Modeling Drug- and System-Related Changes in Body Temperature: Application to Clomethiazole-Induced Hypothermia, Long-Lasting Tolerance Development, and Circadian Rhythm in Rats

Clomethiazole (CMZ) has sedative, hypnotic, anticonvulsive, and neuroprotective properties and has been used clinically in elderly patients as a useful sedative/hypnotic for 40 years (Green, 1998). In a recent investigation, we showed that CMZ is able to induce hypothermia in rats and that even a single injection of CMZ rapidly induces complete tolerance lasting for more than 10 days, with a 50% return of effect after a month (Visser et al., 2005). This observation of tolerance partly explained why conflicting reports exist regarding the ability of CMZ to induce hypothermia and the relationship between hypothermia and neuroprotective properties in vivo (Cross et al., 1991; Green, 1998; Chaulk et al., 2003). For CMZ, it was observed that the tolerance is induced directly by the drug, rather than via a decrease in body temperature, because hypothermic tolerance to CMZ did not affect hypothermic responses to other drugs and could not be attenuated (Visser et al., 2005). Moreover, the tolerance appeared to last for more than 15 days, which suggests that CMZ down-regulated a necessary but so far unknown mediator, which by itself has a slow turnover. In the present investigation the objective was to quantify the CMZ-induced hypothermia and the rapid onset of long-lasting tolerance by developing a pharmacokinetic-pharmacodynamic (PK/PD) model.

The regulation of body temperature is a complex homeostatic control mechanism, the purpose of which is to maintain body temperature at a constant level (Simon et al., 1986). It is affected by, among other things, the neurotransmitter systems of serotonin, GABA, glutamate, and dopamine and modulated by inflammatory processes (Zarrindast and Oveissi, 1988; Corbett et al., 1990; Briese, 1998; Salmi and Ahlenius, 1998; Blatteis, 2000; Perachon et al., 2000). The effect of a drug on body temperature is the result of multiple time-dependent processes with their own specific rate constants, such as compound distribution and elimination, temperature baseline behavior, the effects on body temperature regulation, and the development of tolerance. The pharmacokinetics can practically be determined and quantified separately. Information on drug exposure can then be used as the driving force of the pharmacodynamics. For the modeling of body temperature modulation, a turnover model or a model for homeostatic regulation of body temperature has been applied, accounting for the time delay between maximum exposure and effect (Ackerman et al., 1964; Gabrielsson and Weiner, 1997; Zuideveld et al., 2001). For the CMZ-induced effects on body temperature and tolerance development, a systematic approach based on previously described models was adopted to build a pharmacodynamic model composed of various subsystems with their specific rate constants.

It is also commonly known that body temperature is subject to circadian rhythm at around a constant level with a 1°C lower temperature during the day compared with the night in rats (Lobo et al., 1999; Benstaali et al., 2001). So far, models based on trigonometric functions such as the cosine function or Fourier series have been applied for the description of circadian rhythm (Hempel et al., 1998; Chakraborty et al., 1999). However, here we apply a novel feedback model for circadian rhythm, which is described in more detail elsewhere (Sällström et al., 2005). This is a generic model, which is able to describe the (asymmetric) biorhythm of biomarkers.

Tolerance development can be considered as a homeostatic process of the body to reduce the effect of altered conditions, such as receptor down-regulation and adaptation of signal-transduction processes, during drug administration. The best studied is the glucose-insulin system (Ackerman et al., 1964), but nicotine and nitroglycerin tolerance have also been well studied (Porchet et al., 1988; Bauer et al., 1997; Fattinger et al., 1997). A number of tolerance models have been proposed and applied, depending on the proposed mechanism of action, such as the formation of antagonistic metabolites, tolerance compartment, counter-regulation, feedback, and pool and precursor models (Holford and Sheiner, 1982; Ekblad and Licko, 1984; Mandema and Wada, 1995; Movin-Osswald and Hammarlund-Udenaes, 1995; Wakelkamp et al., 1996; Gabrielsson and Weiner, 1997; Gardmark et al., 1999).

