1. Introduction_Physiological Modeling.pdf
- 1. Physiological modeling and Simulation Introduction Gizeaddis L. (Ph.D.) School of Medicine Johns Hopkins University 2024 1
- 2. Course outline Course Description • This course aims to provide a practical overview of computational modeling in bioengineering, focusing on a range of applications of importance to modeling organs, tissues and devices. • Different method of approaches will be used the model the physiological systems. • The fast eye movement is briefly 2
- 3. Unit I: Introduction to modeling in Bioengineering – Introduction to modeling – Types of Models – Simulation – The mathematical Modeling Process Course Outline 3
- 4. • Unit II: Methods and Tools for Identification of Physiologic systems – Parametric Approach, – Nonparametric Approach – Modular Approach Course Outline 4
- 5. • Unit III: Modeling and control of organs – Cardiovascular models and control, – Respiratory models and control – Models of neuronal dynamics • Hodgkin Huxley model – Modeling glucose insulin regulation by Matlab tools (Proj 1) Course Outline 5
- 6. Unit IV: Control Movement: – Principles of mechanical properties of bones – Modeling of Bones – Model of muscle mechanism Course Outline 6
- 7. Unit IV: The Fast Eye Movement Control System: Saccade – Characteristics, – Westheimer’s Saccadic Eye Movement Model, – Robinson’s Model of the Saccade Controller, – A Linear Homeomorphic Saccadic Eye Movement Model, – Another Linear Homeomorphic Saccadic Eye Movement Model, – Saccade Pathways and Saccade Control Mechanism Course Outline 7
- 8. Teaching and learning methods – Lectures, Tutorials, Term papers, Presentations, Assignments and Homes study Assessment/Evaluation – In class assessment – 35% – Mid exam – 25% – Final Exam – 40% Course Outline 8
- 9. Literature/References – Physiological control systems: Analysis, simulation and estimation., Michale C. k. Khoo. Pub: Prentice Hall of india Pvt. Ltd. New Delhi. – Biomedical engineering principles: an introduction to fluid, heat and mass transport processes, volume 2 of Biomedical engineering and instrumentation, David O. Cooney. – Introduction of modeling in physiology and medicine, Carson Cobell, Academic Press, Netherland, 2008 – Nonlinear dynamic modeling of physiological system, Vasilis Z Mararelis, Jhon Wiley and sons, New Jersey 2004 – Pharmacokinetic and pharmacodynamic data analysis: concepts and applications, Daniel Weiner, Johan Gabrielsson, Sweden, 2000 Course Outline 9
- 10. 10 What is a Model ? A Representation of an object, a system, or an idea in some form other than that of the entity itself. (Shannon)
- 11. Why Modelling? • The aim of physiological modeling to understand biological processes, then to apply identification and control strategies on it • Fundamental and quantitative way to understand and analyse complex systems and phenomena • Complement to Theory and Experiments 11 • Becoming widespread in: Computational Physics, Chemistry, Mechanics, Materials, …, Biology
- 12. 12 Applications: • Designing and analyzing manufacturing systems • Evaluating H/W and S/W requirements for a computer system • Designing communications systems and message protocols for them • Understand body system dynamics and develop drugs
- 13. Model Physical Mathematical Computer 13 Static Dynamic Static Dynamic Static Dynamic Types of Models: • A static model, represents a system at particular point in time. • A dynamic model represents systems as they change over time.
