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Model Definition
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Short description:

The model is a mechanism-based model for oncotherapy by a conjugated mAb drug, Gemtuzumab ozogamicin (GO; commercial name Mylotarg), for patients with acute myeloid leukemia (AML). The model illustrates the interactions of the drug with leukemic blasts expressing a receptor, the cell surface antigen CD33, to which the mAb component of the drug (i.e. Gemtuzumab) binds. The drug-antigen complex is then internalized, allowing for the toxic component (ozogamicin) to induce cell lysis. The system consists of ordinary differential equations describing the dynamics of the drug, receptor, and drug-receptor complex, as well as the drug pharmacokinetics. The model was calibrated using data from the following sources: (1) in vitro GO-treated cultures of the human AML cell line AML193; (2) primary AML blasts derived from ca. 40 patients in a Phase II clinical trial; (3) serum drug levels in AML patients treated with GO in a Phase I clinical trial. Parameter estimation was carried out using Monolix 3.2. The analysis of the model in the original study showed that (a) the initial blast burden, (b) the receptor production rate and (c) the drug efflux rate are key factors determining the intracellular drug exposure (I-AUC), and thus directly influencing drug efficacy. The model can be used, therefore, to optimize GO therapy, i.e. determine GO schedules that achieve sufficiently high I-AUC under minimal GO doses.

Format:	PharmML (0.6.1)
Related Publication:	Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization. Jager E, van der Velden VH, te Marvelde JG, Walter RB, Agur Z, Vainstein V PloS one, 1/2011, Volume 6, Issue 9, pages: e24265 Affiliation: Institute for Medical BioMathematics, Bene Ataroth, Israel. Abstract: Gemtuzumab ozogamicin (GO) is a chemotherapy-conjugated anti-CD33 monoclonal antibody effective in some patients with acute myeloid leukemia (AML). The optimal treatment schedule and optimal timing of GO administration relative to other agents remains unknown. Conventional pharmacokinetic analysis has been of limited insight for the schedule optimization. We developed a mechanism-based mathematical model and employed it to analyze the time-course of free and GO-bound CD33 molecules on the lekemic blasts in individual AML patients treated with GO. We calculated expected intravascular drug exposure (I-AUC) as a surrogate marker for the response to the drug. A high CD33 production rate and low drug efflux were the most important determinants of high I-AUC, characterizing patients with favorable pharmacokinetic profile and, hence, improved response. I-AUC was insensitive to other studied parameters within biologically relevant ranges, including internalization rate and dissociation constant. Our computations suggested that even moderate blast burden reduction prior to drug administration enables lowering of GO doses without significantly compromising intracellular drug exposure. These findings indicate that GO may optimally be used after cyto-reductive chemotherapy, rather than before, or concomitantly with it, and that GO efficacy can be maintained by dose reduction to 6 mg/m(2) and a dosing interval of 7 days. Model predictions are validated by comparison with the results of EORTC-GIMEMA AML19 clinical trial, where two different GO schedules were administered. We suggest that incorporation of our results in clinical practice can serve identification of the subpopulation of elderly patients who can benefit most of the GO treatment and enable return of the currently suspended drug to clinic.
Contributors:	Moran Optimata

Context of model development:	Mechanistic Understanding; Dose & Schedule Selection and Label Recommendation;
Discrepancy between implemented model and original publication:	The PK model was extended to include one peripheral compartment. The main reason is that the model was re-evaluated on the same data, using mixed-effects approach in Monolix.;
Model compliance with original publication:	No;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	The model is a mechanism-based model for oncotherapy by a conjugated mAb drug, Gemtuzumab ozogamicin (GO; commercial name Mylotarg), for patients with acute myeloid leukemia (AML). The model illustrates the interactions of the drug, GO, with leukemic blasts expressing a receptor, the cell surface antigen CD33, to which the mAb component of the drug (i.e. Gemtuzumab) binds. The drug-antigen complex is then internalized, allowing for the toxic component (ozogamicin) to induce cell lysis. The system consists of ordinary differential equations describing the dynamics of the drug, receptor, and drug-receptor complex, as well as the drug pharmacokinetics. ;
Modelling task in scope:	simulation; estimation;
Nature of research:	Early clinical development (Phases I and II); Fundamental/Basic research;
Therapeutic/disease area:	Oncology;

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

Mandatory file
- GO_PK_model.xml

Additional Files

Model owner: Moran Optimata
Submitted: Nov 1, 2016 11:05:06 AM
Last Modified: Nov 1, 2016 11:05:06 AM

Revisions

Version: 5
- Submitted on: Nov 1, 2016 11:05:06 AM
- Submitted by: Moran Optimata
- With comment: Model revised without commit message

