Pharmacokinetics, Pharmacodynamics, and Monte Carlo Simulation EDITORIAL BOARD Co-Editors: Margaret C

® CONCISE REVIEWS OF PEDIATRIC INFECTIOUS DISEASES

CONTENTS Pharmacokinetics, Pharmacodynamics, and Monte Carlo Simulation EDITORIAL BOARD Co-Editors: Margaret C. Fisher, MD, and Gary D. Overturf, MD Editors for this Issue: John S. Bradley, MD Board Members Michael Cappello, MD Charles T. Leach, MD Geoffrey A. Weinberg, MD Ellen G. Chadwick, MD Kathleen McGann, MD Leonard Weiner, MD Janet A. Englund, MD Jennifer Read, MD Charles R. Woods, MD Leonard R. Krilov, MD Jeffrey R. Starke, MD

Pharmacokinetics, Pharmacodynamics, and Monte Carlo Simulation Selecting the Best Antimicrobial Dose to Treat an Infection

John S. Bradley, MD,*† Samira Merali Garonzik, PharmD,‡§ Alan Forrest, PharmD,‡§ and Sujata M. Bhavnani, PharmD, MS‡§

Key Words: Monte Carlo simulation, toxicity and the development of antimicro- failure will be different than in children with antimicrobial, pharmacokinetic, pharmacodynamics bial resistance. normal renal function. Data from popula- (Pediatr Infect Dis J 2010;29: 1043–1046) tions with organ failure are becoming more VARIABILITY IN PLASMA AND widely available, increasing our knowledge of the variability of drug elimination among hen faced with a neonate, infant, or TISSUE CONCENTRATIONS ACROSS POPULATIONS those populations. The description of the Wchild with a suspected infection, the statistical characteristics of the variability of clinician must select a specific antimicrobial Given the availability of sensitive as- antimicrobial concentrations across carefully at a specific dose for a specific duration to says to measure antibiotic concentrations in defined populations is known as “population treat that infection. Many issues require care- plasma and various tissue sites using smaller pharmacokinetics.” ful consideration, and include knowledge of quantities of blood or tissue fluids, our abil- the suspected pathogens and their suscepti- ity to assess antibiotic exposures at the tissue bility to the antimicrobials under consider- level, the actual site of infection, has in- PHARMACODYNAMICS ation, the pharmacokinetic (PK) characteris- creased. As regulatory agencies request more Our understanding of how antimicro- tics of the antimicrobials, and the clinician’s sophisticated antimicrobial exposure data for bial agents eradicate bacteria has also in- assessment of the need to achieve a cure for investigational drugs, these data are fre- creased. The relationship between the anti- that particular patient (Table 1). PK and quently collected in clinical trials and thus, microbial concentrations required at the pharmacodynamics (PD) principles together are becoming more readily available for infection site over the dosing interval to with Monte Carlo simulation can assist the analysis. As a result, our knowledge of the eradicate a pathogen and hence, achieve a 3 clinician in selecting the appropriate antimi- PK of antimicrobials (ie, concentrations in cure, is known as pharmacodynamics. crobial and dosing regimen.1 Recent ad- plasma and in different tissue sites over time) These defined exposures, indexed to the min- vances in our understanding of antimicrobial and the variability inherent between patients imum inhibitory concentration (MIC) of the PK and PD have lead to important insights in receiving the same antimicrobial agent is antimicrobial to that pathogen, have been the parameters associated with a successful better understood. Both the distribution of used to evaluate the PK-PD measure that outcome, and in ways to minimize both drug antimicrobials within tissue compartments best describes antimicrobial activity for that and drug elimination differs by pediatric age particular antimicrobial/pathogen pair. The 3 group “populations,” from the neonate to the most common PK-PD measures associated From the *University of California, San Diego, CA; adolescent. Fortunately, antimicrobial PK with efficacy are (1) the percent of the dosing †Rady Children’s Hospital San Diego, San Diego, and variability in each pediatric “population” interval that a drug concentration remains CA; ‡State University of New York at Buffalo, can also be described.2 Children with organ above the MIC (%T Ͼ MIC); (2) the ratio of Buffalo, NY; and §Institute for Clinical Pharma- dysfunction may not eliminate antimicrobi- the maximal drug concentration to the MIC codynamics, Albany, NY. Copyright © 2010 by Lippincott Williams & Wilkins als as effectively as those with normal organ (Cmax:MIC); and (3) the ratio of the area ISSN: 0891-3668/10/2911-1043 function. For example, the PK of vancomy- under the drug concentration-versus-time DOI: 10.1097/INF.0b013e3181f42a53 cin in children with some degree of renal curve (AUC) to the MIC (AUC:MIC).

The Concise Reviews of Pediatric Infectious Diseases (CRPIDS) topics, authors, and contents are chosen and approved indepen- dently by the Editorial Board of CRPIDS.

