Influence of enterohepatic recycling on the time course of brain-to-blood partitioning of valproic acid in rats.

A widely used metric of substrate exposure in brain is the brain-to-serum partition coefficient (K(p,brain); C(brain)/C(serum)), most appropriately determined at distribution equilibrium between brain tissue and serum. In some cases, C(brain)/C(serum) can peak and then decrease, as opposed to monotonically increasing to a plateau, precluding accurate estimation of partitioning. This "overshoot" has been observed with compounds that undergo enterohepatic recycling (ER), such as valproic acid (VPA). Previous simulation experiments identified a relationship between overshoot in the C(brain)/C(serum) versus time profile and distribution into a peripheral "compartment" (e.g., the ER loop). This study was conducted to evaluate model predictions of that relationship. Initial experiments tested the ability of activated charcoal, antibiotics, or Mrp2 deficiency to impair VPA ER in rats, thereby limiting the apparent volume of distribution associated with ER. Mrp2 deficiency (significantly) and antibiotics (moderately) interrupted VPA ER. Subsequently, brain partitioning was evaluated in the presence versus absence of ER modulation. Although overshoot was not eliminated completely, deconvolution revealed that overshoot was reduced in Mrp2-deficient and antibiotic-treated rats. Consistent with model predictions, overshoot was higher after antibiotic treatment (moderate ER interruption) than in Mrp2 deficiency (substantial ER interruption). Steady-state K(p,brain) was unaffected by experimental manipulation, also consistent with model predictions. These data support the hypothesis that C(brain)/C(serum) may overshoot K(p,brain) based on the extent of peripheral sequestration. Consideration of this information, particularly for compounds that undergo significant extravascular distribution, may be necessary to avoid erroneous estimation of K(p,brain).

Influence of time to achieve substrate distribution equilibrium between brain tissue and blood on quantitation of the blood-brain barrier P-glycoprotein effect.

Active efflux transport processes at the blood-brain barrier (BBB), such as P-glycoprotein (P-gp)-mediated efflux, can limit brain uptake of therapeutics. Accurate determination of the consequent impact on brain uptake is assumed to require sampling post-attainment of brain-to-blood distribution equilibrium. Because this approach is not always feasible, understanding the relationship between apparent degree of efflux (e.g., calculated BBB P-gp effect) and the fraction of time remaining until distribution equilibrium is achieved (FTDE) would be advantageous. This study employed simulation strategies to explore this relationship in the simplest relevant system (absence of protein binding, saturable uptake, or metabolism at the BBB). Concentration-time profiles were simulated with a 4-compartment system (blood, peripheral tissues, BBB endothelium and brain parenchyma). A unidirectional endothelium-to-blood rate constant, PS(e), represented P-gp-mediated efflux. A parameter space was selected to simulate an 18-fold P-gp effect, (K(p,brain) at distribution equilibrium in the absence [K(p,brain)=82] vs. presence [K(p,brain)=4.5] of P-gp-mediated flux), as observed for paclitaxel in P-gp-deficient vs. P-gp-competent mice. Hypothetical compounds with different P-gp effects, peripheral compartment distribution kinetics, or times to achieve distribution equilibrium were simulated by perturbing the values of relevant model parameters. P-gp effects calculated prior to attainment of distribution equilibrium may be substantially erroneous. However, reasonably accurate estimates can be obtained relatively early in the net distributional phase (under 20% error at FTDE>0.36 or 0.11 for bolus or infusion administration, respectively). Potential errors associated with non-equilibrium calculations are dependent on both P-gp-mediated and P-gp-independent components of flux across the BBB.

The influence of distributional kinetics into a peripheral compartment on the pharmacokinetics of substrate partitioning between blood and brain tissue.

