Shear Wave Speed (m/s) vs. Young's Modulus (kPa): Conversion and Accurate Reporting in Elastography
What the Scanner Actually Measures
In shear wave elastography (SWE), a low-frequency pulse (~1 MHz) is applied to the tissue electronically, without operator pressure; shear waves propagate horizontally and move faster in stiffer formations (Berg, Diagnostic Imaging: Breast, 2019). The directly measured value is the shear wave speed c_s in m/s (EFSUMB, Update 2017).
Conversion Formula
The relationship between Young's modulus E and shear wave speed is described by the simplified formula:
| Quantity | Formula | Conditions |
|---|---|---|
| Young's Modulus E (kPa) | E = 3ρc² | ρ = tissue density, assumed to be 1000 kg/m³; c = shear wave speed in m/s (Berg, 2019; EFSUMB Update 2017) |
| Simplified Form | E = 3c_s² | under a number of limiting assumptions, including neglecting structural stiffness (WFUMB, 2015) |
| Shear Modulus G (kPa) — for MRE | G = c_s² = E/3 | MRE systems report the shear modulus G (WFUMB, 2015) |
Why Reporting is Preferable in m/s
EFSUMB (Update 2017) outlines several reasons why results are preferably reported in m/s rather than kPa. Firstly, it is the unit of shear wave speed c_s — the exact quantity measured by the scanner. When requesting the result in kPa, the scanner has to convert the measured data into an elasticity modulus (e.g., Young's modulus E) using the simple equation E = 3ρc², which involves a number of assumptions, usually invalid — including the assumption that tissue density is always 1000 kg/m³.
Practical Conclusions for Reporting
The shear wave speed is closely related to Young's modulus, and there is a simplified formula for transitioning between c and E with a number of assumptions (Cosgrove et al., EFSUMB Part 2, 2013; Bamber et al., EFSUMB Part 1, 2013). Transient elastography (TE) also measures shear wave speed but uses surface mechanical force instead of acoustic radiation force (Bamber et al., 2013).
When compiling a report, it is correct to indicate the unit of measurement (m/s or kPa) and understand that values in kPa are obtained through conversion with assumptions. [clarify — specific thresholds and clinical reference values are not provided in the fragments].
Frequently asked questions
What formula relates Young's modulus and shear wave speed?
E = 3ρc², where ρ is the tissue density (assumed to be 1000 kg/m³), c is the shear wave speed in m/s (Berg, 2019; EFSUMB Update 2017). In simplified form, E = 3c_s² under a number of assumptions (WFUMB, 2015).
Why does EFSUMB recommend reporting in m/s rather than kPa?
Because m/s is the unit of shear wave speed c_s, directly measured by the scanner. Conversion to kPa requires using the formula E = 3ρc² with assumptions that are usually invalid, particularly the assumption of tissue density being 1000 kg/m³ (EFSUMB Update 2017).
What do MRE systems report and how does it relate to E?
MRE systems report the shear modulus G (kPa), related as G = c_s² = E/3 (WFUMB, 2015).
Does transient elastography differ in wave excitation method?
Yes. TE also measures shear wave speed but uses surface mechanical force instead of acoustic radiation force, thus not classified as SWE (Bamber et al., EFSUMB Part 1, 2013).
What assumption is made about tissue density during conversion?
It is assumed that tissue density is always 1000 kg/m³ — this is one of the assumptions of the formula E = 3ρc², which is usually invalid (EFSUMB Update 2017).