Department of Pharmaceutical Sciences, School of Pharmacy, Texas Tech University Health Sciences Center, 1300 S. Coulter, Amarillo, TX, 79106, USA

Abstract

Background

Estimation of pharmacokinetic parameters after intermittent intravenous infusion (III) of antibiotics, such as aminoglycosides or vancomycin, has traditionally been a difficult subject for students in clinical pharmacology or pharmacokinetic courses. Additionally, samples taken at different intervals during repeated dose therapy require manipulation of sampling times before accurate calculation of the patient-specific pharmacokinetic parameters. The main goal of this study was to evaluate the effectiveness of active learning tools and practice opportunities on the ability of students to estimate pharmacokinetic parameters from the plasma samples obtained at different intervals following intermittent intravenous infusion.

Methods

An extensive reading note, with examples, and a problem case, based on a patient’s chart data, were created and made available to students before the class session. Students were required to work through the case before attending the class. The class session was devoted to the discussion of the case requiring active participation of the students using a random participation program. After the class, students were given additional opportunities to practice the calculations, using online modules developed by the instructor, before submitting an online assignment.

Results

The performance of students significantly (

Conclusions

Despite being a difficult subject, students achieve mastery of pharmacokinetic calculations for the topic of intermittent intravenous infusion when appropriate active learning strategies and practice opportunities are employed.

Background

Intermittent intravenous infusion (III) is a mode of drug administration whereby the drug is administered through short intravenous infusions at regular intervals. This method of drug administration may be useful for avoiding dangerously high concentrations that may be achieved by intravenous bolus administration. Additionally, the short infusion time masks the distribution phase, therefore minimizing problems associated with the interpretations of the plasma concentration-time data for drugs that follow multicompartment kinetics.

Important drugs that are administered by the III method are aminoglycosides and vancomycin, which are usually administered by 30–60 min short infusions

There are subtle differences between the III and multiple bolus dosing of drugs in terms of estimation of some pharmacokinetic parameters such as maximum plasma concentration (C_{max}) and volume of distribution (V). The main reason for these differences is a relatively significant elimination of the drug during the drug input (short infusion) for the III mode, as opposed to a negligible elimination of the drug during the bolus input. Consequently, the C_{max} after III, which occurs at the end of the short infusion, is always less than the maximum concentration after the intravenous bolus dosing (C_{o}), which occurs immediately after the bolus dose (Figure _{max} and calculation of volume of distribution after III are more complicated than those after the intravenous bolus dosing.

Plasma/serum concentration-time profiles of a drug administered by intermittent intravenous infusion or intravenous bolus method

**Plasma**/**serum concentration**-**time profiles of a drug administered by intermittent intravenous infusion or intravenous bolus method.** Solid and dashed lines represent the intermittent intravenous infusion and intravenous bolus methods, respectively. Abbreviations: C_{o} = maximum concentration after the bolus dose; C_{max} = maximum concentration after the short infusion; t_{inf} = length of short infusion; C_{min} = minimum concentration.

Additionally, a common practice for sampling at steady state for drugs administered through III is to obtain the peak and trough samples from two subsequent dosage intervals: a trough sample is taken first, followed by the infusion of the next dose and collection of the peak sample

Methods

Educational context

Basic Pharmacokinetics is a 3-semester-credit-hour course that is offered synchronously, using videoconferencing technology, to the local (Amarillo) and distant (Abilene) campuses twice a week with 75 min of instruction time for each session. Although most of the instructions initiate from the Amarillo campus, where the author resides, a second instructor is located in Abilene to assist the students inside and outside the classroom. The course is offered during the second year (P2) of a 4-year Pharm.D. program and runs throughout the fall semester with 16 weeks of instruction, excluding holidays. The prerequisites for the course are P2 academic standing and successful completion of a Principles of Drug Action course that is offered during the spring semester of the first year. The teaching format of the course is based on the active learning principles applicable to large classrooms, as described in more detail in the following sections. For the fall of 2011, the class had a total enrolment of 152 students, with 114 students on the Amarillo campus and 38 students on the Abilene campus.

The overall outcomes of the course are presented in Table _{max}, which occurs at the end of short infusion (Figure _{max} and C_{min}, which is less than one dosage interval, and the estimation of V using newly-introduced equations based on the Sawchuk-Zaske method

1.

Evaluate the primary and secondary drug information literature with regard to the pharmacokinetics and pharmacodynamics of drugs.

2.

Evaluate the basic pharmacokinetics and pharmacodynamic properties of a drug and relate them to the manner in which the drug is used therapeutically.

