Medical imaging ultrasound

Piezo-electric crystal

• Generates e.m.f when shape changes

or

• changes shape when p.d. applied across

Piezo-electric effect

The production of an e.m.f. across a crystal by putting the crystal under stress

• applying p.d. causes it to change shape

How ultrasound is produced

• Varying electric p.d. (alternating voltage) applied to source (transducer)

• Causes it to wibrate (change shape) with frequency of applied p.d.

• Vibrations produce waves of same frequency

Pulse is sent into body, partially reflected pulse of ultrasound is received

Detecting ultrasound

• Varying stress/changing shape of crystal produces a varying e.m.f.

• To maximise, frequency of waves must match the resonant frequency of the crystal

  • Optimum size of crystal is half wavelength of ultrasound

Echo sounding, reflection of pulses

• Ultrasound waves directed into body

• Pass through various tissues, partially reflected at each boundary where speed changes

• Reflected waves are detected and used to construct internal image of the body

Acoustic impedance

The product of density of substance and speed of the ultrasound in the material

• Z = pc

Intensity reflection coefficient

I_r/I_o = (Z₁- Z₂)²/ (Z₁+ Z₂)²

• I_r/I_{o =} Fraction of the intesity of the beam that is reflected

Comparing acoustic impedance

Large change in acoustic impedance = large fraction of reflected intensity

• Bones show up well

• Difficult to see soft tissues

Impedance matching

• Use of gel to reduce intensity of unwanted, reflected ultrasound between two materials

  • For ultrasound on skin, without gel patient’s skin is in contact with air and 99.95% reflected before entering body

  • Use gel with impedance that matches skin

Attenuation of ultrasound

• Waves gradually absorbed

• I = I_oe^-ax

• ^{a is absorption coeffiicient, x is distance travelled through material}