Department of Kinesiology, School of Public Health and Health Sciences, University of Massachusetts, Amherst, Massachusetts.
Department of Molecular Physiology and Biophysics, Larner College of Medicine, University of Vermont, Burlington, Vermont.
Biophys J. 2022 Apr 19;121(8):1424-1434. doi: 10.1016/j.bpj.2022.03.018. Epub 2022 Mar 18.
Viscoelastic properties of striated muscle are often measured using length perturbation analysis and quantified as a complex modulus, whose elastic and viscous components reflect the energy-storage and energy-absorbing properties of the tissue, respectively. The energy stored as inertia is commonly ignored due to the small size of samples examined, typically <1 mm. Considering recent advances in tissue engineering to generate muscle tissues of larger sizes, we questioned whether ignoring the inertial artifact was still reasonable in these samples. To answer this question, we derived and solved the one-dimensional wave equation that describes the propagation of strain along the length of a sample. The inertial artifact was predicted to contaminate the elastic modulus with (2πf)Lρ/6, where f is perturbation frequency, L is muscle length, and ρ is muscle density. We then measured viscoelastic properties up to 500 Hz in mouse skeletal muscle fibers at long (4.8 mm) and short (<1 mm) lengths and up to 100 Hz in rat cardiac slices at long (10-12 mm) and short (<2 mm) lengths. We found the elastic modulus of long preparations was elevated as frequency increased and was about half the magnitude of that predicted by the model. While the prediction tended to overestimate the measured inertial artifact, these results provided some validity to the model. We used the predicted artifact as an overly conservative estimate of error that might arise in a mechanics assay of mammalian striated muscle, whose nominal resting stiffness is on the order 100 kN m. We found that muscle lengths of <1 mm resulted in negligible inertial artifact (<0.5% error) for perturbation frequencies under 250 Hz. Muscle samples longer than 5 mm, on the other hand, would result in >5% error at frequencies of 200 Hz and higher.
横纹肌的黏弹性特性通常使用长度微扰分析进行测量,并被量化为复弹性模量,其弹性和黏性分量分别反映了组织的储能和耗能特性。由于所研究的样本通常小于 1mm,因此由于样本较小而忽略了作为惯性储存的能量。考虑到组织工程技术的最新进展,可以生成更大尺寸的肌肉组织,我们质疑在这些样本中忽略惯性伪影是否仍然合理。为了回答这个问题,我们推导并求解了描述应变沿样本长度传播的一维波动方程。预测惯性伪影会使弹性模量污染(2πf)Lρ/6,其中 f 是微扰频率,L 是肌肉长度,ρ 是肌肉密度。然后,我们在长(4.8mm)和短(<1mm)长度的小鼠骨骼肌纤维中测量了高达 500Hz 的黏弹性特性,在长(10-12mm)和短(<2mm)长度的大鼠心脏切片中测量了高达 100Hz 的黏弹性特性。我们发现,随着频率的增加,长标本的弹性模量升高,并且约为模型预测值的一半。虽然该预测值倾向于高估测量的惯性伪影,但这些结果为该模型提供了一定的有效性。我们将预测的伪影用作哺乳动物横纹肌力学测定中可能出现的误差的过度保守估计,其名义静刚度约为 100kN/m。我们发现,对于低于 250Hz 的微扰频率,小于 1mm 的肌肉长度会导致可忽略的惯性伪影(<0.5%的误差)。另一方面,长度大于 5mm 的肌肉样本在 200Hz 及更高频率下会导致超过 5%的误差。
Phys Rev E Stat Nonlin Soft Matter Phys. 2012-4
J Muscle Res Cell Motil. 1994-4
IEEE Trans Neural Syst Rehabil Eng. 2018-10
Ultrason Imaging. 2013-4
Br J Ophthalmol. 2007-3
Am J Physiol Cell Physiol. 2015-3-15
Can J Cardiol. 2014-7-2
Circ Heart Fail. 2012-9-26
Methods. 2011-9-16