Development of CNS-targeted agents often focuses on identifying compounds with "good" CNS exposure (brain-to-blood partitioning >1). Some compounds undergoing enterohepatic recycling (ER) evidence a partition coefficient, K (p,brain) (expressed as C (brain) /C (plasma)), that exceeds and then decreases to (i.e., overshoots) a plateau (distribution equilibrium) value, rather than increasing monotonically to this value. This study tested the hypothesis that overshoot in K (p,brain) is due to substrate residence in a peripheral compartment. Simulations were based on a 3-compartment model with distributional clearances between central and brain (CL (br)) and central and peripheral (CL (d)) compartments and irreversible clearance from the central compartment (CL). Parameters were varied to investigate the relationship between overshoot and peripheral compartment volume (V (p)), and how this relationship was modulated by other model parameters. Overshoot magnitude and duration were characterized as peak C (brain)/C (plasma) relative to the plateau value (%OS) and time to reach plateau (TRP). Except for systems with high CL (d), increasing V (p) increased TRP and %OS. Increasing brain (V (br)) or central (V (c)) distribution volumes eliminated V (p)-related OS. Parallel increases in all clearances shortened TRP, but did not alter %OS. Increasing either CL or CL (d) individually increased %OS related to V (p), while increasing CL (br) decreased %OS. Under realistic peripheral distribution scenarios, C (brain)/C (plasma) may overshoot substantially K (p,brain) at distribution equilibrium. This observation suggests potential for erroneous assessment of brain disposition, particularly for compounds which exhibit a large apparent V (p), and emphasizes the need for complete understanding of distributional kinetics when evaluating brain uptake.

Mechanisms underlying differences in systemic exposure of structurally similar active metabolites: comparison of two preclinical hepatic models.

Selection of in vitro models that accurately characterize metabolite systemic and hepatobiliary exposure remains a challenge in drug development. In the present study, mechanisms underlying differences in systemic exposure of two active metabolites, furamidine and 2,5-bis (5-amidino)-2-pyridyl furan (CPD-0801), were examined using two hepatic models from rats: isolated perfused livers (IPLs) and sandwich-cultured hepatocytes (SCH). Pafuramidine, a prodrug of furamidine, and 2,5-bis [5-(N-methoxyamidino)-2-pyridyl] furan (CPD-0868), a prodrug of CPD-0801, were selected for investigation because CPD-0801 exhibits greater systemic exposure than furamidine, despite remarkable structural similarity between these two active metabolites. In both IPLs and SCH, the extent of conversion of CPD-0868 to CPD-0801 was consistently higher than that of pafuramidine to furamidine over time (at most 2.5-fold); area under the curve (AUC) of CPD-0801 in IPL perfusate and SCH medium was at least 7-fold higher than that of furamidine. Pharmacokinetic modeling revealed that the rate constant for basolateral (liver to blood) net efflux (k(A_net efflux)) of total formed CPD-0801 (bound + unbound) was 6-fold higher than that of furamidine. Hepatic accumulation of both active metabolites was extensive (>95% of total formed); the hepatic unbound fraction (f(u,L)) of CPD-0801 was 5-fold higher than that of furamidine (1.6 versus 0.3%). Incorporation of f(u,L) into the pharmacokinetic model resulted in comparable k(A_net efflux,u) between furamidine and CPD-0801. In conclusion, intrahepatic binding markedly influenced the disposition of these active metabolites. A higher f(u,L) explained, in part, the enhanced perfusate AUC of CPD-0801 compared with furamidine in IPLs. SCH predicted the disposition of prodrug/metabolite in IPLs.

A modified team-based learning physiology course.

OBJECTIVE: To implement and assess an interactive, clinically applicable first-year physiology course using team-based learning. DESIGN; The course was designed on a team-based learning backbone using 6 modules, pre-class preparation, a readiness-assurance process, and in-class application. Integrative cases were used to review concepts prior to examinations. Various assessment methods were used to measure changes, including course evaluations, an attitudinal survey tool, and a knowledge examination. ASSESSMENT: Course evaluations indicated a higher perception of active learning in the revised format compared with that of the previous year's course format. There also were notable differences in opportunities to promote communication skills, work as part of a team, and collaborate with diverse individuals. The assessment of content knowledge indicated that students who completed the revised format course outperformed the previous year's students in both foundational knowledge and application-type questions. CONCLUSION: Using more team-based learning within a physiology course had a favorable impact on student retention of material and attitudes toward the course.

Examination of the ability of the nasal administration route to confer a brain exposure advantage for three chemical inhibitors of P-glycoprotein.

