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What is Most common cause of gangrene of foot of 30 years old farmer who is a chronic smoker - and explain in detail?
All four can cause gangrene (Myocardial infarction can cause gangrene by thromboembolism)
Lets see, each option one by one.

Raynauds disease 

Is ds of young women* (F:M ratio is 5:1)
commonly the upper limbs* are affected specially the fingers (the thumb is generally escaped)
The disease is characterized by Raynauds phenomenon* which is a series of attacks of
Local syncope → digits become cold and white*
Local asphyxia → digits turn blue with burning sensation*
Local recovery →digits regain normal colour*


Pulses remain unaffected* as this is the disease which affects arterioles
With the help of points (a) and (b) Raynauds ds can be ruled out.

Atherosclerosis (Senile gangrene)

Seen in elderly people over 50 years of age.
Thus because of age factor we can rule out atherosclerosis.

Myocardial infaction

Age factor again helps in ruling it out as MI is generally seen in elderly, though its incidence is increasing in young, but it cannot be a more common cause than Buerger's disease.

Buerger's (Thromboangitis obliterans)  Usual victims of this ds are young men below 40 yrs of age, who are smokers (ds is not seen in females and nonsmokers).

Buerger ds is the inflammatory reaction in the arterial wall with involvement of the neighbouring vein and nerve, terminating in thrombosis of the artery.
It characterstically involves small and medium sized arteries (plantars, tibial and radial artery)
Both upper and lower extremities are affected.
In lower extremity the ds. occurs beyond the popliteal artery. In upper extremity the ds occurs beyond the brachial art.
Early in the course of Buergers ds the superficial veins are involved producing the characterstic migratory, recurrent superficial thrombophlebitis.
An imp difference with atheroselerosis is that, atherosclerosis is a disease of large sized arteries, buergers is a ds of small arteries.