This study investigates the effect that upper body vibration has on the recovery rate of the biceps muscle. A mathematical model that accounts for vibration is developed by adapting three vibration terms into the Stephenson and Kojourahov skeletal muscle regeneration mathematical model. The first term accounts for the increase in the influx rate of type 1 macrophages (${\mathrm{P}}_1$). These cells are part of the body’s immune response to muscle damage. They control the proliferation rate of satellite cells ($\mathrm{S}$) and phagocytize dead myofiber cells. The second term accounts for the rate of the phenotype change of ${\mathrm{P}}_1$ to type 2 macrophages (${\mathrm{P}}_2$). ${\mathrm{P}}_2$ are used to support $\mathrm{S}$ differentiation and prevent apoptosis of myoblasts ($M_{\mathrm{b}}$). The final term accounts for the fusion rate of $M_{\mathrm{b}}$. $M_{\mathrm{b}}$ fuse with each other to create myotubes which align to create myofibers. The addition of these three terms decreases the overall skeletal muscle regeneration time by 47%. The model is validated on the macroscopic scale by subjecting test participants to a muscle damage and recovery protocol involving vibration therapy.

这项研究调查了上身振动对二头肌肌肉恢复率的影响。通过将三个振动项应用到Stephenson和Kojourahov骨骼肌再生数学模型中，开发了一个解释振动的数学模型。第一项解释了1型巨噬细胞的涌入率增加（${\mathrm{P}}_{\mathrm{1个}}$）。这些细胞是人体对肌肉损伤的免疫反应的一部分。它们控制卫星细胞的增殖速率（$\mathrm{小号}$）并吞噬死亡的肌纤维细胞。第二项解释了表型变化的速率${\mathrm{P}}_{\mathrm{1个}}$ 键入2个巨噬细胞（${\mathrm{P}}_2$）。 ${\mathrm{P}}_2$ 用于支持 $\mathrm{小号}$ 分化并阻止成肌细胞凋亡（${\mathrm{中号}}_{\mathrm{b}}$）。最后一项说明了融合率${\mathrm{中号}}_{\mathrm{b}}$。 ${\mathrm{中号}}_{\mathrm{b}}$彼此融合形成肌管，肌管对齐形成肌纤维。将这三个术语相加可使整体骨骼肌再生时间减少47％。通过使测试参与者经受涉及振动疗法的肌肉损伤和恢复协议，可以在宏观尺度上验证该模型。