Independent variable T

Function Definitions

additiveError (additive) = additive

Structural Model sm

Variable definitions

nav = 6.02214

vblood = 4.8

\frac{dA1}{dT} = (((\frac{((((- kb \times A1) \times A2) + ((v1 \times ku) \times A3)) \times A4)}{(vblood \times nav)} - (k \times A1)) - (km \times A1)) + (kn \times A5))

\frac{dA2}{dT} = (((((- \frac{kb}{v1} \times A1) \times A2) + (ku \times A3)) + rp) - (ke \times A2))

\frac{dA3}{dT} = ((((\frac{kb}{v1} \times A1) \times A2) - (ku \times A3)) - (ki \times A3))

\frac{dA4}{dT} = (- alph \times A4)

\frac{dA5}{dT} = ((km \times A1) - (kn \times A5))

output1 = \frac{A1}{v1}

Initial conditions

A1 = 0

A2 = \frac{rp}{ke}

A3 = 0

A4 = n0

A5 = 0

Variability Model

Level	Type
DV	residualError
ID	parameterVariability

Parameter Model

Parameters

POP_kb

;

POP_ku

;

POP_ki

;

POP_ke

;

POP_rp

;

POP_k

;

POP_alph

;

POP_n0

;

POP_v1

;

POP_km

;

POP_kn

;

a

;

omega_kb

;

omega_ku

;

omega_ki

;

omega_ke

;

omega_rp

;

omega_k

;

omega_alph

;

omega_n0

;

omega_v1

;

omega_km

;

omega_kn

;

ETA_kb \sim N (0.0, omega_kb)

— ID

ETA_ku \sim N (0.0, omega_ku)

— ID

ETA_ki \sim N (0.0, omega_ki)

— ID

ETA_ke \sim N (0.0, omega_ke)

— ID

ETA_rp \sim N (0.0, omega_rp)

— ID

ETA_k \sim N (0.0, omega_k)

— ID

ETA_alph \sim N (0.0, omega_alph)

— ID

ETA_n0 \sim N (0.0, omega_n0)

— ID

ETA_v1 \sim N (0.0, omega_v1)

— ID

ETA_km \sim N (0.0, omega_km)

— ID

ETA_kn \sim N (0.0, omega_kn)

— ID

EPS_Y \sim N (0.0, 1.0)

— DV

log (kb) = (log (POP_kb) + ETA_kb)

log (ku) = (log (POP_ku) + ETA_ku)

log (ki) = (log (POP_ki) + ETA_ki)

log (ke) = (log (POP_ke) + ETA_ke)

log (rp) = (log (POP_rp) + ETA_rp)

log (k) = (log (POP_k) + ETA_k)

log (alph) = (log (POP_alph) + ETA_alph)

log (n0) = (log (POP_n0) + ETA_n0)

log (v1) = (log (POP_v1) + ETA_v1)

log (km) = (log (POP_km) + ETA_km)

log (kn) = (log (POP_kn) + ETA_kn)

Correlation matrix for level ID and random effects: ETA_alph, ETA_k

(\begin{matrix} 1 & 0.32 \\ 0.32 & 1 \end{matrix})

Observation Model

Observation Y
Continuous / Residual Data

Parameters

Y = (output1 + (additiveError (a) \times EPS_Y))

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Initial estimates for non-fixed parameters

$POP_kb = 924000$
$POP_ku = 310$
$POP_ki = 0.624$
$POP_ke = 0.199$
$POP_rp = 823$
$POP_k = 0.0135$
$POP_alph = 0.0755$
$POP_n0 = 1.32E-5$
$POP_v1 = 5.42$
$POP_km = 0.00757$
$POP_kn = 0.0185$
$a = 5.83E-4$
$omega_kb = 0$
$omega_ku = 0$
$omega_ki = 0.258$
$omega_ke = 0.281$
$omega_rp = 0.611$
$omega_k = 0$
$omega_alph = 0$
$omega_n0 = 0$
$omega_v1 = 0$
$omega_km = 0$
$omega_kn = 0$

Estimation operations

1) Estimate the population parameters

Algorithm SAEM

Step Dependencies

estimStep_1

DDMODEL00000229: A model for monoclonal antibody-based targeted therapy of Gemtuzumab Ozogamicin (GO) for acute myeloid leukemia (AML)

Revisions

Function Definitions

Structural Model sm

Variability Model

Parameter Model

Observation Model

Observation YContinuous / Residual Data

Estimation Steps

Estimation Step estimStep_1

Estimation parameters

Estimation operations

Step Dependencies

Observation Y
Continuous / Residual Data