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El. knyga: Thyroid Systems Engineering: A Primer in Mathematical Modeling of the Hypothalamus-Pituitary-Thyroid Axis

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In recent years, a considerable amount of effort has been devoted, both in industry and academia, towards the behavioral modeling, evaluation and prediction of the hypothalamus pituitary thyroid system.Thyroid Systems Engineering targets an optimal treatment of people suffering from thyroid hormone disorders. The content is motivated by in-depth observations of such patients whose rich data supported the theoretical framework arising from formal mathematical reasoning, guided by the nature of thyroid physiology. Leveraging on the insights emerging from the unique combination of an electrical engineer working with a clinical thyroidologist, and both being scientists skilled in mathematics, the authors introduce this new discipline and field of scientific investigation aptly designated as Thyroid Systems Engineering.Readers will discover that mathematics can indeed model the behavior of the hypothalamus-pituitary-thyroid (HPT) axis. Focused on modeling, each of the eighteen chapters gives the reader a notion of the application of relevant mathematics to pertinent issues encountered in mainstream thyroidology. Many cellular processes resemble the flux of variables and states in a complex multi-parameter space through time analogous to current flow in electrical networks. It is then logical to apply the principles and physical laws of electrodynamics, electrical network theory, control systems theory and signal theory to many of the biological phenomena encountered in endocrinology. Such an approach is used liberally throughout the book and successfully yields elegant solutions to a number of models presented within.This book can serve as a reference to mathematical modeling in other aspects of endocrine physiology, and as the starting point for a fundamental course in medical modeling. It will appeal to postgraduates in electrical engineering, academic physicians and biomedical researchers. Further, readers equipped with advanced calculus, electrical network theory, control theory and signal theory should be able to follow the mathematical expositions that describe thyrotropic control. They represent a new discipline based on mathematical modeling in physiology applicable to medical diagnostics, measurement and treatment to cooperate in the clinical team and realize an optimized treatment for patients.
Preface xv
Acknowledgements xix
List of Figures xxi
List of Tables xxxiii
List of Abbreviations xxxv
1 General Introduction 1(12)
1.1 Introduction
1(4)
2 Physiology of the HPT Axis
5(1)
2.1 Synopsis of Thyroid Biochemistry and Molecular Biology
5(2)
2.2 Operation of the Hypothalamus-Pituitary (HP) System
7(1)
2.3 Thyroid Physiology
8(1)
2.4 Physiological Feedback Representation of the HPT System
8(2)
References
10(3)
3 Modeling Principles 13(22)
3.1 Introduction
13(2)
3.2 Modeling Examples
15(6)
3.2.1 Modeling Example 1
15(6)
3.3 Electrical Network Representation of the Leaking Water Container
21(3)
3.4 Static Modeling
24(2)
3.5 Modeling Examples from Solid-state Physics and Electronic Engineering
26(2)
3.6 General Appearance and Decay Model with Electrical Network Elements
28(2)
3.7 Appearance Time Constant
30(1)
3.8 Determining the Value of the Appearance Time Constant
31(1)
3.9 Discussion
32(1)
3.10 Conclusion
33(1)
References
34(1)
4 Medical Statistics and Mathematical Modeling Make Strange Bedfellows 35(12)
