Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error

Abstract

Hill-type parameter values measured in experiments on single muscles show large across-muscle variation. Using individual-muscle specific values instead of the more standard approach of across-muscle means might therefore improve muscle model performance. We show here that using mean values increased simulation normalized RMS error in all tested motor nerve stimulation paradigms in both isotonic and isometric conditions, doubling mean simulation error from 9 to 18 (different at p < 0.0001). These data suggest muscle-specific measurement of Hill-type model parameters is necessary in work requiring highly accurate muscle model construction. Maximum muscle force (F (max)) showed large (fourfold) across-muscle variation. To test the role of F (max) in model performance we compared the errors of models using mean F (max) and muscle-specific values for the other model parameters, and models using muscle-specific F (max) values and mean values for the other model parameters. Using muscle-specific F (max) values did not improve model performance compared to using mean values for all parameters, but using muscle-specific values for all parameters but F (max) did (to an error of 14, different from muscle-specific, mean all parameters, and mean only F (max) errors at p ≤ 0.014). Significantly improving model performance thus required muscle-specific values for at least a subset of parameters other than F (max), and best performance required muscle-specific values for this subset and F (max). Detailed consideration of model performance suggested that remaining model error likely stemmed from activation of both fast and slow motor neurons in our experiments and inadequate specification of model activation dynamics.

Motor neuronal activity varies least among individuals when it matters most for behavior

“…There is no simple, linear relationship between motor neuronal activity and muscle force (Hooper and Weaver 2000). Moreover, fitting data to models requires unique parameters for each individual (Blümel et al 2012). During biting, the I2 muscle does not activate immediately even if stimulated at high frequency (Hurwitz et al 1996;Yu et al 1999).…”

“…Averaging parameters from many animals may not solve this problem. A study of model oscillators demonstrated that averaged parameters did not generate oscillations (Beer et al 1999), a study of a conductance-based model neuron demonstrated that averaged parameters did not generate physiologically relevant behavior (Golowasch et al 2002), and using parameter sets measured from individual animals improved muscle models compared with using averaged values (Blümel et al 2012).…”

Muscles: Non-linear Transformers of Motor Neuron Activity

“…6.4), as the measured velocity would depend on both CE properties and D line acceleration over the measurement interval. Alternatively, including D line mass improves model stability, and such models can give very good results (Blümel et al 2012b). Perhaps the most correct conclusion is that the model in the 'a' panels of Figs.…”

“…This approach, in which V CE changes in a non-history dependent fashion to always make F CE + F PE = F SE , is not always used (Blümel et al 2012b;Cheng et al 2000). In these models V CE is updated by calculating dV CE /dt each time step (Δt) and adding Δt · dV CE /dt to the prior V CE to obtain a new V CE .…”

“…Such approaches must use different damper parameters for lengthening vs. shortening to account for F PE being much larger during lengthening. A second parallel damper is sometimes necessary as a modeling construct to prevent excessively rapid D line movement (Blümel et al 2012b).…”