Describe the physiological processes occurring in the muscle fibers that account for the gradual onset of muscle fatigue

The muscle fibres use several substrates in order to perform contractions. ATP is one of them. It binds to the myosin head and causes contraction. Creatine phosphate is another substrate that works in the "background" storing energy to convert ADP into ATP quickly as ATP is being used. Glycogen is another of the muscle fibres' substrates. It's used to produce energy quickly when creatine phosphate runs out of phosphates to use on ADP. The use of glycogen leads to the deposition of lactic acid on the muscles.

When these substrates run low there is muscle fatigue (or also called, in this case, metabolic fatigue) - there's no energy. Another cause may be from the deposition of lactic acid that also leads to such fatigue.