In the present investigation, the CMZ-induced hypothermia and the rapid onset of long-lasting tolerance was quantified by development of a PK/PD model consisting of different submodels for circadian rhythm in baseline, handling events, drug effects, and tolerance development.

Materials and Methods

Temperature and Exposure Measurements. The in vivo experiments have been described previously (Visser et al., 2005). In short, male Sprague-Dawley rats [n = 117, weight (mean ± S.D.): 301 ± 23 g; B&K Universal AB, Sollentuna, Sweden)] were used in pharmacodynamic experiments 7 days after implantation of a telemetric transmitter into the peritoneal cavity (TA10TA-F20; Data Sciences, St. Paul, MN). Satellite groups of male animals were used in separate pharmacokinetic experiments 3 days after implantation of a catheter in the carotid artery and the telemetric transmitter in the peritoneal cavity. The animals were kept in rooms where the artificial light followed a 12-h cycle (lights on at 6:00 AM). Throughout the experiments the rats had access to food and tap water ad libitum. Ethical permission was obtained from the Stockholm Animal Ethics Committee, Sweden. Body temperature was recorded 4 days before dosing until 4 to 6 days after the end of dosing. The telemetry signals were measured every 2 min for a 10-s period and signaled to a receiver. Using the software package Dataquest ART 2.2 (Data Sciences), the temperature data were processed, analyzed, and visualized. The animals were disturbed as little as possible throughout the experiment by allowing entry to the experimental room only during dosing and care. For the assessment of CMZ exposure, blood samples were taken at predefined intervals, with up to 2 ml of blood being withdrawn. The plasma samples were analyzed using high-performance liquid chromatography-UV. Precision and accuracy were previously reported (Visser et al., 2005).

Drugs, Dosages, and Dosing. Clomethiazole (clomethiazole edisilate, mol. wt. 523.46 g mol^–1, the denoted test compound) was obtained from Compound Management (AstraZeneca R&D Södertälje, Södertälje, Sweden). The concentration of CMZ in all solutions was calculated on the basis of the clomethiazole base (mol. wt. 161.7 g mol^–1). All injection solutions were made in saline (9 mg ml^–1, Braun Medical AB, Bromma, Sweden) on the day of the experiment. The rats were randomly assigned to dosing groups and received a weight-adjusted s.c. injection dose or saline as vehicle treatment. The dosing design for the characterization of the hypothermia and tolerance development is given in Table 1. A validation data set was obtained in an additional experiment, in which CMZ was administered three times at an interval of 15 days. Alzet osmotic pumps (model 2001D; Scanbur BK AB, Sollentuna, Sweden) with an average pump rate of 7.4 μl h^–1 were used for s.c. drug infusion at a continuous rate. The osmotic pumps were filled with a solution of CMZ in saline. The pumps were preincubated in saline for a minimum of 2.5 h at 37°C before being inserted s.c. into the neck of the rat under light isoflurane anesthesia.

Data Analysis. A PK/PD model was developed to describe body temperature in vehicle- and CMZ-treated rats (Fig. 1). It consists of a pharmacokinetic model describing the exposure profile after drug administration, a circadian rhythm (biorhythm) model describing the asymmetric day/night temperature profile with a correction for stress-induced temperature elevation seen when animals were handled for drug administration or surgery, and a turnover model comprising CMZ-induced hypothermia and tolerance development.

