Bioimpedance & Bioelectricity

BASICS

CHAPTER 1

Introduction

• Bioimpedance or electrotheraphy : by applying electricity from an external source (exogenic current)– Immittance = Impedance + Admittance

– Bioimmittance : passive properties of tissue

• Bioelctricity : broad concept covering electric currents associated with the life processes and their biopotentials (endogenic).

• Electrical properties of tissue : characterized as a dielectric or an electrolytic biomaterial

Three topics about same things

• Electrolytic theory and electrochemistry form an important basis

• Information about electrochemical processes in the tissue– Characterizing the tissue

– Monitoring physiological changes

• New instruments and methods– EIT

– Body composition

– Cell micromotion

– Organ viability skin hydration

– Skin pathology

Bioimpedance Measurement

CHAPTER 2

Electrolytics2.1 Ionic and electronic dc conduction

2.1.1. Ionization

2.1.2. Molecular Bonds

2.2 The basic electrolytic experiments

2.3 Bulk electrolytic dc conductance

2.4 Interphase phenomena2.4.1. Faraday’s law

2.4.2 Migration and diffusion

2.4.3 The electric double layer, perpendicular fields

2.4.4. The electric double layer, lateral fields

2.4.5. The net charge of particle

2.4.6. Electrokinesis

2.5 Electrodics and ac phenomena

2.5.1. Electrode equilibrium dc potential, zero external current

2.5.2. The monopolar basic experiment

2.5.3. Dc/ac equivalent circuit for electrode processes

2.5.4. Non-linear properties of electrolytics.

• Electrolyte : a substance with ionic dc conductivity

• Living tissue = electrolytic conductor : both intra- & extracellular liquids contain ions free to migrate

• Charge carrier = ion(ionic current) not electron (electronic current) in metals– Local electronic coductance due to free

elctron, e.g. in DNA

– Non-liquid electrolytic materials : new solid materials like organic polymers and glasses

– Some solid media : mixture of ionic & electronic conductivity

2.1. Ionic and Electronic dc Conduction

• Two current carrying electrodes in an electrolyte are the source and sink of electrons: from electrons of the metal, to ions or uncharged species of the electrolyte.

• The electrode is the site of a charge carrier shift, a charge exchange between electrons and ions.

• Migration velocity of– Electrons in metal = ~0.3mm/s

– Ions in solution = ~10mm/s

– No collision phenomena in which charge carriers are stopped

2.1. Ionic and Electronic dc Conduction

• Electric current flow– No transport of substance

– Dc current flow without changing the conductor

• Ionic current – Transport of substance

– Externally applied dc current changes the conductor

– First near the electrode, then spread to the bulk

– Electrolytic long duration dc conductivity is a difficult concept in a closed system

– Transfer of electric charge across the solution-electrode interphase : electrochemical reaction at each electrode(electrolysis).

– “We must keep the phenomena in the bulk of the solution separate from the phenomena at the electrodes.”

2.1. Ionic and Electronic dc Conduction

2.1.1. Ionization

MLK

0.1540.000010.03713.6+10011H

N/AN/A24.6Noble0022He

N/A0.0685.4+10123Li

N/A0.0449.3+20224Be

N/A

N/A

0.133

0.176

0.17

0.26

N/A

NegativeIon

radius(nm)

0.066

0.070

0.077

AtomicRadius(mm)

+1

Noble

-1

-2

-3

±4+3

TypicalElectrovalency

2

8

7

6

5

4

3

11

10

9

8

7

6

5

ProtonIn

nucleus

0.0975.112Na

N/A17.402F

0.02514.502N

0.0358.302B

N/A21.602Ne

0.02213.602O

0.01611.302C

PositiveIon

radius(nm)

IonizationPotential

(eV)

Shell

Table2.1. Electron shell configuration for the lowest atomic number atoms. Ionization potential is here the energy necessary to remove the first electron from the valence (outermost) shell. Values for radii depend on how they are measured, here in vacuum and not aqueous solution.

