Research Summary 08/2010

1. Dr. Andrej Mošat` Prof. A. Linninger, Laboratory for Product and Process Design, M/C 063University of Illinois at Chicago 04 August 2010 Research Summary 08/2010

2. Autoregulation in Brain publication quality network image generator: Vector format

3. Kinetic Inversion on Cyclosporine A case • F(1) = fup*( !+Terminal - fl(1)*cp(1) ) -kph*cp(1)*fup*Vb(1) +khp*ch(1)*fh*Vb(1) -kpa*cp(1)*fup*Vb(1) +kap*ca(1)*fa*Vb(1) - yp(1) • F(2) = fup*( + fl(27)*cp(27) + fl(29)*cp(29) - fl(2)*cp(2) ) -kph*cp(2)*fup*Vb(2) +khp*ch(2)*fh*Vb(2) -kpa*cp(2)*fup*Vb(2) +kap*ca(2)*fa*Vb(2) -kpQ(2)*cp(2)*fup*Vb(2) +kQp(2)*cQ(2)*VQ(2) - yp(2) • F(3) = fup*( + fl(30)*cp(30) - fl(3)*cp(3) ) -kph*cp(3)*fup*Vb(3) +khp*ch(3)*fh*Vb(3) -kpa*cp(3)*fup*Vb(3) +kap*ca(3)*fa*Vb(3) -kpQ(3)*cp(3)*fup*Vb(3) +kQp(3)*cQ(3)*VQ(3) - yp(3) • F(4) = fup*( + fl(16)*cp(16) - fl(4)*cp(4) ) -kph*cp(4)*fup*Vb(4) +khp*ch(4)*fh*Vb(4) -kpa*cp(4)*fup*Vb(4) +kap*ca(4)*fa*Vb(4) -kpQ(4)*cp(4)*fup*Vb(4) +kQp(4)*cQ(4)*VQ(4) - yp(4) • F(5) = fup*( + fl(17)*cp(17) - fl(5)*cp(5) ) -kph*cp(5)*fup*Vb(5) +khp*ch(5)*fh*Vb(5) -kpa*cp(5)*fup*Vb(5) +kap*ca(5)*fa*Vb(5) -kpQ(5)*cp(5)*fup*Vb(5) +kQp(5)*cQ(5)*VQ(5) - yp(5) • F(6) = fup*( + fl(19)*cp(19) - fl(6)*cp(6) ) -kph*cp(6)*fup*Vb(6) +khp*ch(6)*fh*Vb(6) -kpa*cp(6)*fup*Vb(6) +kap*ca(6)*fa*Vb(6) -kpQ(6)*cp(6)*fup*Vb(6) +kQp(6)*cQ(6)*VQ(6) - yp(6) • F(7) = fup*( + fl(28)*cp(28) - fl(7)*cp(7) ) -kph*cp(7)*fup*Vb(7) +khp*ch(7)*fh*Vb(7) -kpa*cp(7)*fup*Vb(7) +kap*ca(7)*fa*Vb(7) -kpQ(7)*cp(7)*fup*Vb(7) +kQp(7)*cQ(7)*VQ(7) - yp(7) • F(8) = fup*( + fl(14)*cp(14) - fl(8)*cp(8) ) -kph*cp(8)*fup*Vb(8) +khp*ch(8)*fh*Vb(8) -kpa*cp(8)*fup*Vb(8) +kap*ca(8)*fa*Vb(8) -kpQ(8)*cp(8)*fup*Vb(8) +kQp(8)*cQ(8)*VQ(8) - yp(8) • F(9) = fup*( + fl(55)*cp(55) - fl(9)*cp(9) ) -kph*cp(9)*fup*Vb(9) +khp*ch(9)*fh*Vb(9) -kpa*cp(9)*fup*Vb(9) +kap*ca(9)*fa*Vb(9) -kpQ(9)*cp(9)*fup*Vb(9) +kQp(9)*cQ(9)*VQ(9) - yp(9) • F(10) = fup*( + fl(21)*cp(21) - fl(10)*cp(10) ) -kph*cp(10)*fup*Vb(10) +khp*ch(10)*fh*Vb(10) -kpa*cp(10)*fup*Vb(10) +kap*ca(10)*fa*Vb(10) -kpQ(10)*cp(10)*fup*Vb(10) +kQp(10)*cQ(10)*VQ(10) - yp(10) • F(11) = fup*( + fl(23)*cp(23) - fl(11)*cp(11) ) -kph*cp(11)*fup*Vb(11) +khp*ch(11)*fh*Vb(11) -kpa*cp(11)*fup*Vb(11) +kap*ca(11)*fa*Vb(11) -kpQ(11)*cp(11)*fup*Vb(11) +kQp(11)*cQ(11)*VQ(11) - yp(11) • F(12) = fup*( + fl(25)*cp(25) - fl(12)*cp(12) ) -kph*cp(12)*fup*Vb(12) +khp*ch(12)*fh*Vb(12) -kpa*cp(12)*fup