Transcript Currents and Voltages in the Body Prof. Frank Barnes 1/22/2015 Variations in Magnetic Field Exposures Over the Course of a Day.

Currents and Voltages in the Body
Prof. Frank Barnes
1/22/2015
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Variations in Magnetic Field Exposures Over the
Course of a Day
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Variations with time of Day
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Electric Field Scaling and Induced Currents
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Induced Electric Fields
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A More Complete Model
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Electrical Voltages and Currents In the Body
1. The Body is an Electro Chemical System
A. Basic Sources of Energy are the Metabolic Processes
in the mitochondria which supply about 95% of the
energy for the cell by combining O2 with glucose to
form ATP. This in turn supplies the energy for the
pumps that maintain the ion gradients across
membranes and generate the electric potentials of
-50 to -100mV between the outside and the inside
of a cell. This leads to trans membrane fields on the
order of 107V/m
B. There are also endogenous electric fields in the
extracellular fluids in the range of 10 to 100V/m
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Cell Models
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Source of Electric Fields
1. Plasma membrane that defines the cell boundary
and the voltage is negative on the inside.
2. The Epithelium that surrounds every organ and
the skin. This leads to the Transepithelial
Potential, TEP, which is positive on the inside.
3. The TEP fields move ions and molecules around and
are the driving force for the growth of embryos
and wound healing etc.
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A Cell Membrane Cartoon
 Voltage inside - 50 to -100mV about 1 charge per 106
atoms
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Transepithelial Potential
 1. Note separation of the Na and K channels 15-60mV
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Current Densities
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3.
Currents across cell membranes 1 μA/cm2 to 10
μA/cm2 the interior of the cell is negative.
The Transepithelial Potential (TEP) is positive at
the inside of the skin. Current densities from 10
μA /cm2 to 100 μA /cm2
Shocks at approximately 10 mA
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• Amputated Limbs 10 to 100μA/cm2 out of the cut.
60 mV/mm to start and down to 25mV/mm within 6hr
(Note in other units these are Volts/meter)
• Growth occurs toward negative electrode. Used to
guide direction of nerve growth.
• The currents during growth in a root or other cell can
flow in one end and back into the side of the cell.
• We have seen effects as low as 0.2 mV across a
membrane in changing the oscillation of pacemaker
cells or fields of 0.01V/m
• Electroporation 1 .5 to 3V/cell
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Chick Embryos
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Effects are Time Dependent
 Applied external currents can cause abnormalities in
the neural-stage embryo stage and not Gastrula-stage
 At 25-75 mV/mm leads to abnormalities
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Measurements Around an
Chick Embryo
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Currents As Function of
Position
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Voltage Gradients
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Currents Near Wounds
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Current Flow at a Cut
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Electric Fields Near a Cut
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Equivalent Circuit Model
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Skin and Muscle Circuit Model
Typical characteristics for muscle is shown in the
textbook. The dielectric constant drops as a function
of frequency. There are three main characteristics due
to the three main components. The reduction in the
dielectric constant is consistent with time for charges
to separate.
The goal is to explain the concept of the dielectric
constant in terms of a circuit model. Recall that
capacitance in series is described with the following
equation.
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Growth of Planarian Flatworm
In an Electric Field.
Wendy Beane
 In vivo studies show that electric fields have a lot to do
in controlling the size and shape of the growth.
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Capacitive Model
 Consider case of two capacitors in series as shown in the figure
where W is the width of a perfectly conducting metal plate that
inserted between the two plates of a parallel plate capacitor
separated by a space d with a dielectric constant for the material
between the plates.
V
d
w
When the width w = 0 then
0 A
C0 
d
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Multiple Layers
1 1
1
1
 
 ... 
C C1 C2
CN
If the capacitance values are equal then the equation
C1
C

simplifies to
N
Now to relate this back to the dielectric constant, recall
the following when dealing with distributed charges
C
A
l

Q
V
and substituting back in for the dielectric
constant we get the following relationship
Ql
Q


AV AE
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Further discussion of Model
Now look at the case of a single capacitor with a plate of
width w inserted between the plates as shown to the left.
1 1
1
The following equations apply   where C  A
C
C1
C2
d
The individual capacitors are described by the following
 A
0 A
C1  0
equations
and
C

2
d w
so
1 d w 1


C1
2A C2
2
and then
d w
2
1 d w

C
A
d
w
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Taking a step back we look at the dielectric constant
again in terms of εo.

0
w
The relationship is
(1  ) which plugs back into the
d
equation for the capacitance as shown in the following
equations.


0 A
0 A  1 
C0


C


(d  w)
d  1  w  (1  w )


d
 d
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Charge flow in Cells
Charge flows back and forth inside the cell which was
shown and illustrated in the class.
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