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<p>The mathematical models with appropriate parameters are important to investigate the fundamental interaction mechanisms among the nervous system, biomechanical system, and external environment. This paper presents an effective multibody model for the <i>Caenorhabditis elegans</i> (<i>C. elegans</i>) swimming in viscous fluids based on the forward recursive formulation. The environmental viscous force is formulated by the resistive force theory. To identify the resistive coefficients, behavioral experiments are performed to track the motion of actual nematodes, and the head motion and the body’s undulatory locomotion are obtained by video analysis. A gradient-based algorithm is presented for resistive coefficients identification by minimizing the difference between the head motion of the simulation and the experiment under the same locomotion. Sensitivity analysis is performed to provide the gradient information, where the sensitivity equations are derived analytically by the direct differentiation method from the multibody equations. The validity of the derived sensitivity equations is verified by the finite difference method. Subsequently, the unknown coefficient identifications are executed for two cases. Compared with the experimental data, the numerical result not only demonstrates that the presented multibody model can effectively describe the mechanical behavior of the nematode but also verifies the validity of the identification. Besides, the identified coefficients give results that agree better with the experimental data than the theoretical coefficients, which illustrates the necessity of the identification. Moreover, the absence of over-fitting is verified by examining the coefficient of variance of the identification results. The presented framework can also be employed for other organisms or bionic robots.</p>

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Multibody modeling and resistive coefficient identification for Caenorhabditis elegans swimming in viscous fluids

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Boyang Wang,
  • Peng Zhao,
  • Yi Rong,
  • Zhaoyu Li,
  • Tao Fang,
  • Zhuyong Liu

摘要

The mathematical models with appropriate parameters are important to investigate the fundamental interaction mechanisms among the nervous system, biomechanical system, and external environment. This paper presents an effective multibody model for the Caenorhabditis elegans (C. elegans) swimming in viscous fluids based on the forward recursive formulation. The environmental viscous force is formulated by the resistive force theory. To identify the resistive coefficients, behavioral experiments are performed to track the motion of actual nematodes, and the head motion and the body’s undulatory locomotion are obtained by video analysis. A gradient-based algorithm is presented for resistive coefficients identification by minimizing the difference between the head motion of the simulation and the experiment under the same locomotion. Sensitivity analysis is performed to provide the gradient information, where the sensitivity equations are derived analytically by the direct differentiation method from the multibody equations. The validity of the derived sensitivity equations is verified by the finite difference method. Subsequently, the unknown coefficient identifications are executed for two cases. Compared with the experimental data, the numerical result not only demonstrates that the presented multibody model can effectively describe the mechanical behavior of the nematode but also verifies the validity of the identification. Besides, the identified coefficients give results that agree better with the experimental data than the theoretical coefficients, which illustrates the necessity of the identification. Moreover, the absence of over-fitting is verified by examining the coefficient of variance of the identification results. The presented framework can also be employed for other organisms or bionic robots.