Bioimpedance and Spectroscopy

Bioimpedance and Spectroscopy is a comprehensive gateway into the applications of bioimpedance and relevant aspects of its instrumentation, which presents cutting-edge knowledge in an accessible and simplified way.

Written by experts from across the field, this book offers a rare focus on applied engineering and instrumentation, covering both theory and practical applications. This text will guide you towards successful experiments and leads to practical examination of the properties of different biological structures, whether single cells, tissues or whole organ systems, by:

• Revealing how the underlying processes of the bioimpedance spectroscopy enhance classic understanding of the impedance measurement
• Introducing new instrumentation methods and applications
• Warning against some common pitfalls and caveats
• Explaining historical perspectives, solutions to engineering problems and real-world case studies of how this technology has been successfully applied

Clear and practical, this book lays out essential requirements, typical challenges, and common compromises for both students and engineers in the field. Students of data acquisition and impedance measurement, graduate students in biomedical engineering, and engineers of practical measurement solutions will also find this book useful.

• Includes new instrumentation methods and applications in bioimpedance spectroscopy
• Covers both the theory and practical applications of this technology
• Describes the underlying processes that occur within bioimpedance spectroscopy and how they are different from classic impedance measurement techniques used in industry and in engineering courses

• Language: English
• Publisher: Academic Press
• Release date: Jun 19, 2021
• ISBN: 9780128197004

Book preview

9780128197004_FC

Bioimpedance and Spectroscopy

First Edition

Paul Annus

Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn, Estonia

Mart Min

Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn, Estonia

Table of Contents

Cover image

Title page

Copyright

Contributors

Preface

Acknowledgments

Introduction

Tuesday (Oliver)

1: Dark side of the human being

2: Troubles with the object

3: Coupling—Intentional and unintentional

4: Parameters of the object

5: Conclusions

Part I: Measurement and instrumentation

1: Coupling and electrodes

Abstract

1: Introduction to the practical measurement of electrical bioimpedance

2: EBI measurement setup and interaction with biological objects

3: Electrodes for practical applications that base on EBI measurements

4: Practical considerations for electrodes in capacitive coupling systems

5: Practical considerations for electrodes in resistive coupling systems

6: Practical considerations for sensors in inductive coupling systems

2: Effects of stray capacitance to ground in impedance measurements

Abstract

1: Introduction

2: Effect of stray capacitance to ground in auto-balancing impedance bridges

3: Effect of stray capacitance from the human body to ground in tetrapolar bioimpedance measurements

4: Method to estimate body capacitance to ground using an auto-balancing impedance bridge

Annex: Equivalent impedance for tetrapolar measurements

3: Designing a current source

Abstract

1: Basic concepts in current source

2: Limiting factors

3: Circuit types overview

4: Defining your current source

4: Characterization of biological material using electrical relaxation spectroscopy

Abstract

Acknowledgements

1: Introduction

2: Impedance, admittance, and permittivity

3: Impedance in frequency and time domain

4: Spectrum calculation using the current i(t) as response to a voltage step

5: Discussion

Part II: Promising use cases and success stories

5: Multifrequency electrical impedance tomography in biological applications: A multimodal perspective

Abstract

1: Impedance tomography in biology

2: Instrumentation and data acquisition

3: Examples of mfEIT of biological samples

4: Conclusions

6: Applications and prospects for impedance cardiography: Stationary and ambulatory implementations

Abstract

1: Introduction

2: The impedance cardiography

3: Research and clinical applications of impedance cardiography

4: Final conclusions: Hopes and limitations

7: Monitoring wound healing

Abstract

1: The skin

2: Acute wounds

3: Chronic wounds

4: Conventional methods for wound assessment

5: State-of-art portable wound assessment methods

6: Bioimpedance measurements in wound monitoring

7: Quasimonopolar bioimpedance configuration for monitoring wound healing

8: Conclusion

8: Monitoring hemorrhagic strokes using EIT

Abstract

Acknowledgments

1: Introduction

2: Theory

3: Prototype stroke EIT device

4: Methods

5: Results and discussion

6: Conclusions and future work

9: The electrical impedance methods in cardiology

Abstract

1: The introduction to clinical applications of impedance methods

2: The evolution of the Kubicek formula

3: The parameters measured by impedance plethyzmography

4: Selected clinical implementation of IC in cardiological procedures

5: The current position of IC in medical diagnostic procedures

6: The impedance method in the pacemaker technology

7: The impedance spectroscopy in cardiology

8: Selected application of EIS method in medicine and particularly in cardiology

9: The final remarks

10: Physiological measurements of cardiorespiratory activity with impedance pneumography

