View source for Moens–Korteweg equation

{{See also|Pulse wave velocity}}

In [[biomechanics]], the '''Moens–Korteweg equation''' models the relationship between wave speed or [[pulse wave velocity]] (PWV) and the incremental [[elastic modulus]] of the arterial wall or its [[distensibility]]. The equation was derived independently by [[Adriaan Isebree Moens]]<ref>{{Cite thesis |publisher=S.C. Van Doesburgh |location=Leiden, The Netherlands |last=Moens |first=Adr. Isebree |title=Over de voortplantingssnelheid van den pols |language=Dutch |trans-title=On the speed of propagation of the pulse |year=1877 |degree=Ph.D.}}</ref><ref>{{cite book |last=Moens |first=A. Isebree |title=Die Pulskurve |publisher=E.J. Brill |location=Leiden, The Netherlands |language=German |trans-title=The Pulse Curve |year=1878 |oclc=14862092 |url=https://archive.org/details/diepulscurve00iseb}}</ref> and [[Diederik Korteweg]].<ref>{{cite journal |last=Korteweg |first=D.J. |title=Über die Fortpflanzungsgeschwindigkeit des Schalles in Elastischen Röhren |journal=Annalen der Physik |year=1878  |volume=241 |issue=12 |pages=525–542 |doi= 10.1002/andp.18782411206 |bibcode=1878AnP...241..525K|url=https://zenodo.org/record/1423762 }}</ref> It is derived from [[Newton's laws of motion|Newton's second law of motion]], using some simplifying assumptions,<ref name=Milnor1982>{{cite book |last=Milnor |first=William R. |title=Hemodynamics |publisher=Williams & Wilkins |location=Baltimore |year=1982 |isbn=978-0-683-06050-8 }}</ref> and reads:
:<math>PWV = \sqrt{\dfrac{E_\text{inc} \cdot h}{2r\rho}}</math>

The Moens–Korteweg equation states that PWV is proportional to the square root of the incremental elastic modulus, (''E''<sub>inc</sub>), of the vessel wall given constant ratio of wall thickness, ''h'', to vessel radius, ''r'', and blood density, ρ, assuming that the artery wall is [[isotropic]] and experiences isovolumetric change with pulse pressure.<ref>{{cite journal |last1=Gosling| first1=R.G. |last2=Budge |first2=M.M. |title=Terminology for Describing the Elastic Behavior of Arteries |journal=Hypertension |year=2003 |volume=41 |pages=1180–1182 |doi=10.1161/01.HYP.0000072271.36866.2A |issue=6|citeseerx=10.1.1.542.5166 |pmid=12756217 }}</ref>

== References==
{{reflist}}

==Further reading==
*{{cite book |last1=McDonald |first1=Donald A. |first2=Wilmer W. |last3=O'Rourke |first3=Michael J. |last4=Hartley |first4=Craig |title=McDonald's Blood Flow in Arteries, Theoretical, experimental and clinical principles |publisher=Arnold |location=London |year=1998 |isbn=978-0-340-64614-4 |edition=4th |last2=Nichols}}.
* Tijsseling A.S.,  Anderson A. (2012) "A. Isebree Moens and D.J. Korteweg: on the speed of propagation of waves in elastic tubes", BHR Group, Proc. of the 11th Int. Conf. on Pressure Surges (Editor Sandy Anderson), Lisbon, Portugal, October 2012, pp.&nbsp;227–245, {{ISBN|978-1-85598-133-1}}.

{{DEFAULTSORT:Moens-Korteweg equation}}
[[Category:Biomechanics]]
[[Category:Fluid mechanics]]