Pharmacokinetics-Pharmacodynamics (PKPD) of Antimicrobials

Choice of Antibiotic Treatment

• Is there a clear indication for antibiotic use? Antibiotics should only be used when a bacterial infection is confirmed or highly suspected to minimize the development of antibiotic resistance.

• What specific pathogen is the antibiotic intended to target? Different antibiotics have varying spectra of activity, making targeted selection crucial.

• What are the pharmacokinetic (PK) properties of the antibiotic, including absorption, distribution, metabolism, and excretion (ADME)?

• Does the antibiotic achieve adequate distribution to the site of infection (e.g., brain, lung, bone)? Consider the drug's ability to cross physiological barriers.

• Are there any organ impairments (renal, hepatic) or pregnancy considerations that may affect antibiotic selection or dosing?

• β-lactams and aminoglycosides are primarily excreted via the kidneys and typically have short half-lives ($t<br>ar{1/2}$), necessitating frequent dosing or continuous infusion.

• Macrolides and rifampicin are mainly metabolized by the liver, making them potentially problematic in patients with hepatic impairment.

Antibiotic Selection: Dosage and Regimen

When determining the appropriate dose and dosing regimen, several factors must be considered:

• The patient's overall condition (healthy adult, neonate, child, elderly) can significantly influence drug metabolism and clearance.

• Pre-existing organ impairment (renal, hepatic) can alter drug pharmacokinetics, requiring dosage adjustments.

• Augmented clearance, as seen in conditions like cystic fibrosis, septic shock, or burn patients, may necessitate higher doses to achieve therapeutic concentrations.

• Effective distribution to the site of infection is crucial. Some infections, such as meningitis, require antibiotics that can cross the blood-brain barrier.

• Knowledge of bacteria susceptibility is essential. Antibiotic choice should be guided by susceptibility testing (e.g., disk diffusion, MIC).

• The bacteria's growth rate can influence the effectiveness of different antibiotics. Rapidly dividing bacteria may be more susceptible to certain agents.

• The patient's immune system strength plays a role in bacterial eradication. Immunocompromised patients may require higher doses or more prolonged treatment courses.

• MIC (minimum inhibitory concentration) is a critical parameter. The antibiotic concentration should ideally exceed the MIC at the site of infection to ensure bacterial eradication.

Pharmacokinetics After Constant Infusion

Clearance (CL)

Clearance is a crucial parameter for determining the steady-state concentration during intravenous (IV) infusion at a constant rate.

• During constant IV infusion, the plasma concentration gradually increases, approaching a steady-state level ($C<br>ar{ss}$).

• At steady state, the rate of drug elimination from the body equals the rate of drug input, resulting in a stable plasma concentration.

$<br>C<br>ar{ss} = \frac{Rate}{CL}<br>$

Plasma Concentration Curve

• At steady-state: $Rate<br>ar{in} = Rate<br>ar{out}$

• $Rate<br>ar{out} = C \cdot CL$

• Concentration at steady-state: $C<br>ar{ss} = \frac{Rate<br>ar{in}}{CL}$

• It takes approximately 3.3 half-lives to reach 90% of the steady-state concentration.

• It takes one half-life to reach 50% of the steady-state concentration.

$<br>t<br>ar{1/2} = \frac{ln2 \cdot V}{CL}<br>$

Clearance (CL) and Repeated Dosing

• Average concentration at plateau with repeated dosing:

  • Intravenous administration:

$<br>C<br>ar{ss,average} = \frac{Dose}{\tau \cdot CL}<br>$

• Extravascular administration:

$<br>C<br>ar{ss,average} = \frac{F \cdot Dose}{\tau \cdot CL}<br>$

• $F$ = Bioavailability

• $\tau$ = Time interval between doses

• $C_{ss}$ = Plasma concentration at steady-state

Half-Life

• Half-life ($t ar{1/2}$) determines the time required to reach steady-state.

  • Approximately 3.3 half-lives are needed to reach 90% of steady state (ss).

• Maximum allowed time between doses:

  • $4 \times t<em>{1/2}$ reaches 94% of $C</em>{ss}$ plateau

Repeated Administration

• If the drug is not given every half-life, but with the same dose per administration:

  • Higher $C<br>ar{ss}$

  • Smaller fluctuations

  • Same time to ss

• If the same dose is given more frequently:

  • Lower $C<br>ar{ss}$

  • Larger fluctuations

  • Same time to ss

Dosage Regimens: Example

• Cefuroxime, $t ar{1/2} = 1.5$ h, MIC = 6 mg/L

  • Typical dose regimen: 1.5 g IV every 8 h ($\tau = 8$ h), three times daily.

    • Total daily dose = 4.5 g

To maintain concentrations above the MIC 100% of the time, consider the following strategies:

• Increasing the dose of the antibiotic.

• Shortening the dosing interval.

