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

Autoregulation in Brain publication quality network image generator: Vector format

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)

Kinetic Inversion on Cyclosporine A case 2 min Bolus Injection

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

Algorithms constrained optimization case studies with documentation on geometry Computer Administration DHCP

First principle model

Empirical model vs. First principle model

First principle model

Approach to PBPK Modeling using Vasculature Network 1.2. Intrinsic Hepatic Clearance Tanaka: CL i = F(Hct, t, organ type) Our proposal: CL i = F(Hct) => const. 3. Kinetic organ models: F(C CyA (t, injection, CL liver, CL organs ), params(C plasma ) )‏ 4. Vasculature network combined with “tissue equations” 5. KIP for 1 parameter: CL i Result: C CyA,i =F(t)‏

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, “We assume that measurements made at distinct times are independent, but measurements made of each concentration are correlated with a response variance--covariance matrix. “

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

Experiment: Rats’ Blood and Tissue concentrations of CyA 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. Blood

ODE Solvers overview at our disposal