• Chemical properties of an atom– Determined by the electron configuration of the

outmost shell (valence electron)

– Ionization potential < 20eV

– Chemical reaction and bonds are related to the valence electrons

– Electrovalence z : number of electrons available for transfer

• Electrochemical properties– Determined by the inclination of an atom to attain

noble gas configuration of the outer electron shell

• Electronegativity– Relative ability of an atom to gain electrons and

become a negative ion

– Useful to predict the strength & polarities of ionic bonds between atoms, and thus possible electrochemical reactions

1.8Fe2.8Br

2.5C3.5O

0.9Na2.5I

2.1P3.0Cl

2.1H3.0N

2.5S4.0F

Table 2.2. Pauling’s scale of electronegativity for

some selected atoms

2.1.2. Molecular Bonds

• Forces acting between atoms in a solid;– Ionic bonding

– Covalent bonding

– Metallic bonding

– Van der Waals bonding

• Ionic bonds– Between unequal atoms

– The atoms are ionized, valence electrons are lost or gained, coulombic forces keep the ions together in the solid

– Solid ionic crystal exhibit no electrical conductivity

– In water, the ions dissociate, causing ionic conductivity

• Covalent bonding– Atoms of the same atomic number (N2 gas, diamond)

– The atoms remain neutral, share valence electron pairs

– Each shared electron pair is a single bond.

– Covalent bonds can be extremely strong, the electrons locally strongly bound

– Solid covalent crystal exhibit no electrical conductivity

– In biomaterials, covalent bonds with carbon are very important

• No molecular ionic or electronic conductivity

• The charges may be far apart, very large dipole moments and strong electric polarization

– Carbon-carbon covalent bond• Single bond : complete freedom of rotation

• Double bonds : shorter and do not allow free rotation

• Important for electrical properties as polarization and relaxation time

0.154DiamondCC

0.10HC

0.147NC

0.0965H2OOH

0.075H2HH

0.143OC

0.12O2OO

0.11N2NN

0.142GraphiteCC

Bond length (nm)

Molecular form

Atom IIAtom I

Table 2.3. Covalent bond length

• Metalic bonds– Covalent type

– Highly mobile valence electrons, do not belong to particular atoms

– Strong electronic conductivity

– The atoms may be regarded as fixed positive ions

• Van der Waals bonding– An electron revolving around nucleus may be

considered as a rotating dipole

– Such rotating dipole induces dipoles in neighboring atoms

– Dipole-dipole attractive forces between atoms

– Forces are weak

– Many organic molecules form aggregates (homogeneous masses of particles)

• An electrolytic cell– An electrochemical cell

used with an externally applied electric current

– A galvanic cell is an electrochemical cell from which energy is drawn

2.2. The Basic Electrolytic Experiment

cathode anode

V A

- +

Electron flow direction

Migration :Cation(Na+)

Migration : Anion(Cl-)

E

Diffusion: neutral species

Figure 2.1. The basic electrolytic

experiment, shown with material

transport directions.

Homogeneous electrolyte solution :

solute(NaCl) + solvent(water) =

solution

Two identical electrodes: Pt,

Ag-AgCl, Carbon

Set up

• Platinum electrodes– At dc=0.5v, no dc current is flowing

– At dc=2v, the current increases rapidly

– With dc current flowing, gas bubbles are seen on both the anode and cathode metal surface

• Carbon electrode– Increase the voltage to about 2v to get a dc

current

– Gas bubbles are seen

– Erosion of the carbon surface

• Ag-AgCl electrode– Large dc current with only 0.1v

– Initially no gas bubbles

– The cathode loses the Ag-Cl layer after some time

Findings

Discussion

• Pt & Carbon– There must be energy barriers in the system– Nonlinear system, not obeying Ohm’s law

– Bulk solution obeys Ohm’s law

– Energy barrier is not in the bulk but near the electrodes

– Without dc current, no electron transfer, no chemical reaction, no faradaic current

• At the cathode

–Na+ ions migrate and are discharged ? (hint : Na+

has a very small electronegativity)

–Two processes with non-charged species transferred by diffusion

• Reduction of dissolved neutral oxygen : small current

• Decomposition of water molecules : larger current

2H2O + 2e = H2 (gas) + 2OH- (base)

• Na+ need not be considered but is necessary for the conductivity of solution, voltage drop in the solution is not too high

– Ag+ ions are reduced, AgCl layer is decomposed, pure Ag appears

• At the anode– discharge of Cl- :

• chloride is highly electronegative, but less energy is necessary for taking electrons from the chloride ions than from water molecules

– Neutral Cl2 gas reacts with carbon, not with Pt

– Water decomposition2H2O = O2 (gas) + 4H+ + 4e-(acid)

– Ag is oxidized and forms more AgCl

• Redox process : the transfer of electrons oxidising or reducing species at an electrode

“the results indicate that if we are to apply large dc currents to tissue, and we are to use noble metals as electrode material directly on the tissue, the passage of dc current is accompanied by the development of H2 gas and a basic milieu at the cathode, and Cl2 gas and perhaps oxygen and an acidic millieu at the anode”

• AC voltage case– At high frequency (~1MHz) : back and forth

migration process in the bulkelectrolyte will take palce, no accumulation or reaction will take place at the electrodes

– At low frequency (~0.1Hz) : result will depend on the dimension of the cell and the degree of reversibility of the reactions. Id the gas has time to bubble away, the process is certainly irreversible.

