Control of Biological and Drug-Delivery Systems for Chemical, Biomedical, and Pharmaceutical Engineering

PREFACE xi ACKNOWLEDGMENTS xv 1 INTRODUCTION 1 1.1 The Role of Process Dynamics and Control in Branches of Biology 1 1.2 The Role of Process Dynamics and Control in Drug-Delivery Systems 10 1.3 Instrumentation 12 1.4 Summary 18 Problems 18 References 19 2 MATHEMATICAL MODELS 21 2.1 Background 22 2.2 Dynamics of Bioreactors 27 2.3 One- and Two-Compartment Models 34 2.4 Enzyme Kinetics 37 2.5 Summary 39 Problems 39 References 41 3 LINEARIZATION AND DEVIATION VARIABLES 43 3.1 Computer Simulations 43 3.2 Linearization of Systems 44 3.3 Glycolytic Oscillation 55 3.4 Hodgkin-Huxley Model 57 3.5 Summary 60 Problems 61 References 63 4 STABILITY CONSIDERATIONS 65 4.1 Definition of Stability 65 4.2 Steady-State Conditions and Equilibrium Points 79 4.3 Phase-Plane Diagrams 80 4.4 Population Kinetics 80 4.5 Dynamics of Bioreactors 83 4.6 Glycolytic Oscillation 85 4.7 Hodgkin-Huxley Model 87 4.8 Summary 88 Problems 88 References 91 5 LAPLACE TRANSFORMS 93 5.1 Definition of Laplace Transforms 93 5.2 Properties of Laplace Transforms 95 5.3 Laplace Transforms of Functions, Derivatives, and Integrals 96 5.4 Laplace Transforms of Linear Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE) 104 5.5 Continuous Fermentation 108 5.6 Two-Compartment Models 110 5.7 Gene Regulation 111 5.8 Summary 113 Problems 113 Reference 115 6 INVERSE LAPLACE TRANSFORMS 117 6.1 Heaviside Expansions 117 6.2 Residue Theorem 126 6.3 Continuous Fermentation 134 6.4 Degradation of Plasmid DNA 136 6.5 Constant-Rate Intravenous Infusion 138 6.6 Transdermal Drug-Delivery Systems 139 6.7 Summary 146 Problems 146 References 148 7 TRANSFER FUNCTIONS 149 7.1 Input-Output Models 149 7.2 Derivation of Transfer Functions 150 7.3 One- and Two-Compartment Models: Michaelis-Menten Kinetics 154 7.4 Controlled-Release Systems 157 7.5 Summary 158 Problems 158 8 DYNAMIC BEHAVIORS OF TYPICAL PLANTS 163 8.1 First-, Second- and Higher-Order Systems 163 8.2 Reduced-Order Models 167 8.3 Transcendental Transfer Functions 169 8.4 Time Responses of Systems with Rational Transfer Functions 171 8.5 Time Responses of Systems with Transcendental Transfer Functions 190 8.6 Bone Regeneration 192 8.7 Nitric Oxide Transport to Pulmonary Arterioles 193 8.8 Transdermal Drug Delivery 194 8.9 Summary 194 Problems 195 References 197 9 CLOSED-LOOP RESPONSES WITH P, PI, AND PID CONTROLLERS 199 9.1 Block Diagram of Closed-Loop Systems 200 9.2 Proportional Control 203 9.3 PI Control 204 9.4 PID Control 206 9.5 Total Sugar Concentration in a Glutamic Acid Production 207 9.6 Temperature Control of Fermentations 209 9.7 DO Concentration 213 9.8 Summary 214 Problems 215 References 217 10 FREQUENCY RESPONSE ANALYSIS 219 10.1 Frequency Response for Linear Systems 219 10.2 Bode Diagrams 227 10.3 Nyquist Plots 229 10.4 Transdermal Drug Delivery 232 10.5 Compartmental Models 236 10.6 Summary 239 Problems 239 References 240 11 STABILITY ANALYSIS OF FEEDBACK SYSTEMS 243 11.1 Routh-Hurwitz Stability Criterion 243 11.2 Root Locus Analysis 248 11.3 Bode Stability Criterion 249 11.4 Nyquist Stability Criterion 254 11.5 Cheyne-Stokes Respiration 257 11.6 Regulation of Biological Pathways 262 11.7 Pupillary Light Reflex 264 11.8 Summary 265 Problems 265 References 267 12 DESIGN OF FEEDBACK CONTROLLERS 269 12.1 Tuning Methods for Feedback Controllers 269 12.2 Regulation of Glycemia 279 12.3 Dissolved Oxygen Concentration 282 12.4 Control of Biomass in a Chemostat 284 12.5 Controlled Infusion of Vasoactive Drugs 285 12.6 Bone Regeneration 286 12.7 Fed-Batch Biochemical Processes 288 12.8 Summary 289 Problems 289 References 291 13 FEEDBACK CONTROL OF DEAD-TIME SYSTEMS 293 13.1 Smith Predictor-Based Methods 294 13.2 Control of Biomass 300 13.3 Zymomonas mobilis Fermentation for Ethanol Production 302 13.4 Fed-Batch Cultivation of Acinetobacter calcoaceticus RAG-1 304 13.5 Regulation of Glycemia 304 13.6 Summary 306 Problems 306 References 309 14 CASCADE AND FEEDFORWARD CONTROL STRATEGIES 311 14.1 Cascade Control 311 14.2 Feedforward Control 317 14.3 Insulin Infusion 321 14.4 A Gaze Control System 323 14.5 Control of pH 326 14.6 Summary 330 Problems 331 References 333 15 EFFECTIVE TIME CONSTANT 335 15.1 Linear Second-Order ODEs 335 15.2 Sturm-Liouville (SL) Eigenvalue Problems 337 15.3 Relaxation Time Constant 340 15.4 Implementation in Mathematica(r) 342 15.5 Controlled-Release Devices 342 15.6 Summary 343 Problems 344 References 345 16 OPTIMUM CONTROL AND DESIGN 347 16.1 Orthogonal Collocation Techniques 348 16.2 Dynamic Programming 350 16.3 Optimal Control of Drug-Delivery Rates 350 16.4 Optimal Design of Controlled-Release Devices 351 16.5 Implementation in Mathematica(r) 352 16.6 Summary 358 Problems 359 References 360 INDEX 361