/*
 * A pharmacokinetic model to predict the PK interaction of L-dopa
 * and benserazide in rats
 * 
 * Model Status
 * 
 * This CellML model runs in PCenv, COR and OpenCell to recreate
 * the published results (Figure 6). This model is simulates the
 * administration of L-dopa only, without benserazide added. This
 * model was created using the paper equations supplemented by
 * suggestions made by Dr. Holford, as the original code was not
 * available.
 * 
 * Model Structure
 * 
 * PURPOSE: To study the PK interaction of L-dopa/benserazide in
 * rats. METHODS: Male rats received a single oral dose of 80 mg/kg
 * L-dopa or 20 mg/kg benserazide or 80/20 mg/kg L-dopa/benserazide.
 * Based on plasma concentrations the kinetics of L-dopa, 3-O-methyldopa
 * (3-OMD), benserazide, and its metabolite Ro 04-5127 were characterized
 * by noncompartmental analysis and a compartmental model where
 * total L-dopa clearance was the sum of the clearances mediated
 * by amino-acid-decarboxylase (AADC), catechol-O-methyltransferase
 * and other enzymes. In the model Ro 04-5127 inhibited competitively
 * the L-dopa clearance by AADC. RESULTS: The coadministration
 * of L-dopa/benserazide resulted in a major increase in systemic
 * exposure to L-dopa and 3-OMD and a decrease in L-dopa clearance.
 * The compartmental model allowed an adequate description of the
 * observed L-dopa and 3-OMD concentrations in the absence and
 * presence of benserazide. It had an advantage over noncompartmental
 * analysis because it could describe the temporal change of inhibition
 * and recovery of AADC. CONCLUSIONS: Our study is the first investigation
 * where the kinetics of benserazide and Ro 04-5127 have been described
 * by a compartmental model. The L-dopa/benserazide model allowed
 * a mechanism-based view of the L-dopa/benserazide interaction
 * and supports the hypothesis that Ro 04-5127 is the primary active
 * metabolite of benserazide.
 * 
 * The original paper reference is cited below:
 * 
 * A pharmacokinetic model to predict the PK interaction of L-dopa
 * and benserazide in rats, Susan Grange, Nicholas H. G. Holford,
 * Theodor W. Guentert, 2001, Pharm Res., volume 18, 1174-1184.
 * PubMed ID: 11587490
 * 
 * model diagram
 * 
 * [[Image file: grange_2001a.png]]
 * 
 * Schematic diagram of the conceptual model to describe kinetics
 * of L-dopa and 3-OMD.
 */

import nsrunit;
unit conversion on;
unit uM=1E-3 meter^(-3)*mole^1;
unit umole=1E-6 mole^1;
unit uM_liter=1E-6 mole^1;
unit hour=3600 second^1;
unit per_hour=2.7777778E-4 second^(-1);
unit liter_per_hour=2.7777778E-7 meter^3*second^(-1);
unit uM_hour=3.6 meter^(-3)*second^1*mole^1;

