More than 80 Cuban specialists are working on the case and they have come up with 14 hypotheses -- from mass hysteria to a toxin or virus.
In rejecting the sonic attacks theory, Cuban investigators point out that not all the Americans suffered hearing loss. If a sonic weapon or sound waves intense enough to produce the array of symptoms were employed, all the diplomats would have shown auditory damage, they said.
"For a sound to be forceful enough to give you a concussion, people would end up deaf," said Dr. Mitchell Joseph Valdes Sosa, head of the Cuban Center for Neuroscience.
"We have discarded the idea that the damages could be produced by any type of sound -- much less by any type of sonic weapon," said Villar.
"This type of weapon doesn't exist in Cuba," added Col. Ramiro Ramirez Alvarez, chief of diplomatic security at Cuba's Interior Ministry. "The United States is the first one that would have this type of thing. They're made there; they're sold there."
A long-range acoustic device (LRAD), a type of sound blaster that emits sound in the 145-151 decibel range, has been used in the U.S. for crowd control as well as internationally to repel Somali pirates and in war situations. Such sound canons are quite large. Smaller machines sold as ultrasonic sound generators, or cannons that emit sonic blasts, are advertised on the internet as devices to scare away pesky wildlife.
If some type of advanced, classified weapon -- one that could specifically direct sound waves from a distance -- is involved in the alleged attacks, it might further complicate the investigations. Cuba wouldn't want the United States to know it has access to such a covert device and Washington wouldn't admit it to Havana either.
"We're not real keen on providing the perpetrators of this a lot of knowledge about what they've done," Secretary of State Rex Tillerson told The Associated Press in January.
The U.S. government has stopped short of saying the Cuban government is behind the incidents, but it does hold authorities on the island responsible for failing to protect its diplomats -- a responsibility of a host government under the Vienna Convention on Consular Relations.
Much of what the American public knows about the case has come from leaks to the media.