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Gillian Browne, a 65-year-old mother of four, was on a 12-hour Air New Zealand flight from Auckland to Los Angeles last Friday when the tragedy occurred.
Ms Browne's former husband, Brent Browne, said she was going to visit her youngest daughter, who was holidaying in Hawaii.
Ms Browne's family were heading to Dunedin to prepare for the arrival of her body, he said.
A date for her funeral had yet to be set.
A Ministry of Foreign Affairs and Trade spokeswoman said the New Zealand Consulate-General in Los Angeles been in contact with Ms Browne's family and repatriation of her body was under way.
Ms Browne's City Catering company had been contracted to operate the Dunedin City Council staff cafeteria and a catering service for council functions since 1997.
A DCC spokesman said the council's thoughts were with Mrs Browne's family at this ''sad and distressing time''. Former councillor Neil Collins said Ms Brown was a delightful woman and they had became good friends over the years.
She spoke to him about her trip to the United States a few days before she left, he said.
''She was excited by the trip. She told me she was looking forward to seeing her granddaughter dance at Disneyland ... Her death has come as a great shock.''
Sergeant Karla Ortiz, from Los Angeles International Airport police, said CPR was unsuccessfully performed on Ms Browne after the plane arrived in Los Angeles last Friday.
A postmortem examination was performed two days later.
Los Angeles County Coroner spokesman Lieutenant David Smith said Ms Browne died as the result of a pulmonary thromboembolism, caused by a blood clot entering one of the main arteries leading into her lungs.
Her body remained with the LA Coroner while her repatriation back to New Zealand was being organised, he said.
Travel Doctor managing director Wendy Penno said pulmonary embolisms were often caused by deep vein thrombosis (DVT).
''It's a blood clot that forms somewhere else in the body that breaks off and then lodges somewhere else - most commonly the lungs, but sometimes also in the brain.''
Around 1% of travellers had a blood clot before flying. However, the chances of them developing into a pulmonary embolism were very low, Ms Penno said.
However, when they did, the chances of dying from a pulmonary embolism were very high, she said.
The Ministry of Health's most recent statistics showed that from 2000 to 2010, an average of 16 people a year died from DVT.
In advice on Air New Zealand's website, the airline's chief medical officer Dr Tim Sprott said the elderly, the overweight, smokers, people who had just had surgery, or were pregnant or on oral contraceptives and those with heart conditions, cancer, or who had a family history of blood clots were most at risk of DVT.
''If you think you may be at risk, however small, we recommend you consult your doctor before you fly.''
Aspirin was not an effective preventive medication for DVT, Dr Sprott said.
How to prevent deep vein thrombosis
• Try to get a seat with extra leg room, such as one next to an emergency exit.
• Drink plenty of water to reduce dehydration.
• Walk around the plane throughout the flight.
• While seated, exercise your calf muscles every half-hour by flexing and rotating your ankles.
• Sleep only for short periods and don't take sleeping pills that could keep you motionless in your seat for hours.
• Consider wearing support stockings.
• Avoid wearing tight clothing around your waist.
Source: Ministry of Health
- Additional reporting: Otago Daily Times