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% 1. Estiamte FT4 values for given time period and drug dose  
% 2. Determine ATD drug dose to achieve a target FT4 for a given time period   
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%Here, take patient 2 as an exampple 

% Estimate FT4 value 

x_dose = [ 3  5  8 10  13]; %% given varisous dosages
t=[35 56 63];    %% given different time periods 
 
ft4= zeros(5,3);

for i=1:5
    for j=1:3
temp1 = 3.024/(58.151 + x_dose(i));
     
temp2 = 0.154/(58.151 + x_dose(i));

ft4(i,j)  = (temp1 * exp(temp1*t(j)))/(0.003*exp(temp1*t(j)) - temp2);
    end
end

ft4

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% find the optimal drug dosage, given time period and target FT4 values

ft4_initial = 75;

target_ft4 = 12;  % set target FT4 value = 12
t=[35 42 49 56 63];  % given review periods
 
epsilon = 10^-8;
x_dose = zeros(5, 1);
 

for i=1:5
    
a_dose = 0;  % (minimum dosage)
fa = Inf; 
b_dose = 300; %(maximum dosage)
fb  = -Inf; 

while b_dose - a_dose > epsilon
    x_dose(i) = (a_dose + b_dose)/2;
   
    temp1 = 3.024/(58.151 + x_dose(i));  
    temp2 = 0.154/(58.151 + x_dose(i));  
    
    fx = (temp1 * exp(temp1*t(i)))/(0.003*exp(temp1*t(i)) - temp2) - target_ft4;
     if fx == 0
         break
     elseif sign(fx) == sign (fa)
         a_dose  = x_dose(i);    fa = fx;
     else
         b_dose = x_dose(i);     fb = fx;
     end
 
 end

end 
 
x_dose