Zelenka was born on February 27, 1976, in Jihlava, and worked as a nurse in the anesthesiology and resuscitation unit of the hospital in Havlíčkův Brod, in the Czech Republic. He had drifted through several health jobs and been let go from more than one for unreliability before the Havlíčkův Brod unit took him on in 1998; there he finished his nursing qualification and in 2005 was promoted to lead the unit's nurses.
On Friday, May 12, 2006, he gave a patient on the unit the first unprescribed dose of heparin, an anticoagulant, and between then and September he gave large doses to at least sixteen more, causing bleeding that could not be stopped. Seven patients died and ten more suffered serious harm and survived. The victims were men and women, most of them elderly and already ill, and the deaths appeared at first to be complications of their conditions. Czech reporting called him the Heparin Killer, after the drug he used.
He was identified when the unit's head physician, Pavel Longin, began to question the number of unexplained bleeding events among his patients, and hospital records were audited. Zelenka was arrested on December 1, 2006, at the hospital in Jihlava, before a night shift.
He was tried at the regional court in Hradec Králové and on February 22, 2008, convicted of seven murders and ten attempted murders and sentenced to life imprisonment. Judge Jiří Vacek said he would have imposed death had the penalty not been abolished in 1990. At trial Zelenka retracted most of his confession, admitting only five of the deaths and alleging that the other admissions had been beaten out of him by police; the court rejected that, and rejected a defense of diminished responsibility. His accounts of motive shifted, at one point saying he wanted to test whether the doctors were competent enough to detect what he was doing, and the court settled on none. The sentence was upheld on appeal in June 2008. Several doctors have publicly disputed the verdict, arguing that heparin could not have caused the deaths in the way alleged.
He was sent to Valdice, one of the most tightly guarded prisons in the country, and in 2016 was reported to be seeking a move to a milder regime. A 2021 report gave 2038 as the earliest year he could be released. The case changed how Czech hospitals control and record the use of heparin. In April 2026, twenty years after the killings, the regional press reported him still serving his life sentence.