Step 1: Group the four choices by how they are done.
A PA catheter sits inside the pulmonary artery, and thermodilution is the calculation done through that same catheter. Both need a line placed inside the heart's blood vessels, so both are invasive.
Step 2: Compare the two non-invasive choices left.
Echocardiography and impedance cardiography do not enter the body, so both qualify as non-invasive. The question is which one is the newer, more recent addition.
Step 3: Recall what impedance cardiography adds.
Electrical impedance (bioimpedance) cardiography uses surface electrodes to track small changes in chest impedance caused by blood moving through the aorta with each heartbeat, and turns that into a continuous cardiac output value. This bedside, wire free approach was the newer non-invasive technique when it became available, compared with the long established echo technique.
Step 4: State the answer.
Electrical impedance cardiography is the most recent non-invasive advance.
\[ \boxed{\text{Electrical impedance cardiograph technology}} \]