Graham's number: Difference between revisions

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Reverted good faith edits by 174.117.160.120 (talk): Larger can mean just larger, eg +1. That just does not cut it for Graham's number. (TW)
en>Jhertel
m Corrected sublink in the "Plank volume" link.
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[[File:Blausen 0460 Heart VentriclesRelaxed.png|thumb|300px|Illustration of the valves of the heart when the ventricles are relaxed. The [[tricuspid valve|tricuspid]] and [[mitral valve]]s are open, while the [[pulmonary valve|pulmonary]] and [[aortic valve]]s are closed. The [[chordae tendineae]] and [[papillary muscles]] are also shown.]]
A '''heart valve''' normally allows [[blood]] flow in only one direction through the [[heart]]. The four valves commonly represented in a mammalian heart determine the pathway of blood flow through the heart. A heart valve opens or closes incumbent upon differential [[blood pressure]] on each side.<ref name='AHAencyclopedia'>{{cite web | url = http://www.americanheart.org/presenter.jhtml?identifier=4598 | title = Heart Valves | accessdate = 2010-08-05 | work = [http://www.americanheart.org/presenter.jhtml?identifier=10000056 Heart and Stroke Encyclopedia] | publisher = American Heart Association, Inc}}</ref><ref name='Klabunde2009PG'>{{cite web | url = http://www.cvphysiology.com/Hemodynamics/H010.htm | title = Pressure Gradients | accessdate = 2010-08-06 | last = Klabunde | first = RE | date = 2009-07-02 | work = Cardiovascular Physiology Concepts | publisher = Richard E. Klabunde}}</ref><ref name='Klabunde2007CVD'>{{cite web | url = http://www.cvphysiology.com/Heart%20Disease/HD003.htm | title = Cardiac Valve Disease | accessdate = 2010-08-06 | last = Klabunde | first = RE | date = 2007-04-05 | work = Cardiovascular Physiology Concepts | publisher = Richard E. Klabunde}}</ref>
 
The four valves in the heart are:<ref>not counting the [[valve of the coronary sinus]], and the [[valve of the inferior vena cava]]</ref>
* The two atrioventricular (AV) valves, which are between the atria and the ventricles, are the [[mitral valve]] (also called the bicuspid valve), and the [[tricuspid valve]].
* The two semilunar (SL) valves, which are in the arteries leaving the heart, are the [[aortic valve]] and the [[pulmonary valve]].
 
A form of heart disease occurs when a valve malfunctions and allows some blood to flow in the wrong direction. This is called regurgitation.
 
==Structure==
Heart valves separate the [[Atrium (heart)|atria]] from the [[ventricle]]s, or the [[ventricle]]s from a [[blood vessel]]. Heart valves are situated around a tendinous ring, and possess ''cusps''. Each valve possesses three cusps, except for the mitral valve, which possesses only two.
 
===Atrioventricular===
[[Image:Apikal4D explained.png|thumb|300px|This is further explanation of the echocardiogram above. MV: Mitral valve, TV: Tricuspid valve, AV: Aortic valve, Septum: Interventricular septum. Continuous lines demarcate septum and free wall seen in echocardiogram, dotted line is a suggestion of where the free wall of the right ventricle should be. The red line represents where the upper left loop in the echocardiogram transects the 3D-loop, the blue line represents the lower loop.]]
[[Image:Heartvalve.jpg|thumb|150px|An [[artificial heart valve]] may be used to surgically replace a patient's damaged valve.]]
 
These are small valves that prevent backflow from the ventricles into the [[atrium (anatomy)|atrium]] during [[Systole (medicine)|systole]]. They are anchored to the wall of the ventricle by [[chordae tendineae]], which prevent the valve from inverting.
 
The [[chordae tendineae]] are attached to [[papillary muscle]]s that cause tension to better hold the valve. Together, the papillary muscles and the chordae tendineae are known as the subvalvular apparatus. The function of the subvalvular apparatus is to keep the valves from prolapsing into the atria when they close. The subvalvular apparatus have no effect on the opening and closure of the valves, however. This is caused entirely by the pressure gradient across the valve. The peculiar insertion of chords on the leaflet free margin however provides systolic stress sharing between chords according to their different thickness.<ref>J Cardiovasc Surg (Turin) 2000 Apr;41(2):193-202 [http://www.fondazionecarrel.org/carrel/cardiac/files/physio/physiofulltext.htm video]</ref>
 
The closure of the AV valves is heard as the '''first heart sound (S1)'''.
 
