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In my case, after formal letter exchange with American Embassy in Italy, a B1 visa was required.
Supporting documents to get a B1 visa are listed here: https://travel.state.gov/content/visas/en/visit/visitor.html
And an interview at the Embassy is also nedeed. You'll get asked the purpouse of your visit and other related questions.
In my specific case I have already a work here in Italy to be started in the months following my trip to the U.S. so it was easy to prove my non-immigrant intent. Also I showed emails between me and the Department that's hosting me and non-disclosure agreement with their hospital. Another important part of the interview was showing them a bank account balance that would suffice to self-fund myself during my staying.
I honestly don't know why VWP isn't suitable for this, but I think sending an email to your local American Embassy is the best option since each case is different.