Electromagnetic vs Sound waves

• EM/Transverse wave can travel in vacuum at a constant velocity.

• Mechanical energy/longitudinal wave requires a medium with variable speed/wavelength

Sound = mechanical energy that propagates through a continuous, elastic medium by the compression and rarefaction of the units in that medium. Speed of a sound wave is purely determined by the medium that it travels in. Dependent on a medium. Unlike light which can propagate continuously in a vacuum at a constant speed. 

• We cannot control speed of soundwave but we can control the frequency. Independent of this the wave will travel at a set speed depending on the medium it travels in. Wavelength is the compensation mechanism that links the set frequency and the predetermined speed of sound in a particular tissue. 

• Plot with x axis representing normal value of tissue. 

• Compression: regions of high localized pressures

• Rarefaction: regions of low localized pressures. 

Speed (c) = frequency (f) x wavelength (w)

• Speed of sound changes depending on the medium that the soundwave is traveling. Certain material properties determine how fast sound travels through it. If medium changes, frequency and wavelength are not coupled.

• Frequency of sound does NOT change. This is what we set/determine. # of cycles in 1 sec measured in Hrz. 

  • Audible sound 20 Hz-20 kHz; US > 20kHz, Dx US >2-20 Mhz

• Wavelength: links frequency and speed. Distance b/n 1 amplitude of compression/rarefaction to the next.

Period (T) = 1 / f

• Amount of time for 1 cycle of a wave to pass a specific point; measured in units of time. 

What inherent properties of a tissue determine the speed of sound?

• c = sqrt (elastic property / inertial property)

  • Elastic property (bulk modulus): tissue stiffness / resistance to compression / ability to move to transfer energy and return to normal. 

    • How readily do units of the material return to their resting state? 

    • The stiffer the tissue, the less compressible the tissue is, the higher the bulk modulus and the faster sound travels. 

    • Contributes the most to ascoustic impedance.

  • Inertial property (density): amount of force required to move units within tissue, represented by density of tissue

    • Density is how tightly packed particles are in medium. the tighter they are the slower sound travels. 

    • The more tightly packed the material is the more force/inertia has to propagate energy through the tissue.  

    • The less dense a material, the faster sound propagates through.  

PRESSURE & INTENSITY

• Pascal (Pa) = local pressure changes in tissue, deflection from baseline pressure of tissue (x axis); amplitude of soundwave; important for calculating power of US.

• Power (W) is proportional to pressure ^2

  • If we double the amplitude, we quadruple the power

• Intensity = Power (W) / Area (cm^2)

  • Difficult to calculate the exact intensity at region of tissues. Use relative decible scale to compare intensities of different regions to one another. dB describe the change in intensity.

  • A change in 3 dB describes a doubling of intensity; a 10 dB increase results in a ten fold increase in intensity

ST attenuation = f x 0.5(dB/cm) / Mhz

• Attenuation is proportional to f; higher f the more attenuation

There are multiple elements inside of the transducer that create their own US waves. Each element can be in or out of phase which each other resulting in interference. 

US beam has varying intensities in cross section; middle of US beam has highest intensity due to constructive interference. Outer edges have last intensity. As beam converges, area decreases causing intensity to increase.

Near field & far field; US beam has varying intensities if cut in cross-section. 

• Deconstructive interference: when waves are out of phase; reduction in intensity

• Constructive intereference: waves are in phase; increased intensity. THis is why intensity is highest in the center of the beam.

Spatial and temporal intensities can be used to determine bioeffects.

• US beam has varying intensities if we cut in cross section

• Middle of beam has most intensity due to constructive interference. Outer edges have least intensity. 

• As area gets smaller, intensity of beam increases

Spatial intensity: Cross sectional view plotted on graph: 

• Y axis, intensity change

• x axis is area of beam.

• Spatial peak intensity - maximal intensity; center of beam

• Spatial avg intensity - all intensities of beam; avg of beam.

Temporal peak: used for bioeffects

• Pulse avg: avg intensity of pulse

Types of US waves

• Continuous: transmit time only; leaves no time to listen to echoes bouncing back

• Pulse echo: transmit & receive time; transmits pulse wave into tissue and wait for reflections from tissue boundaries. 

Differences in tissue acoustic impedance determines how much echo is transmitted through to the next boundary and how much is reflected back.

Range equation: T = 2D/c; Tc/2 = D

• US uses this equation to plot echoes on screen. 

  • The time taken for echoes to come back can determine the distance that tissue is at.

• Depth (D) = distance of echo to tissue interface.

• Avg speed of sound for soft tissue: 1540 m/s

US fires off sequential lines of US pulses, waits for echoes to return, plots tissue boundaries distance based on time it took to return to probe. For each line, multiple pulses are sent. Grayscale values will be assigned to the tissue boundaries based on intensity of the echo returning to the machine.

Tissue boundaries with high differences in acoustic impedance will appear bright.

5 parameters to describe pulse echo that changes with depth.

(1) Pulse duration (PD): # cycles x period or # cycles / f

• • The transmit time; Time taken for entire pulse to be emitted from the machine. 

