DDMoRe Model Repository

Overview
Files
History
Model Definition
Estimation Steps

Short description:

PKPD model for ciprofloxacin

Format:	PharmML (0.6.1)
Related Publication:	A mechanism-based pharmacokinetic/pharmacodynamic model allows prediction of antibiotic killing from MIC values for WT and mutants David Khan, Pernilla Lagerbäck, Sha Cao, Ulrika Lustig, Elisabet I. Nielsen, Otto Cars, Diarmaid Hughes, Dan I. Andersson, Lena E. Friberg J Antimicrob Chemother, 11/2015 Affiliation: Uppsala University Abstract: OBJECTIVES: In silico pharmacokinetic/pharmacodynamic (PK/PD) models can be developed based on data from in vitro time-kill experiments and can provide valuable information to guide dosing of antibiotics. The aim was to develop a mechanism-based in silico model that can describe in vitro time-kill experiments of Escherichia coli MG1655 WT and six isogenic mutants exposed to ciprofloxacin and to identify relationships that may be used to simplify future characterizations in a similar setting. METHODS: In this study, we developed a mechanism-based PK/PD model describing killing kinetics for E. coli following exposure to ciprofloxacin. WT and six well-characterized mutants, with one to four clinically relevant resistance mutations each, were exposed to a wide range of static ciprofloxacin concentrations. RESULTS: The developed model includes susceptible growing bacteria, less susceptible (pre-existing resistant) growing bacteria, non-susceptible non-growing bacteria and non-colony-forming non-growing bacteria. The non-colony-forming state was likely due to formation of filaments and was needed to describe data close to the MIC. A common model structure with different potency for bacterial killing (EC50) for each strain successfully characterized the time-kill curves for both WT and the six E. coli mutants. CONCLUSIONS: The model-derived mutant-specific EC50 estimates were highly correlated (r(2)?=?0.99) with the experimentally determined MICs, implying that the in vitro time-kill profile of a mutant strain is reasonably well predictable by the MIC alone based on the model.
Contributors:	David Khan

Context of model development:	Mechanistic Understanding;
Discrepancy between implemented model and original publication:	M3, B2, MTIME and L2 not included in mdl file. ;
Long technical model description:	PKPD model for ciprofloxacin;
Model compliance with original publication:	Yes;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	PKPD model for ciprofloxacin;
Modelling task in scope:	estimation;
Nature of research:	In vitro;
Therapeutic/disease area:	Anti-infectives;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- executeable_cipro.xml

Additional Files

Model owner: David Khan
Submitted: Oct 13, 2016 1:01:54 AM
Last Modified: Oct 13, 2016 1:01:54 AM

Revisions

Version: 11
- Submitted on: Oct 13, 2016 1:01:54 AM
- Submitted by: David Khan
- With comment: Edited model metadata online.

Independent variable T

Function Definitions

additiveError (additive) = additive

Structural Model sm

Variable definitions

SUS_RES1 = (PROPC \times (((((SUS1 + RES1) + SUS2) + NON1) + RES2) + NON2))

SUS_RES2 = SUS_RES1

RES_SUS1 = 0

RES_SUS2 = 0

DRUGS1 = {\begin{matrix} \frac{(EMAX \times {CAB}^{GAM})}{({EC50_1}^{GAM} + {CAB}^{GAM})} & if & (CAB > 1.0E-11) \\ 0 & otherwise \end{matrix}

DRUGS2 = {\begin{matrix} \frac{(EMAX \times {CAB}^{GAM})}{({EC50_2}^{GAM} + {CAB}^{GAM})} & if & (CAB > 1.0E-11) \\ 0 & otherwise \end{matrix}

FLAG = {\begin{matrix} 1 & if & (T < KSNC_TIME) \\ 0 & otherwise \end{matrix}

\frac{dSUS1}{dT} = ((((((KGS1 \times SUS1) - ((KK + DRUGS1) \times SUS1)) - (SUS_RES1 \times SUS1)) + (RES_SUS1 \times RES1)) + (KNCS1 \times NON1)) - ((KSNC1 \times SUS1) \times FLAG))