The central nervous system (CNS), efficiently isolated from the systemic circulation by the blood-brain barrier (BBB), represents a challenging therapeutic target. For CNS-targeted agents, augmenting brain exposure by increasing blood drug concentrations often is prohibited by systemic toxicity. Therefore, a means for selectively increasing brain exposure, while minimizing systemic exposure, would be desirable. Limited evidence has indicated that nasally-administered compounds can penetrate into brain, although the selectivity of this approach is unclear. This study demonstrated a distinct, but compound-specific, advantage of the nasal administration route in conferring selective CNS delivery (defined as a brain exposure advantage; BEA). Brain and systemic concentrations of three P-glycoprotein-inhibiting agents were evaluated following single nasal or systemic doses to mice, and the influence of administration route on brain exposure (absolute BEA) and on brain-to-blood partitioning (relative BEA) was calculated. Relative and absolute BEA differed markedly among rifampin, quinidine, and GF120918, with relative BEA ranging between 1.53- and 809-fold and absolute BEA between 0.114- and 9.19-fold. Although substantial increases in brain exposure and partitioning in conjunction with nasal administration were demonstrated, the utility of this approach may be limited by inability to deliver a therapeutically relevant mass of drug to the brain.

Transforming a large-class lecture course to a smaller-group interactive course.

OBJECTIVE: To transition a large pharmacokinetics course that was delivered using a traditional lecture format into a smaller-group course with a discussion format. DESIGN: An e-book and Web-based multimedia learning modules were utilized to facilitate students' independent learning which allowed the number of classes they were required to attend to be reduced from 3 to 1 per week. Students were assigned randomly to 1 of 3 weekly class sessions. The majority of lecture time was replaced with active-learning activities including discussion, problem solving, and case studies to encourage higher-order learning. ASSESSMENT: Changes in course delivery were assessed over a 4-year period by comparing students' grades and satisfaction ratings on course evaluations. Although student satisfaction with the course did not improve significantly, students preferred the smaller-group setting to a large lecture-based class. The resources and activities designed to shift responsibility for learning to the students did not affect examination grades even though a larger portion of examination questions focused on higher orders of learning (eg, application) in the smaller-group format. CONCLUSIONS: Transitioning to a smaller-group discussion format is possible in a pharmacokinetics course by increasing student accountability for acquiring factual content outside of the classroom. Students favored the smaller-class format over a large lecture-based class.

Pharmacokinetic and pharmacodynamic implications of P-glycoprotein modulation.

Modulation of P-glycoprotein (Pgp)-mediated transport has significant pharmacokinetic implications for Pgp substrates. Pharmacokinetic alterations may be at the systemic (blood concentrations), regional (organ or tissue concentrations), or local (intracellular concentrations) level. Regardless of the particular location of Pgp modulation, changes in substrate pharmacokinetics will have the potential to alter the magnitude and duration of pharmacologic effect (pharmacodynamics). It is important to understand each of the aspects of Pgp modulation for a given Pgp substrate in order to predict the degree to which Pgp modulation may affect that substrate, to minimize untoward effects associated with that modulation, or to exploit that modulation for specific therapeutic advantage.

A hybrid jigsaw approach to teaching renal clearance concepts.

OBJECTIVES: To evaluate the effectiveness of using a jigsaw cooperative learning approach to teach basic concepts of renal clearance to pharmacy students. DESIGN: Students collected information on the mechanisms of renal clearance for a particular drug and proposed a methodology for circumventing a urine drug screen. Attitudinal surveys, an online quiz, and course examinations were used to assess student learning. ASSESSMENT: The majority of students felt apprehensive toward a group assignment prior to the exercise, and afterwards still preferred individual work over group work. Post-exercise quiz and final examination scores showed students successfully learned the material. CONCLUSIONS: Students were successful in learning from each other and there was no difference in examination performance compared to years when the technique was not used. In addition, the relative negative experiences of previous group work decreased the subjective attitudes related to the current learning experience.

Regional differences in capillary density, perfusion rate, and P-glycoprotein activity: a quantitative analysis of regional drug exposure in the brain.

