AAPS PharmSci 2002; 4 (4) article 42 (

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1 Pharmacodynamic Modeling of Chemotherapeutic Effect: Application of a Tranit Compartment Model to Characterize Methotrexate Effect in Vitro Submitted: May 15, 22; Accepted: September 22, 22; Publihed October 29, 22 Evelyn D. Lobo 1 and Joeph P. Balthaar 1 1 Department of Pharmaceutical Science, Univerity at Buffalo, The State Univerity of New York, Buffalo, NY 1426 ABSTRACT The time coure of chemotherapeutic effect i often delayed relative to the time coure of chemotherapeutic expoure. In many cae, thi delay i difficult to characterize mathematically through the ue of tandard pharmacodynamic model. In the preent work, we invetigated the relationhip between methotrexate (MTX) expoure and the time coure of MTX effect on tumor cell growth in culture. Two cancer cell line, Ehrlich acite cell and arcoma 18 cell, were expoed for 24 hour to MTX concentration that varied more than 7- fold (.19-). Viable cell were counted on day 1, 3, 5, 7, 9, 11, 13, 15, 17, 2, 22, and 24 for Ehrlich acite cell and on day 1, 2, 3, 5, 7, 9, 11, 13, 14, 15, 17, 19, and 21 for arcoma 18 cell, through the ue of a tetrazolium aay. Although MTX wa removed 24 hour after application, cell number reached nadir value more than 1 hour after MTX expoure. Data from each cell line were fitted to 3 pharmacodynamic model of chemotherapeutic cell killing: a cell cycle phae-pecific model, a phae-nonpecific model, and a tranit compartment model (baed on the general model recently reported by Mager and Juko, Clin Pharmacol Ther. 7:21-216, 21). The tranit compartment model captured the data much more accurately than the tandard pharmacodynamic model, with correlation coefficient ranging from.86 to.999. Thi report how the ucceful application of a tranit compartment model for characterization of the complex time coure of chemotherapeutic effect; uch model may be very ueful in the development of optimization trategie for cancer chemotherapy. EYWORDS: methotrexate, cell growth inhibition, modeling, chemotherapeutic effect, tranit compartment model. INTRODUCTION Although everal chemotherapeutic demontrate hort elimination half-live (eg, le than 12 hour), 1, 2 maximal clinical effect (and toxicitie) often occur 14 to 21 day following drug adminitration. 3-5 A uch, peak drug concentration often precede peak drug effect by day or week, greatly complicating attempt Correpondence to: Joeph P. Balthaar Telephone: (716) , x256 Facimile: (716) jb@acu.buffalo.edu to relate the time coure of drug expoure to the time coure of drug effect. Such pharmacokineticpharmacodynamic (PPD) relationhip may be of great value, a they may facilitate the individualization and optimization of chemotherapy. Perhap becaue of the inherent difficultie, relatively few PPD modeling approache have been developed to characterize the time coure of chemotherapeutic effect. 6-8 In lieu of time-coure model, PPD individualization effort have largely attempted to relate a time-averaged value of drug expoure (eg, the area under the plama concentration time curve) to peak effect or peak toxicity (eg, nadir white blood cell count) Unfortunately, uch tatic approache are of limited value, a thee model do not predict the time coure of effect and, thu, may not be ued to predict optimal chedule of drug adminitration. Additionally, it i deirable to relate effect to the entire time coure of drug expoure, becaue chemotherapeutic effect are often found to be protocol dependent (ie, dependent on the duration of drug adminitration and on the duration of drug expoure), where identical area under the curve produce markedly different effect. Recently, a imple, robut approach ha been introduced to model PPD time delay through the ue of tranit compartment. 17 In the preent tudy, we wihed to evaluate the tranit compartment model for ue in relating the time coure of chemotherapeutic expoure to the time coure of chemotherapeutic effect. Repreentative data were collected following invetigation of the cytotoxic effect of MTX, an etablihed anticancer drug, againt 2 cancer cell line in vitro. Conitent with expectation, the peak effect (ie, the time to reach the lowet cell number following MTX treatment) wa delayed tremendouly relative to the time coure of MTX expoure in thi experimental ytem. Thee data were modeled with the tranit compartment model and with 2 etablihed PPD model of chemotherapeutic effect (ie, a phae-pecific model and a phae-nonpecific model) Relative to the etablihed model, the tranit compartment model wa found to provide uperior fitting of the data; conequently, thi model may find broad application in the characterization of chemotherapeutic effect. 1

