Ultrasound Physics: Key Concepts

RULE OF REFLECTION

TRANSMISSION

  • Reflection and scattering are responsible for returning echoes from an interface, but not all the sound energy is sent back.
  • In fact, a very small fraction of energy is sent back to the transducer, while most of the energy continues to move forward.
  • The transmit wave is the sound energy that continues beyond the interface.
  • Without a transmit wave, ultrasound wouldn’t be useful.
  • If the first reflector sent all the sound back, we wouldn’t be able to see into the body.
  • The transmitted wave weakens over distance traveled because of attenuation.

REFRACTION

  • As sound moves from one type of tissue into another, there is the potential for refraction.
  • Refraction is defined as a change in direction of transmission as sound travels into a new medium.
  • Refraction does not always occur; it depends on the tissue the sound is traveling from and into.
  • If the propagation speeds are different and the wave strikes at an angle to the surface, then refraction will occur.
  • Refraction can cause artifacts where anatomy is duplicated because the redirected sound can still interact with reflectors that make it back to the transducer.

IMPEDANCE

  • The reflections produced as sound moves from one medium to another form the basis for ultrasonic imaging.
  • Additionally, transmission is critical to ultrasound’s ability to image structures located deep within the body.
  • Acoustic impedance is a very important tissue property that influences the amount of reflection.
  • Impedance is a characteristic of the medium only. It is not measured; it is calculated.
  • Units: Rayls, often represented by the letter "Z".
  • Typical values range from 1,250,000 to 1,750,000 rayls (1.25–1.75 Mrayls).
  • The reflection of an ultrasound wave depends on the difference in the acoustic impedances at the boundary between the two media.

IMPEDANCE FORMULA

  • The formula for impedance is given by:
    Z=density (kg/m3)×propagation speed (m/s)Z = \text{density (kg/m}^3) \times \text{propagation speed (m/s)}
  • Example:
    • Two media, A & B, have the same propagation speed.
    • Medium A's density is 10% higher than medium B's.
    • Therefore, medium A's impedance is 10% higher than medium B's.
  • An increased density in a medium results in more resistance to sound transmission, and similarly, increased propagation speeds also contribute to greater resistance.
  • Impedance is determined by the physical characteristics of the medium.

ANGLES & INCIDENCES

  • A sound pulse strikes many tissue interfaces as it propagates through soft tissue.
  • The angle at which the wave strikes the boundary determines the behavior of the pulse.

Types of Angles:

  • ACUTE: less than 90°
  • RIGHT: exactly 90°
  • OBTUSE: greater than 90°

Definitions:

  • Right Angle:
    • An angle measuring exactly 90°, created between two lines that are perpendicular.
  • Incidence Angle:
    • The angle at which sound strikes a boundary.
  • Normal Incidence:
    • The angle of the sound beam striking the boundary at a right angle, also known as perpendicular incidence (90° incidence).
  • Oblique Incidence:
    • Occurs when the incident sound beam strikes the boundary at any angle other than 90°.

TERMS TO KNOW

  • Incidence Angle:
    • The angle that the beam strikes the boundary, related to an imaginary perpendicular line.
  • Reflection Angle:
    • The angle that the beam leaves the boundary, related to an imaginary perpendicular line.
  • Transmission Angle:
    • The angle that the sound beam propagates, again related to an imaginary perpendicular line.
  • Medium 1 (Z1 or Speed 1):
    • Describes the medium from which the sound is traveling.
  • Medium 2 (Z2 or Speed 2):
    • Describes the medium to which the sound is entering.
  • Boundary:
    • The interface between two different media.
  • THETA (ѳ):
    • Represents the angles associated with reflections and transmissions.

INCIDENT, REFLECTED & TRANSMITTED SOUND

  • Incident intensity:
    • The intensity of the sound wave just before striking a boundary.
  • Reflected intensity:
    • The portion of the incident intensity that changes direction and returns back after striking a boundary.
  • Transmitted intensity:
    • The portion of incident intensity that continues in the same general direction after striking a boundary.
  • Units for all intensities:
    • W/cm²
  • Energy conservation relation:
    • Incident intensity=Reflected intensity+Transmitted intensity\text{Incident intensity} = \text{Reflected intensity} + \text{Transmitted intensity}
  • There exists a principle of conservation of energy at a boundary, where energy cannot be created or destroyed.