Abstract

1: Introduction

2: Instruments

3: Electrodes and their placement

4: Signal processing

5: Motion artifacts

6: Cardiorespiratory applications (with a multimodal signal acquisition)

7: Discussion

Index

Copyright

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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

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A catalogue record for this book is available from the British Library

ISBN 978-0-12-818614-5

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Contributors

Carles Aliau-Bonet     Department of Electronics Engineering, Universitat Politècnica de Catalunya BarcelonaTech, Castelldefels, Spain

Pedro Bertemes-Filho     Department of Electrical Engineering, Technological Science College, State University of Santa Catarina, Joinville, Brazil

Gerard Cybulski     Department of Mechatronics, Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Warsaw, Poland

Nina Forss     HUS Neurocenter, Helsinki University Hospital, Helsinki, Finland

Asko Hänninen     Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

Jari Hyttinen     Tampere University, Faculty of Medicine and Health Technology, Tampere, Finland

Atte Kekonen     Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland

Ville Kolehmainen     Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

Olli Koskela

Tampere University, Faculty of Medicine and Health Technology, Tampere

HAMK Smart Research Unit, Häme University of Applied Sciences, Hämeenlinna, Finland

Mari Lehti-Polojärvi     Tampere University, Faculty of Medicine and Health Technology, Tampere, Finland

Margus Metshein     Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn, Estonia

Marcel Młyńczak     Faculty of Mechatronics, Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Warsaw, Poland

Kazimierz Peczalski     Department of Biomedical Engineering, Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Warsaw, Poland

Uwe Pliquett     Institut für Bioprozess- und Analysenmesstechnik e.V., Heilbad Heiligenstadt, Germany

Marcos Quílez-Figuerola     Department of Electronics Engineering, Universitat Politècnica de Catalunya BarcelonaTech, Castelldefels, Spain

Tuomo Savolainen     Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

Jussi Toivanen     Department of Applied Physics, University of Eastern Finland, Kuopio, Finland

Jari Viik     Faculty of Medicine and Health Technology, Tampere University, Tampere, Finland

Preface

Mart Min; Paul Annus

The scientific approach to electrical impedance dates back more than a century. Oliver Heaviside introduced the idea of electrical impedance in 1886, and a few years later, in 1893, Arthur E. Kennelly represented the impedance of electrical circuits with complex numbers. Charles P. Steinmetz developed the theoretical basis for using complex variables and vector diagrams for the representation of electrical impedance in electrical circuits and machines by the end of the 19th century.

At the beginning of the 20th century, Peter Debye (in 1912) and Hugo Fricke (in 1924/25) derived a mathematical treatment for the frequency dependence of electrical impedance in diverse chemical and biological environments. Their studies provided the basis for addressing the frequency dependence (spectral view) of chemical and biological impedance, both of which evolved from a common physical/chemical ground but separated later into electrochemical impedance and electrical bioimpedance, mostly due to the specifics of their applications. Since then, many scientists and engineers in the fields of electricity and electrical engineering, electronics, electrochemistry and electrophysics, materials science and technology, and bioelectricity and medicine have worked tirelessly to develop a better understanding and several new applications of electrical impedance and electrical bioimpedance over time.

For many decades, their results were believed to be at least very promising for practical applications, especially for measurements in biology and medical diagnosis. Unfortunately, the reality has not been so obvious and convincing. We have seen successful implementations in rate-adaptive cardiac pacemakers, in analyzers of breathing and lung tomography, cell counters, and just a few other medical devices. There must be reasons and convincing explanations for the much slower than expected introduction of the promising technology in practice. Some of the reasons are: we do not know exactly what the distribution of electrical current is in living tissue, as it has a complicated structure; we do not know well enough the reasons of spectral and spatial distribution of the permittivity in living materials; and we are still, in many cases, guessing regarding electromagnetic properties of tissues. From an engineering point of view, we need more efficient materials, better measurement solutions, and stable biocompatible measurement electrodes and microelectrodes.

The motivation of this book is to address the needs and propose solutions that enable us to move toward wider practical applications through a better understanding of the basics, new instrumentation, and further developed measurement, testing, and diagnosing methods. In this book, impedance measurements in the wide frequency range (spectroscopy) receive the most attention, and the following questions are answered: what to measure, how to measure, and with which instruments to measure?

