Dr Krishnan initially did her medical school, residency, and fellowship training in India. Subsequent to that she moved to the United States to complete her pediatrics residency at New York medical college and her Pediatric Cardiology fellowship at Columbia University. She then returned to India to head the Department of Pediatric Cardiology at the Institute of Cardiovascular Diseases and Madras Medical Mission in Chennai India. She set up the first fellowship program, training Indian and international fellows in Pediatric Cardiology in India and getting accreditation for Pediatric Cardiology with the National board of Education in New Delhi. She also co-founded the Pediatric Cardiology Society of India. In 2001 Dr Krishnan moved back to New York to take a faculty position at New York Medical College. She left there is 2010 to take a position at Columbia University in 2010 where she is currently. She is an Associate Professor of Pediatrics as well as an Associate Medical Director of the Pediatric Pulmonary Hypertension Center which is the first accredited pediatric and adult pulmonary hypertension center in the United States.

In addition to clinical responsibilities, she is actively involved in medical education at every level. She is closely involved with the Pediatric Cardiology fellowship at Columbia University and is the director of the fellowship Clinical Competency Committee, which oversees fellow education and training. She is the director of medical student and resident education in Pediatric Cardiology and is closely involved with the Foundations in Clinical Medicine and Major Clinical Year training at the medical school. She was inducted to the Virginia Apgar Society of Medical Educators at Columbia University in 2018.

She is also actively involved in research, both in Pulmonary Hypertension and Pediatric Cardiology and is PI/co-investigator in multiple clinical trials, both NIH sponsored and other grants. She has co-authored over 50 papers and has multiple invited lectures to her credit. She is actively involved in the Pediatric Pulmonary Hypertension Network and in multiple research activities of the network. She is involved in curriculum development for a Pulmonary Hypertension education series. She is involved in teaching e-learning courses for international fellows in Pediatric Cardiology through the Children's heart link. She is on the editorial board of several journals including the Annals of Pediatric Cardiology and the Advances in Pulmonary Hypertension, and is a reviewer for multiple other journals.