Natick medical device maker Boston Scientific Corp. said Monday that it has agreed to buy Rhythmia Medical Inc., a Burlington developer of software used in medical procedures.

Boston Scientific will pay $90 million upfront and make as much as $175 million in milestone payments if Rhythmia meets regulatory, commercial, and sales targets over the next five years.

While the parties entered into a definitive agreement, disclosed after US financial markets closed Monday, they said they expect to complete the transaction by Friday.

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Rhythmia develops advanced mapping and navigation software for use in cardiac catheter ablations, a way to treat abnormal heart rhythms, and other electrophysi0logy procedures, including atrial fibrillation and atrial flutter. If its technology is approved by regulators in the United States and Europe, Boston Scientific said it expects to begin a limited market launch of the Rhythmia technology used with Boston Scientific’s catheters next year and full market launch in 2014. (Robert Weisman)