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

LAURENT SIMON, PhD, is Associate Professor of Chemical Engineering and Associate Director of the Pharmaceutical Engineering Program at New Jersey Institute of Technology. His research and teaching interests focus on modeling, analysis, and control of drug delivery systems. Dr. Simon is the author of Laboratory Online, a series of educational and interactive modules that help engineers build a strong understanding of drug delivery technologies and their underlying engineering principles. During his time at NJIT, Dr. Simon has received the Excellence in Teaching Award, Master Teacher Designation, and Newark College of Engineering Saul K. Fenster Innovation in Engineering Education Award.

"This text — featuring examples from the biological sciences, including novel drug-delivery systems — will help students and pharmaceutical researchers to develop a better understanding of process dynamics and control theory, so that they can analyze and solve a variety of problems in bioprocess and drug-delivery systems." (Chemical Engineering Progress, 21 May 2013)

• Preface xiAcknowledgments xv1 Introduction 11.1 The Role of Process Dynamics and Control in Branches of Biology 11.2 The Role of Process Dynamics and Control in Drug-Delivery Systems 101.3 Instrumentation 121.4 Summary 18Problems 18References 192 Mathematical Models 212.1 Background 222.2 Dynamics of Bioreactors 272.3 One- and Two-Compartment Models 342.4 Enzyme Kinetics 372.5 Summary 39Problems 39References 413 Linearization and Deviation Variables 433.1 Computer Simulations 433.2 Linearization of Systems 443.3 Glycolytic Oscillation 553.4 Hodgkin–Huxley Model 573.5 Summary 60Problems 61References 634 Stability Considerations 654.1 Definition of Stability 654.2 Steady-State Conditions and Equilibrium Points 794.3 Phase-Plane Diagrams 804.4 Population Kinetics 804.5 Dynamics of Bioreactors 834.6 Glycolytic Oscillation 854.7 Hodgkin–Huxley Model 874.8 Summary 88Problems 88References 915 Laplace Transforms 935.1 Definition of Laplace Transforms 935.2 Properties of Laplace Transforms 955.3 Laplace Transforms of Functions, Derivatives, and Integrals 965.4 Laplace Transforms of Linear Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE) 1045.5 Continuous Fermentation 1085.6 Two-Compartment Models 1105.7 Gene Regulation 1115.8 Summary 113Problems 113Reference 1156 Inverse Laplace Transforms 1176.1 Heaviside Expansions 1176.2 Residue Theorem 1266.3 Continuous Fermentation 1346.4 Degradation of Plasmid DNA 1366.5 Constant-Rate Intravenous Infusion 1386.6 Transdermal Drug-Delivery Systems 1396.7 Summary 146Problems 146References 1487 Transfer Functions 1497.1 Input–Output Models 1497.2 Derivation of Transfer Functions 1507.3 One- and Two-Compartment Models: Michaelis–Menten Kinetics 1547.4 Controlled-Release Systems 1577.5 Summary 158Problems 1588 Dynamic Behaviors of Typical Plants 1638.1 First-, Second- and Higher-Order Systems 1638.2 Reduced-Order Models 1678.3 Transcendental Transfer Functions 1698.4 Time Responses of Systems with Rational Transfer Functions 1718.5 Time Responses of Systems with Transcendental Transfer Functions 1908.6 Bone Regeneration 1928.7 Nitric Oxide Transport to Pulmonary Arterioles 1938.8 Transdermal Drug Delivery 1948.9 Summary 194Problems 195References 1979 Closed-loop Responses with P, Pi, and Pid Controllers 1999.1 Block