Fields, forces and flows in biological systems

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).

Truskey, G. A., F. Yuan, and D. F. Katz. Transport Phenomena in Biological Systems. East Rutherford, NJ: Prentice Hall, 2003. ISBN: 9780130422040.

Haus, H. A., and J. R. Melcher. Electromagnetic Fields and Energy. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780132490207. (A free online textbook.)

Probstein, R. F. Physicochemical Hydrodynamics: An Introduction. New York, NY: Wiley-Interscience, 2003. ISBN: 9780471458302.

Jones, T. B. Electromechanics of Particles. 2nd ed. New York, NY: Cambridge University Press, 2005. ISBN: 9780521019101.

Bird, R. B., E. N. Lightfoot, and W. E. Stewart. Transport Phenomena. New York, NY: Wiley, 2006. ISBN: 9780470115398.

Weiss, T. F. Cellular Biophysics - Volume 1: Transport. Cambridge, MA: MIT Press, 1996. ISBN: 9780262231831.

Morgan, H., and H. Green. AC Electrokinetics: Colloids and Nanoparticles. Baldock, UK: Research Studies Press, 2002. ISBN: 9780863802553.

Hiemenz, P. C., and R. Rajagopalan. Principles of Colloid and Surface Chemistry. New York, NY: Marcel Dekker, 1997. ISBN: 9780824793975.

Dill, K., and S. Bromberg. Molecular Driving Forces. New York: Garland Press, 2002. ISBN: 9780815320517.

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:

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.

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.

Introduction to the course

Fluid 1: Introduction to fluid flow

Logistics

Introduction to the course

Importance of being "multilingual"

Complexity of fluid properties

Fluid drag

Coefficient of viscosity

Newton's law of viscosity

Molecular basis for viscosity

Fluid rheology

Fluid kinematics

Acceleration of a fluid particle

Constitutive laws (mass and momentum conservation)

Acceleration of a fluid particle

Forces on a fluid particle

Force balances

Inertial effects

The Navier-Stokes equation

Flow regimes

The Reynolds number, scaling analysis

Unidirectional flow

Pressure driven flow (Poiseuille)

Bernoulli's equation

Stream function

Viscous flow

Stoke's equation

Why is it important?

Electric and magnetic fields for biological systems (examples)

EM field for biomedical systems (examples)

Integral form of Maxwell's equations

Differential form of Maxwell's equations

Lorentz force law

Governing equations

Quasi-electrostatic approximation

Order of magnitude of B field

Justification of EQS approximation

Quasielectrostatics

Poisson's equation

Dielectric constant

Magnetic permeability

Ion transport (Nernst-Planck equations)

Charge relaxation in aqueous media

Solving 1D Poisson's equation

Derivation of Debye length

Significance of Debye length

Electroneutrality and charge relaxation

Poisson's and Laplace's equations

Potential function

Potential field of monopoles and dipoles

Poisson-Boltzmann equation

Laplace's equation

Uniqueness of the solution

Laplace's equation in rectangular coordinate (electrophoresis example) will rely on separation of variables

Diffusion

Stokes-Einstein equation

Diffusional flux

Fourier, Fick and Newton

Steady-state diffusion

Concentration gradients

Steady-state diffusion (cont.)

Diffusion-limited reactions

Binding assays

Receptor ligand models

Unsteady diffusion equation

Unsteady diffusion in 1D

Equilibration times

Diffusion lengths

Use of similarity variables

Convection-diffusion equation

Relative importance of convection and diffusion

The Peclet number

Solute/solvent transport

Generalization to 3D

Guest lecture: Prof. Kamm

Transendothelial exchange

Solving the convection-diffusion equation in flow channels

Measuring rate constants

Debye layer (revisit)

Zeta potential

Electrokinetic phenomena

Electroosmotic flow

Electroosmotic mobility (derivation)

Characteristics of electroosmotic flow

Applications of electroosmotic flow

Electrophoretic mobility

Theory of electrophoresis

Electrophoretic mobility of various biomolecules

Molecular sieving

Induced dipole (from part 2)

C-M factor

Dielectrophoretic manipulation of cells

Problem of colloid stability

Inter-Debye-layer interaction

Van der Waals forces

Colloid stability theory

Don't show me this again

This is one of over 2,200 courses on OCW. Find materials for this course in the pages linked along the left.

MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum.

No enrollment or registration. Freely browse and use OCW materials at your own pace. There's no signup, and no start or end dates.

Knowledge is your reward. Use OCW to guide your own life-long learning, or to teach others. We don't offer credit or certification for using OCW.

Made for sharing. Download files for later. Send to friends and colleagues. Modify, remix, and reuse (just remember to cite OCW as the source.)

Learn more at Get Started with MIT OpenCourseWare