INTRODUCTION 14 12 13 25 3 14 11 21 22 24 28 32 33 11 24 28 5 32 21 22 33 6 7 31 21 22 33 6 15 27 8 17 1 9 NN NN NN MATERIALS AND METHODS Modeling of Pharmacological Response NN Development of Controller Evaluation of Controller NN Modeling of Pharmacological Response the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health n −1 −1 −1 −1 n −1 −1 n −1 −1 n −1 −1 n n −1 −1 n −1 −1 p −1 −1 −1 −1 1 n FIGURE 1. n left right −1 −1 −1 −1 left right −1 −1 −1 −1 −1 −1  18 4 30 1 −1 −1 −1 −1 ŷ t 1 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \Delta \mathop y\limits^ \wedge (t) = K\left[ {1 - {\hbox{exp}}\left( { - \frac{{t - L}} {{T_{\rm c} }}} \right)} \right] $$\end{document} K L T c t L ŷ t n −1 −1 y * t 2 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \Delta y^* (t) = \sum\limits_{\tau = 0}^{N_{\rm m} } {g(\tau )\Delta Tu(t - \tau )} $$\end{document} \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ g(\tau ) = \frac{{K_{\rm u} }} {{T_{\rm c} }}\exp \left( { - \frac{{\tau - L}} {{T_{\rm c} }}} \right) $$\end{document} u t T N m g t K u T c L T N m −1 −1 −1 −1 1 −1 −1 1 −1 −1 −1 −1 K u T c L g t 1 left TABLE 1. Model parameters in linear-fitting and nonlinear-fitting functions. Drug-response Linear Nonlinefsar K u T c L R 2 p 1 p 2 R 2 DBT-CO 15.8 164.3 30 0.98 105.3 0.028 0.99 DBT-MAP 4.4 65.2 30 0.75 22.8 0.145 0.98 SNP-CO 3.0 40.6 60 0.28 37.7 0.051 0.80 SNP-MAP −12.5 209.4 60 0.96 -26.2 −0.085 0.99 K u T c L p 1 p 2 K u −1 −1 −1 −1 T c L p 1 p 2 R 2 y * t 30 3 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \Delta y'(t) = p_1 \tanh \left( {\frac{{p_2 \Delta y^* (t)}} {2}} \right) $$\end{document} p 1 y t p 2 p 1 p 2 1 right 2 2 −1 −1 −1 −1 1 FIGURE 2. a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2  4 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \left\{ \begin{aligned}{} & \Delta CO_{\bmod } (t) = a_1  \Delta CO'_1 (t) + a_2  \Delta CO'_2 (t) \\ & \Delta MAP_{\bmod } (t) = b_1  \Delta MAP'_1 (t) + b_2  \Delta MAP'_2 (t) \\ \end{aligned} \right. $$\end{document} mod t 1 t 2 t a 1 a 2 mod t 1 t 2 t b 1 b 2 2 a 2 b 2 Development of Controller Control Design 3 NN NN FIGURE 3. NN r e t e t i  4 NN NN Learning Loop Prediction Loop y NN mod mod y NN 5 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \Delta y_{{\rm{NN}}} (t) = f\left[ {\Delta y_{{\hbox{mod}}} (t - 1),\,\Delta y_{{\hbox{mod}}} (t - 2),\,u_1 (t - 1),\, \ldots ,\,u_1 (t - 6),\,u_2 (t - 1),\, \ldots ,\,u_2 (t - 6)} \right] $$\end{document} y mod t y mod t u 1 t u 1 t u 2 t u 2 t Learning of Initial Weights in NN 4 mod NN left mod NN right a 1 a 2 b 1 b 2 m n 1 n 2 m n 1 n 2 K n K n 4 4 FIGURE 4. NN mod NN left mod NN right a 1 a 2 b 1 b 2 left right  m n 1 n 2 4 mod mod NN 6 \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym} 
\usepackage{amsfonts} 
\usepackage{amssymb} 
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}
$$ \left\{ \begin{aligned}{} & J_1 (t) = q_1 \left[ {u_1 (t) - u_1 (t - 1)} \right]^2 + \sum\limits_{i = 1}^{N_{p1} } {\left[ {r_1 (t + i) - \Delta {\hbox{CO}}_{{\rm{NN}}} (t + i)} \right]^2 } \\ & J_2 (t) = q_2 \left[ {u_2 (t) - u_2 (t - 1)} \right]^2 + \sum\limits_{i = 1}^{N_{p2} } {\left[ {r_2 (t + i) - \Delta {\hbox{MAP}}_{{\rm{NN}}} (t + i)} \right]^2 } \\ \end{aligned} \right. $$\end{document} J 1 t J 2 t q 1 q 2 N p N p r 1 r 2 NN NN u 1 t u 2 t 16 27 Determination of Control Parameters Learning of Initial Weights in NN mod mod NN −1 −1 9 27 mod mod mod mod 4 mod NN left mod NN right a 1 a 2 b 1 b 2 K n K n mod mod −1 −1 Controller Tuning N