Example 7-7 Alcohol Metabolism  |POLVER05_3
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