Editing Attenuation (section)

== Ultrasound ==
{{Main|Acoustic attenuation}}
One area of research in which attenuation plays a prominent role is in [[ultrasound]] physics. Attenuation in ultrasound is the reduction in [[amplitude]] of the ultrasound beam as a function of distance through the imaging medium. Accounting for attenuation effects in ultrasound is important because a reduced signal amplitude can affect the quality of the image produced. By knowing the attenuation that an ultrasound beam experiences traveling through a medium, one can adjust the input signal amplitude to compensate for any loss of energy at the desired imaging depth.<ref name="Bushong">Diagnostic Ultrasound, Stewart C. Bushong and Benjamin R. Archer, Mosby Inc., 1991.</ref>

*''Ultrasound attenuation'' measurement in [[heterogeneous]] systems, like [[emulsion]]s or [[colloid]]s, yields information on [[particle size distribution]]. There is an ISO standard on this technique.<ref>ISO 20998-1:2006 "Measurement and characterization of particles by acoustic methods"</ref>
*''Ultrasound attenuation'' can be used for [[extensional rheology]] measurement. There are [[acoustic rheometer]]s that employ [[Stokes' law of sound attenuation|Stokes' law]] for measuring [[extensional viscosity]] and [[volume viscosity]].

Wave equations which take [[acoustic attenuation]] into account can be written on a fractional derivative form.<ref name="Nasholm">S. P. Näsholm and S. Holm, "On a Fractional Zener Elastic Wave Equation," Fract. Calc. Appl. Anal. Vol. 16, No 1 (2013), pp. 26–50, {{doi|10.2478/s13540-013--0003-1}} [https://arxiv.org/abs/1212.4024 Link to e-print]</ref>

In homogeneous media, the main physical properties contributing to sound attenuation are viscosity <ref>Stokes, G.G. "On the theories of the internal friction in fluids in motion, and of the equilibrium and motion of elastic solids", ''Transactions of the Cambridge Philosophical Society'', vol.8, 22, pp. 287–342 (1845)</ref> and thermal conductivity.<ref name="Kirchhoff">G. Kirchhoff, "Ueber den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung", Ann. Phys. , 210: 177-193 (1868). [https://doi.org/10.1002/andp.18682100602 Link to paper]</ref><ref name="Benjelloun">S. Benjelloun and J. M. Ghidaglia, "On the dispersion relation for compressible Navier-Stokes Equations," [https://arxiv.org/abs/2011.06394 Link to Archiv e-print] [https://hal.archives-ouvertes.fr/hal-02994555/ Link to Hal e-print]</ref>

=== Attenuation coefficient ===
{{Main|Attenuation coefficient}}
[[Attenuation coefficient]]s are used to quantify different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency. The attenuation [[coefficient]] (<math>\alpha</math>) can be used to determine total attenuation in [[decibel|dB]] in the medium using the following formula:
: <math> \text{Attenuation} = \alpha \left[\frac{\text{dB}}{\text{MHz}{\cdot}\text{cm}}\right] \cdot \ell [\text{cm}] \cdot \text{f}[\text{MHz}]</math>

Attenuation is linearly dependent on the medium length and attenuation coefficient, as well as – approximately – the [[frequency]] of the incident ultrasound beam for biological tissue (while for simpler media, such as air, the relationship is [[Stokes's law of sound attenuation|quadratic]]). Attenuation coefficients vary widely for different media. In biomedical ultrasound imaging however, biological materials and water are the most commonly used media. The attenuation coefficients of common biological materials at a frequency of 1&nbsp;MHz are listed below:<ref name="Culjat">{{cite journal|last1=Culjat |first1=Martin O. |last2=Goldenberg |first2=David |last3=Tewari |first3=Priyamvada |last4=Singh |first4=Rahul S. |year=2010 |title=A Review of Tissue Substitutes for Ultrasound Imaging |journal=Ultrasound in Medicine & Biology |volume=36 |pmid=20510184 |issue=6 |pages=861–873 |url=http://www.umbjournal.org/article/S0301-5629(10)00075-X |archive-url=https://archive.today/20130416030037/http://www.umbjournal.org/article/S0301-5629(10)00075-X |url-status=dead |archive-date=2013-04-16 |doi=10.1016/j.ultrasmedbio.2010.02.012 }}</ref>

{| class="wikitable" style="margin:1em auto;"
|+
! Material !! <math>\alpha\text{ }\left[\frac{\text{dB}}{\text{MHz}{\cdot}\text{cm}}\right]</math>
|-
| [[Air]], at 20&nbsp;°C<ref>{{cite journal |last1=Jakevičius |first1=L. |last2=Demčenko |first2=A. |title=Ultrasound attenuation dependence on air temperature in closed chambers |journal=Ultragarsas (Ultrasound) |date=2008 |volume=63 |issue=1 |pages=18{{endash}}22 |url=https://www.ndt.net/article/ultragarsas/63-2008-no.1_03-jakevicius.pdf |issn=1392-2114}}</ref>
| 1.64
|-
| [[Blood]]
| 0.2
|-
| [[Bone]], cortical
| 6.9
|-
| Bone, trabecular
| 9.94
|-
| [[Brain]]
| 0.6
|-
| [[Breast]]
| 0.75
|-
| [[Cardiac]]
| 0.52
|-
| [[Connective tissue]]
| 1.57
|-
| [[Dentin]]
| 80
|-
| [[Tooth enamel|Enamel]]<!-- In the article tooth and paint Enamel are discussed -->
| 120
|-
| [[Fat]]
| 0.48
|-
| [[Liver]]
| 0.5
|-
| [[Bone marrow|Marrow]]
| 0.5
|-
| [[Muscle]]
| 1.09
|-
| [[Tendon]]
| 4.7
|-
| [[Tissue (biology)|Soft tissue (average)]]
| 0.54
|-
| [[Water]]
| 0.0022
|}

There are two general ways of acoustic energy losses: [[absorption (acoustics)|absorption]] and [[scattering]].<ref>Bohren, C. F. and Huffman, D.R. "Absorption and Scattering of Light by Small Particles", Wiley, (1983), {{ISBN|0-471-29340-7}}</ref>
Ultrasound propagation through [[Homogeneous (chemistry)|homogeneous]] media is associated only with absorption and can be characterized with [[absorption coefficient]] only. Propagation through [[heterogeneous]] media requires taking into account scattering.<ref>Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, 2002</ref>