Lamar Odom's Heart Responding

10:57 AM PT -- Reports are being posted that Lamar is now communicating in some fashion, but our sources say he is not. There are some body movements, including eye opening, but doctors have made it clear the movements are all involuntary.

Lamar Odom's condition has improved in a hugely important way ... his heart is on the mend ... TMZ has learned.

Sources familiar with the situation tell us, tests on Lamar's heart Friday morning revealed his heart function is "much better." Doctors have told Lamar's friends and family this is a good sign of improvement, that a critical organ is responding.

Doctors have asked for "calm" in Lamar's room because they do not want him stimulated .... because non-stimulation promotes healing.

Toward that end, doctors have ordered that virtually no one have access to Lamar's room. We're told Khloe is still by Lamar's bedside.