Exposure to CMZ. The time course of the CMZ plasma concentration after i.v. infusion has been described previously by a two-compartment disposition model with capacity-limited elimination (Gabrielsson and Weiner, 1997). These data were included to allow better estimation of the maximum metabolic rate and the Michaelis-Menten constant after s.c. dosing. The bolus injection was administered to a s.c. compartment at time 0, and the decrease in the amount of CMZ at the s.c. compartment was described by: where K_a is the absorption rate constant. The amount of CMZ in the s.c. compartment during the 24-h s.c. continuous infusion via an osmotic pump was described by: where D_sc equals the total amount of CMZ infused under the duration of implantation (t_inf) of the osmotic pump. After removal of a pump, the amount in the s.c. compartment equals zero. The CMZ concentrations in the central (p) and peripheral (t) compartments were described by: where F is the s.c. bioavailability, CL_D is the intercompartmental distribution term, and V_c and V_t are the volumes of the central and peripheral compartments, respectively. The capacity-limited clearance (CL) is defined as: where the parameters V_max and K_m define the maximum metabolic rate and the Michaelis-Menten constant, respectively.

Baseline Behavior. A turnover model was developed for the description of asymmetric circadian rhythm in baseline temperature in rats (Sällström et al., 2005). The biorhythm model consists of two interconnected compartments B₁ and B₂. The input and output rates of the compartments are governed by: where α and β are first-order rate constants and the timekeeper g(t) describes the external light conditions following a squared wave function: where d represents the intensity of a night stimulus because the animals are more active at night. The model can account for a low but slowly increasing temperature during the day and a high and relatively stable temperature during the night. The baseline body temperature was defined as: where T_ref is the reference temperature level and amp adjusts the amplitude of the circadian rhythm in B₁ around the reference temperature. Hence, T_baseline represents the model for circadian rhythm, describing the day/night temperature profile of normal rats in an artificial 12/12-h light/dark cycle environment.

Vehicle Treatment. It was observed that handling of the animals caused a temporary temperature increase that was independent of dose level. Therefore, for the individual estimation of the temperature profile upon vehicle treatment (s.c. injection or continuous pump), the model was corrected by an empirical function HD mimicking this handling effect: where P determines the magnitude of the temperature elevation, whereas k_HD determines the rate of the appearance and disappearance of the temporary temperature elevation and t_HD is set to the time of handling. Hence, the temperature profile during vehicle treatment is defined as:

Drug-Induced Hypothermia. The model of temperature regulation applied in this investigation has been described previously and uses concepts of turnover principles and feedback regulation (Ackerman et al., 1964; Gabrielsson and Weiner, 1997; Zuideveld et al., 2001, 2004). It is based on a turnover model for body temperature (T) combined with a thermostat-like regulation of body temperature (X):

The parameters k_in and k_out are the turnover rate and the fractional turnover rate governing the production and loss of heat, respectively. The parameter T_drug is dependent on a function of the drug plasma concentration and is defined by: where T_ref is the reference temperature level in the absence of the drug and baseline variation (see eq. 6). The relationship between the plasma concentration and the stimulus (S₁) on the temperature system is defined by: where C_p is the plasma concentration of CMZ, SC_50,1 is the concentration producing half the maximum stimulus and S_max,1 is the maximum stimulus. Because CMZ induced a temperature decrease down to 31°C at the highest dose (600 μmol kg^–1), it was assumed that CMZ can exert the maximum possible reversible effect on temperature, so S_max,1 was fixed at 1.

The model for temperature regulation with four system parameters to be estimated can lead to parameter unidentifiability (for details, see Zuideveld et al., 2001). In a rescaling strategy, one parameter can be eliminated by making the system dimensionless. The dimensionless system (x,y) is obtained by: where T₀ is equal to T_ref and X₀ is the reference signal of X:

The dimensionless system is given by: where the new parameters A and B are defined by: and

The temperature model in eq. 14 can describe drug-induced hypothermia. It must be noted that eq. 14 is only valid in the absence of tolerance development. In the next section, eq. 14 will be elaborated on further with a model for tolerance development.

