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 6
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Electric Field Scaling and Induced Currents 7
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Induced Electric Fields 8
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A More Complete Model 11
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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 O 2 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 10 7 V/m B. There
are also endogenous electric fields in the extracellular fluids in
the range of 10 to 100V/m 15
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Cell Models 16
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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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K+ K+-selective channels Na+ K+ Cilium Inner Segment Active
transport Figure 1.1 Diagram of a single retinal rod cell
illustrating the segregation of ion chan- nels that leads to the
generation of a dark current. Na + channels found only in the outer
segment are gated by cGMP and pass the positive inward current
there. K+ channels are localized in the inner segment and pass the
outward current. Photon absorbance by rho- dopsin in the outer
segment triggers a transduction reaction that results in the
reduction of cGMP and leads to the reduction of the inward Na+
current. 19
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A Cell Membrane Cartoon Voltage inside - 50 to -100mV about 1
charge per atoms 21
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Transepithelial Potential 1. Note separation of the Na and K
channels 15-60mV 23
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Current Densities 1. Currents across cell membranes 1 A/cm 2 to
10 A/cm 2 the interior of the cell is negative. 2. The
Transepithelial Potential (TEP) is positive at the inside of the
skin. Current densities from 10 A /cm 2 to 100 A /cm 2 3. Shocks at
approximately 10 mA 24
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Amputated Limbs 10 to 100A/cm 2 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 25
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Chick Embryos 26
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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 27
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Measurements Around an Chick Embryo 28
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Currents As Function of Position 29
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Voltage Gradients 30
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Currents Near Wounds 31
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Current Flow at a Cut 32
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Electric Fields Near a Cut 33
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Equivalent Circuit Model 34
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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. 35
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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. 36
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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. 37 When the width w = 0
then
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Multiple Layers 38 If the capacitance values are equal then the
equation simplifies to Now to relate this back to the dielectric
constant, recall the following when dealing with distributed
charges and substituting back in for the dielectric constant we get
the following relationship
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Further discussion of Model 39 Now look at the case of a single
capacitor with a plate of width w inserted between the plates as
shown to the left. The following equations apply where The
individual capacitors are described by the following equationsand
so and then
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Taking a step back we look at the dielectric constant again in
terms of o. The relationship is which plugs back into the equation
for the capacitance as shown in the following equations. 40
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Charge flow in Cells Charge flows back and forth inside the
cell which was shown and illustrated in the class. 41