The in situ brain perfusion technique was used to assess the impact of local capillary density, blood flow rate and P-gp-mediated efflux activity on regional drug exposure for the P-gp substrates colchicine, quinidine, verapamil, and loperamide, the perfusion flow rate marker diazepam, and the vascular volume marker inulin, in mdr1a(+/+) and mdr1a(-/-) mice. Regional perfusion flow rate varied 7.5-fold, and capillary density (based on vascular volume) varied 3.7-fold, across the 13 brain regions examined. The rate of regional flow, as well as P-gp-mediated colchicine efflux activity, was directly proportional to local capillary density. A decrease in perfusion rate attenuated verapamil brain uptake and had significant effect on P-gp-mediated efflux activity for this substrate in brain regions with lower capillary density. Regional brain uptake and calculated logD at pH 7.4 (clogD(7.4)) were well-related in P-gp-deficient mice, indicating that in the absence of P-gp-mediated efflux, physicochemical properties of the compound (i.e., lipophilicity) serve as the primary determinant of regional brain uptake. Loperamide regional brain uptake and P-gp effect during a 60-s brain perfusion or at 30min after subcutaneous administration were significantly correlated with local capillary density. The highest P-gp-mediated efflux activity was consistently observed in cerebral cortex and midbrain regions for loperamide following short-term brain perfusion and at all time points following subcutaneous administration. These results in intact animal emphasize that the regionality of substrate exposure in brain as measured by the in situ brain perfusion technique is actually biologically relevant.

Sex-dependent disposition of acetaminophen sulfate and glucuronide in the in situ perfused mouse liver.

Breast cancer resistance protein (BCRP, ABCG2) is expressed in the hepatic canalicular membrane and mediates biliary excretion of xenobiotics including sulfate and glucuronide metabolites of some compounds. Hepatic Bcrp expression is sex-dependent, with higher expression in male mice. The hypothesis that sex-dependent Bcrp expression influences the hepatobiliary disposition of phase II metabolites was tested in the present study using acetaminophen (APAP) and the generated APAP glucuronide (AG) and sulfate (AS) metabolites in single-pass in situ perfused livers from male and female wild-type and Abcg(-/-) (Bcrp-deficient) mice. Pharmacokinetic modeling was used to estimate parameters governing the hepatobiliary disposition of APAP, AG, and AS. In wild-type mice, the biliary excretion rate constant was 2.5- and 7-fold higher in males than in females for AS and AG, respectively, reflecting male-predominant Bcrp expression. Sex-dependent differences in AG biliary excretion were not observed in Bcrp-deficient mice, and AS biliary excretion was negligible. Interestingly, sex-dependent basolateral excretion of AG (higher in males) and AS (higher in females) was noted in wild-type mice with a similar trend in Bcrp-deficient mouse livers, reflecting an increased rate constant for AG formation in male and AS formation in female mouse livers. In addition, the rate constant for AS basolateral excretion was increased significantly in female mouse livers compared with that in male mouse livers. It is interesting to note that multidrug resistance-associated protein 4 was higher in female than in male mouse livers. In conclusion, sex-dependent differences in conjugation and transporter expression result in profound differences in the hepatobiliary disposition of AG and AS in male and female mouse livers.

Pharmacokinetic analysis of trichloroethylene metabolism in male B6C3F1 mice: Formation and disposition of trichloroacetic acid, dichloroacetic acid, S-(1,2-dichlorovinyl)glutathione and S-(1,2-dichlorovinyl)-L-cysteine.

Trichloroethylene (TCE) is a well-known carcinogen in rodents and concerns exist regarding its potential carcinogenicity in humans. Oxidative metabolites of TCE, such as dichloroacetic acid (DCA) and trichloroacetic acid (TCA), are thought to be hepatotoxic and carcinogenic in mice. The reactive products of glutathione conjugation, such as S-(1,2-dichlorovinyl)-L-cysteine (DCVC), and S-(1,2-dichlorovinyl) glutathione (DCVG), are associated with renal toxicity in rats. Recently, we developed a new analytical method for simultaneous assessment of these TCE metabolites in small-volume biological samples. Since important gaps remain in our understanding of the pharmacokinetics of TCE and its metabolites, we studied a time-course of DCA, TCA, DCVG and DCVG formation and elimination after a single oral dose of 2100 mg/kg TCE in male B6C3F1 mice. Based on systemic concentration-time data, we constructed multi-compartment models to explore the kinetic properties of the formation and disposition of TCE metabolites, as well as the source of DCA formation. We conclude that TCE-oxide is the most likely source of DCA. According to the best-fit model, bioavailability of oral TCE was approximately 74%, and the half-life and clearance of each metabolite in the mouse were as follows: DCA: 0.6 h, 0.081 ml/h; TCA: 12 h, 3.80 ml/h; DCVG: 1.4 h, 16.8 ml/h; DCVC: 1.2 h, 176 ml/h. In B6C3F1 mice, oxidative metabolites are formed in much greater quantities (approximately 3600 fold difference) than glutathione-conjugative metabolites. In addition, DCA is produced to a very limited extent relative to TCA, while most of DCVG is converted into DCVC. These pharmacokinetic studies provide insight into the kinetic properties of four key biomarkers of TCE toxicity in the mouse, representing novel information that can be used in risk assessment.