The editors have received 10 excellent contributions that address the above problems. It is hoped that this compilation will further develop the practical applications of electrical bioimpedance, help readers to find working solutions, and guide them away from known pitfalls.

Acknowledgments

Paul Annus; Mart Min

It has been a great pleasure to work on this book together with the authors of the chapters. Our sincere thanks go to our good friends and colleagues Margus Metshein, Carles Aliau-Bonet, Marcos Quílez-Figuerola, Pedro Bertemes-Filho, Uwe Pliquett, Mari Lehti-Polojärvi, Jari Hyttinen, Olli Koskela, Gerard Cybulski, Atte Kekonen, Jari Viik, Jussi Toivanen, Asko Hänninen, Tuomo Savolainen, Nina Forss, Ville Kolehmainen, Kazimierz Peczalski, and Marcel Młyńczak. We are also very grateful to the members of Tallinn Impedance Group—Hip Kõiv, Raul Land, Ksenija Pesti, Andrei Krivošei, Olev Märtens, Jaan Ojarand, Eiko Priidel Marek Rist, and many others—for their support and frequent good advice.

Our efforts in bioimpedance spectroscopy have been greatly supported by Stig Ollmar, Eberhard Gersing, Rodney W. Salo, and Nils Holmström. We are grateful for the backing from the author of the great complementary classic Bioimpedance and Bioelectricity Basics, Ørjan Grøttem Martinsen.

Finally, it was strong encouragement from Fiona Geraghty and firm and steady pacing from Rachel Pomery, which got the book written. Also, Sojan P. Pazhayattil, whom I got to know only after the text has been written. They are truly helpful, very positive, and professional; similarly, it was a pleasure working with everyone else at Elsevier Publishing. Our dear colleague, great engineer, inventor, and very good person Toomas Parve is always in our thoughts.

Introduction

Measurement of electrical impedance seems simple. Investigators should acquire the voltage value between the relevant points on the object under scrutiny and measure the passing current. Impedance is a straightforward ratio of complex numbers between these values. Nevertheless, it is hardly ever fully true in real measurement situations. Even researchers with good, precise, and expensive impedance measurement devices such as Keysight (Agilent, HP) E4990A, Wayne Kerr 65120P, or Zurich Instruments MFIA Impedance Analyzer may experience problems.

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Zurich Instruments MFIA Impedance Analyzer. Source: wikipedia.org.

Over time, many good articles have been written on the subject, but unfortunately, they often go unnoticed or are considered unimportant as the heading of one recent article elegantly states impedance surprises (Brown, 2015). The impedance measurement causes surprises and in so many different ways. Apparently, there is much more to consider than just connecting wires and conducting the experiment. Instead of being a purely technical question, measuring impedance turns into a tangled web of interlocking disciplines in a very fundamental way or by paraphrasing well-known book by Horowitz and Hill: into the art (Horowitz, 2015). Therefore, straightforward reading (and interpreting) of the measurement results could easily be grossly misleading or simply wrong.

Things get considerably more complicated if attention is shifted from general impedance measurements of material samples and simple objects to bioimpedance and spectroscopy. This is because biological objects are incredibly complex, and they change during the life cycle and even during the measurement cycle. As a result, the bioimpedance method is often discarded as too complicated and unreliable for acquisition of data from biological objects. This book will shed light on some potentially troublesome measurement situations and, more importantly, will recount success stories, illustrating that the bioimpedance method can be very useful and has great potential for reliable assessment of biological objects. A brief overview follows of the development of the concept of bioimpedance and measurement solutions.

Tuesday (Oliver)

New York, April 18, 1893.

It was Tuesday. The seventy-sixth meeting of the Institute was held this date at 12 West Thirty-first Street (in New York), and was called to order at 8.30 P. M. by Vice-President William J. Hammer (Kennelly, 1893). Members of the American Institute of Electrical Engineers (AIEE), engineers, inventors, innovators, and scientists will have the pleasure of listening to Mr. A. E. Kennelly’s paper on ‘Impedance.’ At this time, the Institute had existed for nine years. It was established by great inventors of the time, starting with Thomas Alva Edison and Alexander Graham Bell (Hochheiser, 2009). After a merger with the Institute of Radio Engineers (IRE) on January 1, 1963, the Institute of Electrical and Electronics Engineers (IEEE) was born.

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Picture of Arthur Edwin Kennelly. Source: wikipedia.org.

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Picture of Charles Proteus Steinmetz. Source: wikipedia.org.

