As for travelling to the US, it might be helpful to refer to the US Customs & Border Control Site.
Do I have to declare currency when entering the U.S. in-transit to a foreign destination?
When entering the U.S. in-transit to a foreign destination, you will be required to clear U.S. Customs Border Protection (CBP) and Immigration and Customs Enforcement. If you have “negotiable monetary instruments” (i.e. currency, personal checks (endorsed), travelers checks, gold coins, securities or stocks in bearer form) valued at $10,000 or more in your possession a “Report of International Transportation of Currency or Monetary Instruments” form FinCEN 105 must be submitted to a CBP Officer upon your entry into the United States.
Monetary instruments that are made payable to a named person but are not endorsed or which bear restrictive endorsements are not subject to reporting requirements, nor are credit cards with credit lines of over $10,000. Gold bullion is not a monetary instrument for purposes of this requirement. The requirement to report monetary instruments on a FinCEN 105 does not apply to imports of gold bullion.
Failure to declare monetary instruments in amounts of or over $10,000 can result in its seizure.
Take a look at the details of the form listed in the last line of this link. It may provide additional helpful information.
Here is another link from the same site on:
Foreign visitor having to carry a certain amount of money to enter the U.S.
Published 06/15/2004 03:46 PM | Updated 06/04/2010 09:05 AM | Notify Me
_Does a foreign visitor have to carry a certain amount of money to enter the U.S.?
Yes. Travelers visiting the U.S. from a foreign country must be able to prove to a CBP Officer that they have sufficient funds (i.e. credit cards, cash, travelers checks, money orders etc.) to cover their travel, lodging, entertainment, meals, etc. in order to be admitted into the U.S._
CBP Officers are aware that there may be circumstances in which a traveler may have limited funds. In those cases they will determine the admissibility of the traveler based on the information provided to support the reason the traveler has insufficient funds.
If you have invited someone to visit you with the understanding that you will be hosting them at your house and providing meals, etc., it is advised that you confirm your invitation in writing so that they have something to show the CBP Officer. The letter should include your full name and address. This will not guarantee their admission into the U.S., but it will help the CBP Officer fully assess their situation.
If you need to have a certain amount of money on hand, and it cannot be put on a credit or debit card, then it sounds as if it would be best to get a letter from the medical center performing the operation and notify the US CBC in advance.