#Example 9-7 Alcohol Metabolism |POLVER05_3 |1 d(Vs)/d(t) = -ks*Vs #Absorption from stomach d(Cc)/d(t) = (-vl*(Cc-CL10)-vt*(Cc-Ct))/Vc #Alcohol Balance on Central Compartment d(Cca)/d(t) = (-vl*(Cca-CLa10)-vt*(Cca-Cta))/Vc #Aldehyde Balance on Central Compartment d(Ct)/d(t) = (vt*(Cc-Ct))/Vt #Alcohol Balance on Tissues d(Cta)/d(t) = (vt*(Cca-Cta))/Vt #Aldehyde Balance on Tissues d(CL1)/d(t) = (vl*((1/3)*Cc+(2/3)*Cg-CL1)+(-VmAL*CL1+Vrev*CLa1)/(KmAL+CL1+Krev*CLa1)*dVl)/dVl #Alcohol Balance on Liver Compartment 1 d(CL2)/d(t) = (vl*(CL1-CL2)+(-VmAL*CL2+Vrev*CLa2)/(KmAL+CL2+Krev*CLa2)*dVl)/dVl #Alcohol Balance on Liver Compartment 2 d(CL3)/d(t) = (vl*(CL2-CL3)+(-VmAL*CL3+Vrev*CLa3)/(KmAL+CL3+Krev*CLa3)*dVl)/dVl #Alcohol Balance on Liver Compartment 3 d(CL4)/d(t) = (vl*(CL3-CL4)+(-VmAL*CL4+Vrev*CLa4)/(KmAL+CL4+Krev*CLa4)*dVl)/dVl #Alcohol Balance on Liver Compartment 4 d(CL5)/d(t) = (vl*(CL4-CL5)+(-VmAL*CL5+Vrev*CLa5)/(KmAL+CL5+Krev*CLa5)*dVl)/dVl #Alcohol Balance on Liver Compartment 5 d(CL6)/d(t) = (vl*(CL5-CL6)+(-VmAL*CL6+Vrev*CLa6)/(KmAL+CL6+Krev*CLa6)*dVl)/dVl #Alcohol Balance on Liver Compartment 6 d(CL7)/d(t) = (vl*(CL6-CL7)+(-VmAL*CL7+Vrev*CLa7)/(KmAL+CL7+Krev*CLa7)*dVl)/dVl #Alcohol Balance on Liver Compartment 7 d(CL8)/d(t) = (vl*(CL7-CL8)+(-VmAL*CL8+Vrev*CLa8)/(KmAL+CL8+Krev*CLa8)*dVl)/dVl #Alcohol Balance on Liver Compartment 8 d(CL9)/d(t) = (vl*(CL8-CL9)+(-VmAL*CL9+Vrev*CLa9)/(KmAL+CL9+Krev*CLa9)*dVl)/dVl #Alcohol Balance on Liver Compartment 9 d(CL10)/d(t) = (vl*(CL9-CL10)+(-VmAL*CL10+Vrev*CLa10)/(KmAL+CL10+Krev*CLa10)*dVl)/dVl #Alcohol Balance on Liver Compartment 10 d(CLa1)/d(t) = (vl*((1/3)*Cca+(2/3)*Cga-CLa1)-(-VmAL*CL1+Vrev*CLa1)/(KmAL+CL1+Krev*CLa1)*dVl-(CLa1*VmaxAc/(KmAc+CLa1))*dVl)/dVl #Aldehyde Balance on Liver Compartment 1 d(CLa2)/d(t) = (vl*(CLa1-CLa2)-(-VmAL*CL2+Vrev*CLa2)/(KmAL+CL2+Krev*CLa2)*dVl-(CLa2*VmaxAc/(KmAc+CLa2))*dVl)/dVl #Aldehyde Balance on Liver Compartment 2 d(CLa3)/d(t) = (vl*(CLa2-CLa3)-(-VmAL*CL3+Vrev*CLa3)/(KmAL+CL3+Krev*CLa3)*dVl-(CLa3*VmaxAc/(KmAc+CLa3))*dVl)/dVl #Aldehyde Balance on Liver Compartment 