*Vb(12) +kap*ca(12)*fa*Vb(12) -kpQ(12)*cp(12)*fup*Vb(12) +kQp(12)*cQ(12)*VQ(12) - yp(12) • F(13) = fup*( + fl(32)*cp(32) - fl(13)*cp(13) ) -kph*cp(13)*fup*Vb(13) +khp*ch(13)*fh*Vb(13) -kpa*cp(13)*fup*Vb(13) +kap*ca(13)*fa*Vb(13) -kpQ(13)*cp(13)*fup*Vb(13) +kQp(13)*cQ(13)*VQ(13) - yp(13) • F(14) = fup*( - fl(34)*cp(1) + fl(1)*cp(1) - fl(14)*cp(14) ) -kph*cp(14)*fup*Vb(14) +khp*ch(14)*fh*Vb(14) -kpa*cp(14)*fup*Vb(14) +kap*ca(14)*fa*Vb(14) - yp(14) • F(15) = fup*( + fl(8)*cp(8) - fl(15)*cp(15) ) -kph*cp(15)*fup*Vb(15) +khp*ch(15)*fh*Vb(15) -kpa*cp(15)*fup*Vb(15) +kap*ca(15)*fa*Vb(15) - yp(15) • F(16) = fup*( - fl(35)*cp(34) + fl(34)*cp(34) - fl(16)*cp(16) ) -kph*cp(16)*fup*Vb(16) +khp*ch(16)*fh*Vb(16) -kpa*cp(16)*fup*Vb(16) +kap*ca(16)*fa*Vb(16) - yp(16) • F(17) = fup*( - fl(37)*cp(35) + fl(35)*cp(35) - fl(17)*cp(17) ) -kph*cp(17)*fup*Vb(17) +khp*ch(17)*fh*Vb(17) -kpa*cp(17)*fup*Vb(17) +kap*ca(17)*fa*Vb(17) - yp(17) • F(18) = fup*( + fl(5)*cp(5) - fl(18)*cp(18) ) -kph*cp(18)*fup*Vb(18) +khp*ch(18)*fh*Vb(18) -kpa*cp(18)*fup*Vb(18) +kap*ca(18)*fa*Vb(18) - yp(18) • F(19) = fup*( - fl(38)*cp(37) + fl(37)*cp(37) - fl(19)*cp(19) ) -kph*cp(19)*fup*Vb(19) +khp*ch(19)*fh*Vb(19) -kpa*cp(19)*fup*Vb(19) +kap*ca(19)*fa*Vb(19) - yp(19) • F(20) = fup*( + fl(6)*cp(6) - fl(20)*cp(20) ) -kph*cp(20)*fup*Vb(20) +khp*ch(20)*fh*Vb(20) -kpa*cp(20)*fup*Vb(20) +kap*ca(20)*fa*Vb(20) - yp(20) • F(21) = fup*( - fl(39)*cp(38) + fl(38)*cp(38) - fl(21)*cp(21) ) -kph*cp(21)*fup*Vb(21) +khp*ch(21)*fh*Vb(21) -kpa*cp(21)*fup*Vb(21) +kap*ca(21)*fa*Vb(21) - yp(21) • F(22) = fup*( + fl(10)*cp(10) - fl(22)*cp(22) ) -kph*cp(22)*fup*Vb(22) +khp*ch(22)*fh*Vb(22) -kpa*cp(22)*fup*Vb(22) +kap*ca(22)*fa*Vb(22) - yp(22) • F(23) = fup*( - fl(40)*cp(39) + fl(39)*cp(39) - fl(23)*cp(23) ) -kph*cp(23)*fup*Vb(23) +khp*ch(23)*fh*Vb(23) -kpa*cp(23)*fup*Vb(23) +kap*ca(23)*fa*Vb(23) - yp(23) • F(24) = fup*( + fl(11)*cp(11) - fl(24)*cp(24) ) -kph*cp(24)*fup*Vb(24) +khp*ch(24)*fh*Vb(24) -kpa*cp(24)*fup*Vb(24) +kap*ca(24)*fa*Vb(24) - yp(24) • F(25) = fup*( - fl(41)*cp(40) + fl(40)*cp(40) - fl(25)*cp(25) ) -kph*cp(25)*fup*Vb(25) +khp*ch(25)*fh*Vb(25) -kpa*cp(25)*fup*Vb(25) +kap*ca(25)*fa*Vb(25) - yp(25) • F(26) = fup*( - fl(42)*cp(41) + fl(41)*cp(41) - fl(26)*cp(26) ) -kph*cp(26)*fup*Vb(26) +khp*ch(26)*fh*Vb(26) -kpa*cp(26)*fup*Vb(26) +kap*ca(26)*fa*Vb(26) - yp(26) • F(27) = fup*( + fl(12)*cp(12) + fl(26)*cp(26) - fl(27)*cp(27) ) -kph*cp(27)*fup*Vb(27) +khp*ch(27)*fh*Vb(27) -kpa*cp(27)*fup*Vb(27) +kap*ca(27)*fa*Vb(27) - yp(27) • F(28) = fup*( - fl(43)*cp(42) + fl(42)*cp(42) - fl(28)*cp(28) ) -kph*cp(28)*fup*Vb(28) +khp*ch(28)*fh*Vb(28) -kpa*cp(28)*fup*Vb(28) +kap*ca(28)*fa*Vb(28) - yp(28) • F(29) = fup*( + fl(7)*cp(7) - fl(29)*cp(29) ) -kph*cp(29)*fup*Vb(29) +khp*ch(29)*fh*Vb(29) -kpa*cp(29)*fup*Vb(29) +kap*ca(29)*fa*Vb(29) - yp(29) • F(30) = fup*( - fl(44)*cp(43) + fl(43)*cp(43) - fl(30)*cp(30) ) -kph*cp(30)*fup*Vb(30) +khp*ch(30)*fh*Vb(30) -kpa*cp(30)*fup*Vb(30) +kap*ca(30)*fa*Vb(30) - yp(30) • F(31) = fup*( + fl(3)*cp(3) - fl(31)*cp(31) ) -kph*cp(31)*fup*Vb(31) +khp*ch(31)*fh*Vb(31) -kpa*cp(31)*fup*Vb(31) +kap*ca(31)*fa*Vb(31) - yp(31) • F(32) = fup*( + fl(44)*cp(44) - fl(32)*cp(32) ) -kph*cp(32)*fup*Vb(32) +khp*ch(32)*fh*Vb(32) -kpa*cp(32)*fup*Vb(32) +kap*ca(32)*fa*Vb(32) - yp(32) • F(33) = fup*( + fl(13)*cp(13) - fl(33)*cp(33) ) -kph*cp(33)*fup*Vb(33) +khp*ch(33)*fh*Vb(33) -kpa*cp(33)*fup*Vb(33) +kap*ca(33)*fa*Vb(33) - yp(33) • F(34) = fup*( - fl(14)*cp(1) + fl(1)*cp(1) - fl(34)*cp(34) ) -kph*cp(34)*fup*Vb(34) +khp*ch(34)*fh*Vb(34) -kpa*cp(34)*fup*Vb(34) +kap*ca(34)*fa*Vb(34) - yp(34) • F(35) = fup*( - fl(16)*cp(34) + fl(34)*cp(34) - fl(35)*cp(35) ) -kph*cp(35)*fup*Vb(35) +khp*ch(35)*fh*Vb(35) -kpa*cp(35)*fup*Vb(35) +kap*ca(35)*fa*Vb(35) - yp(35) • F(36) = fup*( + fl(4)*cp(4) - fl(36)*cp(36) ) -kph*cp(36)*fup*Vb(36) +khp*ch(36)*fh*Vb(36) -kpa*cp(36)*fup*Vb(36) +kap*ca(36)*fa*Vb(36) - yp(36) • F(37) = fup*( - fl(17)*cp(35) + fl(35)*cp(35) - fl(37)*cp(37) ) -kph*cp(37)*fup*Vb(37) +khp*ch(37)*fh*Vb(37) -kpa*cp(37)*fup*Vb(37) +kap*ca(37)*fa*Vb(37) - yp(37) • F(38) = fup*( - fl(19)*cp(37) + fl(37)*cp(37) - fl(38)*cp(38) ) -kph*cp(38)*fup*Vb(38) +khp*ch(38)*fh*Vb(38) -kpa*cp(38)*fup*Vb(38) +kap*ca(38)*fa*Vb(38) - yp(38) • F(39) = fup*( - fl(21)*cp(38) + fl(38)*cp(38) - fl(39)*cp(39) ) -kph*cp(39)*fup*Vb(39) +khp*ch(39)*fh*Vb(39) -kpa*cp(39)*fup*Vb(39) +kap*ca(39)*fa*Vb(39) - yp(39) • F(40) = fup*( - fl(23)*cp(39) + fl(39)*cp(39) - fl(40)*cp(40) ) -kph*cp(40)*fup*Vb(40) +khp*ch(40)*fh*Vb(40) -kpa*cp(40)*fup*Vb(40) +kap*ca(40)*fa*Vb(40) - yp(40) • F(41) = fup*( - fl(25)*cp(40) + fl(40)*cp(40) - fl(41)*cp(41) ) -kph*cp(41)*fup*Vb(41) +khp*ch(41)*fh*Vb(41) -kpa*cp(41)*fup*Vb(41) +kap*ca(41)*fa*Vb(41) - yp(41) • F(42) = fup*( - fl(26)*cp(41) + fl(41)*cp(41) - fl(42)*cp(42) ) -kph*cp(42)*fup*Vb(42) +khp*ch(42)*fh*Vb(42) -kpa*cp(42)*fup