Electrical Impedance Imaging Technology for Needle Guidance During Medical Needle Insertion Procedures Von der Fakultät 7 – Konstruktions-, Produktions- und Fahrzeugtechnik der Universität Stuttgart zur Erlangung der Würde eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung Vorgelegt von Jan Liu geb. in Berlin Hauptberichter: Prof. Dr. rer. nat. habil. Peter P. Pott Mitberichter: Prof. Dr. rer. nat. habil. Tilman E. Schäffer Tag der mündlichen Prüfung: 15.10.2024 Institut für Medizingerätetechnik der Universität Stuttgart 2024 Contents Acknowledgements V Abbreviations VII Symbols XI Zusammenfassung XV Abstract XVII 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Theoretical Background 7 2.1 Medical Needle Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Anatomical Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Electrical Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Bioimpedance Measurements . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Electrode Systems . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 Electrical Properties of Tissues . . . . . . . . . . . . . . . . . . 27 2.4.3 Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4.4 Transfer Impedance and Spatial Sensitivity . . . . . . . . . . . . 37 2.4.5 Impedance Measurement Methods . . . . . . . . . . . . . . . . . 41 2.5 FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6 Classification Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.6.1 Classical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.6.2 Machine Learning Methods . . . . . . . . . . . . . . . . . . . . 48 3 State of the Art 53 3.1 Imaging-Based Needle Guidance . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Sensor-Based Needle Guidance . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 Impedance Measurements on Needles . . . . . . . . . . . . . . . . . . . 56 4 Tissue Identification 63 4.1 Tissue Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.1.1 Phantom Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 64 4.1.2 Phantom Characterization . . . . . . . . . . . . . . . . . . . . . 66 4.2 Bipolar Needle Electrode Measurements . . . . . . . . . . . . . . . . . 70 4.2.1 Bipolar Needle Electrode Design . . . . . . . . . . . . . . . . . . 70 4.2.2 Measurement System . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2.3 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . 76 I Contents Jan Liu 4.2.4 Discussion Bipolar Needle Electrode Measurements . . . . . . . 80 4.3 Multi-Local Needle Electrode Measurements . . . . . . . . . . . . . . . 81 4.3.1 Multi-Local Needle Electrode Design . . . . . . . . . . . . . . . 82 4.3.2 Experimental Analysis . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 89 4.3.4 Discussion Multi-Local Needle Electrode Measurements . . . . . 93 4.4 Monopolar Needle Electrode Measurements . . . . . . . . . . . . . . . . 96 4.4.1 Experimental Investigation . . . . . . . . . . . . . . . . . . . . . 96 4.4.2 Investigative Results . . . . . . . . . . . . . . . . . . . . . . . . 98 4.4.3 Discussion Monopolar Needle Electrode Measurements . . . . . 100 4.5 Discussion Tissue Identification . . . . . . . . . . . . . . . . . . . . . . 101 5 Simulative Analysis 105 5.1 FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2 Bipolar Needle Electrode Simulation . . . . . . . . . . . . . . . . . . . 106 5.2.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . 106 5.2.2 Sensitivity Analysis Bipolar Needle Electrode . . . . . . . . . . 107 5.3 Multi-Local Needle Electrode Simulation . . . . . . . . . . . . . . . . . 108 5.3.1 Simulation Model Setup . . . . . . . . . . . . . . . . . . . . . . 108 5.3.2 Impedance Simulation . . . . . . . . . . . . . . . . . . . . . . . 112 5.3.3 Singularity Treatment . . . . . . . . . . . . . . . . . . . . . . . 114 5.3.4 Sensitivity Analysis Multi-Local Needle Electrode . . . . . . . . 118 5.4 Monopolar Needle Electrode Simulation . . . . . . . . . . . . . . . . . . 120 5.4.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.4.2 Sensitivity Analysis Monopolar Needle Electrode . . . . . . . . 123 5.5 Discussion Simulative Analysis . . . . . . . . . . . . . . . . . . . . . . . 124 6 Needle Guidance System 131 6.1 Software Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.1.1 Hardware Control . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.1.2 Classification Algorithm . . . . . . . . . . . . . . . . . . . . . . 135 6.1.3 Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . 137 6.1.4 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 6.2 Local Tissue Visualization . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.3 Global Tissue Visualization . . . . . . . . . . . . . . . . . . . . . . . . 149 6.4 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.4.1 Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 6.4.2 Study Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6.5 Discussion Needle Guidance System . . . . . . . . . . . . . . . . . . . . 159 7 Conclusion 161 7.1 Tissue Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.2 Simulative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.3 Needle Guidance System . . . . . . . . . . . . . . . . . . . . . . . . . . 162 References 163 Appendices 179 A Tissue Identification 181 A.1 Multi-Local Needle Electrode Measurements . . . . . . . . . . . . . . . 181 II Institut für Medizingerätetechnik Jan Liu Contents A.1.1 Manufacturing Process of the Multi-Local Needle Electrode . . . 181 A.1.2 Classification Results . . . . . . . . . . . . . . . . . . . . . . . . 183 B Simulative Analysis 187 B.1 Multi-Local Needle Electrode Simulation . . . . . . . . . . . . . . . . . 187 B.1.1 Line Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 C Needle Guidance System 189 C.1 Needle Guidance System . . . . . . . . . . . . . . . . . . . . . . . . . . 189 C.1.1 Graphical User Interface Tabs . . . . . . . . . . . . . . . . . . . 189 C.2 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 C.2.1 Study Questions . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Research Output 197 Institut für Medizingerätetechnik III Acknowledgements I would like to express my sincere gratitude to my thesis advisor, Prof. Peter P. Pott, for his guidance and advice throughout the course of this research. The invaluable input and feedback he provided was greatly appreciated in navigating this project. His comments and suggestions contributed significantly to the final structure of this dissertation. My sincere thanks also go to my second examiner, Prof. Tilman Schäffer, for generously offering to review and evaluate my dissertation. I am immensely grateful to my colleagues, whose collaboration and companionship made the research process both productive and enjoyable. Their support and discus- sions were instrumental in shaping many of the ideas presented here. I would like to thank my friends and family for their understanding and support throughout this journey. Finally, I am indebted to my students for their incredible work and passion. Working with them on a daily basis has been very exciting and has taught me a tremendous amount. Their contribution was an important cornerstone in the completion of this dissertation. Stuttgart, December 2024 Jan Liu V Abbreviations 1D One-Dimensional 2D Two-Dimensional 3D Three-Dimensional AC Alternating Current AI Artifical Intelligence AISI American Iron and Steel Institute ANN Artificial Neural Network ASCII American Standard Code for Information Interchange ASIC Application-Specific Integrated Circuit BNC Bayonet Neill Concelman CAD Computer-Aided Design CC Current-Carrying CNB Core Needle Biopsy CNT Carbon Nanotube COM Communication Port CPE Constant Phase Element CPU Central Processing Unit CSF Cerebrospinal Fluid CSV Comma-Separated Values CT Computed Tomography DC Direct Current DEMUX Demultiplexer DUT Device Under Test E-field Electric Field ec Electric Currents ECG Electrocardiogram EF Excitation Factor EIS Electrical Impedance Spectroscopy EIT Electrical Impedance Tomography EMC Electromagnetic Compatibility EMG Electromyography EN Enable FE Finite Element FEM Finite Element Method FNAB Fine Needle Aspiration Biopsy FPGA Field-Programmable Gate Array VII Abbreviations Jan Liu GB Gigabyte GCS Global Coordinate System GND Ground GUI Graphical User Interface HF High Frequency HST Heat Shrink Tube IA Impedance Analyzer ID Inner Diameter IMT Institut für Medizingerätetechnik IP Internet Protocol IT’IS Foundation for Research on Information Technologies in Society IV Intravenous JST Japan Solderless Terminal kNN k-Nearest Neighbors LCR L: Inductance, C: Capacitance, R: Resistance LED Light Emitting Diode LF Low Frequency LiPo Lithium Polymer LM Line Method LTI Linear Time-Invariant LU Lower-Upper MCS Monte Carlo Simulation ML Machine Learning MRI Magnetic Resonance Imaging MUX Multiplexer NaCl Sodium Chloride NIR Near-Infrared OD Outer Diameter OpAmp Operational Amplifier PC Personal Computer PCB Printed Circuit Board PDE Partial Differential Equation PDPH Postdural Puncture Headache PGA Programmable Gain Amplifier PI Polyimide PIA Precision Impedance Analyzer VIII Institut für Medizingerätetechnik Jan Liu Abbreviations PIVC Peripheral Intravenous Catheter PLA Polylactic Acid PTFE Polytetrafluoroethylene PU Pick-Up PVDF Polyvinylidene Difluoride QR Q: Orthogonal matrix, R: Triangular matrix RF Radio Frequency RFA Radio Frequency Ablation rNN Fixed-Radius Nearest Neighbors RT Room Temperature RTD Resistance Temperature Device SCL Serial Clock SD Standard Deviation SDA Serial Data SEL Select SIG Signal SMA SubMiniature Version A SSt Stainless Steel STEP Standard for the Exchange of Product Data STL Stereolithography SVM Support Vector Machine TCP Transmission Control Protocol TFQMR Transpose-Free Quasi-Minimal Residual Method UART Universal Asynchronous Receiver Transmitter US Ultrasound USA United States of America USB Universal Serial Bus UV Ultraviolet VCC Voltage Common Collector VEID Vein Entry Indicator Device VM Volume Method WHO World Health Organization Institut für Medizingerätetechnik IX Symbols Symbol Description SI derived unit A Ampère A A Area m2 a Acceleration m/s2 ae Acceleration of electrons m/s2 a⃗ Vector a⃗ 1 a⃗N N -th component of vector a⃗ 1 α Alpha parameter, coefficient of relaxation 1 αN Alpha parameter of the N -th term 1 α0 Temperature coefficient of resistivity at reference tem- perature Θ0 K−1 B Susceptance S b⃗ Vector b⃗ 1 b⃗N N -th component of vector b⃗ 1 C Capacitance F Cdiel Capacitance of a dielectric F CI Capacitance of the boundary layer F Cp Parallel capacitance F Cs Series capacitance F Cvac Capacitance of vacuum F C Coulomb 1 c Molar concentration mol/m3 cN Molar concentration of the N -th ion mol/m3 D Distance 1 D⃗ Electric flux density C/m2 E Electric field strength V/m Ea Activation energy J/mol E⃗ Electric field V/m E⃗vak Electric field in vacuum V/m E⃗diel Electric field in a dielectric V/m Err Maximum permissible error range 1 e Euler’s number, e = 2.718281... 