62 lines
2.1 KiB
Mathematica
62 lines
2.1 KiB
Mathematica
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function diffusion_mab
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% bulk properties
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V_b = 1.075; % volume of bulk solution (cm^3)
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n = 16000; % number of microcarriers in bulk volume
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% ligand properties (IgG)
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m_L0 = 4; % mass of ligand (ug)
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MW_L = 150000; % molecular weight of ligand (g/mol)
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D_LW = 4.8e-7; % ligand diffusion coefficient in water (cm^2/s)
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a = 1; % rxn stoic coeff (L per R)
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% fixed carrier properties
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geometry = 0.190; % geometric diffusion factor of microcarriers
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R = 0.01275; % microcarrier radius (cm)
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C_R0 = 144; % receptor density in carriers (pM/cm^3, nM)
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D_L_app = D_LW*geometry*60; % apparent ligand diffusion coeff. (cm^2/min)
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% init
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t_0 = 0; % initial time (min)
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t_f = 90; % final time (min)
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alpha = 0.999999999999; % fudge factor to prevent MATLAB implosion
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r_i0 = R * alpha; % init interfatial radius in microcarriers (cm)
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C_Lb0 = m_L0 / MW_L * 1e6 / V_b; % init conc. of ligand in bulk (pmol/cm^3, nM)
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% y1 = r_i, y2 = C_Lb
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dydt = @(t,y) [
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((R * D_L_app * y(2) / a))/(C_R0 * y(1) * (y(1) - R));
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(4 * pi * n * D_L_app * y(2) * R * y(1)) / (V_b * (y(1) - R))];
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[t,Y] = ode45(dydt,[t_0 t_f],[r_i0 C_Lb0]);
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r_i = Y(:,1); % interfacial radius (cm)
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C_Lb = Y(:,2); % bulk ligand concentration (pmol/cm^3, nM)
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% fluxes (pmol/cm^2/min)
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N_L = (D_L_app*C_Lb.*r_i)./(R^2*(r_i/R+(-1)));
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% NOTE: flow rates (pmol/min) will be the same at interface and at r=R due
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% to pseudo-steady state assumption
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w_L = -(4*pi*R^2*N_L);
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% concentration profiles (nM) as function of interfacial radius
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C_r = diff(cumtrapz(t,-w_L))./diff(4/3*pi*r_i.^3);
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% total bound mass (ug)
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m_bt_L = trapz(t,w_L)*MW_L/1e6*n;
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disp(['total bound mass at ',num2str(t(end)),' min']);
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disp([num2str(m_bt_L),' ug, ', num2str(m_bt_L/m_L0*100), '% (ligand)']);
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figure;
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plot(t,C_Lb*MW_L/1e6);
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xlabel('t (min)');
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ylabel('concentration (ug/ml)');
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legend('ligand');
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title ('bulk concentration');
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end
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