*Vb(42) +kap*ca(42)*fa*Vb(42) - yp(42) • F(43) = fup*( - fl(28)*cp(42) + fl(42)*cp(42) - fl(43)*cp(43) ) -kph*cp(43)*fup*Vb(43) +khp*ch(43)*fh*Vb(43) -kpa*cp(43)*fup*Vb(43) +kap*ca(43)*fa*Vb(43) - yp(43) • F(44) = fup*( - fl(30)*cp(43) + fl(43)*cp(43) - fl(44)*cp(44) ) -kph*cp(44)*fup*Vb(44) +khp*ch(44)*fh*Vb(44) -kpa*cp(44)*fup*Vb(44) +kap*ca(44)*fa*Vb(44) - yp(44) • F(45) = fup*( + fl(33)*cp(33) - fl(45)*cp(45) ) -kph*cp(45)*fup*Vb(45) +khp*ch(45)*fh*Vb(45) -kpa*cp(45)*fup*Vb(45) +kap*ca(45)*fa*Vb(45) - yp(45) • F(46) = fup*( + fl(31)*cp(31) + fl(45)*cp(45) - fl(46)*cp(46) ) -kph*cp(46)*fup*Vb(46) +khp*ch(46)*fh*Vb(46) -kpa*cp(46)*fup*Vb(46) +kap*ca(46)*fa*Vb(46) - yp(46) • F(47) = fup*( + fl(2)*cp(2) + fl(46)*cp(46) - fl(47)*cp(47) ) -kph*cp(47)*fup*Vb(47) +khp*ch(47)*fh*Vb(47) -kpa*cp(47)*fup*Vb(47) +kap*ca(47)*fa*Vb(47) - yp(47) • F(48) = fup*( + fl(24)*cp(24) + fl(47)*cp(47) - fl(48)*cp(48) ) -kph*cp(48)*fup*Vb(48) +khp*ch(48)*fh*Vb(48) -kpa*cp(48)*fup*Vb(48) +kap*ca(48)*fa*Vb(48) - yp(48) • F(49) = fup*( + fl(22)*cp(22) + fl(48)*cp(48) - fl(49)*cp(49) ) -kph*cp(49)*fup*Vb(49) +khp*ch(49)*fh*Vb(49) -kpa*cp(49)*fup*Vb(49) +kap*ca(49)*fa*Vb(49) - yp(49) • F(50) = fup*( + fl(20)*cp(20) + fl(49)*cp(49) - fl(50)*cp(50) ) -kph*cp(50)*fup*Vb(50) +khp*ch(50)*fh*Vb(50) -kpa*cp(50)*fup*Vb(50) +kap*ca(50)*fa*Vb(50) - yp(50) • F(51) = fup*( + fl(18)*cp(18) + fl(50)*cp(50) - fl(51)*cp(51) ) -kph*cp(51)*fup*Vb(51) +khp*ch(51)*fh*Vb(51) -kpa*cp(51)*fup*Vb(51) +kap*ca(51)*fa*Vb(51) - yp(51) • F(52) = fup*( + fl(36)*cp(36) + fl(51)*cp(51) - fl(52)*cp(52) ) -kph*cp(52)*fup*Vb(52) +khp*ch(52)*fh*Vb(52) -kpa*cp(52)*fup*Vb(52) +kap*ca(52)*fa*Vb(52) - yp(52) • F(53) = fup*( + fl(15)*cp(15) + fl(52)*cp(52) - fl(53)*cp(53) ) -kph*cp(53)*fup*Vb(53) +khp*ch(53)*fh*Vb(53) -kpa*cp(53)*fup*Vb(53) +kap*ca(53)*fa*Vb(53) - yp(53) • F(54) = fup*( !+Terminal - fl(54)*cp(54) ) -kph*cp(54)*fup*Vb(54) +khp*ch(54)*fh*Vb(54) -kpa*cp(54)*fup*Vb(54) +kap*ca(54)*fa*Vb(54) - yp(54) • F(55) = fup*( + fl(54)*cp(54) - fl(55)*cp(55) ) -kph*cp(55)*fup*Vb(55) +khp*ch(55)*fh*Vb(55) -kpa*cp(55)*fup*Vb(55) +kap*ca(55)*fa*Vb(55) - yp(55) • F(56) = fup*( + fl(9)*cp(9) - fl(56)*cp(56) ) -kph*cp(56)*fup*Vb(56) +khp*ch(56)*fh*Vb(56) -kpa*cp(56)*fup*Vb(56) +kap*ca(56)*fa*Vb(56) - yp(56) • F(57) = fup*( + fl(56)*cp(56) - fl(57)*cp(57) ) -kph*cp(57)*fup*Vb(57) +khp*ch(57)*fh*Vb(57) -kpa*cp(57)*fup*Vb(57) +kap*ca(57)*fa*Vb(57) - yp(57)