1 e Elementary charge, e = 1.602176634 · 10−19 C C ϵ Permittivity F/m ϵ0 Vacuum permittivity, ϵ0 ≈ 8.85 · 10−12 F/m F/m ϵr Relative permittivity 1 ϵs Permittivity for small frequencies F/m ϵ∞ Permittivity for high frequencies F/m ϵ′ Real part of the permittivity F/m ϵ′′ Imaginary part of the permittivity F/m ϵ Complex permitivity F/m F Farad or Faraday constant 1 or C/mol F Force N F⃗ Force vector N f Frequency Hz fr Resonant frequency Hz XI Symbols Jan Liu G Electrical conductance S G Gauge 1 H Henry 1 H⃗ Lead vector Ω/m Hz Hertz 1 I Electric current A Ireci Current level supplied in the PU electrodes A I Complex electric current A IR Current of all resistive components A Ir Current at resonant frequency fr A IC Current of all capacitive components A i Alternating current A iC Current of an capacitor A iL Current of an inductor A î AC current amplitude of i A J Joule 1 J⃗ Electric current density A/m2 J⃗ ′ Electric current density normalized to unit current m−2 J⃗CC Excitation current density A/m2 J⃗ ′ CC Excitation current density normalized to unit current m−2 J⃗reci Reciprocal lead field A/m2 J⃗ ′ reci Reciprocal lead field normalized to unit current m−2 j Imaginary unit, j2 = −1 1 K Kelvin 1 K Cell constant m−1 K1 Kohlrausch correction constant 1 kB Boltzmann constant, kB = 1.380649 · 10−23 J/K J/K L Inductance H L1 Manhattan distance 1 L2 Euclidean distance 1 L∞ Chebyshev distance 1 Lp Minkowski distance 1 l Length m lt Traveled distance m l⃗ Length vector m l⃗CC CC dipole length vector m l⃗PU PU dipole length vector m lw Thickness of a vein wall m Λm Molar conductivity Sm2/mol Λ0 m Limiting molar conductivity Sm2/mol λD Debye length m λ+ Limiting molar conductivity of cations Sm2/mol λ− Limiting molar conductivity of anions Sm2/mol M Molar, 1 M = 1 mol/l mol/l m Meter 1 me Mass of an electron kg m⃗ Dipole moment Am N Newton 1 N Natural number N 1 NA Avogadro constant, NA = 6.02214076 · 1023 mol−1 mol−1 n Natural number n 1 ne Electron density m−3 XII Institut für Medizingerätetechnik Jan Liu Symbols n⃗ Unit vector 1 νN Stoichiometric number of the N -th ion 1 ν+ Stoichiometric number of cations 1 ν− Stoichiometric number of anions 1 O Point in space O 1 O1 Point in space O1 1 O2 Point in space O2 1 Ω Ohm 1 ω Angular frequency rad/s ωr Relaxation frequency rad/s P Power W p Integer 1 Φ Magnetic flux Wb ϕO Electric potential at point O V ϕO1 Electric potential at point O1 V ϕO2 Electric potential at point O2 V φ Phase angle rad φv Phase angle of v rad φi Phase angle of i rad Π Proportion of the attribute in the population 1 π Pi number, π = 3.141592... 1 Ψ Interlinking flux Wb Q Charge C Qf Quality factor 1 q Sample charge C qN Charge of the N -th ion C R Electrical resistance or the gas constant, R = 8.314462... Ω or J/K mol RN Nernst resistance Ω Rel Resistance of the bulk electrolyte Ω RTIA Transimpedance amplifier gain resistor Ω RCAL Calibration resistor Ω ρ Resistivity Ωm ρ0 Resistivity at reference temperature Θ0 Ωm S Siemens 1 SDϵr Standard deviation of ϵr 1 SDσ Standard deviation of σ S/m S Spatial sensitivity distribution m−4 s Second 1 σ Electrical conductivity S/m σ0 Pre-exponential factor S/m σi Ionic conductivity S/m σ Complex electrical conductivity S/m T Time period S t Time s τc Average collision period s τr Relaxation time s Θ Absolute temperature K Θ0 Reference temperature K θ Angle rad uN Mobility of the N -th ion m2/Vs u+ Mobility of cations m2/Vs u− Mobility of anions m2/Vs Institut für Medizingerätetechnik XIII Symbols Jan Liu V Volt 1 V Electric voltage V V Complex electric voltage V V V 1 Complex electric voltage V 1 V V 2 Complex electric voltage V 2 V V AB Bridge voltage between terminal A and B V V r Voltage at resonant frequency fr V vC Voltage of a capacitor V v Alternating voltage or velocity V or m/s vDrift Drift velocity of electrons m/s vL Voltage of an inductor V vi Induced voltage V v̂ AC voltage amplitude of v V W Work J X Reactance Ω XC Capactive reactance Ω XL Inductive reactance (inductance) Ω Y Admittance S Z Apparent resistance Ω Ztr Transfer impedance Ω Z Impedance Z Ω Z1 Impedance Z1 Ω Z2 Impedance Z2 Ω Z3 Impedance Z3 Ω Z4 Impedance Z4 Ω ZW Warburg impedance Ω z z value 1 zN Charge number of the N -th ion 1 z+ Charge number of cations 1 z− Charge number of anions 1 XIV Institut für Medizingerätetechnik Zusammenfassung Bei der Einführung medizinischer Nadeln kann es trotz der Häufigkeit ihrer Durch- führung regelmäßig zu Komplikationen kommen, die auf eine falsche Positionierung der Nadel zurückzuführen sind. Die häufigste Anwendung ist die Venenpunktion zur Blutentnahme. In einer Studie mit 4.050 Patientinnen und Patienten traten in 12,3 % der Fälle Blutergüsse und Hämatome auf. Diese entstehen, weil das Blutgefäß nur teil- weise punktiert oder vollständig durchstochen wird (Überschießen der Nadel). Das Ein- führen der Nadel erfolgt in der Regel manuell und hängt stark von den Fähigkeiten der praktizierenden Person und der Physiologie der Patientin oder des Patienten ab. Beste- hende Nadelführungsmethoden sind entweder umständlich und für den Routineeinsatz ungeeignet oder fehleranfällig. In dieser Dissertation wurde eine neue bildgebende Technologie basierend auf elektrischen Impedanzmessungen als Alternative zu den derzeitigen Führungssystemen untersucht werden. Die zugrundeliegende Hypothese besagt, dass die Integration mehrerer lokalisierter Impedanzmessungen auf einer Nadel eine erfolgreiche Gewebeidentifikation und räumliche Verortung ermöglicht. Diese In- formation kann genutzt werden, um ein 3D-Bildgebungssystem zu entwickeln, das für die Nadelführung bei medizinischen Punktionsverfahren verwendet werden kann. Um diese Hypothese zu untersuchen, wurden in dieser Dissertation drei Aspekte unter- sucht. Der erste Aspekt ist die impedanzbasierte Gewebeerkennung mit Hilfe von medi- zinischen Nadeln. Es wurden ein bipolarer, ein multi-lokaler (bipolar) und ein monopo- larer Ansatz entwickelt und getestet. Bei der bipolaren Methode wurden zwei konzen- trisch angeordnete Nadeln als Teil eines Messsystems verwendet. Die Identifizierung des Gewebes anhand der Leitfähigkeitswerte war bei Fett-, Haut- und Blutphantomen erfolgreich. Für den multi-lokalen Ansatz wurde eine Nadel mit 12 Drahtelektroden modifiziert. Es wurde ein System entwickelt, um die aktiven Messelektroden auf der Nadel abwechselnd durchzuschalten. Ein k-nächste-Nachbarn-Algorithmus zur Klas- sifikation ordnete die gemessenen Impedanzwerte den entsprechenden Gewebetypen zu. Der monopolare Ansatz wurde mit Bezug zur Periduralanästhesie getestet. Eine Anordnung, bestehend aus einer Tuohy-Nadel und einer EKG-Elektrode, konnte er- folgreich Fett und NaCl-Lösung als Ersatz für Zerebrospinalflüssigkeit unterscheiden. XV Zusammenfassung Jan Liu Der zweite Aspekt befasst sich mit der simulativen Untersuchung nadelbasierter Impe- danzmessungen. Die oben genannten Konfigurationen wurden in CAD-Modelle umge- setzt und in eine FEM-Umgebung integriert. Die FEM-Simulationen wurden durchge- führt, um Impedanzwerte als mögliche Grundlage für eine Klassifizierungsaufgabe zu erzeugen. Ebenfalls wurde die Stromdichteverteilung untersucht, um einen Be- reich mit relevanter räumlicher Messempfindlichkeit zu definieren. Die sogenannten sensitiven Volumina konnten erfolgreich in den dritten Aspekt, die Entwicklung des Nadelführungssystems, integriert werden. Für das Nadelführungssystem wurde eine grafische Benutzeroberfläche implementiert, die als Steuerungs- und Visualisierungsschnittstelle für den Benutzenden dient. Die Benutzeroberfläche kann zur Steuerung der Hardwarekomponenten verwendet werden, die für das Schalten der Elektrodenpaare und die Impedanzmessung verantwortlich sind. Die Visualisierungsumgebung zeigt die Nadel während des Einstechens und die umgebenden Gewebetypen entsprechend der Form der sensitiven Volumina. Das en- twickelte System wurde schließlich in Bezug auf Effizienz der Nadelführung evaluiert. Eine erste Studie zum Vergleich einer ultraschallgestützten Nadelführung und einer impedanzbasierten Nadelführung wurde mit drei Teilnehmenden durchgeführt. Trotz der geringen Teilnehmendenzahl zeigte die Studie, dass die impedanzbasierte Nadelfüh- rung aufgrund ihrer Intuitivität und Handhabung bevorzugt wurde und die Effektivität stark von der Klassifikationserfolgsrate abhing. XVI Institut für Medizingerätetechnik Abstract Although performed on a daily basis, medical needle insertion procedures are often associated with complications due to incorrect needle positioning. The most common needle insertion procedure is venipuncture for blood collection. In a study of 4,050 patients, bruising and hematoma occurred in 12.3 % of cases. These are the result of only partial penetration of the blood vessel or complete perforation (needle overshoot). Needle insertion is usually performed manually, highly dependent on the clinician’s skill and the patient’s physiology. Existing needle guidance methods are either cumbersome and inadequate for routine procedures, or prone to error. This dissertation aims to explore a new imaging technology based on electrical impedance measurements as an alternative to current guidance systems. It is hypothesized that the integration of multiple localized impedance measurements on a needle enables successful tissue identification and spatial localization. This information can be exploited to develop a 3D imaging system that can be used for needle guidance during medical needle insertion procedures. In this dissertation, the hypothesis is investigated through the exploration of three aspects. The first aspect involves impedance-based tissue identification using medical needles. A bipolar, multi-local (bipolar), and monopolar approach were established and tested. In the bipolar approach, two concentrically placed needles were used as part of a measurement system. Successful tissue identification based on conductivity values was achieved for fat, skin, and blood phantoms. The multi-local approach involved the modification of a hypodermic needle with 12 stainless steel wire electrodes. A system was established to sequentially switch the active measurement electrodes on the needle. The measured impedance values were assigned to the corresponding tissue types using a k-nearest neighbors classification algorithm. Additionally, the monopolar approach was tested in the context of epidural anesthesia. A setup comprising a Tuohy needle and an ECG electrode successfully discriminated between fat and sodium chloride solution, which was used as a substitute for cerebrospinal fluid. XVII Abstract Jan Liu The second aspect deals with the simulative assessment of needle-based impedance measurements. The above configurations were translated into CAD models and inte- grated into an FEM environment. The FEM simulations were performed to generate impedance data as a potential basis for a classification task. Also, the current density distribution was investigated to define a region of relevant spatial measurement sensi- tivity. The so-called sensitive volumes could be successfully integrated into the third aspect, which is the development of the needle guidance system. For the needle guidance system, a graphical user interface was implemented to serve as the user’s control and visualization interface. The user interface can be used to control hardware components responsible for switching electrode pairs and measuring imped- ance. The visualization environment displays the needle during insertion and shows the surrounding tissue types corresponding to the shape of the sensitive volumes. Eventu- ally, the developed system was evaluated for needle guidance effectiveness. An initial study comparing ultrasound guidance with impedance-based guidance was performed with three subjects. Despite the small sample size, the study found that impedance- based needle guidance was preferred due to its intuitiveness and handling, and the efficacy was highly dependent on the classification success rate. XVIII Institut für Medizingerätetechnik 1 Introduction This chapter presents a description of the rationale and motivation for the present dissertation. It also details the objectives of this research. 1.1 Motivation Medical needle insertion has become vital in a wide range of modern-day health care practices. In particular, the procedure of inserting a needle into tissue is performed for blood draw, medication delivery, tissue biopsies, and cancer treatments such as brachytherapy, radiofrequency ablation, and cryoablation. These procedures require needle insertions through tissue layers such that the needle tip is positioned in a par- ticular region of interest, typically also requiring positioning accuracy in the range of a millimeter and below. The most common invasive needle insertion routine is venipuncture for blood draw. In the United States of America (USA), over 2.7 million blood samples are taken daily [1–3]. Intravenous access is also required for blood donations, which are esti- mated at 15,000 per day in Germany [4]. Also, 70 % of patients in acute care set- tings require catheterization [5]. Furthermore, approximately 1.6 million breast and 1 million prostate needle biopsies are taken annually in the USA alone [6, 7]. Over 5 million gastrointestinal needle biopsies are performed each year worldwide [8]. Even though these procedures are very commonplace, complications still arise fairly often due to incorrect needle positioning [1–3]. In a study with 4,050 patients, minor bruising and hematoma was seen to occur in 12.3 % of the venipuncture procedures performed (approx. 