Douglas ChristensenDepartment of Bioengineering

University of Utah

Salt Lake City, Utah 84121

Bringing an Integrative Modeling Experience to Freshman

Biomedical Engineering Courses

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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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‘Textbook’

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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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Equivalent circuit

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Approximations in modeling

students fill in:

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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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Equivalent circuit

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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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Photo of typical circuit

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Oscilloscope recording from circuit

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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