Repeated Dosing: Summary

• The average concentration at steady state ($C<br>ar{average}$) depends on the dose rate ($\frac{Dose}{\tau}$), clearance (CL), and bioavailability (F):

$<br>C<br>ar{ss,average} = \frac{F \times Dose}{\tau \times CL}<br>$

• Half-life ($t ar{1/2}$) is dependent on CL and V and determines:

  • Fluctuations in plasma concentration

  • Time to plateau (steady state)

$<br>t<br>ar{1/2} = ln2 \times \frac{V}{CL}<br>$

Loading Dose of CMS on Colistin PK

• CMS (colistimethate sodium) serves as a prodrug, converting to the active compound colistin. Different loading doses are administered at Time=0, followed by 240 mg (3MU) every 8 hours.

• $C<em>u = f</em>u \cdot C<em>p$, where $C</em>u$ represents unbound colistin concentrations and $C_p$ represents total colistin concentrations.

• Unbound concentrations ($C_u$) are the free, pharmacologically active form that drives bacterial killing.

Example Questions

A patient received vancomycin for a severe multi-resistant Staphylococcus infection, initiated with a continuous intravenous infusion.

The clearance (CL) of vancomycin was calculated as:

$<br>CL (L/h) = [0.689 \times 95 + 3.66] \times \frac{60}{1000} = 4.1 L/h<br>$

The half-life ($t<br>ar{1/2}$) was calculated as:

$<br>t<br>ar{1/2} (h) = \frac{ln2 \times V}{CL} = \frac{0.72 \times 75}{4.1} = 9 h<br>$

• If the vancomycin infusion rate was 2000 mg over 24 hours, would the steady-state plasma concentration fall within the target range of 15-25 mg/L?

• What was the concentration after one half-life?

• Was at least 90% of steady state reached during the 24-hour infusion period?

Variability in PK Between Patients

• High inter-patient variability in clearance is observed, often attributed to differences in kidney function (Glomerular Filtration Rate = GFR).

Therapeutic Window

To achieve optimal treatment outcomes:

• Achieve a satisfactory clinical response (e.g., resolution of infection).

• Minimize intolerable side effects.

• Ideally, all patients should have drug concentrations within the therapeutic window, necessitating individualized dosing strategies.

When to Individualize?

Individualization of drug therapy is particularly important when the drug exhibits:

• A narrow therapeutic window, where small changes in dose can lead to significant changes in effect or toxicity.

• High variability in PK and/or PD (pharmacodynamics) between patients, making it difficult to predict response based on standard dosing.

Causes of Variability

• Body size (mass) influences drug distribution and clearance.

• Liver enzyme activity affects drug metabolism.

• Kidney function influences drug excretion.

• Age-related changes in physiology affect PK/PD.

• Sex-related differences in body composition and hormone levels can impact drug disposition.

• Disease states (kidney, liver, circulation) can significantly alter PK/PD.

• Drug-drug interactions can affect drug metabolism, transport, or receptor binding.

• Lifestyle factors such as food, smoking, alcohol consumption, and overall lifestyle can contribute to variability.

• Random, unidentified causes may also play a role.

Individualizing Drug Treatment

Before treatment starts:

• Choice of drug: Select the most appropriate agent based on the patient and infection characteristics.

• Choice of formulation: Consider factors like bioavailability and route of administration.

• Choice of dose and dosing interval: Determine the initial dose and frequency based on patient-specific factors.

• Consider:

  • Weight

  • Age

  • Genotype: Genetic polymorphisms can affect drug metabolism and response.

  • Renal function

After treatment started:

• According to response: Monitor clinical and laboratory parameters to assess treatment efficacy.

• According to side effects: Adjust the dose to minimize adverse effects while maintaining therapeutic benefit.

• According to drug concentrations: Therapeutic drug monitoring (TDM) can help optimize dosing, especially for drugs with narrow therapeutic windows.

Relationships of Importance for Drug Therapy: PK/PD

• Pharmacokinetics (PK): Describes what the body does to the drug (ADME).

• Pharmacodynamics (PD): Describes what the drug does to the body (effects).

The Sigmoidal Emax Model (Hill Equation)

$<br>E = E*0 + \frac{E<em>{\max} \cdot C^{\gamma}}{EC</em>{50}^{\gamma} + C^{\gamma}}<br>$

Where:

• $E$ = Effect

• $E_0$ = Effect at zero concentration (baseline/placebo effect)

• $E_{\max}$ = Maximum effect of drug

• $C$ = Concentration

• $EC*{50}$ = Concentration at half of $E_{\max}$

• $\gamma$ = Hill (Slope) factor

The Importance of the Hill (Slope) Factor ($\gamma$)

• Low slope factor (e.g., = 1): Response is easily adjusted by changing the dose.

• High slope factor (e.g., = 5): Response can rapidly transition from no effect to full effect with small changes in concentration.

MIC (Minimum Inhibitory Concentration)

The lowest drug concentration that completely inhibits visible growth of bacteria.

