Dielectric properties of tissuesDielectric properties of tissuesand cellsand cells

Prof. Prof. Dr.Dr. Alois Alois LoidlLoidl

Studies on the issue, if macroscopic dielectric properties of tissues have unlimited validity in both cellular and subcellular dimensions

Part of the German Mobile Telecommunication Research Programme

Participants:

• Dielectric Spectroscopy (A. Loidl, D. Egger, P. Lunkenheimer)

• Patch clamp measurements (A. Wixforth, M. Schneider)

• Theoretical calculations (P. Hänggi, G. Schmidt)

EKM / Institute of Physics, University of Augsburg, Germany

The project is financially supported by the Federal Office for Radiation Protection (BfS).

Studies on the issue, if macroscopic dielectric properties of tissues have unlimited validity in both cellular and subcellular dimensions

Introduction

Dielectric spectroscopy

Electrolytic solutions

Cell suspensions

Summary

• Permittivity ε and conductivity σ are determining factors in absorption of electromagnetic radiation

• dosimetry essentially relies on the knowledge of dielectric properties of tissue

Specific Absorption Rate

Introduction

2ESAR σ

ρ=

Behaviour of dielectric parameters at cellular and subcellular dimensions

σ: conductivity (S/m)

E: field strength (V/m)

ρ: mass density (kg/m³)

Studies on the issue, if macroscopic dielectric properties of tissues have unlimited validity in both cellular and subcellular dimensions

Introduction

Dielectric spectroscopy

Electrolytic solutions

Cell suspensions

Summary

Dielectric spectroscopy

ε* = ε' - i ε"complex permittivity:

dielectric constant dielectric loss

complex conductivity:

σ* = i ω ε0 ε* relaxation hopping conduction

reorientingdipolarmolecule

peak in ε"(ν,T), step in ε'(ν,T) at ν = 1/(2πτ)

s < 1ωs,

σdc

σ"

σ'

log [ν (Hz)]

log

[σ (Ω

-1cm

-1)]

chargedparticle in double-wellpotential

σ' = σdc + σ0 νs (s < 1)

εs

ε''

ε'

ε∞

ε*

log [ν (Hz)]

T

σ * = σ ' + i σ "

Dielectric spectroscopy

10

*( )1 ( )

dcs ii

βα

ε εε ω εε ωωτσ∞

∞ −

−= + −⎡ ⎤+⎣ ⎦

0 exp( )B VF

Ek T T

ττ τ⎛ ⎞⎟⎜= ⋅ ⎟⎜ ⎟⎜ ⎟−⎝ ⎠

0 expdcB

Ek T

σσ σ⎛ ⎞⎟⎜= ⋅ − ⎟⎜ ⎟⎜ ⎟⎝ ⎠

10-2 100 102 1010-2

10-1

100

∼ν0.5

∼ν1

∼ν-0.5

∼ν-1

Debye CD CC

ε"

ωτ

38B

RH

k TDrπη

=

12 RD

τ =2 2

0 00 6 B

n q ak T

νσ =

( )2B dck TDneσσ=

Rotational diffusion coefficient

η viscosity

rH hydrodyn. radius(Nernst-Einstein)

Conductivitydiffusion

or

Dielectric spectroscopy

α-dispersioncounter-ion relaxation? membrane structure/channels?

β-dispersion1 kHz...100 MHz charging of cell membranes

γ-dispersion> 100 MHz rotation of water molecule

δ-dispersionbound waterrelaxation of macromolecules

Major dispersion regimes in biological matter

Broadband dielectric spectroscopy

for details, see U. Schneider, P. Lunkenheimer, A. Pimenov, R. Brand, and A. Loidl, Ferroelectrics 249, 89 (2001).

• Measurement of dielectric constant and complex conductivity• Parameters: frequency, temperature (0.1 K < T < 1000 K), doping, magnetic field• Extremely broad frequency range: 10-6 Hz < ν < 1015 Hz

Open-ended coaxial probe (100 MHz - 40 GHz)

© Agilent Technologies, Inc.

