North American Pharmacist Licensure Examination (NAPLEX) Pharmacokinetics, Pharmacodynamics, and Calculations Syllabus

What are conventional (traditional) target peak and trough levels for gentamicin/tobramycin?

For conventional dosing of gentamicin/tobramycin: peak $5$–$10\ \mu g/mL$ (higher, $8$–$10$, for serious infections) and trough $< 2\ \mu g/mL$ (ideally $< 1$) to minimize nephro-/ototoxicity. Amikacin: peak $20$–$30$, trough $< 10\ \mu g/mL$.

What is the rationale for extended-interval (once-daily) aminoglycoside dosing?

Aminoglycosides show concentration-dependent killing and a post-antibiotic effect. High peaks maximize bactericidal activity while the long drug-free interval (low troughs) reduces saturable uptake into renal/cochlear cells, lowering toxicity. Typical dose $\sim 5$–$7\ \text{mg/kg}$ q24h.

Which body weight is used for aminoglycoside dosing in obese patients?

Use adjusted body weight: $$ABW = IBW + 0.4(TBW - IBW)$$ Aminoglycosides distribute mainly in extracellular fluid, not adipose tissue, so total body weight would overdose obese patients.

State the Devine formula for ideal body weight (IBW).

Men: $IBW = 50\ \text{kg} + 2.3 \times (\text{inches over } 60)$. Women: $IBW = 45.5\ \text{kg} + 2.3 \times (\text{inches over } 60)$.

Why has vancomycin AUC-guided dosing replaced trough-only monitoring?

Efficacy for MRSA correlates with the ratio $AUC_{0-24}/MIC$, not trough alone. Targeting troughs of $15$–$20\ \mu g/mL$ overexposed patients and increased nephrotoxicity. AUC monitoring achieves efficacy at lower exposure with less toxicity.

What is the target vancomycin $AUC_{0-24}/MIC$ ratio for serious MRSA infections?

Target $AUC_{0-24}/MIC$ of $400$–$600$ (assuming MIC $= 1\ \text{mg/L}$ by broth microdilution). This corresponds to an $AUC_{0-24}$ of roughly $400$–$600\ \text{mg·h/L}$.

How is vancomycin $AUC_{0-24}$ estimated from peak and trough using the trapezoidal method?

$AUC_{0-24} = AUC_{inf} + AUC_{elim}$ summed over the interval and scaled to 24 h. Practically, two levels (peak and trough) yield $k$ and $V_d$; $AUC_{24} = \frac{\text{Dose}_{24h}}{CL}$, where $CL = k \times V_d$. Bayesian software can use a single trough.

Define steady state and what determines the average steady-state concentration.

Steady state occurs when the rate of drug in equals the rate of drug out, so average concentration is constant over intervals. $$C_{ss,avg} = \frac{F \times \text{Dose}}{CL \times \tau}$$ It depends on dosing rate and clearance, not on $V_d$.

What does a steady-state trough (Cmin) represent and when is it drawn?

The trough is the lowest concentration in a dosing interval, drawn just before the next dose at steady state ($\geq 4$–$5$ half-lives). It is used to confirm adequate exposure and avoid toxicity (e.g., vancomycin, aminoglycosides, digoxin).

How does changing the dosing interval vs. the dose affect peak-trough fluctuation at steady state?

Shortening the interval (or giving smaller, more frequent doses) reduces peak-to-trough fluctuation while keeping $C_{ss,avg}$ the same. Larger, less frequent doses increase fluctuation. $C_{ss,avg}$ depends only on total daily dose and clearance.

How is drug clearance generally adjusted in renal impairment?

Renal clearance falls proportionally with $CrCl$ for renally eliminated drugs. Doses are reduced and/or intervals extended based on estimated $CrCl$. Total clearance $CL = CL_{nonrenal} + CL_{renal} \times \frac{CrCl_{patient}}{CrCl_{normal}}$.

