软组织非受限压缩实验附加力消除方法
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摘要
针对非受限压缩试验中软组织样本附加力对样本高度以及力学响应存在影响的问题,提出了一种能够消除样本附加力的修正方法,使得到的本构模型参数更加接近于真实.首先对软组织本构模型提出了修正,包括用以消除附加力对几何参数影响的几何修正项和用以消除样本自身重力对力学响应影响的应力修正项.然后通过对肝脏样本进行压缩松弛实验,依次施加不同载荷并测量给定载荷条件下的样本高度,利用二阶的Prony级数拟合得到松弛阶段的稳定值作为样本的准静态响应.基于获得的软组织样本的准静态力学响应,利用修正后本构模型与无修正本构模型拟合得到模型参数,对比修正前后模型的拟合误差来验证方法的有效性.结果显示:修正后的模型具有更小的拟合误差,尤其在小应变区域误差要明显小于无修正模型,表明所提修正方法能够在一定程度上消除附加力的影响.
In the unconstrained compression test,the preload force and gravity have a lot influence on the mechanical response of soft tissue samples.Aiming at this problem,a correction method that can eliminate the additional force of the sample was proposed.Firstly,the soft tissue constitutive model was modified including geometric correction term for the effect of additional forces and the stress correction term for the samples' gravity on the mechanical response.Secondly,a uniaxial compression-relaxation test was performed on the liver samples.Different loads were applied in sequence and the height of the sample was measured under given loading conditions.The second-order Prony series fitting was used to obtain the stable value of the relaxation phase as the quasi-static response of the sample.Finally,based on the quasi-static mechanical responses of the obtained soft tissue samples,the model parameters were fitted by using the modified constitutive model and the unmodified constitutive model.The fitting errors of the model before and after correction were compared to verify the validity of the method.The result shows that the modified model has a smaller fitting error,especially in the small strain region,and the error is obviously smaller than the uncorrected model,which proves that the proposed correction method can eliminate the influence of additional force to a certain extent.
In the unconstrained compression test,the preload force and gravity have a lot influence on the mechanical response of soft tissue samples.Aiming at this problem,a correction method that can eliminate the additional force of the sample was proposed.Firstly,the soft tissue constitutive model was modified including geometric correction term for the effect of additional forces and the stress correction term for the samples' gravity on the mechanical response.Secondly,a uniaxial compression-relaxation test was performed on the liver samples.Different loads were applied in sequence and the height of the sample was measured under given loading conditions.The second-order Prony series fitting was used to obtain the stable value of the relaxation phase as the quasi-static response of the sample.Finally,based on the quasi-static mechanical responses of the obtained soft tissue samples,the model parameters were fitted by using the modified constitutive model and the unmodified constitutive model.The fitting errors of the model before and after correction were compared to verify the validity of the method.The result shows that the modified model has a smaller fitting error,especially in the small strain region,and the error is obviously smaller than the uncorrected model,which proves that the proposed correction method can eliminate the influence of additional force to a certain extent.
引文
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[2]WANG M,YANG N.A review of bioregulatory and coupled mechanobioregulatory mathematical models for secondary fracture healing[J].Medical Engineering&Physics,2017,48:90-102.
[3]BROUWER I,USTIN J,BENTLEY L,et al.Measuring in vivo animal soft tissue properties for haptic modeling in surgical simulation[J].Stud Health Technol Inform,2001,81:69-74.
[4]MALUKHIN K,EHMANN K.Mathematical modeling and virtual reality simulation of surgical tool interactions with soft tissue:a review and prospective[J].Journal of Engineering and Science in Medical Diagnostics and Therapy,2018,1(2):20802.
[5]MATTEI G,AHLUWALIA A.Sample,testing and analysis variables affecting liver mechanical properties:a review[J].Acta Biomaterialia,2016,45:60-71.
[6]MILLER K.Method of testing very soft biological tissues in compression[J].Journal of Biomechanics,2005,38(1):153.
[7]ZHANG X,FISHER M B,WOO L Y,et al.The assumption of a negligible preload on the determination of viscoelastic properties based on the quasi-linear viscoelastic(QLV)theory[C]//Proc of IEEE/ICME International Conference on Complex Medical Engineering.Beijing:IEEE,2007:1617-1620.
[8]HRAPKO M,van DOMMELEN J A,PETERS G W,et al.The influence of test conditions on characterization of the mechanical properties of brain tissue[J].Journal of Biomechanical Engineering,2008,130(3):10.
[9]AYYILDIZ M,CINOGLU S,BASDOGAN C.Effect of normal compression on the shear modulus of soft tissue in rheological measurements[J].Journal of the Mechanical Behavior of Biomedical Materials,2015,49:235-243.
[10]MATTEI G,PATRIA V D,TIRELLA A,et al.Mechanostructure and composition of highly reproducible decellularized liver matrices[J].Acta Biomaterialia,2014,10(2):875-882.
[11]SANTAMARIA V A A,AZNAR J M G,OCHOA I,et al.Effect of sample pre-contact on the experimental evaluation of cartilage mechanical properties[J].Experimental Mechanics,2013,53(6):911-917.
[12]曾衍均,许传青,杨坚,等.软组织的生物力学特征[J].中国科学:G,2003,33(1):1-5.
[13]MILLER K.How to test very soft biological tissues in extension[J].Journal of Biomechanics,2001,34(5):651-657.
[14]赵玉婷.基于猪眼球整体膨胀试验对角膜生物力学性能的研究[D].太原:太原理工大学力学学院,2017.