Conceived and designed the experiments: VHT MN. Performed the experiments: VHT. Analyzed the data: VHT MN. Contributed reagents/materials/analysis tools: MN. Wrote the paper: VHT.
Vincent H. Tam has received unrestricted research grants from Achaogen, AstraZeneca and Merck. He has also received speaking honoraria from Merck. Michael Nikolaou: none to declare.
Pharmacodynamic modeling has been increasingly used as a decision support tool to guide dosing regimen selection, both in the drug development and clinical settings. Killing by antimicrobial agents has been traditionally classified categorically as concentration-dependent (which would favor less fractionating regimens) or time-dependent (for which more frequent dosing is preferred). While intuitive and useful to explain empiric data, a more informative approach is necessary to provide a robust assessment of pharmacodynamic profiles in situations other than the extremes of the spectrum (e.g., agents which exhibit partial concentration-dependent killing). A quantitative approach to describe the interaction of an antimicrobial agent and a pathogen is proposed to fill this unmet need. A hypothetic antimicrobial agent with linear pharmacokinetics is used for illustrative purposes. A non-linear functional form (sigmoid Emax) of killing consisted of 3 parameters is used. Using different parameter values in conjunction with the relative growth rate of the pathogen and antimicrobial agent concentration ranges, various conventional pharmacodynamic surrogate indices (e.g., AUC/MIC, Cmax/MIC, %T>MIC) could be satisfactorily linked to outcomes. In addition, the dosing intensity represented by the average kill rate of a dosing regimen can be derived, which could be used for quantitative comparison. The relevance of our approach is further supported by experimental data from our previous investigations using a variety of gram-negative bacteria and antimicrobial agents (moxifloxacin, levofloxacin, gentamicin, amikacin and meropenem). The pharmacodynamic profiles of a wide range of antimicrobial agents can be assessed by a more flexible computational tool to support dosing selection.
Antimicrobial agents have been the mainstay of treatment for a variety of infectious diseases such as urinary tract infections and pneumonia. Due to the increasing incidence of antimicrobial resistance, there is an ever demanding need to develop new antimicrobial agents rapidly. These agents can be given in different ways, both in terms of the daily dose and dosing frequency. The traditional approach to the design of antimicrobial agent dosing regimen relies primarily on a categorical classification, which often could be restrictive. We proposed a new computational method to provide quantitative insights to the interaction between an antimicrobial agent and a pathogen (pharmacodynamics). With a more robust understanding of this relationship, the effectiveness of different antimicrobial dosing regimens can be compared efficiently, which would facilitate new agent development by rationally guiding dosing regimen selection. The relevance of our approach was supported by a series of experimental validation using different antimicrobial agents and bacteria. A higher probability of resistance suppression could be achieved with optimal dosing regimens, which may prolong the clinical utility of new agents under development.
Microbial resistance is rising at an alarming rate, rendering many antimicrobial agents ineffective. There is an ever demanding need to develop new antimicrobial agents and optimize available agents to curb the rising resistance prevalence. There are experimental and clinical evidence that dosing exposure could have an impact on patient outcomes and the development of resistance
Microbial killing by unbound antimicrobial agents has been traditionally classified categorically as concentration-dependent or time-dependent. The pharmacodynamics of many antimicrobial agents are well accepted to be linked to surrogate indices such as peak concentration (Cmax)/minimum inhibitory concentration (MIC), area under the concentration-time profile (AUC)/MIC or the proportion of dosing interval in which the concentration is above the MIC (%T>MIC)
While the dose fractionation design is intuitive and commonly used, there may be situations where such a categorical approach to pharmacodynamic assessment is overly restrictive. It is especially so with new drugs (or drug classes) with complex pharmacokinetics and pharmacodynamics. We propose an alternative approach to pharmacodynamic characterization of the interaction between an antimicrobial agent and a pathogen. Instead of relying on time-dependent endpoints such as Cmax or MIC, the time course of a bacterial population when subjected to an antimicrobial agent exposure is captured by a dynamic mathematical model. The advantages of such a modeling approach have been reviewed previously
A hypothetic drug is used for illustrative purposes. The pharmacokinetics of this drug is linear and characterized by a one-compartment intravenous bolus model. The volume of distribution of this drug is 20 liters, with an elimination half-life of 1 hour and negligible protein binding. A daily dose of 6000 mg can be given once daily (6000 mg q24h), twice daily (3000 mg q12h) or 4 times daily (1500 mg q6h). The respective serum concentration-time profiles and exposures achieved are as shown in
Dosing regimen | Cmax (mg/l) | AUC24 (mg.h/l) | % T>4mg/l |
6000 mg q24h | 300 | 433 | 25 |
3000 mg q12h | 150 | 433 | 42 |
1500 mg q6h | 75 | 433 | 67 |
Note: AUC24 may not be identical in drugs with an elimination half-life of ≥4 hours. The discrepancy is due residual drug at the end of the 24 hour period, which is more prominent with a drug of long half-life. One simple way to circumvent the discrepancy is to focus on AUC 0–infinity (total cumulative exposure) instead of AUC 0–24.