2 A. k ng C B. k g C k r C r k d k r C k ng C 4 Figure 1. Schematic repreentation of the model evaluated for characterization of MTX cytotoxicity. (A) Phae-nonpecific model: C, viable cell; k ng, net growth rate contant;, cell kill contant. (B) Phae-pecific model: C, cell enitive to MTX; C r, cell reitant to MTX; k g, cell proliferation rate contant; k d, cell lo rate contant; k r and k r, cell cycling rate contant. (C) Tranit compartment model: 1, 2, 3, and 4 refer to the cell kill rate contant in the tranit compartment;, tranit time; k ng, net growth rate contant; C, viable cell. For each model, the cell kill contant i a nonlinear function of MTX concentration: = max M/(EC 5 +M), where max i the maximal value of the cell kill contant, EC 5 i a Michaeli contant, and M refer to the MTX concentration, which i a time-dependent variable. MATERIALS AND METHODS Material MTX and 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide (MTT) were purchaed from Sigma Chemical (St Loui, MO). Sodium dodecyl ulfate (SDS) wa obtained from Bio-Rad Laboratorie (Hercule, CA). Cell culture media (RPMI 164), certified fetal bovine erum, and gentamicin were obtained from Invitrogen Corporation (Grand Iland, NY). Ehrlich acite cell and arcoma 18 cell were obtained from American Type Cell Culture (Manaa, VA). In vitro cell growth inhibition The cancer cell line were grown within a humidified, 5% CO 2 incubator at 37. RPMI 164 media wa prepared to contain approximately 1 ng/ml folic acid and wa upplemented with 1% fetal bovine erum and gentamicin (1 g/ml). Cell upenion containing 1 cell/ml and 5 cell/ml were prepared for Ehrlich acite cell and arcoma 18 cell, repectively, and.1 ml of upenion (ie, containing 1 or 5 cell) wa dipened into well of well plate. After allowing the cell to attach for 48 hour, media wa apirated through a 25-gauge needle. Preliminary tudie demontrated that thi method of apirating media did not reult in ignificant lo of cell (recovery wa found to be %, n = 12). Following apiration, 1 L of media containing MTX (, 2. g/ml, 14. g/ml, or 14. g/ml) wa added. Each plate wa prepared in an identical fahion, with 4 well ued for each concentration of MTX. Cell were incubated with MTX for 24 hour, and media wa then apirated. Each well wa then wahed 4 time with 1 L of MTX-free media. Cell number wa determined on day 2

3 1, 3, 5, 7, 9, 11, 13, 15, 17, 2, 22, and 24 for Ehrlich acite cell and on day 1, 2, 3, 5, 7, 9, 11, 13, 14, 15, 17, 19, and 21 for arcoma 18 cell, uing 1 plate per aay, via the tetrazolium aay. 21 Briefly, on the day of analyi, media wa apirated from all well of the aay plate. Exactly 1 L of freh media and 25 L of MTT olution (5 mg/ml in phophate aline buffer, ph 7.4) were added to each well, and the plate wa then incubated for 4.5 hour at 37 in the incubator. After incubation, 1 L of 1% SDS-.1 M hydrochloric acid (1%SDS-HCl) wa added to each well, and the plate wa incubated overnight at 37. Aborbance in each well wa determined at 59 nm uing a plate reader (Spectromax, Molecular Device Sunnyvale, CA). Cell number wa determined through the ue of a tandard curve (run on each plate) that related aborbance to cell count (linear range: 156 to 1 cell for arcoma 18 cell, and 156 to 12 5 for Ehrlich acite cell). Cell number wa determined for each treatment group until aay repone exceeded the upper limit of the tandard curve (ie, where aay repone indicated cell number greater than 1 cell/well or 12 5 cell/well for arcoma 18 cell or Ehrlich acite cell, repectively). Pharmacodynamic modeling Three pharmacodynamic model were ued to fit the time coure of MTX effect: (1) a cell cycle phae-nonpecific model of cytotoxicity, (2) a phae-pecific model of cytotoxicity, and (3) a cell kill model that wa baed on the general tranit compartment model of Mager and Juko. 17 Schematic repreentation