Diagram of Closed-Loop Systems 2009.2 Proportional Control 2039.3 PI Control 2049.4 PID Control 2069.5 Total Sugar Concentration in a Glutamic Acid Production 2079.6 Temperature Control of Fermentations 2099.7 DO Concentration 2139.8 Summary 214Problems 215References 21710 Frequency Response Analysis 21910.1 Frequency Response for Linear Systems 21910.2 Bode Diagrams 22710.3 Nyquist Plots 22910.4 Transdermal Drug Delivery 23210.5 Compartmental Models 23610.6 Summary 239Problems 239References 24011 Stability Analysis of Feedback Systems 24311.1 Routh–Hurwitz Stability Criterion 24311.2 Root Locus Analysis 24811.3 Bode Stability Criterion 24911.4 Nyquist Stability Criterion 25411.5 Cheyne–Stokes Respiration 25711.6 Regulation of Biological Pathways 26211.7 Pupillary Light Reflex 26411.8 Summary 265Problems 265References 26712 Design of Feedback Controllers 26912.1 Tuning Methods for Feedback Controllers 26912.2 Regulation of Glycemia 27912.3 Dissolved Oxygen Concentration 28212.4 Control of Biomass in a Chemostat 28412.5 Controlled Infusion of Vasoactive Drugs 28512.6 Bone Regeneration 28612.7 Fed-Batch Biochemical Processes 28812.8 Summary 289Problems 289References 29113 Feedback Control of Dead-time Systems 29313.1 Smith Predictor-Based Methods 29413.2 Control of Biomass 30013.3 Zymomonas mobilis Fermentation for Ethanol Production 30213.4 Fed-Batch Cultivation of Acinetobacter calcoaceticus Rag-1 30413.5 Regulation of Glycemia 30413.6 Summary 306Problems 306References 30914 Cascade and Feedforward Control Strategies 31114.1 Cascade Control 31114.2 Feedforward Control 31714.3 Insulin Infusion 32114.4 A Gaze Control System 32314.5 Control of pH 32614.6 Summary 330Problems 331References 33315 Effective Time Constant 33515.1 Linear Second-Order ODEs 33515.2 Sturm–Liouville (SL) Eigenvalue Problems 33715.3 Relaxation Time Constant 34015.4 Implementation in Mathematica ® 34215.5 Controlled-Release Devices 34215.6 Summary 343Problems 344References 34516 Optimum Control and Design 34716.1 Orthogonal Collocation Techniques 34816.2 Dynamic Programming 35016.3 Optimal Control of Drug-Delivery Rates 35016.4 Optimal Design of Controlled-Release Devices 35116.5 Implementation in Mathematica ® 35216.6 Summary 358Problems 359References 360Index 361Preface xiAcknowledgments xv1 Introduction 11.1 The Role of Process Dynamics and Control in Branches of Biology 11.2 The Role of Process Dynamics and Control in Drug-Delivery Systems 101.3 Instrumentation 121.4 Summary 18Problems 18References 192 Mathematical Models 212.1 Background 222.2 Dynamics of Bioreactors 272.3 One- and Two-Compartment Models 342.4 Enzyme Kinetics 372.5 Summary 39Problems 39References 413 Linearization and Deviation Variables 433.1 Computer Simulations 433.2 Linearization of Systems 443.3 Glycolytic Oscillation 553.4 Hodgkin–Huxley Model 573.5 Summary 60Problems 61References 634 Stability Considerations 654.1 Definition of Stability 654.2 Steady-State Conditions and Equilibrium Points 794.3 Phase-Plane Diagrams 804.4 Population Kinetics 804.5 Dynamics of Bioreactors 834.6 Glycolytic Oscillation 854.7 Hodgkin–Huxley Model 874.8 Summary 88Problems 88References 915 Laplace Transforms 935.1 Definition of Laplace Transforms 935.2 Properties of Laplace Transforms 955.3 Laplace Transforms of Functions, Derivatives, and Integrals 965.4 Laplace Transforms of Linear Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE) 