UNIVERSITY OF MORATUWA
AN ELECTRICAL PARAMETRIC MODEL OF
HUMAN SKIN AND BLOOD GLUCOSE
SPECTROSCOPY
By
Thumeera Ruwansiri Wanasinghe
This thesis is submitted to the Department of Electronic &
Telecommunication Engineering
of the University of Moratuwa
in partial fulfillment of the requirements for
the degree of Master of Science in Full Time Research.
University of Moratuwa, Sri Lanka
July, 2011
DECLARATION
I declare that this is my own work and this thesis does not incorporate without
acknowledgement any material previously submitted for a Degree or Diploma in
any University or institute of higher learning and to the best of my knowledge
and belief. Furthermore, it does not contain any material previously published or
written or orally communicated by another person except where the acknowledge-
ment is made in the text and due reference is made in the text or in the figure
captions or in the table captions.
Also I here grant to University of Moratuwa the non-exclusive right right to
reproduce and distribute my thesis, in whole or in part in print, electronic or other
medium. I retain the right to use this content in whole or part in future works.
Thumeera R. Wansinghe
The above candidate has carried out research for the Masters thesis under my
supervision and to the best of our knowledge the above particulars are true and
accurate.
Dr. E. C. Kulasekere
Research Supervisor,
Head of the Department,
Electronic and Telecommunication Engineering.
i
To my parents, family, teachers and friends for giving me constant support and
motivating me.
ii
ACKNOWLEDGMENT
First and foremost, I extend my gratitude to my supervisor, Dr. E.C. Ku-
lasekere for supporting me throughout the project and providing valuable sugges-
tions. In addition I wish to also express my gratitude for guiding me on the correct
path and also inspiring me to do better research.
Secondly, I thank Dr.Ranga Rodrigo, director of Zone24x7 Advanced Elec-
tronic Research Laboratory at University of Moratuwa for providing facilities and
support where necessary. I also thank Dr. S. Gamwarige and Zone24x7 Inc. for
providing me laboratory facilities and also providing me the best possible environ-
ment to carry out my research.
My profound thanks go to Prof. I. J. Dayawansa, Dr. A. A. Pasqual , Dr.
N. W. N Dayananda, Dr. S. R. Munasinghe and Eng. A. T. L. K. Samarasinghe
who are lecturers of the Electronics department of the University of Moratuwa for
supporting me to carry out experiments and giving valuable feedbacks.
Mr. K. Jayawardana and Mr. D. N. De Silva of Arther C Clarke Institution
for Modern Technology helped me by granting access to their laboratory facilities
and guiding me in high frequency sensor design. Dr. M. Jayasooriya, Ms T.
Fernando and Ms. Laksha of National Diabetes Centre, Sri Lanka helped me to
find volunteers for clinical experiments and obtain a data set to compare clinical
glucose reading with measured impedance value. I thank all of them and people
who volunteered for blood glucose tests at National Diabetes Center, Sri Lanka.
Finally, I thank all the individuals and organizations who are not mentioned
above and have given any kind of direct or indirect help to accomplish my research
goals.
iii
ABSTRACT
An Electrical Parametric Model of Human Skin and Blood
Glucose Spectroscopy
by
Thumeera Ruwansiri Wanasinghe
Submitted to the Department of Electronic and Telecommunication Engineering,
in partial fulfillment of the requirements for the degree of
Master of Science in Engineering
Index Term: Skin impedance model, non-invasive blood glucose measure-
ment, dielectric spectroscopy, compact annular ring slot antenna
Diabetes is well known as a leading cause of death all around the world. Mainly,
invasive methods are used for blood glucose monitoring in the current context.
The monitoring is done either as an inpatient procedures or using home based
measuring devices. Invasive or minimally invasive methods make it difficult when
it comes to frequent measurements required by diabetes patients. It also has other
issues such as the associated pain, phobia, and the spread of diseases like AIDS.
These issues are heightened in the case of home based monitoring devices. As
a result many researchers have attempted to introduce non-invasive measuring
techniques for home based glucose monitoring devices. However none of then have
met the accuracy requirements for medical use.