of the model are hown in Figure 1. Differential equation were a follow: Phae-nonpecific model dc dt EC ng max M M 5 Where C repreent the cell number, k ng i a firt-order rate contant of net growth (mathematically equivalent to a firtorder growth rate contant [k g ] minu a firt-order death rate contant [k d ]; ie, k ng = k g k d ), i a nonlinear function of MTX cell kill, which i dependent on the MTX concentration in media, M; the maximal MTX cell kill rate, max ; and a Michaeli contant, EC 5. Phae-pecific model dc dt dc dt r EC g r max M M r r r r d r 5 Two cell population are aumed: a enitive population (where C refer to the number of enitive cell) and a reitant population (where C r refer to the number of reitant cell). The firt-order rate contant k r and k r refer to rate of cell cycling between the population; k g and k d refer to rate of cell growth and cell death, repectively. i a defined above. Tranit compartment model dc ng 4 dt d1 1 1 dt d dt d dt d dt maxm EC M 5 C, max, EC 5, M, and are a defined above; however, the operative rate function of MTX-induced cell killing, 4, i related to via a erie of tranit compartment (ie, 1-4). refer to the mean tranit time in each tranit compartment. A hown, the tranit compartment delay the time coure of cell kill, relative to the time coure of drug expoure. Four tranit compartment are employed in thi model; however, only 1 parameter i ued to decribe tranit kinetic ( ). A uch, the model i both flexible (becaue of the number of tranit compartment) and highly table (becaue of the ue of a mall number of parameter [k ng, max, EC 5, ]). Becaue i a function of M, a time-dependent variable, each model i a dynamic model of drug effect. That i, the cell kill contant change with time, a influenced by factor that control the time coure of drug expoure (eg, the doing regimen, the relevant pharmacokinetic of the ytem). Additionally, cell number i alo a time-dependent variable. A uch, each model allow dynamic characterization of cell growth and drug-induced cell killing. All model parameter were fitted to mean cell number veru time data, where mean number wa determined from 4 well aayed at each time point. Data for all MTX expoure were fitted imultaneouly, for each cell line, with ADAPT II oftware. 22 RESULTS In vitro MTX cell inhibition The time coure of cell growth for the 2 tumor cell line are hown in Figure 2, 3, and 4. In the abence of MTX, each cell line demontrated exponential growth. MTX induced concentration-dependent inhibition in apparent cell growth; however, MTX effect were ignificantly delayed relative to the time coure of drug expoure. Little change in cell number wa oberved during the 24-hour incubation 3

4 Ehrlich acite cell Hour Sarcoma 18 Cell 2 14 g/ml 14 g/ml 2 g/ml.19 g/ml 14 g/ml 14 g/ml 2 g/ml.19 g/ml Hour Figure 2. Phae-nonpecific model prediction of MTX effect on the time coure of cell growth. Ehrlich acite cell (A) and arcoma 18 cell (B) were treated with MTX for 24 hour (concentration ranging from to 14 μg/ml). After removal of MTX, cell were fed with freh media every 48 hour. Solid ymbol and bar refer to the mean and SD (n = 4). Model-predicted profile are hown a olid line. 4

5 2 Erhlich Acite Cell Hour Sarcoma 18 Cell Hour Figure 3. Phae-pecific model prediction of MTX effect on the time coure of cell growth. Ehrlich acite cell (A) and arcoma 18 cell (B) were treated with MTX for 24 hour (concentration ranging from to 14 μg/ml). After removal of MTX, cell were fed with freh media every 48 hour. Solid ymbol and bar refer to the mean and SD (n = 4). Model-predicted profile are hown a olid line. 5

6 Ehrlich Acite Cell Hour Sarcoma 18 Cell Hour Figure 4. Tranit compartment model prediction of MTX effect on the time coure of cell growth. Ehrlich acite cell (A) and arcoma 18 cell (B) were treated with MTX for 24 hour (concentration ranging from to 14 μg/ml). After removal of MTX, cell were fed with freh media every 48 hour. Solid ymbol and bar refer to the mean and SD (n = 4). Model-predicted profile are hown a olid line. 6