3.

Estimate patient-specific kinetic parameters for any drug and route of administration from a limited number of biological samples.

4.

Design dosage regimens based on the patient-specific or population (average) pharmacokinetic/ pharmacodynamic data.

5.

Predict the effects of route and/or method of drug administration on the plasma concentration-time profiles using the individual or population (average) kinetic data and judge the appropriateness of dosage form and route of administration.

6.

Predict the effects of changes in the physiological parameters (due to drug interactions, disease states, or special populations) on the pharmacokinetics and plasma concentration-time profile of drugs, and recommend a dosage regimen based on the altered parameters.

1.

Expected outcome:

1.1 Estimate major kinetic parameters (elimination rate constant or half life, volume of distribution, and clearance) from two or more plasma concentration-time data collected after intermittent intravenous infusion of drugs during the first dose or at steady state.

2.

Learning objectives:

2.1 Define the applications of intermittent intravenous infusion method.

2.2 Recognize the differences between the maximum and peak and between the minimum and trough concentrations.

2.3 Estimate the elimination rate constant and half life from the peak and trough concentrations after the first dose.

2.4 Estimate elimination rate constant and half life from a trough concentration collected at the end of one dosage interval and a peak concentration collected subsequently after the infusion of the next dose at steady state.

2.5 Estimate the maximum and minimum concentrations from the peak or trough concentrations and elimination rate constant for the first dose or at steady state.

2.6 Estimate volume of distribution after the first dose or at steady state.

2.7 Estimate clearance after the first dose or at steady state.

To achieve the stated outcome and learning objectives (Table

Descriptions of the major elements of the reading note^{a}

A reading handout was prepared by the instructor, which was made available to students online via the course website. The reading note starts with the expected outcomes and learning objectives for the lesson (Table _{max} and between the trough and C_{min} are explained (Figure

Estimation of the elimination rate constant (k) and half life (t_{1/2})

First, the simple situation when the peak and trough samples are taken from the same interval is discussed. For this method, the calculation of

where T_{trough} and T_{peak} are the sampling time of peak and trough, respectively. Subsequently, t_{1/2} may be obtained using

Additionally, a major emphasis is made on the estimation of _{1/2} for a case when the trough and peak samples are taken from two different dosage intervals at steady state. In these cases, a trough is first taken around the end of an interval, followed by the administration of the next dose and collection of the peak sample. This is usually done for the sake of convenience and/or expediency. Otherwise, one may have to wait close to one dosage interval to collect both the peak and trough samples from the same dosage interval. An example of data (Figures ^{th} interval is the same as that if it had been taken at the same time within the 5^{th} interval (Figure ^{th} dose is indeed the trough sample after the 5^{th} dose, the same interval that the peak was taken. Consequently, the T_{trough} (1500) has to be extended by one dosage interval (8 h) before substitution in equation (1) (Figures

Chart data

**Chart data.** Excerpts from a patient’s chart data containing the medication administration record and laboratory (plasma concentration-time) data after administration of multiple doses of gentamicin to a patient (**A**) and manipulation of sampling time of trough or peak or calculation of sampling time within the interval for use in equation (1) (**B**).

Serum/plasma concentration-time Profiles

**Serum**/**plasma concentration**-**time Profiles.** Serum/plasma concentration-time course of gentamicin after intermittent intravenous infusion in a patient after intravenous infusion of 80 mg of the drug over 30 min every 8 h, demonstrating the manipulation of peak or trough time (**A**) and calculation of sampling time for peak (T_{peak}) and trough (T_{trough}) within the interval (**B**). Solid triangles: peak and trough after the first dose; solid circles: peak and trough at steady state; dotted open circles: transposed peak or trough at steady state.

Similarly, the peak concentration taken 0.5 h after the infusion is stopped (4.68 mg/L) after the 5^{th} dose is the same as that if it had been taken 0.5 h after the completion of the 4^{th} dose (Figure _{peak} (1630) may be moved back by one dosage interval (8 h) to the interval when the trough was taken (Figures

Another method for the estimation of T_{trough} and T_{peak} for substitution in equation (1) is to use the sampling time relative to the beginning of the dosing interval in which the sample is taken. In the example here (Figures _{trough} is 7.5 h (15–7.5). Similarly, the beginning of dosage interval for the sample taken at 1630 is 1530, hence resulting in a T_{peak} value of 1.0 h (16.5-15.5) (Figures

Estimation of C_{max} and C_{min}

In addition to the estimation of _{1/2}, the note also discusses, with examples, the estimation of C_{max} and C_{min} for any dosage interval (e.g., before and at steady state) using the following general equation:

This equation can be used for the estimation of drug concentration at any time when another concentration-time data (peak or trough) and _{2} is the lower concentration (at the later time of t_{2}) and C_{1} is the higher concentration (at the earlier time of t_{1}). If the estimated C_{max} and C_{min} are after the first dose, they may be multiplied by the accumulation factor to predict their corresponding values at steady state.

