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High-Intensity Focused Ultrasound Scattering at Mammal Vertebrae 哺乳动物椎骨的高强度聚焦超声散射
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-24676
D. Sanford, C. Schaal
High-intensity focused ultrasound (HIFU) is used clinically to heat cells therapeutically or to destroy them through heat or cavitation. In homogeneous media, the highest wave amplitudes occur at a predictable focal region. However, HIFU is generally not used in the proximity of bones due to wave absorption and scattering. Ultrasound is passed through the skull in some clinical trials, but the complex geometry of the spine poses a greater targeting challenge and currently prohibits therapeutic ultrasound treatments near the vertebral column. This paper presents a comprehensive experimental study involving shadowgraphy and hydrophone measurements to determine the spatial distribution of pressure amplitudes from induced HIFU waves near vertebrae. First, a bone-like composite plate that is partially obstructing the induced waves is shown to break the conical HIFU form into two regions. Wave images are captured using pulsed laser shadowgraphy, and hydrophone measurements over the same region are compared to the shadowgraphy intensity plots to validate the procedure. Next, shadowgraphy is performed for an individual, clean, ex-vivo feline vertebra. The results indicate that shadowgraphy can be used to determine energy deposition patterns and to determine heating at a specific location. The latter is confirmed through additional temperature measurements. Overall, these laboratory experiments may help determine the efficacy of warming specific nerve cells within mammal vertebrae without causing damage to adjacent tissue.
高强度聚焦超声(HIFU)在临床上用于加热细胞或通过加热或空化来破坏细胞。在均匀介质中,最高的波幅出现在可预测的震源区域。然而,由于波的吸收和散射,HIFU通常不用于靠近骨骼的地方。在一些临床试验中,超声是通过颅骨进行的,但脊柱的复杂几何形状带来了更大的靶向挑战,目前禁止在脊柱附近进行治疗性超声治疗。本文介绍了一项综合实验研究,包括阴影成像和水听器测量,以确定椎骨附近诱导HIFU波的压力振幅的空间分布。首先,骨样复合板部分阻挡诱导波,将HIFU的锥形形态分成两个区域。使用脉冲激光阴影成像捕获波浪图像,并将同一区域的水听器测量结果与阴影成像强度图进行比较,以验证该程序。接下来,对一个单独的、干净的、离体的猫椎骨进行阴影成像。结果表明,阴影法可以用于确定能量沉积模式和确定特定位置的加热。后者通过额外的温度测量得到证实。总的来说,这些实验室实验可能有助于确定加热哺乳动物椎骨内特定神经细胞的功效,而不会对邻近组织造成损害。
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引用次数: 1
The Condition of Dynamic Stability for Self-Paced Treadmill Walking Based on Inverted Pendulum Model 基于倒立摆模型的自定速跑步机行走动态稳定性条件研究
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23461
Yuyang Qian, Kaiming Yang, Yu Zhu, Wen Wang, C. Wan
A self-paced treadmill automatically adjusts speed in real-time to match the user’s walking speed, presumably leading to a more nature gait than fixed-speed treadmill. However, previous study has proven that the acceleration applied to the subjects would influence the gait stability. In order to have insights on to which extent will the accelerations affect gait stability, simulation analysis based on conceptual model has been done in the current study. This paper utilized a non-inertial frame based spring-loaded inverted pendulum model to analysis the condition of stability during continuous self-paced treadmill walking. Simulations were done for 100 continuous self-paced treadmill walking at the normal walking speed. And 10ms impulse accelerations of different magnitudes with the range of (−1g, 1g) were applied at different gait events such as toe-off, foot-flat and heel-strike. The simulation results showed that the magnitude of the accelerations had significantly influence on continuous self-paced treadmill walking and directional-dependency was also found. However, no significantly difference was found when applying the impulse acceleration at different gait events.
自定速跑步机会自动实时调整速度,以匹配用户的行走速度,这可能会比固定速度跑步机更自然。然而,先前的研究已经证明,施加在受试者身上的加速度会影响步态的稳定性。为了了解加速度对步态稳定性的影响程度,本研究基于概念模型进行了仿真分析。本文采用基于非惯性系的弹簧倒立摆模型,分析了自定速跑步机连续行走时的稳定性条件。在正常步行速度下,对100个连续的自定步跑步机进行了模拟。在脱趾、平足和撞跟等不同步态事件中施加10ms不同量级的脉冲加速度,范围为(- 1g, 1g)。仿真结果表明,加速度的大小对跑步机连续自定步行走有显著影响,并且存在方向依赖性。然而,在不同的步态事件中施加脉冲加速度时,没有发现显著差异。
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引用次数: 0
Initial Study Towards the Integrated Design of Bone Scaffolds Based on Cell Diffusion, Growth Factor Release and Tissue Regeneration 基于细胞扩散、生长因子释放和组织再生的骨支架一体化设计初步研究
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23940
M. Şahin, A. Tabak, Gullu Kiziltas Sendur
Three-dimensional (3D) porous tissue scaffolds combined with bioactive molecules and cells offer key advantages for bone repair mechanisms. A functional bone tissue scaffold should provide mechanical support with an adequate combination of porosity and permeability for nutrients, oxygen supply, waste removal, and growth factors release as well as controlled degradation. Although a vast amount of work exist to address these challenges, to the best of our knowledge, a design framework taking tissue differentiation, diffusion, and growth factor (GF) release into account in time-domain simultaneously does not exist. In this paper, we provide an initial effort to address such a need by laying down the foundations for a simulation framework incorporating these effects within a Finite Element Analysis (FEA) model in COMSOL Multiphysics® software. The effectiveness of the numerical model is demonstrated via preliminary mechano-biology analyses on a simulated 3D poroelastic bone scaffold. Initial time-dependent results demonstrate the suitability of this model for an optimization framework. More specifically, it is demonstrated that coupled Multiphysics equations of diffusion, GF release, and differentiation could provide valuable inputs for ideal bone scaffold systems for effective bone repair tasks in the future.