7 of MTX (ie, immediately following MTX removal, cell number wa not ignificantly different from the untreated cell, P >.5 for each cell line). Cell number reached nadir value at 168 hour for arcoma 18 cell and at 264 hour for Ehrlich acite cell. The rate of cell growth after recovery from MTX treatment appeared to be imilar to that of the untreated cell. Pharmacodynamic modeling Bet-fit prediction of the phae-nonpecific model, following imultaneou fitting to the data, are hown in Figure 2. The model provided atifactory characterization of cell growth for untreated cell (r 2 =.999, for each cell line). Model prediction are cloe to oberved value of cell number in the recovery phae (ie, after 15-2 hour); however, the model wa unable to capture the oberved increae in cell number that occurred during MTX incubation, everely underpredicting cell number between 24 hour and 12 hour for each cell line. Model prediction of cell number data following MTX treatment were generally poor (Figure 2), with correlation coefficient (r 2 ) between predicted and oberved value of cell number a low a.99 (eg, for 2 μg/ml MTX applied to Ehrlich acite cell). Additionally, parameter etimate were aociated with high variability (eg, EC 5 =.21 [percentage coefficient of variation, %CV, = 89%] for Ehrlich acite cell, EC 5 =.84 [%CV = 35%] for arcoma 18 cell). Prediction of the phae-pecific model are hown in Figure 3. A with the nonpecific model, the phae-pecific model provided poor prediction of the cell count in MTXtreated well between 24 hour and 12 hour. Correlation coefficient for the fitted curve were generally poor, ranging from.16 to.99, and parameter etimate were aociated with high variability (ie, %CV value and 95% confidence interval were too large for etimation by ADAPT II). The phae-pecific model, which had twice the number of fitted parameter of the phae-nonpecific model (ie, 6 v 3 parameter), wa found to have a uperior Akaike criterion value (ie, 48 v 489 for fitting to arcoma 18 data, and 556 v 574 for fitting to Ehrlich acite data), which ugget that thi model may be uperior to the phae-nonpecific model for fitting to thee data. Prediction of the tranit compartment model are preented in Figure 4. A hown, the tranit compartment model provided atifactory characterization of the entire time coure of cell count data, for each cell line. Correlation coefficient ranged from.86 to.999. We alo evaluated model with 2, 3, and 5 tranit compartment (not hown), and we found that the preent model, with 4 tranit compartment, provided uperior fitting to the data. Etimated parameter value for fitting to the Ehrlich acite cell line were = 34.1 hour (%CV = 3.4), max =.29 h 1 (%CV = 5.8), EC 5 =.1 μg/ml (%CV = 48.7), and k ng =.2 h 1 (%CV = 4.9). Doubling time for Ehrlich acite cell wa etimated from k ng to be 34.6 hour. Etimated parameter value following fitting to the arcoma 18 data were = 3. hour (%CV = 2.5), max =.34 h 1 (%CV = 2.1), EC 5 =.32 μg/ml (%CV = 14.2), and k ng =.35 h 1 (%CV = 1.9). The doubling time for arcoma 18 wa etimated to be 19.8 hour. DISCUSSION The pharmacodynamic of chemotherapeutic have been extenively invetigated in vitro and in vivo. In mot experimental etting, chemotherapeutic effect are ignificantly delayed relative to chemotherapeutic expoure. The time coure of drug effect i of great interet in the field of cancer chemotherapy; however, becaue of the lack of imple mathematical model capable of characterizing the time coure of effect, mot analye have reported relationhip of drug expoure to drug effect at a fixed time point (eg, often at the time of peak effect for in vivo tudie, and often 1, 12, 13, 23, 24 at an arbitrary time point for in vitro tudie). When drug effect i examined at a fixed time point, expoure-effect relationhip may be eaily characterized through the ue of imple, tatic relationhip (eg, the Hill Emax C function: Effect, where E max, EC 5, and EC5 C are contant, and where C may refer to the chemotherapeutic doe, teady-tate concentration, or, mot commonly, area under the concentration v time curve). Static expoure-effect relationhip have been uccefully applied for the optimization of chemotherapy 9, 25, 26 in everal cae; however, characterization of the entire time coure of chemotherapeutic effect may provide additional information to allow further optimization. For example, modeling of the time coure of drug effect may facilitate the cheduling of ubequent coure of chemotherapy and may ait in the election of optimal drug combination. In the early 197, Juko propoed 2 model to decribe the kinetic of chemotherapeutic effect (a hown in Figure 1). 