# Modeling of Muscle Activation from Electromyography Recordings in Patients with Cerebral Palsy
## 1 Introduction  
An exact description of the way deficient neuronal activity leads to motor impairments and deficient sensorimotor integration in cerebral palsy (CP) is still missing. CP has its origin in damage during early brain development. The main symptoms are impairments of motor function [1; 2], but other problems, such as learning disability, speech disorders and behavioral problems, are often also present [3; 4]. Depending on the extent of the brain damage, motor limitations can range from a slightly limited ability to walk to a permanent dependence of a wheelchair to move. Muscular imbalances in CP, together with increased spastic muscle tone, lead to severe contractures and joint deformities [1]. Injury to cerebral motor cortex in CP affects the neuronal input to corticospinal and reticulospinal tracts, and consequently affects the input of motor neurons to muscle fibers they innervate [2; 5]. These alterations in neuronal-muscular pathways lead to alterations in musculoskeletal functioning. Despite the neuronal origin of the multifactorial disability in CP, it is not entirely understood to what extent and exactly how damage to the corticospinal tract neurons affects functioning of the muscles they innervate. Modeling neuromusculoskeletalt processes, and the kinematics of the associated movements can help to understand the alterations in neuromotor processes underlying disabilities in CP. Knowledge of inter-muscular forces during movement could also be an important direction for developing rehabilitation programs for patients with CP. The relationship between EMG and muscle force output has long been a subject of discussion [6; 7; 8]. Some investigators described a linear relationship between electromyography signal (EMG) and force produced by voluntary isometric contraction in human muscle [6], while others have found a nonlinear relationship [9]. Some suggest the combination of linear and nonlinear relationship depending on the muscle fiber composition and fiber distribution [7]. In case of children with CP, the EMG-force relationship has been studied using gait analysis, estimating the joint moment of lower limbs [10; 11; 12; 13; 14]. However, abnormal muscle activity in patients with CP influences the choice of estimation method to find a close relationship between EMG and force [14]. Studies of isometric bicep contraction in children with CP with secondary distonia showed a larger force variability in these children compared to controls [12]. Several previous studies [15; 16; 17; 18] have analyzed EMG recordings during cycling on the ergometer and have reported more frequent co-contractions and prolonged EMG activity in patients with CP, when compared to a group of healthy controls [15; 16]. Analysis of EMG signals at different crank angles [16; 19] confirms the often reported variability in EMG signals across patients, and points to the necessity of individual rehabilitation strategies. The study presented here is a first step in the attempt to understand the neuromusculoskeletalt transformations during cycling in patients with CP. Specifically, models presented in previous studies were here applied to convert the EMG signal recorded during cycling into a processed signal from which the force output of leg muscles can be determined. Despite the debate surrounding the exact relationship between a recorded EMG signal and the force output of the corresponding muscle mentioned above, it is the general understanding that there is no direct relationship between these two quantities. Transformations of the original EMG signal are therefore necessary before the force output of a muscle can be determined and compared with equivalent experimental measures. Those transformations take into account, amongst other factors, filtering effects, the electromechanical delay and nonlinear effects between the neuronal signal and the effective activation of muscle fibers.