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Douglas Christensen Department of Bioengineering University of Utah Salt Lake City, Utah Bringing an Integrative Modeling Experience to Freshman Biomedical Engineering Courses

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Univ of Utah Goals for our freshman courses Welcome students to the University and Department. Give students early exposure to exciting aspects of Biomedical Engineering. But …..

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Univ of Utah But ….. Need to challenge students with realistic engineering tasks for them to accurately assess: their skill level their interest level. Goals for our freshman courses (cont)

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Univ of Utah 1st Semester - Biomechanical and bioelectrical 2nd Semester - Biochemical, cellular and biosensors Two freshman courses

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Univ of Utah 1st semester course structure Major lab project (modeling the human cardiovascular system) - entire semester. Lectures - “just-in-time” for project steps. Based on 15 units: Laws and Principles - most (80%) are needed for solution of major project.

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Univ of Utah Laws and principles 1. Numbers, Units and Consistency Checks 2. Darcy’s Law (membranes) 3. Poiseuille’s Law (flow through tubes) 4. Hooke’s Law (elasticity and compliance) 5. Starling’s Law (cardiac adjustment ) 6. Euler’s Method (finite-difference solutions) 7. Muscle, Force and Leverage 8. Work, Energy and Power

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Univ of Utah Laws and principles (cont) 8. Ohm’s Law (current, voltage, resistance) 9. Kirchhoff’s Laws (circuit analysis) 10. Operational Amplifiers (gain, feedback) 11. Coulomb’s Law (capacitors, fluid analog) 12. Thevenin Equiv (1 st -order time constants) 13. Nernst Potential (cell membrane) 14. Fourier Series

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Univ of Utah ‘Textbook’

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Univ of Utah Major lab project Modeling the human systemic cardiovascular system (pressures and flows) by: A.Matlab simulation (1 st half of semester) B. Electrical circuit analog (2 nd half of semester) Guyton & Hall

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Univ of Utah Equivalent circuit

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Univ of Utah Approximations in modeling students fill in:

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Univ of Utah Part A. Matlab model Write finite-difference equations of pressure vs. flow for compliant vessels including conservation of mass.

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Univ of Utah Part A - Matlab model (cont) Poiseuille’s Q 1 = (P 1 - P 2 ) / R Conservation of mass (vol) Q 2 = Q 1 - Q 3 Compliance (Hooke’s) ∆P 2 /∆t = Q 2 /C

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Univ of Utah Approx. 1/2 of Matlab program

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Univ of Utah Beat-by-beat pressure waveforms example: normal CV system but skip beats #13 & 14 to illustrate Starling’s Law

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Univ of Utah Modeling some human CV diseases 1. Aortic valve stenosis. 2. Anaphylactic shock. 3. Left heart failure (congestive heart failure). 4. Hypovolemia.

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Univ of Utah Modeling some human CV diseases Students research: probable causes of each disease clinical symptoms one major CV parameter to change Students run model to see effects (CO, P, etc.)

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Univ of Utah Beat-by-beat pressure waveforms disease example: anaphylactic shock (increased venous compliance)

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Univ of Utah Equivalent circuit

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Univ of Utah Part B - electrical circuit analog Op amp (capacitance multiplier) for left ventricle. Resistances and capacitors for vessels. Diodes for valves. Students assemble circuit (teams of two). Measure voltages (for pressure) and current (for cardiac output).

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Univ of Utah Photo of typical circuit

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Univ of Utah Oscilloscope recording from circuit

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Univ of Utah Modeling some additional diseases 5. Atherosclerosis (increase R’s). 6. Aortic valve regurgitation (add R around diode).

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Univ of Utah Conclusions Students learn by “doing”. Major lab project a mix of defined tasks and open-ended tasks. Close tie between lectures and lab project. Topics covered: modeling, computer programing, cardiovascular physiology, electricity & instrumentation. Supported in part by NSF EEC

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