Estimation of volume of distribution

The notes also discuss the estimation of V for the first dose, steady state, and dosage intervals between the first dose and steady state using equations (4), (5), and (6), respectively, which are derived based on the Sawchuck-Zaske method

where R_{o}, t_{inf}, τ, C_{max}
^{∞}, and C_{predose} are the rate of infusion, length of infusion, C_{max} at steady state, and predose C_{min}, respectively. Additionally, the degree of error associated with the estimation of V using the bolus dose equations (7) (for the first does) and (8) (for the steady state), listed below, are discussed in the notes with numerical examples

The notes state that the degree of overestimation of V using the equations for the bolus route is dependent on the magnitude of difference between C_{o} (if the drug were administered by IV bolus route) and C_{max}. This means the longer the length of the infusion or the faster the decline in the plasma concentration (shorter half life), the larger is the difference between the C_{o} and C_{max} values, hence resulting in a higher overestimation of V

Estimation of clearance (Cl)

The discussion of the estimation of Cl for this topic in the notes is limited because this calculation (multiplying k by V) is not unique to this route of administration.

Practice problem for in-class discussion^{b}

A practice problem was designed to cover the learning objectives of the lesson (Table

**Questions for the first dose data**

**Questions for the steady**-**state data**

1. Elimination rate constant and half life

1. Elimination rate constant and half life

2. C_{max} for the first dose

2. C_{max} at steady state

3. C_{min} for the first dose

3. C_{min} at steady state

4. C_{max} at steady state

4. Volume of distribution

5. C_{min} at steady state

5. Clearance

6. Volume of distribution

7. Clearance

As with any other topic in the course, students were expected to work on the practice problem, consulting the reading note, before attending the class session.

Class session

During the first 10–15 min of the class session, the instructor briefly outlined the general concepts of the intermittent intravenous infusion and its potential applications. The remaining time of the session was then devoted to the discussion of the practice problem. The discussion was conducted by calling on students randomly, using an online registration process described previously

Online homework assignment

An online, interactive module was designed with a structure identical to the in-class practice problem using a system described before

Assessment

To assess the effectiveness of the tools used to achieve the learning objectives of the session, an online pretest was given to students at the end of the class for the multiple dosing session, which was two days before the session on the III topic. The students did not have access to the notes, practice problem, or the online assignment/practice modules before the pretest. The pretest presented dosage regimen and peak and trough data for the steady state using the simulated chart data for a case when the trough sample was obtained before the next dose peak sample (similar to the data in Figure _{max}, C_{min}, and V. Similar to the online assignments, the pretest for each student had individual, unique data. The students were given 15 minutes to answer the questions. After the pretest, notes, practice problem, and the online assignment/practice modules were made available to students. Two days after the pretest, the III topic was presented to students in a class session, and a posttest was administered at the end of the session using the same questions used in the pretest but with different data set. Again, students were allowed 15 min to complete the test online. In addition to the pre- and posttest, the student grades on the homework assignment for the same questions were compiled. Finally, the grades of the students for the same 4 questions in the mid-term examination, which was administered 3 weeks after the session, was compiled.

A one-way ANOVA with repeated measures (4 assessments), followed by post-hoc Tukey’s multiple comparison, was used to test the differences between the total grades of all students in different assessments. Additionally, to test the effect of location (Abilene and Amarillo) on the performance of students in the 4 assessments, the grades were separated based on the campus. A two-way ANOVA with repeated measures, followed by Bonferroni post-hoc tests, was then used for the statistical analysis of data.

The study was approved by the Institutional Review Board of Texas Tech University Health Sciences Center under the exempt status (IRB#: A11-3674).

