Predicting human chronically paralyzed muscle force: a comparison of three mathematical models

J Appl Physiol, 2006 · DOI: 10.1152/japplphysiol.00935.2005 · Published: March 1, 2006

Spinal Cord Injury Neurology Biomechanics

Simple Explanation

This study compares three mathematical models to predict the force of paralyzed muscles stimulated with electricity. The models include a simple linear model and two more complex nonlinear models. The forces produced by the soleus muscle of four individuals with spinal cord injury were used to test the models. The models were optimized using a ramp-like stimulation pattern and then tested with constant and variable stimulation patterns. The results showed that the nonlinear models were generally more accurate than the linear model in predicting muscle force. The choice of model may depend on the specific application.

Study Duration

Not specified

Participants

Four individuals with complete, chronic SCI

Evidence Level

Not specified

Key Findings

1
Nonlinear models more accurately predicted paralyzed muscle force-time profiles than the linear model.
2
The Hill-Huxley-type nonlinear model and the second-order nonlinear model provided nearly equivalent force predictions, despite differences in modeling strategies.
3
The linear model is best able to predict paralyzed muscle forces using constant, low-frequency stimulation trains.

Research Summary

This study evaluated three mathematical models for predicting the force of electrically stimulated paralyzed muscles in individuals with chronic spinal cord injury (SCI). The models included a linear model and two nonlinear models (Hill-Huxley-type and second-order nonlinear). The models were optimized using experimental data from the soleus muscle of four individuals with SCI and tested with various stimulation patterns. The results indicated that the nonlinear models generally provided more accurate force predictions than the linear model, particularly at higher stimulation frequencies or with variable stimulation patterns. The choice of model may depend on the specific therapeutic application.

Practical Implications

Rehabilitation Strategies

The use of subject-specific mathematical models can aid in the development of individualized rehabilitation strategies to optimally stress the musculoskeletal system after SCI using electrical stimulation.

Model Selection

The choice of muscle model (linear vs. nonlinear) may depend on the specific application, such as the frequency and pattern of electrical stimulation used in therapy.

Therapeutic Application

Any one of the three models could prove to be an ideal choice, depending on the intended therapeutic application, and thus the frequency and/or stimulation patterns used.

Study Limitations

1
The results are limited to supramaximally stimulated, isometric contractions in paralyzed soleus muscle at a single joint angle.
2
The parameter values and errors obtained for the soleus muscle may not be representative of those for other paralyzed muscles.
3
The test protocol stimulations induced a minimal but measurable level of fatigue (≤10 % mean decrease in PF of the doublet ramp train).

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