State the Cockcroft-Gault equation for creatinine clearance.

$$CrCl = \frac{(140 - \text{age}) \times \text{weight (kg)}}{72 \times S_{cr}\,(\text{mg/dL})} \times (0.85 \text{ if female})$$ Weight is typically IBW (use adjusted or actual depending on body habitus).

How does hepatic impairment alter pharmacokinetics of high vs. low extraction-ratio drugs?

For high-extraction drugs, cirrhosis (reduced flow and portosystemic shunting) sharply raises oral bioavailability and concentrations. For low-extraction drugs, hepatic dysfunction reduces intrinsic metabolic capacity, lowering clearance. Reduced albumin also raises free fraction.

What is the alligation method used for, and how do the parts get assigned?

Alligation determines proportions of two strengths (high and low) to mix for a desired intermediate strength. Place desired strength in the middle; subtract diagonally. Parts of higher strength = $|\text{desired} - \text{lower}|$; parts of lower strength = $|\text{higher} - \text{desired}|$.

How many grams of a 1% and a 5% hydrocortisone cream are needed to make 100 g of 2% cream (alligation)?

Parts of 5%: $|2-1| = 1$; parts of 1%: $|5-2| = 3$; total $4$ parts. 5% cream $= \frac{1}{4} \times 100 = 25\ \text{g}$; 1% cream $= \frac{3}{4} \times 100 = 75\ \text{g}$.

State the dilution/concentration relationship $C_1 V_1 = C_2 V_2$ and what it assumes.

$$C_1 V_1 = C_2 V_2$$ The quantity of active ingredient is conserved when diluting or concentrating. $C_1, V_1$ are initial strength and volume; $C_2, V_2$ are final. Strength varies inversely with volume.

How do you convert percent strength (w/v) to mg/mL?

$\%\ \text{w/v}$ means grams per 100 mL. Multiply percent by 10 to get mg/mL. Example: $2\%\ \text{w/v} = 2\ \text{g}/100\ \text{mL} = 20\ \text{mg/mL}$.

How is the number of milliequivalents (mEq) calculated from milligrams?

$$mEq = \frac{\text{mg} \times \text{valence}}{\text{molecular (formula) weight}}$$ Equivalently, $1\ \text{mEq} = \frac{\text{mg}}{\text{equivalent weight}}$, where equivalent weight $= \frac{\text{MW}}{\text{valence}}$.

How many milliequivalents of sodium are in 1 g of NaCl? (MW = 58.5, valence = 1)

$$mEq = \frac{1000\ \text{mg} \times 1}{58.5} \approx 17.1\ \text{mEq}$$ Thus 1 g NaCl provides about $17\ \text{mEq}$ each of $\ce{Na+}$ and $\ce{Cl-}$.

How are millimoles (mmol) calculated and how do they differ from milliequivalents?

$$mmol = \frac{\text{mg}}{\text{molecular weight}}$$ Millimoles count molecules/ions; milliequivalents account for charge: $mEq = mmol \times \text{valence}$. For monovalent ions, $mEq = mmol$.

Define osmolarity and give the formula for a solution from its components.

Osmolarity is the number of osmoles (osmotically active particles) per liter of solution. $$\text{mOsmol/L} = \frac{\text{wt of substance (g/L)}}{\text{MW}} \times \text{number of particles} \times 1000$$ Example: NaCl dissociates into 2 particles.

Calculate the osmolarity of 0.9% NaCl (MW 58.5).

$0.9\% = 9\ \text{g/L}$. $$\text{mOsmol/L} = \frac{9}{58.5} \times 2 \times 1000 \approx 308\ \text{mOsmol/L}$$ This is why normal saline is iso-osmotic with plasma ($\approx 285$–$310$).

How do you calculate an IV flow rate in drops per minute (gtt/min)?

$$\text{Rate (gtt/min)} = \frac{\text{Volume (mL)} \times \text{drop factor (gtt/mL)}}{\text{Time (min)}}$$ The drop factor depends on tubing (e.g., 10, 15, 20, or 60 gtt/mL for microdrip).