• Dissociation theory (by Arrhenius)– Molecules of acids, bases, and salts react with

water molecules to form separate ions.

– Water ionizes the substances

– Ions provide conducting properties

– Positive and negative ions free to migrate in the electric field contribute separately and unequally (due to diffierent mobilities) to the electric current flow

2.3. Bulk Electrolytic dc Conductance

Environment of Ions

• Two zones surroundan ion in aqueous solutions : ions of opposite sign & water molecules

• Hydration– Solvation (the process of solvent molecules forming

a sheath each electrolyte ion) by water

– Strong because water molecules have a large permanent dipole moment

– Ion-dipole forces

– Stabilizes and hinders the ion

– hydration number : average number of water molecule forming the sheath

Na+

--

++

--++

--+

+

--+ +

--++

--++

--++

--

++

--

++

-- ++

--

++

-- +

+

--

++

--+

+

--

++

--+ +

--+

+

--

++

--

++

--

++

--++

--++

Na+ ion hydrated by water molecules forming a sheath around it

Environment of Ions

• Ionic atmosphere– Central ion is also surrounded by a slight excess of

ions of the opposite charge

– Ion-ion forces

– Statistical concept

– Debye length : at surface potential drops by 1/e

• Relaxation time– Example : If the charge of an ion suddenly

disappeared, it would take a time of the order of 1 µs for the molecules to rearrange and for the ionic atmosphere to disappear

Contributions to ionic conductivity

• Ohm’s law for volume conductors• J = (nzev)+ + (nzev)- = Fcγ(µ+ + µ-)E

– 0< γ <1 : activity coefficient , µ : mobility

• J = σE : valid for DC under the condition that electrochemical changes at the electrodes do not spread to the bulk

– Electroneutrality : in a volume L the sum of charges is zero

• LΣ(nze)+ + LΣ(nze)- = 0

– conductivity of NaCl• σ = F(cγ)NaCl(µNa + µCl) : σ is frequency independent up through

whole kHz range

– molar conductivity (equivalent conductance) : conductivity per mole of solute per volume

• Λ = σ/c = Fγ(µ+ + µ-) (S/m) per (mol/m3) or (Sm2/mol), S=Ω-1

• Directly linked with mobility not with concentration

198OH--350H+/H3O+

10

4

5

Hydration no.

072CO32-119Ca2+

045HCO3-74K+

076Cl-50Na+

Hydration no.Λ0AnionΛ0

Cation

Table 2.4. Limiting molar conductivity Λ0 in aqueous solution. Λ0 in S•cm2 per

mol•z at infinite dilution and 25°C. Hydration number is the average number of

water molecules in the hydration sheath.

- Both hydration and ionic atmosphere reduce the molar conductivity

• increases effective radius of ion, therefore the friction

• reduces the effective charge of the ion

23.011Na6.93Li

16.08O

40.120Ca14.07N

39.119K12.06C

35.517Cl10.85B

19.09F1.01H

Gram weight/mol

Gram weight/mol

ProtonsProtons

Table 2.5. Relative atomic mass = gram weight per 1 mole (gram mole)

- Conductivity of 0.9% NaCl by weight

• 0.9% : 9g / 1000g = 9 g/liter

• 23.0 + 35.5 = 58.5 g NaCl = 1 mol

• 0.9% NaCl = 154 mmol/liter

• σ = Λc = (50+76) x 0.154 x 0.1 = 1.94 (S/m)

Figure 2.3. Conductivity as a function of NaCl concentration in aqueous

solution (20°C)

- NaCl concentration in body fluid• Physiological concentration = 0.9%

• Sweat = somewhat lower

• Urine = higher

• Sea water = 3.5%

• Contact electrolyte = much higher

- Higher temp and permittivity give less friction and higher

conductivity : interaction between ions reduces their mobility

Conductivity of water itself

• Water = hydroxyl ions + hydrogen ions– Strongly polar

– To a small extent, an electrolyte itself

– Intrinsic conductivity is low, but not zero

– Protonic self-ionizing process : transfer one of its protons to another water molecule

• H2O + H2O = H3O+ + OH-

– Hydrogen(H+) and oxonium(H3O+) have irregularly high molar

conductivity due to a special proton hopping mechanism

– The hydrogen ions will often dominate the conductance found. (ex : H+>Cl- in HCl, Na+ < Cl- in NaCl, K+≈Cl- in KCl)