Tolerance Model. It was proposed that CMZ induces long-lasting tolerance by the irreversible removal of an unknown mediator Q₀ (e.g., irreversible degradation of a receptor or second messenger), which has a slow turnover (Visser et al., 2005). Preliminary analysis of the data showed also that the tolerance development did not occur instantaneously but needed time to develop. To estimate this delay, it was assumed that Q₀ was cascaded through a number of transit compartments before it reduced the effect of CMZ on the temperature (Sun and Jusko, 1998). The proposed full model for tolerance is given by:

The parameters k_inQ and k_outQ are the turnover rate and the fractional turnover rate governing the production and loss of Q₀, respectively. τ reflects the transit time of Q₀ to Q₁ and from Q₁ to Q₂, etc. S₂ is a sigmoidal function of the plasma concentration: in which S_max,2 is the maximum rate of loss from compartment Q₀ and SC_50,2 is the concentration giving half the maximum stimulus. Q₀ is normalized to unity (=1) which means that k_inQ = k_outQ. The turnover time of Q₀ and the half-life of the irreversible emptying of Q₀ are defined by, respectively: and

The complete model for temperature regulation and acute tolerance development after administration of CMZ is defined by: in which S_tol is given by:

In this way, tolerance development occurs with a delay and the total stimulus (S_tol) is equal to 0 when CMZ exposure is 0, and therefore tolerance will not affect the body temperature itself but only by means of CMZ.

Modeling Procedure. A sequential modeling approach was adapted. All fitting procedures were performed using NONMEM V. First, the individual concentration-time profiles were fitted simultaneously to eq. 2. Population pharmacokinetic parameter estimates were used to simulate concentrations to the temperature measurements. For the determination of the circadian rhythm in temperature, 6 days of baseline recordings (each 2 min) in vehicle groups (1A and 6A, n = 6 per group) were averaged to a 24-h profile and fitted to eq. 6;3 h of data after the time of handling were removed to avoid interference.

In the subsequent analysis, all temperature data were reduced to one observation per 20 min to reduce computational time. Individual temperature profiles in all vehicle groups were analyzed by means of eq. 8, allowing a different magnitude of temperature elevation after s.c. injection and implantation of the pump. The population parameter estimates for the circadian rhythm and handling were used to simulate the vehicle baseline temperature (T_vehicle). This profile was used to normalize the temperature during drug treatment to vehicle treatment. The temperature data were rescaled following:

The rescaling of the temperature data to make the data dimensionless was necessary to enable the use of the reduced parameter temperature model (see eq. 21). For graphical purposes, the final temperature predictions (pred) were recalculated to T_body,pred via:

The interindividual variability of all estimated parameters was modeled by an exponential equation: where θ is the population estimate for parameter P, P_i is the individual estimate, and θ_i is the random deviation of P_i from P. The values of η_i are assumed to be independently normally distributed with mean zero and variance ω². The covariance structure of the variability parameters was assumed to be diagonal. The residual error in the plasma drug concentration and pharmacodynamics was characterized by a constant coefficient of variation error model: where y_pij represents the jth observation for the ith individual predicted by the model. y_mij represents the predicted concentration or temperature, and ϵ_ij accounts for the residual deviation of the model-predicted value from the observation. The values for ϵ were assumed to be independently normally distributed with mean zero and variance σ². The first-order estimation method (FOCE interaction) was used to estimate the population θ, ω², and σ² for the pharmacokinetic analysis. A centering first-order conditional estimation method was used for the pharmacodynamic analysis. Individual parameter estimates were obtained in a Bayesian post hoc step.

Results

Pharmacokinetics. Concentration-time profiles of CMZ displayed typical nonlinear kinetics with increasing doses of the test compound. A two-compartment model with capacity-limited elimination described the exposure profiles best. The population and individual fits are shown in Fig. 2. Population parameter estimates are summarized in Table 2. Intravenous infusion data (Gabrielsson and Weiner, 1997) were used to estimate the Michaelis-Menten constants. The bioavailability was around 100%. The absorption rate from the s.c. site (K_a) decreased with increases in the CMZ dose (Table 2). The CMZ concentration in the injection solutions for 15, 150, 300, and 600 μmol kg^–1 s.c. bolus doses and 20 and 40 μmol kg^–1 h^–1 s.c. infusion doses were 10, 100, 200, 400, 680, and 1380 μmol ml^–1, respectively. The pH decreased in this concentration range from 7 to 1 and was not adjusted for reasons of low solubility at higher pH.