Details of the experimental setup have been reported previously
The saturable killing rate of an antimicrobial agent is characterized by a sigmoid Emax model, commonly used in many investigations
The average kill rate can be used quantitatively to compare the effectiveness of various dosing regimens, in relation to the growth rate of the target pathogen. This approach assumes eradication of the bacterial population cannot be achieved within one dosing interval; a large killing rate shortly after dose administration is as important as a large killing rate towards the end of the dosing interval. The importance of the average kill rate (
Using the same structural form, three typical pharmacodynamic profiles can be shown (
In
In
An important point should be raised here. The above example is illustrated with only one daily dose (6000 mg daily). Using a qualitative (yes / no) outcome assessment (e.g., mortality, clinical cure, resistance suppression), different categorical interpretations may be arrived at with the same pharmacodynamic profile. To further exemplify this point, the average kill rate is graphed as a function of both daily dose and dosing interval, using a 3-dimensional surface response as detailed previously
Finally in
In all 3 typical pharmacodynamic profiles described, the same structural form of killing rate was used (a sigmoid Emax model). Different profiles were simply reflected in the values of the model parameters, which could be derived from actual experimental data observed between an antimicrobial agent and a pathogen within a short timeframe (e.g., 24 hours). Of note, knowledge of specific mechanism(s) of resistance was not necessary as inputs. As shown above, an antimicrobial agent can be shown to exhibit both concentration and time-dependent killing, but the proposed model was flexible enough to describe different distinct pharmacodynamic profiles (and any intermediates in between).
Antimicrobial kill kinetics has been previously examined using a related approach. In one study, concentration dependency of bacterial killing was primarily attributed to the sigmoidicity constant (i.e.,
To extend these pharmacodynamic concepts previously reviewed, we put forth herein a novel concept to derive the dosing intensity of a dosing regimen by comparing the average killing rate to the growth rate of the target pathogen. A similar approach was proposed in linking pharmacokinetics to drug effects in circular / proliferative systems using the concept of reproduction minimum inhibitory concentration (RMIC) and equivalent effective constant concentration (ECC)
We believe our proposed approach would enhance the applicability of these concepts in drug development and clinical settings. Specifically, the pharmacodynamics of antimicrobial agents are characterized as a continuum (as opposed to discrete categories), allowing relatively simple numeric computational methods to be applied. The efficiency to objectively compare the effectiveness of a large number of dosing regimens (to be investigated in pre-clinical or clinical studies) would be improved as a result. Furthermore, we have also justified our rationale using supportive data derived under more clinically relevant experimental conditions (multiple sets of experimental data involving fluctuating drug concentrations over at least 72 hours, as shown in
Bacteria | ||||
Drug | Levofloxacin | Gentamicin | Amikacin | Meropenem |
Design | Similar AUC24/MIC (45 and 10); q24h vs q12h | Similar AUC24/MIC (40); q24h vs q8h | Similar AUC24/MIC (72); q24h vs q8h | Similar Cmax/MIC (64) q8h; Cmin/MIC 6 vs 2 |
Results | q24h similar to q12h at both AUC24/MIC; AUC24/MIC 10 failed to suppress resistance development; AUC24/MIC 45 suppressed resistance development | q24h similar to q8h; both regimens failed to suppress resistance development | q24h superior to q8h in suppressing resistance development | Cmin/MIC 6 superior to 2 in suppressing resistance development |
Categorical interpretation | AUC/MIC most important | AUC/MIC most important | Cmax/MIC most important | AUC/MIC or Cmin/MIC most important |
Reference | Unpublished data |
In this study, the mathematical model used was to characterize the behavior of a heterogeneous bacterial inoculum, which consists of multiple sub-populations associated with different susceptibility. This modeling approach (involving a time-variant parameter to account for adaptation of the bacterial population) would enable us to better capture regrowth and / or emergence of resistance over time. Nonetheless, the mathematical model is flexible and can be modified easily to accommodate a homogeneous inoculum by not allowing
In summary, pharmacodynamic modeling is an important decision-support tool to guide the selection of dosing regimens. The use of surrogate pharmacodynamic indices has taught us much on the differences in the killing profiles of different antimicrobial agents, resulting in several rational dosing strategies to optimize patient outcomes. As we are dealing with drugs with more complex pharmacokinetics and pharmacodynamics, it is also clear that using simple surrogate pharmacodynamic indices may not always be informative enough to make good decisions to dosing selection. In the interest of further accelerating new drug development and for the benefits of our patients, alternative modeling and computational approaches, such as the one proposed herein should be explored.