3 d(CLa4)/d(t) = (vl*(CLa3-CLa4)-(-VmAL*CL4+Vrev*CLa4)/(KmAL+CL4+Krev*CLa4)*dVl-(CLa4*VmaxAc/(KmAc+CLa4))*dVl)/dVl #Aldehyde Balance on Liver Compartment 4 d(CLa5)/d(t) = (vl*(CLa4-CLa5)-(-VmAL*CL5+Vrev*CLa5)/(KmAL+CL5+Krev*CLa5)*dVl-(CLa5*VmaxAc/(KmAc+CLa5))*dVl)/dVl #Aldehyde Balance on Liver Compartment 5 d(CLa6)/d(t) = (vl*(CLa5-CLa6)-(-VmAL*CL6+Vrev*CLa6)/(KmAL+CL6+Krev*CLa6)*dVl-(CLa6*VmaxAc/(KmAc+CLa6))*dVl)/dVl #Aldehyde Balance on Liver Compartment 6 d(CLa7)/d(t) = (vl*(CLa6-CLa7)-(-VmAL*CL7+Vrev*CLa7)/(KmAL+CL7+Krev*CLa7)*dVl-(CLa7*VmaxAc/(KmAc+CLa7))*dVl)/dVl #Aldehyde Balance on Liver Compartment 8 d(CLa8)/d(t) = (vl*(CLa7-CLa8)-(-VmAL*CL8+Vrev*CLa8)/(KmAL+CL8+Krev*CLa8)*dVl-(CLa8*VmaxAc/(KmAc+CLa8))*dVl)/dVl #Aldehyde Balance on Liver Compartment 8 d(CLa9)/d(t) = (vl*(CLa8-CLa9)-(-VmAL*CL9+Vrev*CLa9)/(KmAL+CL9+Krev*CLa9)*dVl-(CLa9*VmaxAc/(KmAc+CLa9))*dVl)/dVl #Aldehyde Balance on Liver Compartment 9 d(CLa10)/d(t) = (vl*(CLa9-CLa10)-(-VmAL*CL10+Vrev*CLa10)/(KmAL+CL10+Krev*CLa10)*dVl-(CLa10*VmaxAc/(KmAc+CLa10))*dVl)/dVl #Aldehyde Balance on Liver Compartment 10 d(Cg)/d(t) = ((2/3)*vl*(Cc-Cg)+ks*Cso*Vs)/Vg #Alcohol Balance on GI Track d(Cga)/d(t) = ((2/3)*vl*(Cca-Cga))/Vg #Aldehyde Balance on GI Track vl = 1.35 #Liver Flow Rate (l/min) vt = 1.5 #Tissue Flow Rate (l) Vc = 11.56 #Volume of Central Compartment (l) Vt = 25.8 #Volume of Muscle (l) Vg = 2.4 #Volume of GI track (l) Vl = 1.1 #Volume of Liver (l) dVl = Vl/10 #Liver Volume subdivided VmAL = 2.2 # Vrev = 29.1 # KmAL = .3898 # Krev = 1 # VmaxAc = 2.74 # KmAc = .0015 # Cso = 1623 #Stomach concentration in mM @ t=0 a1 = 1.5 #Stomach Absorption Parameter 1 a2 = .06 #Stomach Absorption Parameter 2 ks = a2/(1+a1*(Ds/1000)^2) # Vs1 = 0.15 #Volume of Stomach Contents @ t=0 Ds = Vs1*Cso #Initial Dose in the Stomach t(0)=0 Vs(0)=0.15 Cc(0)=0 Cca(0)=0 Ct(0)=0 Cta(0)=0 CL1(0)=0 CL2(0)=0 CL3(0)=0 CL4(0)=0 CL5(0)=0 CL6(0)=0 CL7(0)=0 CL8(0)=0 CL9(0)=0 CL10(0)=0 CLa1(0)=0 CLa2(0)=0 CLa3(0)=0 CLa4(0)=0 CLa5(0)=0 CLa6(0)=0 CLa7(0)=0 CLa8(0)=0 CLa9(0)=0 CLa10(0)=0 Cg(0)=0 Cga(0)=0 t(f)=180