%Everything is in SI units"
function Single_pellet_model
clear all

%Initial geometry
R0=300E-6;  Rb0=300E-6+6E-6; Ra0=Rb0-2E-9; Rc0=Rb0+30E-6;

%Dissolution Time [s]
TIME=80*3600; 
%Densities [kg/m^3]
rho10=1000; rho20=1200; rho30=1200; rho40=1200;

%Diffusivities [m^2/s]
D2b=1.5E-10;    % from doi:10.1016/j.ijpharm.2015.03.054
D1b=2.2E-9;     % from doi:10.1016/j.ijpharm.2015.03.054
D2c=2*3.2E-13;  % from Kazlauske et al. (submitted)
D1c=1.99E-12;   % from Kazlauske et al. (submitted)
D2d=8.21E-10;   % from doi:10.1016/S0168-3659(01)00424-2
D1self=3E-9;    % from doi:10.1039/B005319H
%See the Transport coefficients definition

%Initial mass fractions
%Domain A
w2sat=0.0115;   % from doi:10.1002/jps.2600740209
w2a0=0.9; w3a0=1-w2a0;
%Domain B
w2b0=0; 
w3b0=0;
%Domain C
w4c0=1; 
w2c0=0;
rhoc0=((1-w2c0-w4c0)/rho10+w2c0/rho20+w4c0/rho40)^(-1);
%Domain D
w2d0=0; %w1d0=1-w2d0; 


Omegad0=1E-3; % Initial dissolution medium [m^3]
Np=5000; % Total number of pellets

function dy = odesystem (t,y)
dy=zeros(9,1); %Initialization

Ra=y(1);
w2b=y(2);
Rb=y(3);
w2c=y(4);
Rc=y(5);
w2d=y(6);
Omegad=y(7);
w3b=y(8);
w4c=y(9);
rhoa=(w2a0/rho20+w3a0/rho30)^(-1); %Density of domain A 
rhob=((1-w2b-w3b)/rho10+w2b/rho20+w3b/rho30)^(-1); %Density of domain B 
rhoc=((1-w2c-w4c)/rho10+w2c/rho20+w4c/rho40)^(-1); %Density of domain C 
rhod=((1-w2d)/rho10+w2d/rho20)^(-1); %Density of domain D 
w1b=1-w2b-w3b; %
w1c=1-w2c-w4c; %
w1d=1-w2d; %

%////Stop condition when Ra reach R0 or when there is not enough water
w2bStar=w2b/(w1b+w2b);
kdiss0=D2b/Ra; 
if Ra>R0 && (w2sat-w2bStar)>0
    kdiss=kdiss0;
else
    kdiss=0;
end
%/////////////////////////////////

%///////Transport coefficients///////////
    k2b=D2b/(Rb-Ra);
    k2c=D2c/(Rc-Rb);
    k2d=D2d/Rc;
    U2b=(1/(k2b)+1/(k2c))^(-1);
    U2c=(1/(k2c)+1/(k2d))^(-1);
    k1b=D1b/(Rb-Ra);
    k1c=D1c/(Rc-Rb);
    m1=4.95; %w1b=m1*w1c
    U1b=(1/(k1b)+m1/(k1c))^(-1);
    k1d=D1self/Rc;
    m2=0.2; %w1c=m2*w1d
    K1c=(1/(k1c)+m2/(k1d))^(-1);
    
