Mathematical models of human paralyzed muscle after long-term training

Abstract

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models’ parameters were best fit to a single force train in the trained soleus muscle (N = 4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

1. Introduction

Spinal cord injury (SCI) transforms skeletal muscle causing decreased muscle mass (Round et al., 1993; Castro et al., 1999), faster contractile properties (Shields et al., 1997; Gerrits et al., 1999), and increased fatigability (Shields, 1995; Gerrits et al., 1999; Castro et al., 2000; Shields et al., 2006). Early resistance training with electrical stimulation prevents many neuromuscular and skeletal adaptations that occur following SCI (Shields, 2002; Shields et al., 2006a). Thus, repetitive use of a neuroprosthetic device will likely cause adaptations in paralyzed muscle.

Functional electrical stimulation (FES) may be used to restore function as well as a training mechanism to sustain torque-generating capacity. Mathematical models to predict paralyzed muscle force properties must be robust to accommodate the potential range of physiological adaptations resulting from time and training following SCI. Further, functional use of neuro-prosthetic devices in humans may depend on muscle activation algorithms that are sensitive and adaptable to a wide range of muscle physiological properties.

Mathematical muscle models provide a means to determine optimal muscle activation strategies (Bobet, 1998). While several modeling approaches have been proposed (Stein et al., 1992; Bobet and Stein, 1998; Ding et al., 1998; Gollee et al., 2001), direct between model comparisons have revealed a 2nd order nonlinear and a Hill Huxley type model to be most accurate (Bobet et al., 2005; Frey Law and Shields, 2006). However, whether these models are equally capable of representing paralyzed muscle after a period of training is unknown.

Chronically untrained paralyzed muscle is comprised of primarily fast fatigable fibers (unadapted) whereas trained paralyzed muscle has a mixture of fiber types (adapted) and may, therefore, be more difficult to model. Animal studies suggest that model errors depend on muscle speed properties, with greater error occurring in predominantly slow muscle (Wexler et al., 1997; Bobet and Stein, 1998; Gollee et al., 2001).

The purpose of this study was to determine the accuracy of three muscle models for predicting the force properties in a trained limb and contrasting these findings with our previous findings in the untrained limb (opposite leg) (Frey Law and Shields, 2006). We hypothesized that the two nonlinear models would continue to provide more accurate predictions of muscle force properties than the linear model, but that the trained condition would yield greater error with altered parameter values with respect to the untrained condition (Frey Law and Shields, 2006).

2. Methods

Four males with complete SCI (see Table 1), concurrently participating in a unilateral soleus muscle training study (Shields and Dudley-Javoroski, 2006; Shields et al., 2006a,b), were recruited for this study. The training regimen, described in detail elsewhere (Shields et al., 2006a), involved unilateral, isometric soleus muscle training five days/week. Subjects were asked to perform four sets of 120 contractions (15 Hz, 1 on: 2 off work-rest cycle) with 5 min rests between sets, for a total session time of approximately 30 min. Training compliance (Table 1) was monitored using a custom-designed stimulator instrumented with a microprocessor and memory chips to log each stimulus train with a date and time stamp. All subjects provided written informed consent prior to inclusion in the study, as approved by the Institutional Review Board.

Table 1.

Subject Characteristics

Subject characteristic	Subject
	1	2	3	4
Age (yr)	33.5	23.8	25.1	23.0
Height (cm)	180	185	188	188
Mass (kg)	111	68	77	68
Level of Injury	T9	T10	T4	T4
ASIA Scalea	A	A	A	A
Time Since Injury (yr)	4.2	1.5	2.7	1.7
Training Duration (yr)	4.0	1.4	2.4	1.5
Compliance (%)b	81%	66%	102%	88%

^aAmerican Spinal Cord Injury Association (ASIA) classification scale.

^bMean percent of goal contractions performed throughout 6 months prior to testing.

Training produced significant muscle adaptations in our subjects, as exhibited by a mean increase in peak force (8.9%), force time integral (13.5%), contraction time (7.5 ms), and half-relaxation time (10.6 ms) as compared to the untrained limb. The force frequency curve shifted to the left by 14.9 and 7.8% at 5 and 10 Hz, respectively.

