Table 2. To increase the tumor delivery of liposomal DOX, the smaller k rel is more efficient, however the Cecs also decreases with the decrease of k rel . As shown in Fig. 3, when the k RES was fixed at 0.06 (h 21 ), the highest AUC ecs was achieved in the lowest k rel (50.006 h 21 ), however the rate of tumor cell killing was much higher at k rel 50.06 (h 21 ) as shown in Fig. 4B. Since AUC determines the antitumor effect of type-I drugs [16,17,40], the AUC of Cecs (AUC ecs ) is expected as an index of antitumor effect of DOX. However, we regarded the condition at k rel 50.06 (h 1 ) better than that at k rel 50.006 (h 21 ) according to the criteria
described above. This criteria includes not only the extent of bioavailability of DOX but also the rate of bioavailability of DOX from LCL in terms of antitumor effect of DOX. In the clinical situation, the rate of tumor cell killing is one of the most important factors for the antitumor drugs classified into type-I. Under such circumstances, this simulation clearly shows the existence of the optimum rate of drug release around 0.06 (h 21 ) in this condition. This result may depend upon the conditions of other parameters such as physiological / anatomical parameters of tumor cells. Therefore, we have performed simulations by altering tumor proliferation time which was represented by k s in the pharmacodynamic model in Fig. 2. As shown in Fig. 6, it was found that liposomes with k rel 50.06 (h 21 ) always exert highest antitumor effect and the pattern of time courses of tumor cells were similar for each k s . The tumor sensitivity to DOX which was represented by k is one of the most important parameters in performing simulations, however, it is difficult to assume a certain value for k, because tumor sensitivity can vary depending on the type of tumor, and heterogeneity of tumor cells. Therefore simulations in a wide range of tumor sensitivity should be required to evaluate the characteristics of liposomes. As shown in Fig. 6, there is a tendency that the rate of tumor cell killing decreased with the decrease of k, however, there is still the same order of efficiency of liposomes among different k rel in each k. This simulation confirmed that the optimum rate of drug release from liposomes is independent on the tumor sensitivity to antitumor drug. The effect of tumor blood flow-rate on the antitumor effect was also examined as an important physiological parameter of tumor tissues. As shown in Fig. 7, the antitumor effect of liposomal DOX was compared between normal blood flow-rate (A) and higher blood flow-rate (B). The antitumor effect decreased after increasing the Q, which may be different from the expectation that antitumor effect will increase in higher tumor blood flow-rate due to increased delivery of liposomal DOX to tumor tissue. This result can principally be explained by the wash-out effect of free DOX in ECS by the blood flow. The delivery of liposomal DOX is not increased by increasing tumor blood flow because the
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106
rate of liposomal delivery from capillary to interstitial compartment is limited by the CLup , not by tumor blood flow-rate [18]. The order of antitumor efficiency was still the same between these conditions. These simulations confirmed the superiority of k rel 50.06 (h 21 ) to exert highest antitumor effect in every condition examined above. In this simulation, we did not include tumor heterogeneity which has been known as an anatomical as well as physiological parameter of tumor tissue [28]. Vascular space in tumor varies from 1% to 28% depending on the tumor type, tumor size and tumor growth rate [28]. A two-compartment model has also been postulated for the pharmacokinetic analysis of drug disposition after intratumoral injection in a tissue isolated tumor perfusion system [30,41]. These studies indicated that a homogenous one-compartment model is not enough to analyze the intratumor disposition of drugs accurately. Therefore the physiological model composed of vascular space, interstitial space and tumor cell should be altered for further precise prediction of drug disposition in tumor tissue. The effect of the efflux of DOX from RES on the antitumor effect should also be evaluated. In the case of conventional liposomes (k RES 50.6), the effluxed DOX from RES can contribute to increase the antitumor effect, however little effect was observed in the case of LCL (k RES 50.06,0.006), where increase of Cecs in the LCL is generally negligible in any efflux rate of DOX from RES (data not shown). LCL has been shown to extravasate into the interstitial space from the tumor capillary, but usually not to be taken up by tumor cells in the C-26 colon carcinoma [3,19], rat mammary adenocarcinoma [42] and human colon adenocarcinoma LS174T cells [20]. The optimum diameter was shown to exist around 100 nm in Yoshida sarcoma [18]. The underlying mechanism of this transport process is not understood well, however tumor vessels are permeable presumably due to large pores in the vessel wall — the cutoff size of the pores seems to be between 400 and 600 (nm) [43]. Based on these experimental evidences, DOX in LCL is considered to be delivered into the interstitial space slowly and then encapsulated DOX is released into the interstitial compartment. The local sustained
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release of DOX from liposomes can elevate the extracellular concentration of free DOX which is the driving force for the antitumor effect of DOX and DOX in LCL are not necessarily endocytosed by the tumor cell for its antitumor activity [44–46]. Horowitz et al. showed no evidence for direct cellular uptake of liposome-entrapped DOX by human ovarian cancer cells for liposomes with various compositions [44]. On the other hand, Forsen et al. have shown the smaller IC 50 of DaunoXome (SUV) than that of free daunorubicin in the in vitro experiment at longer incubation period [47]. This result suggested the contribution of intracellular action of liposomal daunorubicin to the antitumor effect as well as local sustained release effect [47]. Therefore, the antitumor effect of liposomal DOX after endocytosis should also be included especially in the case of SUV as drug carrier. One of the principal toxicities of DOX is a cardiotoxicity, which limits the total cumulative dose of 550 mg / m 2 in humans associated with the development of congestive heart failure [48]. This toxicity can be reduced by modification of the administration schedule [49] or liposomal encapsulation [50–52], through reducing the peak plasma concentration of DOX. Myelosuppression is also a major toxicity for DOX [9]. Remarkable efficacy and safety of DOX in LCL has been shown in clinical studies of AIDS-related Kaposi’s sarcoma [12], where appearance of myelosuppressive toxicity was greatly decreased compared to conventional liposomes [12]. The reduced toxicity of DOX in LCL is also an advantage of this carrier system by limiting the distribution of free drug to normal tissue. Quantitative evaluation of both antitumor effect and toxicity of DOX in LCL is a further subject to be solved.