Figure 2.4. Proton hopping conductance, same molecules as three different

times: (a) water molecule rotation; (b) hopping; (c) new proton position

Conductivity of weak acids

• With salts and strong acids, water dissociates all molecules

• With weak acids, some of the acids molecules stay undissociatesd

• Guldberg-Waage law (mass action law) : states the rate of a chemical reaction is proportional to the mathematical product ofthe masses of the reacting substances, and that equilibrium can be expressed by an equilibrium constant characterizing the chemicalreaction

• Dissolved CO2 gas conductivity

– [H3O+][HCO3

-]/[H2CO3]=KI=10-6.3

– Electroneutrality : [H3O+]=[HCO3

-]

– Conductivity toughly proportional to √[CO2]

• Water conductivity

– Kw = 1x10-14 = [H+][OH-], therefore [H+]=[OH-]=10-7 & pH = 7,

• Note that water is omitted from the expression because it is present in such vast excess that its concentration changes negligibly on the formation of equilibrium and is therefore effectively constant.

• σ = (Λ++Λ-)c = (350+198) x 10-7 x 0.1 = 5.5x10-6 (S/m)

Other factors influencing Conductivity

• Temperature dependence of conductivity of most ions = +2.0%/°C due to decrease in viscosity of water

• Increase in pressure -> increase viscosity -> the conductivity is reduced

• True electrolyte• Completely ionized (strong acids) in water

• Partly ionized (weak acids) in water

• Substances has to be polar to be soluble in water

• Pure HCl liquid is an insulator

• Non-electrolyte• Sugar/glucose

• Not ionized or not dissociated by water

• Colloidal electrolyte : the colloidal particles free to migrate contribute to the solution’s electrical dc conductance

• Colloid : Microscopic particles suspended in some sort of liquid medium. The particles are between 1 nm ~ 1 µm in size and can be macromolecules.

Special electrolytes

• Solid electrolyte : relatively low conductivity• AgCl : Ag+ are genuine charge carriers giving a certain electrolytic

ionic conductivity• Glass membrane in a pH electrode :

– Exhibit solid electrolytic conductivity(Li+, Na+, K+ have mobilities 103-104

larger than the protons)– Water absorbed in the leached surface layers, and there the proton

mobility is high and contributes to local dc conductance)

• NaCl solid crystal – Atoms in ionized form, not free to migrate, no dc conductance– Dissolved in water : NaCl is dissociated into free Na+ and Cl- ions– Warmed to 800°C it melt, ions are free to migrate with high mobility

(fused electrolyte)

• Mixed conductors• With both ionic and electronic conductance• Sulphides, selenides and tellurides of silver and lead• New plastic materials with ionic conductance : Nafion

• Polymers with mixed conductance• polymer with purely electronic conductor

• Carbon : graphite(electronic conductor), diamond(insulator)

• Protein in the body liquid• Colloidal electrolyte solute in a water solvent• Mixed conductor : electronic in the dry state, ionic with water

content• Keratin : dry protein (e.g. hair, nail, stratum corneum), water

content is dependent on the relative humidity of the ambient air

plasma

180153Sum180153Sum

13010

HPO42-

+SO42-

+organic acids

302Mg2+

1024HCO3-1404K+

intracellularplasmaintracellular

Protein-

Cl-

Anion(meq/L)

4x10-54x10-5H+ (pH7.4)

361610-45Ca2+

410310142Na+

Cations(meq/L)

Table 2.6. Concentration of electrolytes in body liquids (meq/L) is ion concentration in milliequivalents (mmole•valency z) per liter

• Body liquid electrolytes (Table 2.6)• Anion HCO3

- (bicarbonate) is related to the transport of carbon dioxide (CO2) in the blood

• A change in bicaronate (anion) concentration will therefore have consequences for the cation concentration (electroneutrality)

Ionic and electronic conduction with respect to semiconductor theory

• Idea of a possible semiconductive mechanism (electrons & holes) in biomaterials

• Electronic, semiconductive conduction for the DNA molecule

• Ions do not obey the laws applying to semiconductors

• Concept of local energy wells can also be adapted to ionic conduction.

Figure 2.5. Electronic semiconductivity. Energy levels in a semiconductor

without (left) and with impurities. Local impurities create local energy levels

(energy wells) as local reservoirs in the forbidden energy gap.

Materials classified according to conductivity

• Semicondictor & ionic conductor have a positive dσ/dT

• Metals have a negative dσ/dT

• Ionic conductor : in the conductivity range of pure semiconductor, but the nature of charge carriers and therefore the conduction mechanism is very different.

Table 2.7. Electronic(e) or ionic(I) dc

conductivity σ at 20°C if not differently

specified.