I can’t post the loshon of Mesilas Yeshorim for some reason. Perhaps the site automatically blocks posts mostly in foreign languages? Anyway I assume everyone has a Mesilas Yeshorim. Or go here: http://www.hebrewbooks.org/pdfpager.aspx?req=52042&st=&pgnum=100&hilite=
In the first paragraph about pachad, what he is describing is clearly anxiety, and he finishes the paragraph by advising Bitochon to counter it.
Later, again, he starts by saying we should have Bitochon (‘ויהיה נכון לבו בטוח בה) and not be anxious and worry always. The only type of worry we should have is one based on logic, וזאת היראה המיוסדת על הנהגת החכמה והשכל, היא הראויה, anything which isn’t logical (ie anxiety) is היראה השוטה, i.e. when it isn’t שכיח היזיקא .
In summary, it is clear that Bitochon is the antidote to illogical unwarranted feelings of anxiety. And if you ask, how can something in your head stop a feeling in your heart, the answer I believe is that Bitochon isn’t supposed to be only in your head, but deeply felt in your heart as well.