The word contrite in Hebrew is 'dakah' which means one that is crushed to pieces. Paul wrote of being a 'living sacrifice' holy and acceptable to God. Being a living sacrifice means we often can walk off the altar. To be a continual living sacrifice we need to renew our minds day to day! Let your mind be renewed -- off the things which are worldly and onto those things which are Godly. When our minds are focused on those things above, on His holiness, His righteousness, His grace, and His mercy -- we realize that we can always be closer to Him! We understand what Isaiah meant when he said, "our righteousness is nothing but filthy rags before the Lord."
When God provided for Himself the perfect sacrifice, the Messiah, 2000 years ago -- His heart bursted! His heart was cut through -- cut for you! God desires you to be a living sacrifice and a necessary ingredient is a heart that has been cut through by God's sharp knife. When you allow your heart to be continually cut through by God's Spirit, then your life will be a living sacrifice, holy and acceptable before Him!
It's wonderful what God can do with a broken heart, especially when we give Him all the pieces!