User talk:Mahesh kur
Derivation for elastic work of breathing
[edit]Here it is the relation between work done by respiratory muscles only against the elastic recoil of lungs. Actually, lung compliance is the stretchability of lung.
Compliance c = dv/dp So c.dp = dv. ........(eq.2)
Integrate for both the sides
P.c = v + a .....(a will be const.). .....(eq.1)
This relation holds true for constant compliance. The compliance will remain constant only for short interval. For the short interval...
Expression for work done by muscles on elastic recoil will be
dW = P.dv
dW = P.c.dp. .....( From eq.1). Integrate both the sides
W = p^2.c/2 . W = v^2/2c
That means, work done against elastic recoil of lungs is inversely proportional to compliance of lung for constant ventilation. Compliance of lung is variable and it is less in case of less volume (due to surface tension effect) and at high lung volume(due to reached elastic limit of lungs). The compliance of lung cancer be understood by the slope of volume pressure graph for lungs.
(Note: this derivation has some considerations, this derivation is only to find the relation of lung compliance with the work done against elastic recoil) Mahesh kur (talk) 06:07, 30 January 2019 (UTC)