Currents and Voltages in the Body Prof. Frank Barnes 1/22/2015 1

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Variations in Magnetic Field Exposures Over the Course of a Day 5

Variations with time of Day 6

Electric Field Scaling and Induced Currents 7

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

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. 18

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

Current Densities 1. Currents across cell membranes 1 μA/cm 2 to 10 μA/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 μA /cm 2 to 100 μA /cm 2 3. Shocks at approximately 10 mA 24

Amputated Limbs 10 to 100μA/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

Chick Embryos 26

Effects are Time Dependent Applied external currents can cause abnormalities in the neural-stage embryo stage and not Gastrula-stage At mV/mm leads to abnormalities 27

Measurements Around an Chick Embryo 28

Currents As Function of Position 29

Voltage Gradients 30

Currents Near Wounds 31

Current Flow at a Cut 32

Electric Fields Near a Cut 33

Equivalent Circuit Model 34

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

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

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

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

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

Taking a step back we look at the dielectric constant again in terms of ε o. The relationship is which plugs back into the equation for the capacitance as shown in the following equations. 40

Charge flow in Cells Charge flows back and forth inside the cell which was shown and illustrated in the class. 41