Equations & Glossary

≈ 1,540 m/s

Approximately constant; insensitive to myocardial stiffness.

≈ 1–10 m/s

Varies with the shear modulus (μ) — the basis of SWE.

μ = ρc²

ρ ≈ 1,000 kg/m³ (soft tissue density); c = shear wave velocity.

Section: 3-3 (introduced) · also 3-4 (assumptions examined)

E ≈ 3μ

Valid under the near-incompressibility assumption. Both μ and E are reported in kPa.

Section: 3-3 (introduced) · also 3-4 (assumptions examined)

frame time ≈ (2d / c₀) × N

d = imaging depth, c₀ = speed of sound in tissue (~1,540 m/s), N = number of scan lines.

frame interval = 1 / FR

FR = frame rate (Hz).

The mechanical force created when part of an ultrasound wave's energy transfers into momentum inside tissue, acting in the direction of wave propagation. A focused push pulse concentrates ARF at the beam focal point to create the localized displacement that launches a shear wave.

Section: 3-2 (introduced) · also referenced in 3-4 ("ARF-induced waves")

Directional dependence of mechanical properties; in the myocardium, shear wave velocity varies with the angle to local fiber orientation.

The decrease in shear wave amplitude with propagation distance, due to geometric spreading, viscous absorption, and scattering.

Conventional grayscale ultrasound imaging, reconstructed from compressional (sound) wave echoes. Relies on compressional wave velocity staying constant regardless of tissue stiffness.

Combining images from multiple angled plane wave transmissions to recover image quality while keeping frame rates well above conventional imaging.

A mechanical wave in which particles oscillate parallel to the direction of propagation, producing alternating compression and rarefaction.

Mass per unit volume of tissue; approximated as ≈1,000 kg/m³ for soft myocardial tissue in μ = ρc².

Section: 3-3 (introduced) · also used in 3-4 equations

The micrometric axial tissue motion produced by a passing shear wave, extracted by cross-correlation of successive RF frames.

A high-intensity ultrasound burst (several hundred microseconds) that concentrates ARF at the beam focal point to launch a shear wave.

Number of image frames acquired per second (fps). Must exceed roughly 1,000 fps to resolve shear wave propagation, versus 30–100 fps for conventional line-by-line imaging.

A wave whose propagation is shaped by bounding surfaces (here, the endocardium and epicardium) when wavelength approaches wall thickness.

Having identical mechanical properties in all directions. μ = ρc² assumes isotropic tissue — an assumption the anisotropic myocardium violates.

Image sharpness in the direction perpendicular to the ultrasound beam axis. Lower for single-angle plane wave transmission than for a focused beam.

The intrinsic mechanical property of cardiac tissue describing its resistance to deformation. This is the quantity SWE aims to estimate, by measuring shear wave velocity and converting it to shear modulus via μ = ρc².

Section: Home page / Module 3 intro (3-1)

A shear wave generated spontaneously by mechanical events in the cardiac cycle, such as valve closure, without an external push pulse.

Section: 3-2 (introduced) · also referenced in 3-4 (dispersion discussion)

An unfocused ultrasound transmission that illuminates the entire field of view in a single transmit event, enabling frame rates far beyond focused, line-by-line imaging.

A secondary wave front produced when a propagating shear wave meets a tissue boundary (endocardium, pericardium) or structural discontinuity; can interfere with the primary wave and complicate velocity estimation.

A measure of a tissue's resistance to sideways (shear) deformation; relates to shear wave velocity via μ = ρc².

Section: 3-1 (introduced) · defined formally in 3-3 · assumptions examined in 3-4

A mechanical wave in which particles move perpendicular to the direction of propagation. Cannot travel through liquids.

The phenomenon in which higher-frequency shear wave components travel faster than lower-frequency ones in a viscoelastic material.

A technique that infers tissue stiffness from the velocity of shear waves traveling through it.

Section: Home page / Module 3 intro (3-1)

A measure of image quality; lower for single-angle plane wave transmission than for a focused beam, recovered in part by coherent compounding.

An imaging system's ability to resolve events closely spaced in time. Ultrafast frame rates (>1,000 fps) provide the temporal resolution needed to track shear wave propagation frame by frame.

Mitral valve closure (isovolumetric contraction) and aortic valve closure (isovolumetric relaxation) generate transients that propagate through the myocardium as shear waves.

A material behavior combining elastic and viscous components, so tissue response depends on the rate of deformation. The myocardium's viscoelasticity is what causes shear wave dispersion.

Tissue stiffness measure derived from the shear modulus via E ≈ 3μ under the near-incompressibility assumption; reported in kPa.

Section: 3-3 (introduced) · assumptions examined in 3-4