500 patients) [9]. In addition, the World Health Organization (WHO) estimates the incidence rate of hematomas to be 2-3 % for blood donation, which is significant given the number of procedures performed per day [3]. Furthermore, the difficulties of venipuncture are exacerbated by the physiology of pediatric, geriatric, obese, and dark-skinned individuals [2, 10]. 1 Chapter 1. Introduction Jan Liu (a) Partial venipuncture. (b) Needle overshoot. (c) Potential nerve damage. (d) Needle at vein wall. (e) Needle at vein valve. (f) Potential vein collapse. Figure 1.1: Different incorrect needle tip positions during venipuncture. Some of the complications arising from incorrect needle placement are visualized by Figure 1.1. If the blood vessel is partly punctured (Figure 1.1a), or the needle has penetrated through the blood vessel (Figure 1.1b), hematomas, which cause discomfort to the patient, occur due to blood leaking into the tissue [3]. The hematoma formation typically occurs under the skin adjacent to the puncture site and is the most frequent complication associated with venipuncture [1, 11]. Further, the hematoma formation can also potentially cause nerve damage through the exerted pressure [3]. As shown in Figure 1.1c, clinicians might also completely miss the vein and potentially cause serious nerve damage, which often results in malpractice lawsuits [1]. Further needle mispositioning cases include the tip being on the vein wall (Figure 1.1d), or on a vein valve (Figure 1.1e), both resulting in restricted blood flow during blood collection. This can also happen if the vessels are at risk of collapsing due to an excessive pressure difference applied (Figure 1.1f) [3]. Currently, the needle insertion is performed manually after having identified the target blood vessel, and having estimated an appropriate angle and depth of insertion. The only feedback of the appropriate insertion depth is a change in the force needed to advance the needle, or the visible backflow (flash) of blood in a special window of the 2 Institut für Medizingerätetechnik Jan Liu 1.2. Research Objective needle assembly. Thus, the success rate is strongly dependent on clinician skills and patient physiology [1, 2]. Existing needle guidance methods, including computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound (US), are inadequate for common proce- dures like blood draws and tissue biopsies due to their limitations, such as high costs, incompatibility with standard needles, and the potential for errors, e.g., in ultrasound imaging (cf. Chapter 3) [12–15]. At present, there is potential for improvement of needle guidance methods. The research this dissertation is based on was conducted at the Institute of Medical De- vice Technology (ger. Institut für Medizingerätetechnik) at the University of Stuttgart. The Institut für Medizingerätetechnik (IMT) at the University of Stuttgart was founded in 2017 under the direction of Prof. Dr. Peter P. Pott. The core competencies of IMT include medical applications in the field of robotics, novel sensor principles, and intel- ligent systems. The present work is a pilot project, initiated in 2018. The research was carried out without additional funding from external sources. Originally aimed at automating blood sampling, the initial idea was refined and transformed. By exploring general concepts for improving venipuncture, the idea of creating an impedance-based imaging system emerged as an alternative approach to conventional needle guidance methods. 1.2 Research Objective The research presented here primarily focuses on the investigation of electrical prop- erties of tissues with particular emphasis on utilizing them to identify tissue types surrounding the needle during insertion. The objective of this dissertation is to inves- tigate its central hypothesis: The incorporation of multiple localized impedance measurements on a needle will lead to the successful identification and spatial containment of surrounding tissue types, resulting in the development of a 3D imaging system that can be used for needle guidance during medical needle insertion procedures. Therefore, this work aims to develop methods for multi-local identification of tissue types around the needle, and their visualization to serve as a tool for needle guidance. Institut für Medizingerätetechnik 3 Chapter 1. Introduction Jan Liu The needle guidance system utilizes needle models structured with multiple electrodes in combination with a simulative assessment of the distribution of the current within the tissue of interest. The distribution of the current helps visualize the tissue type by spatially enclosing the measurement range. The primary focus of this research is on venipuncture, due to its relevance and familiarity. Tissue phantoms are mainly used as sample material. However, the developed methods are applicable beyond this specific application and can be extended to other medical needle insertion procedures. In order to achieve the research objective and to investigate the research hypothesis, three sub-hypotheses will be addressed. i) Tissue Identification Tissue can be identified during needle insertion by impedance measurements with the needle. There are different approaches to use impedance measurements for tissue identifica- tion. Therefore, a comprehensive study is performed, in which three different needle models are investigated: a bipolar needle electrode, a multi-local needle electrode, and a monopolar needle. The necessary measurement systems are developed and two differ- ent classification approaches are tested: a conductivity-based approach and a k-nearest neighbors based approach. The goal is to identify the most appropriate needle model and classification algorithm with respect to the research objective. ii) Geometric Sensitivity Analysis The distribution of the current density of impedance measurements can be as- sessed and a measurement zone can be identified where the contained tissue is the largest contributor to the measured impedance. Bioimpedance measurements are usually dependent on the geometrical electrode con- figuration (cf. Subsection 2.4.4). Finite element method (FEM) is used to investigate the current density and the measured impedances of different electrode configurations. An electrode configuration with a high current density around the measuring electrodes is favorable to obtain a good spatial resolution of the measurement. 4 Institut für Medizingerätetechnik Jan Liu 1.2. Research Objective iii) Needle Guidance System Using a multi-local electrode configuration, the combination of information ac- quired from tissue identification and geometric sensitivity analysis can be inte- grated producing a visual representation useful for needle guidance. The only established method for obtaining non-invasive images based on electrical bioimpedance thus far is electrical impedance tomography (EIT) [16, 17]. It is based on numerous surface electrode measurements around a body part and incorporates image reconstruction algorithms to create a 2D tomographic image. In this dissertation, an alternative approach is proposed using a modified needle with multiple electrodes that measure the local impedances. The impedance information is used to identify the tissue type at the active measurement electrodes. Exploiting the current density information obtained through FEM enables the possibility to visualize the tissue types surrounding the needle. Assuming a certain tissue structure, the visualization can be used for needle guidance during venipuncture. Finally, the needle guidance system is evaluated in a comparative study with US guidance. The structure of this dissertation is based on the outlined objectives of this research. While Chapter 2 provides a description of the theoretical basics and Chapter 3 presents the current state of research, the following Chapters 4, 5 and 6 deal with the substan- tive exploration of the research hypotheses. Chapter 4 focuses on tissue identification during needle insertion using different needle electrodes for testing and evaluation. In Chapter 5, simulated analyses of the geometric sensitivities of electrode configurations for impedance measurements are performed. In Chapter 6, the development of a needle guidance system, integrating the results of Chapters 4 and 5, is explained. Chapter 7 provides concluding statements about this research. Institut für Medizingerätetechnik 5 2 Theoretical Background In this chapter, the theoretical background that may be necessary to un- derstand this dissertation is explained. The anatomy relevant to the appli- cation of venipuncture, basic electrical phenomena, fundamentals of bioim- pedance measurement, and FEM will be discussed in this chapter. The theoretical background is intended to provide answers to the following questions: • How is the skin structured at typical venipuncture sites and what are the electrical properties of interest? • How can impedance measurements be exploited to analyze and classify the present tissue type? • How can the identified tissue information be spatially contained and visualized? Section 2.1 provides general explanations about medical needle insertion, followed by an overview of the anatomical basics relevant to venipuncture in Section 2.2 as well as the required electrical basics in Section 2.3. This is followed by an in-depth analysis of bioimpedance measurements in Section 2.4. Finally, basic concepts related to FEM simulations are explored in Section 2.5. 2.1 Medical Needle Insertion In general, instruments used to puncture the human body vary in shape and manufac- ture. A distinction can be made between a needle and a cannula, which is a hollow needle. However, in the literature, the terms cannula and needle are often used inter- changeably, with the exact shape depending on the context. The shape, manufacture, and requirements for disposable cannulas are specified in DIN EN ISO 6009, 7864, 9626, and DIN 13097-4 [18–21]. Essentially, a cannula consists of a hollow cylinder with a specific bevel at one end. The size of a cannula is primarily determined by its outer diameter. Common measurements for cannula sizes are given in millimeters, gauge (G), 7 Chapter 2. Theoretical Background Jan Liu or according to the Pravaz system, or in Charrière (also known as French). Gauge is borrowed from the American unit of measurement for wire diameters. Values are standardized in DIN 13097-4 and range from 10 G to 34 G [21]. The higher the gauge value, the smaller the outer diameter of the cannula. According to DIN EN ISO 6009, each gauge value can be assigned a color for better visibility (see Table 2.1) [18]. Var- ious bevel types are used to achieve the desired needle tip shape. The most common bevel types are single bevel, faceted bevel (hypodermic needle), and back bevel. Table 2.1: Sizes and gauges for common hypodermic needles according to DIN EN ISO 6009 and 9626 [18, 20] Gauge Color Outer diameter (mm) French Pravaz size Example Application 14 Pale Green 2.1 6.3 Blood transfusion, CNB 17 Red-violet 1.4 4.2 Blood donation, CNB, brachytherapy 18 Pink 1.2 3.6 Blood donation, CNB, brachytherapy 20 Yellow 0.9 2.7 1 Intramuscular injection, CNB 21 Deep Green 0.8 2.4 2 Blood draw 22 Black 0.7 2.1 12 Blood draw 23 Deep Blue 0.6 1.8 16 Blood draw 25 Orange 0.5 1.5 18 Subcutaneous injection, FNAB In medical applications, cannulas used for blood collection are typically attached to a plastic hub at the non-beveled end. This allows for a connection to other containers such as infusion tubing or syringes. The connection is based on the Luer system to ensure a user-friendly, manufacturer-independent and standardized connection, spec- ified in DIN EN ISO 80369 [22]. Essentially, the Luer system consists of a hollow truncated cone that fits snugly into its counterpart. This is referred to as Luer Slip. In this context, the cone stump is referred to as the male and the counterpart as the female [23]. A slightly modified system exists where the cone stump has an external thread for secure connection to the counterpart with a slight twist (Luer Lock). There are many different medical procedures that require the insertion of a medical needle into soft tissue with accurate positioning. Some procedures involving needle insertion and the types of needles used are described below. 