- 14. 14 Types of Models: Physical (Scale models, prototype plants,…) Mathematical (Analytical queueing models, linear programs, simulation)
- 15. Ways to Study a System 15 System Experiment with a model of the System Experiment with actual System Physical Model Mathematical Model Analytical Solution Simulation Frequency Domain Time Domain Hybrid Domain
- 16. Physical model • Physical model is a smaller or larger physical copy of an object. • The geometry of the model and the object it represents are often similar in the sense that one is a rescaling of the other; in such cases the scale is an important characteristic 16
- 17. Mathematical Modeling? • A mathematical model is a description of a system using mathematical concepts and language. • Mathematical modeling seeks to gain an understanding of science through the use of mathematical models on computers. 17
- 18. Mathematical Modeling • Complements, but does not replace theory and experimentation in scientific research. Experiment Computation Theory 18
- 19. Mathematical Modeling • Is often used in place of experiments when experiments are too large, too expensive, too dangerous, or too time consuming. • Can be useful in “what if” studies; e.g. to investigate the use of pathogens (viruses, bacteria) to control an insect population. • Is a modern tool for scientific investigation. 19
- 20. Classification of Mathematical Models 20
- 21. Mathematical Modeling • Has emerged as a powerful, indispensable tool for studying a variety of problems in scientific research, product and process development, and manufacturing. • Seismology • Climate modeling • Economics • Environment • Material research • Drug design • Manufacturing • Medicine • Biology Analyze - Predict 21
- 22. Different Types of Lumped-Parameter Models Input-output differential equation State equations Transfer function Nonlinear Linear Linear Time Invariant System Type Model Type
- 25. Real World Problem Identify Real-World Problem: – Perform background research, focus on a workable problem. – Conduct investigations (Labs), if appropriate. – Learn the use of a computational tool: Matlab, Mathematica, Excel, Java. Understand current activity and predict future behavior. 25
- 26. Working Model • Simplify → Working Model: – Identify and select factors to describe important aspects of Real World Problem; determine those factors that can be neglected. – State simplifying assumptions. – Determine governing principles, physical laws. – Identify model variables and inter-relationships. 26
- 27. Mathematical Model Represent → Mathematical Model: • Express the Working Model in mathematical terms; • write down mathematical equations whose solution describes the Working Model. In general, the success of a mathematical model depends on how easy it is to use and how accurately it predicts. 27
- 28. Computational Model Translate → Computational Model: • Change Mathematical Model into a form suitable for computational solution. • Computational models include software such as Matlab, Excel, or Mathematica, or languages such as Fortran, C, C++, or Java. 28
- 29. Results/Conclusions Simulate → Results/Conclusions: • Run “Computational Model” to obtain Results; • Draw Conclusions – Verify your computer program; use check cases; explore ranges of validity. – Graphs, charts, and other visualization tools are useful in summarizing results and drawing conclusions. 29
- 30. Real World Problem Interpret Conclusions:. – Compare with Real World Problem behavior – If model results do not “agree” with physical reality or experimental data, reexamine the Working Model (relax assumptions) and repeat modeling steps. – Often, the modeling process proceeds through several iterations until model is “acceptable”. 30
- 31. What do you do with the model? • Solutions—Analytical/Numerical • Interpretation—What does the solution mean in terms of the original problem? • Predictions—What does the model suggest will happen as parameters change? • Validation—Are results consistent with experimental observations? 31
- 32. What are some Limitations of Mathematical Models • Not necessarily a ‘correct’ model • Unrealistic models may fit data very well leading to erroneous conclusions • Simple models are easy to manage, but complexity is often required • Realistic simulations require a large number of hard assumptions to obtain parameters 32
- 33. Why is it Worthwhile to Model Biological Systems • To help reveal possible underlying mechanisms involved in a biological process • To help interpret and reveal contradictions/incompleteness of data • To help confirm/reject hypotheses • To predict system performance under untested conditions 33 • To supply information about the values of experimentally inaccessible parameters • To suggest new hypotheses and stimulate new experiments
- 34. Applications of Modeling Example 1: Tumor Progression • Mathematical models have been developed that describe tumor progression and help predict response to therapy. 34
- 35. Applications Example 2: Electrophysiology of the Cell • In the 1950’s Hodgkin and Huxley introduced the first model to design and to reproduce cell membrane action potentials • They won a nobel prize for this work and sparked the a new field of mathematics - excitable systems 35
- 36. Applications Example 3: Medical Imaging • The image formation in MRI, exemplified for a gradient echo sequence 36