2.1. Experimental set-up

The experimental set-up has been described previously in detail (Shields, 1995). Briefly, each subject was seated (wheelchair) with the knee positioned at 90° of flexion and the ankle secured in a neutral position to a custom force plate (Genisco AWU-250 load cell). Soleus muscle electromyography (EMG) was collected using pre-amplified surface electrodes (Therapeutics Unlimited, Iowa City, IA) with a fixed 2 cm inter-electrode distance (Frey Law and Shields, 2006).

2.2. Stimulation protocol

The tibial nerve was supramaximally stimulated in the popliteal fossa using a custom computer-controlled constant-current stimulator (Shields, 1995). We used the same stimulation protocol previously reported for the untrained limb (Frey Law and Shields, 2006). Following a brief warm-up, a pre-programmed set of 11 different stimulation patterns were performed with 2 s intervals between each pattern, for a total duration of approximately 30 s. The set consisted of two components, one doublet ramp train (Bobet and Stein, 1998) used to parameterize the three models and a series of test trains to evaluate the predictive accuracy of the resulting fitted models. The order of the parameterization and test trains were as follows: (1) a single pulse (twitch); (2) a doublet ramp consisting of 15 pulses with increasing then decreasing frequencies ranging from 5 to 20 Hz with two doublets at 167 Hz; (3) three constant frequency trains (CT) of 8, 10, and 12 pulses at 5, 10, and 20 Hz, respectively; (4) three single doublet trains (DT) with a doublet (167 Hz) followed by a train of pulses at frequencies of 5, 10, and 20 Hz for a total of 9, 11, and 13 pulses, respectively; and (5) three dual doublet trains (DDT) with base frequencies of 5, 10, and 20 Hz, but with doublets at the start and in the middle of the trains.

These diverse patterns represent a range of possible stimulation approaches in accordance with the force frequency curves of paralyzed soleus muscle (Shields, 2002). Additionally, sustained frequencies higher than 20 Hz were avoided to reduce the likelihood of musculoskeletal injury from high muscle forces, as the risk of fracture is considerably higher in individuals with SCI than in able-bodied individuals (Ingram et al., 1989; Hartkopp et al., 1998; Lazo et al., 2001).

2.3. Model equations

The models investigated, a traditional linear and two contemporary nonlinear models, have been described in detail previously (Frey Law and Shields, 2006). Each of these models can accommodate any combination of discrete interpulse intervals (IPI). This input flexibility is crucial for predicting a wide-range of force responses, including the impulse-response (twitch), variable or constant frequency trains, doublets, and/or randomly spaced stimulation pulses. Each model was programmed into Matlab following previously published equations.

The simplest model is a 2nd order linear model (Close and Frederick, 1995) and has been successfully used to represent human soleus muscle (Bawa and Stein, 1976). The second, a moderately complex model, is also based on a 2nd order systems approach, but with added static nonlinearities, proposed by Bobet and Stein (1998). The third, and most complex model, was initially derived from the original Hill model (Wexler et al., 1997) with several adaptations resembling a Huxley-type approach, the distribution-moment model (Zahalak and Ma, 1990).

The linear model is comprised of a single 2nd order differential equation, (Eq. (1)). The solution, f(t), is muscle force and the input, x(t), is a series of pulses represented by dirac delta functions (δ(t) = 1/dt) at the time of each pulse (t_i) and zero otherwise (x(t) = Σδ(t_i−t₀) for i = 1−n)

$$\frac{{\mathrm{d}}^{2}f}{\mathrm{d}{t}^2}+2{\omega }_{\mathrm{n}}\xi \frac{\mathrm{d}f}{\mathrm{d}t}+{\omega }_{\mathrm{n}}^{2}f(t)=\beta {\omega }_{\mathrm{n}}^{2}x(t).$$ (1)

This linear model uses three parameters (β, ζ, and ω_n) to modulate force output (Close and Frederick, 1995).