An order reads dopamine $5\ \mu g/kg/min$ for an 80 kg patient using a 1600 µg/mL bag. What is the infusion rate in mL/h?

Dose $= 5 \times 80 = 400\ \mu g/min = 24{,}000\ \mu g/h$. $$\text{Rate} = \frac{24{,}000\ \mu g/h}{1600\ \mu g/mL} = 15\ \text{mL/h}$$

State the Mosteller formula for body surface area (BSA).

$$BSA\,(\text{m}^2) = \sqrt{\frac{\text{height (cm)} \times \text{weight (kg)}}{3600}}$$ BSA is used for chemotherapy and pediatric dosing because it correlates with metabolic rate and cardiac output.

How is a weight-based or BSA-based dose calculated, and why is BSA preferred for chemotherapy?

Weight-based: $\text{dose} = \text{mg/kg} \times \text{weight}$. BSA-based: $\text{dose} = \text{mg/m}^2 \times BSA$. BSA correlates better with physiologic parameters (GFR, blood volume) and narrows interpatient variability for narrow-therapeutic-index cytotoxic drugs.

Define an isotonic solution and the freezing-point depression / NaCl-equivalent methods to achieve it.

Isotonic solutions have the same tonicity as body fluids ($\approx 0.9\%$ NaCl, freezing point depression $0.52^\circ\text{C}$). The NaCl equivalent (E value) method: $E$ = grams of NaCl that produce the same osmotic effect as 1 g of the drug; add NaCl to reach the equivalent of $0.9\%$.

Using the E-value method, how much NaCl is needed to make 30 mL of a 1% drug solution isotonic if the drug's E value is 0.20?

NaCl needed for isotonicity (30 mL) $= 0.009 \times 30 = 0.27\ \text{g}$. NaCl equivalent provided by drug $= 0.20 \times (0.01 \times 30\ \text{g}) = 0.20 \times 0.3 = 0.06\ \text{g}$. NaCl to add $= 0.27 - 0.06 = 0.21\ \text{g}$.

Distinguish potency from efficacy on a dose-response curve.

Potency is the amount of drug needed to produce an effect (position on the x-axis; lower $EC_{50}$ = more potent). Efficacy ($E_{max}$) is the maximal effect achievable (height of the plateau). A drug can be more potent but less efficacious than another.

Define $EC_{50}$ and $ED_{50}$.

$EC_{50}$ is the concentration producing $50\%$ of maximal effect (graded response). $ED_{50}$ is the dose producing a defined effect in $50\%$ of a population (quantal response). Both index potency.

Compare full agonists, partial agonists, and inverse agonists.

A full agonist binds and produces maximal response (high efficacy). A partial agonist produces a submaximal response even at full occupancy (lower intrinsic efficacy) and can antagonize a full agonist. An inverse agonist binds and produces an effect opposite to the agonist (reduces constitutive activity).

Contrast competitive and noncompetitive (irreversible) antagonists on the agonist dose-response curve.

A competitive antagonist shifts the agonist curve right (increased $EC_{50}$) but $E_{max}$ is unchanged and surmountable by more agonist. A noncompetitive/irreversible antagonist lowers $E_{max}$ (insurmountable) and may also shift the curve right.

Define the therapeutic index (TI) and write its formula.

The therapeutic index quantifies drug safety as the ratio of toxic to effective dose. $$TI = \frac{TD_{50}}{ED_{50}}$$ (or $\frac{LD_{50}}{ED_{50}}$). A larger TI means a wider safety margin.

What is the certain safety factor (margin of safety) and how does it differ from TI?

The margin of safety (certain safety factor) $= \frac{TD_{1}}{ED_{99}}$, the ratio of the dose toxic to $1\%$ versus effective in $99\%$. It is more conservative than $TI$ because it accounts for the extremes/overlap of the dose-response curves.

Name three drugs considered to have a narrow therapeutic index and a key consequence.

Warfarin, digoxin, phenytoin, lithium, theophylline, and aminoglycosides. Small concentration changes cause loss of efficacy or toxicity, so they require therapeutic drug monitoring.