This 76th meeting and the presented work of Arthur E. Kennelly on impedance were later associated with the birth of the discipline. Terms such as intellectual treat (Brittain, 1984) have been used in relation to the event. Yet the 31-year-old Arthur E. Kennelly and Charles P. Steinmetz (28) were only the translators. And indeed, the concept of electrical impedance (or apparent resistance) had been introduced 6 years earlier by the British Oliver Heaviside, genius and curmudgeon (Nahin, 1983), very shy and retiring by nature, and much honored, but personally almost unknown (Kennelly, 1936), as an opposition that an object presents to a current when sinusoidal excitation is applied. It has been pointed out on his death that Mr. Heaviside has been recognized as one of the most eminent exponents of electrical science, particularly for his development of the electromagnetic theory. His retiring character and desire to avoid society, partly due to almost complete deafness since childhood, has resulted in his name being unknown to the general public but those who have come in contact with his work regard him as an illustrious successor to Wheatstone, Maxwell, and Kelvin (Oliver Heaviside, 1925). Initially, starting in 1885, The Electrician was the main publisher of Heaviside’s papers in London. These articles were far above the reach of most electrical engineers of that time. The editors often begged him to simplify his mathematics, but to Heaviside’s mind they seemed to be already very simple (Kennelly, 1936)—hence the need for translators.

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Picture of Oliver Heaviside. Source: wikipedia.org.

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Picture of James Clerk Maxwell. Source: wikipedia.org.

If Kennelly was a translator of Heaviside’s ideas, then Heaviside translated James Clerk Maxwell's equations, General Equations of the Electromagnetic Field, to the form known today (Donaghy-Spargo and Yakovlev, 2018). Maxwell’s original 20 equations were reorganized into four. A little-known fact is that Maxwell had a close encounter with electrical impedance long before Heaviside’s work. This is mentioned also in the remarkable AIEE publication referenced earlier (Kennelly, 1893), where not only can the article Impedance be found but also the discussion after the presentation. It was Dr. Mihajlo Idvorski Pupin who made a remark that the problematic so-called Ferranti effect is in fact only a special case of the more general effect which I call the resonance, and that it could have been foreseen from Maxwell’s equations. Even more than that: Maxwell, at that time, was a young man. That was about 1865, if I do not err … Maxwell who had not had very much experience in experimental electricity at that time, was at a loss. But he spent that night in working over his problem, and the next morning he wrote a letter to Sir William Grove explaining the whole theory of the condenser in multiple connection with a coil. It is wonderful what a genius can do in one night! The second thing brought up by Dr. Pupin is that The primary law is Ohm’s law in its generalized form, therefore the origins of the impedance could be related also to the much earlier Die galvanische. Kette, mathematisch bearbeitet by Georg Simon Ohm (1827). Impedance, while generally complex, obviously has the same unit as a real part of it—the resistance, that is, ohm (Ω) in the SI system of units.

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Picture of Henry Cavendish. Source: wikipedia.org.

But the story continues. In 1871, James Clerk Maxwell became the first Cavendish Professor of Physics on his return to Cambridge; he remained in that post until 1879 (Cambridge University Physics Society, 1995). The opening of the new laboratory was financed by the Chancellor of Cambridge University who was the seventh Duke of Devonshire, William Cavendish, and most importantly, a distant relative of Henry Cavendish. Perhaps it is not so strange, then, that Maxwell was greatly involved in collecting, editing, and publishing The Scientific Papers of the Honourable Henry Cavendish (Cavendish, 2010) and most importantly for readers interested in impedance and specifically electrical bioimpedance, the Electrical Researches of the Honorable Henry Cavendish (Maxwell, 2019). Henry Cavendish (1731–1810) was the grandson of the second Duke of Devonshire. Almost 100 years passed before most of the works that this notoriously shy man wrote on electrical topics and on his electrical experiments were finally recognized. This happened in 1879, long after other scientists had been credited for the same results. Many things in Henry Cavendish's writings seem strange by today’s standards for example, he used the term degree of electrification for what we now call electric potential, and velocity for what we now call current. Nevertheless, regardless of these naming issues, the ideas do mostly stand today. When considering his contribution, it may be easily overlooked that he did not have even elementary resources for conducting experiments—they had simply not yet been discovered. These resources were shortly to be developed, however; the gold-leaf electroscope was introduced by Abraham Bennet in 1786, the frog galvanoscope by Luigi Galvani in 1791, voltaic pile by Alessandro Giuseppe Antonio Anastasio Volta in 1799, the galvanometer by Hans Oersted in 1820, and the thermocouple by Thomas Johann Seebeck in 1821, to name a few. The last one was key for Ohm’s experiments because it was the first stable voltage source. None of these resources existed when Henry Cavendish conducted his experiments in 1781, however His instrument at hand was the Honourable Henry Cavendish himself; he measured the level of pain he felt when the current passed through his body. Significantly, this means that Cavendish did actually experiment with bioimpedance, because his body was part of the circuit (Falconer, 2015).