18, 19 For each of thee model, the kinetic of cell killing i defined to be directly related to drug concentration in plama. A uch, thee model are not well uited to characterize chemotherapeutic effect in cae where effect i ubtantially delayed relative to the time coure of drug expoure. Perhap becaue chemotherapeutic effect often appear day or week following drug expoure, thee model have not found wide ue in the field of cancer chemotherapy. Time delay between the time coure of drug expoure and the time coure of drug effect have been typically decribed through the ue of effect ite model or indirect repone model. The effect ite model attribute the delay in effect to the delay aociated with drug ditribution to the ite of effect. 27 Indirect repone model predict a delayed time coure of apparent drug repone a a conequence of indirect mechanim of drug action (eg, where the drug may act via timulation or inhibition of the procee involved in the production or lo of the meaured repone). 28 Recently, Sun and Juko propoed a tranit compartment model to characterize delayed drug effect, where the time delay i captured through the ue of 7

8 Table 1. Akaike Information Criterion Value for the Model Evaluated Model Ehrlich Acite Sarcoma 18 Phae nonpecific Phae pecific Tranit compartment a erie of tranit compartment. 2 The model, which wa originally developed to decribe the kinetic of ignal tranduction, wa later hown to have general utility in characterizing effect that occur via a cacade. 17 We were intereted in evaluating thi model for utility in characterizing chemotherapeutic effect, which often occur via a complicated cacade of event. In the preent work, the time coure of MTX effect on cancer cell growth wa aeed in vitro, following 24 hour of MTX expoure to arcoma 18 cell and Ehrlich acite cell, grown in culture. Conitent with the reult of tudie invetigating MTX effect in vivo, 29 we oberved a ignificant delay between the time coure of MTX expoure and the time coure of MTX effect in thi model ytem. For example, at the concluion of MTX expoure (ie, 24 hour after the initiation of MTX treatment), no difference wa found when comparing cell number in MTX-treated well and untreated well (Figure 4, P >.5), and the apparent peak effect (ie, the nadir cell count) occurred at 168 hour and at 264 hour for arcoma 18 cell and Ehrlich acite cell, repectively. Data were fitted to 3 pharmacodynamic model, including a tranit compartment model and 2 etablihed model of chemotherapeutic effect, the cell cycle phae-pecific model and the phae-nonpecific model. The 3 model are imilar in many repect. For example, each model aume that cell growth follow firt-order kinetic. Thi aumption appear appropriate for our data, a cell number increaed exponentially in the abence of MTX treatment (and alo following recovery from MTX treatment). However, each model may be modified to incorporate more complex growth function, a may be needed to decribe cell growth in certain experimental etting. Additionally, each model relate MTX effect (ie, cell killing) to MTX concentration in media. It i quite likely that there i a complex relationhip between MTX concentration in media and MTX concentration at the biophae (eg, the intracellular ite of MTX effect), and it i plauible that the kinetic that define thi relationhip may contribute to the oberved diociation between the time coure of MTX treatment and the time coure of MTX effect. We have made no attempt to characterize the kinetic of MTX uptake or intracellular proceing, and the tranit compartmental model doe not attempt to infer MTX concentration at the biophae (ie, thi i not a variant of an effect ite model). A uch, the model may be decribed a traditional pharmacodynamic model becaue they relate drug effect to drug concentration in an acceible fluid (eg, media, plama). Nonethele, the cell kill rate function of each model may be eaily modified to be a function of MTX concentration at the biophae (if thee concentration are known). The mot important difference between the tranit compartment model and the tandard model of chemotherapeutic effect i that the tranit compartment model incorporate a erie of firt-order