Dielectric spectroscopy (DS) is one such methods which has been proposed
for non-invasive glycaemia monitoring. In DS, the variation of skin impedance
has been used to derive an index representing blood glucose fluctuation. As a re-
sult of the lack of knowledge of the impedance characteristics of the skin and the
tissue underneath, and its relation to the level of blood glucose, the consistency
and accuracy of the measurements are questionable. The ensuing research pro-
poses a theoretical framework for skin impedance variations with the blood glucose
level and also provides experimental verification of the same. This research also
iv
proposes an electrical parametric (impedance) model for human skin and blood
glucose spectroscopy which consists of human skin, electrode-electrolyte interface
and coupling capacitance between transmitter and receiver. Such a mathematical
model of the physiological system will enable us to further analyze the relationship
the physiological parameters have with the fluctuation of the blood glucose levels
for different individuals.
Moreover, the thesis analyzes the influence from bio-sensor to sensitivity mea-
surements and proposes a concentric annular ring slot antenna (CARSA) as a
possible sensor for non-invasive blood glucose measurement via DS. Compared
to early research of Cadaff et al. [1], CARSA showed a 13 fold increment of the
measurement sensitivity. Further, it could be seen that, this sensitivity increment
was 40 fold when the effective length of CARSA decreases from 10 cm to 6.5 cm.
The thesis further highlights the importance of careful design of this sensor and
proposes a rigorous mathematical model of its derivation.
v
CONTENTS
Declaration of the Candidate and Supervisor i
Dedication ii
Acknowledgement iii
Abstract iv
Table of Content vi
List of Figures ix
List of Tables xiii
Abbreviations xv
Notations xvi
1 Motivation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Significance of the Study . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Background 4
2.1 Skin Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Epidermis Layer . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Dermis Layer . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Subcutaneous Tissues . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Blood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Blood Composition . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Blood Content of Skin and Layered Architecture of Skin . . 6
vi
2.3 Diabetes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Measurement Technique . . . . . . . . . . . . . . . . . . . . 9
2.4 Dielectric Property of Body Tissues . . . . . . . . . . . . . . . . . . 12
2.4.1 Dielectric Spectroscopy . . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Frequency Dispersion of Biological Tissues . . . . . . . . . . 13
2.4.3 Parametric Modeling of Dielectric Spectrum of a Tissue . . . 14
2.4.4 Simulation Results of Dielectric Property . . . . . . . . . . . 16
2.5 Skin Impedance Models . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.1 Basic R-RC Model . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.2 R-RC-RC Model . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.3 Nonlinear Skin Impedance Model . . . . . . . . . . . . . . . 25
2.5.4 Two Current Path Model . . . . . . . . . . . . . . . . . . . 27
2.5.5 Cole-Cole Impedance Model . . . . . . . . . . . . . . . . . . 27
2.5.6 Non-Cole-Cole Impedance Model . . . . . . . . . . . . . . . 29
2.6 Effect From Electrode-Electrolyte Interface . . . . . . . . . . . . . . 30
2.7 AC Impedance and Non linearity of Skin Impedance . . . . . . . . . 31
3 System Identification 33
3.1 Selection of Frequency Band . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Selection of the Stimulation Signal . . . . . . . . . . . . . . . . . . 34
3.3 Factors That Influence Skin Impedance . . . . . . . . . . . . . . . . 34
3.3.1 Sensor Design . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.2 Measurement Environment . . . . . . . . . . . . . . . . . . . 39
3.3.3 Temperature Variation and Skin Impedance . . . . . . . . . 40
3.3.4 Body Movements and Skin Impedance . . . . . . . . . . . . 40
3.3.5 Force on a Sensor and Skin Impedance . . . . . . . . . . . . 41
3.4 Transfer function of Skin . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4.1 Measurement Environment . . . . . . . . . . . . . . . . . . . 43
3.4.2 Transfer Function from S-Parameters . . . . . . . . . . . . . 44
4 Skin Impedance and Blood Glucose Level 48
4.1 Soda Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
vii
4.1.1 Analysis of Stage 1 of Experiment . . . . . . . . . . . . . . . 49
4.1.2 Analysis of Stage 2 of the Experiment . . . . . . . . . . . . 53
4.2 Sensor Geometry and Measurement Sensitivity . . . . . . . . . . . . 54