8 Institut für Medizingerätetechnik Jan Liu 2.1. Medical Needle Insertion • Injection: Injections deliver liquid medications, fluids, or nutrients directly into the human body. Injection methods include intravenous, intramuscular, subcu- taneous, intraosseous (into the bone), and intradermal injection [24, 25]. The choice of needle gauge and size depends on the type of injection and the amount of medication. For example, the needle used for subcutaneous injection is usually small and short with a gauge of 25 (cf. Table 2.1). Insulin for diabetes or heparin (anticoagulant) can be given subcutaneously. Intramuscular injections require a longer and thicker needle, e.g., a 20 G needle (cf. Table 2.1). Most vaccines are administered by intramuscular injection. • Venipuncture: Venipuncture is performed to obtain blood samples (e.g., for diagnostic tests) or to deliver medications by needle insertion into the desired area [3]. The insertion is commonly performed by a clinician after identifying the target blood vessel and planning an appropriate angle and depth. Once the needle is inserted, blood drawing is commonly performed by creating a pressure difference, using either a syringe or a vacuum extraction tube. Venipuncture can also be performed for placing a peripheral intravenous catheter (PIVC). After a needle is inserted into an appropriate vein, a catheter is advanced through the needle into the vein. Subsequently, the needle is removed, and the catheter is secured to the skin with tape or a dressing [26]. Fluid solutions, anesthesia, or pain medication can be delivered through the catheter. For adult patients, 21-23 G hypodermic needles are usually used for venipuncture (cf. Table 2.1) [3]. • Tissue Biopsies: If only a small amount of tissue needs to be taken, a needle biopsy can be performed. Two approaches of needle biopsy exist: fine needle aspiration biopsy (FNAB) and core needle biopsy (CNB) [27, 28]. For both procedures, a needle is inserted into the tissue to be sampled. For FNAB, a small amount of cells is aspirated into the needle by applying suction. Usually, smaller needles in the range of 25 to 27 G are used for FNAB (cf. Table 2.1) [29]. For CNB, small pieces of tissue are taken with a punch biopsy. CNB is typically performed with a larger gauge needle, ranging from 14 to 20 G (cf. Table 2.1) [30]. • Brachytherapy: A proven treatment for prostate cancer is prostate brachyther- apy. Long, hollow needles (17-18 G, cf. Table 2.1) are used to place radioactive seeds in the organ according to a precise preoperative treatment plan. The ef- Institut für Medizingerätetechnik 9 Chapter 2. Theoretical Background Jan Liu fectiveness of the procedure depends on how accurately the needles are placed. In general, numerous needles are required for prostate brachytherapy to be effec- tive [31, 32]. 2.2 Anatomical Basics Since this work is primarily concerned with the application of venipuncture, this section provides a theoretical overview of the anatomy of the skin and blood vessels of the arm, where the most common venipuncture sites are located. Dermal papilla Sebaceous gland Pacini corpuscle Arrector pili muscle Adipose tissue Hair shaft Epidermis (⁓150 µm) Dermis (⁓1.5 mm) Eccrine sweat gland Hypodermis (⁓2 mm) (subcutis) Figure 2.1: Layers of the skin and associated structures (adapted from [33], used under CC BY-SA 4.0). The layer thicknesses are intended to give a general idea of the thickness relations [34]. Before a vein can be punctured, several layers of skin must be penetrated. The skin, the body’s largest organ, covers approximately 1.5 to 2 m2 of the body’s surface [35, 36]. It serves as a barrier between the body’s internal environment and the external en- vironment, protecting against chemical, physical, biological, and mechanical damage. This protective function includes defense against pathogens and shielding against cel- lular damage from exposure to ultraviolet (UV) radiation. In addition, the skin plays a vital role in regulating body temperature, acts as a sensory organ, stores energy, protects against dehydration, and contributes to vitamin D production [35–37]. Struc- 10 Institut für Medizingerätetechnik https://creativecommons.org/licenses/by-sa/4.0/ Jan Liu 2.2. Anatomical Basics turally, the skin consists of three layers: the epidermis, dermis and subcutis, as shown in Figure 2.1. The outermost layer, known as the epidermis, acts as the primary protective barrier. It is made up of squamous epithelium and contains cells called keratinocytes, which are responsible for producing the protein keratin, giving the skin firmness and water repel- lency. The epidermis is stratified into layers, starting with the stratum corneum, which consists of flat, anucleate keratinocytes, followed by the stratum lucidum, stratum gran- ulosum, stratum spinosum, and the stratum basale, where new cells are formed [36, 38]. As the epidermis lacks blood vessels, it relies on the underlying dermis for nourish- ment. The dermis gives the skin its elasticity and resistance to tearing and is made up of collagenous and elastic connective tissue that contains blood vessels, adipose tissue, nerves, hair follicles, mechanosensory receptors, and ducts. Together, the epidermis and dermis form the cutis. The deepest layer, the subcutis, consists of loose connective tissue and is adjacent to muscles and bones. This layer is rich in fatty tissue and serves as a protection against cold, a mechanical buffer and an energy reserve [39]. Major blood vessels and nerves are located in the subcutis [36, 38]. Veins are responsible for transporting deoxygenated blood from the periphery to the heart. Successful venipuncture involves selecting a suitable vein based on criteria such as accessibility, visibility, structure, and the patient’s general health. Commonly used veins for blood sampling or catheter access are superficial veins of the crook of the arm, the back of the hand, or the forearm [3]. The Vena cephalica, Vena basilica, and Vena mediana cubiti in the crook of the arm are the preferred options (cf. Figure 2.2). Alternatively, veins in the dorsal venous network on the dorsum (back) of the hand can be used for venipuncture [40]. In cases where venipuncture in these veins is not possible, for instance, because of skin lesions or scar tissue, the Vena saphena magna in the lower extremities can be used [41]. For infants (0-1 years) or toddlers (1-4 years), the dorsal venous networks (hand and foot) are preferred. Alternatively, the saphenous vein at the ankle or the scalp veins are recommended sites for pediatric patients [42]. The microscopic anatomy of a vein is layered, similar to the skin. The wall of large vessels consists of three layers: the Tunica interna, the Tunica media and the Tunica adventitia (see Figure 2.3). The innermost Tunica interna contains endothelial cells on a basement membrane and has very little influence on the mechanical properties Institut für Medizingerätetechnik 11 Chapter 2. Theoretical Background Jan Liu Subclavian Axillary Cephalic Subscapular Brachial Basilic Median cubital Cephalic Radial Median antebrachial Basilic Ulnar Palmar venous arches Digital Figure 2.2: Major veins of the upper limb (adapted from [43], used under CC BY 4.0). 12 Institut für Medizingerätetechnik https://creativecommons.org/licenses/by/4.0/ Jan Liu 2.3. Electrical Basics of the vein. The Tunica media consists mainly of three components: collagen, elastic fibers and smooth muscles. The outermost layer of the venous wall, the Tunica adven- titia, consists mainly of longitudinally aligned collagen fibers and is connected to the surrounding tissue [44, 45]. Vein valve Endothelium Tunica media Tunica adventitia Basement membrane Lumen Figure 2.3: Structure of a vein (adapted from [46], used under CC BY-SA 3.0). 2.3 Electrical Basics Etymologically, a dielectric is a material that the electric field penetrates (gre. dia meaning through). A perfect dielectric is a substance without free charges. They can be referred to as insulators or nonconductors. In contrast, conductors or electrolytes do not allow static electric field penetration. Charges can move freely when an electric field (E-field) is applied (cf. Figure 2.4). Biomaterials have properties of both categories and can therefore be regarded as conductors or dielectrics [47]. – – – – – – – – A l Ԧ𝐹 𝐸 Ԧ𝐽 Figure 2.4: E-field in a material. E⃗: E-field; F⃗ : force on charge carriers caused by E⃗; J⃗ : current density. An E-field is usually generated by charges, which are introduced from external sources, e.g., from a battery. Thereby, the E-field causes a force F⃗ on the charge q: Institut für Medizingerätetechnik 13 https://creativecommons.org/licenses/by-sa/3.0/deed.en Chapter 2. Theoretical Background Jan Liu F⃗ = qE⃗, [︂ E⃗ ]︂ = N C = V m . (2.1) Thus, the free charges in the material experience acceleration [48]. Each point O within the E-field can be assigned a potential ϕO: ϕO = ∫︂ ∞ O E⃗ · d⃗l. (2.2) The potential describes the work that can be gained when a sample charge is brought from an infinite distance, where the potential is set equal to zero, to the point O [49]. The potential difference between two points O1 and O2 along the conductor is called the electric voltage V : V = ϕO1 − ϕO2 , [V ] = V. (2.3) A quantity of charge Q = Nq, which crosses a certain cross-section in the conductive material in a certain time interval, is defined as a current I: I = dQ dt , [I] = C s = A. (2.4) The ratio between the current I and the cross-sectional area A in the direction of the unit normal vector n⃗ is called the current density J⃗ : J⃗ = I A n⃗, [︂ J⃗ ]︂ = A m2 . (2.5) The current density resulting from an E-field depends on the material. There is a linear relationship between the current density and the E-field, in which the electrical conductivity σ comes into play as a proportionality factor. This relationship is known as Ohm’s law: J⃗ = σE⃗, [σ] = S m . (2.6) 14 Institut für Medizingerätetechnik Jan Liu 2.3. Electrical Basics In scalar form, Ohm’s law can be equivalently expressed through the linear relationship between current and voltage: V = RI. (2.7) R is the electrical resistance and is a proportionality factor, which describes the material as well as the geometry dependence of the Ohmic load: R = l σA = ρ l A , [R] = V A = Ω. (2.8) ρ (in Ωm) is called resistivity, A is the cross-sectional area, and l the length of the conductive material. Similar to the electrical conductivity and resistivity, the reciprocal of the resistance G = 1/R can be defined, which is called the conductance. Due to the amount of charge moved in the potential field, work W is done: W = QV, [W ] = J. (2.9) Thus, the potential energy is converted into kinetic energy and the dielectric acts as an Ohmic load. The electric power P is the time derivative of the work W : P = dW dt = dQV dt = IV = V 2 R = I2R, [P ] = W. (2.10) So far, only direct currents have been considered whose current intensity does not change over time. Thus, all other basic electrical quantities also remain constant over time. For currents which change over time, these quantities can be described as a function of time t. A special case are the periodically excited alternating currents in which both the current and the voltage change sinusoidally. The quantities change back and forth between positive and negative values. Institut für Medizingerätetechnik 15 Chapter 2. Theoretical Background Jan Liu Thus, the directions of electric current i and voltage v change accordingly with the sign: v = v̂ sin (ωt + φv) (2.11) i = î sin (ωt + φi). (2.12) Here v̂ and î are the amplitudes of the voltage