Giesl Peter, Meisel Dorothea, Scheurle Jürgen, Wagner Heiko
Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching bei München, Germany.
J Theor Biol. 2004 May 7;228(1):115-25. doi: 10.1016/j.jtbi.2003.12.006.
We present a model of the human elbow and study the problem of existence and stability of equilibrium states. Our main goal is to demonstrate that stable equilibrium states exist just on grounds of the mechanical properties of the muscles and the skeleton. In particular, additional control mechanisms such as reflexes are not necessary to obtain stability. We assume that the activation of flexor and extensor muscles is constant and such that the right angle is an equilibrium state. We give a complete bifurcation diagram of all equilibrium states in terms of the elbow angle, the activation of the muscles and the mass of a load. Moreover, we define a dimensionless model parameter which allows to determine whether or not there are stable equilibria at an angle of ninety degrees. It turns out that the dependency of the muscle forces on the length of the muscles is the crucial factor for the stability of such an equilibrium.
我们提出了一个人体肘部模型，并研究平衡状态的存在性和稳定性问题。我们的主要目标是证明仅基于肌肉和骨骼的力学特性就存在稳定的平衡状态。特别是，诸如反射等额外的控制机制对于获得稳定性并非必要。我们假设屈肌和伸肌的激活是恒定的，使得直角为平衡状态。我们根据肘部角度、肌肉激活和负载质量给出了所有平衡状态的完整分岔图。此外，我们定义了一个无量纲模型参数，该参数可用于确定在九十度角处是否存在稳定平衡。结果表明，肌肉力对肌肉长度的依赖性是这种平衡稳定性的关键因素。
