Ecen 5341 4341 lecture 12 feb 12 2014
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. ECEN 5341/4341 Lecture 12 Feb 12,2014. Amplifiers A Space 2.Nonlinear Effects of AC Fields on Cells A Rectification B. Mode Locking C. Coherence D. Minimum Detectable Fields . Amplifiers. 1. Basic Definition

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Ecen 5341 4341 lecture 12 feb 12 2014


ECEN 5341/4341Lecture 12 Feb 12,2014


A Space

2.Nonlinear Effects of AC Fields on Cells

A Rectification

B. Mode Locking

C. Coherence

D. Minimum Detectable Fields


  • 1. Basic Definition

    • A small signal is used to extract energy from another source to produce a larger signal.

      2. A typical transistor amplifier will extract energy from a DC source. Note with a BJT the control signal is separated in energy from the signal to be controlled. With MOSFET they are separated in space.

      3. A parametric amplifier extracts energy from an AC source that is at a higher frequency.

      4. A stochastic amplifier extracts energy from a noise source.

Some biological amplifiers
Some Biological Amplifiers

  • 1. Chemical Energy drives the Na+, K+pumps store energy of -50 to -70 mV in nerve cells. A sum dendritic pulses can trigger an action potential that in turn can activate a muscle. A single pulse from an action potential release thousands of neural transmitters.

  • 2. At a synaptic junction a neural transmitter can release thousands of Ca2+ ions.

  • 3. The gain in the body for temperature control = -33 and for arterial blood pressure it is -2

The concentration of electric fields across membranes
The Concentration of Electric Fields Across Membranes

  • Figure 2. A rectangular model for a cell and an approximant equivalent circuit for it.

The membranes are typically 5 to 10nm thick while the cell may range from a few micrometers to a centimeter or so in length. The effective membrane resistance (Rm) per unit area takes on values of 0.14 to 15 Ω/m2in the transverse direction. This corresponds to resistivities in the range of ρm = 107 Ω m to ρm= 10 9 Ω m. The relative dielectric constant for the membrane is typically in the range of 2 to 4. Both the surrounding fluid and the interior of a cell have resistivitiesρf of about ρf= 2 Ω m and a relative dielectric constant of 50 to 80.

Currents through cells
Currents Through Cells

Where Jm is the current density through the cell and ρ is the resistivity of the membrane. Typical cell membrane thicknesses are t= 6 to 10 nm, and typical dimensions are 10 to150 µm. Setting L = 100 µm and ρ2t =10Ωm2 V = (10Ωm2+2x10-6Ωm2)Jm

Cell membranes
Cell Membranes

  • Nerve Cell Membranes contain Na+, K+, Ca++ channels

  • The fields across a membrane are generated by voltages of 50 to 100mV across a thickness of 5 to 10nm

  • This yields E ≈ 107V/m Pulses are in the range 10-3 sec

  • Current Densities 1.5 A/m2 and I≈ 10-9 A

  • If we look at the fields that are required to move proteins or some ACh receptors along a membrane to one end E≈ 102 to 103 V/m. Times are 30 min.

  • External Current Densities ≈ 10mA/m2 to get changes.

Nonlinear characteristics
Nonlinear Characteristics

Currents through a membrane.

Note the membrane is a poor rectifier at frequencies

Below approximately 1to 10MHz

At high frequency have not detected nonlinear characteristics at low

Power levels with very sensitive receivers.

Nonlinear effects of ac fields on cells
Nonlinear Effects of AC Fields on Cells

  • 1. Fundamental for frequency mixing

  • 2. Assume we have a membrane with the Nernst

    Equation and apply a voltage Vm = Vo +V1cos ωt. A Taylor series expansion gives

    This give a DC current off set and a second harmonic


  • 1 The DC term leads to

  • Where Rm is the membrane resistance.

  • The rectification is about 1/1000 for frequencies below 1 Mhz. Above this is drops to nearly zero.

Adding a signal to the hodgkin huxley equations
Adding a Signal to the Hodgkin Huxley Equations

  • A Depolarizing Pulse at High Frequency Shifts the firing time.

Phase locking for injected current in a pacemaker cell
Phase Locking for Injected Current in a Pacemaker Cell

  • 1

  • Another expression for phase lock conditions

Injection of 0 6na into a pacemaker cell as a function of frequency
Injection of 0.6nA into a Pacemaker Cellas a Function of Frequency


  • 1 Litovtiz showed that 10µT at 55 or 65 Hz for 10sec or longer over a 4hr period doubled the specific activity of ornithine decarboxylase cells.

  • This effect decreases with increasing signal to noise ratios. Over all he shows a need for both space and time coherence.

Increase odc with coherence time
Increase ODC with Coherence Time.

Also shows abnormalities in Chick Embryos for 1µT pulses. Add noise and it goes away.

Parametric amplifiers
Parametric Amplifiers

  • 1

    Conservation of energy is

Stochastic resonance
Stochastic Resonance

  • 1 A means for extracting coherent energy from noise

Mechanism for bio effects of magnetic fields
Mechanism for Bio Effects of Magnetic Fields

  • 1. Induced Electric Fields ( Ion currents, Molecular Orientation and Configuration

  • 2. Direct Effects (Free radical Lifetimes and Concentrations.)

  • 3. Coherence for Good Signal to Noise

  • 4. Thermal Effects

  • 5. Amplification

  • 6.Measured Effects at E = 0.1 V/m and B= 1µT

Electric Field Effects 0n Bovine Fibroblast Cells in Culture Show a Reduction in Growth with a Minimum Near 10Hz

Time delay b etween voltage and current
Time Delay Show a Reduction in Growth with a Minimum Near 10HzBetween Voltage and Current

Variations in capacity and conductance with frequency giant squid axon
Variations in Capacity and Conductance Show a Reduction in Growth with a Minimum Near 10HzWith Frequency Giant Squid Axon

Neural network model for biological systems
Neural Network Model for Biological Systems Show a Reduction in Growth with a Minimum Near 10Hz

  • 1