Optical Mapping

In Chapter 7 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I mention an optical technique that is used to measure the transmembrane potential in the heart.

Experimental measurements of the transmembrane potential often rely on the use of a voltage sensitive dye whose fluorescence changes with the transmembrane potential [Knisley et al. (1994); Neunlist and Tung (1995); Rosenbaum and Jalife (2001)].

This method, often called optical mapping, has revolutionized cardiac electrophysiology, because it allows you to use optical methods to make electrical measurements. If you want to learn more, take a look at the book Optical Mapping of Cardiac Excitation and Arrhythmias, by David Rosenbaum and Jose Jalife (2001). The chapters in this book were written by the stars of this field.

1. Optical Mapping: Background and Historical Perspective. Guy Salama.
2. Mechanisms and Principles of Voltage-Sensitive Fluorescence. Leslie M. Loew.
3. Optical Properties of Cardiac Tissue. William T. Baxter.
4. Optics and Detectors Used in Optical Mapping. Kenneth R. Laurita and Imad Libbus.
5. Optimization of Temporal Filtering for Optical Transmembrane Potential Signals. Francis X. Witkowski, Patricia A. Penkoske, and L. Joshua Leon.
6. Optical Mapping of Impulse Propagation within Cardiomyocytes. Herbert Windisch.
7. Optical Mapping of Impulse Propagation between Cardiomyocytes. Stephan Rohr and Jan P. Kucera.
8. Role of Cell-to-Cell Coupling, Structural Discontinuities, and Tissue Anisotropy in Propagation of the Electrical Impulse. André G. Kléber, Stephan Rohr, and Vladimir G. Fast.
9. Optical Mapping of Impulse Propagation in the Atrioventricular Node: 1. Todor N. Mazgalev and Igor R. Efimov.
10. Optical Mapping of Impulse Propagation in the Atrioventricular Node: 2. Guy Salama and Bum-Rak Choi.
11. Optical Mapping of Microscopic Propagation: Clinical Insights and Applications. Albert L. Waldo.
12. Mapping Arrhythmia Substrates Related to Repolarization: 1. Dispersion of Repolarization. Kenneth R. Laurita, Joseph M. Pastore, and David S. Rosenbaum.
13. Mapping Arrhythmia Substrates Related to Repolarization: 2. Cardiac Wavelength. Steven Girouard and David S. Rosenbaum.
14. Video Imaging of Cardiac Fibrillation. Richard A. Gray and José Jalife.
15. Video Mapping of Spiral Waves in the Heart. William T. Baxter and Jorge M. Davidenko.
16. Video Imaging of Wave Propagation in a Transgenic Mouse Model of Cardiomyopathy. Faramarz Samie, Gregory E. Morley, Dhjananjay Vaidya, Karen L. Vikstrom, and José Jalife.
17. Optical Mapping of Cardiac Arrhythmias: Clinical Insights and Applications. Douglas L. Packer.
18. Response of Cardiac Myocytes to Electrical Fields. Leslie Tung.
19. New Perspectives in Electrophysiology from The Cardiac Bidomain. Shien-Fong Lin and John P. Wikswo, Jr..
20. Mechanisms of Defibrillation: 1. Influence of Fiber Structure on Tissue Response to Electrical Stimulation. Stephen B. Knisley.
21. Mechanisms of Defibrillation: 2. Application of Laser Scanning Technology. Stephen M. Dillon.
22. Mechanisms of Defibrillation: 3. Virtual Electrode-Induced Wave Fronts and Phase Singularities; Mechanisms of Success and Failure of Internal Defibrillation. Igor R. Efimov and Yuanna Cheng.
23. Optical Mapping of Cardiac Defibrillation: Clinical Insights and Applications. Douglas P. Zipes.

For those who are tired of reading, two videos have recently been published in the Journal of Visualized Experiments that explain the technique step-by-step. One video is about studying the rabbit heart and the other is about the mouse heart. These excellent video clips were filmed in the laboratory of Igor Efimov, of Washington University in Saint Louis.

My former graduate student, Debbie Janks, is now a post doc in Efimov’s lab. Regular readers of this blog may recognize Janks’ name, as she provides many insightful comments following these blog entries. Janks studied optical mapping from a theoretical perspective when she was here at Oakland University. She published a nice paper that examined the question of averaging over depth during optical mapping. The optical method does not measure the transmembrane potential at the tissue surface. Rather, light penetrates some distance into the tissue, and the optical signal is a weighted average of the transmembrane potential over depth. Janks looked at the effect of this averaging during an electrical shock. Rather than explaining the whole story, I will present it as a new homework problem. That way, you can figure it out for yourself. Enjoy.

Section 7.10

Problem 47 1/2 The signal measured during optical mapping, V, is a weighted average of the transmembrane potential, V_m(z), as a function of depth, V=∫₀^∞V_m(z)w(z)dz, where w(z) is a normalized weighting function. Suppose the light decays with depth exponentially, with an optical length constant δ. Then w(z) = exp(−z/δ)/δ. Often a shock will cause V_m(z) to fall off exponentially with depth, V_m(z)=V_o exp(−z/λ), where V_o is the transmembrane potential at the tissue surface and λ is the electrical length constant (see Sec. 6.12).
(a) Perform the required integration to find an analytical expression for the optical signal, V, as a function of V_o, δ and λ.
(b) What is V in the case δ much less than λ? Explain this result physically.
(c) What is V in the case δ much greater than λ? Explain this result physically.
(d) For which limit do you obtain an accurate measurement of the transmembrane potential at the surface, V=V_o?

In cardiac tissue, δ is usually on the order of a millimeter, whereas λ is more like a quarter of a millimeter, so averaging over depth significantly distorts the measured signal. For a more detailed analysis of this problem, see Janks and Roth (2002).