Re depending on estimates from the literature [73,74]. doi:ten.1371/journal.pcbi.1003944.tS-type 800 300 130FR-type 50 150 65FF-type 50 150 65PLOS Computational Biology | www.ploscompbiol.orgLarge-Scale Neuromusculoskeletal Model of Human Upright Standinglinear technique) applied on the MN spike trains. The filter output was followed by a non-linear function that provided a smooth saturation [52,79,80]. The non-linear function (Equation (1)) accounted for the mechanisms responsible for the muscle force saturation (e.g. Cazz release saturation in the sarcoplasmic reticulum): aMU SAT (t) 1{ exp c:aMU (t) 1z exp c:aMU (t) LMT LT zLM cos (LM )in which, LMT is the MTU length (in m), whose value is given by inverse kinematics data (see below); and a(LM ) is the pinnation angle as a function of the normalised muscle fibre length. a(LM ) arcsin sin(a0 ) LM ! in which, aMU SAT (t) is the saturated activation signal produced by a given MU; aMU (t) is the activation signal of a given MU before the saturation (i.e., after the second-order linear filter); and c is the shape parameter of the saturation function. For each MU the parameter c was adjusted so that the tetanic activation was achieved at a given firing rate (see [52]), i.e., a low (high) threshold MU achieved its tetanic activation at a low (high) firing rate. There was also an amplitude scaling depending on the MU type, i.e., S-type MU produced activation signals with amplitudes relatively lower than F-type MU. For more details regarding the distribution of parameter values, see [52]. The sum of all activation signals produced by S-type MUs resulted in the activation signal to the CEI [aI (t)]. Similarly, the activation signal to the CEII [aII (t)] was generated by the sum of all activation signals produced by FR- and FF-type MUs. These global activation signals were normalised with respect to the maximum muscle activation, which was calculated as the sum of all tetanic activations produced by the MUs of a given muscle. A similar approach was adopted in [75]. Passive properties. The i-th spike train was modelled as a non-homogeneous Gamma point process with a mean intensity [Afi (t)] modulated by the output of a muscle receptor (spindle or GTO) and with an order (or shape factor) adjusted to produce a variability compatible with experimental data [86]. The total number of afferents for each muscle (see Table 5) and conduction velocities (see Table 6) were based on estimates from the literature [58,87,88]. Afferent fibres were recruited according to a recruitment law given by Equation 12 [79].Jb A (t) TA (t)zmb :g:hb : sin A (t) h3in which, Jb is the body inertia (in kg.m2 ) given by Jb 4=3:mb :h2 ; b mb is the body mass CXCR2-IN-1 manufacturer excluding the feet (in kg); hb is the COM height with respect to the ankle joint (in m); TA (t) is the restoring torque around the ankle joint (see Equation (13)); and g is the gravity (set to 9.81 m/s2 ). _ TA (t) Tm (t){BA hA (t){KA hA (t) 4Afi (t) AfMR (t){RTi zIFRi2in which, Afi (t) is the mean firing rate (intensity) of the i-th afferent; AfMR (t) is the output of the muscle receptor models (spindle or GTO) for a given afferent type; RTi and IFRi are the recruitment threshold and the initial PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20175080 firing rate of the i-th afferent, respectively. The i-th afferent was recruited when the output produced by a specific muscle receptor afferent [AfMR (t)] crossed a recruitment threshold (RTi ). Irrespective of the afferent type (i.e., Ia, II, and Ib) the RTi was linearly varied.
