Overview
This lecture explores how differences in acoustic impedance between tissues cause the reflection and transmission of ultrasound waves. It focuses on three main types of reflection—perpendicular, specular, and non-specular (diffuse)—and explains how to calculate the proportion of ultrasound energy that is reflected or transmitted at tissue boundaries. The lecture also discusses practical examples and introduces the concept of refraction for future study.
Acoustic Impedance
- Definition: Acoustic impedance is the product of a tissue’s density and the speed of sound through that tissue.
- Determinants: The bulk modulus (stiffness or resistance to compression) of a tissue strongly influences its acoustic impedance, as it affects the speed of sound within the tissue.
- Role in Ultrasound: The difference in acoustic impedance between two tissues at a boundary determines how much of the incident ultrasound beam is reflected back toward the ultrasound machine and how much is transmitted through the boundary.
Types of Reflection
- Perpendicular Reflection
- Occurs when the ultrasound beam strikes a large, smooth tissue boundary at a right angle (perpendicular to the surface).
- The amount of reflection depends on the difference in acoustic impedance between the two tissues.
- If the difference is very large (e.g., between soft tissue and air), almost all the ultrasound is reflected, resulting in complete reflection and little to no transmission.
- Example: The capsule of the kidney, surrounded by fat, forms a large, smooth, perpendicular boundary with different acoustic impedances, causing some ultrasound to be reflected and some transmitted.
- Specular Reflection
- Happens when the ultrasound beam hits a large, flat surface at an angle (not perpendicular).
- The angle of reflection equals the angle of incidence (measured from the perpendicular to the surface).
- Reflected echoes from specular reflectors may not return to the ultrasound probe, as they are directed away from the machine.
- The ultrasound machine only detects echoes that return directly to the probe, so specular reflection can result in a loss of signal.
- Non-Specular (Diffuse) Reflection
- Occurs when the ultrasound beam encounters a boundary that is not perfectly smooth (rough or irregular surfaces).
- The incident beam is scattered in multiple directions, so some echoes return to the probe, but the signal is weaker and less crisp compared to perpendicular reflection.
- Analogy: Like looking at your reflection in a broken or rough mirror—some image is visible, but it is scattered and less clear.
Reflection and Transmission Calculations
- Relationship to Acoustic Impedance
- The greater the difference in acoustic impedance between two tissues, the more ultrasound energy is reflected at the boundary.
- If the acoustic impedances are identical, all the ultrasound energy is transmitted with no reflection.
- As the difference increases, a larger proportion of the incident ultrasound is reflected.
- Reflection Coefficient (R) Formula
- Used to calculate the fraction of incident ultrasound energy reflected at a tissue boundary:
- ( R = \left( \frac{Z_2 - Z_1}{Z_2 + Z_1} \right)^2 )
- Where ( Z_1 ) and ( Z_2 ) are the acoustic impedances of the two tissues.
- The value of R is always less than or equal to 1, as the difference between the two impedances cannot exceed their sum.
- The fraction of energy transmitted through the boundary is ( 1 - R ).
- This formula applies only to perpendicular reflection at large, smooth tissue boundaries.
- Energy Conservation
- The total energy of the incident ultrasound beam is conserved: the sum of the reflected and transmitted fractions equals 1.
Practical Examples
- Muscle-Bone Boundary
- Acoustic impedance values: muscle = 1.71, bone = 7.8 (in Rayls).
- Using the formula: ( R = \left( \frac{7.8 - 1.71}{7.8 + 1.71} \right)^2 = \left( \frac{6.09}{9.51} \right)^2 \approx 0.41 )
- About 41% of the incident ultrasound energy is reflected, and 59% is transmitted.
- Despite this, bone is highly attenuating, so much of the transmitted ultrasound is lost due to scattering and heat production, not just reflection.
- Tissue-Air Boundary
- Air has an extremely low acoustic impedance compared to soft tissue.
- Nearly all the ultrasound is reflected at this boundary (reflection value in the high 99%), with almost no transmission.
- This is why imaging into the lungs is not possible with ultrasound—almost all the energy is reflected at the tissue-air interface.
- Bone and Air Shadows
- Both bone and air create acoustic shadows on ultrasound images.
- For bone, this is due to both high reflection (from impedance difference) and high attenuation (from scattering and absorption).
- For air, the shadow is almost entirely due to reflection, as very little energy is transmitted.
Key Terms & Definitions
- Acoustic Impedance: The product of tissue density and the speed of sound; determines how much ultrasound is reflected or transmitted at a boundary.
- Bulk Modulus: A measure of tissue stiffness or resistance to compression; influences the speed of sound and thus acoustic impedance.
- Perpendicular Reflection: Reflection of ultrasound from a boundary that is perpendicular to the incident beam; produces strong echoes if impedance difference is large.
- Specular Reflection: Reflection from a large, flat surface at an angle; reflected echoes may not return to the probe.
- Non-Specular (Diffuse) Reflection: Reflection from a rough or irregular surface; scatters echoes in multiple directions, resulting in weaker signals.
- Reflection Coefficient (R): The proportion of incident ultrasound energy reflected at a boundary, calculated using the difference and sum of acoustic impedances.
Action Items / Next Steps
- Review and practice using the reflection coefficient formula with different tissue impedance values to understand how reflection and transmission change at various boundaries.
- Understand the limitations of the formula (applies only to perpendicular, smooth boundaries).
- Prepare for the next lecture, which will cover the concept of refraction—how ultrasound waves change direction when passing through tissue boundaries at an angle due to differences in the speed of sound.