After the surgery, she had to undergo a painful recovery period.

undergo 由前缀 under-（表示"在...之下"）和动词 go（"走、经历"）组成，字面意思是"从下方经过"，引申为"经历、经受（困难或痛苦的过程）"。在句中指"经历康复期"这个艰难过程。