4. Kinetic Inversion on Cyclosporine A case2 min Bolus Injection

5. Future Goals • Semi – automatic vasculature equation generator • Continuity equations • Drug equations • Mass transfer equations • Different compartments: • Blood • 1. Plasma • Plasma Proteins • Hematocrit • Tissue • CSF

6. Algorithms constrained optimization case studies with documentation on geometryComputer Administration DHCP

7. First principle model

8. Empirical model vs. First principle model

9. First principle model

10. Approach to PBPK Modeling using Vasculature Network 1. 2. Intrinsic Hepatic Clearance Tanaka: CLi = F(Hct, t, organ type)Our proposal: CLi = F(Hct) => const. 4. Vasculature network combined with “tissue equations” Result:CCyA,i=F(t)‏ 3. Kinetic organ models:F(CCyA(t, injection, CLliver, CLorgans ), params(Cplasma) )‏ 5. KIP for 1 parameter: CLi

11. Literature Review Cierra found: Gueorguieva, I.; Aarons, L.; Ogungbenro, K.; Jorga, K.; Rodgers, T. & Rowland, M. Optimal Design for Multivariate Response Pharmacokinetic Models Journal of Pharmacokinetics and Pharmacodynamics, 2006, 33, 97-124 “We assume that measurements made at distinct times are independent, but measurements made of each concentration are correlated with a response variance--covariance matrix. “

12. Outlook • Test rSQP for KIP of a “Rat50” model • Research Global optimization methods • Outline of a paper • REU preparation

13. Experiment: Rats’ Blood and Tissue concentrations of CyA Blood Tissue concentration-to-time profiles of CyA in various organs of rats after 1.2- (circles), 6- (squares), and 30- (triangles) mg/kg doses. Each measurement in the unit of mg/ml or g represents an average value from three rats with S.D. (vertical bar). The solid line is log-linear interpolation between the measurements.

14. ODE Solvers overview at our disposal