Assessment of blood-brain barrier permeability using the in situ mouse brain perfusion technique.

PURPOSE: To assess the blood-brain barrier (BBB) permeability of 12 clinically-used drugs in mdr1a(+/+) and mdr1a(-/-) mice, and investigate the influence of lipophilicity, nonspecific brain tissue binding, and P-gp-mediated efflux on the rate of brain uptake. METHODS: The BBB partition coefficient (PS) was determined using the in situ mouse brain perfusion technique. The net brain uptake for 12 compounds, and the time course of brain uptake for selected compounds ranging in BBB equilibration kinetics from rapidly-equilibrating (e.g., alfentanil, sufentanil) to slowly-equilibrating (fexofenadine), was determined and compared. RESULTS: There was a sigmoidal relationship in mdr1a(-/-) mice between the log-PS and clogD(7.4) in the range of 0-5. The brain uptake clearance was a function of both permeability and blood flow rate. The brain unbound fraction was inversely proportional to lipophilicity. Alfentanil achieved brain equilibrium approximately 4,000-fold faster than fexofenadine, based on the magnitude of PSxfu,brain. CONCLUSIONS: In situ brain perfusion is a useful technique to determine BBB permeability. Lipophilicity, ionization state, molecular weight and polar surface area are all important determinants for brain penetration. The time to blood-to-brain equilibrium varies widely for different compounds, and is determined by a multiplicity of pharmacokinetic factors.

Breast cancer resistance protein interacts with various compounds in vitro, but plays a minor role in substrate efflux at the blood-brain barrier.

Expression of breast cancer resistance protein (Bcrp) at the blood-brain barrier (BBB) has been revealed recently. To investigate comprehensively the potential role of Bcrp at the murine BBB, a chemically diverse set of model compounds (cimetidine, alfuzosin, dipyridamole, and LY2228820) was evaluated using a multiexperimental design. Bcrp1 stably transfected MDCKII cell monolayer transport studies demonstrated that each compound had affinity for Bcrp and that polarized transport by Bcrp was abolished completely by the Bcrp inhibitor chrysin. However, none of the compounds differed in brain uptake between Bcrp wild-type and knockout mice under either an in situ brain perfusion or a 24-h subcutaneous osmotic minipump continuous infusion experimental paradigm. In addition, alfuzosin and dipyridamole were shown to undergo transport by P-glycoprotein (P-gp) in an MDCKII-MDR1 cell monolayer model. Alfuzosin brain uptake was 4-fold higher in mdr1a(-/-) mice than in mdr1a(+/+) mice in in situ and in vivo studies, demonstrating for the first time that it undergoes P-gp-mediated efflux at the BBB. In contrast, P-gp had no effect on dipyridamole brain penetration in situ or in vivo. In fact, in situ BBB permeability of these solutes appeared to be primarily dependent on their lipophilicity in the absence of efflux transport, and in situ brain uptake clearance correlated with the intrinsic transcellular passive permeability from in vitro transport and cellular accumulation studies. In summary, Bcrp mediates in vitro transport of various compounds, but seems to play a minimal role at the BBB in vivo.

Roles of innovation in education delivery.

This paper reviews trends in higher education, characterizing both the current learning environments in pharmacy education as well as a vision for future learning environments, and outlines a strategy for successful implementation of innovations in educational delivery. The following 3 areas of focus are addressed: (1) rejecting the use of the majority of classroom time for the simple transmission of factual information to students; (2) challenging students to think critically, communicate lucidly, and synthesize broadly in order to solve problems; and (3) adopting a philosophy of "evidence-based education" as a core construct of instructional innovation and reform.

Relationship between drug/metabolite exposure and impairment of excretory transport function.

