Electrode theory and ultrasonic bloodflow meter

Electrode theory

An electrode is a conductor (metal) that connects the body (ionic conduction) with the electronic instrument (electronic conduction). When a metal is placed in an electrolyte (body fluid), a layer of ions forms:

• Metal atoms dissolve as ions into the solution, leaving electrons in the metal; or ions from the solution deposit on the metal.
• A double layer of charge (Helmholtz layer) forms at the interface and produces a potential difference called the half-cell potential (Ehc), e.g. about +0.223 V for Ag/AgCl. It depends on the metal and on the electrolyte concentration.
• When current flows, the electrode is polarised: its potential moves away from the equilibrium value, causing an overpotential and noise. Non-polarisable electrodes such as silver–silver chloride are used for bio-potentials because their polarisation is very small.

Equivalent circuit of an electrode

                   Rd
              +---[  ]---+
  o---[Rs]----+          +----(+ Ehc -)----o  to amplifier
  skin/       +----||----+
  electrolyte      Cd
                (Rd parallel Cd)

Ehc = half-cell potential (series DC source); Rd and Cd = resistance and capacitance of the double layer (polarisation impedance), connected in parallel; Rs = series resistance of the electrolyte and the leads.

Equivalent circuit of a transducer

  Thevenin form:   [Vs]--[Zs]----o--------> to amplifier input
                                  |  Zin
                                 gnd

A transducer acts as a signal source Vs with a source impedance Zs (resistive, capacitive or inductive). The amplifier input impedance must be much greater than Zs to avoid loading.

Transducer in ultrasonic blood flow meter

A piezoelectric crystal transducer (PZT or quartz) is used. As a transmitter it converts electrical energy into ultrasonic waves, and as a receiver it converts the returning echoes back into electrical signals.

Function (Doppler flowmeter)

 [Master oscillator 5-10 MHz] -> [RF amp] -> (Tx crystal)
                    |                           ) beam
                    |                           v
                    |                    skin ===== vessel (blood, v)
                    |                           ^ echo
                    v                           (
 [Demodulator] <- [RF amp] <------------------(Rx crystal)
        |
 [Audio amp] -> speaker / recorder (flow)

The transmitted beam, at angle θ to the vessel, is reflected by the moving red cells with a Doppler shift:

fd = 2 f0 v cos θ / c

where f0 is the transmitted frequency, v the blood velocity and c the speed of sound in tissue (about 1540 m/s). The receiver mixes the echo with the oscillator signal, giving fd (typically 1 to 15 kHz, which is audible). fd is proportional to velocity, and flow Q = v × area. The direction of flow can be found with a quadrature detector.