When an individual works out with weights, there is an increase in blood flow which triggers the slow-twitch muscle fibers. Then, as this person continues, and he/she reaches maximum effort, this effort will activate all the motor units and the fast-twitch muscle fibers will then be utilized. The recruitment of these muscle fibers offers the increase of stimuli, which then contributes to growth and increase in muscle size. This muscle hypertrophy involves an increase in the size of skeletal muscle through an increase in the size of the component cells of the muscle. The cells of muscles grow from stimulation and stress and an adequate supply of amino acids because the stimulation and essential amino acids cause changes in protein synthesis which effect growth.
There has been an interesting study conducted by Dr. Ralph N. Carpinelli, Human Performance Laboratory at Adelphi University in Garden City, New York, that concluded,
The commonly repeated suggestion that maximal strength methods (resistance heavier than a 6 RM) produce greater neural adaptations or increases in neural drive was not substantiated in this study.
Instead, Carpinelli found that effort was a greater contributor to muscle fiber activation because it involved both slow-twitch and fast-twitch muscle fibers. This study can be reviewed at the links cited below.