%/////////////////////////////////////////////////////////


%////////Parameters defined during the ODEs rearrangement///////////////////////////////// 
rho2b3=rho10*rho20-rho20*rho30; %
rho2b2=rho10*rho30-rho20*rho30; %
rhostar=(rho20*rho30*(1-w2b-w3b)+rho10*rho30*w2b+rho10*rho20*w3b)^2/(rho10*rho20*rho30); %
alfa=w3b*(rho2b2/rhostar)/(rhob-w3b*rho2b3/rhostar); % 
beta=-rhob*w3b*3*Rb^2/((Rb^3-Ra^3)*(rhob-w3b*rho2b3/rhostar)); %
gamma=rhob*w3b*3*Ra^2/((Rb^3-Ra^3)*(rhob-w3b*rho2b3/rhostar));  %
delta=3*Ra^2*rhob*kdiss*w3a0*(w2sat-w2bStar)/(w2a0*(Rb^3-Ra^3)*(rhob-w3b*rho2b3/rhostar)); %
lambda=3*Rb^2*rhob-(Rb^3-Ra^3)*beta*rho2b3/rhostar; %
chsi=3*Ra^2*rhob+gamma*(Rb^3-Ra^3)*rho2b3/rhostar; %
eps=rho2b2/rhostar*(Rb^3-Ra^3)+rho2b3*alfa*(Rb^3-Ra^3)/rhostar; %
zeta=(Rb^3-Ra^3)*rho2b3*delta/rhostar+3*Rb^2*U1b*(m1*w1c*rhoc-w1b*rhob)-3*Rb^2*U2b*(w2b*rhob-w2c*rhoc)+3*Ra^2*kdiss*rhob*(w2sat-w2bStar)/w2a0; %
fi=rhob*(Rb^3-Ra^3)-w2b*(Rb^3-Ra^3)*(rho2b2/rhostar+rho2b3*alfa/rhostar)+eps/lambda*(rhob*w2b*3*Rb^2-w2b*(Rb^3-Ra^3)*beta*rho2b3/rhostar); %
eta=-(-rhob*w2b*3*Ra^2-w2b*(Rb^3-Ra^3)*rho2b3*gamma/rhostar+chsi/lambda*(rhob*w2b*3*Rb^2-w2b*(Rb^3-Ra^3)*rho2b3*beta/rhostar)); %
tau=-zeta/lambda*(rhob*w2b*3*Rb^2-w2b*(Rb^3-Ra^3)*rho2b3*beta/rhostar)+w2b*(Rb^3-Ra^3)*rho2b3*delta/rhostar+3*Ra^2*kdiss*rhob*(w2sat-w2bStar)-3*Rb^2*U2b*(w2b*rhob-w2c*rhoc); %
a=rho40*(rho10-rho20); %
b=rho20*(rho10-rho40); %
rhocstar=(rho20*rho40*(1-w2c-w4c)+rho10*rho40*w2c+rho10*rho20*w4c)^2/(rho10*rho20*rho40); % 
A1=rhoc*(Rc^3-Rb^3)-b*w4c*(Rc^3-Rb^3)/rhocstar; %
B1=-rhoc*w4c*3*Rc^2; %
C1=3*Rb^2*rhoc*w4c/lambda*(chsi+eps*eta/fi); %
D1=a*w4c*(Rc^3-Rb^3)/rhocstar; %
E1=3*Rb^2*rhoc*w4c/lambda*(eps*tau/fi+zeta); %
F1=3*rhoc*Rc^2-(Rc^3-Rb^3)*b*B1/(rhocstar*A1); %
G1=rhoc*3*Rb^2*(chsi/lambda+eps*eta/(lambda*fi))+(Rc^3-Rb^3)*b*C1/(rhocstar*A1); %
H1=(Rc^3-Rb^3)*(b*D1/(rhocstar*A1)+a/rhocstar); %
I1=(Rc^3-Rb^3)*b*E1/(rhocstar*A1)+3*Rc^2*K1c*(m2*w1d*rhod-w1c*rhoc)-3*Rb^2*U1b*(m1*w1c*rhoc-w1b*rhob)+3*Rb^2*U2b*(w2b*rhob-w2c*rhoc)-3*Rc^2*U2c*(w2c*rhoc-w2d*rhod)+rhoc*3*Rb^2*(eps*tau/(lambda*fi)+zeta/lambda); %
L1=rhoc*w2c*3*Rc^2*H1/F1+rhoc*(Rc^3-Rb^3)+w2c*(Rc^3-Rb^3)*(-a/rhocstar-b*(D1+B1*H1/F1)/(rhocstar*A1)); %
M1=-(rhoc*w2c*(3*Rc^2*G1/F1-3*Rb^2*chsi/lambda-3*Rb^2*eta*eps/(lambda*fi))-w2c*(Rc^3-Rb^3)*b*(C1+B1*G1/F1)/(rhocstar*A1)); %
N1=-rhoc*w2c*(3*Rc^2*I1/F1-3*Rb^2*(zeta+eta*tau/fi)/lambda)+w2c*(Rc^3-Rb^3)*b/(rhocstar*A1)*(E1+B1*I1/F1)+3*Rb^2*U2b*(w2b*rhob-w2c*rhoc)-3*Rc^2*U2c*(w2c*rhoc-w2d*rhod); %
rhodstar=rho10*rho20*(rho20-rho10)/(rho20*(1-w2d)+rho10*w2d)^2; %


