volume source and volume conductor2

8/7/2019 Volume source and volume conductor2

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Volume source and volume conductor


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Concepts of volume source and

volume conductor

What are volume source and volume conductor?

-In electronics circuit :

components are concentrated.condutors are ordinary one dimensional wire.

-In bioelectromagnetism

Components are distributed.

Conductors are extended in three dimensions.


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So Voulme sources are distributed sources.

and volume conductors are three dimensional

conductors. Volume emphasizes that current flow is

three-dimensional, in contrast to the

confined one dimensional flow within

insulated wires.


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Bioelectric sources and its electric filed

Preconditions:

Source: Volume sources

Conductor: Infinite, homogenous

So what is the bioelectric sources ?

-Impressed current density : Ji(x, y, z, t)


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It is the current source in the cell due to

depolarization or repolarization process duringthe flow of ions through the membrane.

Each of this sources act like electric current

dipole.

The total current density will form the volume

dipole moment density of the source.


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Assume conductivity of the volume source is

The impressed current density generate an electricfield E.

From Ohms law, a conduction current density Ewill flow in the volume conductor.

Total current

J = E + J

i

J i exist only in the depolarizing or repolarizngcells.


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J = J i +E


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For quasistatic condition

E =

J = J i

Applying divergence of the above equation

and solving for the electric potential outside

the source region in infinite homogenous

volume conductor

(x, y, z) =


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In reality homogenous volume conductor

does not exist.

Preconditions:

Source: Volume sources

Conductor: inhomogeneous Modeled by piecewise homogenous volume

conductor.

Dividing the region into a finite number ofhomogenous regions.

The boundary conditions


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Applying Greens theorem

electric potential within an inhomogeneous volumeconductor containing internal volume sources is :

The first term: contribution of the volume source. The second term: due to the inhomogeneties

Error


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THE CONCEPT OF MODELING

In real life the source and conductors are very

complicated.

- Very hard to solve.

- Solution: Modeling

Basic models of volume sources

Dipole

- The most simple model of a source.

- Fixed location, variable orientation and magnitude.

- Three independent variable.


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Moving dipole

Variable location, magnitude and orientation

Six independent variable

Multiple dipole

Several dipole

Fixed location, varying magnitude and orientation

For N dipole 3*N independent variabl.


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Multipole

Dipole(3), quadruple (5), octapole(7), etc .

Higher source configuration


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Fig. 1.2

Dipole moving dipole

Multiple Dipole MultipoleFig. 1.1 models of volume source


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THE HUMAN BODYASAVOLUME

CONDUCTOR

As a volume conductor

Human body

Resistive, piecewise homogenous and linear

Most of the tissues are isotropic.

Heart muscle, skeletal muscle and brain tissue are example of

anisotropic conductors.

Blood depend on Hct (hematocrit) values.


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Modeling the Head

Head is modeled by a concentric sphere.

Fig. 1.2 Four layered head model; scalp, skull, CSF and brain


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Forward and inverse problem

Fig1.3 forward and inverse problem


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Clinically inverse problem has a lot of significance

But it solving the solution is challenging

some possible approach

The Empirical Approach based on the experience

Imposition of Physiological Constraints Knowing the position of the source could also help in solving the

inverse problem.

Lead Field Theoretical Approach This approach uses sensitivity of leads.

Modeling method


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Amodel is constructed for the source

Amodel is constructed for the volume conductor

At least as many independent measurements are made as the

source model has. Now we can solve the source

But is the constructed model good enough to represent the real

physiological counter part?


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Reference

1. J. Malmivuo and R. Plonsey,

Bioelectromagnetism: principles and

applications of bioelectric and biomagnetic

fields, Oxford University Press, 1995.

2. Plonsey, R. Volume Conductor Theory. The

Biomedical Engineering Handbook: Second

Edition.Ed. Joseph D. Bronzino Boca Raton:

CRC Press LLC, 2000

volume source and volume conductor2

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