====Mitral valve====
{{main|mitral valve}}
Also known as the "bicuspid valve" because it contains two flaps, the mitral valve gets its name from the resemblance to a [[bishop]]'s [[mitre]] (a type of hat). It allows the blood to flow from the [[left atrium]] into the [[left ventricle]]. It is on the left side of the heart and has two cusps.
 
A common complication of [[rheumatic fever]] is thickening and [[stenosis]] of the mitral valve.
 
====Tricuspid valve====
{{main|tricuspid valve}}
The tricuspid valve is the three-flapped valve on the right side of the heart, between the [[right atrium]] and the [[right ventricle]] which stops the backflow of blood between the two. It has three cusps.
 
===Semilunar===
[[File:Wiggers Diagram.svg|thumb|400px|[[Wiggers diagram]], showing various events during a [[cardiac cycle]], with closures and openings of the aortic and mitral marked in the pressure curves.]]
 
These are located at the base of both the pulmonary trunk (pulmonary artery) and the aorta, the two arteries taking blood out of the ventricles. These valves permit blood to be forced into the arteries, but prevent backflow of blood from the arteries into the ventricles. These valves do not have chordae tendineae, and are more similar to valves in veins than atrioventricular valves. Closure of the semilunar valves causes the [[second heart sound]].
 
====Aortic valve====
 
{{main|aortic valve}}
The aortic valve lies between the  [[left ventricle]] and the [[aorta]].  The aortic valve has three cusps. During ventricular [[Systole (medicine)|systole]], pressure rises in the left ventricle.  When the pressure in the left ventricle rises above the pressure in the aorta, the aortic valve opens, allowing blood to exit the left ventricle into the aorta. When ventricular systole ends, pressure in the left ventricle rapidly drops. When the pressure in the left ventricle decreases, the aortic pressure forces the aortic valve to close.  The closure of the aortic valve contributes the A2 component of the second [[heart sound]] (S2).
 
The most common congenital abnormality of the heart is the [[bicuspid aortic valve]]. In this condition, instead of three cusps, the aortic valve has two cusps.  This condition is often undiagnosed until the person develops calcific aortic [[stenosis]].<ref>Bertazzo, S. ''et al.'' Nano-analytical electron microscopy reveals fundamental insights into human cardiovascular tissue calcification. ''Nature Materials'' '''12''', 576-583 (2013).</ref><ref>Miller, J. D. Cardiovascular calcification: Orbicular origins. ''Nature Materials'' '''12''', 476-478 (2013).</ref> Aortic stenosis occurs in this condition usually in patients in their 40s or 50s, an average of over 10 years earlier than in people with normal aortic valves.
 
====Pulmonary valve====
{{main|pulmonary valve}}
 
The pulmonary valve (sometimes referred to as the pulmonic valve) is the semilunar valve of the heart that lies between the right ventricle and the pulmonary artery, and has three cusps. Similar to the aortic valve, the pulmonary valve opens in ventricular systole, when the pressure in the right ventricle rises above the pressure in the pulmonary artery. At the end of ventricular systole, when the pressure in the right ventricle falls rapidly, the pressure in the pulmonary artery will close the pulmonary valve.
 
The closure of the pulmonary valve contributes the P2 component of the second heart sound (S2). The right heart is a low-pressure system, so the P2 component of the second heart sound is usually softer than the A2 component of the second heart sound. However, it is physiologically normal in some young people to hear both components separated during inhalation.
 
===Cusps===
The ''cusps of the heart valves'' serve to seal the [[heart valve]]s when closed. There are three cusps for each valve except for the [[mitral valve]], which has only two (hence its alternate name, "bicuspid valve"). "Nodules" are located at the tip of the valve, to form a tighter seal.
* The pulmonary valve has a left, right, and anterior cusp<ref>{{SUNYAnatomyLabs|20|21|01|02}} - "Heart: The Pulmonic Valve"</ref>
* The aortic valve has a left, right, and posterior cusp. <ref>{{SUNYAnatomyLabs|20|29|01|04}} - "Heart: The Aortic Valve and Aortic Sinuses"</ref>
* The tricuspid valve has an anterior, posterior, and septal cusp.
* The mitral valve only has two cusps, the anterior and posterior cusp.
 