The 2nd order nonlinear model consists of two first order differential equations (Eqs. (2) and (4)), a force saturation nonlinearity equation (3) and an equation defining a variable parameter, b (Eq. (5)) (Bobet and Stein, 1998). A total of six constant parameters (a, B, n, b₀, b₁, and k) are used in this 2nd order nonlinear model to modulate the force output, F(t), based on binary pulse inputs, u(t).

$$q(t)=\int {\mathrm{e}}^{-\mathit{\text{aT}}}u(t-T)\mathrm{d}T,$$ (2)

$$x(t)=\frac{q{(t)}^n}{q{(t)}^n+k^n},$$ (3)

$$F(t)=\mathit{\text{Bb}}\int {\mathrm{e}}^{-\mathit{\text{bT}}}x(t-T)\mathrm{d}T,$$ (4)

$$b=b_0{(1-\frac{b_{1}F(t)}{B})}^2.$$ (5)

The Hill Huxley nonlinear muscle model is comprised of two nonlinear differential equations (Ding et al., 2002, 2003), the first represents calcium kinetics and the calcium–troponin interaction (Eq. (6)), the second (Eq. (8)) represents force (Ding et al., 2002). The force output, F(t), is ultimately controlled by six constant parameters (A, τ₁, τ₂, τ_c, k_m, and R₀) similar to the 2nd order nonlinear model. However, the solution to the force (Eq. (8)) has no analytical solution, contributing to the complexity of this model.

$$\mathit{\text{Cn}}={\displaystyle \sum _{i=1}^n}{R}_i\frac{t-t_i}{{\tau }_{\mathrm{c}}}{\mathrm{e}}^{(-t-t_i/{\tau }_{\mathrm{c}})},$$ (6)

$$R_i=1+(R_0-1)\text{ exp }(-\frac{t_i-t_{i-1}}{{\tau }_{\mathrm{c}}}),$$ (7)

$$\frac{\mathrm{d}F}{\mathrm{d}t}=A\frac{C_N}{k_m+C_N}-\frac{F}{{\tau }_1+{\tau }_2{C}_N/(k_m+C_N)}.$$ (8)

The model parameters for each individual were optimized using the Matlab optimization toolbox function, lsqnonlin, a least-squares approach using the Levenberg–Marquardt method, to best fit the experimental doublet ramp force profile (Bobet and Stein, 1998). Then using these optimized parameter values, force predictions for the nine test trains (constant, doublet, and dual doublet trains at 5, 10, and 20 Hz) were determined for each model and individual.

2.4. Error calculations

Error was assessed for the nine test trains only. Overall model error (mean absolute error) was calculated as the absolute difference between predicted and experimental force-time profiles, normalized by the experimental peak force (% error). We also calculated mean directional errors to consider over or under predictions of force.

Error assessments of specific muscle properties included: normalized peak force (% PF); normalized force time integral (% FTI); half relaxation time (HRT, ms), and relative doublet difference (% DDiff) as a measure of the catch-like property of muscle (Frey Law and Shields, 2006). HRT was operationally defined as the time required for force to decay from 90% to 50% following the final stimulation peak. Relative doublet difference was the difference in force between a doublet train and its corresponding non-doublet train (DDT – DT and DT – CT), normalized by the twitch PF. Both mean absolute and constant errors were calculated.

2.5. Statistical analysis

Three-way (3 × 3 × 2), univariate repeated-measures analysis of variance (ANOVA) tests were used to analyze the overall % error, the % PF, and % FTI errors for within-subject analyses of model (linear, 2nd order nonlinear, and Hill Huxley type nonlinear), stimulation frequency (5, 10, and 20 Hz), and stimulation pattern (constant and dual doublet trains only) for simple and interaction effects (SAS 9.0). The force time property errors, HRT, and % DDT, were analyzed using separate two-way (3 × 3) repeated-measures ANOVAs for model and frequency. Repeated measures p-values were adjusted using the Huynh–Feldt epsilon when necessary to correct for violation of homogeneity of variance between measures (Huynh and Feldt, 1976). Follow-up analyses for between model effects were performed using paired t-tests with the Bonferroni correction (n = 3) as other multiple comparison procedures (e.g., Tukey’s) assume sphericity and may not be as appropriate for within-subject designs (Maxwell, 1980).