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Picture of Andreas Cunaeus working with Leyden jar in Pieter von Muschenbroek's lab.

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Picture of Otto von Guericke's experiments with the sulfur globe. Source: wikipedia.org.

This was not the first time that a human being had been on the receiving end of a electric shock, however In October of 1745, the Leyden jar was invented by the German Ewald Georg von Kleist. The jar's name came actually from an independent experiment conducted a year later by Pieter van Musschenbroek, a Dutch physicist at the University of Leyden. After charging the jar with an electrostatic generator connected to the water, von Kleist was able to give himself a painful shock by touching the lead to the water while still holding the jar (Ho et al., 2010). While painful, it was not the only attempt at this experiment. Guericke’s sulfur globe electrostatic generator (de Heathcote, 1950), together with the Leyden jar, made rows of 20 soldiers jump for the amusement of the nobleman; this experiment led to Stephen Gray’s Flying Boy and Georg Matthias Bose’s Electric Kiss (Benjamin, 1898). It is arguable whether or not these were dubious experiments with dubious results (Bazerman, 1993), but one thing is certain: conductivity of biological objects, in the form of humans, was being investigated already in the early days of scientific research into electricity. In the next section, we will take a closer look at the human body from the viewpoint of impedance.

1: Dark side of the human being

As the name bioimpedance suggests, it is the impedance of biological objects under investigation or impedance of living organisms. It can include detection of impedance changes when certain molecular interactions are identified, impedance of bodily fluids, impedance of single cells or cellular structures, and impedance of body parts and organs and of the whole body. It was shown in the previous section that the current-passing capabilities of the human body were already known and being extensively studied in the early 18th century. It had been proven also that electricity can kill. Benjamin Franklin killed and prepared several turkeys with electrical current and was almost electrocuted himself during the process, as he describes in his Christmas Days 1750 letter. Probably the first person in history known to die while conducting electrical experiments was Georg Wilhelm Richmann on August 6, 1753, while trying to quantify the response of an insulated rod to a nearby storm (Krider, 2010).

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Picture of Benjamin Franklin experiment. Source: wikipedia.org.

Two hundred years on from these early steps, the might of electrical energy in everyday life has become apparent. We are strongly indebted to, among others, Thomas Alva Edison and Nikola Tesla for our modern electrified society (Sulzberger, 2003b).

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Picture of Thomas Alva Edison. Source: wikipedia.org.

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Picture of Nikola Tesla. Source: wikipedia.org.

In 1879, Edison introduced high-resistance carbonized cotton filament, and the first practical incandescent light was born. A temporary demonstration of his direct current (DC) lightning system was conducted at Holborn Viaduct in London; this was followed soon after by the First District installation in Lower Manhattan on September 4, 1882. The Edison electrical system was born, but it had many inherent problems, such as losses in the copper wires. In 1884, Edison hired an unknown immigrant from Croatia, Nikola Tesla, to improve the system. After several months, it became clear that cooperation was impossible. In 1887, seven important US patents were issued for Tesla. These were soon followed by the demonstration of his polyphase alternating current (AC) motor at an American Institute of Electrical Engineers meeting, and the battle of currents started. George Westinghouse purchased Tesla’s seven patents and employed him to develop the AC distribution system. It was crucial for Edison to prove that the AC system, which was promoted by George Westinghouse and produced by the Westinghouse Electric Company, was inferior. One of the claims against AC was its unsafe nature compared with DC. This was not entirely unsubstantiated because several deaths were caused by AC lighting lines in New York. Self-educated Harold Pitney Brown was to become one of the key figures in the battle of currents; public electrocution of animals with AC was his trademark, and he was not without support from Edison, who publicly denounced capital punishment (Essig, 2003; Triumph of AC. 2. The battle of the currents, 2003a). Replacement of hanging with electrocution in New York State was a direct consequence of Professor Brown's actions. AC of roughly 2000 V caused axe-murderer William Kemmler’s body to smolder and burn on August 6, 1890. To rise the heat, the term Westinghousing was suggested for the electrocution.

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Picture of Electric chair. Source: wikipedia.org.

