人体运动离不开神经—肌肉—骨骼系统。微纳米尺度上,构成这一系统的生物材料均具有自相似结构,但其本构忽略了结构的分形特征,功能上难以刻画其黏弹性响应的超长时程性。宏观尺度上,肌肉会相对其缠绕的骨骼纵向滑移、横向接触,给肌骨系统有限元仿真带来巨大的计算量,而多体动力学难以建模肌肉在这一过程中的流动与变形。因此,本文基于“自相似几何与分数阶力学”与“肌骨系统柔性多体动力学建模”两大思路,研究了神经—肌肉—骨骼系统的动力学:微观尺度上,针对生物纤维的黏弹性力学建模问题,本文由韧带/肌腱的微纳米自相似结构出发,将胶原纤维与基体分别简化为线性弹簧、黏壶元件,自下而上地抽象出分形弹簧—黏壶网络,称之为黏弹性胞元。基于Heaviside算子代数方法,建立胞元的分数阶黏弹性本构,成功刻画了膝关节与脊柱韧带的松弛响应。胞元理论揭示了生物纤维的阶梯分形结构与其分数阶黏弹性响应的内在联系,并给出了其短时程与长时程黏弹性响应的不同机制。进一步将胞元理论推广至神经冲动建模,从光滑与含棘突神经纤维的功能结构出发,自下而上地抽象出神经脉冲传导对应的分形电阻—电容电路。在此基础上,分别建立两类神经元分数阶LIF模型,发现了分数阶微分算子调制含棘突神经元的冲动传导过程。宏观尺度上,针对肌肉—骨骼相互作用建模问题,本文在Hill肌肉模型的基础上,提出基于ALE描述的骨骼肌索单元。引入物质坐标将肌肉物质滑动与其网格的空间运动解耦,实现了肌肉—骨骼间纵向滑移建模。提出基于ALE描述的羽状肌单元,定义物质坐标为肌肉厚度,物质坐标变化改变肌肉截面积与羽状角,实现了肌肉—骨骼间的接触挤压建模。上述建模方法分别应用在二腹肌—舌骨、小腿三头肌、以及膝关节肌骨系统柔性多体动力学模型当中,实现了肌骨包覆的动力学仿真,并提高了仿真结果与超声弹性成像、等速加载等实验的一致性。最后,本文基于柔性多体动力学方法,建立了考虑腹压的人体胸—腰椎模型。提出肌肉膜单元,将肌肉几何由索推广至直纹面,模拟腹压引起的核心肌群几何变化。基于理想气体假设建立腹压气柱模型,实现了核心肌群与腹压耦合的正向动力学仿真。在此基础上探讨了腹压对脊柱传力路径的影响,揭示了其降低椎间盘载荷的力学机制。
The neuromusculoskeletal system is essential for human locomotion. At the nano-micro level, the soft tissues of this system are made up of self-similar structures, whereas their constitutive theories have not considered the fractal structural patterns. Functionally, these equations cannot describe the ultra-long characteristics of bio-tissue viscoelasticity. At the macro level, the skeletal muscles can always slide and contact with their wrapping bones during human locomotion. To simulate these effects, the finite element models would lead to a large computational expense. Meanwhile, it is difficult for multibody models to describe material sliding and deformations of muscle tissues. Therefore, this thesis investigates the multilevel dynamic performances of human neuromusculoskeletal systems based upon the two basic approaches, i.e., fractalization of biomaterial structures and functions, and flexible modeling of musculoskeletal systems.At the micro level, to describe the bio-fiber viscoelasticity, a spring-dashpot fractal network with self-similar topology, named hyper-cell element, is abstracted from the micro-nano structure of ligaments and tendons. Based on a bottom-up approach, linear springs and dashpots are the mechanical simplifications of the collagen fibers and the protein matrix, respectively. The fractional-order viscoelastic constitutive equations of the hyper-cell element are derived by the Heaviside operational calculus. The responses of these fractional functions are consistent with available knee/spinal ligament relaxation experiments. The hyper-cell theory reveals the correlations between the fractal structures of bio-fibers and their fractional-order viscoelastic responses, and it also explains the different mechanisms for the initial and long-term viscoelastic behaviors. Moreover, the proposed hyper-cell theory is also utilized in the neuronal spiking models. Two types of self-similar resistor-capacitor networks are developed based on the functional structures of smooth and spiny dendrites, respectively. Then, two types of fractional leaky integrate-and-fire (LIF) models are established by this hyper-cell network, and the spiking patterns of spiny dendrites are found to be modulated by the standard 0.5-order fractional derivative.At the macro level, to describe the interactions between the muscle and its underlying bones, a novel cable element of the skeletal muscle is developed based on an arbitrary Lagrangian-Eulerian description. In this ALE element, the mesh nodes and the material points are not associated with each other, where the material coordinate $s$ is introduced to characterize the muscular mass flow over its wrapping bones. Moreover, to characterize the muscle-bone transverse contact and compression, another ALE-type element for the pennated muscle is formulated by describing $s$ as the muscle thickness. The proposed ALE elements are utilized in the musculoskeletal models, including the digastric-hyoid interactions, the triceps surae, and the knee system. As a result, these muscle-bone wrapping systems are successfully characterized by the proposed multibody formulation, which improves the simulation accuracy compared with the sonoelastographic and isokinetic measurements.Finally, based on the flexible multibody approach, a musculoskeletal model for the human thoracic-lumbar spine is proposed, which considers the effect of the intra-abdominal pressure (IAP). To discrete the core muscles, a membrane element is formulated by changing the muscular geometry from one-dimensional cable to a ruled surface. Therefore, the three-dimensional changes of core muscles due to IAP can be described based on this element. Moreover, a column model of IAP is presented by assuming the gas inside ideal and isothermal. Based on the flexible musculoskeletal model, one can perform the forward dynamics simulations for the coupling between the core muscles and IAP. The influence of IAP on the spinal load transmission is discussed, where the mechanism of IAP to reduce intervertebral disc loading is also presented.