tranfer tep to allow characterization of delay between drug expoure and cell killing. The phae-nonpecific model and the phae-pecific model aume a direct relationhip between MTX concentration and cell killing; conequently, thee model predicted a rapid decreae in cell number during the coure of MTX expoure (Figure 2 and 3). However, a noted above, and a hown in Figure 2 through 4, no decreae in cell number wa oberved during the 24 hour of MTX treatment. A uch, the tandard chemotherapeutic model dramatically under predict cell number at early point in the tudy. The cell cycle phae-pecific model appeared to characterize the data better than the phaenonpecific model both viually and baed on model-fitting criteria (Table 1); however, neither model provided prediction conitent with the obervation of continued cell growth during the 24-hour treatment with MTX. On the other hand, we found that the tranit compartment model could adequately decribe the entire cell count veru time profile, for each cell line, for each treatment (ie, without MTX expoure, or for 24-hour MTX expoure at concentration ranging from.19 to 14 μg/ml). Conitent with the oberved data, thi model predicted increae in cell number during the MTX treatment, with nadir cell count occurring 1 to 2 hour after MTX removal. Perhap becaue of the implicity of the tranit compartment model, parameter were etimated with good preciion (Table 2 and 3). The etimated %CV of EC 5 for Ehrlich acite cell wa 49%; however, etimated %CV value were lower than 15% for all other fitted parameter. The high %CV aociated with the Ehrlich acite EC 5 i likely due, in part, to unavailability of data near or below the etimated EC 5 (ie, the etimated EC 5 wa.1 μg/ml, which wa lower than the lowet MTX concentration ued in thi tudy,.19 μg/ml). The tranit time wa found to be imilar for the 2 cell line and wa etimated to be 3 hour and 34 hour for arcoma 18 cell and Ehrlich acite cell, repectively. The value of the parameter max and EC 5 were dependent on the tumor cell line. The EC 5 for Ehrlich acite cell (.1 g/ml) wa 3 time lower than the EC 5 of arcoma 18 (.3), uggeting that the Ehrlich acite cell line wa more enitive to the cell-killing effect of MTX. 8

9 Table 2. Parameter Etimate Obtained Following Analyi of Ehrlich Acite Data* Parameter Etimated Value SD %CV Phae nonpecific k ng (h 1 ) max (h 1 ) EC 5 ( g/ml) Phae pecific k g (h 1 ).6 NE k d (h 1 ).1 NE k r (h 1 ).36 NE k r (h 1 ).25 x 1 5 NE max (h 1 ) 1.9 NE Tranit compartment k ng (h 1 ) (h) max (h 1 ) EC 5 ( g/ml) *CV indicate coefficient of variation; NE, not etimated Table 3. Parameter Etimate Obtained Following Analyi of Sarcoma 18 Data* Parameter Etimated Value SD %CV Phae nonpecific k ng (h 1 ) max (h 1 ) EC 5 ( g/ml) Phae pecific k g (h 1 ).6 NE k d (h 1 ).9 NE k r (h 1 ).9 NE k r (h 1 ).87 x 1 7 NE max (h 1 ) 2.9 NE EC 5 ( g/ml) 1.5 NE Tranit compartment k ng (h 1 ) (h) max (h 1 ) EC 5 ( g/ml) *CV indicate coefficient of variation; NE, not etimated Of note, thi model utilize a erie of tranit compartment to decribe delay between the time coure of drug expoure and the time coure of drug effect. The model ha a mechanitic foundation, where tranit compartment are related to a cacade of kinetic event that precipitate drug effect. However, the model tructure alo erve a an exceptionally robut, empiric framework for characterization of delayed drug effect. For example, it i likely that a cacade of event precipitate MTX-induced cellular toxicity (eg, MTX uptake into cell, MTX diffuion to the ite of action, MTX binding to and competitive inhibition of dihydrofolate reductae, depletion of reduced folate, interruption of cellular ynthetic procee). The tranit compartment model tructure i amenable to the characterization of the time coure of each event, where different value might be ued in conjunction with a tranit compartment aociated with each event. However, in lieu of data ufficient for characterizing each event in the cacade, the tranit compartment model may be ued empirically, where the number of compartment i determined by the fitting of the data (ie, imilar to the approach ued for fitting data to a 1-, 2-, or 3-compartment pharmacokinetic model). In the preent application, the model ha been ued empirically, and only pure 9