• Ideal for liquids or semisolids

• measurements with network analyzer (Agilent E8363B PNA Series)

Example: glycerol

10-6 10-3 100 103 106 109 101210-2

10-1

100

101

179K

223K

ν (Hz)

323K295K273K

ε''

413K

363K

184K 195K 204K 213K 234K

glycerol

253K

P. Lunkenheimer et al., PRL 77, 318 (1996); P. Lunkenheimer et al., Contemp. Phys. 41, 15 (2000); U. Schneider et al., PRL 84, 5560 (2000).

C3H8O3network glass former (hydrogen bonded)Tm=291 K; Tg ≈185 K

Ubiquitin

10-1

100

101

102

103

104

solution, 1 mM/lσdc subtractedpressed powder

τ ≈ 7.3 ps

ε''

12 ns

3 4 5 6 7 8 9 10 11

0.045

0.050

0.055

log10[ν(Hz)]

0.33 µs

ε''

0

20

40

60

80

100

102 104 106 108 1010 1012

100

101

102

ε'

DYCCCD

ε"

ν (Hz)

Dielectric properties of pure water

50

60

70

80

90

280 300 320 340 36010-6

10-5

17kHz 50kHz 143kHz 414kHz literature

ultrapure

ε'

σ' (Ω

-1cm

-1)

T (K)

Dielectric properties of pure water

50

60

70

80

90

280 300 320 340 36010-6

10-5

17kHz 50kHz 143kHz 414kHz literature

ultrapure

ε'

σ' (Ω

-1cm

-1)

T (K)

0

20

40

60

80

100

ε'

DYCCCD

102 104 106 108 1010 1012

100

101

102

ε"

ν (Hz)

Studies on the issue, if macroscopic dielectric properties of tissues have unlimited validity in both cellular and subcellular dimensions

Introduction

Dielectric spectroscopy

Electrolytic solutions

Cell suspensions

Summary

20

40

60

80

108 109 10104

10

40

108 109 1010

10-3

10-2

10-1

100

10°C 50°C 20°C 60°C 30°C 70°C 40°C 80°C10 mM NaCl

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Electrolytic solutions

20

40

60

80

100

108 109 1010

10

100

1000

108 109 101010-3

10-2

10-1

100

1 M NaCl 0.5 M NaCl 0.154 M NaCl 0.100 M NaCl 0.010 M NaCl

37°C

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Electrolytic solutions

Fitparameters: NaCl electrolytes

2.8 3.0 3.2 3.4 3.62

10

20

250 300 350

0.010

0.015

0.020

10-3

10-2

10-1

1000/T(K)

τ (p

s)

1/Δε

T(K)

1 M NaCl 0.5 M NaCl 0.154 M NaCl 0.100 M NaCl 0.010 M NaCl

σ dc(Ω

-1cm

−1)

0.01 0.1 1

0.1

1

10

0.1

0.2

0.3

0.0

0.1

0.2

0.01 0.1 10.000

0.005

0.010

0.015

c (mol/l)

σ 0 (Ω-1cm

-1)

Eτ (e

V)

NaCl

Eσ (e

V)

NaCl

τ 0 (ps)

c (mol/l)

Hindering barriers and prefactors of electrolytic solutions

Electrolytic solutions (concentration dependence)

100

108 109 1010100

101

102

103

ε'

KCl

1 mMol 10 mMol 0.1 Mol 1 Mol

ν (Hz)

ε"

6.6

6.8

7.0

10-3 10-2 10-1 100

60

65

70

10-4

10-3

10-2

10-1

τ (p

s)

Δε

concentration (mol/l)

Δε = 70.6-10.8 x

σ dc(Ω

-1cm

−1)

Electrolytic solutions (temperature dependence)

0

25

50

75

100

108 109 1010

10

50

5°C 24°C 42°C 60°C

ε'

0.01 mol/l KCl in H20

ν (Hz)

ε"

3.0 3.2 3.4 3.64

81216

0 20 40 600.012

0.014

0.016

10-3

2x10-3

3x10-3

E=0.20 eV

1000/T(K)

τ (p

s)

1/Δε

T(°C)

σ dc(Ω

-1cm

−1)