Results

A total of 126 students (34 from Abilene and 92 from Amarillo) completed all 4 assessments, and therefore, were included in the analysis. As demonstrated in Figure

Performance data for the entire assessments

**Performance data for the entire assessments.** Grades of students in Pretest, Posttest, Assignment, and Examination for the entire class (**A**) and Abilene (**B**). Columns and bars represent mean and SEM, respectively. ***

The percentages of students who answered each of the questions related to _{max}, C_{min}, and V correctly in the 4 assessments are shown in Figure _{min} question (Figure _{max} and V questions, although the performance of the students in the pretest, posttest, and assignments progressively improved, the number of students answering the questions correctly in the mid-term exam was significantly lower than that in the take-home assignment for these two questions (Figure

Performance data for the individual questions

**Performance data for the individual questions.** Percentages of students who answered each of the four questions correctly in Pretest, Posttest, Assignment, and Examination (_{max} = maximum concentration; C_{min} = minimum concentration; V = volume of distribution.

As for the use of online practices, an overwhelming majority of students (88.1%) generated one or more practices before the submission of the online assignment, as opposed to only 11.9% of the students who did not generate any practices. Of those who generated practices, 55.5%, 19.0%, and 7.1% generated one, two, or three practices, respectively. The remaining students (6.3%) generated ≥ 4 practices. The linear regression analysis of the assignment grades against the number of generated practices for students who generated 0–3 practices (94% of students) are presented in Figure

Effects of online practice generation on the online assignment grade

**Effects of online practice generation on the online assignment grade.** Grades of students in the online assignment as a function of the number of online practices generated before the submission of the assignment. The percentages of students who generated zero, one, two, or three practices were 11.9%, 55.5%, 19.0%, and 7.1%, respectively. Symbols and bars represent mean and SEM, respectively.

Discussion

The main goal of the instructor for the III session was to design learning tools for students so that they learn how to estimate major patient-specific pharmacokinetic parameters after this route of administration. To accommodate the requirements of some Advanced Pharmacy Practice Experience rotations that students be able to estimate the kinetic parameters using the patient chart data and plasma concentrations taken from two intervals, learning tools were designed with special emphasis on these requirements. The performance data presented in Figures

It could be argued that the students’ performance in the take-home assignment is inflated relative to the other tests because of two main differences between the assignment and other tests. First, other than a due date and time, the assignment lacked the time stress present for the other tests. Therefore, students could spend as much time as they needed for each question while answering the assignment questions. Second, whereas the pretest, posttest, and mid-term exam were not open book (except for provision of an equation sheet), students had access to all course materials for the take-home assignment. Therefore, one might expect that the performance of the students in the mid-term exam to be lower than that in the assignment. Although the grades of students in the mid-term exam (83%) were lower than those in the assignment (89%), this difference did not reach statistical significance (Figure

At Texas Tech School of Pharmacy, the courses offered during the first and second year of the pharmacy curriculum are delivered synchronously to Amarillo and Abilene campuses. The instruction may be initiated from either campus depending on the location of the instructor. For the Pharmacokinetics course, all the sessions initiated from Amarillo. Therefore, the Abilene campus was considered the distant campus. To assure equality of performance between the two campuses, all the performance data were routinely monitored separately for the two campuses. As shown in Figure

The performance data on the individual questions (Figure

Although the trend for the C_{min} data was similar to that for _{max} or V questions correctly in the mid-term exam was significantly lower than that in the take-home assignment (Figure

Conclusions

In conclusion, learning tools used in a basic pharmacokinetics course offered to second-year pharmacy students are presented here for the topic of intermittent intravenous infusion. In addition to the estimation of pharmacokinetic parameters from the plasma concentrations obtained during one interval, emphasis was placed on a unique case when peak and trough are obtained from two separate dosage intervals at steady state. Additionally, simulated chart data were used to present the dosing schedules and laboratory data. Although students were familiar with the estimation of elimination rate constant before the introduction of the intermittent intravenous infusion topic, >95% of them could not estimate the elimination rate constant accurately when the peak and trough samples were from two separate intervals. Active learning exercises and practice opportunities employed for this topic substantially facilitated students’ mastery of these calculations, as evidenced by performance data.

Endnotes

^{a}A complete copy of the reading note is available from the author by request.

^{b}A complete copy of the practice problem is available from the author upon request.

Competing interests

The author reports no competing interest.

Authors’ contributions

RM designed and carried the study, analyzed the data, and wrote the manuscript.

Authors’ information

RM, PharmD, PhD, is a Professor of Pharmaceutical Sciences who has taught basic and clinical pharmacokinetics courses to pharmacy students for over 25 years. He has developed numerous active learning strategies for teaching pharmacokinetics, for which he has received several awards including Innovation in Teaching Award from the American Association of Colleges of Pharmacy and President’s and Chancellor’s Awards in Teaching from the Texas Tech University Health Sciences Center.

Pre-publication history

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