Advantages:

• Overall (single) measure of antibiotic activity.

• Simple to determine, making it useful in clinical practice.

Drawbacks:

• Threshold value: Does not capture the full concentration-effect relationship.

• Summary measurement of growth and kill: Provides limited insight into the dynamics of bacterial killing.

• No dynamics - single time point.

• Poor precision.

• Low start inoculum.

Static Time-Kill Experiment

The simplest experimental setup for detailed characterization of PKPD, covering the full concentration-effect range.

PK/PD In Vivo: Animal Infection Model

Dose fractionation study for 24 hours, measuring CFU/organ (Colony Forming Unit).

The 3 PK/PD Indices

• $C_{\max}$/MIC

• AUC/MIC

• T>MIC

Where:

• $C_{\max}$ = highest (peak) concentration

• AUC = Area Under the Curve

• T = Time

PKPD Indices Examples

• Fluoroquinolones (levofloxacin): AUC/MIC is considered the 'best' predictor of response.

• Carbapenems (doripenem): fT>MIC demonstrates the highest correlation to response.

Where:

• f = "free", unbound drug

• $C<em>u = f</em>u \cdot C$

PKPD Indices: Traditional Classification

• $C_{\max}$/MIC:

  • E.g., Aminoglycosides (gentamicin), daptomycin, fluoroquinolones

• AUC/MIC:

  • E.g., Aminoglycosides (gentamicin), daptomycin, fluoroquinolones, tetracyclines, macrolides

• Time (T) > MIC, e.g., 50% or 80% of the dosing intervals:

  • E.g., Penicillins, cephalosporins, carbapenems

Example Exam Questions

1. The PK/PD of lefamulin was studied in thigh-infected neutropenic mice where the cfu counts were determined 24h after the first dose was given. The results for Streptococcus pneumoniae are shown below. Which of the three indices demonstrate the best correlation? A motivation is required in your response.

2. At 24h, the maximum observed log cfu/thigh count was approximately 8.5 log10 (see figure above) What was the minimum count observed? Assuming this is the maximum kill that can be achieved, what is the approximate Emax of the drug in this animal model?

3. The patient that was treated for severe multi-resistant Staphylococcus infection with i.v. vancomycin changed treatment to a fluoroquinolone orally. The fluoroquinolone has, in the average patient, a CL of 33L/h and a bioavailability of 65 % The fluoroquinolone was given orally as tablets, 600 mg twice daily.

   • What total exposure (AUC), during 24 hours is expected with this administration?

   • The best PK/PD index for this antibiotic is AUC/MIC. If a 24-h AUC/MIC of 50 is aimed for and MIC is 0.5 mg/L, was this target AUC/MIC reached with the treatment?

Additional Example Exam Questions

• The risk of dizziness as a side effect of the fluoroquinolone treatment can be expressed as a function of average concentration of the antibiotic. What was the average plasma concentration of the antibiotic during the oral treatment?

• If the risk of side effect is expressed as an Emax function with Emax = 100 % and EC50 for risk = 5 mg/L, what was the risk of dizziness during the oral treatment?

MIC Neglecting Time-Course of Bacteria Kill

The Same CFU/ml at 24 hours. What about the Immune system?

Adaptive Resistance of Gentamicin

Same “dose” – lower effect due to the drug disappearing with a $t<br>ar{1/2}$ mimicking patient PK

Adaptive Resistance

• Emerges typically at the administration of the first dose

• Underlying mechanism can be a reversible down regulation of the active transport of antibiotic into the bacteria

• Phenotypic, not genetic resistance

PAE (Post-Antibiotic Effects)

Persistent suppression of bacterial growth after antimicrobial exposure

MPC (Mutant Preventive Concentration)

The concentration threshold at which the least susceptible bacteria present in a population of $10^{10}$ susceptible cells are inhibited. MSW (Mutant selective window)

Optimization of Dosing Strategies

Traditional:

• MIC

• PK/PD indices

Pharmacometrics (PKPD modeling):

• Time courses of effects

• Resistance

• Time-varying drug concentrations

• Drug combinations

• Test “what-if” scenarios

Simulate Bacterial Count Profiles

Based on allometric scaling of PK. Examples with Aminoglycoside with adaptive resistance

Integrating Pre-clinical and Clinical PK Studies

To arrive at a good dosing strategy

Summary

Dose and Dose frequency depend on Pharmacokinetics and Pharmacodynamics. PK/PD indices, combined with human PK, are central in suggesting the human dose for antibiotics

Self-Assessment Questions

• How are PKPD-relationships often described? What is a (sigmoid) Emax-model?

• What is a therapeutic window?

• Which factors influence variability in PK?

• What is steady-state? What is influencing the level and time to steady-state?

• How can we individualize drug treatment?

• How are PK/PD indices defined? Which are the three commonly used PK/PD indices? How do you define the PK/PD target?

• What is PAE, MPE, MSW?