Week 3 Physics

Amplitude verse Frequency

Amplitude refers to the maximum displacement of particles in the medium through which the sound wave is traveling, affecting the perceived loudness, while frequency indicates the number of oscillations (vibrations) of the wave per second, measured in Hertz (Hz), which influences the pitch of the sound.

Relationship between Power & Amplitude

Power is directly related to the square of the amplitude; as the amplitude increases, the power transmitted by the sound wave also increases exponentially.

Example of non-linear relationship

Relationship Between Amplitude, Intensity, and Power

Power is proportional to the square of amplitude:

P ower∞Amplitude2

Intensity = Power/Area

Doubling amplitude increases power by a factor of four and intensity by a factor of four also, assuming constant area.

Attenuation in Ultrasound

Loss of sound energy as it travels through tissue

Measured in units of Decibels (dB).

Needs to be compensated by the diagnostic instrument as the sound travel.

exponential and non-linear

Factors influencing attenuation

Tissue type (density and composition)

Frequency of the ultrasound (higher frequencies attenuate more).

Types of attenuation

Absorption, reflection, scattering and refraction

Absorption

Refers to the conversion of sound energy into other forms of energy, often thermal.

Tissue types absorb differently: fat, muscle, and bone exhibit varying absorption rates.

Reflection

Sound bouncing off a boundary between two different media

Occurs at an interface between 2 dissimilar mediums

Each has an acoustic impedance value (Z values)

Scattering

Dispersal of sound energy in various directions, important for imaging

Refraction

Bending of sound waves when entering different mediums i.e. change in direction of sound when it crosses a boundary, leading to artifacts in imaging such as lateral position artifact and edge shadowing

Time gain compensation and attenuation

Without time gain compensation, tissue attenuation causes gradual loss of display of deeper tissues

By applying increasing amplification or gain to the backscattered signal to compensate for this attenuation a uniform echo return can be generated, allowing for a clearer image of the deeper tissues that may otherwise be obscured by the effects of sound wave scattering and absorption.

Factors affecting attenuation:

Frequency of the sound beam.

Type of medium through which sound is traveling.

Distance the sound has traveled.

Attenuation coefficient

Attenuation = a x f (MHz) x L (cm)

Depth and Attenuation

As imaging depth increases:

The length path of the ultrasound pulse increases, thereby increasing attenuation.

For soft tissue, there is an increase in attenuation of 0.5 dB/cm for every MHz of frequency used.

Reflection and Transmission

The extent of sound energy reflection depends on the difference in acoustic impedance between two adjacent media:

Large difference in = significant reflection of energy.

If Z2 >> Z1, near-complete reflection occurs.

Minor differences allow for continued sound propagation

Percent Reflection and Transmission

% Reflection and % transmission at a boundary interface can be measured

Total reflection and transmission at an interface equals 100%:This means that

the sum of the percent reflection and percent transmission must always add up

to 100%, indicating that all incident acoustic

The brightness of structures on ultrasound images depends on reflection strength

Larger acoustic impedance differences result in hyper-echoic interfaces (bright images).

Smaller differences in result in less echogenic interfaces (dimmer images).

Anechoic structures (e.g., fluid-filled areas) present no reflection when Z1 = Z2

Small differences in Z = homogenous

Larger differences in Z = heterogenous

Importance of Ultrasound Gel

Significant acoustic impedance mismatch in air and soft tissue

Minimize the reflection of ultrasound waves at the transducer/air interface to improve transmission through the body.

Reflection at the metal/air interface is significant (>99.998%); coupling with gel ensures effective sound transmission into the body.

Reflection types

Specular Reflection

Diffuse Reflection

Scattering

Wave Interference

Rayleigh Scattering

Specular Reflection

Mirror-like reflections from large, smooth, and flat structures.

Specular Reflection Characteristics

Produces bright echoes, especially at perpendicular incidence

Frequency independent

Highly angle dependent

Diffuse reflection characteristics

Occurs from rough surfaces

Reflects sound in many directions

Typically has a low echo amplitude

Diffuse vs specular reflection

Specular: one direction, strong echoes

Diffuse: many directions, weaker echoes

Scattering

Occurs when the surface of a reflector is rough and similar or smaller in comparison to the sound wavelength.

Scattering characteristics

Angle independent

Produces low echo amplitude

Contributes to the echotexture of organs

More common than specular reflections

Frequency dependent

Creates a speckle pattern referred to as "tissue textur

Speckle

Form of acoustic noise resulting from interference of echoes

Types of Interference

Constructive Interference:

Occurs when two similar waves arrive nearly simultaneously, resulting in a higher amplitude echo.

Destructive Interference:

Two similar echoes with different arrival times cancel each other, resulting in a lower or nearly zero amplitude echo.

Speckle effects on images

Contribute to image texture and noise in ultrasound imaging

Rayleigh Scattering

Refers to scattering that occurs when reflecting structures are very small relative to the wavelength.

Rayleigh Scattering characteristics

Often occurs with red blood cells (RBCs) because the diameter of RBCs are small in comparison to the wavelength of diagnostic ultrasound

Scatter is more significant with higher frequencies (degree of Rayleigh scattering α f4 )

Angle independent but frequency dependent

Rouleaux

Clumping of RBCs occurs at slow speeds

Clumps producer stronger reflections compared to individual RBCs

Echo strength varies based on

Change in acoustic impedance (Z)

Size of the reflector

Smoothness of the reflector

Interference type

Important parameters for refraction

Incident Wave: The wave coming toward the boundary.

Reflected Wave: The wave that bounces back from the boundary.

Transmitted Wave: The wave that continues into the second medium

Oblique Incidence

Direction of travel of the incident sound wave is not perpendicular to the interface of two media.

Undesirable effects may occur where reflected sound travels off in a different direction.

Snell’s Law

Governing principle that describes refraction.

It determines how much the wave bends based on the angle of incidence and speeds in the two media.

Conditions for refraction

1. The angle of incidence is oblique (i.e., not perpendicular).

2. There must be differing propagation speeds in each medium

Types of Artifacts from Refraction

Lateral Position Artifact:

Incorrect positioning of structures due to bending of sound waves.

Edge Shadowing:

Shadowing effects at the edges of structures due to refraction.

Double Aorta Artifact:

Misinterpretation of anatomy resulting from sound waves bending at oblique

angles.

Factors Influencing Refraction

Angle of Incidence: Transition from 0° (perpendicular) to critical angles.

Speed of Sound: Different propagation speeds lead to different bending outcomes:

Slower medium: Sound refracts towards the vertical.

Faster medium: Sound refracts away from the vertical.

Critical Angle and No Refraction

If the angle of incidence exceeds the critical angle, refraction cannot occur, and reflection is the only outcome.

Conditions for no refraction:

Beam is perpendicular: .

No change in propagation velocity between the media: Ci = Ct.

Distance Determination Process

1. Time Tracking: The ultrasound system tracks echo return time.

2. Range Equation:

Distance = Time x Velocity

Corrected for round-trip time to provide accurate measurements.

Complete Range Equation

Pulse round trip (us) = 2 x Distance (mm) / Propagation speed (mm/us)