and current, φv and φi are the phase angles of the excitation. ω = 2πf is the angular frequency of the excitation with the frequency f in Hz. The frequency is calculated from the reciprocal of the period T . The phase difference between the current and the voltage is only zero for pure Ohmic transformers. Therefore, the calculation of the alternating current (AC) resistance for Ohmic loads is constant over time. For simplification, it is mathematically advanta- geous to use the complex AC calculation as an aid. Here, both the current and the voltage are given as complex-valued functions of time: V = v̂ej(ωt+φv) (2.13) I = îej(ωt+φi), (2.14) where j represents the imaginary unit for which j2 = −1 holds. From these two equa- tions, the AC resistance Z, also called impedance, can be calculated in analogy to Ohm’s law as follows: Z = V I = v̂ej(ωt+φv) îej(ωt+φi) = v̂ î ej(φv−φi). (2.15) In an electric circuit, the Ohmic resistor is one of the three basic passive compo- nents [50]. The other two important components are the inductor (coil) and the ca- pacitor. These components have an external effect on other components due to the electric and magnetic fields induced by the alternating current. In electrical engineering, these components are idealized in order to simplify the anal- ysis. These effects are concentrated only inside the component and do not reach the 16 Institut für Medizingerätetechnik Jan Liu 2.3. Electrical Basics outside [51]. Furthermore, electrical circuits consisting of these components are as- sumed to be linear time-invariant (LTI). In the simplest case, an inductor can be made from a wound conductor. Its behavior in an AC circuit can be described by the law of induction in which the E-field and thus the induced voltage vi, which is generated by electromagnetic induction of a conductor loop with the magnetic flux Φ, are directed in such a way that they counteract the cause according to Lenz’s rule: vi = ∮︂ E⃗ · d⃗l = −dΦ dt . (2.16) In contrast to a simple conductor loop, a coil winding with N turns has an area pen- etrated by the magnetic flux multiplied by approximately N . Therefore, the following applies approximately: vi = −dNΦ dt . (2.17) NΦ is also called the interlinking flux Ψ. For an inductive load, vL = −vi holds, and thus vL = dNΦ dt = dΨ dt = dLi dt = L di dt + i dL dt . (2.18) L is referred to as the inductance of the inductor. Since it does not change over time in LTI systems, the voltage that drops across the inductor is given by vL = L di dt , [L] = H. (2.19) Inserting Eq. 2.14 into Eq. 2.19 gives: vL = L dIL dt = îej(ωt+φi)jωL = iLjωL. (2.20) The expression vL/iL is an impedance with a purely imaginary component, which is why it is also called inductive reactance: XL = Im{jωL} = ωL. (2.21) Institut für Medizingerätetechnik 17 Chapter 2. Theoretical Background Jan Liu The behavior of a capacitor can be derived in a similar way as that of the inductor. In the simplest case, the capacitor consists of two plane-parallel conductive plates. In a capacitor, the amount of charge on the plates is proportional to the voltage, with the capacitance C as the proportional constant: Q = CvC . (2.22) In an ideal plate capacitor, the capacitance also remains constant over time. It depends only on the geometry (plate area A and plate distance l) and the material between the two plates: C = ϵA l = ϵ0ϵrA l , [C] = F. (2.23) ϵ is called permittivity. It is a property of the material that is located between the two plates of the capacitor and is composed of the vacuum permittivity ϵ0 ≈ 8, 85 · 10−12 F m and the relative permittivity ϵr. The vacuum permittivity is a fundamental constant of nature, and links electrical and mechanical quantities, which are related via the (attractive or repulsive) Coulomb force [48, 52]. The temporal variation of this charge quantity leads to the differential equation of the capacitor: dQ dt = iC = C dvC dt . (2.24) In analogy to the inductor, the equation for voltage, Eq. 2.13, can be used: iC = C dV C dt = v̂ej(ωt+φv)jωC = vCjωC. (2.25) The capacitive reactance is also the imaginary part of the expression vC/iC : XC = Im {︄ 1 jωC }︄ = − 1 ωC . (2.26) 18 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements The two reactances XL and XC are considered separately in complex AC circuit anal- ysis because their phase differences are π/2 and −π/2, respectively, indicating a time dependence between the current and the voltage, which is not present in Ohmic resis- tances (cf. Eq. 2.15). In network analysis of electrical circuits, the resulting impedance of the system can be described as a complex number, representing the combination of the active component R and the reactive component X: Z = R + jX, [Z] = Ω. (2.27) The AC analogy of electrical conductance is called admittance: Y = 1 Z = G + jB = R R2 + X2 + j −X R2 + X2 . (2.28) Here, conductance G and susceptance B represent the active and reactive components, respectively. 2.4 Bioimpedance Measurements To perform bioimpedance measurements, at least one pair of measurement electrodes is required to introduce the measurement signal into the tissue and capture the response. Electrode systems as well as polarization effects, which occur at the electrode-tissue interface, are described in this section. Next, the behavior of tissue in an alternating electric field, which is characterized by charge transport in ionic tissue fluids and po- larization in membranes and molecules, is described [53]. Lastly, this section provides an overview of common impedance measurement methods and devices. 2.4.1 Electrode Systems Electrodes are the most important components of bioimpedance measuring systems. The measurement instrumentation incorporates electronic circuitry and wires coupled to the electrodes. The charge carriers flowing in the wires are electrons. The charge carriers in living tissue are predominantly ions. In the context of bioimpedance mea- suring, an electrode is the site of charge carrier shift or a charge exchange between electrons and ions. It is the interphase at which electronic and ionic conduction come together. An alternative definition describes an electrode as a terminal in an electrical Institut für Medizingerätetechnik 19 Chapter 2. Theoretical Background Jan Liu circuit to generate an electric field between itself and another electrode [47]. Typical electrode materials are composed in Table 2.2. Table 2.2: Electrode Materials (adapted from [47]). Metal Properties Use Ag/AgCl Stable DC reference, low DC polarization, not biocompatible Skin surface electrocardio- gram, electromyogram Platinum metals Noncorrosive, biocompatible, polarizable Needles, implants Au Noncorrosive, less biocompatible than platinum Needles, implants Titanium Highly biocompatible Implants Stainless steel Mechanically strong, noncorrosive, highly DC po- larizable and noisy, very alloy-dependent Needles, implants Tin, lead Low noise, soft and moldable Electroencephalogram Nickel Thin flexible plates, skin allergic reactions Skin surface electrocardio- gram, electromyogram Silver, zinc, iron, alu- minum Pharmaceutical or batericidal properties DC therapy and skin in- tophoresis Carbon X-ray translucent, soft and flexible multiuse rub- ber plates and wires Skin surface electrocardio- gram, electromyogram Polymers Also found as ionic or mixed versions, special consideration must be taken for the ionic con- tact medium. May be a part of the contact elec- trolyte. Mercury In research laboratories. Unique as a mercury dripping electrode with the metal surface contin- uously renewed. The metals listed are usually in alloy form. In practical scenarios, oxides tend to form, resulting in a coating on the surface (with the exception of dripping mercury). The use of different metals in an electrode pair has the potential to generate significant DC voltages which could lead to saturation of the input stage of biopotential amplifiers. In the context of bioimpedance measurements, the presence of two current-carrying (CC) electrodes is required to establish the flow of electric current through the body. Applying a voltage results in a current flow through the CC electrodes, leading to their polarization. In addition, to record a voltage between two contact points on or in the body, pick-up (PU) electrodes are required. The current flowing through the PU electrodes is negligible. Without external excitation, the biopotential signal is derived from electrical activity within a body organ and is therefore endogenous. With an exogenous signal source, the bioimpedance can be measured using two CC electrodes and two PU electrodes. This configuration enables the transmission of the 20 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements signal from the CC electrode pair to the PU electrode pair. Alternatively, bioimpedance measurements can be performed using only two electrodes, with each electrode serving the dual purpose of acting as both a PU and CC electrode (bipolar, cf. Table 2.3). i) Electrode Polarization An electrolytic cell is considered polarized when it conducts current. A CC electrode is therefore considered polarized. In contrast, a PU electrode is typically nonpolarized. However, even with zero current flow in the electrode, local wire currents can flow due to inhomogeneities of the metal surface or contact with non-isoelectric tissue areas [47]. At the interface between electrode material and liquid phase, the conversion from electronic to ionic conduction takes place. The electrode serves as an electron source or sink. The transfer of electrons is the primary process through which the electrode exchanges charges with the incoming ions or ionizes neutral substances. A second mechanism for charge transfer occurs through the oxidation of the electrode metal, in which case the metal departs from the surface as charged cations and enters the solution [47]. At the sharp boundary between an electronic conductor and an ionic conductor, an extremely thin electric double layer forms (cf. Figure 2.5) [47]. The double layer can be viewed as a molecular capacitor, with one plate represented by metal charges and the other plate represented by ions located at a minimum distance within the solution. The distance between these plates is molecularly sized, resulting in an enormous ca- pacitance. This basic electric double layer model was first proposed by Helmholtz in 1879 and is applicable only to high-concentrated electrolyte solutions (see Figure 2.5a). The Poisson equation dictates the generation of an electrical potential at the inter- face [47]. This potential exhibits linearity within the Helmholtz layer and remains constant within both the electrode and the electrolyte [47]. An expansion of the Helmholtz double layer is the Gouy-Chapman layer (see Fig- ure 2.5b). This theory considers both the Coulomb forces and the diffusion- or temperature-induced ion transport, making it a very robust model [47, 55–58]. In contrast to the Helmholtz layer, the change in potential is not linear but exponen- tial. Institut für Medizingerätetechnik 21 Chapter 2. Theoretical Background Jan Liu (a) Helmholtz (b) Gouy-Chapman (c) Stern Figure 2.5: Double layer models. Adapted from [54], used under CC BY-SA 4.0. The thickness of the double layer λD (also referred to as Debye length) is given by: λD = √︄ ϵkBΘ NAe2∑︁ N q2 NcN , [λD] = m, (2.29) where NA is the Avogadro constant, kB is the Boltzmann constant, Θ is the abso- lute temperature, e is the elementary charge, qN is the charge of the N -th ion, and cN is its molar concentration [59]. In physiological electrolyte solutions, it is in the order of 0.1-10 nm, with smaller lengths associated with higher electrolyte concentrations [47]. The Gouy-Chapman model is inadequate for highly charged double layers. The Stern model, introduced in 1924, is a hybrid approach combining the concepts of Helmholtz and Gouy-Chapman (see Figure 2.5c). It takes into account the finite size of ions and their binding properties at the surface. According to Stern, the double layer can be divided into an inner layer (the Stern layer) as proposed by Helmholtz and an outer diffuse layer (the Gouy layer) according to the Gouy- Chapman model. However, the Stern model also has limitations because it considers ions as point charges and makes assumptions such as all double-layer interactions being coulombic [17, 47]. A further division of the Stern layer into an inner Helmholtz layer and an outer Helmholtz layer is proposed by Grahame [60]. Regardless of the model, the extra potential drop due to electrode polarization results in an overestimation of the impedance attributed to the object under investigation during measurement. Additionally, the double layer acts as a capacitor, exhibiting a high reactance for low excitation frequencies and dominating the signal due to limited charge movement caused by diffusion processes. This complicates the interpretation of the measured impedance spectrum [55]. In most cases, electrode polarization is a 22 Institut für Medizingerätetechnik https://creativecommons.org/licenses/by-sa/4.0/ Jan Liu 2.4. Bioimpedance Measurements nuisance because it is only the tissue impedance that is of interest. Electrode polariza- tion impedance introduces errors in tissue impedance measurements [47]. The extent of polarization effects depends on factors such as the electrode surface (topography and chemistry) or the tissue properties, including the conductivity of the bulk material as well as the excitation parameters, such as the applied voltage level and the result- ing current density [55, 61]. There are several approaches to dealing with electrode polarization [62]: • Mathematical Compensation: By using equivalent circuit models, electrode polarization can be compensated for mathematically. A possible electric circuit representation of a double layer according to Stern is given by the lumped model shown in Figure 2.6. Further equivalent circuit representations can be found in Subsection 2.4.3. In this circuit diagram, the capacitance of the boundary layer CI acts in parallel with two resistive elements: the nearly Ohmic Nernst resis- tance RN and the Warburg impedance ZW. The Nernst impedance results from charge transfer at the boundary layer. The Warburg impedance describes the diffusion-induced limitation of ion mobility in the Gouy-Chapman layer. A resistor Rel represents the remaining resistance of the bulk electrolyte, which is independent of electrode behavior [59]. However, such models are highly diverse and may not fully represent reality. Rel RN ZW CI Figure 2.6: Electric circuit representation of a double layer according to Stern. Rel: resis- tance of the bulk electrolyte; CI: capacitance of the boundary layer; RN: Nernst resistance; ZW: Warburg impedance. • Reduction of Polarization Effects: Another approach is to adjust the hard- ware of the system to reduce the effects of electrode polarization. For example, large electrodes can be used to keep the thickness of the double layer in Eq. 2.29 Institut für Medizingerätetechnik 23 Chapter 2. Theoretical Background Jan Liu negligibly small compared to the dimensions of the electrodes. The distance between the electrodes can also be varied to increase the weight of the sample impedance compared to the electrode polarization. In addition, increasing the excitation frequency can help reduce parasitic effects. Tetrapolar electrode con- figurations (cf. Table 2.3) can also be used to ensure that the polarization of the CC electrodes does not affect the unpolarized PU electrodes [55, 59]. How- ever, bipolar configurations (cf. Table 2.3) are more commonly used in practice, not least because of the complexity associated with controlling tetrapolar mea- surements [59]. Furthermore, different degrees of polarization can be observed depending on the electrode material. For example, stainless steel is considered to be highly polarizable, while platinum and gold are less affected [47]. Therefore, in the context of bioimpedance measurements, the electrode material should be selected carefully to be less susceptible to polarization effects and to be biocom- patible (cf. Table 2.2) [47, 63]. • Acknowledging Polarization Effects: Another approach is to acknowledge the presence of polarization effects and account for them in subsequent data pro- cessing steps and applications, such as tissue classification. The total impedance, including tissue impedance and polarization effects, is therefore measured. For example, impedance spectra can be recorded for different tissue types, including polarization. To identify a tissue type, a newly acquired impedance spectrum is correlated with the previously acquired spectra. This approach eliminates the need for prior calibration or any polarization compensation [61]. ii) Electrode Configurations In the context of bioimpedance measurements, electrodes are used in varying numbers and geometries. The actual electrode configuration for a measurement is not deter- mined by the total number of electrodes in the setup, but rather by the number of electrodes involved in excitation and sensing at a given time as well as their spatial arrangement. For example, in EIT, setups can include up to 256 electrodes, with one electrode pair used as CC electrodes and one electrode pair used as PU electrodes at a given time [64–67]. In other electrical impedance sensing modalities, commonly used con- figurations include one dominant and one neutral electrode, two equivalent electrodes, 24 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements three electrodes, four electrodes, and five electrodes, as shown in Figure 2.7. The Latin and Greek terms describing electrode configurations are often used interchangeably in literature. An overview of the terms is given in Table 2.3 [47]. Table 2.3: Differentiation between the number of electrodes (adapted from [47]). Latin Greek Significance in impedance measurements Unipolar Monopolar One electrode dominant in a non-symmetrical system of two or more electrodes Bipolar Dipolar Two equivalent electrodes in a symmetrical system Tripolar Tripolar System of three electrodes Quadropolar Tetrapolar System of four electrodes ~ V 1 GND (a) Unipolar/Monopolar ~ 1 2 V (b) Bipolar/Dipolar ~ V 1 GND2 3 (c) Tripolar/Tripolar ~ 1 4 V 2 3 (d) Quadropolar/Tetrapolar Figure 2.7: Schematic representation of common electrode configurations in electrical imped- ance sensing. • Monopolar: (Quasi-)Monopolarity signifies that the outcome of the measure- ment is influenced primarily by one specific electrode while the remaining elec- trodes are considered neutral or indifferent [47]. The specific electrode, typically the smaller electrode, is referred to as the working electrode. When current is introduced, the current density increases particularly at the smaller electrode. As a result, there is an increased potential drop along the constricted current path near the small electrode, resulting in the small electrode having a predominant in- fluence on the overall results. The term neutral indicates that the current density at the surface of the electrode is negligibly small. These neutral CC electrodes are also referred to as indifferent, silent, passive, or dispersive electrodes. The Institut für Medizingerätetechnik 25 Chapter 2. Theoretical Background Jan Liu theoretical ideal of a neutral CC electrode is a giant spherical electrode placed infinitely far away and at zero potential. In practice, however, it can be difficult to achieve sufficiently large electrode areas with low current densities, and the neutral electrode can introduce unwanted effects. Note that this distinction does not apply to potentiometry, where the electrode area is not relevant when no current is flowing [47]. • Bipolar: In a bipolar configuration, the current is passed through two approx- imately equivalent CC electrodes and the voltage is measured across the same electrodes. Therefore, two approximately equivalent electrodes contribute to the measured impedance [47]. While this configuration is the simplest way to connect the device under test (DUT), it is accompanied by several sources of error in- cluding lead inductance, lead resistance, stray capacitance between two leads and contact resistance between the electrodes and the DUT, all of which contribute to the measured impedance [68]. • Tripolar: Tripolar systems are an extension of monopolar systems. In monopo- lar systems, it is challenging to determine the influence of the neutral electrode. Tripolar systems have an additional measuring electrode that is common for both current injection and voltage recording [47]. Consequently, the impedance of the neutral electrode is no longer taken into account. Instead, only the impedance of the additional electrode and the potential recording electrode (with no current flow and no polarization) are measured. Furthermore, quasi-tripolar systems have been reported. In these systems, an additional neutral electrode is introduced, which is responsible for the current return and serves as the reference potential. The voltage measurement is still performed using two PU electrodes positioned near the CC electrode [69]. • Tetrapolar: An approach to reduce the effects of electrode polarization imped- ance and increase measurement accuracy is to use a four-electrode system. This system consists of two distinct CC electrodes and two distinct PU electrodes. Us- ing this configuration, the signal can be transmitted from the CC electrode pair to the PU electrode pair, with the signal source being exogenous. This method ef- fectively minimizes the effects of lead and contact impedances because the signal current path and the voltage sensing leads remain independent [17, 47, 68, 70]. 26 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements iii) Cell Constants The expression A/l or its reciprocal appears frequently in various equations (cf. Eqs. 2.8, 2.23, 2.35, 2.45, 2.47 and 2.48), indicating that the impedance depends not only on the material but also on the geometric conditions. In the context of impedance measure- ments, this factor is referred to as the cell constant K, which represents the geometric portion of the impedance. However, it is only as simple as A/l for basic geometries. K is used to derive the intrinsic material properties from the measured impedance. In general, it must be determined by measuring the impedance of a solution with known material properties (K = Rσ) [47, 71, 72]. This eliminates geometric dependencies in the measurements and makes the measurement itself independent of the measurement setup used. The following applies [73]: K = G σ , [K] = 1 m , (2.30) where G is the conductance in S and σ is the conductivity of the medium in S/m. According to Eq. 2.28, the conductance G (as well as the susceptance B) can be calculated using the measured resistance R and the measured reactance X. 2.4.2 Electrical Properties of Tissues i) Conductivity and Permittivity For the electrical characterization of tissue, two material parameters are of great im- portance: electrical conductivity and permittivity. • Conductivity: The conductivity of a material depends on the number and density of free charge carriers. These can be the valence electrons of the atoms, as found in metals, as well as ions or delocalized electrons in organic molecules. In metals, the valence electrons form a cloud that can be moved by an external electric field. However, according to the Drude model, this motion or acceler- ation is not unhindered, as Eq. 2.1 might suggest. Instead, the electrons collide with the atoms of the material and move chaotically due to their temperature, resulting in a slowdown [74]. The superposition of all prevailing forces leads to Institut für Medizingerätetechnik 27 Chapter 2. Theoretical Background Jan Liu an acceleration in the direction of the force F⃗ , according to the second law of motion, where me is the mass of the electron [75]. Since the direction of motion is known, this acceleration can be expressed in scalar form with F = ⃓⃓⃓ F⃗ ⃓⃓⃓ and E = ⃓⃓⃓ E⃗ ⃓⃓⃓ using the corresponding equation of motion as ae = F me = eE me . (2.31) This acceleration is associated with a drift velocity of the electrons, which is related to the collision period τc: vDrift = aeτc = eE me τc. (2.32) The collision period τc is defined as the average time interval between two suc- cessive collisions of electrons in a conductor when current flows through it. In a conductor with a constant cross-section A and length l, subjected to a homo- geneous electric field, the current – as mentioned in Eq. 2.4 – is the number of electrons passing through this cross-section in a given time t, resulting from the applied voltage V = El. The number of electrons per unit volume, ne (electron density), moved from one end of the potential difference to the other during this time period, forms the total charge Q responsible for the current: Q = eneAvDriftt. (2.33) According to Eq. 2.4, differentiating with respect to time gives: I = dQ dt = eneAvDrift = τc me e2neAE = τc me e2ne A l V (2.34) or G = 1 R = I V = τc me e2ne A l . (2.35) Thus, an alternative description of Eq. 2.8 is derived [51]. A coefficient com- 28 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements parison with this equation shows that electrical conductivity σ in metals can be expressed as: σ = τce 2ne me . (2.36) In an electrolyte, the application of a voltage does not result in an electric current (flow of electrons) but in an ionic current. All cations and anions present con- tribute to the conductivity of the solution or solid electrolyte. Ionic conductivity is therefore not specific to a given substance [76]. The number of charge carriers is expressed by the molar concentration c. To describe the electrical conductiv- ity independently of the concentration, a new quantity is introduced, the molar conductivity Λm [77]: Λm = σ c , [Λm] = Sm2 mol . (2.37) The molar conductivity of an electrolyte depends primarily on the type of ions involved and the concentration of the ions. This relationship was studied by Kohlrausch and is known as the square root law of Kohlrausch (2nd Kohl- rausch law) [77]: Λm = Λ0 m − K1 √ c. (2.38) Here, Λ0 m is the limiting molar conductivity. This is the molar conductivity of a substance at infinite dilution. The second term describes the interactions between ions at higher concentrations. K1 is the Kohlrausch correction constant. The molar limiting conductivity, Λ0 m, depends on the limiting conductivities of the ions involved [77]: Λ0 m = ν+λ+ + ν−λ−. (2.39) This relationship is called the law of independent migration of ions. The coeffi- cients ν+ and ν− represent the stoichiometric numbers of the dissociation reaction of the involved ions, while λ+ and λ− denote their limiting molar conductivities. Institut für Medizingerätetechnik 29 Chapter 2. Theoretical Background Jan Liu These are directly related to the experimentally accessible ionic mobilities u+ and u−: λ+ = z+ · u+ · F; λ− = z− · u− · F. (2.40) where F is the Faraday constant and z+ and z− are the charge numbers of the cations and anions, respectively. Substituting Eq. 2.40 into Eq. 2.39 yields Λ0 m = (z+ν+u+ + z−ν−u−)F. (2.41) This quantity is used to calculate the electrical conductivity σ in electrolytes: σ = Λm · c ≈ Λ0 m · c = ∑︂ N zNνNuNcNF. (2.42) The summation is over all ionic components and takes into account individual charge numbers, stoichiometric numbers, mobilities and concentrations. In this approximation, the Kohlrausch correction is neglected. Therefore, the calcu- lation method is only applicable to electrolytes with high dilution [47, 77]. In general, electrical conductivity is dependent on temperature. The nature of this dependence is influenced by the structure and properties of the material, as well as the dominant mechanisms governing the transport of electrical charges. In metals, conductivity decreases with increasing temperature due to increas- ing lattice vibrations that impede the flow of electrons. For small temperature changes, a linear approximation for the resistivity, ρ = 1 σ , can be expressed as: ρ(Θ) = ρ0[1 + α0(Θ − Θ0)], (2.43) where α0 is the temperature coefficient of resistivity at reference temperature Θ0, and ρ0 is the resistivity at reference temperature Θ0 [78]. In electrolytes, the mobility of charge carriers increases with temperature, lead- ing to an increase in conductivity. The temperature dependence of the ionic 30 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements conductivity in an amorphous phase below the glass transition temperature can be described by an Arrhenius expression: σ(Θ) = σ0e −Ea RΘ . (2.44) Here, the pre-exponential factor σ0 is approximately constant, Ea is the activation energy, R is the gas constant, and Θ is the absolute temperature in K [79]. • Permittivity: The permittivity of a material describes its ability to be polarized by an E-field. It can be determined using a parallel plate capacitor setup. When a voltage V is applied to the capacitor in vacuum, a certain amount of charge Q is established on the capacitor plates after some time, with one plate being positively charged and the other negatively charged. This creates an E-field E⃗vak within the capacitor. According to Eq. 2.22, the capacitance of the capacitor is the ratio of the charge to the applied voltage. When a dielectric material is inserted between the capacitor plates, it can be observed that the capacitance of the capacitor increases [80]. This suggests that the dielectric material has an effect on the capacitance. The electric field between the capacitor plates causes atomic dipoles to form in the dielectric material or causes existing dipoles to align with their poles opposite to the charges on the plates. This leads to polarization of the entire material, which in turn generates a counter E-field that superimposes and weakens the existing E-field, resulting in a new E-field, E⃗diel [48]. As a result, the voltage across the capacitor decreases, leading to an increase in capacitance. The ratio between the capacitance with the dielectric material, Cdiel, and the capacitance in vacuum, Cvac = ϵ0A l (2.45) gives the relative permittivity ϵr = Cdiel Cvac . (2.46) When a material contains both dipoles and free charges, a complex notation is required for its electrical description [81]. When a partially conducting dielectric Institut für Medizingerätetechnik 31 Chapter 2. Theoretical Background Jan Liu material is subject to a sinusoidal voltage V (with dV dt = jwV ), the total current is the combination of the resistive and capacitive components, expressed as: I = IR + IC = V R + C dV dt = V A l (σ + jωϵ0ϵr) . (2.47) So the admittance is: Y = G + jωC = A l (σ + jωϵ0ϵr) . (2.48) The so-called complex conductivity is defined as: σ = σ + jωϵ0ϵr. (2.49) Alternatively, Eq. 2.47 can be written as: I = jωϵ0A d (ϵr − jσ ωϵ0 )V . (2.50) Anologously, the complex permittivity can be defined, given by: ϵ = ϵr − jσ ωϵ0 = ϵ′ r − jϵ′′ r , (2.51) in which ϵ′ = ϵr and ϵ′′ = σ ωϵ0 . Eqs. 2.49 and 2.51 provide equivalent descriptions of the material. The complex permittivity is generally preferred, where the imag- inary component includes the conventional conductivity and the real component represents the relative permittivity [81, 82]. Complex conductivity and complex permittivity are related by: σ = jωϵ. (2.52) ii) Dispersion For the majority of materials, σ and ϵr are not constant. They vary with the frequency of the applied signal [82]. The parameter’s frequency dependence in the context of bioimpedance measurement is called dispersion. In biological tissues, different disper- sions are observed over a wide range of frequencies [82]. Dispersion occurs because the dipoles in the material have a certain inertia. In the sinusoidal alternating field, the 32 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements dipoles realign with each half excitation period. At low frequencies, the dipoles can still follow the alternating excitation, resulting in a maximum ϵr. At high frequencies, the random orientation of the dipoles is maintained and ϵr approaches unity. This re- sponsive behavior of the dipoles, which adjusts to the new state within a certain time, is mathematically described by the relaxation time τr and the relaxation frequency ωr = 1/τr [81]. Figure 2.8 illustrates the frequency-dependent change in complex per- mittivity due to dispersion. The relative permittivity, in general, decreases in three main steps, leading to the distinction of α-, β- and γ-dispersion, while other dispersions may exist for additional frequencies [83]. The α-dispersion occurs in the low frequency range (below about 10 kHz) and is attributed to ionic diffusion at the cell membrane. The β-dispersion occurs in the MHz range and is caused by capacitive charging of cel- lular membranes, and dipolar relaxation effects of proteins. The γ-dispersion occurs in the GHz range and is caused by the polarization of water molecules [81, 83]. Hz kHz MHz GHz α β γ σ εr f Figure 2.8: Qualitative representation of the dispersions of conductivity and relative permit- tivity of biological tissue. Various authors have compiled electrical tissue data in numerous review articles and book chapters, including notable contributions by Schwan and Kay (1957) [84], Schwan (1963) [85], Geddes and Baker (1967) [86], Foster and Schwan (1986) [87], Stuchly and Stuchly (1990) [88], Duck (1990) [89], and Holder (2005) [90]. Gabriel et al. conducted a literature review and contributed with own measurements in a frequency range from 10 Hz to 20 GHz [91, 92]. The database by Gabriel et al., together with the measurement data of Peyman et al., has been compiled into a comprehensive common database by the Foundation for Research on Information Technologies in Society (IT’IS), which serves as the basis for many bioimpedance-based investigations [93–95]. It is hereinafter referred to as the IT’IS database. Miklavcic Institut für Medizingerätetechnik 33 Chapter 2. Theoretical Background Jan Liu undertook a comprehensive review of tabulated data, an excerpt of which is presented in Table 2.4 [82]. In addition, values provided by Gabriel et al./IT’IS complement this table. Table 2.4: Comparison of reported conductivity values in S/m. Miklavcic et al. [82] Gabriel et al./IT’IS [92, 95] Frequency DC 10 Hz 100 kHz Skin, dry (human) 0.00002 0.0002 0.000451 Skin, lower-lying layers 0.227 - - Stratum corneum 0.0000125 - - Subcutis (fat) 0.02-0.04 0.0377 0.0434 Blood 0.43-0.7 0.7 0.703 The electrical properties of the skin are dominated by the outermost cell layer, the highly insulating stratum corneum, which is a layer of the epidermis. According to Miklavcic et al., the conductivity of the stratum corneum is highly frequency de- pendent, ranging from 1.25 · 10−5 S/m at direct current (DC) to 2 · 10−2 S/m at 800 kHz [82]. They also reported a DC conductivity for all layers below the stratum corneum (lower-lying layers) as 0.227 S/m [82]. The veins for venipuncture are usu- ally located in the subcutis (see Section 2.2). Since this layer is predominantly fat, conductivity values for fat tissue can also be used approximatively. In contrast to the different layers of skin, blood contains better conductive properties due to electrically charged molecules, which induce an averaged conductivity of approximately 7·10−1 S/m (cf. Table 2.4) [47, 92, 95]. 2.4.3 Equivalent Circuits Electrical impedance spectroscopy (EIS) is used to record the frequency-dependent ma- terial parameters by excitation over a frequency spectrum. The acquired data can then be used for impedance-based applications. Ideally, the data should reveal a functional relationship between the applied frequency and the resulting material properties. To achieve this, the underlying model must be properly selected. Electrical modeling of biological tissue is accomplished using equivalent circuit diagrams [96]. The simplest way to model a resulting impedance with resistive and capacitive com- ponents is to use a two-component model, as shown in Figure 2.9. In Figure 2.9a, the capacitor is connected in parallel with the Ohmic resistance, although it can also be modeled in series (see Figure 2.9b). These two models are important because any other model can be reduced to them within a certain frequency range. 