4.2.1 Analysis of Stage 1 of Experiment . . . . . . . . . . . . . . . 55
4.2.2 Analysis of Stage 2 of Experiment . . . . . . . . . . . . . . . 56
5 Modeling of Skin Impedance 60
5.1 Modeling of Measurement Environment . . . . . . . . . . . . . . . . 60
5.1.1 Co-axial Probe and MMCX Connectors . . . . . . . . . . . . 60
5.1.2 Annular Ring and Microstrip Transmission Line . . . . . . . 61
5.1.3 Air Gap Capacitance . . . . . . . . . . . . . . . . . . . . . . 62
5.1.4 CARSA Sensor . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.5 Measurement and Simulation . . . . . . . . . . . . . . . . . 65
5.2 Cell Membrane and Ionic Conduction . . . . . . . . . . . . . . . . . 66
5.2.1 Intracellular and Extracellular Medium . . . . . . . . . . . . 69
5.3 Mathematical Model for Composite System . . . . . . . . . . . . . 70
5.3.1 Measurement and Simulation . . . . . . . . . . . . . . . . . 72
5.3.2 Blood Glucose Variation and Skin Impedance: Simulation . 74
5.4 Mathematical Model for Human Skin and Blood Glucose Spec-
troscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 Degenerative Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5.1 Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5.2 Mode 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5.3 Mode 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.5.4 Mode 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.5.5 Mode 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.5.6 Mode 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.5.7 Mode 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6 Summary, Conclusions and Recommendations 83
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
viii
6.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Reference List 87
ix
LIST OF FIGURES
2.1 Structure of skin [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Blood Component [3] . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Layered skin architecture proposed by Meglinski [4] . . . . . . . . . 7
2.4 Skin layered model given by Eric C. Green [5] . . . . . . . . . . . . 8
2.5 An idealized plot of the frequency variation of the relative permit-
tivity or a typical biological tissue [6] . . . . . . . . . . . . . . . . . 13
2.6 Permittivity and conductivity of tissues . . . . . . . . . . . . . . . . 18
2.6 Permittivity and conductivity of tissues . . . . . . . . . . . . . . . . 19
2.7 Basic skin impedance model . . . . . . . . . . . . . . . . . . . . . . 21
2.8 Applied voltage pulse [7] . . . . . . . . . . . . . . . . . . . . . . . . 21
2.9 Measured current waveform [7] . . . . . . . . . . . . . . . . . . . . . 22
2.10 R RC RC skin impedance model [7, 8] . . . . . . . . . . . . . . . . . 26
2.11 Skin impedance model with variable resister to represent nonlinear
skin behavior [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.12 More specific equivalent electrical scheme of an outermost layer of
skin, with two parallel pathways are shown. Rm and Cm refer to
lipid-corneocyte matrix, and Ra and Ca refer to appendages . . . . 28
2.13 Cole-Cole Impedance model . . . . . . . . . . . . . . . . . . . . . . 28
2.14 Non-Cole-Cole impedance model [10] . . . . . . . . . . . . . . . . . 30
2.15 Equivalent circuit for electrode-electrolyte interface . . . . . . . . . 31
2.16 Skin impedance model with parameter for electrode-electrolyte in-
terface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Sensor proposed by Cadaff et al. . . . . . . . . . . . . . . . . . . . . 35
3.2 Close-up of spiral micro strip with plastic thumb-guiding fixture. . . 36
x
3.3 Inner view of measuring cell . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Bio-sensor proposed by Rahman et al. [11] . . . . . . . . . . . . . . 37
3.5 Top view of CARSA bio-sensor proposed by Ruwansiri et al. [12] . . 37
3.6 Schematic drawing of CARSA . . . . . . . . . . . . . . . . . . . . . 38
3.7 Parallel gap coupled co-planer slot-line . . . . . . . . . . . . . . . . 38
3.8 Electric and Magnetic field line of CARSA . . . . . . . . . . . . . . 38
3.9 Block diagram of skin impedance measurement system . . . . . . . 39
3.10 Skin impedance variation with temperature . . . . . . . . . . . . . . 40
3.11 Skin impedance variation with hand movement . . . . . . . . . . . . 41
3.12 Skin impedance variation with force on a sensor . . . . . . . . . . . 41
3.13 Component used in experiment set up . . . . . . . . . . . . . . . . 43
3.14 A two-port network . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.15 Bode plot of skin (3.15) . . . . . . . . . . . . . . . . . . . . . . . . 47
3.16 Pole-Zero plot of skin (3.15) . . . . . . . . . . . . . . . . . . . . . . 47
4.1 Skin impedance variation with blood glucose level . . . . . . . . . . 49
4.2 Schematic representation of cell membrane . . . . . . . . . . . . . . 50
