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ECEN 4341/5341

ECEN 4341/5341. Currents and Voltages in the Body Prof. Frank Barnes 1/22/2014. 1. 1. 1. Variations in Magnetic Field Exposures Over the Course of a Day. Variations with time of Day. Electric Field Scaling and Induced Currents. Induced Electric Fields . 1. 1. A More Complete Model. 1.

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ECEN 4341/5341

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  1. ECEN 4341/5341 Currents and Voltages in the Body Prof. Frank Barnes 1/22/2014

  2. 1

  3. 1

  4. 1

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

  6. Variations with time of Day

  7. Electric Field Scaling and Induced Currents

  8. Induced Electric Fields

  9. 1

  10. 1

  11. A More Complete Model

  12. 1 • 1

  13. 1

  14. 1

  15. 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

  16. Cell Models

  17. 1

  18. A Cell Membrane Cartoon • Voltage inside - 50 to -100mV about 1 charge per atoms

  19. 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 TransepithelialPotential, 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.

  20. Transepithelial Potential • 1. Note separation of the Na and K channels 15-60mV

  21. Current Densities 1. Currents across cell membranes 1 μA/cm2 to 10μA/cm2 the interior of the cell is negative. 2. The Transepithelial Potential (TEP) is positive at the outside of the skin. Current densities from 10μA /cm2 to 100 μA /cm2 3. Shocks at approximately 10 mA

  22. Limb Currents 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

  23. Chick Embryos

  24. 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

  25. Measurements Around an Chick Embryo

  26. Currents As Function of Position

  27. Voltage Gradients

  28. Currents Near Wounds

  29. Current Flow at a Cut

  30. Electric Fields Near a Cut

  31. Equivalent Circuit Model

  32. 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.

  33. 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. When the width w = 0 then

  34. Multiple Layers 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

  35. 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. The following equations apply where The individual capacitors are described by the following equations and so and then

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

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

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