OCR Specification focus:
‘Define acoustic impedance Z = ρc for a medium and its significance at boundaries.’
Ultrasound imaging relies on predictable wave behaviour in different tissues, and understanding acoustic impedance is essential for explaining reflection, transmission, and signal quality in clinical practice.
Ultrasound imaging depends on how sound waves travel through different tissues, and acoustic impedance provides a vital measure of how strongly each medium resists wave motion at boundaries.
Acoustic Impedance in Medical Ultrasound
Acoustic impedance is a central property governing how ultrasound behaves when it meets a boundary between two media. It determines the balance between reflected and transmitted waves, strongly influencing image quality and diagnostic clarity in clinical practice.
Acoustic Impedance: The product of a medium’s density and the speed of sound within that medium; it quantifies how much the medium resists ultrasound propagation.
The value of the impedance depends on the physical characteristics of the tissue. For example, bone has a very high impedance because it is dense and transmits sound quickly, whereas air has a very low impedance due to its extremely small density and slow sound speed. These contrasting values explain why ultrasound cannot effectively image structures behind bone or air pockets without special techniques.
After defining acoustic impedance, it becomes essential to express it mathematically, as this reinforces its role in boundary interactions and imaging design.
EQUATION
—-----------------------------------------------------------------
Acoustic Impedance (Z) = ρc
Z = Acoustic impedance (kg m⁻² s⁻¹ or Rayl)
ρ = Density of the medium (kg m⁻³)
c = Speed of sound in the medium (m s⁻¹)
—-----------------------------------------------------------------
Acoustic impedance grows proportionally with both density and sound speed, meaning a medium with either higher density or higher propagation speed will offer more resistance to wave motion. This directly shapes how ultrasound interacts with tissue boundaries.
Influence of Impedance on Boundary Interactions
When an ultrasound wave passes from one medium to another, such as soft tissue to muscle or soft tissue to bone, the difference in their acoustic impedances determines the proportion of the wave that is reflected.
A small mismatch in impedance produces weak reflections, ideal for imaging deeper structures because most of the energy continues forward. A large mismatch, however, causes strong reflections that may obscure underlying detail.
Key factors influencing reflection at boundaries
The magnitude of impedance difference between two media
The angle of incidence, which in clinical scanning is typically kept close to perpendicular
The frequency of the ultrasound wave, which influences scattering but not impedance itself
When impedance mismatch is considerable—such as between tissue and air—the reflected intensity becomes so high that almost no useful signal enters the second medium. This is the reason why ultrasound gel is essential during scanning.
At a boundary between two media with different acoustic impedances, part of the ultrasound is reflected and part is transmitted.
A schematic diagram illustrating how an ultrasound beam enters a medium and is partially reflected at internal boundaries. The incident and reflected components demonstrate how impedance differences produce echoes. The German labelling is not required for OCR but supports conceptual understanding of reflection at boundaries. Source.
Acoustic Impedance and the Reflection Coefficient
The reflection coefficient describes the fraction of ultrasound intensity reflected at a boundary. It directly depends on the impedances of the two media involved.
EQUATION
—-----------------------------------------------------------------
Intensity Reflection Coefficient (R) = [(Z₂ − Z₁)/(Z₂ + Z₁)]²
R = Fraction of incident intensity reflected (dimensionless)
Z₁ = Acoustic impedance of first medium (Rayl)
Z₂ = Acoustic impedance of second medium (Rayl)
—-----------------------------------------------------------------
Even a modest difference between Z₁ and Z₂ can produce measurable reflections. Clinically, this property enables imaging: returning echoes are interpreted to form a representation of internal structures. However, excessive reflection—as in tissue–air interfaces—causes information loss, reinforcing the need for impedance matching strategies.
Normal tissue boundaries, such as those between fat, muscle, and organs, present small to moderate impedance differences. These allow enough reflection to generate meaningful images while allowing sufficient transmission for deeper penetration.
Practical Significance of Acoustic Impedance in Ultrasound Imaging
Acoustic impedance underpins nearly every stage of ultrasound imaging, from the design of transducers to clinical scanning techniques.
Key applications in imaging practice
Determining echo strength
Larger mismatch → stronger echoes
Smaller mismatch → weaker but usually diagnostically useful echoes
Optimising transducer materials
Piezoelectric crystals are chosen for specific impedance values to maximise energy transfer to tissue.
