Those who knew him well say that Burian ranked with Gillies, Esser, Kilner and McIndoe as one of the masters and founders of modern plastic surgery. Burian was born in Prague on 17 September 1881, exactly 9 months to the day before Sir Harold Gillies was born. He studied medicine at Charles University in Prague, and following his graduation, he spent 1 year at the Institute of Pathology before starting on his surgical training in 1907 at the First Department of Surgery.

At the outbreak of the Balkan Wars (1912–1913), Burian was working as surgical assistant to Professor Kukula in Prague, but he joined the surgical team of Professor Tobiasek in October 1912 and set out for Belgrade. The wars brought about a tremendous feeling of unity amongst the Slavs, and even those countries which were not directly involved in the conflict willingly came to the help of their neighbours. Professor Kukula had responded to the requests for help by the Bulgarian Red Cross and formed a medical team composed largely of Slavs from Prague, which was second in size only to that of the Russians.

The wars were of the old-fashioned type with open fighting, infantry attacks and cavalry encounters, which produced none of the dreadful destructive facial injuries seen in the First World War. Nevertheless, Burian became interested in facial wounds and made a study of the reconstructive possibilities, such as they were at this time.

In January 1913, Burian moved to Sofia, where he took over the second Czech Mission in the Military Hospital from Karel Stepan. The Mission settled on the first floor of the Military Academy in Sofia where Burian cleared the rooms and halls of all unnecessary furniture in order to reduce infection. He had 400 beds at his disposal, and he soon showed his colours as a good administrator.

The records, complete with sketches by Burian, are extant and reveal that besides his interest in facial wounds, he was heavily involved with all the skull and brain injuries. His wife, Anna Lakasora-Burianova, who was one of the very first women to graduate as a doctor under the Austrian monarchy, assisted him during this period and, for many years thereafter, was his only assistant.