Data-driven modelling of fatigue in pelvic floor muscles when performing Kegel exercises

A Dual Control Approach to Solve Exploration Versus Exploitation Trade-Offs in the Design of Personalized Physical Exercise Sessions

“…We test the capabilities of our approach via simulations where we use the pelvic floor muscles model in [14] for modeling the dynamics of fatiguing in Kegel exercising. The proposed compartmental model is an extension of the work in [15] and involves active muscles m a , fatigued muscles m f , and resting muscles m r , where the total number of muscular units is M .…”

“…Note that the underlying true system is considered to be the more complex model derived in [16] where cramping muscles m c are additionally used to capture a particular dynamic often observed when people perform Kegel exercises, which is a more realistic situation where the underlying system is more complex than the proposed model. We consider here, however, the original model in [14], where the discrete-time, time-invariant, control-affine system is given by…”

“…Here the input u k , called the brain force, is a normalized amount of effort (i.e., relative to some pre-defined maximum) exerted by the person performing the exercises at time k. Moreover, w k ∼ N (0, 0.25), ϕ fa is the recovery rate from a fatigued to an active state, ϕ af is the fatiguing rate, ϕ ar is the rate of relaxation, and ϕ ra is the activating rate from a rested state to an active state. We should note that the model in [14] is only validated for maximum effort or no effort, i.e., one or zero. However, Hill-type models are commonly used in biomechanics to model muscular contractions, where the normalized excitation input u can range between zero and one [15].…”

“…To be able to use OED for parameter identification, we need to have an identifiable model. We know from [14] that ϕ = ϕ fa ϕ af ϕ ar ϕ ra ⊤ are identifiable parameters for known M = 1.…”