A MODEL OF FATIGUE AND RECOVERY IN PARAPLEGICS QUADRICEPS MUSCLE SUBJECTED TO INTERMITTENT FES

The objective of this paper was to propose a mathematical model for th e fatigue and recovery phases of a paraplegic's quadriceps muscle subj ected to intermittent functional electrical stimulation (FES). The mod el is based on in vivo, noninvasive, recording of fatigue related meta bolic parameters recorded during stimulation and recovery. Records of the time variations of the muscle's phosphorus metabolites, particular ly the phosphocreatine (PCr) and inorganic phosphorus (Pi), obtained f rom P-31 magnetic resonance spectroscopy (MRS), were used to calculate the intracellular pH level in the muscle and this latter parameter wa s incorporated in a musculo-tendon model. The fatigue-recovery model a llows the transition from the fatiguing phase to the recovery phase as soon as the stimulation terminates and vice versa. This model was inc orporated into a Huxley type muscle model expressing the dynamics of t he muscle. Two ordinary differential equations describing the musculo- tendon dynamics and the dynamics of the activation were solved simulta neously and records of the force trajectory during intermittent stimul ations were obtained. Study cases ranging from 5 to 30 s for each of t he stimulation and recovery alternating phases were stimulated. The fo rce and the total impulse in the modeled quadriceps muscle were comput ed. It was found that the greatest impulse was produced in intermitten t stimulation of 40-50 s duty cycle, with a 50 percent ratio between t he stimulation and recovery intervals. An additional series of six run s, including two contractions, one of 3 min and one of 1 min, separate d by rest periods of 3, 6, 9, 12, 15, and 30 min was performed. From t he predicted force trajectories obtained, the maximal force values ser ved for comparison with measured values made on one patient.