Final answer:
The mylohyoid muscle, which forms the floor of the oral cavity and attaches to the mylohyoid lines on the mandible, determines the spread of an infection from an abscessed mandibular first molar in the soft tissues.
Step-by-step explanation:
The muscle that determines the space to which the infection will spread in the soft tissues, after perforating the lingual cortex of an abscessed permanent mandibular first molar, is the mylohyoid muscle. This muscle forms the floor of the oral cavity and is attached to the mylohyoid lines on both sides of the mandible. When an infection breaches the lingual cortex, the spread is determined by the anatomical spaces adjacent to the mylohyoid muscle. This muscle is responsible for raising the tongue and is instrumental in forming the floor of the mouth, affecting how an oral infection might spread within the soft tissues.