Nephi promises blessing to those who avoid such a hardening. In 1 Nephi 14 he writes "And it shall come to pass, that if the Gentiles...harden not their hearts against the Lamb of God...they shall be a blessed people upon the promised land forever" and he continues in chapter 15 to say "If ye will not harden your hearts, and ask me in faith, believing that ye shall receive, with diligence in keeping my commandments, surely these things shall be made known unto you". So though the heart can stop the flow of blood and metaphorically the flow of truth, the heart's most critical and beautiful job is softening.
The phrases "burning of the bosom" or "swelling of the heart" aren't strictly metaphorical; anyone who has experienced moments of wonderful emotion or intense, emotional pain has felt this. Emotion is physically felt in the heart for the heart is more than an organ but a threshold for deep feeling. I have the experienced forms and variations the Book of Mormon attaches to the heart. My heart has felt hardened toward truth, my heart has softened toward my fellow men, my heart has been filled with vain pride and my heart has presented itself to God, broken and discouraged. Luckily, God accepts us wholeheartedly and I am thankful for that. And I am thankful for my heart and all it can do.