结合生物活性分子和细胞的三维多孔组织支架为骨修复机制提供了关键优势。一个功能性的骨组织支架应该提供机械支持,并具有足够的孔隙度和渗透性,以供营养、供氧、清除废物、释放生长因子以及控制降解。尽管存在大量的工作来解决这些挑战,但据我们所知,在时域内同时考虑组织分化、扩散和生长因子(GF)释放的设计框架尚不存在。在本文中,我们通过为COMSOL Multiphysics®软件中的有限元分析(FEA)模型中包含这些效果的仿真框架奠定基础,提供了解决此类需求的初步努力。通过模拟三维多孔弹性骨支架的初步力学生物学分析,证明了数值模型的有效性。初始的时间相关结果证明了该模型对于优化框架的适用性。更具体地说,研究表明,扩散、GF释放和分化的耦合多物理场方程可以为未来有效骨修复任务的理想骨支架系统提供有价值的输入。
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引用次数: 1
Regional and Layer Distribution of Residual Stresses in an Unloaded Aortic Medial Wall 卸载主动脉内侧壁残余应力的区域和层状分布
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23632
A. Tamura, K. Matsumoto
The mechanical and structural characteristics of aortic media have profound effects on the physiology and pathophysiology of an aorta. However, many aspects of the aortic tissue remain poorly understood, partly due to the intrinsic layered wall structure and regionally varying residual stresses. Our recent works have demonstrated that a mechanical interaction between the elastic lamina (EL) and smooth muscle layer in the aortic media can be computationally reproduced using a simplified finite element (FE) model. However, it is questionable whether the simplified FE model we created was representative of the structure of a real medial wall and its modeling technique would be applicable to develop a more sophisticated and structure-based aortic FE model. This study aimed to computationally represent EL buckling in the aortic medial ring at an unloaded state and successfully reproduced transmural variation in EL waviness across the aortic wall. We also aimed at confirming the inner and outer layers of the medial wall are subjected to compressive and tensile residual stresses, respectively, at the unloaded state, implying that the ring model will open spontaneously when it is radially cut. Moreover, the computed residual stresses were found to be within the reasonable range of the predicted values, 1–10 kPa, supporting the validity of our modeling approach. Although further study is required, the information obtained here will greatly help improve the understanding of basic aortic physiology and pathophysiology, while simultaneously providing a basis for more sophisticated computational modeling of the aorta.
主动脉介质的力学和结构特性对主动脉的生理和病理生理有着深远的影响。然而,主动脉组织的许多方面仍然知之甚少,部分原因是由于其固有的层状壁结构和区域变化的残余应力。我们最近的工作表明,主动脉介质中弹性层(EL)和平滑肌层之间的力学相互作用可以使用简化的有限元(FE)模型进行计算再现。然而,我们创建的简化有限元模型是否能代表真实的内侧壁结构,其建模技术是否适用于开发更复杂的基于结构的主动脉有限元模型,这一点值得怀疑。本研究旨在通过计算再现主动脉内侧环在无载荷状态下的EL屈曲,并成功再现了主动脉壁上EL波形的跨壁变化。我们还旨在确认内侧壁的内层和外层在卸载状态下分别受到压缩和拉伸残余应力,这意味着环形模型在径向切割时会自发打开。计算得到的残余应力在预测值1 ~ 10 kPa的合理范围内,验证了模型方法的有效性。虽然还需要进一步的研究,但这里获得的信息将极大地有助于提高对主动脉基本生理和病理生理的认识,同时为更复杂的主动脉计算建模提供基础。
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引用次数: 1
Shape Memory Polymer Foam With Tunable Properties for Treatment of Intracranial Aneurysm 具有可调特性的形状记忆聚合物泡沫治疗颅内动脉瘤
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-24291
S. Pineda-Castillo, Jishan Luo, B. Bohnstedt, Chung-Hao Lee, Yingtao Liu
Intracranial aneurysms have the potential to be fatal; when detected, they must be treated promptly by surgical clipping or by endovascular methods. The latter, while having better long-term overall survival than the former, fail to provide complete occlusion of the aneurysm lumen, creating risks for therapy-related adverse events, such as embolic device migration or recanalization. Polyurethane shape memory polymers (SMPs) have the potential to provide patient-specific treatment to reduce rates of incomplete occlusion and mass effect. In this study, SMP matrices are infiltrated with carbon nanotubes (CNTs) to induce electrical conductivity and provide a precise triggering method for deployment of the embolic device. Through thermomechanical characterization of the composite, it was determined that CNTs play a significant role in resistivity of the SMP foam and its ultimate shape recovery properties. Cyclic mechanical testing allowed to determine that CNTs might induce polymeric matrix damage, creating the need for new approaches to CNT infiltration. The studied composite foams were able to occlude an in vitro idealized aneurysm phantom model, which allowed to conclude that the proposed CNT-infiltrated SMP foams exhibit potential as biomedical devices for endovascular therapy of intracranial aneurysms.