p N p q 1 q 2 mod mod N p N p q 1 q 2 mod mod K n K n r 1 t −1 −1 r 1 −1 −1 r 2 5 NN mod mod a 1 a 2 b 1 b 2 q 1 = q 2 N p N p q 1 = q 2 N p N p q 1 = q 2 N p N p N p N p q 1 q 2 NN N p N p q 1 q 2 −1 −1 mod mod mod mod −1 −1 FIGURE 5. NN mod mod a 1 = a 2 = b 1 = b 2 = q 1 q 2 N p N p K n K n  Evaluation of Controller Simulations NN 22 30 −1 −1 6 7 −1 −1 1 −1 −1 t 1 u 1 t u 2 t 5 22 Drug Interactions 6 30 a 1 a 2 b 1 b 2 6 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 FIGURE 6. NN a 1 a 2 b 1 b 2 mod mod  NN a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 Acute Disturbances 10 20 NN mod mod −1 −1 mod mod −1 −1 mod mod 9 NN −1 −1 mod mod −1 −1 −1 −1 a 1 a 2 b 1 b 2 10 NN −1 −1 mod mod −1 −1 −1 −1 a 1 a 2 b 1 b 2 11 NN a 1 a 2 b 1 b 2 −1 −1 mod mod 11 Time-variant Changes 2 26 30 L 12 a 1 a 2 b 1 b 2 12 −1 −1 mod mod. −1 −1 mod mod 12 Animal Study NN −1 −1 u 1 t u 2 t RESULTS Simulations Drug Interactions 6 NN N p N p q 1 q 2 K n K n −1 −1 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 −1 −1 −1 −1 6 2 NN N p N p q 1 q 2 K n K n a 1 a 1 7 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 TABLE 2. Average errors between setpoints and model responses in CO and MAP under various sensitvities to drugs and drug interactions. a 1 Low Mid. High a 2          b 1 b 2 Low Mid. High Low Mid. High Low Mid. High Low Low 5.5 (0.5) 4.8 (0.4) 3.4 (0.3) 2.9 (0.3) 2.7 (0.3) 2.2 (0.2) 1.3 (0.1) 1.2 (0.1) 1.2 (0.1) Mid. 5.3 (10.3) 4.1 (4.8) 3.0 (1.0) 3.3 (1.9) 2.6 (1.0) 2.0 (0.7) 1.3 (0.5) 1.2 (0.5) 1.2 (0.4) High 5.7 (45.0*) 3.8 (25.1*) 4.2 (3.0) 3.5 (17.3) 2.9 (6.1) 2.2 (1.6) 4.2 (3.4) 3.9 (3.5) 1.5 (1.2) Mid. Low 6.0 (1.2) 5.7 (1.2) 5.8 (1.1) 3.2 (0.6) 2.9 (0.6) 2.4 (0.5) 1.5 (0.4) 1.4 (0.4) 1.3 (0.3) Mid. 5.5 (0.6) 4.7 (0.5) 3.5 (0.4) 3.2 (0.5) 2.8 (0.5) 2.1 (0.4) 1.6 (0.4) 1.4 (0.4) 1.3 (0.3) High 5.3 (29.6*) 3.8 (12.2) 3.4 (1.9) 3.3 (3.9) 2.7 (1.4) 2.0 (1.0) 1.9 (1.1) 1.7 (0.9) 1.3 (0.7) High Low 6.0 (2.5) 5.9 (2.5) 6.2 (2.3) 2.8 (0.7) 2.8 (0.6) 2.7 (0.7) 1.3 (0.6) 1.3 (0.5) 1.3 (0.4) Mid. 6.0 (4.1) 6.2 (3.9) 7.0 (3.4) 2.9 (0.6) 2.8 (0.6) 2.5 (0.6) 1.4 (0.6) 1.3 (0.5) 1.3 (0.4) High 5.6 (1.0) 4.8 (0.7) 6.4 (4.3) 3.2 (0.8) 2.9 (0.8) 2.3 (1.3) 2.0 (1.6) 1.8 (1.6) 1.5 (1.5) 7 FIGURE 7. NN a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 top middle bottom left right  NN 7 −1 −1 8 NN N p N p q 1 q 2 K n K n a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 −1 −1 a 1 8 left −1 −1 a 1 a 2 b 1 b 2 −1 −1 a 1 a 2 b 1 b 2 8 NN FIGURE 8. NN a 1 a 2 b 1 b 2 a 1 a 2 b 1 b 2 top middle bottom left right  Acute Disturbances 9 NN N p N p q 1 q 2 K n K n −1 −1 −1 −1 a 1 a 2 b 1 b 2 mod mod −1 −1 mod NN −1 −1 9 FIGURE 9. NN mod mod mod mod  10 NN N p N p q 1 q 2 K n K n mod mod 10 a 1 a 2 b 1 b 2 10 FIGURE 10. NN mod mod mod mod −1 −1  −1 −1  mod mod a 1 a 2 b 1 b 2  11 NN N p N p q 1 q 2 K n K n −1 −1 mod mod −1 −1 −1 −1 a 1 a 2 b 1 b 2 FIGURE 11. NN −1 −1 mod mod −1 −1 −1 −1 −1 −1 a 1 a 2 b 1 b 2 top middle bottom left right  11 NN N p N p q 1 q 2 K n K n −1 −1 a 1 a 2 b 1 b 2 −1 −1 b 1 Time-variant Changes 12 NN N p N p q 1 q 2 K n K n −1 −1 −1 −1 −1 −1 −1 −1 12 FIGURE 12. NN L a 1 a 2 b 1 b 2 mod mod mod mod  Animal Study 13 NN N p N p q 1 q 2 K n K n NN −1 −1 FIGURE 13. NN  DISCUSSION NN 6 9 12 13 1 14 β 1 β 2 30 1 6 6 9 12 13 NN 12 13 25 NN 6 9 12 13 6 NN 7 10 NN 9 12 2 26 NN 12 NN 13 6 9 12 3 21 5 2 14 NN NN 6 9 12 13 NN 9 1 22 29 NN NN 7 8 10 11 NN 8 11 NN 7 8 11 b 2 b 1 7 NN NN NN 7 7 11 NN a 1 8 11 NN NN Modeling of Pharmacological Response 19 CONCLUSIONS NN NN 2