Using previously reported results from the untrained limbs of these subjects (Frey Law and Shields, 2006), each repeated measures ANOVA was increased by one level, trained versus untrained limb, to test for differences due to training. Trained versus untrained parameter values for each model were compared using paired t-tests. Significance was set at α = 0.05; for the post-hoc tests the Bonferroni correction was employed (α = 0.05/3 = 0.0167). Primarily repeated measures ANOVA F statistics are reported in the text for clarity, while figures display significant differences between models resulting from the post-hoc paired t-tests.

3. Results

A representative example of the constant and dual doublet experimental and model predictions are shown in Fig. 1. The mean overall percent error was greatest for the linear model and least for the Hill Huxley type model (Fig. 2A; F_2,6 = 68.15, p = 0.0004). Although significant, the mean pair wise differences were relatively small, ranging from 2.2% to 8.0%. Significant interactions between model and frequency occurred (F_4,12 = 16.05, p = 0.009); the two nonlinear models produced less error at higher frequencies whereas the linear model resulted in greater errors with increased frequency (Fig. 2B). Overall, the dual doublet and constant frequency trains responded relatively similarly across the three models (Fig. 2C; F_1,3 = 5.78, p = 0.10).

Fig. 1.

Representative example of the three model force predictions for the 5, 10, and 20 Hz constant frequency trains (left column) and dual doublet trains (right column) for a single subject. Experimental results are shown as the solid line in each panel. The linear model (dotted) is shown in row 1, 2nd order nonlinear model (dash-dot) in row 2, and Hill Huxley model (dashed) in row 3.

Fig. 2.

Overall % error between modeled and experimental forces; (A) mean (SEM) overall % error; (B) mean (SEM) % error by frequency; and (C) mean (SEM) % error by stimulation pattern. ^*Indicates significant difference between model pair, p-value ≤ 0.0167, for overall absolute error using post-hoc paired t-test with Bonferroni correction.

3.1. Muscle property errors

The linear model produced greater absolute errors for PF (Fig. 3A; F_2,6 = 53.62, p = 0.0006) and FTI (Fig. 4A; F_2,6 = 31.23, p = 0.0007) than the nonlinear models. The two nonlinear models predicted PF and FTI equally well (Figs. 3A, 4A). The linear model had difficulty predicting PF and FTI with higher frequency (Figs. 3B, 4B) and/or dual doublet (Figs. 3C, 4C) conditions.

Fig. 3.

Peak force (PF) error between modeled and experimental forces; (A) mean (SEM) overall absolute % error; (B) mean (SEM) constant % error by frequency; and (C) mean (SEM) constant % error by stimulation pattern. ^*Indicates significant difference between model pair, p-value ≤ 0.0167, for overall absolute error using post-hoc paired t-test with Bonferroni correction.

Fig. 4.

Force time integral (FTI) error between modeled and experimental forces; (A) mean (SEM) overall absolute % error; (B) mean (SEM) constant % error by frequency; and (C) mean (SEM) constant % error by stimulation pattern. ^*Indicates significant difference between model pair, p-value ≤ 0.0167, for overall absolute error using post-hoc paired t-test with Bonferroni correction.

Muscle force decay HRT was best predicted by the Hill Huxley type model and least accurately by the linear model (Fig. 5A, F_2,6 = 47.98, p = 0.003). The HRT errors were independent of frequency overall (F_2,6 = 4.38, p = 0.067), however the significant interaction between model and frequency (F_4,12 = 8.68, p = 0.0017) would indicate the nonlinear models may more accurately represent contractile speed at the lowest frequency (Fig. 5B).

Fig. 5.

Half relaxation time (HRT) error between modeled and experimental forces; (A) mean (SEM) overall absolute % error; (B) mean (SEM) constant % error by frequency. ^*Indicates significant difference between model pair, p-value ≤ 0.0167, for overall absolute error using post-hoc paired t-test with Bonferroni correction. Note stimulation pattern was not included in this analysis.

The errors associated with doublet activation (representing the catch-like property of muscle) for the linear model were more than twice that of the two nonlinear models (Fig. 6A, F_2,6 = 46.90, p = 0.006). However, this difference was driven largely by the substantial doublet error at 20 Hz (Fig. 6B, F_2,6 = 67.48, p < 0.0001). At the lower frequencies the linear model produced relatively similar errors as the nonlinear models.

