Douglas ChristensenDepartment of Bioengineering
University of Utah
Salt Lake City, Utah 84121
Bringing an Integrative Modeling Experience to Freshman
Biomedical Engineering Courses
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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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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1st Semester -
Biomechanical and bioelectrical
2nd Semester -
Biochemical, cellular and biosensors
Two freshman courses
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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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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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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 (1st-order time constants)
13. Nernst Potential (cell membrane)
14. Fourier Series
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Major lab project
• Modeling the human systemic
cardiovascular system
(pressures and flows) by:
A. Matlab simulation (1st
half of semester)
B. Electrical circuit analog
(2nd half of semester)Guyton & Hall
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Part A. Matlab model
Write finite-difference
equations of pressure vs.
flow for compliant vessels
including conservation of
mass.
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Part A - Matlab model (cont)
Poiseuille’s
Q1 = (P1 - P2 ) / R
Conservation of mass (vol)
Q2 = Q1 - Q3
Compliance (Hooke’s)
∆P2 /∆t = Q2 /C
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Approx. 1/2 of Matlab program
% Main program for modeling cardiovascular system.pf=input('What parameter file do you want to use? \n','s');eval(pf)for b=1:20 % Outer loop, once each cardiac cycle; about 20 second's worth -
for i=1:N % Inner loop, once each time increment dt -% Find pressures from volumes:
Ph(i)=(Vh(i)-Vh0)/Ch(i); Po(i)=(Vo(i)-Vo0)/Co; Pa(i)=(Va(i)-Va0)/Ca;Pc(i)=(Vc(i)-Vc0)/Cc; Pv(i)=(Vv(i)-Vv0)/Cv;
% Use Poiseuille's law to calculate flows:if Ph(i)>Po(i); Q1(i)=(Ph(i)-Po(i))/Rho;else Q1(i)=0;endQ3(i)=(Po(i)-Pa(i))/Roa; Q5(i)=(Pa(i)-Pc(i))/Rac;Q7(i)=(Pc(i)-Pv(i))/Rcv;if Pv(i)>Ph(i); Q9(i)=(Pv(i)-Ph(i))/Rvh;else Q9(i)=0;end
% Apply conservation of volume at each junction:Q2(i)=Q1(i)-Q3(i); Q4(i)=Q3(i)-Q5(i); Q6(i)=Q5(i)-Q7(i);Q8(i)=Q7(i)-Q9(i); Q10(i)=Q9(i)-Q1(i);
% Use Euler's method to update volumes:Vh(i+1)=Vh(i)+Q10(i)*dt;Vo(i+1)=Vo(i)+Q2(i)*dt; Va(i+1)=Va(i)+Q4(i)*dt;Vc(i+1)=Vc(i)+Q6(i)*dt; Vv(i+1)=Vv(i)+Q8(i)*dt;
end % End of time increment loop
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Beat-by-beat pressure waveforms
example:
normal CV system
but skip beats #13 & 14 to illustrateStarling’s Law
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
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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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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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Beat-by-beat pressure waveforms
disease example:
anaphylactic shock
(increasedvenous compliance)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
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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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Modeling some additional diseases
5. Atherosclerosis (increase R’s).
6. Aortic valve regurgitation (add R around diode).
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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-0080452