Hindawi Publishing Corporation Computational and Mathematical Methods in Medicine Volume 2013, Article ID 625427, 10 pages http://dx.doi.org/10.1155/2013/625427 Research Article An Approach for Simulation of the Muscle Force Modeling It by Summation of Motor Unit Contraction Forces Rositsa Raikova, 1,2 Hristo Aladjov, 1 Jan Celichowski, 2 and Piotr Krutki 2 1 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Academy G. Bonchev Street, Block 105, 1113 Soia, Bulgaria 2 Department of Neurobiology, University School of Physical Education, 27/39 Krolowej Jadwigi St., 61-871 Poznan, Poland Correspondence should be addressed to Rositsa Raikova; rosi.raikova@biomed.bas.bg Received 30 May 2013; Accepted 16 August 2013 Academic Editor: Georgios Archontis Copyright © 2013 Rositsa Raikova et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Muscle force is due to the cumulative efect of repetitively contracting motor units (MUs). To simulate the contribution of each MU to whole muscle force, an approach implemented in a novel computer program is proposed. he individual contraction of an MU (the twitch) is modeled by a 6-parameter analytical function previously proposed; the force of one MU is a sum of its contractions due to an applied stimulation pattern, and the muscle force is the sum of the active MUs. he number of MUs, the number of slow, fast-fatigue-resistant, and fast-fatigable MUs, and their six parameters as well as a ile with stimulation patterns for each MU are inputs for the developed sotware. Diferent muscles and diferent iring patterns can be simulated changing the input data. he functionality of the program is illustrated with a model consisting of 30 MUs of rat medial gastrocnemius muscle. he twitches of these MUs were experimentally measured and modeled. he forces of the MUs and of the whole muscle were simulated using diferent stimulation patterns that included diferent regular, irregular, synchronous, and asynchronous iring patterns of MUs. he size principle of MUs for recruitment and derecruitment was also demonstrated using diferent stimulation paradigms. 1. Introduction he force of a skeletal muscle is an accumulation of forces generated by active motor units belonging to this muscle. A motor unit (MU) is a motor neuron and all the muscle ibers innervated by its axon. he MU is the smallest functional element of the neuromuscular system. Motor units develop forces in response to trains of motoneuronal action potentials transmitted to the muscle ibers by motor axons. he central nervous system controls the muscle force by two basic mechanisms: (1) rate coding alters interpulse intervals (IPIs) between successive action potentials, which is measured as discharge rate and (2) recruitment-derecruitment processes regulate the number of active MUs [1–5]. Since it is very diicult to study these processes using in vivo experiments, the modeling of muscle force as a result of diferent types of MUs’ activity patterns can enhance our understanding of force control processes. Several muscle models consisting of MUs were proposed [6–10]. he most complex and frequently used model in various modiications appears to be the one proposed by the group of Fuglevand [6, 11]. Several elements of physiological knowledge should be taken into account with respect to the evaluation of a realistic muscle model. he force developed by one MU in response to a single stimulus (the twitch) has oten been modeled by an analytical function, which accounts for only two parameters: the maximal twitch force and the contraction time. Fuglevand et al. [6] model the MU twitch force using a power function which results in a ixed relationship between the maximum twitch force and the contraction time. he distribution of MUs based on maximum twitch force and contraction time within a modeled MUs’ pool has been approximated using general exponential equations based on experimental indings [6, 9, 12, 13]. However, it was shown in [14] that the contraction time and the maximal force amplitude of an MU twitch are insuicient to describe the considerable variability of the twitch forms in a real muscle. Moreover, diferent