Improving boundary transmission
Good impedance matching between components enhances signal efficiency and improves image resolution.
Understanding how impedance affects reflection provides clinicians with insight into image artefacts, such as shadowing behind bone and bright echoes at tissue–gas boundaries.
On a B-mode scan, bright echoes mark boundaries where there is a large difference in acoustic impedance between adjacent tissues.
Abdominal ultrasound image showing the liver, gallbladder, and common bile duct. Bright edges indicate strong reflections caused by significant acoustic impedance differences at tissue boundaries. This real clinical scan includes anatomical detail beyond the syllabus but effectively demonstrates how impedance governs echo brightness. Source.
Acoustic Coupling and Impedance Matching in Clinical Use
Because air has very low acoustic impedance compared with skin, any air gaps between the transducer and the patient cause almost total reflection of the ultrasound waves. This would prevent any meaningful imaging signal from entering the body.
To avoid this problem, coupling gel is applied.
Functions of ultrasound gel
Eliminates air gaps between transducer and skin
Creates a continuous medium with impedance similar to soft tissue
Allows efficient transmission of ultrasound energy
Enhances the clarity and depth of resulting images
The gel therefore ensures that the acoustic impedance transition at the skin surface is small, enabling the majority of ultrasound energy to penetrate the body instead of being reflected.
Acoustic impedance remains one of the foundational concepts of ultrasound physics, enabling predictable interactions at tissue boundaries and forming the physical basis for reliable diagnostic images.
FAQ
The Rayl (kg m⁻² s⁻¹) represents how much resistance a medium provides to the passage of a sound wave. It combines both density and sound speed into a single measure of how “hard” it is for ultrasound to propagate.
A higher Rayl value means the medium strongly resists motion of the particles in the wave, producing stronger reflections at boundaries. Air has extremely low impedance, while bone has very high impedance, creating extreme contrasts in imaging.
Frequency does not alter the acoustic impedance value itself, but it changes how ultrasound interacts with boundaries.
Higher-frequency waves experience more scattering and may generate sharper, more detectable reflections, making impedance differences appear more pronounced. Lower frequencies penetrate further but may produce less clearly defined reflections, indirectly affecting the role impedance plays in image formation.
Soft tissues often differ just enough in density and speed of sound to produce small but detectable reflections.
Ultrasound machines are designed to amplify these weak echoes, allowing even minor impedance mismatches to create visible contrast between structures such as muscle, fat, and organs. Enhanced digital processing further emphasises these subtle differences.
Small increases in temperature generally decrease density while increasing sound speed.
Because acoustic impedance is the product of density and speed, the two effects partially cancel each other out. As a result, tissue impedance changes only marginally with physiological temperature variation, ensuring consistent imaging under normal conditions.
Bone has a very high impedance compared with surrounding soft tissue. This causes most of the ultrasound intensity to reflect at the bone surface.
Only a small fraction transmits through, and that transmitted portion is rapidly absorbed or scattered. The region beyond the bone receives little to no ultrasound energy, producing the characteristic acoustic shadow seen in scans.
Practice Questions
Question 1 (2 marks)
Define acoustic impedance and state its equation. Explain what physical properties of a medium determine its acoustic impedance.
Question 1 (2 marks)
• Acoustic impedance is the product of the density of a medium and the speed of sound in that medium (1)
• Correct equation: Z = ρc (1)
Question 2 (5 marks)
An ultrasound beam passes from soft tissue into muscle.
Explain how the difference in acoustic impedance between the two tissues affects:
(a) the proportion of the ultrasound intensity that is reflected at the boundary
(b) the transmitted intensity and the quality of the ultrasound image formed deeper in the body
(c) why coupling gel is necessary at the skin surface before scanning.
Question 2 (5 marks)
(a)
• Reflection occurs because the acoustic impedances of soft tissue and muscle are different (1)
• A larger difference in impedance leads to a higher proportion of reflected intensity (1)
(b)
• The remaining intensity is transmitted into the second tissue (muscle) (1)
• Smaller impedance mismatch means more transmission and better imaging of deeper structures; larger mismatch reduces transmitted intensity and may reduce image quality (1)
(c)
• Coupling gel removes air gaps between transducer and skin, preventing almost total reflection due to the large impedance difference between air and tissue (1)
