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Mechanism-based pharmacokinetic–pharmacodynamic modeling of antimicrobial drug effects

  • Czock
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Abstract

Mathematical modeling of drug effects maximizes the information gained from an experiment, provides further insight into the mechanisms of drug effects, and allows for simulations in order to design studies or even to derive clinical treatment strategies. We reviewed modeling of antimicrobial drug effects and show that most of the published mathematical models can be derived from one common mechanism-based PK–PD model premised on cell growth and cell killing processes. The general sigmoid Emax model applies to cell killing and the various parameters can be related to common pharmacodynamics, which enabled us to synthesize and compare the different parameter estimates for a total of 24 antimicrobial drugs from published literature. Furthermore, the common model allows the parameters of these models to be related to the MIC and to a common set of PK–PD indices. Theoretically, a high Hill coefficient and a low maximum kill rate indicate so-called time-dependent antimicrobial effects, whereas a low Hill coefficient and a high maximum kill rate indicate so-called concentration-dependent effects, as illustrated in the garenoxacin and meropenem examples. Finally, a new equation predicting the time to microorganism eradication after repeated drug doses was derived that is based on the area under the kill-rate curve.

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Abbreviations

Abbreviation :

Name (Unit)

AUC:

Area under the concentration-time curve (h · μg/ml)

AUETC:

Area under the effect-time curve (None)

C :

Drug concentration (μg/ml)

CFU:

Colony forming unit (None)

C max :

Maximum concentration (μg/ml)

C stat :

Stationary concentration (μg/ml)

EC50 :

Concentration where the half-maximum effect is present (μg/ml)

E d(C):

Fractional increase in the death rate depending on concentration (None)

E max :

Maximal stimulation of the death rate (None)

E r(C):

Fractional decrease in the replication rate depending on concentration (None)

H :

Hill coefficient (None)

IC50 :

Concentration where the half-maximum effect is present (μg/ml)

I max :

Maximum inhibition of the replication rate (None)

k death0 :

Death-rate constant (without drug) (h−1)

k death(C):

Death rate depending on concentration (h−1)

k e :

Elimination rate constant (h−1)

k growth0 :

Growth-rate constant (without drug) (h−1)

k growth(N):

Growth-rate depending on microorganism number (h−1)

k kill(C):

Kill rate depending on concentration (h−1)

k kill(t):

Kill rate depending on time (h−1)

k kill max :

Maximum kill rate (h−1)

k replic0 :

Replication-rate constant (without drug) (h−1)

k replic(N):

Replication-rate depending on microorganism number (h−1)

k replic max :

Maximum replication rate (h−1)

MIC:

Minimum inhibitory concentration (μg/ml)

N :

Number of microorganisms (CFU/ml)

N 0 :

Initial number of microorganisms (CFU/ml)

N t :

Number of microorganisms at time t (CFU/ml)

N τ :

Number of microorganisms after one dosing interval (CFU/ml)

N 50 :

Number of microorganisms at which the replication rate is half maximal (CFU/ml)

N max :

Maximum number of microorganisms (CFU/ml)

t :

Time (h)

T >MIC :

Time above MIC (h)

TE:

Time to microorganism eradication (h)

τ :

Dosing interval (h)

VGmax :

Maximum velocity of bacterial replication (h−1 · CFU/ml)

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  1. Division of Nephrology, Medical Department, University Hospital Ulm, Robert-Koch-Str. 8, 89081, Ulm, Germany

    David Czock & Frieder Keller

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  1. David Czock
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  2. Frieder Keller
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Correspondence to David Czock.

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Czock, D., Keller, F. Mechanism-based pharmacokinetic–pharmacodynamic modeling of antimicrobial drug effects. J Pharmacokinet Pharmacodyn 34, 727–751 (2007). https://doi.org/10.1007/s10928-007-9069-x

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