4.1 Introduction
35(1)
4.2 Pitfalls in the Application of Inferential Statistical Methods
36(5)
4.2.1 Explanation of the Observed Log-linear Relationship between [ TSH] and [ FT4]
40(1)
4.3 Abuse of Mathematical Models
41(2)
4.3.1 Critical Notes
41(2)
4.4 Future Developments
43(1)
4.5 Conclusion
44(1)
References
45(2)
5 Systems Theory Applied on the Modeling of the HPT Axis and First Principles of Feedback and Homeostasis 47(24)
5.1 Introduction
47(7)
5.2 Definition of System Components
54(4)
5.3 System Dynamics
58(3)
5.4 Frequency Response of the First-order Low-pass Section
61(3)
5.5 Cascading System Blocks
64(1)
5.6 Example of a Feedback System
64(5)
5.6.1 Feed Forward Compensation
68(1)
5.7 Discussion
69(1)
References
69(2)
6 The Mathematical Relationship between [ FT4] and [ TSH] 71(22)
6.1 Introduction
71(4)
6.1.1 History
71(4)
6.2 Linear-logarithmic Relationship between [ FT4] and [ TSH]
75(5)
6.3 Modeling the Curved [ FT4]-[ TSH] Characteristic
80(3)
6.4 Properties of the Exponential Function
83(4)
6.4.1 Effect of the Multiplier Model Parameter S
84(1)
6.4.2 Effect of the Exponential Model Parameter phi
85(2)
6.5 Dynamic Signal Transfer of the HP Characteristic
87(1)
6.6 Generalized Expression of the HP Characteristic
88(1)
6.7 Discussion
89(1)
References
90(3)
7 The Thyroid Gland and the Relationship Between [ TSH] and [ FT4] 93(6)
7.1 Introduction
93(1)
7.2 Model of the Thyroid Gland
94(3)
7.3 Discussion
97(1)
References
98(1)
8 The Hypothalamus-Pituitary (HPT) Set Point Theory 99(36)
8.1 Introduction
99(1)
8.2 The Hypothalamus-Pituitary (HP) Control System
100(2)
8.3 Derivation of the Point of Maximum Curvature from the HP Function
102(2)
8.4 Theory Behind of the Physiology of the Homeostatic Control Process
104(1)
8.5 Point of Maximum Curvature of the Thyroid Characteristic
105(2)
8.6 Discussion
107(1)
References
108(3)
9 The Human Hypothalamus-Pituitary-Thyroid Control System
111(1)
9.1 Introduction
111(3)
9.2 Analysis of the HP Unit and Thyroid in the Closed-Loop Situation
114(5)
9.3 Small-Signal Model of the Thyroid
119(1)
9.4 Small-Signal Modeling of the Hypothalamus-Pituitary (HP) Unit
120(1)
9.5 Loop Gain Analysis
121(3)
9.6 Hypothalamus (TRH)-Pituitary (TSH) Transfer
124(3)
9.7 The Detailed HPT Loop
127(1)
9.8 Large-Signal Intercept Set Point
128(3)
9.9 Discussion
131(1)
References
132(3)
10 Reference Ranges for TSH and FT4 135(10)
10.1 Introduction
135(1)
10.2 Reference Ranges for [ FT4] and [ TSH]
136(2)
10.3 Set Point Determined Euthyroid Ranges for [ TSH]
138(1)
10.4 Different Reference Ranges in Different Laboratories
139(3)
10.5 Discussion
142(1)
10.6 Concluding Remarks
143(1)
References
144(1)
11 Extrapolation to the Set Point from a Single Available Measurement 145(30)
11.1 Introduction
145(1)
11.2 Calculation of [ FT4] Assuming a Pre-determined Set Point Value of [ TSH]
146(3)
11.3 Calculation of [ TSH] Assuming a Set Point Value of [ FT4] = 15 pmol/L
149(1)
11.4 Extrapolation to a Set Point Using a "Phantom" [ FT4]-[ TSH] Point
150(4)
11.5 Discussion
154(3)
12 Measurement Methods, Error Sources, and Error Interpretation of FT4 and TSH Concentration Values
157(1)
12.1 Introduction
157(3)
12.2 Error Definitions and Error Sources
160(1)
12.3 Measurement Theory
161(1)
12.4 [ FT4] and [ TSH] Measurement or Thyroid Function Tests (TFTs)
162(1)
12.5 Sensitivity of Model Parameter phi as a Function of [ FT4] and [ TSH]
163(1)
12.6 Measurement Errors from [ FT4] Rounding or Truncation Procedure
163(2)
12.7 Absolute Deviation of [ FT4] as a Function of Relative [ TSH] Error
165(1)