E=0.12 eV

Universal description of electrolytic solutions

10

*( )1 ( )

s dcii

βαε ω ε

ε ωωτε ε σ

−∞

∞= + −⎦

−⎡ ⎤+⎣

0 expB

Ek T

ττ τ⎛ ⎞⎟⎜= ⋅ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

0 expdcB

Ek T

σσ σ⎛ ⎞⎟⎜= ⋅ − ⎟⎜ ⎟⎜ ⎟⎝ ⎠

SC

CT T

ε ε ε∞Δ = − =−

Max. 14 Parameter: ε∞, α, β, Acurie, Bcurie, ATcurie, BTcurie, Aσ0, AEσ, BEσ, Aτ0, Bτ0, AEτ, BEτ,

ε and σ as function of ν, c, T

60

70

80

10-3 10-2 10-1 10010-4

10-3

10-2

10-1

calculation literature: εSW-11c

KCl

ε'

37° C

σ' (Ω

-1cm

-1)

c (mol/l)

20

40

60

80

108 109 10101

10

40

37° C

measurement calculation

1 mM KCl

ε'

ν (Hz)

ε"

Studies on the issue, if macroscopic dielectric properties of tissues have unlimited validity in both cellular and subcellular dimensions

Introduction

Dielectric spectroscopy

Electrolytic solutions

Cell suspensions

Summary

Dielectric properties of cell suspensions

Unilamellar vesicels as cellular model systems

Dielectric properties of cell suspensions

Red cell isolation:

• Addition of isotonic buffer to the whole blood

• Centrifugation at 600 x g

• Removing the supernatant and resuspending in isotonic buffer

Dielectric properties of cell suspensions

20

40

60

80

100

108 109 101010

100

108 109 1010

10-2

10-1

100

24°C 30°C 37°C 44°C 50°C

sanguis

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Measurements of whole blood:

Indications of a δ-relaxation?

Dielectric properties of cell suspensions

20

40

60

80

108 109 101010

100

108 109 1010

10-2

10-1

100

Red blood cells (Ht 90%) Red blood cells (Ht 60%) Red blood cells (Ht 30%)

37°C

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Dielectric properties of cell suspensions

fibroblasts

melanoma cells

PC12 nerve cells

hepatocytes

Incubator for cell cultivation:

37° C

5 % CO2

20

40

60

80

108 109 1010

10

100

500

24°C 30°C 37°C 44°C 50°C

PC12 nerve cellsin PBS-buffer

ε'

ν (Hz)

ε"Dielectric properties of cell suspensions

20

40

60

80

108 109 1010

10

100

500

24°C 30°C 37°C 44°C 50°C

PC12 nerve cellsin mannitol-buffer

ε'

ν (Hz)

ε"

20

40

60

80

108 109 10104

10

40

108 109 101010-4

10-3

10-2

10-1

100

24°C 30°C 37°C 44°C 50°C

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Dielectric properties of cell suspensions

fibroblastsin mannitol-buffer

80 million cellsper ml

Dielectric properties of cell suspensions

20

40

60

80

108 109 10105

10

50

108 109 1010

10-3

10-2

10-1

100

10 million cells per ml 50 million cells per ml 80 million cells per ml

37° C

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

fibroblastsin mannitol-buffer

101

103

105

107

109

0 2 4 6 8 10

102

104

106

108

0 2 4 6 8 1010-4

10-3

10-2

10-1

100

37°C

ε'

ν (Hz)

ε"

σ' (Ω

-1cm

-1)

ν (Hz)

Dielectric properties of cell suspensions

fibroblastsin mannitol-buffer

200 million cellsper ml

Summary and outlook

• Dielectric properties of electrolytes and cell suspensions in the relevant frequency regime are dominated by γ dispersion: Smooth functions of temperature, frequency and concentration. In whole blood indications of additional processes. No indications of resonant processes beyond experimental uncertainties.

• When compared to pure water, ε´ decreases while σ´ strongly increases due to dc conductivity. However, with increasing cell concentrations the conductivity becomes suppressed again.

• So far all investigations were perfomed with SAR values close to 0.1 W/kg (with respect to the external electric field). Field dependent and non-linear experiments are planned in the near future.