34 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements G CP (a) Parallel 1R-1C. R CS (b) Serial 1R-1C. Figure 2.9: Two-component equivalent circuits. R: resistance; G: conductance, Cp, Cs: par- allel/series capacitance. Equivalent circuit models, in general, do not cover the entire frequency spectrum. Eq. 2.48 already shows that the admittance diverges at high frequencies. The imped- ance of the two-component model in series connection is calculated as Z = R − j ωCs . (2.53) Here, the impedance converges at high frequencies but diverges at DC. Both models are therefore not suitable or too simplistic to fully describe the observed tissue, as these divergences do not occur. The parallel and series two-component models are complementary, converging in each other’s divergent frequency range. The so-called constant phase element (CPE) provides a solution to this problem. It is modeled so that the resistive and capacitive components have a constant phase angle with respect to each other (︂ R C = constant )︂ . Another alternative extension, known as the three-component model, also deals with this problem by combining the characteristics of both series and parallel equivalent cir- cuits. In essence, there are four equivalent circuits, labeled 2R-1C or 1R-2C, according to the number of components. They are best described in parallel by admittance and in series by impedance. The 1R-2C configurations limit the current at both low and high frequencies, while the 2R-1C configurations allow these frequencies as well. The equiv- alent circuit diagrams used in Figure 2.10 are suitable for modeling different materials. While the circuit in Figure 2.10a is used for living tissue, where R and G represent the cell interior and Cs represents the cell membrane, the circuit in Figure 2.10b is used to model skin, where R represents the deep tissue layers and G and R represent the Institut für Medizingerätetechnik 35 Chapter 2. Theoretical Background Jan Liu skin itself. The circuits in Figures 2.10c and 2.10d are used to model simple dipole relaxations that occur during tissue polarization, resulting in the Debye equation. G R CS (a) Parallel 2R-1C. G CP R (b) Serial 2R-1C. CP R CS (c) Parallel 1R-2C. G CP CS (d) Serial 1R-2C. Figure 2.10: Three component equivalent circuits. R: resistance; G: conductance, Cp, Cs: par- allel/series capacitance. Debye modeled dipoles as spherical particles with macroscopic viscosity, based on gases and solutions of polar liquids. However, the Debye equation, ϵ(ω) = ϵ∞ + ϵs − ϵ∞ 1 + jωτr = ϵ∞ + ∆ϵ 1 + jωτr , (2.54) where ϵ∞ and ϵs represent the permittivities at very high and very low frequencies, respectively, and τr represents the relaxation time of the dipoles, cannot fully describe the dispersions, as shown in Figure 2.8 [97]. An alternative description was introduced by Cole and Cole, which is based on empirical data and provides a better description of the dispersions [98]: ϵ(ω) = ϵ∞ + ϵs − ϵ∞ (1 + jωτr)1−α with 0 ≤ α ≤ 1. (2.55) The Alpha parameter α (also referred to as Cole exponent), is the coefficient of re- laxation. The Cole model effectively captures the broad spectrum of relaxation ob- served in materials with high dipole concentrations. The difference between Debye and Cole can be reflected in their corresponding equivalent circuit models. Debye uses frequency independent components, while Cole uses a CPE in conjunction with frequency dependent parameters [99]. 36 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements Both the Debye equation and the Cole-Cole equation serve as a basis for further modeling of different types of tissues. For example, Hurt extended the Debye equa- tion to model the dielectric spectrum of muscle by adding five additional Debye terms and a conductivity term, where σi is the ionic conductivity [83, 100]: ϵ(ω) = ϵ∞ + 5∑︂ N=1 ∆ϵN (1 + jωτrN) + σi 1 + jωϵ0 . (2.56) Gabriel et al. formulated a similar approach using an arbitrary number of Cole- Cole terms to fit material parameter functions based on empirical data: ϵ(ω) = ϵ∞ + ∑︂ N ∆ϵN (1 + jωτrN)1−αN + σi 1 + jωϵ0 , (2.57) Note that these functions are only valid for the frequency spectrum in which the data are recorded. 2.4.4 Transfer Impedance and Spatial Sensitivity The transmission of an excitation signal depends on the geometry. Therefore, certain electrical characteristics in the context of bioimpedance measurements can only be de- rived from the geometrical configuration [47]. To understand this, two concepts are introduced: the concept of duality between dielectric and conductive materials, and the concept of reciprocity. The concept of duality states that, assuming linear behav- ior, complex conductivity and complex permittivity contain the same information and are considered dual parameters (cf. Eqs. 2.49, 2.51 and 2.52). Other dual parame- ters include D⃗ ⇔ J⃗ and q ⇔ I. The concept of reciprocity was first described by Helmholtz [101]. It states that the connections of excitation and measurement can be interchanged and the same signal is still measured (see Figure 2.11) [102]. In the context of these two concepts, the basic model of electrical signal transmission consists of a CC dipole with the dipole length l⃗CC (center-to-center distance) and the corresponding dipole moment m⃗: m⃗ = Il⃗CC, [m⃗] = Am. (2.58) Institut für Medizingerätetechnik 37 Chapter 2. Theoretical Background Jan Liu Excitation i v Signal transfer v Signal transfer Excitation i PU PU CC CC CC CC PU PU Tissue Tissue Figure 2.11: Principle of reciprocity in a tetrapolar configuration. CC dipole refers to a current injecting electrode pair using two equal electrodes (bipo- lar/dipolar, cf. Table 2.3). In the presence of two such dipoles (a CC dipole with dipole length l⃗CC and a PU dipole with dipole length l⃗PU) separated by a distance l, the PU dipole can sense a potential difference and thus measure a voltage (a signal) v = (︃ Iρ 4πl3 )︃ l⃗CCl⃗PU = H⃗m⃗, (2.59) where H⃗ is the lead vector indicating the direction of signal transfer and the transfer factor between the two dipoles: H⃗ = (︃ ρ 4πl3 )︃ l⃗PU. (2.60) The ratio of the signal to the current gives the transfer impedance, which is the actual measured impedance: Ztr = (︃ ρ 4πl3 )︃ l⃗CCl⃗PU = H⃗l⃗CC. (2.61) These and similar analytical solutions are only valid in ideal volumes. Ideal here means that the volume has infinite size and linear isotropic electrical properties [47]. 38 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements For a volume that deviates from this ideal, the concept of reciprocal excitation is used, introduced by McFee and Johnston in 1953 [103]. In this electrode configuration, the PU electrodes are used as CC electrodes and are excited with a current amplitude of 1 A (unit current). This results in a current density vector field normalized to the unit current, called the reciprocal lead field: J⃗ ′ reci = J⃗reci 1 A , [︂ J⃗ ′ reci ]︂ = 1 m2 . (2.62) The measured signal voltage is obtained from the current density resulting from the CC excitation and the reciprocal lead field of the entire volume: v = ∫︂∫︂∫︂ ρJ⃗CC · J⃗ ′ recidV. (2.63) This equation is called the general signal transfer equation. However, to determine the signal, the reciprocal excitation does not have to be excited with a unit current. Any current Ireci can be used, whereby the general signal transfer equation can be expressed as: v = I−1 reci ∫︂∫︂∫︂ ρJ⃗CC · J⃗recidV. (2.64) Thus, the lead field is given by: J⃗ ′ = J⃗ Ireci . (2.65) Dividing Eq. 2.64 by the excitation current gives the general transfer impedance equa- tion: Ztr = ∫︂∫︂∫︂ ρJ⃗ ′ CC · J⃗ ′ recidV. (2.66) The determination of transfer impedance using reciprocal excitation was proposed by Geselowitz [104]. Instead of current densities, he describes the conductivity fields in terms of the electric fields generated by the excitation. Both quantities can be Institut für Medizingerätetechnik 39 Chapter 2. Theoretical Background Jan Liu converted into each other in the isotropic case using Ohm’s law (cf. Eq. 2.6) [102]. The contribution of each infinitesimal volume element to the transfer impedance is given by ρJ⃗ ′ CC · J⃗ ′ reci. While ρ represents the material-dependent component of this impedance, the spatial sensitivity distribution S = J⃗ ′ CC · J⃗ ′ reci, [S] = 1 m4 , (2.67) is defined as the geometric component of the transfer impedance. It serves as a measure of the spatial resolution of a particular electrode setup. Multiplying this field by the local resistivity ρ gives the impedance contribution or impedance volume density for each voxel (cf. Eq. 2.66). Vice versa, the impedance contribution from a particular sub- volume can be determined by integrating over that particular volume using Eq. 2.66. Since the sensitivity can take positive, negative, and zero values, it is possible for the measured impedance of some electrode setups to be zero (see Figure 2.12) [47]. v PU PU CC CC i Ԧ𝐽CC ′Ԧ𝐽reci ′ Figure 2.12: Tetrapolar electrode configuration with respective lead fields. However, this does not mean that the measured tissue is particularly conductive, but rather that there is no signal transfer between the CC and PU electrodes. In the monopolar and bipolar case, J⃗ ′ CC = J⃗ ′ reci = J⃗ ′ holds, and therefore S = ⃓⃓⃓ J⃗ ′ ⃓⃓⃓2 [47, 102, 104]. In a two-electrode setup, a potential plot is a straight-forward way to visualize the sensitivity field. Once the current density and impedance volume density are known for each voxel, the potential drop caused by a voxel (or the cumulative effect of all voxels in a volume) can be calculated. Consequently, the ratio of the potential drop between two equipotential lines to the total potential gives the ratio of the impedance contribution for that subvolume to the total impedance [105]. 40 Institut für Medizingerätetechnik Jan Liu 2.4. Bioimpedance Measurements 2.4.5 Impedance Measurement Methods In general, the electrical behavior of a DUT is unknown. It can be considered a black box with a general impedance [47]. By measuring the general impedance, the DUT can be characterized and material parameters can be determined. For impedance measurements, the current, voltage, and phase relationship between them is essential (cf. Eq. 2.15). Various circuits and devices are available to measure these quantities. In general, impedance measurement devices stimulate the DUT with a constant amplitude (current or voltage) and measure the corresponding voltage or current response, as well as the phase shift, to calculate the polar coordinate representation of the impedance with Z = |Z| and φ, or the Cartesian coordinate representation with R and X. Depending on the author and reference manual, different methods are distinguished, such as the current/voltage method, the resonance method, the bridge method, and the network analysis method [68, 106–108]: • Current/Voltage Method: In the current/voltage method, also known as the direct method, the DUT of unknown impedance Z is connected to a circuit where it is stimulated with an AC voltage V and the resulting current is measured. This circuit includes a well-defined resistor R, a current meter, and a voltage meter (Figure 2.13a). In a more practical implementation, two voltage meters are used instead (Figure 2.13b). The unknown impedance can be determined using [106]: Z = (︄ V 1 V 2 − V 1 )︄ R. (2.68) This type of measurement is divided into a regular current/voltage method and a high-frequency/radio frequency (HF/RF) method using a coaxial cable [68]. R V A Z I V V1 (a) Measurement principle. R VZV V1V V2 (b) Measurement with two voltmeters. Figure 2.13: Current/voltage impedance measurement method. V : excitation voltage; V 1, V 2: measured voltages; Z: unknown impedance. Institut für Medizingerätetechnik 41 Chapter 2. Theoretical Background Jan Liu • Resonant Method: The resonant method determines the unknown impedance in two steps. In the first step, the excitation frequency of the circuit is varied according to Figure 2.14 until the resonant frequency fr = 1 2π √ LC (2.69) is reached to determine the reactive component. This step requires prior knowl- edge of L or C. If this is the case, the other quantity can be calculated from Eq.