The limits for safe (or rather lethal) current and voltage were still largely unknown, and investigations had begun. Thanks to the electric chair, it became evident that the most lethal range of current is roughly 100–200 mA. Currents of 10 mA and more were found to cause muscular contractions and pain, and should be deemed unsafe. It is known today that usage of safety extra-low voltage (SELV) AC and protected extra-low voltage ensure little risk of injury. Even more importantly, it is now known that low frequency (50–60 Hz) AC in excess of 30 mA must be considered lethal, and this knowledge is borne in mind when designing residual-current circuit breakers.

One of the first investigators of safety limits was Tesla himself. Among his findings was the fact that high-frequency currents are safer and often do not even cause a sensation of electric shock. He also suggested that high-frequency currents might have beneficial uses in medicine (Vujić, 2006). In 1887, Kennelly became an assistant in Thomas Alva Edison’s West Orange laboratory and joined the battle. His studies compared effects of DC and AC on human and animal subjects (Brittain, 2006; Bush, 1940). Because the result was not surprising, he took sides in the battle and mentioned painless death by AC. In a book written in 1895 he writes, A marked difference exists between the physiological effects of an alternating and a continuous current. When a continuous current is sent through human body, chemical and physiological effects are produced, entirely distinct from those which attend the passage of an alternating current under similar circumstances. When passing through the vital organs of the body, any electric current, whether continuous or alternating, may, if sufficiently powerful, cause death. Alternating currents, however, at commercial frequencies and pressures, are much more apt to produce fatal effects on the human body than continuous currents. In New York State, alternating electric currents are used for the execution of criminals, and, when properly employed, produce absolute, instantaneous, and painless death. Yet in the next paragraph, he recognizes Tesla’s research on the subject: The experiments of Tesla and others have shown that at frequencies and pressures far higher than those employed for ordinary commercial purposes, the physiological effects of alternating currents become less severe, and that at extraordinarily high frequencies, enormous pressures may be handled with impunity (Houston and Kennelly, 1895).

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Picture of Alexanderson alternator. Source: wikipedia.org.

A joint study with Ernst Frederick Werner Alexanderson was published by Kennelly on the topic in 1910. The tolerance current was defined as the limiting currents strength which the subject could take through the arms and body without marked discomfort or distress (Brittain, 2006). They used saline solution that contained electrodes when experimenting, very similar to that Henry Cavendish did much earlier. The Alexanderson radio frequency alternator, invented in 1904, enabled Alexanderson and Kennelly to experiment up to 100 kHz and to conclude that a man could tolerate a current of about 500 mA at 100 kHz, but only 5 mA at 60 Hz due to reduced nervous sensibility at high frequencies (Brittain, 2006). Knowledge on this topic has evolved ever since, and one of the latest discussions on electrical safety and physiological effects of electrical current flowing through the human body can be found in the fifth edition of very Medical Instrumentation: Application and Design (Webster, 2020).

In addition, a multitude of electrical safety standards should be studied very carefully before design and development of medical equipment are considered. Most relevant in the context of the electrical bioimpedance spectroscopy is undoubtedly standard IEC 60601. This is a widely accepted series of international standards for the basic safety and essential performance of medical electrical equipment. Ultimately, the measurement current should not be higher than allowable safe leakage current for medical devices.

2: Troubles with the object

Backed with today’s knowledge, it is tempting to say that even the very early electrical experiments were closely tied to bioimpedance spectroscopy as it is known now. Indeed, Leyden jars were discharged through the human body; hence the conductance or impedance of biological matter was involved and the resultant sharp excitation pulses could be viewed as related to modern ultra-wideband (UWB) signals, giving a spectroscopic (that is, wideband) response. Henry Cavendish tubes with salted water, copper wire, and Leyden jars are even closer to the subject as his experiments can be associated with the early discovery of Ohm’s law. If all that is debatable, then starting with Heaviside’s definition, the link between the past and present becomes firm and traceable, so Tesla, Kennelly, and others were working in the field of bioimpedance, much as it is known today.

Very public almost warlike start of the research was given, with many interested parties involved. Bearing this in mind, why did the interaction between electrical current and human flesh remain underexplored for almost half a century after its discovery? It is easy to say that the available technology was not yet up to the task. It was very bulky, limited in capabilities, and expensive, such as the Alexanderson radio frequency alternator, mentioned earlier. Ethical considerations can be brought up as well. Experimenting with animals and humans has always been ethically questionable and is increasingly so, but this did not stop experiments in US prisons during executions or wartime crimes. Yet the biggest issue was, and to a certain extent still is, related to the complexity of living tissue and its varying nature.