The Pediatric Infectious Disease Journal • Volume 29, Number 11, November 2010 www.pidj.com | 1043 Concise Reviews The Pediatric Infectious Disease Journal • Volume 29, Number 11, November 2010

TABLE 1. Considerations in Antimicrobial Management of the Infected Child

Patient-specific Site(s) of infection Consideration for how important it is to cure the infection (eg what risk is the clinician willing to accept for treatment failure) Patient-specific plasma antimicrobial concentrations over time Patient-specific tissue site antimicrobial concentrations over time Pathogen-specific Documented or suspected pathogen(s) Susceptibility of pathogen(s) (if cultures are positive) Variability of the susceptibilities of pathogen(s) in specimens collected in the population of children being treated, if therapy is empiric Antibiotic-specific Antibacterial spectrum of activity Antibiotic tissue penetration characteristics Variability of antimicrobial plasma and tissue concentrations over time among children in the population being treated Antimicrobial pharmacodynamics Treatment-specific Size of dose (mg/kg) Frequency of dosing Duration of dosing

For aminoglycosides (eg, gentami- have the ability to acquire mechanisms of PK-PD target. The clinician compares the cin) and fluoroquinolones (eg, ciprofloxa- resistance from other bacteria. For a popula- proportion of simulated children predicted to cin), the PK-PD measure that is most pre- tion of children who are all treated for the be cured with the proportion desired to be dictive of efficacy is one for which same infection, otitis media for example, a cured (eg, 95% of children treated for pneu- bactericidal activity is concentration-de- range of susceptibilities of otitis pathogens to mococcal pneumonia should be cured when pendent (Cmax:MIC for gentamicin, and each antimicrobial can be described. Pub- treated). Such an analysis allows the clini- AUC:MIC for ciprofloxacin). In contrast, lished data are available on the susceptibility cian to understand, given the variability in amoxicillin and other beta-lactam agents of Streptococcus pneumoniae causing ear in- the inputs, the statistical likelihood of demonstrate a time-dependent pattern of fections in children from Kentucky to Costa achieving a cure for a particular child using a bactericidal activity (%T Ͼ MIC).4 There- Rica, to Israel.5–7 These data assist us in particular dosing regimen. fore, when fluoroquinolone concentrations predicting how likely an infecting pathogen To illustrate this concept, one can ex- increase, the rate and extent of bacterial erad- will be susceptible to each of several differ- amine amoxicillin treatment of pneumococ- ication will increase. For amoxicillin, maxi- ent antimicrobials we are considering for cal pneumonia. A cure is expected if amoxi- mal bacterial eradication occurs when infec- therapy. This variability in bacterial suscep- cillin concentrations are present in lung tion site concentrations exceed the MIC for tibility to specific agents can be described tissue (epithelial lining fluid) at concentra- approximately 40% of the dosing interval. and tracked as it changes over time, provid- tions above the MIC of the infecting pneu- Eradication rates do not further increase as ing the clinician with an accurate and ongo- mococcus for approximately 40% of the dos- the amoxicillin concentration at the infection ing assessment of the likelihood of drug ing interval.8 Assuming a child is infected by site increases or as the percent of time that resistance. The distribution of MIC values a relatively resistant strain demonstrating an the amoxicillin concentration is present at for specified pathogens, considered together MIC of 2.0 mcg/mL, if the child is treated the infection site above the MIC, increases with the distribution of antimicrobial expo- with 90 mg/kg/d divided into 2 doses, then beyond 40%. For each antimicrobial/patho- sure in the population of children all given only 65% of children will achieve the PK-PD gen pair, the degree of exposure described by the same antimicrobial dose, is used in the target associated with cure; if 90 mg/kg/d is the PK-PD measure, that is associated with a Monte Carlo simulation to evaluate the prob- given, but divided into 3 doses (increasing positive outcome (eg, cure), is commonly ability of achieving a cure at that dose. the duration that amoxicillin is present in referred to as the “PK-PD target.” This can lung tissue), the chance of achieving the most easily be evaluated in a nonclinical COMPUTER MODELING AND PK-PD target increases to about 90%. To system (eg, in vitro or animal infection mod- MONTE CARLO SIMULATION achieve a 95% likelihood of cure in this els), but is increasingly being assessed in Monte Carlo simulation provides a child, a dose of about 100 mg/kg/d divided human clinical trials. In other words, one can computer-based mathematical construct that into 3 doses will be required. If pneumococ- now demonstrate for a patient infected by a can simultaneously integrate different vari- cal resistance to amoxicillin increases to 4.0 particular organism and treated with a par- ables such as tissue concentrations of an mcg/mL, the percent of children who ticular antimicrobial, the magnitude, shape, antibiotic and antimicrobial susceptibility, achieve the desired target will decrease, and and duration of antimicrobial exposure that each with its own probability distribution, the dose of amoxicillin will need to be in- is likely to result in a cure. together with information about the PK-PD creased further to achieve the goal of 95% measure associated with efficacy, to estimate cure. On the other hand, if resistance de- STATISTICAL DESCRIPTION OF the likelihood of achieving the PK-PD target creases to 0.5 mcg/mL, then an overwhelm- ANTIMICROBIAL RESISTANCE (and thus, the likelihood of achieving cure). ing 99.6% of children given 90 mg/kg/d in 2 Antimicrobial resistance is an increas- With these data inputs, antimicrobial expo- doses will achieve the PK-PD target associ- ing problem. Certain bacterial species con- sures associated with a particular dosing reg- ated with cure. The Figure 1 illustrates a tain intrinsic resistance mechanisms that are imen for a virtual population of children Monte Carlo simulation using one of many induced as we apply antimicrobial pressure; (often 5000, but any number can be selected) different software programs (Oracle Crystal other species have the ability to mutate can be simulated, determining the proportion Ball, version 11.1.1.30, Oracle Corporation). quickly to develop resistance while others of infected children expected to achieve the In this illustration, a 30 mg/kg dose of am-

