Anterior cruciate ligament (ACL) injury ranks among the most common injuries in high-intensity physical activities. When such an injury occurs, the knee joint becomes unstable, leading to gradual atrophy and weakening of the quadriceps muscle group, thereby affecting physical activities. Functional recovery post-ACL injury aims to minimize the risk of secondary knee structural damage, restore the entire range of motion, regain lower limb muscle strength, and improve function to pre-injury levels. Achieving this goal necessitates resistance training programs, as the process of protein breakdown and synthesis in the quadriceps muscles undergoes changes during resistance training. Developing mathematical equations to describe the changes in quadriceps muscle size relative to training load via alterations in protein synthesis processes will significantly enhance the effectiveness of resistance training programs in functional rehabilitation. Utilizing regression methods and statistical analysis of experimental scientific data, our findings clearly demonstrate that muscle growth is significantly influenced by training intensity in an exponential function, highlighting the complexity of muscle growth dynamics and the necessity for high-intensity training in achieving significant hypertrophy. This study could serve as a foundation for general muscle strengthening and rehabilitation.