\frac{dRES1}{dT} = (((- KK \times RES1) + (SUS_RES1 \times SUS1)) - (RES_SUS1 \times RES1))

\frac{dSUS2}{dT} = ((((((KGS2 \times SUS2) - ((KK + DRUGS2) \times SUS2)) - (SUS_RES2 \times SUS2)) + (RES_SUS2 \times RES2)) + (KNCS2 \times NON2)) - ((KSNC2 \times SUS2) \times FLAG))

\frac{dNON1}{dT} = ((((KSNC1 \times SUS1) \times FLAG) - (KNCS1 \times NON1)) - ((KK + DRUGS1) \times NON1))

\frac{dRES2}{dT} = ((- KK \times RES2) + (SUS_RES2 \times SUS2))

\frac{dNON2}{dT} = ((((KSNC2 \times SUS2) \times FLAG) - (KNCS2 \times NON2)) - ((KK + DRUGS2) \times NON2))

ATOT = (((SUS1 + RES1) + SUS2) + RES2)

LN_ATOT = log ((ATOT + 1.0E-8))

Initial conditions

SUS1 = SUS1_INIT

RES1 = 0

SUS2 = SUS2_INIT

NON1 = 0

RES2 = 0

NON2 = 0

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Covariate Model

Continuous covariate STR

Continuous covariate CAB

Continuous covariate BASE

Parameter Model

Parameters

POP_KGS1

;

POP_KK

;

POP_EMAX

;

POP_EC50_202

;

POP_GAM

;

POP_PROPC

;

POP_KGS2

;

POP_EC50_2

;

POP_MUT

;

POP_KSNC_MAX

;

POP_SFNCS

;

POP_HILL

;

POP_TR50

;

POP_KSNC_TIME

;

RUV_ADD

;

log_k = 10

;

EPS_Y \sim N (0.0, 1.0)

— DV

KGS1 = POP_KGS1

KK = POP_KK

EMAX = POP_EMAX

EC50_1 = POP_EC50_202

GAM = POP_GAM

PROPC = (POP_PROPC \times 1.0E-7)

SBASE = exp (BASE)

KGS2 = POP_KGS2

EC50_2 = POP_EC50_2

MUT = POP_MUT

KSNC_MAX = POP_KSNC_MAX

SFNCS = POP_SFNCS

HILL = POP_HILL

TR50 = POP_TR50

KSNC_TIME = POP_KSNC_TIME

SUS1_INIT = (SBASE \times (1 - (MUT \times 1.0E-6)))

SUS2_INIT = ((MUT \times 1.0E-6) \times SBASE)

KSNC1 = \frac{(KSNC_MAX \times {\frac{CAB}{EC50_1}}^{HILL})}{({\frac{CAB}{EC50_1}}^{HILL} + {TR50}^{HILL})}

KSNC2 = \frac{(KSNC_MAX \times {\frac{CAB}{EC50_2}}^{HILL})}{({\frac{CAB}{EC50_2}}^{HILL} + {TR50}^{HILL})}

KNCS1 = \frac{(SFNCS \times EC50_1)}{(CAB + 1.0E-10)}

KNCS2 = \frac{(SFNCS \times EC50_2)}{(CAB + 1.0E-10)}

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (LN_ATOT + (additiveError (RUV_ADD) \times EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Fixed parameters

$POP_KK = 0.179$
$POP_KGS2 = 0.344$
$POP_EC50_2 = 1.25$
$POP_MUT = 0.81$
$POP_KSNC_MAX = 5.83$
$POP_HILL = 20$
$POP_KSNC_TIME = 5.47869$

Initial estimates for non-fixed parameters

$POP_KGS1 = 1.7$
$POP_EMAX = 5.24$
$POP_EC50_202 = 0.057$
$POP_GAM = 1.98$
$POP_PROPC = 0.0186$
$POP_SFNCS = 0.17$
$POP_TR50 = 0.24$
$RUV_ADD = 2.544$

Estimation operations

1) Estimate the population parameters

Algorithm FOCEI

Step Dependencies

estimStep_1

DDMODEL00000225: PKPD model for ciprofloxacin