Optimization of Active Muscle Force-Length Models Using Least Squares Curve Fitting

Area of Science:

• Biomechanics
• Skeletal Muscle Physiology
• Computational Biology

Background:

• Active force-length relationships are crucial for understanding skeletal muscle function.
• Existing models for active force-length relationships have limitations.
• Accurate modeling is essential for simulating human and animal movements.

Purpose of the Study:

• To propose an asymmetric Gaussian function as a novel model for active muscle force-length relationships.
• To optimize and compare the proposed model against existing force-length models.
• To evaluate model performance using simulated and experimental skeletal muscle data.

Main Methods:

• Development and parametrization of an asymmetric Gaussian function.
• Least squares curve fitting method for model optimization.
• Validation using simulated sarcomere data and rabbit extensor digitorum II experimental data.

Main Results:

• All tested force-length models, including the asymmetric Gaussian function, provided reasonable fits to the data.
• The Gordon-Huxley-Julian model and the proposed asymmetric Gaussian function showed slightly better performance based on RMSE and R-squared.
• Statistical differences in performance between the best models were minor for both simulated and experimental datasets.

Conclusions:

• The asymmetric Gaussian function is a viable alternative for modeling active muscle force-length relationships.
• The proposed parametrization method facilitates the application of these models in biomechanical studies.
• These models can be utilized in research investigating skeletal muscle forces driving human and animal body movements.