Acknowledgements This study was partly supported by a Grant-in-Aid for Scientific Research provided by the Ministry of Education, Science and Culture of Japan (09557197) and the Takeda Science Foundation. The authors would also like to thank Mr. Rick Cogley for his helpful advice in writing the English manuscript.
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Appendix A. Nomenclature AUC BLOOD CAP Cb Cb
lipo
Cint
lipo
Ccap
lipo
Cecs Cs Ctu CLtu CLup DOX ECS INT k k 10 k 12 k 21 k et k rel k RES ks k te k tu Q RES Vc
Area under the concentration–time curve (mg h / ml) Blood compartment Capillary compartment Concentration of free DOX in BLOOD (mg / ml) Concentration of liposomal DOX in BLOOD (mg / ml) Concentration of liposomal DOX in INT (mg / ml) Concentration of liposomal DOX in CAP (mg / ml) Concentration of free DOX in ECS (mg / ml) Density of tumor cell (number / ml) Concentration of free DOX in TUMOR (mg / ml) Tumor uptake clearance of liposomal DOX (ml / h) Intrinsic tumor uptake clearance of liposomal DOX (ml / h) Doxorubicin Extracellular compartment Interstitial compartment Drug-induced irreversible cell death rate constant [(h?mg / ml)21 ] Elimination rate constant of free DOX from BLOOD (h 21 ) Rate constant for DOX from BLOOD to TISSUE (h 21 ) Rate constant for DOX from TISSUE to BLOOD (h 21 ) Rate constant for DOX from ECS to TUMOR CELL (h 21 ) Rate constant for release rate of DOX from liposomes (h 21 ) Rate constant for liposomal uptake by RES (h 21 ) Cell proliferation rate constant (h 21 ) Rate constant for DOX from TUMOR CELL to ECS (h 21 ) Rate constant for liposomal DOX from CAP to INT (h 21 ) Tumor blood flow-rate (ml / h / g) Reticuloendothelial system Central volume of distribution for free DOX (ml)
Vcap Vint Vtu
Capillary space in tumor tissue (ml) Interstitial space in tumor tissue (ml) Cellular space in tumor tissue (ml)
Appendix B. Mass balance equations in the pharmacokinetic model The mass balance equations for the free and liposomal DOX in the model (Fig. 1) are described as follows.
5.1. Free DOX (a) BLOOD Vc dCb / dt 5 k relVc lipo Cb lipo 2 k 12 Vc Cb 1 k 21 X 1 Q ? Cecs 2 QCb
(B.1)
(b) TISSUE dX / dt 5 k 12Vc Cb 2 k 21 X
(B.2)
(c) ECS Vecs dCecs / dt 5 Q ? Cb 1 k teVtu Ctu 2 Q ? Cecs 2 k etVecs Cecs 1 k rel (Vcap Ccap lipo 1Vint Cint lipo )
(B.3)
(d) TUMOR CELL Vtu dCtu / dt 5 k et Vecs Cecs 2 k teVtu Ctu
(B.4)
5.2. Liposomal DOX (a) BLOOD Vc lipo dCb lipo / dt 5 Q ? Ccap lipo 2 Q ? Cb lipo 2 (k RES 1 k rel )Vc lipo Cb lipo
(B.5)
(b) RES dXRES / dt 5 k RESVc lipo Cb lipo
(B.6)
(c) CAP Vcap dCcap lipo / dt 5 Q ? Cb lipo 2 Q ? Ccap lipo 2 (k rel 1 k tu )Vcap Ccap lipo
(B.7)
H. Harashima et al. / Journal of Controlled Release 61 (1999) 93 – 106
(d) INT Vint dCint lipo / dt 5 k tu Vcap Ccap lipo 2 k relVint Cint lipo (B.8)
Appendix C. Calculation of k tu from CLtu The tumor uptake of liposomal DOX was approximated by the first order rate constant k tu , calculated according to the following equations: CLtu 5 Q ? CLup /(Q 1 CLup )
(C.1)
k tu 5 CLup /Vcap
(C.2)
k tu 5 Q ? CLtu /(Q 2 CLtu ) /Vcap
(C.3)
where CLup represents the intrinsic uptake clearance of liposomes by the tumor based on the capillary concentration of liposomes.
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