The quantitative impact of excretory transport modulation on the systemic exposure to xenobiotics and derived metabolites is poorly understood. This article presents fundamental relationships between exposure and loss of a specific excretory process that contributes to overall clearance. The mathematical relationships presented herein were explored on the basis of hepatic excretory data for polar metabolites formed in the livers of various transporter-deficient rodents. Experimental data and theoretical relationships indicated that the fold change in exposure is governed by the relationship, 1/(1 - f(e)), where f(e) is the fraction excreted by a particular transport protein. Loss of function of a transport pathway associated with f(e) < 0.5 will have minor consequences (<2-fold) on exposure, but exposure will increase exponentially in response to loss of function of transport pathways with f(e) > 0.5. These mathematical relationships may be extended to other organs, such as the intestine and kidney, as well as to systemic drug exposure. Finally, the relationship between exposure and f(e) is not only applicable to complete loss of function of a transport pathway but also can be extended to partial inhibition scenarios by modifying the equation with the ratio of the inhibitor concentration and inhibition constant.

Fexofenadine brain exposure and the influence of blood-brain barrier P-glycoprotein after fexofenadine and terfenadine administration.

P-glycoprotein (P-gp) plays an important role in determining net brain uptake of fexofenadine. Initial in vivo experiments with 24-h subcutaneous osmotic minipump administration demonstrated that fexofenadine brain penetration was 48-fold higher in mdr1a(-/-) mice than in mdr1a(+/+) mice. In contrast, the P-gp efflux ratio at the blood-brain barrier (BBB) for fexofenadine was only approximately 4 using an in situ brain perfusion technique. Pharmacokinetic modeling based on the experimental results indicated that the apparent fexofenadine P-gp efflux ratio is time-dependent due to low passive permeability at the BBB. Fexofenadine brain penetration after terfenadine administration was approximately 25- to 27-fold higher than after fexofenadine administration in both mdr1a(+/+) and mdr1a(-/-) mice, consistent with terfenadine metabolism to fexofenadine in murine brain tissue. The fexofenadine formation rate after terfenadine in situ brain perfusion was comparable with that in a 2-h brain tissue homogenate in vitro incubation. The fexofenadine formation rate increased approximately 5-fold during a 2-h brain tissue homogenate incubation with hydroxyl-terfenadine, suggesting that the hydroxylation of terfenadine is the rate-limiting step in fexofenadine formation. Moreover, regional brain metabolism seems to be an important factor in terfenadine brain disposition and, consequently, fexofenadine brain exposure. Taken together, these results indicate that the fexofenadine BBB P-gp efflux ratio has been underestimated previously due to the lack of complete equilibration of fexofenadine across the blood-brain interface under typical experimental paradigms.

Using answer-until-correct examinations to provide immediate feedback to students in a pharmacokinetics course.

OBJECTIVES: To implement an answer-until-correct examination format for a pharmacokinetics course and determine whether this format assessed pharmacy students' mastery of the desired learning outcomes as well as a mixed format examination (eg, one with a combination of open-ended and fill-in-the-blank questions). METHODS: Students in a core pharmacokinetics course were given 3 examinations in answer-until-correct format. The format allowed students multiple attempts at answering each question, with points allocated based on the number of attempts required to correctly answer the question. Examination scores were compared to those of students in the previous year as a control. RESULTS: The grades of students who were given the immediate feedback examination format were equivalent to those of students in the previous year. The students preferred the testing format because it allowed multiple attempts to answer questions and provided immediate feedback. Some students reported increased anxiety because of the new examination format. DISCUSSION: The immediate feedback format assessed students' mastery of course outcomes, provided immediate feedback to encourage deep learning and critical-thinking skills, and was preferred by students over the traditional examination format.

Opioid tolerance development: a pharmacokinetic/pharmacodynamic perspective.

The opioids are commonly used to treat acute and severe pain. Long-term opioid administration eventually reaches a dose ceiling that is attributable to the rapid onset of analgesic tolerance coupled with the slow development of tolerance to the untoward side effects of respiratory depression, nausea and decreased gastrointestinal motility. The need for effective-long term analgesia remains. In order to develop new therapeutics and novel strategies for use of current analgesics, the processes that mediate tolerance must be understood. This review highlights potential pharmacokinetic (changes in metabolite production, metabolizing enzyme expression, and transporter function) and pharmacodynamic (receptor type, location and functionality; alterations in signaling pathways and cross-tolerance) aspects of opioid tolerance development, and presents several pharmacodynamic modeling strategies that have been used to characterize time-dependent attenuation of opioid analgesia.