10 peculation would allow dicuion of the biologic meaning of each compartment in the preent model. Nonethele, the preent tudy demontrate the robutne of the model, a we found that a imple tranit compartment model, coniting of only 4 parameter, provided very good characterization of the relatively complex time coure of cell growth following MTX expoure in vitro. Thi imple model may be eaily modified to characterize in vivo data by defining the cell kill function (ie, max M ) a a EC5 M function of plama MTX concentration (eg, M = MTX plama concentration), where MTX concentration in plama may be defined by an appropriate pharmacokinetic function. In thi work, we have invetigated the uefulne of the tranit compartment model to characterize MTX cytotoxic effect in vitro. We uccefully characterized the complex time coure of cell growth in the preence of MTX with a imple pharmacodynamic model. The tranit compartment model may find utility a a general model to characterize chemotherapeutic effect that are delayed relative to chemotherapeutic expoure. Modeling the time coure of chemotherapeutic effect i deirable becaue it may facilitate the development of individualization and optimization trategie for chemotherapy. REFERENCES 1. Lokich J, Anderon N. Doe intenity for bolu veru infuion chemotherapy adminitration: review of the literature for 27 anti-neoplatic agent. Ann Oncol. 1997;8: Ainer J, Van Echo DA, Whitacre M, Wiernik PH. A phae I trial of continuou infuion VP (etopoide). Cancer Chemother Pharmacol. 1982;7: Frei ED, Bicker JN, Hewlett JS, et al. Doe chedule and antitumor tudie of arabinoyl cytoine (NSC 63878). Cancer Re. 1969;29: Wiernik PH, Schwartz EL, Strauman JJ, et al. Phae I clinical and pharmacokinetic tudy of taxol. Cancer Re. 1987;47: O'Dwyer PJ, Hude GR, Walczak J, et al. Phae I and pharmacokinetic tudy of the novel platinum analogue CI-973 on a 5-daily doe chedule. Cancer Re. 1992;52: Minami H, Saaki Y, Saijo N, et al. Indirectrepone model for the time coure of leukopenia with anticancer drug. Clin Pharmacol Ther. 1998;64: Minami H, Saaki Y, Watanabe T, Ogawa M. Pharmacodynamic modeling of the entire time coure of leukopenia after a 3-hour infuion of paclitaxel. Jpn J Cancer Re. 21;92: Friberg LE, Freij A, Sandtrom M, arlon MO. Semiphyiological model for the time coure of leukocyte after varying chedule of 5-fluorouracil in rat. J Pharmacol Exp Ther. 2;295: Jodrell DI, Egorin MJ, Canetta RM, et al. Relationhip between carboplatin expoure and tumor repone and toxicity in patient with ovarian cancer. J Clin Oncol. 1992;1: Stewart CF, Baker SD, Heideman RL, et al. Clinical pharmacodynamic of continuou infuion topotecan in children: ytemic expoure predict hematologic toxicity. J Clin Oncol. 1994;12: Cellarier E, Terret C, Labarre P, et al. Pharmacokinetic tudy of cytemutine, adminitered on a weekly chedule in cancer patient. Ann Oncol. 22;13: Van eteren C, Mathot RA, Raymond E, et al. Population pharmacokinetic and pharmacokineticpharmacodynamic relationhip of the novel anticancer agent E77 in four phae I tudie. Br J Clin Pharmacol. 22;53:553P. 13. Zhou H, Choi L, Lau H, et al. Population pharmacokinetic/toxicodynamic (P/TD) relationhip of SAM486A in phae I tudie in patient with advanced cancer. J Clin Pharmacol. 2;4: Gimmel S, Maurer HR. Growth kinetic of L121 leukemic cell expoed to different concentration coure of methotrexate in vitro. Cancer Chemother Pharmacol. 1994;34: Braakhui BJ, Ruiz van Haperen VW, Boven E, et al. Schedule-dependent antitumor effect of gemcitabine in in vivo model ytem. Semin Oncol. 1995;22: ihi S, Goto N, Nakamura T, Ueda T. Evaluation of cell-killing effect of 1-beta-D-arabinofuranoylcytoine and daunorubicin by a new computer-controlled in vitro pharmacokinetic imulation ytem. Cancer Re. 1999;59: Mager DE, Juko WJ. Pharmacodynamic modeling of time-dependent tranduction ytem. Clin Pharmacol Ther. 21;7: Juko WJ. Pharmacodynamic of chemotherapeutic effect: doe-time-repone relationhip for phae-nonpecific agent. J Pharm Sci. 1971;6: Juko WJ. A pharmacodynamic model for cellcycle-pecific chemotherapeutic agent. J Pharmacokin Biopharm. 1973;1: Sun YN, Juko WJ. Tranit compartment veru gamma ditribution function to model ignal tranduction 1

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