Kidneys were organs present in most humanoid species. After House murdered the Time Lord known as the Corsair, his kidneys were given to Uncle, one of House's patchwork slaves. (TV: The Doctor's Wife)
When the Doctor's TARDIS matrix was transported into the body of Idris, her energy was burning out the body where she had been placed. As one of the first signs, she stated that one kidney had already given out. (TV: The Doctor's Wife)
While dying from the Judas tree poison, the Eleventh Doctor stated that the kidneys were "always the first to quit". (TV: Let's Kill Hitler)
After his regeneration, the Twelfth Doctor noted he had new kidneys, adding that he didn't like the colour. (TV: The Time of the Doctor)