Frey Law Laura A, Shields Richard K
Graduate Program in Physical Therapy and Rehabilitation Science, 1-252 Medical Education Bldg,, The University of Iowa, Iowa City, IA, USA.
J Neuroeng Rehabil. 2005 May 31;2:12. doi: 10.1186/1743-0003-2-12.
Mathematical muscle models may be useful for the determination of appropriate musculoskeletal stresses that will safely maintain the integrity of muscle and bone following spinal cord injury. Several models have been proposed to represent paralyzed muscle, but there have not been any systematic comparisons of modelling approaches to better understand the relationships between model parameters and muscle contractile properties. This sensitivity analysis of simulated muscle forces using three currently available mathematical models provides insight into the differences in modelling strategies as well as any direct parameter associations with simulated muscle force properties.
Three mathematical muscle models were compared: a traditional linear model with 3 parameters and two contemporary nonlinear models each with 6 parameters. Simulated muscle forces were calculated for two stimulation patterns (constant frequency and initial doublet trains) at three frequencies (5, 10, and 20 Hz). A sensitivity analysis of each model was performed by altering a single parameter through a range of 8 values, while the remaining parameters were kept at baseline values. Specific simulated force characteristics were determined for each stimulation pattern and each parameter increment. Significant parameter influences for each simulated force property were determined using ANOVA and Tukey's follow-up tests (alpha <or= 0.05), and compared to previously reported parameter definitions.
Each of the 3 linear model's parameters most clearly influence either simulated force magnitude or speed properties, consistent with previous parameter definitions. The nonlinear models' parameters displayed greater redundancy between force magnitude and speed properties. Further, previous parameter definitions for one of the nonlinear models were consistently supported, while the other was only partially supported by this analysis.
These three mathematical models use substantially different strategies to represent simulated muscle force. The two contemporary nonlinear models' parameters have the least distinct associations with simulated muscle force properties, and the greatest parameter role redundancy compared to the traditional linear model.
数学肌肉模型可能有助于确定适当的肌肉骨骼应力，从而在脊髓损伤后安全地维持肌肉和骨骼的完整性。已经提出了几种模型来表示瘫痪肌肉，但尚未对建模方法进行任何系统比较，以更好地理解模型参数与肌肉收缩特性之间的关系。使用三种当前可用的数学模型对模拟肌肉力进行的敏感性分析，有助于深入了解建模策略的差异以及与模拟肌肉力特性的任何直接参数关联。
比较了三种数学肌肉模型：一个具有3个参数的传统线性模型和两个当代非线性模型，每个非线性模型具有6个参数。针对三种频率（5、10和20Hz）下的两种刺激模式（恒定频率和初始双峰序列）计算模拟肌肉力。通过在8个值的范围内改变单个参数来对每个模型进行敏感性分析，而其余参数保持在基线值。针对每种刺激模式和每个参数增量确定特定的模拟力特征。使用方差分析和Tukey后续检验（α≤0.05）确定每个模拟力特性的显著参数影响，并与先前报道的参数定义进行比较。
3个线性模型的每个参数最明显地影响模拟力大小或速度特性，这与先前的参数定义一致。非线性模型的参数在力大小和速度特性之间显示出更大的冗余性。此外，对其中一个非线性模型的先前参数定义得到了一致支持，而另一个仅得到了该分析的部分支持。
这三种数学模型使用截然不同的策略来表示模拟肌肉力。与传统线性模型相比，两个当代非线性模型的参数与模拟肌肉力特性的关联最不明显，且参数作用冗余性最大。
