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AMK/AMK_PlasmaODEs.m

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+%% =======================================================================
+%  AMK_PlasmaODEs.m  —  Two-Compartment Plasma PK ODEs for Amikacin
+%  ========================================================================
+%
+%  DESCRIPTION
+%    Right-hand side function for a two-compartment PK model of amikacin
+%    with zero-order IV infusion input and first-order elimination from
+%    the central compartment. Intended to be called by an ODE solver
+%    (e.g. ode45) from AMK_PopPK.
+%
+%  MODEL
+%    Reimplementation of Tod et al., 1998.
+%    Michel Tod et al. "Population pharmacokinetic study of amikacin administered 
+%    once or twice daily to febrile, severly neutropenic adults". In: *Antimicrobial 
+%    agents and chemotherapy* 42.4 (1998), pp. 849-856.
+%
+%  INPUTS
+%    t       - Time (h); scalar supplied by the ODE solver.
+%    y       - State vector of drug amounts (mg):
+%                y(1) = central compartment amount
+%                y(2) = peripheral compartment amount
+%    params  - Parameter vector:
+%                params(1) = Vc/F  central volume (L)
+%                params(2) = Vp/F  peripheral volume (L)
+%                params(3) = CL/F  clearance (L/h)
+%                params(4) = Q/F   intercompartmental clearance (L/h)
+%                params(5) = dose  dose for this interval (mg)
+%                params(6) = infusion duration (h)
+%
+%  OUTPUTS
+%    dy      - Derivative vector (mg/h):
+%                dy(1) = d(central)/dt
+%                dy(2) = d(peripheral)/dt
+%
+%  AUTHORS
+%    Trevor Shoaf
+%    Copyright: Elsje Pienaar's Computational Systems Pharmacology Lab,
+%               Weldon School of Biomedical Engineering, Purdue University
+%
+%    Original implementation: Meghna Nair, 2024-01-28
+%
+%  VERSION
+%    Created:        2024-01-28
+%    Tested on:      MATLAB R2026a
+%  ========================================================================
+
+function dy = AMK_PlasmaODEs(t,y,params)
+
+% Extracting parameter values from params variable to assign to local variables 
+
+% Departmental constants
+V_Fs = [...
+    params(1)           %(L) Central compartment Vc/F
+    params(2)           %(L) Peripheral compartment Vp/F
+    ];
+rates = [...
+    params(3)           % CL/F  Clearance 
+    params(4)           % Q/F   Intercompartmental Clearance 
+    ];
+dose = params(5);        % Dose for this interval (mg)
+infusionDuration = params(6);   % IV infusion duration (h)
+
+% Handle dosing duration
+
+if t < infusionDuration
+    RateIn = dose / infusionDuration;    % (mg/h) zero-order IV input
+else 
+    RateIn = 0;                          % no input after infusion ends
+end
+
+% ODE Y value assignments
+A = [...
+    y(1)            %Drug amount in central compartment (mg)
+    y(2)            %Drug amount in peripheral compartment (mg)
+    ];
+
+% Define ODEs
+
+% ODE around CENTRAL compartment 
+% ------------------------------------------
+% ODE_1 terms
+dA1_term1 =   RateIn;                          % 
+dA1_term2 = - rates(2) * A(1) / V_Fs(1);       % Flow out to Peripheral: -Q * A1 / Vc
+dA1_term3 =   rates(2) * A(2) / V_Fs(2);       %  +Q * A2 / Vp
+dA1_term4 = - rates(1) * A(1) / V_Fs(1);       % Clearance from system: -CL * A1 / Vc
+
+dA1dt = dA1_term1 + dA1_term2 + dA1_term3 + dA1_term4; %(mg/h)
+
+% ODE around PERIPHERAL compartment 
+% ------------------------------------------
+% ODE_2 terms
+dA2_term1 =   rates(2) * A(1) / V_Fs(1);       %  +Q * A1 / Vc
+dA2_term2 = - rates(2) * A(2) / V_Fs(2);       % -Q * A2 / Vp
+
+dA2dt = dA2_term1 + dA2_term2;                 %(mg/h)
+
+% ODE Outputs
+
+dy = [...
+    dA1dt
+    dA2dt
+    ];
+
+end