FIGURE 1. Distribution of free-drug % T Ͼ MIC for ampicillin 30 mg/kg administered IV every 8 hours among 5000 simulated pediatric patients infected by a relatively resistant population of pneumococci.

picillin is given intravenously to a child in a ANTIMICROBIAL STEWARDSHIP more likely to fail treatment, whereas those population of otherwise healthy children. Minimizing antimicrobial resistance whose exposures are above a certain PK-PD 12 The serum concentrations over time after a by using the most appropriate dosing regi- target, are more likely to be cured. While single dose are evaluated against a collection men for the most appropriate duration is a limited data exist for children treated for 13,14 of pneumococci isolated during an era of priority.11 While lowering the dose of an otitis media, no data yet exist for inva- relative resistance, with approximately 20% antimicrobial may save a healthcare system sive infections such as pneumonia, meningi- of strains having an MIC of 2.0 mcg/mL or funds and decrease dose-dependent toxicity, tis, or osteomyelitis. As one might expect, greater, but most being susceptible at 0.06 it may ultimately lead to increased resis- prospective studies would require appropri- mcg/mL. The blue-shaded areas denote the tance, and thus, more difficult-to-treat infec- ate plasma and tissue site antimicrobial con- proportion of children who will achieve se- tions that require more costly and toxic centration profiling for the population stud- rum concentrations that are above the MICs antimicrobials. Prospective data on the dura- ied, together with confirmation of bacterial noted in the population of pneumococci, for tion of therapy required to achieve cure with- etiology and antimicrobial susceptibility test- 40% or more of an 8 hour dosing interval out relapse is an area of great importance for ing. Furthermore, a study design using as- (3.2 hours). In this simulation of 5000 virtual future research. Some orally administered cending doses, in which doses and resulting children, 88% given this dose will achieve beta-lactam antimicrobials are Food and exposures straddle the drug exposure “break- this PK-PD target and be expected experi- Drug Administration-approved for a 5-day point” associated with efficacy (eg, exposures ence a cure. One can also calculate the dose treatment course of streptococcal pharyngi- below which patients fail and above which, that would be required to achieve a cure in tis. It seems logical that most beta-lactams they are cured), is inherently unethical to per- 95% of children, by either increasing the that display similar PK-PD measures and form in children. Pediatric investigators and mg/kg dose, or by dividing the total daily tissue penetration characteristics should also human research committees would not know- dose into more frequent intervals. be prescribed for no more than 5 days. How- ingly administer a dose of antimicrobial to a Similarly, in treating a child with ever, prospectively collected data on the ef- child that is likely to fail. For the moment, streptococcal pharyngitis, given the high de- ficacy of a 5-day treatment course for strep- animal studies remain the most widely avail- gree of susceptibility of Streptococcus pyo- tococcal pharyngitis for each and every able in vivo support to validate the outcomes of genes to penicillins, once daily dose of penicillin and cephalosporin antimicrobial Monte Carlo simulation. amoxicillin at 50 mg/kg predicted a tonsillar are not available, and for generic antibiotics, Additional PK data that provide rele- antimicrobial exposure that would result in such studies are not likely to be performed. vant tissue concentration values are needed an approximately 95% of children achieving for a wide variety of infections. For some the targeted exposure for cure.9,10 In addition infections such as staphylococcal pneumo- to predicting targets for antimicrobial/patho- FUTURE DIRECTIONS nia, multiple tissue sites of infection require gen pairs for bacterial infections, population Human validation of these concepts step-wise modeling, with each subsequent PK and PK-PD relationships have been ex- has lagged far behind their creation. Data step integrating PK data from each of the plored for antimicrobial agents for tubercu- from in vitro systems and animal models different potential intrathoracic infection losis, as well as for anti-infective agents for validate the concepts, and limited retrospec- sites (eg, pneumonia, empyema, lung ab- fungal and viral infections, thus permitting tive data in adults with invasive infections scess, and necrotic pulmonary tissue) to ac- similar evaluations of dosing regimens using such as pneumonia have demonstrated that, count for all the sites of antimicrobial expo- Monte Carlo simulation, as described above. below a certain drug exposure, patients are sure. Another complexity that is difficult to

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