Interaction of Sound and Medium & Range Equation

Flashcards testing core concepts of ultrasound interaction with media and the range equation, including attenuation, decibels, impedance, reflection, refraction, diffraction, and range calculation rules.

How is acoustic attenuation defined in ultrasound physics?

Progressive weakening of sound as it travels through a medium, characterized by a decrease in amplitude, power, and intensity

What unit is used to measure attenuation, and how is it compensated for by an ultrasound system?

Measured in decibels ($\text{dB}$) and compensated for using Overall Gain and Time Gain Compensation (TGC or DGC)

What is the average attenuation coefficient for soft tissue?

$$0.5\,\text{dB/cm/MHz}$$

What is the formula used to calculate total attenuation in soft tissue?

$$\text{Total Attenuation (dB)} = \frac{1}{2} \times \text{frequency (MHz)} \times \text{Depth (cm)}$$

What is the total attenuation for a $10\,\text{MHz}$ transducer scanning a mass at a depth of $5\,\text{cm}$?

$$25\,\text{dB}$$

Which tissue has the highest attenuation coefficient?

Lung

Why are decibels considered a relative logarithmic notation rather than an absolute unit of measurement?

They report relative changes comparing a final intensity to an initial intensity based on logarithms, not absolute numbers

What relative intensity changes correspond to a $+3\,\text{dB}$ increase and a $+10\,\text{dB}$ increase?

$+3\,\text{dB}$ doubles the intensity ($2\times$), and $+10\,\text{dB}$ increases intensity ten times ($10\times$)

What relative intensity changes correspond to $-6\,\text{dB}$ and $-20\,\text{dB}$?

$-6\,\text{dB}$ reduces intensity to $\frac{1}{4}$ of original, and $-20\,\text{dB}$ reduces intensity to $\frac{1}{100}$ of original

What is Half Value Layer Thickness?

The depth in tissue where the original sound intensity is reduced to half ($-3\,\text{dB}$)

What are the three primary mechanisms of attenuation?

Absorption, Scattering, Reflection

What is the dominant factor contributing to attenuation in soft tissue, and into what energy form is sound converted?

Absorption; converted into heat energy and directly related to frequency

What is Rayleigh scattering, and how is its intensity related to frequency?

Omnidirectional scattering occurring when a reflector is much smaller than the wavelength; intensity is proportional to $f^4$

Describe the scattering phenomenon characterized by uniform redirection in all directions when striking a reflector much smaller than the wavelength.

Rayleigh scattering, which is omnidirectional and proportional to $f^4$

How does specular reflection differ from diffuse reflection (backscattering)?

occurs at smooth, large boundaries in one direction, while the other occurs at rough surfaces redirecting sound in many random directions

What type of acoustic reflection occurs at smooth, large boundaries relative to wavelength in a single direction?

Specular reflection

What is acoustic impedance ($Z$), what are its units, and how is it calculated?

Hindrance to sound travel in a medium; units are Rayls; calculated as $Z = \rho \times c$ (density $\times$ propagation speed)

Between which media interfaces do the strongest and weakest reflections occur?

Strongest occur between air/soft tissue ($99\%$); weakest occur between similar soft tissue interfaces like liver/kidney ($1\%$)

What formula is used to calculate the Intensity Reflection Coefficient (IRC\%) at normal incidence?

$$\text{IRC\%} = \left[\frac{Z_2 - Z_1}{Z_2 + Z_1}\right]^2 \times 100$$

What is the relationship between the Intensity Reflection Coefficient (IRC) and Intensity Transmission Coefficient (ITC)?

$$\text{IRC\%} + \text{ITC\%} = 100\%$$

What mathematical equation represents Snell's Law during oblique incidence?

$$\frac{c_2}{c_1} = \frac{\sin(\theta_2)}{\sin(\theta_1)}$$

According to Snell's Law, how does the transmission angle compare to the incident angle

If $c_2 > c_1$, then $\theta_2 > \theta_1$; if $c_2 < c_1$, then $\theta_2 < \theta_1$

What factor accounts for differing transmission angles relative to the incidence angle in Snell's Law?

Difference in propagation speed ($c_1$ vs $c_2$) between the two media

What is refraction, and what two conditions are required for it to occur?

Change in direction of sound crossing a boundary; requires oblique incidence and different propagation speeds in the two media

What is diffraction in ultrasound physics?

The spreading out of an ultrasound beam after passing through a small aperture

What is the 13 microsecond rule in soft tissue?

Every $13\,\mu\text{s}$ of go-return time means the reflector is located $1\,\text{cm}$ deeper in the body (round-trip distance of $2\,\text{cm}$)

What formula calculates the depth to a reflector based on go-return time?

$$\text{Depth (cm)} = \frac{\text{Go-return time } (\mu\text{s}) \times \text{speed (mm/}\mu\text{s})}{2}$$

If a sound pulse emitted from a transducer has a go-return time of $52\,\mu\text{s}$ in soft tissue, how deep is the reflector?

$4\,\text{cm}$ deep (calculated as $52\,\mu\text{s} \div 13\,\mu\text{s/cm}$)

How is minimum Pulse Repetition Period (PRP) calculated from imaging depth in soft tissue?

$$\text{Min. PRP } (\mu\text{s}) = \text{imaging depth (cm)} \times 13\,\mu\text{s/cm}$$

How is maximum Pulse Repetition Frequency (PRF) calculated from imaging depth in soft tissue?

$$\text{Max. PRF (Hz)} = \frac{77,000\,\text{cm/s}}{\text{Imaging depth (cm)}}$$