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Picture of human body by Leonardo da Vinci. Source: wikipedia.org.

Objects can be systematized as conductors, insulators, or semiconductors depending on their level of conductivity. It is relatively easy to measure bulk conducting materials and even some composites based on them, such as metals and metal alloys. Insulators and semiconductors may be a bit more problematic but can be handled as well. Some precautions are in order; for example, the impedance of the connecting cables must be considered. However, this issue was largely solved by William Thomson, better known as Lord Kelvin (1824–1907), in 1861, when he invented the Kelvin bridge and four-point measurements. When the geometry of objects is a bit odd, the Leo J. van der Pauw method enables the calculation of potential distribution in a thin, conductive layer of any shape (van der Pauw, 1958) and so on. All these methods can and should be applied when acquiring data related to bioimpedance spectroscopy. Yet the results can be grossly misleading because of the underestimation of the problem's complexity, which can be a significant issue, and also the fundamental uncertainty involved in the prediction of any value of any variable.

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Picture of William Thomson. Source: wikipedia.org.

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Picture of commercial Kelvin Bridge. Source: wikipedia.org.

The first aspect to consider is partitioning of the environment (all-inclusive, all-embracing, and therefore beyond grasp) into interesting, information-bearing objects or systems of objects into conditionally separated spaces. In other words, the environment and the object under study should be reasonably separated; furthermore, the object itself should be reasonably segmented when warranted. Any such partitioning is subjective and depends on the needs (and tastes and knowledge) of the partitioner. At the same time, success of the examination (ability to conquer) and its value to the community (amount of systemized repeatably acquirable information) or simply signal-to-noise ratio depend on the quality of this division. Or to paraphrase Shannon’s version of Kerckhoffs’s principle: the allies should know the system. Perhaps one of the best articles on the subject was written by the great mathematician David S. Slepian as the summary of the second Shannon Lecture (the first one was given by Claude Elwood Shannon himself) (Slepian, 1976). While arguing whether signals are bandlimited or not, he introduces two facets. Facet A consists of observations on, and manipulations of, the ‘real world’. Do not ask me what this real world is: my thoughts become hopelessly muddled here, and Facet B is something else again. It is a mathematical model and the means for operating with the model. It consists of papers and pencils and symbols and rules for manipulating the symbols. It also consists of the minds of the men and women who invent and interpret the rules and manipulate the symbols, for without the seeming consistency of their thinking processes there would be no single model to consider. Slepian goes on: we like to think that there is an intimate relationship between Facet A and Facet B of a given science. … in fact, under closer scrutiny one sees the correspondence as tenuous, most incomplete, and imprecise … Worse yet, many key parts of the model—many of its concepts and operations—have no counterpart in Facet A. To the extent that there is some correspondence between Facets A and B, we have the miracle of modem science—the deepening understanding of our universe, and the bounty and ease of the technological society in which we live. A second-order miracle, little recognized or appreciated, is that this first miracle could arise from such a really ragged fit between the facets.

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Picture of Jonas Ferdinand Gabriel Lippmann, Nobel laureate in physics. Source: wikipedia.org.

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Picture of David Slepian.

And that is one of the cornerstones to the understanding of why impedance surprises. Impedance-related partitioning of the environment has a long history. The problem of measuring electrolytic resistivity without electrode-impedance error was investigated by Jonas Ferdinand Gabriel Lippmann before the term impedance was introduced by Heaviside in 1886. Lippmann reported the results in his 1875 thesis Relations entre les phénomènes électriques et capillaires. He used a very sensitive capillary electrometer, which he had invented, to measure the resistivity of the fluid column between the voltage-sensing electrodes, which were separated from the current-carrying electrodes. Georg Simon Ohm was already aware of the difficult nonlinear nature of the electrode–electrolyte interfaces. Luckily for Ohm, Thomas Johann Seebeck had already discovered the thermoelectric effect (1822). Upon the suggestion from Johann Christian Poggendorff, he gave up his experiments with electrochemical batteries and turned his attention toward bismuth-copper thermopiles for his Die galvanische Kette, mathematisch bearbeitet (1827) (Geddes, 1996).