Baseline Temperature. Six days of temperature observations in groups 1A and 6A were averaged for all individuals (n = 6 × 6 days = 36 days per treatment group). Three hours of observations were removed after each handling event to avoid influence of handling. Baseline profiles were fitted using eq. 6. The asymmetric temperature baseline is shown in Fig. 3A. During the day a gradual increase in temperature was observed, followed by an abrupt increase in temperature when the lights were turned off. During the night, the body temperature was reasonably stable around 38°C and decreased in 1 to 2 h to 37°C when the lights were turned on. Population parameter estimates can be found in Table 3.

Vehicle Treatment. Two days of temperature recordings in the vehicle treatment groups (1A, 1B, 6A, and 6B) were analyzed simultaneously using eq. 8, allowing a different magnitude of temperature elevation after s.c. injection (n = 15) and implantation of the pump (n = 9). Injection or implantation of the pump occurred between 9:00 and 12:00 AM on day 1. The population parameter estimates are given in Table 3. Two typical profiles are shown for s.c. vehicle injection and implantation of the pump in Fig. 3B. The temporary elevation of temperature after administration varies between animals and is three times higher after s.c. injection than after implantation of the pump.

Drug-Induced Hypothermia and Tolerance. The population prediction for the vehicle response was used to rescale the temperature data after drug treatment (see eq. 23). The exposure-related decrease in body temperature after s.c. bolus injections of 15, 150, 300, and 600 μmol kg^–1 CMZ or following a 24-h s.c. continuous infusion of 0, 20, or 40 μmol kg^–1 h^–1 CMZ could simultaneously be described by the temperature-tolerance model (eq. 21). The observed and fitted time-effect profiles are shown in Fig. 4 and all population pharmacodynamic parameter estimates are given in Table 4.

The differences in profiles after a s.c. bolus injection or s.c. continuous infusion were crucial for determination of the number of transit compartments. For the s.c. bolus injections, a clockwise hysteresis was observed and the return phase shifted to the right with increasing doses, indicating the tolerance development. In contrast, for the s.c. continuous infusion, a counterclockwise hysteresis was observed (Fig. 5). This difference arose because of the pharmacokinetics being the rate-limiting step for the s.c. continuous infusions, whereas for the s.c. bolus injections, the time constants in temperature regulation were rate-limiting. A delay for tolerance development was observed and on the basis of the combined analysis of s.c. bolus and s.c. continuous infusion, the optimal number of transit compartments could be determined at 4. The delay in tolerance development, defined as four transit times, was 7.6 ± 2 h. After a single s.c. bolus injection of 600 μmol kg^–1, the theoretical hypothermic effect is reduced by 28% because of tolerance development, whereas after a s.c. continuous infusion of 40 μmol kg^–1 h^–1, the maximum possible temperature effect was reduced by 66%. This is graphically illustrated in Fig. 6.

The single dose data did not yield information on the slow turnover of Q₀ (k_outQ) and were therefore fitted with k_outQ fixed at 0.022 day^–1. This corresponded to a turnover time of 32 days. This value was graphically derived from the average minimum effect (mean ± S.D.) for all individuals measured at 100 min after injection on days 1, 3, 6, 10, 16, 24, and 32. This relationship is shown in gray in Fig. 7. Thereafter, parameter k_outQ was estimated in the analysis of the repeated dosing data with all other pharmacodynamic parameters fixed at the single dose estimates. The turnover rate constant k_outQ was estimated at 0.015 ± 0.001 (10%) day^–1, yielding a turnover time of 46 ± 3 days. The results are shown in Fig. 7. The predicted time courses of Q₀ to Q₄ are shown in Fig. 8.

The predictive performance of the model was tested by simulation of the profile of the validation data set (Fig. 9). The model successfully predicted the effect on days 1 and 15 but underestimated the effect on day 32.