12.8 The Effect of Absolute Errors in [ FT4] Resulting in Deviations of [ TSH]
166(1)
12.9 Errors from Physiological Memory Effects, or Hysteresis
167(2)
12.10 Errors from Biochemical Assay Technology for [ TSH] and [ FT4]
169(2)
12.11 Discussion
171(1)
12.12 Conclusion
172(1)
References
173(2)
13 Model Identification, Validation, and Outlier Selection 175(12)
13.1 Introduction
175(2)
13.1.1 A Brief History of Celestial Modeling as a Prelude to Model Validation
175(2)
13.2 Model Identification
177(5)
13.3 Examples of [ TSH], [ FT4], and [ FT3] Outlier Identification
182(1)
13.4 Discussion
183(1)
References
184(3)
14 Half-Life and Plasma Appearance Dynamics of T3 and T4 187(20)
14.1 Introduction
187(1)
14.2 Half-Life (t1/2) of T4 and Calculation of the Decay Time Constant
188(4)
14.2.1 Half-Life Modeling with Electrical Networks
190(2)
14.3 Drug Input and Output Signals
192(9)
14.3.1 Network Model
197(4)
14.4 Decay Behavior after Finalization of Drug Appearance
201(4)
14.5 Discussion
205(1)
References
206(1)
15 Pharmacokinetics of Liothyronine (L-T3) and Levothyroxine (L-T4) 207(26)
15.1 Introduction
207(2)
15.2 Thyroxine Kinetics
209(2)
15.2.1 PK of L-T4 with T4 Level Dependent and Constant t1/2 When Administered as a Daily Dose
209(1)
15.2.2 Derivation of the Steady-State Level
209(2)
15.3 Average Value of Time-Dependent Functions
211(1)
15.4 RMS Value of Continuous Time-Dependent Functions
212(1)
15.5 Weekly Administration of L-T4 at Seven Times the Normal Daily Dose
213(2)
15.6 Triiodothyronine Kinetics
215(3)
15.6.1 Accumulation of T3 Based on Various Dosages of Daily Liothyronine (L-T3)
215(1)
15.6.2 Accumulation of T3 over a Period of 9 days with a Daily Dose Dd of 12.5 microg L-T3
215(3)
15.7 Compensation Strategies When L-T4 Is Not Taken Regularly
218(6)
15.7.1 Acceleration Toward Steady State for a 100 microg L-T4 Daily Dosing Scheme Within 1 Week
218(6)
15.8 Calculation of a Reduced Dosing Scheme
224(1)
15.9 Negative Long-term Effects of Externally Administered T3
225(1)
15.10 Discussion
226(2)
Appendix
228(2)
References
230(3)
16 Circadian Feedback Dynamics and Set Point Stability Analysis of the Hypothalamus Pituitary Thyroid System 233(22)
16.1 Introduction
233(2)
16.2 Oscillators
235(3)
16.3 Influence of [ FT4] and [ TSH] on Feedback Dynamics
238(2)
16.4 [ TSH] Oscillations
240(1)
16.5 Data Analysis
240(4)
16.6 Fourier Analysis
244(3)
16.7 Convolution and Deconvolution
247(1)
16.8 Thyroid Response
248(1)
16.9 Set Point Stability
248(2)
16.10 Discussion
250(2)
16.11 Concluding Remarks
252(1)
References
252(3)
17 HPT Simulation with Trans-linear Circuits 255(24)
17.1 Introduction
255(2)
17.2 Generalized Stimulated Gland Characteristics
257(3)
17.3 Large-signal Intercept Set Point
260(3)
17.4 Differential Amplifiers
263(4)
17.5 Trans-linear Circuits
267(3)
17.5.1 Introduction
267(2)
17.5.2 Examples of Signal Processing with Trans-linear Circuits
269(1)
17.6 HPT Functions with Trans-linear Circuits
270(2)
17.7 The Electronic HP System Implementation
272(1)
17.8 The Electronic Thyroid Implementation
273(2)
17.9 Discussion
275(1)
References
276(3)
18 From Theory to Practice: Computer-aided Set Point Application 279(10)
18.1 Introduction
279(1)
18.2 Thyroid-SPOT Software
280(2)
18.3 Clinical Studies Using Thyroid-SPOT
282(1)
18.4 Thyroid-SPOT (Set Point Optimization and Targeting)
283(2)
18.5 Thyroid Function Tests
285(2)
18.6 Interpretation of Test Results
287(1)
References
288(1)
Appendix 289(4)
Index 293(6)
About the Authors 299
Simon Goede, Melvin Khee-Shing Leow
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