city center vs metropolitan core

city center

noun
  • The central business and shopping area of a city. 

metropolitan core

noun
  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see metropolitan, core. 

How often have the words city center and metropolitan core occurred in a corpus of books? (source: Google Ngram Viewer )