BMEN E 3500, fall 1999

Biomedical Engineering E3500, fall 1999

Grades have been submitted to the registrar.  There is an analysis of the grade distribution on a PDF page.  Click here.  FINAL EXAM QUESTION SHEET and SOLUTION are available as PDF's as of 12/27/99. 

CORRECTED Practice Problems covering Chapter 7 of Weiss, Volume 1 are posted as a .pdf document.  Click here.   (EFL 12/9/99)  Practice Problems covering ALL ADDITIONAL MATERIAL are also now posted (Click here) as a .pdf document.   Corrections, some solution material, hints, will be posted as time permits.

new.gif - 3.0 K Midterm Examination solution is posted as a .pdf document.  Click here.    (What is posted is the exam statement with the solutions inserted in red.  Practice exam is still available:   Click here.  Table below shows distribution of normalized grades on the midterm examination (mean 27.8, standard deviation 12.73)  To normalize your grade, subtract the mean, divide the result by the standard deviation, and add 2.5.  The "worry line" is about 1.5.   Scores lower than that are seriously behind the class' performance.

Score 5.0 - 4.5 4.5 - 4.0 4.0 - 3.5 3.5 - 3.0 3.0 - 2.5 2.5 - 2.0 2.0 - 1.5 1.5 - 1.0 1.0 - 0.5 0.5 - 0.0
Number with score 1 1 5 2 11 4 7 5 1 1

The chart below gives the distribution of grades for each of the 4 midterm questions:

midtr.gif (26339 bytes)

Recitations:   Will resume, week of 11/22  -- Tuesday, 6:10 -- 7:00 pm and Wednesday, 5:10 -- 6:00 pm in 805A Mudd.   Sessions will deal with the solution of the mid-term examination.  This material will be covered on the final examination.  A study guide with problems covering ion transport, electrochemical equilibrium, and propagation of action potentials will be posted before or over the Thanksgiving holiday.  Weiss book "Cellular Biophysics" (volume 1, Transport, dealing with Nernst potential and small cell steady states, and volume 2, dealing with electrical phenomena) is on reserve in Fairchild Library. 

Last update:  12/29/99

 

Instructor:  Edward F. Leonard  814 Mudd (office and laboratory). Best contacted by e-mail: [email protected].  

Read below about meeting times, grading, and notes.

Preliminary List of Topics and Lectures

(Click on date to access lecture notes and assignments. This is valid only for lectures that have been delivered. Click on (PS) in date column to access appropriate problem set. When lectures and subject matter diverge, you will be directed to notes and problems that correspond to the topics.)

Problem Set

Lecture Notes
(PS1) 1.  Concept of control volume. Concepts of concentration and conservation. Convection, diffusion, reaction. Fundamental conservation equation.
(PS2) 2.  Free and forced diffusion. Chemical activity. Thermal conduction. Diffusion of momentum. Equations for each. Reaction kinetics. Equilibrium. Catalysis. Kinetic equations.
(PS3) 3.  Compartmental analysis. Integration of fundamental conservation equation in uniform concentration fields. Intracellular compartments. Inter and extracellular space. Organs as compartments.
(PS4) 4.  Intracompartmental kinetics, I. First order reactions, reversible, irreversible. Other orders. Enzyme-catalyzed and reversible reactions.  4a.   Special notes on "automatic" derivation of equations describing multiple-substrate, reversible, and inhibited enzyme reactions.

 

 

 5.  Intracompartmental kinetics, II. Systems of reactions. Sources and sinks. Infinite sources and sinks. Steady and transient states. Metabolite inventory. Rate-limiting steps.

20

 

 6.  Transport among compartments. Membranes. Mechanisms of transport across membranes: diffusion (mobility and solubility). Transporters.

22

 7.  Combinations of transport and reaction. Additive resistances. Controlling resistance and rate-limiting step. Covered under lecture topic 5.

25

 8.  Receptor-mediated reactions. Signal transduction. Role of transport and rate processes.

27

 

 9.  Macroscopic applications: Convective-reactive balance in organs. Clearance. Homeostasis.

29

 10,  Pharmacokinetics.

October 1

 11.  Compartmental analysis of artificial kidney operation.

4

 Reprise and review.

6

 Hour Test I (See note, below)

8

 12.  Spatial gradients: steady, one-dimensional diffusion in a non-reactive medium. Counter-diffusion. Low-concentration limit. Oxygen diffusion across a lipid barrier. Diffusion to a reacting surface.

11

 13.  Extension to cylindrical and spherical coordinates. Sources and sinks. Controlled release of drugs.

13

 14.  Diffusion in a reactive medium. Spacing of capillaries in metabolizing tissue. Tissue cylinder concept of Krogh.

15

 15.  Unsteady (transient) diffusion in a non-reactive medium. Use of heat transfer analogy and charts. Application to pharmacokinetics.

18

 16.  Convection: Comparison of convective and diffusive transport. Concept of blood as organ. Essential role of blood. Morphological, chemical, physical characterization of blood.

20

 17.  Hydrostatics. Balance of internal and potential energy. Importance of pressure differences. Manometry.

22

 18.  Stress and momentum flux. Newton's law of viscosity. Non-Newtonian fluids. Viscoelasticity. Typical viscosity values.

25

 19.  "Real" blood flow: distension, tapering, pulsatility in the arterial tree. Nature of flow in precapillary and capillary vessels. Venous flow. Branching vs. fully developed flow. Separated and secondary flows.

27

 20,  Development of Hagen-Poiseuille equation. Extension to arbitrary cross-sections.

29

 21.  Analysis of Hagen-Poiseuille equation: Entrance region, balance of axial pressure gradient and momentum flux to wall, irrelevance of axial momentum. Mean velocity, shear rate. Stress distribution. Reynolds' number.

November 3

 22.  Development of Stokes' law: concept of creeping flow. Viscometry: capillary, couette, cone-plate, and falling-ball viscometers.

5

 23.  Application of Stokes' law to cells. Microrheology: Movement of cells in a shear field.

8

 24.  Pulsatile flow in a rigid tube. Wormersly's parameter.

10

 Reprise

12

 Hour Test II (See note, below)

15

 25.  Convective diffusion: the Leveque equation.

17

 26.  Analysis of Leveque result. Platelet deposition on a biomaterial surface.

19

 27.  Graetz-Nusselt equation.

22

 28.  Dimensionless groups: Sherwood, Nusselt, Prandtl, Schmidt, Peclet numbers. Theoretical results expressed as "film coefficients".

24

 29.  Device design: log-mean driving force. Countercurrent, concurrent, and crosswise flows. Flow ratios.

29

 30.  Convective diffusion: the Lightfoot "zero order" approximation.

December 1

 31.  Analysis of Lightfoot result; application to oxygenation of hemoglobin.

3

 32.  Coaxial convection and diffusion: concentration polarization. Plasmapheresis.

6

 Catch-up or extra topics.

8

 Catch-up or extra topics.

10

 Catch-up or extra topics.

13

 Last class:  Review and reprise of course.

Course Time

Monday, Wednesday and Friday, 11:00 - 12:00, 627 Mudd on Monday and Wednesday, 833 Mudd on Friday.

Grading

Fifty percent of the course grade will be determined by testing during the term and the remaining fifty percent by the final examination.  

Recitation sessions will be offered outside of regularly scheduled class hours by the instructor.  However solutions to assignments will not be routinely distributed.

Course Materials

There is no text. Students are expected to take notes and the instructor's notes will be posted on this web site.