Bioelectricity: The Mechanism of Origin of Extracellular Potentials

About this course: Most people know that electrically active cells in nerves, in the heart and in the brain generate electrical currents, and that somehow these result in measurements we all have heard about, such as the electrocardiogram. But how? That is, what is it that happens within the electrically active tissue that leads to the creation of currents and voltages in their surroundings that reflect the excitation sequences timing, and condition of the underlying tissue. This course explores that topic. Rather than being a primer on how to interpret waveforms of any kind in terms of normality or disease, the goal here is to provide insight into how the mechanism of origin actually works, and to do so with simple examples that are readily pictured with simple sketches and one’s imagination, and then moving forward into comparison with experiments and finding outcomes quantitatively.

Created by:  Duke University

• Taught by:  Dr. Roger Barr, Anderson-Rupp Professor of Biomedical Engineering and Associate Professor of Pediatrics

  Biomedical Engineering, Pediatrics

Level Intermediate Commitment 7 weeks of study, 1-3 hours/week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.4 stars Average User Rating 4.4See what learners said Coursework

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Syllabus


WEEK 1


Week 1
A brief history of extracellular measurements, and an example of such a recording. The goal is to understand the amplitudes and time variation of such measurements, as well as learn about some interesting and useful historical events.


3 videos, 3 readings expand

1. Video: Welcome
2. Reading: Course Overview
3. Reading: Assessments, Grading and Certificates
4. Video: The First Extracellular Measurements
5. Video: Observing Wave Forms Between Human Hands
6. Reading: Week 1 Slides

Graded: 1

WEEK 2


Week 2



A presentation of the cylindrical fiber model of a nerve. The goal is to see how this geometrically simple model of a nerve actually is sufficient to explain complex bioelectric events within and around electrically active tissue. One learns that currents are driven forward by voltages across cell membranes,. Current loops are created, with some parts of the current loop inside and other parts outside the active cells. Electrical potentials are created by the current loops, and are positive when these are approaching, negative when they are receding. In so doing they form the basis of all extracellular wave forms.


9 videos, 3 readings expand

1. Video: Geometry
2. Video: Left or right side stimulation
3. Video: Simultaneous stimulation model
4. Reading: Cylinderical Fiber Model Slides
5. Video: Definitions and questions
6. Video: Origin in the membrane
7. Video: Big loops as well as small
8. Reading: Current Loops Slides
9. Video: Approaching wave forms
10. Video: Departing wave forms
11. Video: Observations
12. Reading: Current Loops and the Extracellular Waveforms Slides

Graded: 2

WEEK 3


Week 3
Notable and useful aspects of extracellular wave forms are their changes in shape. What causes such changes? Two illuminating examples are studied, one that does not, and then another that does.


7 videos, 3 readings expand

1. Video: Left side stimulation, then right
2. Video: Vm and current inside
3. Reading: When do Wave Shapes Change? Slides
4. Video: Vm patterns
5. Video: Current loops
6. Reading: Simultaneous Left and Right Stimulation Slides
7. Video: Experimental setup, cardiac Purkinje
8. Video: Stimulation at the left or right
9. Video: Stimulation at both ends, collision
10. Reading: Experimental Data Slides

Graded: 3

WEEK 4


Week 4



Weeks 1 to 3 present some intriguing concepts and explain them with drawings and sketches. Do the wave forms so drawn have any connection with real tissue? Indeed they do. The goal of this week is to examine some specific experimental wave forms that were measured in cardiac Punkinje fibers, and to compare them those anticipated in earlier weeks.Week 4 is the end of the standard course. The remaining weeks are for honors study.


4 videos, 1 reading expand

1. Video: Two-fiber model, synchronous
2. Video: Two-fiber model, asynchronous
3. Video: Experimental findings
4. Video: Multiphasic summary
5. Reading: Multiphasic Recordings Slides

Graded: 4

WEEK 5


Week 5



The concepts of week 3 give insight, but there is power in equations and numbers. The goal of week 5 is to show how the models of week 3 can be represented quantitatively, so that one can go beyond asking “What?” and ask “How much?” With equations available, the lectures and questions for this week focus on finding specific numerical results for several examples.


18 videos, 6 readings expand

1. Video: Introduction
2. Video: A Thought experiment
3. Video: Resistance of a fiber gap
4. Video: Conductivity and conductance
5. Reading: Resistivity and Resistance Slides
6. Video: The circuit
7. Video: The extracellular resistance
8. Video: The axial current numerically
9. Reading: Axial Current Slides
10. Video: The source and sink
11. Video: Potential at e1
12. Video: Voltage from e1 to e2
13. Reading: Extracellular Voltage Formula Slides
14. Video: Source strength
15. Video: Source distances
16. Video: Finding the voltage
17. Video: Summary
18. Reading: Extracellular Voltage Numbers Slides
19. Video: Mathematics
20. Video: Python program
21. Reading: Python program and sample output
22. Video: Wave form comparison
23. Video: Summary
24. Reading: Extracellular V as a Function of Time Slides

Graded: 5

WEEK 6


Week 6



This week’s goal is to introduce the concept and the mathematical definition of dipole sources. Such sources pair a current source and current sink, separated in a specific orientation by a small distance. A dipole model allows easy evaluation of many electrode configurations, such as the widely used “bipolar” configuration, often used experimentally to determine the timing of excitation. extensive models also allow consideration of action potential repolarization (return to resting potentials) as well as excitation.


14 videos, 3 readings expand

1. Video: Mathematics of sources
2. Video: Dipole representation
3. Video: Iso-potential lines
4. Video: Summary
5. Reading: Dipole Representation Slides
6. Video: Bipolar lead configuration
7. Video: Bipolar wave form
8. Video: Bipolar math
9. Video: Why use bipolar?
10. Video: Summary
11. Reading: Bipolar Electrodes Slides
12. Video: Repolarization profile
13. Video: Two axial currents
14. Video: Three membrane sources
15. Video: Extracellular potentials
16. Video: Summary
17. Reading: A Fiber Model with Repolarization Slides

Graded: 6

WEEK 7


Week 7



As a conclusion to the course, two diverse subjects are considered. One, the multipole expansion, is used when one has no model of the true origin of observed potentials but still needs to create an “equivalent” model to represent the data. The other, cardiac excitation, is characterized by large, broad excitation waves. One sees that an equation for the extracellular potentials has the same components as the expression for a simple cylindrical fiber, translated into a geometrically suitable form.


13 videos, 2 readings expand

1. Video: Unknown sources and the equivalent generator
2. Video: Gulrajani, Multipole calculations
3. Video: Geselowitz, quality of reproduction
4. Video: vanOosterom, dipole sources for the heart
5. Video: Summary
6. Reading: Multipole Expansion Slides
7. Video: Body Isopotentials from cardiac sources
8. Video: Heart sources with unipolar and bipolar measurements
9. Video: Excitation waves in the ventricles
10. Video: Plonsey’s equation
11. Video: Solid angles
12. Video: Body potentials from cardiac excitation
13. Video: Major factors summarized
14. Video: Summary
15. Reading: Cardiac Potentials Slides

Graded: 7