Fig. 6.

Doublet difference (DDiff), an indicator of the ‘catch-like’ property of muscle, error between modeled and experimental forces; (A) mean (SEM) overall absolute % error; (B) mean (SEM) constant % error by frequency. ^*Indicates significant difference between model pair, p-value ≤ 0.0167, for overall absolute error using post-hoc paired t-test with Bonferroni correction. Note stimulation pattern was not included in this analysis.

3.2. Trained versus untrained

The three models were equally capable of predicting trained and untrained paralyzed muscle force for all error measures (Fig. 7, p-values ranged from 0.062 to 0.934). However, a significant four-way interaction occurred for the overall % error (training × frequency × stimulation × model) and a significant three-way interaction for the % PF error (training × frequency × model). While no other error terms resulted in significant training interactions, these two highlight the complexity and challenges associated with modeling the nonlinear nature of muscle force.

Fig. 7.

Mean errors by subject for the overall % error for trained versus untrained limbs. The linear model is shown in row 1, 2nd order nonlinear model in row 2, and Hill Huxley model in row 3. No significant error differences were observed with training.

All three muscle models were sensitive to changes in muscle properties following this training regimen, as evidenced by significant differences in parameter values between conditions. These included parameters: β and ω_n for the linear model; B and a for the 2nd order nonlinear model; and τ_c and k_m for Hill Huxley type nonlinear model (Table 2).

Table 2.

Optimized parameter values

Model	Parameter	Definition	Subject				Mean (trained)	Mean (untrained)d
			1	2	3	4
Lineara	B, N/s	Gain	35.4	38.3	30.2	37.2	35.3*	30.5
	ζ	Damping coefficient	0.65	0.68	0.69	0.74	0.69	0.69
	ωn, rad/s	Natural frequency	12.1	9.9	13.2	9.7	11.2*	14.4
2nd order nonlinearb	B, N	Gain	631	632	656	750	667*	554
	a, 1/s	Rate constant	17.1	15.0	16.0	13.0	15.2*	18.3
	b0, 1/s	Rate constant	10.1	12.5	13.9	11.4	12.0	13.3
	b1	Force feedback coefficient	−0.37	−0.04	−0.15	0.00	−0.14	−0.25
	k	Unspecified constant	0.40	0.36	0.56	0.62	0.49	0.38
	n	Unspecified constant	4.4	2.5	2.4	2.2	2.9	4.8
Hill Huxley type nonlinearc	A, N/ms	Gain	7.3	7.4	8.8	6.7	7.6	7.7
	τ1, ms	Decay time constant	27.6	16.4	43.0	49.2	34.0	30.1
	τ2, ms	Decay time constant	88.3	102.4	62.7	94.5	87.0	68.6
	τc, ms	Calcium time constant	19.7	33.2	21.4	28.9	25.8*	17.0
	km	‘Sensitivity’ time constant	0.07	0.13	0.17	0.17	0.14*	0.06
	R0	‘Force enhancement’	3.7	1.2	3.0	2.4	2.6	5.0

^aParameters, units and definitions standard for 2nd order linear model.

^bParameters, units and definitions based on Bobet and Stein (1998).

^cParameters, units and definitions based on Ding, et al. (2002).

^dUntrained mean parameter values as reported in Frey Law and Shields (2006).

^*Significantly different from untrained parameter values, p ≤ 0.05.

4. Discussion

The main finding of this study was that the Hill Huxley type nonlinear, the 2nd order nonlinear, and the linear mathematical muscle models were able to predict most aspects of muscle force equally well in this example of trained and untrained paralyzed muscle. The linear model produced the least accurate force predictions overall, with nearly equal predictive accuracy for both nonlinear modeling strategies. The force nonlinearities exhibited above the fusion frequency were not well represented by the linear model.