INTENSITY REFLECTION COEFFICIENT (IRC)

  • Intensity Reflection Coefficient (IRC):
    • The percentage of ultrasound intensity that is bounced back when the sound beam passes from one medium to another.
  • Intensity Transmission Coefficient (ITC):
    • The percentage of ultrasound intensity that is allowed to pass through when the beam reaches an interface or boundary between two media.
  • Noteworthy point:
    • Coefficients and factors are usually unitless (percentages).
  • Typical Values:
    • Both IRC and ITC are unitless and range from 0% to 100% or 0 to 1.0.

INTENSITY REFLECTION COEFFICIENT (CONTINUED)

  • At the boundary between two media:
    • If IRC and ITC are added, the sum must equal 100%.
    • If reflected and transmitted intensities are added, they must equal the incident intensity.
  • Summary of Energy Conservation at a Boundary:
    • Typically, in soft tissue, only 1% or less of the incident ultrasound energy is reflected at a boundary between two soft tissues.
    • A greater percentage of the wave is reflected when sound strikes a boundary such as soft tissue and bone or soft tissue and air.
  • Units and Reporting:
    • Intensities are reported in W/cm².
    • Coefficients are reported without units as percentages.

RULES TO REMEMBER

  • RULE # 1: Energy cannot be created or destroyed.
    • Applies to intensities and coefficients for both normal and oblique incidence.
    • Incident Intensity=Reflected Intensity+Transmitted Intensity\text{Incident Intensity} = \text{Reflected Intensity} + \text{Transmitted Intensity}
    • 100%=IRC %+ITC %100\% = \text{IRC \%} + \text{ITC \%}
  • RULE #2:
    • With normal incidence, no reflection occurs if $Z1 = Z2$.
    • There must be a difference in impedances at 90°.
    • Small mismatched impedances create small reflections, while huge mismatched impedances create huge reflections.
  • RULE #3:
    • With normal incidence, 100% transmission will occur if $Z1 = Z2$.
    • This restates Rule #2.
    • Since there is no reflection, all the sound must keep traveling due to Rule #1.
  • RULE #4:
    • Reflection & Transmission with oblique incidence cannot be predicted.
    • There is uncertainty as to whether sound will reflect, transmit, or both at any given interface with oblique incidence.
  • RULE #5:
    • With oblique incidence, the reflection angle equals the incident angle.
    • No matter how the sound beam enters the boundary, it will exit at the same angle.
  • RULE #6:
    • For refraction to occur, the incidence must be oblique, and there must be two different propagation speeds.
    • If these criteria are met and transmission occurs, the transmission wave will not travel in the same direction as the incident wave.

PHYSICS OF NORMAL INCIDENCE

  • When a sound beam comes to an interface with normal incidence, it is perpendicular or 90 degrees to the boundary.
  • For reflection to occur, the impedances of medium 1 and medium 2 must differ.
  • The proportion of energy that is reflected versus transmitted is based on the impedances of the media:
    • Same impedance = no reflection
    • Small mismatch = small reflection
    • Large mismatch = large reflection

REFLECTION NORMAL INCIDENCE

  • Reflection only occurs if the two media at the boundary have different acoustic impedances, and a sound beam strikes a tissue boundary at 90°.
  • No reflection occurs if the impedances of the two media are identical.
  • A small reflection occurs with slightly different impedances, while a large reflection occurs with substantially different impedances.
  • The percentage of the incident beam reflected is related to the differences in impedances of the tissues.
  • Intensity Reflection Coefficient (%):
    • $Z1$ and $Z2$ refer to the impedances of the different media through which the sound wave is propagating.
    • Medium 1 is where the sound is currently, and medium 2 is where the sound is entering.
    • Greater impedance differences between two media lead to greater IRC and greater reflection.

TRANSMISSION WITH NORMAL INCIDENCE

  • Questions relating to reflection imply that whatever remains after transmission must be reflected.
  • Reflective transmission illustrates conservation of energy at the boundary.
  • Energy Relation Example:
    • Incident Intensity=Reflected Intensity+Transmitted Intensity\text{Incident Intensity} = \text{Reflected Intensity} + \text{Transmitted Intensity}
    • If:
    • Incident intensity = 60 mW/cm²