<gallery>
File:Gray495.png |Base of ventricles exposed by removal of the atria. (Valves visible on top of heart.)
File:Gray497.png |Aorta laid open to show the semilunar valves. (Note that captions don't align with current terminology.)
</gallery>
 
===Variation===
{{Seealso|Bicuspid aortic valve}}
 
==Physiology==
In general, motion of the heart valves is determined using the [[Navier-Stokes equation]]; using boundary conditions of the blood pressures, pericardial fluid, and external loading as the constraints.
 
Motion of the heart valves is used as a boundary condition in the Navier-Stokes equation in determining the fluid dynamics of blood ejection from the left and right ventricles into the aorta and the lung.
 
===Relationship between pressure and flow in open valves===
 
The pressure drop, <math> {\Delta}p </math>, across an open heart valve relates to the flow rate, Q, through the valve:
 
<math> a{{\partial}Q\over{\partial}t} + bQ^2 = {\Delta}p </math>
 
If:
 
-Inflow energy conserved
 
-Stagnant region behind leaflets
 
-Outflow momentum conserved
 
-Flat velocity profile
 
===Valves with a single degree of freedom===
 
Usually the aortic and mitral valves are incorporated in valve studies within a single degree of freedom. These relationships are based on the idea of the valve being a structure with a single degree of freedom.  These relationships are based upon the [[Euler equations (fluid dynamics)|Euler equations]].
 
Equations for the aortic valve in this case:
 
<math> {\rho}\left({{\partial}u\over{\partial}t} + {u{\partial}u\over{\partial}x}\right) + {{\partial}p\over{\partial}x} = 0</math>
 
<math> {{\partial}A\over{\partial}t} + {{\partial}\over{\partial}x}(Au) = 0</math>
 
<math> A(x,t) = A_0 \left(1-[1-{\Lambda}(t)]{x\over{L}}\right)^2 </math>
 
<math> \int_{0}^{L} p(x,t) {{\partial}A\over{\partial}x}\, dx = [A_0 - A(L,t)]p(L,t) </math>
 
where:
 
u=axial velocity
 
p=pressure
 
A=cross sectional area of valve
 
L=axial length of valve
 
<math>{\Lambda}</math>(t)=single degree of freedom; when <math> {\Lambda}^2 (t) = {A(L,t)\over{A_0}} </math>
 
Atrioventricular valve
 
==Clinical relevance==
[[Image:Apikal4D.gif|thumb|300px| GIF-animation of a moving echocardiogram; a [[Echocardiography#Three-dimensional echocardiography|3D&nbsp;-&nbsp;loop]] of a heart viewed from the apex (top), showing the apical part of the ventricles removed and the mitral valve clearly visible. Due to missing data the leaflets of the tricuspid and aortic valves are not clearly visible, but the openings are; the pulmonary valve is not visible. On the left are two standard 2D views (taken from the 3D dataset) showing tricuspid and mitral valves (above) and aortal valve (below).]]
===Stenosis===
===Regurgitation===
===Infective endocarditis===
 
==See also==
* [[Artificial heart valve]]
* [[Cardiac fibrosis]]
* [[Congenital heart disease]]
* [[Pericardial heart valve]]
*Disorders of the valves ([[Valvular heart disease]])
** Aortic valve disorders:
*** [[Aortic insufficiency]]
*** [[Aortic stenosis]]
*** [[Aortic valve repair]]
*** [[Aortic valve replacement]]
*** [[Aortic valvuloplasty]]
** Mitral valve disorders
*** [[Mitral valve prolapse]]
*** [[Mitral valve repair]]
*** [[Mitral valve replacement]]
*** [[Mitral valvuloplasty]]
*** [[Mitral stenosis]]
** [[Pulmonary valve disorder]]s
** [[Tricuspid valve disorder]]s
* [[Endocarditis]]
* [[Heart sounds]]
* [[Bjork–Shiley valve]]
 
==Notes==
{{reflist}}
 
==Additional images==
<gallery>
File:Blausen 0469 HeartValves.png|Illustration of heart valves (superior view)
File:Blausen 0459 Heart VentriclesContract.png|Illustration of the valves of the heart when the ventricles are contracting.
 
</gallery>
 
==External links==
* [http://www.mitralvalverepair.org/content/view/51/ Mitral Valve Repair at The Mount Sinai Hospital – "Mitral Valve Anatomy"]
* [http://pie.med.utoronto.ca/PIE/PIE_whatWeDo_valves.html 3D, animated, rotatable heart valves (Rich media including Javascript and Flash player required)]
 
{{Heart}}
 
[[Category:Cardiac anatomy]]
[[Category:Valves]]

Revision as of 20:15, 22 February 2014

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