4.3 Schematic representation of lipid bi-layer . . . . . . . . . . . . . . . 50
4.4 Permittivity and conductivity of tissues . . . . . . . . . . . . . . . . 52
4.5 Variation of impedance of blood with glucose level . . . . . . . . . . 52
4.6 Impedance characteristics when sensor faced to air . . . . . . . . . . 53
4.7 Impedance and glucose level variation with time . . . . . . . . . . . 54
4.8 Electric and Magnetic Field line of CARSA . . . . . . . . . . . . . 55
4.9 Averaged impedance curve for six subjects at the FBS and OGTT . 57
4.10 Impedance difference between OGTT to FBS for typical subject. . . 58
4.11 Sensitivity comparison for three sensors. . . . . . . . . . . . . . . . 59
5.1 Equivalent circuit for co-axial probe and MMCX connector . . . . . 61
5.2 Equivalent circuit annular ring, microstrip line and co-axial to mi-
crostrip interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Side view of CARSA and electrical field distribution . . . . . . . . . 62
5.4 Gap-coupling capacitance of CARSA . . . . . . . . . . . . . . . . . 63
xi
5.5 Equivalent circuit for CARSA sensor . . . . . . . . . . . . . . . . . 64
5.6 Equivalent circuit for measurement environment . . . . . . . . . . . 65
5.7 Comparison of Simulated and measured impedance for measure-
ment environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.8 Ion channel and cell membrane . . . . . . . . . . . . . . . . . . . . 66
5.9 Mathematical model for cell membrane . . . . . . . . . . . . . . . . 69
5.10 Block diagram of composite system of skin, CARSA and co-axial
probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.11 Block diagram of composite system of skin, CARSA, co-axial probe
and electrode-electrolyte interface. . . . . . . . . . . . . . . . . . . . 70
5.12 Coupling capacitance through skin air and substrate . . . . . . . . . 71
5.13 Coplanar strip line on multi-layer dielectric substrate . . . . . . . . 71
5.14 Block diagram for composite system of measurement environment
and skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.15 Mathematical model for composite system of measurement environ-
ment and skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.16 Comparison of simulated and measured impedance for composite
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.17 Simulated of impedance for composite system at different blood
glucose level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.18 Impedance model for human skin and blood glucose spectroscopy . 75
5.19 Multi-layer, multi-path impedance model for human skin and blood
glucose spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.20 Comparison of measured impedance using three sensor under iden-
tical glucose level, temperature and force on a sensor . . . . . . . . 77
5.21 Bode-plot of proposed impedance model for skin impedance and
blood glucose spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 78
5.22 Degenerative mode-1 . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.23 Degenerative mode-2 . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.24 Degenerative mode-3 . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.25 Degenerative mode-4 . . . . . . . . . . . . . . . . . . . . . . . . . . 81
xii
5.26 Degenerative mode-5 . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.27 Degenerative mode-6 . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.28 Degenerative mode-7 . . . . . . . . . . . . . . . . . . . . . . . . . . 82
xiii
LIST OF TABLES
2.1 Volume fraction of blood and water in each skin layer presented in
Figure 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Parameters of equation (2.7) used to predict the dielectric proper-
ties of tissues in figure [13] . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Classification of skin impedance non-linearity [14] . . . . . . . . . . 32
4.1 Parameter for the Single-, Two- and Three-pole Cole-Cole Model [15] 51
4.2 Dimensions of Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 55
xiv
ABBREVIATIONS
Following abbreviations or acronyms have been used in this thesis.
Abbreviations/Acronyms Meaning
CARSA Concentric Annular Ring Slot Antenna
CPE Constant Phase Element
CVD Cardiac Vascular Disease
DC Direct Current
DS Dielectric Spectroscopy
EM Electromagnetic
FBS Fasting Blood Sugar
FNS Functional Neuromuscular Stimulation
IR Infrared
IS Impedance Spectroscopy
MIT Massachusetts Institute of Technology
MMCX Micro-Miniature Coaxial
MWS Microwave Studio
NA Network Analyzer
NIBGM Non-Invasive Blood Glucose Monitoring
NIDAQ National Instrument Data Acquisition
OGTT Oral Glucose Tolerance Test
PTFE Polytetrafluoroethylene
RF Radio Frequency
SC Stratum Corneum
TNC Threaded Neill-Concelman
VCO Voltage Controlled Oscillator
WHO World Health Organization
xv
NOMENCLATURE
Following symbols or notations have been used in this thesis.
