It is common in the Bible for people to "rise up," and it would be easy to pass over the phrase as simply describing a physical action. But in fact it represents an elevation in spiritual state, moving to a more internal frame of mind closer to the Lord. Often it has to do with understanding a new or important idea; we "rise up" to a state of greater perception and enlightenment. Obviously context is crucial to the exact meaning of the phrase in a given passage -- it matters greatly who it is that is rising up, and why.

The heart means love. A good heart means love to the Lord and to the neighbor, while a hard or stony heart means the love of self or the world -- riches and things. When the psalmist asks the Lord to search his heart, he wants the Lord to see what it is that he loves. And we are what we love. What we eat may form our earthly body, but it's only temporary, what we love forms our spiritual body, beautiful or ugly as we have chosen. It's interesting to note that the first multi-cellular motion of our embryo is the pulsating that starts in a twist of blood vessel that is to become our heart, and the last motion of our natural body is our heartbeat. It is there for all of our natural life. And of course there is a beating heart in our spiritual bodies when we come to put them on.