Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Tutorials (optional): 1 session / week, 1 hour / session
This page includes a course calendar.
This course develops and applies scaling laws and the methods of continuum mechanics to biomechanical phenomena over a range of length scales, from molecular to cellular to tissue or organ level. It is intended for undergraduate students who have taken a course in differential equations (18.03), an introductory course in molecular biology, and a course in transport, fluid mechanics, or electrical phenomena in cells (e.g. 6.021, 2.005, or 20.320).
Part I: Mechanical Driving Forces
- Conservation of momentum
- Inviscid and viscous flows
- Convective transport
- Dimensional analysis
Part II: Electrical Driving Forces
- Maxwell's equations
- Ion transport
- E and B field in biological systems
- Poisson's and Laplace's equation
Part III: Chemical Driving Forces
- Conservation of mass
- Steady and unsteady diffusion
- Diffusion with chemical reactions
Part IV: Electrokinetics
- Debye layer
- Zeta potential
- Application of electrokinetics
- Debye layer repulsion forces
Textbooks and Reference Materials
Required Text (to purchase)
Additional Texts with Assigned Readings (not required to purchase)
Haus, H. A., and J. R. Melcher. Electromagnetic Fields and Energy. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780132490207. (A free online textbook.)
Other Useful References
20.330/2.793/6.023 will be taught in lecture format (3 hours/week), but with liberal use of class examples to link the course material with various biological issues. Readings will be drawn from a variety of primary and text sources as indicated in the lecture schedule.
Optional tutorials will also be scheduled to review mathematical concepts and other tools (Comsol FEMLAB) needed in this course.
Weekly homework problem sets will be assigned each week to be handed in and graded.
Office hours by the TA will be scheduled to help you in exams and homeworks.
There will be two in-class midterm quizzes (1 hour long), and a comprehensive final exam (3 hours long) at the end of the term.
The term grade will be a weighted average of exams, term paper and homework grades. The weighting distribution will be:
|Two quizzes (20% each)||40%|
|A comprehensive final exam||30%|
Homework is intended to show you how well you are progressing in learning the course material. You are encouraged to seek advice from TAs and collaborate with other students to work through homework problems. However, the work that is turned in must be your own. It is a good practice to note the collaborator in your work if there has been any.
Homework is due at the end of the lecture (11 am), on the stated due date. Solutions will be provided on-line after the due date and time.
We will not accept late homework for any reason. Instead, we will not use 2 lowest homework grades (out of 9 total) for the calculation of the term homework grade (30%). Students are encouraged to use this to their benefit, to accommodate special situations such as interview travel/illness.
Midterm Quizzes and Final Exam
There are two in-class (1 hour) closed-book midterm quizzes scheduled for the term. Please note the schedule for the exam dates. There will also be a closed-book, three-hour-long, comprehensive final exam during the finals week. The final exam will cover the whole course content.
Exam problems will be similar (in terms of difficulty) to homework problems, and if one can work all the homework problems without looking at notes one should be able to solve the exam problems as well.
Make-up exams will only be allowed for excused absence (by Dean's office) and if arranged at least 2 weeks in advance. Students must sign an honor statement to take a make-up exam. Exams missed due to an excused illness and other reasons excusable by Dean's office will be dropped and the term grade will be calculated based on the remaining exams and homework.
The table below provides information on the course's lecture (L) and tutorials (T) sessions.
|Part 1: Fluids (Instructor: Prof. Scott Manalis)|
Introduction to the course
Fluid 1: Introduction to fluid flow
Introduction to the course
Importance of being "multilingual"
Complexity of fluid properties
|T1||Curl and divergence|
|L2||Fluid 2: Drag forces and viscosity||
Coefficient of viscosity
Newton's law of viscosity
Molecular basis for viscosity
|L3||Fluid 3: Conservation of momentum||
Acceleration of a fluid particle
Constitutive laws (mass and momentum conservation)
|L4||Fluid 4: Conservation of momentum (example)||
Acceleration of a fluid particle
Forces on a fluid particle
|L5||Fluid 5: Navier-Stokes equation||
The Navier-Stokes equation
|L6||Fluid 6: Flows with viscous and inertial effects||
The Reynolds number, scaling analysis
|L7||Fluid 7: Viscous-dominated flows, internal flows||
Pressure driven flow (Poiseuille)
|L8||Fluid 8: External viscous flows||
|L9||Fluid 9: Porous media, poroelasticity||
|L10||Fluid 10: Cellular fluid mechanics (guest lecture by Prof. Roger Kamm)||How cells sense fluid flow|
|Part 2: Fields (Instructor: Prof. Jongyoon Han)|
|L11||Field 1: Introduction to EM theory||
Why is it important?
Electric and magnetic fields for biological systems (examples)
EM field for biomedical systems (examples)
|L12||Field 2: Maxwell's equations||
Integral form of Maxwell's equations
Differential form of Maxwell's equations
Lorentz force law
|L14||Field 3: EM field for biosystems||
Order of magnitude of B field
Justification of EQS approximation
|L15||Field 4: EM field in aqueous media||
Ion transport (Nernst-Planck equations)
Charge relaxation in aqueous media
|L16||Field 5: Debye layer||
Solving 1D Poisson's equation
Derivation of Debye length
Significance of Debye length
Electroneutrality and charge relaxation
|L17||Field 6: Quasielectrostatics 2||
Poisson's and Laplace's equations
Potential field of monopoles and dipoles
|L18||Field 7: Laplace's equation 1||
Uniqueness of the solution
Laplace's equation in rectangular coordinate (electrophoresis example) will rely on separation of variables
|L19||Field 8: Laplace's equation 2||Laplace's equation in other coordinates (solving examples using MATLAB®)|
|L20||Field 9: Laplace's equation 3||Laplace's equation in spherical coordinate (example 7.9.3)|
|Part 3: Transport (Instructor: Prof. Scott Manalis)|
|L22||Transport 2||Diffusion based analysis of DNA binding proteins|
Fourier, Fick and Newton
Steady-state diffusion (cont.)
Receptor ligand models
Unsteady diffusion equation
Unsteady diffusion in 1D
Use of similarity variables
|L26||Transport 6||Electrical analogy to understanding cell surface binding|
Relative importance of convection and diffusion
The Peclet number
Generalization to 3D
Guest lecture: Prof. Kamm
Solving the convection-diffusion equation in flow channels
Measuring rate constants
|Part 4: Electrokinetics (Instructor: Prof. Jongyoon Han)|
|L31||EK1: Electrokinetic phenomena||
Debye layer (revisit)
|L32||EK2: Electroosmosis 1||
Electroosmotic mobility (derivation)
|L33||EK3: Electroosmosis 2||
Characteristics of electroosmotic flow
Applications of electroosmotic flow
|L34||EK4: Electrophoresis 1||
Theory of electrophoresis
|L35||EK5: Electrophoresis 2||
Electrophoretic mobility of various biomolecules
Induced dipole (from part 2)
Dielectrophoretic manipulation of cells
Problem of colloid stability
Van der Waals forces
Colloid stability theory
|L39||EK9: Forces||Summary of the course/evaluation|
|3 hour final exam (comprehensive of the course) during the finals week|