Week 4 beam geometry

Ultrasound Beam

  • The ultrasound beam represents the area through which sound energy is emitted from the transducer.

  • The width of the beam changes with the distance from the transducer.

  • Intensity is not uniform across the beam.

  • The beam is three-dimensional and symmetrical around its axis.

  • Divided into:

    • Near Field (Fresnel Zone): Cylindrical shape.

    • Far Field (Fraunhofer Zone): Cone-shaped, diverging.

Factors Affecting Beam Shape

  • Frequency and Wavelength: Higher frequency leads to longer near field and reduced far field divergence.

  • Transducer Diameter (Aperture): Narrow crystals create narrower beams but shorter near fields; larger crystals result in wider beams with longer near fields.

  • Transducer Design: Causes alterations in beam shape; includes phased and linear arrays which enhance the number of focal zones.

Aperture size and beam shape

  • Aperture is the size of the source of ultrasound, a single crystal or group of crystals

  • Narrow crystal diameter (smaller aperture) results in a narrower beam in the near field but near field length is shorter and there is more divergence in the far field

  • Wider crystal diameter (larger aperture) results in a wider beam in the near field but produces a longer near-field length and has less divergence in the far field

Transducer design and beam shape

  • Phased and Linear arrays transduces can alter the beam shape by increasing the number of focal zones

  • Lenses focus because the propagation speed is higher than through tissues

  • Refraction at the surface of the lens forms the beam so that a focal region occurs (transducer B)

  • Crystal transducer also applies a degree of focusing to the beam (transducer A)

Focusing the Beam

  • Focusing brings the end of the near zone closer to the transducer face

  • Focusing can only be achieved in the near zone, where the beam is narrowest

  • Effects of focusing:

    • Reduces beam width in the focal zone, improves lateral resolution.

    • Focal length is the distance from the transducer to the focal center.

Mathematical Relationships

  • Beam width at the near zone's (focal length) end is approximately half of the transducer aperture

  • At the far zone, beam width is double the size of the beam in the focal point

  • The length of the focal zone is:

    Inversely proportional to the wavelength

    Directly proportional to the diameter of the crystal (D)

    Directly proportional to the propagation speed ©

    Has a square relationship with the aperture diameter

  • Formulae:

    • f = c{D^2}{c ƛ}

    • where f = focal length, D = transducer diameter, c = propagation speed, and ƛ = wavelength.

Beam Intensity

  • Intensity is measured as power (watts) per unit area.

  • Factors affecting intensity uniformity - intensity is not uniform throughout the length or width of the beam

    • Non-defined edges of the beam - intensity will decrease from the centre outward

    • Divergence of beam - intensity will be distributed over a larger area in the far field

    • Interference effects in the near field from the multiple points source of the crystals

    • Broadband transducer will show fewer interference effects and more uniformity due to its numerous frequency components

  • Reflection Strength: A small reflector at beam center (max intensity) yields stronger echo at the centre of the beam than on the periphery. This can lead to a false interpretation of the reflective properties of the tissue being examined, as the variability in echo strength may not accurately represent the underlying anatomy.

  • Further non-uniformity of intensity can be caused when the beam is focused to improve spatial resolution because a narrower beam will be within the focal zone

  • Intensity is greatest in the focal zone and therefore a stronger echo will be received from a given structure that lies within the focal zone

Side Lobes

  • Energy from the transducer radiates at various angles (side lobes), which can create artefacts in images.

  • 3D and have the same frequency as the main beam

  • Any interfaces encountered by any of these side lobes will return echoes which the ultrasound machine assumes to have been received by the main beam

Grating Lobes

  • Arise from multi-crystal transducers (array transducers), can generate additional beams at various angles.

  • These lobes may lead to image artefacts and degrade lateral resolution due to the effective widening of the beam

Slice Thickness

  • Refers to the beam dimension at 90° to the scan plane.

  • Symmetrical beams have equal beam width and slice thickness at circular apertures.

  • Differences in rectangular apertures can lead to larger slice thickness than beam width, causing imaging artifacts.

Recap on Transducers

  • Common types:

    • Linear array

    • Convex array

    • Phased array

    • Vector array

  • Key features:

    • Beam scanning, focusing techniques, dimensions (rectangles, sectors).

Summary

  • Transducers produce sound beams with distinct near and far zones.

  • Various factors influence the beam's three-dimensional shape and its intensity uniformity.

  • Artifacts can arise from inherent beam characteristics such as side lobes, beam width, and slice thickness inconsistencies.

Further Readings

  • Links to additional resources for in-depth study on ultrasound beam characteristics and artifacts.