1045.5 Continuous Fermentation 1085.6 Two-Compartment Models 1105.7 Gene Regulation 1115.8 Summary 113Problems 113Reference 1156 Inverse Laplace Transforms 1176.1 Heaviside Expansions 1176.2 Residue Theorem 1266.3 Continuous Fermentation 1346.4 Degradation of Plasmid DNA 1366.5 Constant-Rate Intravenous Infusion 1386.6 Transdermal Drug-Delivery Systems 1396.7 Summary 146Problems 146References 1487 Transfer Functions 1497.1 Input–Output Models 1497.2 Derivation of Transfer Functions 1507.3 One- and Two-Compartment Models: Michaelis–Menten Kinetics 1547.4 Controlled-Release Systems 1577.5 Summary 158Problems 1588 Dynamic Behaviors of Typical Plants 1638.1 First-, Second- and Higher-Order Systems 1638.2 Reduced-Order Models 1678.3 Transcendental Transfer Functions 1698.4 Time Responses of Systems with Rational Transfer Functions 1718.5 Time Responses of Systems with Transcendental Transfer Functions 1908.6 Bone Regeneration 1928.7 Nitric Oxide Transport to Pulmonary Arterioles 1938.8 Transdermal Drug Delivery 1948.9 Summary 194Problems 195References 1979 Closed-loop Responses with P, Pi, and Pid Controllers 1999.1 Block Diagram of Closed-Loop Systems 2009.2 Proportional Control 2039.3 PI Control 2049.4 PID Control 2069.5 Total Sugar Concentration in a Glutamic Acid Production 2079.6 Temperature Control of Fermentations 2099.7 DO Concentration 2139.8 Summary 214Problems 215References 21710 Frequency Response Analysis 21910.1 Frequency Response for Linear Systems 21910.2 Bode Diagrams 22710.3 Nyquist Plots 22910.4 Transdermal Drug Delivery 23210.5 Compartmental Models 23610.6 Summary 239Problems 239References 24011 Stability Analysis of Feedback Systems 24311.1 Routh–Hurwitz Stability Criterion 24311.2 Root Locus Analysis 24811.3 Bode Stability Criterion 24911.4 Nyquist Stability Criterion 25411.5 Cheyne–Stokes Respiration 25711.6 Regulation of Biological Pathways 26211.7 Pupillary Light Reflex 26411.8 Summary 265Problems 265References 26712 Design of Feedback Controllers 26912.1 Tuning Methods for Feedback Controllers 26912.2 Regulation of Glycemia 27912.3 Dissolved Oxygen Concentration 28212.4 Control of Biomass in a Chemostat 28412.5 Controlled Infusion of Vasoactive Drugs 28512.6 Bone Regeneration 28612.7 Fed-Batch Biochemical Processes 28812.8 Summary 289Problems 289References 29113 Feedback Control of Dead-time Systems 29313.1 Smith Predictor-Based Methods 29413.2 Control of Biomass 30013.3 Zymomonas mobilis Fermentation for Ethanol Production 30213.4 Fed-Batch Cultivation of Acinetobacter calcoaceticus Rag-1 30413.5 Regulation of Glycemia 30413.6 Summary 306Problems 306References 30914 Cascade and Feedforward Control Strategies 31114.1 Cascade Control 31114.2 Feedforward Control 31714.3 Insulin Infusion 32114.4 A Gaze Control System 32314.5 Control of pH 32614.6 Summary 330Problems 331References 33315 Effective Time Constant 33515.1 Linear Second-Order ODEs 33515.2 Sturm–Liouville (SL) Eigenvalue Problems 33715.3 Relaxation Time Constant 34015.4 Implementation in Mathematica ® 34215.5 Controlled-Release Devices 34215.6 Summary 343Problems 344References 34516 Optimum Control and Design 34716.1 Orthogonal Collocation Techniques 34816.2 Dynamic Programming 35016.3 Optimal Control of Drug-Delivery Rates 35016.4 Optimal Design of Controlled-Release Devices 35116.5 Implementation in Mathematica ® 35216.6 Summary 358Problems 359References 360Index 361