NEW YORK (AFP) - Actor John Travolta and his wife Kelly Preston said they were "heartbroken" over the death last week of their son Jett, 16, who was found unconscious during a family vacation in the Bahamas. "Jett was the most wonderful son that two parents could ever ask for and lit up the lives of everyone he encountered. We are heartbroken that our time with him was so brief," the family said in a statement Sunday. "We have received many messages of condolence from around the world and we want to thank everyone for their prayers and support. It has meant so much to us," the statement said, signed: "With love, John, Kelly and Ella." Jett Travolta had a history of seizures since he was a toddler and his father's attorney said he may have suffered a lethal one on Friday. The youth was the only son of the 54-year-old film star " also a trained jet pilot " and actress Preston, 46. Their daughter Ella is aged eight. The precise cause of death was not known. He was last seen on New Year's Day when he went to use the bathroom at the family's residence at the Old Bahama Bay Resort on Grand Bahama island, Police Chief Superintendent Basil Rahming said in a statement. "He was discovered in the bathroom in an unconscious state around 10:00 am" the next day by a caretaker, the statement said. "Arrangements are being made to have an autopsy performed, in order to determine the exact cause of death," the police chief said. A burial was planned after an autopsy in Ocala, Florida, where the family has a home. Travolta has denied reports that his son was autistic, saying he suffered from Kawasaki Syndrome, a condition that can lead to heart disease, US media reported. Kawasaki Syndrome, also known as lymph node syndrome, is a febrile illness that affects many organs, including the skin and mucous membranes, lymph nodes, blood vessel walls, and the heart. It was first described in 1967 by Dr. Tomisaku Kawasaki in Japan. The condition mostly affects children under the age of five and though found worldwide its highest incidence is in Japan, according to the US Centers for Disease Control and Prevention. In more serious cases, the syndrome can lead to an inflammation of the blood vessels. The teen had a life complicated by health woes from a young age. "Preston, who also said Jett suffered from asthma, blamed household cleaners, fertilizers and pesticides for sparking (his health) condition and lobbied for more detailed labeling on chemical products," People magazine said in its online edition. "She credited a detoxification program based on the writings of Scientology founder L. Ron Hubbard with helping to improve Jett's health," People reported. Both Travolta and his wife belong to the Church of Scientology. Travolta, famous for roles on television and in films such as "Grease," "Pulp Fiction" (1994) and "True Colors" (1991), received Academy Award nominations for the disco epic "Saturday Night Fever" (1977) and gritty "Pulp Fiction." Raised in Englewood, New Jersey, Travolta first gained fame in the 1970s playing a wise-cracking high school student in the television show "Welcome Back, Kotter" before he landed his role in "Saturday Night Fever."