Mandel – Propofol Cortínez 2010

MATLAB Code

Implements the propofol model of Cortinez et al.[1]

Contributed by Jeff E Mandel

function [sys] = cortinez(Age, Weight, stepSize)
% Implements the model of Cortinez using table S2a for the pooled data
% Cortínez LI, Anderson BJ, Penna A, Olivares L, Muñoz HR, Holford NH, Struys MM, Sepulveda P. 
% Influence of obesity on propofol pharmacokinetics: derivation of a pharmacokinetic model. 
% Br J Anaesth. 2010;105:448-56.

    % Standard volumes (Liters for 70 kg patient)
    V1std = 4.48;
    V2std = 21.2;
    V3std = 237;

    %Standard clearances (Liters/min  for 70 kg patient)
    CL1std = 1.92;
    Q2std = 1.45;
    Q3std = 0.86;

    %Age correction factors
    SLV2 = -0.0164;
    SLQ2 = -0.0153;

    wa = Weight/70;
    wap = wa^0.75;
    aa = Age - 50;

    V1 = V1std * wa;
    V2  = V2std * wa * exp(SLV2*aa);
    V3 = V3std * wa;

    volume = [V1 V2 V3];

    CL1 = CL1std* wap;
    CL2 = Q2std* wap * exp(SLQ2*aa);
    CL3 = Q3std*wap;

    clearance = [CL1 CL2 CL3];

    % Solve for the value of ke0 which yields a time to peak effect of 1.4
    % minutes. We search in the range of .1 to 2.0
    tpeak = 1.6;
    ike0 = [.1;2];
    t=0:.0005:3;
    u=zeros(size(t));
    u(1)=1;

    options = optimset('Display','off'); % Turn off Display
    ke0 = fzero(@getKe0, ike0, options);
    %disp(ke0);

        function [error] = getKe0(tke0)
            [sys] = mam2ss(clearance,volume,tke0);
            [y,t] = lsim(sys,u,t);
            s = lsiminfo(y,t,0);  % final value is 0
            error = tpeak - s.MaxTime;
        end

    sys = mam2ss(clearance,volume, ke0);
    if (nargin==3)
        sys=c2d(sys, stepSize,'zoh');
    end
end

function [sys] = mam2ss(clearance,volume, ke0)
% returns a state space model from vectors of clearance
% and compartment volumes. All states are drug amount
% in the compartment; to get concentration, divide by compartment
% volume in the C matrix. Note that this code can handle an
% arbitrary number of compartments, but assumes the first compartment is
% the central compartment (mam is short for mamillary).
% The effect site compartment is represented as a compartment of negligible
% volume adjoined to the central compartment.

n = length(clearance);
if (nargin == 2)
    k1 = clearance./volume(1);
    k2 = clearance(2:n)./volume(2:n);
    A = [-sum(k1) k2;transpose(k1(2:n)) -diag(k2)];
    B = [1;zeros(n-1,1)];                   % Direct addition of drug into the central compartment
    C = [1/volume(1) zeros(1,n-1)];     % Observation of the central compartment concentration.
else
    EFFECT_VOL_FACTOR=10000; % ratio of central compartment vol to effect
    k1 = [clearance./volume(1) ke0/EFFECT_VOL_FACTOR];
    k2 = [clearance(2:n)./volume(2:n) ke0];
    A = [-sum(k1) k2;transpose(k1(2:n+1)) -diag(k2)];
    B = [1;zeros(n,1)];                   % Direct addition of drug into the central compartment
    C = [zeros(1,n) EFFECT_VOL_FACTOR/volume(1)];     % Observation of the effect site compartment concentration.
end


C = C./1000; % All compartment volumes are in L, convert to ml
D=0;

sys = ss(A,B,C,D);
end