Where Cu Refers to the Circulating (Serum) Unbound G-Csfconcentration

Appendix:System of differential equations corresponding to semi-mechanistic model used for the Monte Carlo simulations

The pharmacokinetics of free circulating G-CSF was described by using a one-compartment model with zero-order input kGCSF to mimic the endogenous production of G-CSF. Free G-CSF could bind to receptors R present on circulating neutrophils at a second-order rate constant kon to form the drug receptor complex RC. The RC complex couldeither dissociate (rate constant koff) or be internalized at a rate kint. The internalized complex was supposed to be degraded in the endosomes and not to recycle. Because of the quasi-equilibrium assumption, we could write:

(1)

where Cu refers to the circulating (serum) unbound G-CSFconcentration.

Apart from the elimination of G-CSF by internalization to circulating neutrophil receptors, free G-CSF could also be eliminated by renal elimination or by binding to neutrophil precursors after distribution in the bone marrow. This was accounted for in the model by the first-order kel rate constant.

The differential equation describing the total G-CSF concentrationwas:

(2)

where is the maximal number of receptors present on circulating neutrophils. Inputequals 0 for patients off-G-CSF and has the following expression whenexogenous G-CSF is given (subcutaneous administration):

(3)

kawas the first-order absorption rate constant, VD the volume of distribution and F the bioavailability. In our model, was taken from the literature (Roskos et al, 2006; Krzyzanskiet al, 2010).

As refers to the total concentration in G-CSF receptorsin blood, it was set proportional to the ANC as follows:

(4)

where Circ is the circulating neutrophil count (ANC) and the proportionality constant representing the amount of receptors per cell.In that context, the G-CSF receptor complex RC was assumed to be pharmacologically inactive and the effect of G-CSF on proliferation and maturation processes in bone marrow was assumed to be drivenby the free circulating G-CSF concentration Cu. Standard Emax models H1 et H2 were used for that purpose:

whereEmax1 is the maximal effect for proliferation, Emax2is the maximal effect for maturation and EC501 andEC502 their respective potency parameters.

The concentration of free-G-CSF wascalculated as follows:

(5)

Five compartments were used to describe the production and maturation of granulocytic cell lineage. The first compartment representedthe proliferating cells (Prol), then three compartments were used to model the transit of the maturing cells (Transit1,2,3) and the last compartment representedthe circulating neutrophils(Circ).The rate constant kprol determined the rate constant for proliferation. The rate constants ktr(transit between compartments) and kcirc(elimination of neutrophils from the bloodstream) were assumed to be equal. Regarding carboplatin toxicity, carboplatin was assumed to induce cell loss from the proliferationcompartment (Prol). The drug effect, was proportional to the ultrafiltrable-plasma concentration Ccarbo(with Slope= sensitivity to carboplatin myelotoxicity).The differential equations describing the system were:

(6)

(7)

(8)

(9)

(10)

MTT was defined as (11)

Prior to any treatment, the system was supposed to be at a steady-state.Therefore, derived from equation (6):

Where and

We deduce that: (12)

Furthermore, the baseline equations derived from equations(7), (8), (9) and (10) were:

As we can deduce:

Steady-state at the initial conditions for equations (2), (4) and (11) allows the following parameters to be calculated:

(13) (14)

(15)

(16)

Free circulating G-CSF concentration at baseline, Cu0,was not estimated but taken from Krzyzanskiet al, 2010 (Cu0=0.0246ng/mL or 24.6ng/L).

A two-compartment model was used to describe the pharmacokinetics of carboplatin after intravenous administration. This model was parameterized in clearance of elimination (Cl), clearance of distribution (Q), volume of distribution of the central compartment (Vc) and volume of distribution of the peripheral compartment (Vp). Carboplatin concentrations in the central (Cc) and peripheral (Cp) compartments were described with the following equations:

(17)

(18)