  • Fixed according to frequency; We can only change the receive time; we cannot repeat next pulse until echoes return to probe to prevent interference. 

    • To image superficial structures, decrease receive time. 

    • The deeper we want to scan, the larger the receive time must be. 

  • When we set the depth on US, we are changing the receive time, which will change 3 separate factors.

(2) Spatial pulse length (SPL): # cycles x wavelength of single wave

• • Length of pulse as it moves through space.

  • Distance from start of pulse to end of pulse.

  • Dependent on f and wavelength of wave.

(3) Pulse repetition period (PRP)

• Time between start of one pulse and the start of the next; transmit time + receive time. 

  • Pulse duration (transmit time) cannot be changed

• As we image shallower depths we can reduce our receive time and thus PRP. 

• PRP is inversely proportional to PRF

(4) Pulse repetition frequency (PRF)

• # of pulses that we can fit in within 1 sec. 

• Different from frequency of wave (# waves of 1 cycle passing a point in a set period of time)

• Relationship b/n PRP and PRF is like a seesaw

  • As PRP increases we can image at further depth bc we have more receive time.

(5) Duty factor (DF): PD / PRP

• • Determines the % of time the US is transmitting pulse compared to entire time of exam

  • Determines intensity that patient is receiving in a given exam. 

  • Of that exam time, how long are we transmitting wave compared to how long we are listening?

  • During listening period, we are not imparting any power into the patient. Just passively waiting for echoes to return.

• Tissue boundaries are where interactions occur. Acoustic impedance is what determines the interaction that occurs.

• Reflection: Complete, Partial, Specular, Nonspecular

• Refraction: US wave hits at an angle

• Scattering: when US wave interacts with units in tissue that are smaller than incidence wave, loss of energy with small sound waves produced in all directions. 

• Acoustic impedance (Z) = pc

  • Determines interactions at tissue boundaries. High Z is stiff/resistant to compression.

  • Inherent property that is specific to a specific tissue type. 

  • Calculated by product of tissue density and speed of sound within that tissue. The bulk modulus accounts for the wide difference in Z across tissues.

  • When US pulse interacts with the tissue boundary,  it is the difference b/n acoustic impedance that will determine how much US wave is transmitted through boundary or how much is reflected back as echo.

  • At tissue boundary, Z1 vs Z2 is compared and if there is a large difference there is more reflection.

  • Amount of reflection is determined by the difference between 2 tissue's Z

• How much will be reflected (R) vs transmitted (T)?

  • R = (Z2-Z1 / Z1+Z2)^2

    • Only for perpendicular reflectors

    • Bigger difference b/n Z, the more reflected

  • T = 1 - R

• Perpendicular:

  • When incident US beam comes into contact with boundary that is perpendicular, large, and smooth.

  • Think of like flat mirror. 

• Specular:

  • Beam comes at an angle to large flat surface. Angle from perpendicular line to reflector is the incidence angle.

  • If surface is large and flat, the reflection angle will be equal to the incidence angle. 

• Nonspecular / diffuse:

  • Incident US beam comes into not perfectly smooth surface causing beam to reflect off in multiple different directions.

  • Some come back to detector but wont have a strong signal like perpendicular.

• Refraction only happens at a nonperpendicular angle

  • Incidence angle (i) = reflected angle (r) bc they are the same tissue.

  • Transmittance angle (t) occurs when pulse is transmitted into different tissues it is either larger or smaller than incidence angle.

• Angle change is determined by the difference in speed of sound (c) between tissues (C2 vs C1). 

  • If C2 < C1 (slows down) -> reduced t

  • If C2 = C1 (same) -> t = i

  • If C2 > C1 (speeds up) -> increased t

• Speed change determines angle change. Amount of energy transferred is determined by differences in acoustic impedance values.

• f doesn't change as wave travels through tissues. Wavelength changes to account for change in speed of sound. 

  • If speed of sound (tissue bulk modulus & density) is faster, the wavelength must increase -> increased t angle

  • If speed of sound is slower, wavelength will decrease -> decreased t angle

• Scatter: 

  • Occurs when US wave comes into contact with unit of object that is smaller than wavelength.  Thus, if there are smaller units in the medium than the incident wavelength then we get scatter. 

  • Vast majority of the wave will pass through unaffected but those that interact with the small units will let off small US waves in all different directions losing beam intensity. 

  • This is contributor to attenuation and to a tissues echogenicity.

    • Unlike x-ray, scatter patterns provide us some value and can determine echotexture of organ. 

      • More scatter = hyperechoic. 

      • Less scatter = hypoechoic

  • The more dense the units are, the more scatter. wider the radius of units, the more scatter. If we change f of incident us beam, the higher frequency, the higher change that US beam will interact with small units.

• Attenuation: loss of US intensity / amplitude as it travels through tissue. Lose amplitude of wave. Lose intensity 2/2 

  • Scattering 

    • Depends on frequency of incident wave

    • depth 

    • tissue 

  • Loss of heat

• Low frequency sounds are not as attenuated as quickly as high frequency

  • Cant hear lyrics but can

• Intensity loss is logarithmic

• Dynamic range