Unfortunately, it is impossible to dismiss the properties of electrolytes when measuring electrical impedance of objects of biological origin. Even the simplest constituent of biological matter—water—requires special treatment. The present great debate on the structure of water and its changes with temperature, pressure, and solutes has produced a bewildering variety of models, all more or less supported by the same thermodynamic, spectroscopic, conduction, and diffraction data, stated the acknowledged pioneer in the study of dielectrics, semiconductors, ferromagnetics, and ferroelectrics, Arthur Robert von Hippel, in his later years (von Hippel, 1988). An equation for single relaxation of the complex permittivity of the linear medium by the teacher of von Hippel, Peter Joseph William Debye, lays the foundation for later discussions (Cole and Cole, 1941).

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Picture of Peter Joseph William Debye, Nobel laureate in Chemistry. Source: wikipedia.org.

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Picture of Kenneth Stewart Cole.

In the case of linear systems, the permittivity ɛ contains the same information as admittance Y or impedance Z. Soon it was recognized that the real relaxation curve is flatter than that predicted by the above mentioned equation (Cole, 1928). Later discussion can be found in an article written by Kenneth Stewart Cole and Robert H. Cole on the subject (Cole and Cole, 1941). Experimental evidence suggested that parameter α should be introduced: The remarkable fact is that the experimental results are so generally expressed by an empirical formula involving a single new constant α. In other words, a constant phase element (CPE) replaced Debye’s ideal capacitor in the model. The words empirical and experimental must be noted because the integral model does not take good care when explaining the intricacies of the measured impedance. It does a (relatively) good job in giving an empirical estimate for the behavior of the measured bioimpedance, but it fails when a plausible explanation should be given, and accordance with the general relaxation theory should be shown. Researchers concerned with this controversy have tried to explain things and have proposed alternative equivalent circuits (Grimnes and Martinsen, 2005). However, resistor-capacitor (RC) models are tempting and have been discussed and verified in detail by many researchers. As Jan Gimsa and Derk Wachner state, The RC model makes it possible to describe structural Maxwell-Wagner dispersions and explains the interdependencies of IMP (impedance) (Gimsa and Wachner, 1998). Seemingly more general RC-CPE models could be viewed as RC models with a multitude of components.

The first well-documented measurements of the biological matter with cellular structure were probably carried out by Hugo Fricke and Sterne Morse for cream (Fricke and Morse, 1925) and blood (Fricke, 1925). Fricke and Morse found that their measurements of the resistance and capacity of suspensions of red blood cells at various frequencies could be accurately fitted to a Cole circuit of type A, where they thought of R1 as due to the suspending medium, R2, due to the interiors of the corpuscles, and C due to the capacities at their surfaces, according to Kenneth S. Cole (1928). Later studies have expanded the view, added more elements, and introduced a rather well-defined dispersion structure consisting of (sometimes multiple) α, β, and γ regions.

Future problems are based on achievements of the past. They may be unresolved problems of a more basic nature or future practical applications made possible by recent technical innovations, wrote Herman P. Schwan in his 1999 overview article (Schwan, 1999). One of those unresolved problems is related to the enormous dielectric constant ɛ of the α dispersion (Schwan, 1994). Many explanations have been given by various researchers, but they all seem to be somewhat incomplete. On the more practical side, a comprehensive work was filed for the Defense Technical Information Center by Camelia Gabriel from the Physics Department of King’s College in London (Gabriel, 1996) and published together with Sami Gabriel and W. Lau as a three-part article on The dielectric properties of biological tissues (Gabriel et al. 1996a,b,c). Frequency dependence of the permittivity and conductivity of most of the biological tissues present in the body was modeled, measured, and presented in four dispersion regions from 1 to 10¹¹ Hz. This is by far the best presentation of inhomogeneous and often anisotropic biological matter. There is also a web calculator available based on Gabriel et al. work (http://niremf.ifac.cnr.it/tissprop/).

3: Coupling—Intentional and unintentional

Herman P. Schwan, sometimes referred to as a founding father of the field of biomedical engineering (Foster, 2005), was a very productive scientist. He published more than 300 scientific papers on impedance and bioimpedance and on the measurement methods and tools required for the acquisition of those, including papers on coupling and electrodes. Thousands of pages can be written on the subject of coupling. From fundamental physics, we know that there are four basic interactions in nature: gravitational, electromagnetic, strong, and weak interactions. Two later ones are observable at subatomic distances and can be generally omitted when conducting measurements on macroscopic objects. Gravitational interaction occurs between objects with mass and is significant also over cosmic distances; yet at the atomic scale, it is by far the weakest of the four. This leaves electromagnetism as the prevailing method of interaction in our everyday world, including interaction with biological matter, which is nicely presented in the book