717 Module 1

Physics principles of diagnostic ultrasound

Speed of sound

1540m/s

Frequency

Number of waves per second. Typically 2-20MHz.

Propagation speed equation

C = frequency x wavelength

Period

T = 1/f (time of one cycle or oscillation)

Sound waves

Longitudinal waves that consist of alternating regions of compression and rarefaction (areas of increased and decreased density), caused by vibrations of particles in a medium.

wavelength

Length of one cycle, typically 0.1-1mm

Acoustic impedance

Resistance to the movement of a wave.

Acoustic impedance equation

z = pc (tissue density (kg/m3) x propagation speed (m/s))

Attenuation equation

attenuation coefficient x L (distance in cm, x2 for round path) x frequency

What factors influence attenuation?

type of tissue, frequency and total distance travelled.

Relationship between depth and frequency

Inversely related. If frequency is double then the depth of penetration will be halved, vice versa. Therefore low frequencies should be used to scan deep regions.

Factors that influence reflection

Determined by the degree to which the acoustic impedances of the two tissues are different

Fraction reflected equation

R = reflected intensity/incident intensity = (Z2 - Z1)²/ (Z2 + Z1)

R = 1

When Z1 and Z2 are very different there is total reflection.

R = 0

When Z1 = Z2 there is total transmission.

Transmission coefficient

T = transmitted intensity/incident intensity = (4 x Z1 x Z2) / (Z2 + Z1)

Perpendicular incidence

when the ultrasound is incident on the interface at right angles (90 degrees). When incidence is not perpendicular the reflected ultrasound does not travel back to the transducer.

Scattered energy

Distributed in all directions. Generally weaker and therefore displayed as grey tones. Granular echo texture.

Refraction

Occurs when ultrasound passes through an interface between tissues with different propagation speeds. Causes the beam to change direction.

Snell’s law

Determines the amount of refraction. If sound enters a faster medium (higher c) → it bends away from the normal. If it enters a slower medium (lower c) → it bends toward the normal. If the difference between the two propagation speeds increases then the difference between the two angles also increases.

Snell’s law equation

Sin θincidence /c1 = Sin θtransmission /c2

What happens when the ultrasound is perpendicular to the incident and transmitted angles?

No deflection of the beam regardless of the propagation speeds.

Critical angle equation

sinθc​ = c2​/c1​​

Critical angle

When the propagation speed is higher in the second tissue. Angle of incidence at which the refracted ultrasound beam travels exactly along the boundary between two tissues (i.e., angle of refraction = 90°). No ultrasound transmitted.

What happens when the incident angle exceeds the critical angle?

Total reflection

What two mechanisms cause total reflection?

Very large differences in acoustic impedance.

When propagation speed is higher in the second tissue and the incident angle exceeds the critical angle.