dRa=-kdiss*rhob/(rhoa*w2a0)*(w2sat-w2bStar);  %
dw2b=(eta*dRa+tau)/fi; %
dRb=(chsi*dRa+eps*dw2b+zeta)/lambda; %
dw3b=alfa*dw2b+beta*dRb+gamma*dRa+delta; %
dw2c=(M1*dRa+N1)/L1; %
dRc=(G1*dRa+H1*dw2c+I1)/F1; %
dw4c=(B1*dRc+C1*dRa+D1*dw2c+E1)/A1; %
dw2d=Np*4*pi*Rc^2/(rhod*Omegad)*(w2d*K1c*(m2*w1d*rhod-w1c*rhoc)+(1-w2d)*U2c*(w2c*rhoc-w2d*rhod)); %
dOmegad=-Omegad*rhodstar*dw2d/rhod+1/rhod*(-Np*4*pi*Rc^2*K1c*(m2*w1d*rhod-w1c*rhoc)+Np*4*pi*Rc^2*U2c*(w2c*rhoc-w2d*rhod)); %
%////////////////////////////////////////////////////////////////////////////////////////////

%//////System of ODEs//////
dy(1) = dRa;
dy(2) = dw2b;
dy(3) = dRb;
dy(4) = dw2c;
dy(5) = dRc;
dy(6) = dw2d;
dy(7) = dOmegad;
dy(8) = dw3b;
dy(9) = dw4c;
%//////////////////////////
end

y0=[Ra0,w2b0,Rb0,w2c0,Rc0,w2d0,Omegad0,w3b0,w4c0]; %Initial conditions
options=odeset('RelTol',1e-9);
[t,y] = ode15s(@odesystem,[0 TIME],y0,options); %ODEs solver

%Results
%Domain A
Ra=y(:,1);
%Domain B
w2b=y(:,2);
w3b=y(:,8);
w1b=1-w3b-w2b;
Rb=y(:,3);
%Domain C
w2c=y(:,4);
w4c=y(:,9);
w1c=1-w2c-w4c;
Rc=y(:,5);
%Domain D
w2d=y(:,6);
w1d=1-y(:,6);
Omegad=y(:,7);

dsfilm=Rc-Rb;
swelling=(Rc-Rc0)/Rc0*100;

rhod=((1-w2d)/rho10+w2d/rho20).^(-1);
rhob=((1-w2b-w3b)/rho10+w2b/rho20+w3b/rho30).^(-1);

Omegaa0=4/3*pi*(Ra0^3-R0^3);
m20a=w2a0*rho20*Omegaa0*Np;
m20=m20a;

m2d=w2d.*rhod.*Omegad;
m2d0=w2d0*((1-w2d0)/rho10+w2d0/rho20)^(-1)*Omegad0;

Omegab=4/3*pi.*(Rb.^3-Ra.^3);
m2b=(w2b.*rhob.*Omegab).*Np;

Omegaa=4/3*pi.*(Ra.^3-R0^3);
m2a=(w2a0*rho20.*Omegaa).*Np;

release=(m2d-m2d0)/m20;

%//////////Figures//////////////////////////////

figure
plot(t/3600,Ra*10^6,'-',t/3600,Rb*10^6,'--',t/3600,Rc*10^6,'.')
title('Radii evolution')
xlabel('Time [h]') 
ylabel('Radius [um]') 
legend('Ra','Rb','Rc')

figure
%plot(t/3600,w1b,'-',t/3600,w2b,'-',t/3600,w3b,'-')
plot(t/3600,w2b,'-')
title('Mass fractions in OmegaB')
xlabel('Time [h]') 
ylabel('Mass fraction [-]') 
legend('w2b')

figure
%plot(t/3600,w1c,'-',t/3600,w2c,'-',t/3600,w4c,'-')
plot(t/3600,w2c,'-')
title('Mass fractions in OmegaC')
xlabel('Time [h]') 
ylabel('Mass fraction [-]') 
legend('w2c')

figure
%plot(t/3600,w1d,'-',t/3600,w2d,'-')
plot(t/3600,w2d,'-')
title('Mass fractions in OmegaD')
xlabel('Time [h]') 
ylabel('Mass fraction [-]') 
legend('w2d')


figure 
plot(t/3600,m2a*10^6,'-r',t/3600,m2b*10^6,'-g',t/3600,m2d*10^6,'-b')
title('Drug Mass in the system')
xlabel('Time [h]') % x-axis label
ylabel('Mass [mg]') % y-axis label
legend('m2a','m2b','m2d')

%//////////End Figures//////////////////////////////


end