Fields, Forces and Flows in Biological Systems >> Content Detail



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This page includes a course calendar.

Course Objectives

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).

Topic Outline

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
  • Electroquasistatics
  • Poisson's and Laplace's equation

Part III: Chemical Driving Forces

  • Conservation of mass
  • Diffusion
  • Steady and unsteady diffusion
  • Diffusion with chemical reactions

Part IV: Electrokinetics

  • Debye layer
  • Zeta potential
  • Electroosmosis
  • Electrophoresis
  • Application of electrokinetics
  • Dielectrophoresis
  • Debye layer repulsion forces

Textbooks and Reference Materials

Required Text (to purchase)

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

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.)

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

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

Other Useful References

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

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

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

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

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

Class Structure

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.

Term Grade

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 exam30%


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

T1Curl and divergence
L2Fluid 2: Drag forces and viscosity

Fluid drag

Coefficient of viscosity

Newton's law of viscosity

Molecular basis for viscosity

Fluid rheology

L3Fluid 3: Conservation of momentum

Fluid kinematics

Acceleration of a fluid particle

Constitutive laws (mass and momentum conservation)

L4Fluid 4: Conservation of momentum (example)

Acceleration of a fluid particle

Forces on a fluid particle

Force balances

L5Fluid 5: Navier-Stokes equation

Inertial effects

The Navier-Stokes equation

L6Fluid 6: Flows with viscous and inertial effects

Flow regimes

The Reynolds number, scaling analysis

L7Fluid 7: Viscous-dominated flows, internal flows

Unidirectional flow

Pressure driven flow (Poiseuille)

L8Fluid 8: External viscous flows

Bernoulli's equation

Stream function

L9Fluid 9: Porous media, poroelasticity

Viscous flow

Stoke's equation

L10Fluid 10: Cellular fluid mechanics (guest lecture by Prof. Roger Kamm)How cells sense fluid flow
Part 2: Fields (Instructor: Prof. Jongyoon Han)
L11Field 1: Introduction to EM theory

Why is it important?

Electric and magnetic fields for biological systems (examples)

EM field for biomedical systems (examples)

L12Field 2: Maxwell's equations

Integral form of Maxwell's equations

Differential form of Maxwell's equations

Lorentz force law

Governing equations

L13Quiz 1
L14Field 3: EM field for biosystems

Quasi-electrostatic approximation

Order of magnitude of B field

Justification of EQS approximation


Poisson's equation

L15Field 4: EM field in aqueous media

Dielectric constant

Magnetic permeability

Ion transport (Nernst-Planck equations)

Charge relaxation in aqueous media

L16Field 5: Debye layer

Solving 1D Poisson's equation

Derivation of Debye length

Significance of Debye length

Electroneutrality and charge relaxation

L17Field 6: Quasielectrostatics 2

Poisson's and Laplace's equations

Potential function

Potential field of monopoles and dipoles

Poisson-Boltzmann equation

L18Field 7: Laplace's equation 1

Laplace's equation

Uniqueness of the solution

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

L19Field 8: Laplace's equation 2Laplace's equation in other coordinates (solving examples using MATLAB®)
L20Field 9: Laplace's equation 3Laplace's equation in spherical coordinate (example 7.9.3)
Part 3: Transport (Instructor: Prof. Scott Manalis)
L21Transport 1


Stokes-Einstein equation

L22Transport 2Diffusion based analysis of DNA binding proteins
L23Transport 3

Diffusional flux

Fourier, Fick and Newton

Steady-state diffusion

Concentration gradients

L24Transport 4

Steady-state diffusion (cont.)

Diffusion-limited reactions

Binding assays

Receptor ligand models

Unsteady diffusion equation

L25Transport 5

Unsteady diffusion in 1D

Equilibration times

Diffusion lengths

Use of similarity variables

L26Transport 6Electrical analogy to understanding cell surface binding
L27Quiz 2
L28Transport 7

Convection-diffusion equation

Relative importance of convection and diffusion

The Peclet number

Solute/solvent transport

Generalization to 3D

L29Transport 8

Guest lecture: Prof. Kamm

Transendothelial exchange

L30Transport 9

Solving the convection-diffusion equation in flow channels

Measuring rate constants

Part 4: Electrokinetics (Instructor: Prof. Jongyoon Han)
L31EK1: Electrokinetic phenomena

Debye layer (revisit)

Zeta potential

Electrokinetic phenomena

L32EK2: Electroosmosis 1

Electroosmotic flow

Electroosmotic mobility (derivation)

L33EK3: Electroosmosis 2

Characteristics of electroosmotic flow

Applications of electroosmotic flow

L34EK4: Electrophoresis 1

Electrophoretic mobility

Theory of electrophoresis

L35EK5: Electrophoresis 2

Electrophoretic mobility of various biomolecules

Molecular sieving

L36EK6: Dielectrophoresis

Induced dipole (from part 2)

C-M factor

Dielectrophoretic manipulation of cells


Problem of colloid stability

Inter-Debye-layer interaction

L38EK8: Forces

Van der Waals forces

Colloid stability theory

L39EK9: ForcesSummary of the course/evaluation
3 hour final exam (comprehensive of the course) during the finals week


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