Phy Ultrasound

Ultrasound Overview

• The goal is to investigate flow rate measurement techniques and examine the correlation between pressure drop, flow rate, fluid velocity, and ultrasound signal frequency.
• Sounds include audible, inaudible, unpleasant, pleasant, soft, loud, noise and music.
• Ultrasound (US) functions as a mechanical energy form that transmits through adjacent molecules through collisions.
• It is characterized by compressions and rarefactions, and acts as a longitudinal wave.
• Key properties: wavelength, frequency.

Waves

• Waves' two main types are electromagnetic and mechanical.
• Electromagnetic waves do not need a medium.
• Examples of electromagnetic waves are radio waves, microwaves, infrared, light, X-rays, ultraviolet, and gamma rays.
• Mechanical waves do require a medium.
• Transverse waves' particle vibrates perpendicular to the direction of wave propagation.
• Longitudinal waves' particle vibrates parallel/along to the direction of wave propagation.

Frequencies

• Infrasonic waves (infrasound) have frequencies below 20 Hz, are is inaudible to the human ear.
• Scientists use infrasound to detect earthquakes, volcanic eruptions, map rock, petroleum formations underground, and to study heart activity.
• The human audio spectrum relates to sounds audible to humans which falls between 20 Hz to 20,000 Hz.
• Ultrasonic waves (ultrasound) produce sound waves at frequencies higher than 20,000 Hz.
• It is inaudible because it occurs at frequencies outside the human hearing range.

Ultrasound vs. Ultrasonography

• Ultrasound refers to sound waves, typically with frequencies above the human audible range, exceeding 20,000 Hz.
• Ultrasonography refers using ultrasound waves to create images of internal body structures.

Characteristics of Ultrasound Waves

• Ultrasound waves, like all sound waves, are mechanical.
• It requires a medium for propagation.
• Ultrasound is inaudible, operating at high frequencies beyond 20 kHz.
• The wavelength of ultrasound waves has an inverse relationship with its frequency.
• Shorter wavelengths produce higher resolution for imaging, while longer wavelengths enable deeper penetration into materials or tissues.
• The medium affects how fast ultrasound waves travel.

Production of Ultrasonic Waves

• Ultrasonic generation comes from the piezoelectric effect, and starts with transducer converting energy into mechanical energy.
• Alternating voltage applied to a piezoelectric crystal creates compressive and tensile stresses that cause the crystal to oscillate.
• The piezoelectric effect produces a voltage by mechanical deformation of certain materials (piezoelectric crystals).
• Applying an alternating potential to a crystal changes its molecular configuration and dimensions.
• This configuration produces rapid, periodic changes in crystal shape to generate ultrasound waves.
• The piezoelectric effect is reversible, deforming the crystal when external voltage applies.
• Depending on the polarity, it is compressed or stretched, which results in electrical energy converting into mechanical energy.
• Materials that do not conduct electricity but support an electric field are called dielectrics.
• Well defined arrangement - crystal lattice
• it is possible by applying an alternating potential to a crystal its molecular configuration changes which equates to dimensions (shape) changing also.

Detection of Ultrasonic Waves

• This process works opposite of producing ultrasound waves.
• Vibrations change the arrangement of the molecules, causing a subsequent change in the crystal polarity, producing alternating electrical pulses.
• Alternating electrical signal source applies a periodically changing voltage to the piezo crystal.
• Crystal vibrations cause a potential difference (electrical signal) detectable by a voltmeter.

Ultrasound Interactions

• Acoustic impedance, expressed as z = ρ x vₛ, represents the resistance of tissue to an ultrasound beam.
• Variables affecting it includes the medium's density (ρ) in kg/m³ and sound speed (vₛ) in m/s.
• When sound waves move between two materials with differing acoustic impedances (Z1 and Z2), phenomena occur at their boundary.
• Part of the wave reflects back into the original medium, while part transmits into the second.
• The magnitude of reflection and transmission depends on the relative difference in acoustic impedance.
• Reflection coefficient shows the proportion of the wave's intensity reflected back into the first medium*.
• A larger difference between Z1 and Z2 results in greater reflection.
• Transmission coefficient indicates the wave's intensity transmitted into the second medium.