Neuro-prosthetic devices would benefit from accurate but simplistic control algorithms to span the range of input parameters necessary for functional movement. Often devices use simplistic elastic or linear representations of muscle force, which may include significant force errors. The Hill Huxley type nonlinear model, although quite accurate, may be more difficult to incorporate into a control algorithm due to its dependence on numerical analysis techniques. The two 2nd order models (linear and nonlinear) would be relatively simple to integrate into a control strategy, with greater accuracy resulting from the nonlinear model. However, if specific force time properties such as HRT were essential for a particular application, the Hill Huxley type model may be preferred. These considerations may be particularly important depending on whether fine-motor tasks versus gross movements were desired outcomes from the neuro-prosthetic device.

The observed error differences between fast and slow animal muscle (Bobet and Stein, 1998) were not reproduced in this example of trained versus untrained human paralyzed muscle. This may be a result of the specific training protocol used in this study and not be representative of other training conditions possible. Repetitive FES training does not fully reverse the muscle adaptations seen with SCI, and may vary with specific protocol. However, the significant differences in muscle properties suggest that in at least this one example, the training adaptations do not adversely affect the predictive accuracy of these muscle models. Additionally, slow cat or rat muscle may not provide an equivalent model for trained human paralyzed muscle properties. The differences seen in the animal models were not large in magnitude (4.0–5.5% error for slow versus 2.4–2.8% error for fast), but were consistent across their sample population (n = 3) (Bobet and Stein, 1998). The original Hill Huxley type model was validated using rat gastrocnemius and soleus muscle, with lower correlation coefficients for the soleus (Wexler et al., 1997). However, this model has undergone numerous advances since that introductory paper.

In accordance with our hypothesis, all three models consistently showed one parameter associated with predicted muscle contractile properties (ω_n and decreased as rate constants; τ_c increased as a time constant, see Table 2). The significant differences in these parameter values between trained versus untrained paralyzed muscle might suggest that parameter values determined using able-bodied muscle may not provide the best representation for all paralyzed conditions.

Interestingly, each model did not consistently vary their analogous gain parameters. The gain parameters, β, B, and A, decreased, increased, and remained constant in response to training for the linear, 2nd order nonlinear and the Hill Huxley models, respectively. However, with training, the Hill Huxley type model parameter k_m increased, which also has a significant positive influence on PF (Frey Law and Shields, 2005) and could have acted in place of gain parameter, A. The linear model tended to over-predict force above the fusion frequency. For slower muscle, this would occur at lower frequencies. Thus, in the trained condition the linear model may have decreased the system gain factor as a compensatory mechanism to minimize the overall error.

These results further support our previous conclusion that physiologic parameter definitions should be used judiciously (Frey Law and Shields, 2005). Indeed, the slower muscle speed properties were consistently represented by the three models’ parameters; however, the muscle gain values, which could be interpreted as indicators of “strength,” would have produced different conclusions (i.e. increased, decreased, and no change in strength) for each model.

4.1. Limitations

This small sample size provides initial support for differences in model parameter values resulting from training adaptations, without a concomitant loss in predictive accuracy. However, these findings may or may not extend to widely varying training regimens. As the first study to investigate model predictions using trained paralyzed muscle, we are unable to compare our results to previous reports. Variability between subjects and between stimulation patterns adds to the challenge of model comparisons and practical implementation. A range of stimulation trains should be investigated for a more complete overall analysis, but the model of choice for a particular application may rely on the most relevant frequencies and patterns. Future work is needed to determine the influence of parameterization input trains on the final optimized model as only one pattern was used for comparison purposes in this study.

4.2. Functional implications

Untrained paralyzed muscle is highly fatiguable, shows faster contractile speeds, and post fatigue potentiation (Shields et al., 2006b) all properties that can be attenuated with early training programs (Shields and Dudley-Javoroski, 2006). These variations in muscle properties between trained and untrained muscle may be problematic for the optimal use of certain feedback control algorithms during FES. An important goal of FES research is to develop neuro-prostheses that are useful for grasping, standing, and walking (Popovic et al., 2001). Some of these functional activities may require higher levels of accuracy (e.g., eating with utensils) than others (e.g., supported standing), resulting in potentially different ideal modeling strategies. The present study illustrates that training status may not adversely affect the predictive accuracy of a model, however the optimally determined muscle model is influenced by the type of model used and the relative physiological state (trained versus untrained) of the paralyzed muscle.