It may differ depending on the situation. Direct translation would be... 私の心臓はドキドキorバクバクしています。 Watashi no shinzou ha dokidoki(bakubaku) shite imasu. If that happens when you see someone you like, you would like to use ドキドキ.

胸がどきどきする mune ga do ki do ki su ru

I don't think Japanese have a heartbeat. I have heard that they're all zombies.

In a sentimental way, like when you see someone you like or you are anxious about something you say: 心がドキドキする。Kokoro ga doki doki suru. In a physiological way you say: 心臓が鼓動する。 Shinzou ga kodou suru.

Japanese: "胸(or心臓)がドキドキする。" Romaji : "Mune(Shinzou) ga dokidoki suru." Katakana: ムネ(シンゾウ)ガドキドキスル。 Hiragana: むね(しんぞう)がどきどきする。