actually you cannot 'grow' new muscle strands. you were born with as many muscle fibers as you will ever have. muscle tissue cannot regenerate once it is cut or severed.
from wiki:
Skeletal muscle hypertrophy is initiated by microtrauma occurring in the exercised muscle tissue. The cells that make up the tissue (myofibers) are polynucleated, gaining additional nuclei from activated satellite cells, which fuse to the already mature muscle cell. The satellite cells, and the signaling that activates them, are believed to be the secret behind muscle hypertrophy. In an effort to prevent future trauma, the nuclei, whose number has increased due to the signaling created by the exercise and integration of satellite cells, increase synthesis of sarcomeric proteins, such as actin and myosin, increasing the size of the myofibrils that make up the sarcomeres contained in the muscle cell. Increased contractile proteins increase the strength of the muscle, contribute towards increased sarcomeric size and make the muscle, as a whole, look larger. Skeletal muscle cells do not divide, size increases occur only at the sarcomeric level