Discussion

In the present investigation, a pharmacodynamic model using various components was put forward for the quantification of the CMZ-induced hypothermia, vehicle treatment, baseline behavior, and tolerance development. Exposure to CMZ was described by means of a pharmacokinetic model with nonlinear elimination. The absorption rate constant was dose-dependent, which is most likely explained by the decrease in pH of injection fluids with higher doses, resulting in slower absorption. Adjustment of the pH to physiological values was avoided for reasons of low solubility at physiological pH. The variability observed in the bioavailability may be due to the different occasions of the pharmacokinetic experiments. Nevertheless, the primary goal of the pharmacokinetic model was to predict the population exposure profiles as adequately as possible to function as driver of the pharmacodynamics.

To characterize the complex dynamic system with circadian rhythm in baseline, hypothermia, and tolerance development, a systematic approach was adopted to building a pharmacodynamic model. The baseline and vehicle temperature profiles were first analyzed and fixed in the analysis of CMZ-induced temperature decreases. The asymmetric behavior, with a relatively constant temperature during the night followed by a sudden fall of 1°C at the start of the day and a gradually increasing temperature during the day, was successfully captured (Achermann and Kunz, 1999; Lobo et al., 1999; Benstaali et al., 2001; Sällström et al., 2005). The advantage of quantifying baseline behavior lies in improving quantification of the pure drug effect for low doses or low efficacy agonists that cannot produce a maximum decrease in temperature. The maximal possible physiological reversible decrease in body temperature is ∼5°C. A larger temperature decrease might result in a very long recovery time or even death. Thus, a circadian rhythm of 1°C represents 20% of the maximum physiological temperature decrease.

The baseline model, combined with an empirical function of temporary elevation of temperature due to handling events, served as model for vehicle treatment. Transient elevation of temperature during insertion of the osmotic pump was lower than after injections, which is probably due to opposing effects of the short period of isoflurane anesthesia necessary for pump implantation and removal (Prudian et al., 1997). However, the significant influence of handling underlines the need to control experimental settings. It may therefore be likely that the size of the drug effect depends on the time of drug administration and experimental conditions such as handling (Lemmer, 1999).

For the temperature regulation, both a turnover model and a feedback model were tested. In the model optimization step, it appeared that a basic turnover model fitted the data reasonably well (Dayneka et al., 1993), although the feedback model performed better due to increased flexibility (Zuideveld et al., 2001). The feedback model might also describe the physiological regulation of the temperature in a more mechanistic way by using a feedback loop. This model, however, might also be preferred in studying a low efficacy agonist as oscillatory behavior of the model (and observations) are more pronounced at low stimulation (Zuideveld et al., 2004). On the other hand, for application in routine analysis, the complexity and calculation time for the feedback model might be a disadvantage (Sällström et al., 2005).

Parameter estimability of the feedback model was improved by rescaling the data to the maximum observed temperature decrease. Combined with a correction for vehicle treatment and baseline (see eq. 23), this enabled the characterization of the pure drug effect. The drug-induced hypothermia and counteracting tolerance could not be independently measured in a single response profile, but only when multiple doses and infusion rates were analyzed simultaneously. In this investigation, the data obtained by s.c. continuous infusion were crucial for the characterization of the tolerance, whereas the s.c. bolus doses were more informative regarding the temperature regulation (as illustrated in Fig. 6).

The tolerance was modeled by means of a separate turnover model that counteracted the CMZ-induced hypothermic effect and to describe the long-lasting nature of the tolerance. During exposure to CMZ, the compartment Q₀ was irreversibly emptied with a half-life of 8 min (see eq. 20). It was estimated via transit compartments that the tolerance development was delayed by 7.6 ± 2 h. Therefore, the tolerance is less apparent (only 22%) after a single s.c. bolus injection (a fair amount of CMZ has already been eliminated) but more pronounced (66%) during s.c. continuous administration. Similar observations are seen with nitroglycerin and nifedipine as examples for which the separation of the beneficial effect and tolerance development to the same effect is highly dependent on the rate of administration (Kleinbloesem et al., 1987; Bauer et al., 1997; Wang et al., 2004). Also a similar tolerance pattern (although less long-lasting) was observed for prolactin release after administration of remoxipride (Movin-Osswald and Hammarlund-Udenaes, 1995).