Acoustic Impedance Examples

• Similar acoustic impedance (Z1 and Z2) results in most sound energy transmitting into the second medium with minimal reflection.
• Different acoustic impedance (Z1 and Z2) results in a large portion of the sound energy reflecting back, so little passes through.
• Minimal reflection occurs when Z1 ≈ Z2, transmitting most of the sound wave.
• Ideal for imaging similar tissues like muscle, liver, or fat where impedance differences are small.
• Difference is small between muscle (Z ≈ 1.68 × 10⁶) and blood (Z ≈ 1.66 × 10⁶), most sound waves transmit, giving clear images with little reflection.
• Soft tissue (Z ≈ 1.63 × 10⁶) to bone (Z ≈ 6.22 × 10⁶) boundary results in large portion reflected at this boundary, and makes it hard to image structures behind the bone.
• Max resolution of an US image is defined by a wavelength
• The Acoustic impedance is the resistance experienced by the US beam as it passes through the tissues (tissue acoustic impedance characterizes the tissue).

The Role of Gel

• Gel eliminates air gaps between the transducer and skin for better ultrasound transmission, facilitating sound wave transmission, reducing signal loss and enhancing image quality.
• Air-tissue interfaces reflect all incidental ultrasound waves (does not allow the ultrasound waves to penetrate through the skin).
• By using gel the air between the probe and the skin is displaced, and reduces reflection from air-skin interface.
• Water-based to conduct sound well and remain non-reactive.
• Non-greasy for easy application and removal.
• Hypoallergenic to avoid skin irritation.
• Ultrasound gel mixes propylene glycol and water.

Image Spatial Resolution

• Reflection creates echoes.
• Reflection determines image spatial resolution.
• Higher resolution is achieved with:
  • measure of smallest interface size at which wave can reflect is limited by US wavelength
  • smaller US wavelength translates to smaller resolvable structure
• The magnitude of impedance determines the attenuation of the image.
• By determining Reflected fraction of the ultrasound waves is determined the difference in of the tissue type on both sides of the interface is known.
• Acoustic impedance* is measured in kg/m2*sec.

Refraction

• Refraction changes US wave direction, from one medium to another with differing impedances Z.
• From lower to higher impedance, waves propagate closer to the normal line (perpendicular to the interface).
• From higher to lower impedance, waves propagate away from the normal line.
• Refraction decreases both intensity of the echoes and resolution.

Scattering

• Ultrasound scatters when encountering small particles, bubbles, or irregularities in a medium like tissue or fluids.
• Scattering stems from differences in acoustic impedance between ultrasound waves and the materials.
• Smaller wavelengths produces more scattering.
• Smaller parts interface is the smaller the part of the interface that can be resolved.
• Small parts of an interface are regarded as a rough surface.
• Key factors influencing ultrasound scattering:
  • Particle size: Scattering is most effective when particles are as big or smalller than ultrasound wavelength.
  • Acoustic impedance: A material medium to another such as bone-to-tissue there is a contrast in how well the materials conduct sound. This contrast influences the sounds waves becoming reflected or transmitted.
  • Medium Homogeneity: changes in the density and consistency within a material including different densities which are a tumor or presence of cysts.
  • Frequency: increased frequency of ultrasound produces greater scatter which is enhanced detection for visualizing details in structure.

Attenuation

• Attenuation is the gradual reduction in a wave's intensity or strength (like sound, light, or electromagnetic waves) as it travels.
• Loss of intensity with distance is caused by
  • reflection
  • refraction
  • scattering
  • tissue absorption.
  • spreading of the beam which follows the inverse square law
• Ultrasound weakens/attenuates rapidly by the inverse square law from the transducer.
• Better visualization occurs with structures closer to the transducer.
• Transducers are adapted to get them close to the imaged structures.
• Absorption refers to the energy of a wave that is transferred to the material medium it is traveling. As a result the energy is converted into other forms or heat decreasing how intense the wave is.
• Refraction bends or changes direction of waves going from one medium to another when speeds vary.
• Scattering spreads waves in different directions among particles or irregularities within the medium. It limits the waves progression and lessens intensity upon reaching observation points.
• Reflection accounts energy as it hits of different mediums.