Chapter 2
Ic Ionic conduction current
Id Displacement current
j
√−1
εˆ Complex relative permittivity
ε′ Real part of complex relative permittivity
ε′′ Imaginary part of complex relative permittivity
εr Dielectric constant (Relative permittivity)
ε Permittivity of the medium
ε◦ Permittivity of free space
σ Total ionic conductivity of the medium
ω Frequency in rad/s
τ Dispersion time constant
ε∞ Permittivity at ωτ  1
εs Permittivity at ωτ  1
∆ε Magnitude of the dispersion (εs − ε∞)
σ Static ionic conductivity of tissue
α Distribution Parameter (2.6); an exponent (2.19), (2.24)
Rs Ohmic resistor for basic R-RC skin model
Cp Polarization capacitance for basic R-RC skin model
Cp Parallel resistor to polarization capacitor for basic R-RC skin model
xvi
Chapter 2 con’t
Vpeak Peak voltage from Figure 2.8
Ipeak Peak current from Figure 2.9
Isteady state Steady-state current from Figure 2.9
A Cross sectional area of the conductor
R◦ Resistance at very low frequency
R∞ Resistance at very high frequency
ω Angular frequency (rad/s)
τz Characteristics time constant
Rm Resistance of lipid-corneocyte matrix
Cm Capacitance of lipid-corneocyte matrix
Ra Resistance of appendages current path
Ca Capacitance of appendages current path
ϕCPE Phase angle of CPE
CCPE Capacitance of CPE
∆G Conductance of CPE , R◦ −R∞ = 1/∆G
K Real proportionality factor for the CPE admittance
m exponent
Rpol Polarization resistance at the electrode-electrolyte interface
Cpol Polarization capacitance at the electrode-electrolyte interface
β exponent
xvii
Chapter 3
w1 CARSA inner ring width
w2 CARSA outer ring width
r Inner radial of inner ring of CARSA
s Gap between two rings of CARSA
εr Relative dielectric constant of substrate
Rref Resistance of reference resistor Figure 3.9
Vref Voltage just before the Rref Figure 3.9
Vsens Voltage just after the Rref Figure 3.9
ρ Resistivity of the tissue
` Thickness of the tissue layer
A Effective area under measurement
ε Permittivity of the tissue
ω Radial frequency (rad/s)
S11, S12, S21, S22 Full 2-port scattering parameters
A,B,C,D Full 2-port ABCD parameters
Zl Load impedance
Zs Source impedance
Z◦ Reference impedance
Z?s Complex conjugate of the source impedance
H(s) System transfer function
Chapter 4
OGTTimp OGTT impedance at a given frequency
FBSimp FBS impedance at the same frequency
Iaiv Average impedance shift
OGTTglu OGTT value from invasive method
FBSglu FBS value from invasive method
xviii
Chapter 5
ε Permittivity of the dielectric material
ε◦ Permittivity of the free space
εr Relative dielectric constant of the dielectric material
µ Permeability of the dielectric material
µ◦ Permeability of the free space
µr Relative Permeability of the dielectric material
D Inner diameter of the shield (co-axial cable)
d Outer diameter of the inner conductor (co-axial cable)
w1 CARSA inner ring width
w2 CARSA outer ring width
r Inner radial of inner ring of CARSA
s Gap between two rings of CARSA
Ccup air Coupling capacitance through air
Ccup substrate Coupling capacitance through substrate
h Thickness of the substrate
K(k) Elliptical integral of first kind
K(k′) Complementary elliptical integral of second kind
Cgap cup Gap couple capacitance
Z11 Driven point impedance
Z◦ Reference impedance
Rm Resistance of ionic channel
gn Conductance of the ionic channel
α, β, γ Constants
τϕ Activation time constant
τχ Inactivation time constant
ϕ◦ Initial value for activation
χ◦ Initial value for inactivation
ϕ∞ Steady state value for activation
χ∞ Steady state value for inactivation
xix
Chapter 5 con’t
σ, ω, ε◦, εˆ, ω,
A, d
As same as Chapter 2
d◦ The tissue layer thickness when the sensor is at the proximity
df The tissue layer thickness when F N force is applied on a skin (sensor)
F Force on a sensor
αf The force coefficient
βf The force exponent
Rm◦ The ionic channel resistance at zero temperature
Rmθ The ionic channel resistance at θ C
◦ temperature
θ Temperature
αt The temperature coefficient
βt The temperature exponent
Cm Capacitance of lipid bilayer
Ri Resistance of the intracellular medium
Re Resistance of the extracellular medium
V Applied voltage across anode and cathod
ICm Dielectric current through lipid bilayer capacitor
IRm Ohmic current through ionic channel
Ccup skin Coupling capacitance through skin
Ci(t, ω, c, f) Capacitance across the dielectric layer (tissue layer) of thickness hi
hi Thickness of the i
th tissue layer
(εri − εr(i+1)) Relative dielectric constant between ith and (i− 1)th tissue layers
xx