How do I transition from a Ph.D. in engineering to a career in medicine? I am in a Ph.D. program in Engineering and I do probability, statistics and differential equations. My relevant previous works are: Modelling of blood flow, programming using DNA molecules. (But most of things I do, which will lead to a Ph.D. are very mathematical and don't involve any medicine.)

But lately I feel very inspired to pursue a career in Medicine instead. I am planning to complete my Ph.D. (I am from India) and then join a MD program (in USA).


I am interested in the mathematical modelling of living systems. I have read some papers in this area. I noticed some of these papers don't get the maths or physics right at times. I feel I would have the right skills to contribute here.
I am also interested in Bio-medical instrumentation. I have degree in Mechanical Engineering and I feel I would have the right skills for this industry.


I am aware that to be able to pursue either of above, I don't need a MD degree. But lately, I feel very passionate about actually saving lives and working closely with people. It is like a dream that keeps me inspired and working all the time. I want the MD degree.

So I want to know:


Is such a thing possible? Would I be eligible to apply? I am not very well clear about 'pre-med' course requirements. 
I am asking specifically about the MD program in USA on mind. However     information about MD programs in other countries, would also be useful.
If it is possible, I want some advice on how to go about preparing for it? 


(If you feel strongly the need to discourage my decision, please feel free to do so, giving adequate reasons. I would find that useful too.)

Thanks!
Medical doctors with a previous experience in engineering are indeed in an excellent position to do clinical research involving technology or modelling. From your question it seems like you are more interested in the practice of medicine than research, and that is fine because in some fields of medicine (e.g. radiology) an engineering background is a definite advantage to practice medicine efficiently.

I know 3 people who started (a 6 years) medical school after another degree. Two after a degree in Physics and one after a PhD in biomedical engineering. All 3 are happy with their choice but their situation is not yours. Can you afford to go to school for many more years?

If you do, in North America a previous degree (and engineering is a frequent one) is usually required prior to entering medical school. Med school usually lasts 4 years. Admission criteria vary between schools but the previous degree should typically include the following, according to the Association of American Medical Colleges:


  At a minimum, students will likely complete the following types of courses:
  
  
  One year of biology
  One year of physics
  One year of English
  Two years of chemistry (through organic chemistry)
  


To browse through institutions, you might find this site useful.

At the institution I know, the requirements include:


1 year of biology
2 years of chemistry
1 year of physics
some laboratory experience
1 year of maths (calculus and stats)
1 year of a course requiring writing.
"[being] comfortable with upper-level mathematics (through differential equations and linear algebra), biochemistry, and molecular biology


An additional requirement is that you completed at least one year of university in the USA or Canada. 

In Europe it varies a lot. For Germany, Switzerland and Austria, there are no requirements for a previous undergrad degree and it's usually hard to skip years if you have one. Most universities require that you have a high school diploma from a country they recognize. The programs are usually over a 6 years period. They typically involve a lot less mathematics than in North America. You need to be reasonably fluent in the local language.