Measuring Electrical Conductivity of Brain Tissue

By:Maher Elbohouty

Supervisors:Dr Marcus Wilson

AProf Alistair Steyn-Ross

12 April 2023

Has anyone measured the conductivity ? • Gabril et al.* (2009) in his review shown that the

conductivity of brain tissue depends on many parameters as:

• The animal and the part of the brain investigated

• The stimulus frequency

• The direction of measurements

• He found that it ranges from:0.01 to 0.47 S/m* Phys. Med. Biol. 54 (2009) 4863–4878

• Logothetis et al.** (2007) said that: “ Our results show that impedance is independent of frequency, is homogeneous and tangentially isotropic within gray matter, and can be theoretically predicted assuming a pure-resistive conductor ”.

** Neuron 55, 809–823, September 6, 2007

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…slicing…

Brain removal…

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Three methods:

1. One dimension

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2. Two dimensions

3. Three dimensions

1. Modified syringe and two stainless steel plate electrodes (Flat Electrodes):

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Taking the sample ..

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The resistivity of brain slices at 10 kHz

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The Syringe (V3) digital calliper (DIGMATIC- Mitutoyo Corporation, Model CD-6”) and LCR meter (Agilent E4980A)

Defining equation in 1D

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𝐑𝐀𝝆𝒂 = 𝒅 𝟏𝑨𝒔𝑨ቀ𝝆𝒂𝝆𝒔−𝟏ቁ+𝟏 − 𝟏൩+ 𝒙

Where:

R: measured resistance

A: electrode area.

As: brain slice area

a: ACSF resistivity

s: slice resistivity

x: electrode separation

d: slice thickness

Slice ACSF

s a

RA/a (m)

x (m)

Measurement of resistance (R) against different separation of electrodes (x)

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-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06

RA

/a

(m)

x (m)

ACSF only

ACSF with real slice

The measured conductivity is affected by the uncertainty of y-intercept and….

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• Slice surface area (As) and ACSF resistivity (a) was studied• 0.0 - 0.7 S/m

y-intercept electrodes surface area (A)

The measured conductivity is affected by the uncertainty of ...

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ACSF resistivity (a) electrodes surface area (A)

• Also slice surface area (As) was studied• 0.5 – 0.7 S/m

Next Step ..• More accurate measurements using...

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Advantages:• Electrodes will be used as a cutters so the brain slice area will

equal the surface area of the electrodes • Ag/AgCl electrodes are more efficient with measurements • The random and systematic error in the electrodes separation will

be minimizedDisadvantages:• The brain slice folding• The tube leakage of ACSF and many other limitations

2. 2D Electrical conductivity by4 Cylindrical electrodes

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4 Tiny Cylindrical electrodes:

• The difference is 1 %

Defining equation in 2D

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Where:

: is the fluid conductivity

I: the measured current.

D: the depth of the fluid

: the voltage

 

r1: distance between Iin and V2.

r2: distance between Iout and V2.

r3: distance between Iin and V1.

r4: distance between Iout and V1.

For the ACSF we expect the relationship:

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b

d

where:

z = effective measured impedance of the tissue

b = separation between the two voltmeter electrodes

d = separation between the inward and the outward current electrodes

 

3. 3D Electrical Conductivity

16

Multielectrode Array

We place the brain slice on a commercially available multielectrode array (MEA) consisting of 60 three-dimensional platinum electrodes.

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1.6 mm 20 m

Options of 4 point electrodes:

• Not suitable because: the distances or they are mechanically unstable

• The difference range from 2% up to 25 %

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5 mm

1 mm

2 mm

Conclusion:

• 1D is the most encouraging.

• The conductivity ranges from 0 to 0.7 S/m which is consistent with Gabril et al. (2009) review.

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What is the problem?

mouse brain slices

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1 cm

• Is there a link between seizure activity and electrical conductivity?

• Can we measure changes in electrical conductivity of mouse cortex just before, during and after seizure-like events.

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Further work:

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Thank you

Thanks to my friends in the University of Waikato Cortical Modelling Group

THE UNIVERSITY OF WAIKATO

INTERNATIONAL DOCTORAL SCHOLARSHIP

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The importance of conductivity

• Neurons communicate electrically through gap junctionsgap junctions

• Neurons touch

• A conductive channel through their two membranes

• Ions can flow, implying electrical conductivity

• Is this effect measurable?

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Gap junctions and seizures

• Gap junction blockade increases the frequency and amplitude of seizure events in rat and mouse brain slices

• Voss et al. (2009). Epilepsia, 50(8), 1971 – 1978.

• Voss et al. (2010). European Journal of Pharmacology 643, 58 – 62.

•Our questions:

• Can we measure changes in electrical conductivity due to opening / closing of gap junctions?

• Is there a link between seizure activity and electrical conductivity?

Modelling:The approximate calculation our equation is supported by more accurate computer modelling of the electric fields between the three-dimensional electrodes using COMSOL Multiphysics. We have used COMSOL Multiphysics to investigate electric field between the array.

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Modeling shows very high current density on the electrodes which make them burning