Half-Intensity Depth

• Half-intensity depth relates to the depth at which its original intensity will be absorbed.
• L1/2 = C / f represents this relationship, where C is a depends on of the medium and f is the US frequency.
• High-frequency ultrasound waves attenuate more than low-frequency.
• Low-frequency waves cannot resolve small body parts.

Measuring Depth

• Total traveled distance x and depth d can be calculated:
  • x = vₛ × t
  • d = (vₛ × t) / 2
  • vₛ = the speed of US wave in the medium
  • t = the time interval in which the wave travels over distance x
• Ultrasound machine determines depth by:
  • Detecting the intensity of echoes.
  • Determining the depth in the body at the interface of reflected ultrasound waves.
    • Average speed of ultrasound waves is known.
    • It has a timer which measures the time elapsed between generation and detection of the echo.

Image Reconstruction

• A-scan:: it does not give a clear spatial structure, but gives a signal against a one line path.
• B-Scan: It constitutes many A-scans.

Types of Ultrasound Images

• 2D: Greyscale, Cross-section of the body tissues, realtime - 30 fps
• 3D: Combination of 2D images
• 4D: Combination of 2D images, Dynamic review in time

Doppler Effect

• The Doppler Effect refers to the shift in wave frequency or wavelength perceived by an observer moving relative to wave source.
• Utilized in Doppler ultrasound to measure the movement of objects, especially blood flow.
• Sound wave reflects at an interface which either approaches or recedes.
• Echo is detected with the apparent change in its frequency, which is the doppler shift.
• Car produces a sound and is moving toward an observer that will reach at the observer with apparently higher velocity.
• if v = vₛ + v꜀, then, the apparent frequency
  • f' = f₀ + f₀ (v꜀/vₛ)

Measured With Ultrasound

• The speed of flowing fluids (blood flow).
• It measures moving objects (e.g., heart valves).
• Measurements in a way that arterial blood approaches, and venous blood recedes.

What Positive/Negative Doppler Shifts Show

• Positive Doppler shift: Blood flows toward the transducer.
  • Indicated via red in color Doppler ultrasound; increase in frequency allows calculating speed/direction of blood flow.
• Negative Doppler shift: Blood flows away from the transducer.
  • Indicated using blue in color Doppler ultrasound; decrease in frequency allows calculating speed/direction.

Dopplerography

• Dopplerography refers to imaging techniques utilizing the Doppler effect to visualize and measure fluid movement (like blood flow).
• This includes the Doppler Effect, Ultrasound Transducer, Color Coding.
  • Red in color indicates flow toward the transducer.
  • Blue in color indicates flow away from it.
• Applications: blood vessel/heart assessments, kidney blood flow, neurological applications.
• It can detect stenosis, a narrowing to due fatty deposits on the inner wall of the blood vessel. Blood flow rate, pressure show changes.

Bernoulli’s Principle and Venturi Effect

• Bernoulli Principle states that as fluid velocity increases, pressure exerted by the fluid decreases.
• Fast moving fluid generates low pressure.
• Slow moving fluid generates high pressure.
• A fast-flowing fluid reduces the pressure created by the fluid. Slow-flowing fluid increases the pressure created by the fluid.
  • P₁ + 1/2 ρυ₁² + pgh₁ = P₂ + 1/2 ρυ₂² + pgh₂

Poiseuille's Law

• This law describes viscous fluid flow through a cylindrical pipe that Quantifies flow rate relative to pressure differential. Volume Flowrate relates in the form π(Pressure difference)(radius)⁴/8(viscosity)(length).*

Applications of Ultrasound

• Ultrasound is useful to monitor the progress of a pregnancy, visualize the fetus within the womb, other forms of prenatal testing for birth defects
• Useful for cardiovascular studies to explore the structure of the heart and the circulatory system
• Useful in gynecological cases to help structure the uterus with it surroundingregions, detect tumors or cysts structure the or ovaries
• It can be a beneficial tool in doing prostate examinations, and breast exams to look at tumors or cysts.
• Abdominal examinations (structure of organs) and renal studies (Kidney image)
• It is useful for looking at Thyroid examinations, tumors, and cysts.
• Ophthalmologic examinations (visualizing the structures behind the retina, seeing past opaque obstacles) which include eye tumors retinal detachments foreign bodies hemorrhages
• Guidance during a surical. This includes tumor biopsies, drainage of cysts, and treatments for infertility.