For tolerance modeling, standard feedback or pool models were not appropriate because of the predicted rebound effects upon withdrawal of the drug. For CMZ, only a slight rebound of 0.3°C could be observed during daytime after the highest doses (300 and 600 μmol kg^–1) after averaging data and comparing with the baseline. The question is whether this is physiologically significant. It might be the result of a slight disturbance of the circadian rhythm similar to that observed after anesthesia (Prudian et al., 1997). Many approaches to modeling delays between exposure and response have been proposed, such as a link model for distributional delay (Sheiner et al., 1979), a model for slow on/off binding to a receptor (Shimada et al., 1996), various turnover models for time-dependent transductions (see Mager and Jusko, 2001 for review), and empirical transit compartments (Sun and Jusko, 1998). Here we have applied transit compartments. The delay in onset of tolerance could indicate that a metabolite of CMZ (Green et al., 2000) is responsible for the observed tolerance instead of CMZ. However, this possibility will not alter the proposed turnover model for tolerance but rather account for a part of the delay as formulated by means of the transit compartments.

The turnover time of Q₀ was estimated to be 46 ± 3 days. This was longer than graphically derived from the data in Fig. 6 as the maximum decrease in temperature does not linearly reflect the return of the effect. This long turnover time suggests that to elucidate the mechanism of tolerance, experiments should be designed to find the mediator responsible with a similar turnover rate. It had been shown previously that GABA_A receptors, 5-hydroxytryptamine_1A, and N-methyl-d-aspartate receptors at least are not involved in tolerance development (Visser et al., 2005). We are not aware of any reports on such an extensive adaptation in a small animal like the rat.

The prediction of the effect after three dose occasions was not completely satisfactory because it underestimated the effect at 32 days, whereas days 1 and 15 were well predicted. Our model assumes that after a second dose of CMZ on day 15, Q₀ is irreversibly emptied again and that the effects of the third dose on day 32 will be almost similar to those of the second dose. However, the remarkable observation was that a third dose gave a larger effect than on day 15 with a larger variability. One reason could be that in this group of rats the actual turnover of Q₀ was faster and so the predicted effects would be larger. Another factor, which might influence the observations, is that the actual plasma levels during the final dose were higher than simulated. Doses were adjusted to body weight, which was considerable over 32 days but clearance may have remained relatively constant. However, this discrepancy remains to be investigated in further experiments.

The model design was solely dependent on information derived from temperature data. An approach in which mechanistic information is derived from various parts using multiple biomarkers (e.g., the information on the molecular mechanism of the tolerance and circadian rhythm) might improve future generations of complex dynamic models in terms of mechanistic significance. Furthermore, a future step in model development for temperature regulation could be the integration of the model for circadian rhythm into the set-point model in such a way that T_ref is subject to a biorhythm. Another focus could be the independent estimation of k_out, with keeping the flexibility of the set-point model. Because of rescaling of the temperature model, it was not possible to independently derive an estimate (see eqs. 9 and 14). However, on the basis of an analysis using an indirect response model, k_out was estimated between 0.006 and 0.02 min^–1, yielding a 30- to 80-min half-life k_out. Although the prediction of other dose regimens in routine research would benefit from simpler models with a high predictive value, the development of simpler models should still recognize specific patterns and the overall rate-limiting step in drug response.

For CMZ in particular, it allowed us to estimate the in vivo potency and to predict and understand the absence of hypothermia upon repeated dosing. The modeling of the CMZ-induced hypothermia and tolerance provided an example of modeling of various complex dynamic systems such as baseline temperature, handling effects, tolerance development, delays, and temperature regulation.