math main {
	realDomain time hour;
	time.min=0;
	extern time.max;
	extern time.delta;
	real F_b_dopa dimensionless;
	real A_dopa_b(time) umole;
	when(time=time.min) A_dopa_b=101;
	real ka_b_dopa per_hour;
	ka_b_dopa=2.11;
	real F_G dimensionless;
	real F_H dimensionless;
	real CL_H liter_per_hour;
	real Q liter_per_hour;
	Q=0.828;
	real f_H dimensionless;
	f_H=0.13;
	real CL_dopa_0 liter_per_hour;
	CL_dopa_0=0.823;
	real C_dopa_b(time) uM;
	when(time=time.min) C_dopa_b=0;
	real V_dopa liter;
	V_dopa=0.496;
	real CL_dopa(time) liter_per_hour;
	real C_OMD_b(time) uM;
	when(time=time.min) C_OMD_b=0;
	real CL_OMD_b liter_per_hour;
	CL_OMD_b=0.012;
	real V_OMD_b liter;
	V_OMD_b=0.196;
	real CL_COMT liter_per_hour;
	real CL_AADC(time) liter_per_hour;
	real CL_AADC0 liter_per_hour;
	real C1_M(time) uM;
	when(time=time.min) C1_M=0;
	real CL_REST liter_per_hour;
	real ki uM;
	ki=0.00246;
	real A_bens(time) umole;
	when(time=time.min) A_bens=19.51;
	real ka_Bens per_hour;
	ka_Bens=0.94;
	real F_Bens dimensionless;
	F_Bens=0.022;
	real C_bens_central(time) uM;
	when(time=time.min) C_bens_central=0;
	real V1_B liter;
	V1_B=0.202;
	real CLd_B liter_per_hour;
	CLd_B=0.072;
	real C_bens_peripheral(time) uM;
	when(time=time.min) C_bens_peripheral=0;
	real CL_bens_total liter_per_hour;
	real V2_B liter;
	V2_B=0.127;
	real CL_Ro liter_per_hour;
	real CL_B liter_per_hour;
	CL_B=1.67;
	real fm dimensionless;
	fm=0.15;
	real A_Ro(time) umole;
	when(time=time.min) A_Ro=1.3658;
	real ka_M per_hour;
	ka_M=2.47;
	real F_Ro dimensionless;
	F_Ro=1;
	real V1_M liter;
	V1_M=0.0691;
	real CLd_M liter_per_hour;
	CLd_M=1.06;
	real CL_M liter_per_hour;
	CL_M=4.29;
	real C_Ro_peripheral(time) uM;
	when(time=time.min) C_Ro_peripheral=0;
	real V2_M liter;
	V2_M=3.2;

	// <component name="environment">

	// <component name="gastrointestinal_compartment_L_dopa">
	F_H=(1-CL_H/Q);
	F_G=.244;
	CL_H=(f_H*CL_dopa_0);
	F_b_dopa=(F_H*F_G);
	A_dopa_b:time=((-1)*ka_b_dopa*A_dopa_b);

	// <component name="body_compartment_L_dopa">
	C_dopa_b:time=(1/V_dopa*(ka_b_dopa*A_dopa_b*F_b_dopa-CL_dopa*C_dopa_b));

	// <component name="body_compartment_3_OMD">
	C_OMD_b:time=(1/V_OMD_b*(CL_COMT*C_dopa_b-CL_OMD_b*C_OMD_b));

	// <component name="L_dopa_clearance">
	CL_dopa=(CL_AADC+CL_COMT+CL_REST);
	CL_AADC=(CL_AADC0/(1+C1_M/ki));
	CL_AADC0=(CL_dopa_0*.69);
	CL_COMT=(CL_dopa_0*.1);
	CL_REST=(CL_dopa_0*.21);

	// <component name="gastrointestinal_compartment_benserazide">
	A_bens:time=((-1)*ka_Bens*A_bens);

	// <component name="central_compartment_benserazide">
	C_bens_central:time=(1/V1_B*(ka_Bens*A_bens*F_Bens-CL_bens_total*C_bens_central+CLd_B*(C_bens_peripheral-C_bens_central)));

	// <component name="peripheral_compartment_benserazide">
	C_bens_peripheral:time=(1/V2_B*CLd_B*(C_bens_central-C_bens_peripheral));

	// <component name="benserazide_clearance">
	CL_bens_total=(CL_B/(1-fm));
	CL_Ro=(CL_bens_total*fm);

	// <component name="gastrointestinal_compartment_Ro">
	A_Ro:time=((-1)*ka_M*A_Ro);

	// <component name="central_compartment_Ro">
	C1_M:time=(1/V1_M*(ka_M*A_Ro*F_Ro-CL_M*C1_M+CL_Ro*C_bens_central+CLd_M*(C_Ro_peripheral-C1_M)));

	// <component name="peripheral_compartment_Ro">
	C_Ro_peripheral:time=(1/V2_M*CLd_M*(C1_M-C_Ro_peripheral));
}