颅内动脉瘤有可能是致命的;一旦发现,必须立即通过手术夹或血管内方法进行治疗。后者虽然比前者有更好的长期总生存率,但不能完全闭塞动脉瘤腔,造成治疗相关不良事件的风险,如栓塞装置迁移或再通。聚氨酯形状记忆聚合物(SMPs)具有提供患者特异性治疗的潜力,可以降低不完全闭塞率和质量效应。在这项研究中,SMP基质中渗透了碳纳米管(CNTs)以诱导导电性,并为栓塞装置的部署提供了精确的触发方法。通过对复合材料的热力学表征,确定了CNTs对SMP泡沫的电阻率和最终形状恢复性能起着重要作用。循环力学测试可以确定碳纳米管可能会引起聚合物基体损伤,从而需要新的碳纳米管渗透方法。所研究的复合泡沫能够封闭体外理想化的动脉瘤幻影模型,这使得我们可以得出结论,所提出的碳纳米管浸润的SMP泡沫具有作为颅内动脉瘤血管内治疗的生物医学设备的潜力。
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引用次数: 0
Influence of Composite Polymer Coatings on the Insertion Force of Needle-Like Structure in Soft Materials 复合聚合物涂层对软质材料针状结构插入力的影响
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-24341
Kavi Patel, Long Zhu, S. T. R. Gidde, Fei Ren, P. Hutapea
This study is aimed to evaluate the effects of coated surgical needles with composite polymers such as polydopamine (PDA), polytetrafluoroethylene (PTFE), and carbon. The coated needle’s lubrication properties were measured using 3 DOF force sensors and 3D robot system by the repetitive insertion in soft tissue materials. Needle durability is a measure of needle sharpness after repeated passage through high stiffness tissue materials. The composite coatings were shown to reduce the insertion force by ∼49% and retraction forces by ∼46% when tested using a bovine kidney. The surface roughness and the lateral friction force of the needle are measured using the Atomic Force Microscope (AFM). The adhesion energy of the different coating on the needle will be measured using a nano-scratch method.
本研究旨在评估复合聚合物如聚多巴胺(PDA)、聚四氟乙烯(PTFE)和碳涂层手术针的效果。利用三自由度力传感器和三维机器人系统,通过在软组织材料中重复插入的方式,对涂层针的润滑性能进行了测试。针的耐久性是指在高刚度组织材料中反复穿过后,针的锋利程度。在使用牛肾脏进行测试时,复合涂层可将插入力降低~ 49%,收回力降低~ 46%。利用原子力显微镜(AFM)测量了针的表面粗糙度和侧向摩擦力。用纳米划痕法测量不同涂层在针上的粘附能。
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引用次数: 0
Influence of Carotid Artery Stenosis Location on Lesion Progression Using Computational Fluid Dynamics 颈动脉狭窄位置对病变进展的影响
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23451
Muhamed Albadawi, Yasser Abuouf, S. Ookawara, Mahmoud A. Ahmed
Atherosclerosis is a major arterial disease characterized by the thickening of the arteries’ walls. The development of stenosis at the carotid bifurcation affects the local variations in blood flow dynamic factors. The carotid artery dynamic factors: including the wall shear stress (WSS), time-averaged wall shear stress (TAWSS) and pressure gradient affect the rate of progression of the stenosis. It is essential to analyze the flow in three-dimensional reconstructed patient-specific geometries with realistic boundary conditions to estimate the blood flow dynamic factors. Hence, a three-dimensional comprehensive model is developed including the non-Newtonian blood flow under pulsatile flow conditions. The model is numerically simulated using computational fluid dynamics solvers along with the medical imaging to investigate the effect of stenosis locations on its progression. The numerically predicted blood flow dynamic factors are analyzed. It was found that the blood flow dynamic factors have the importance to influence the diagnosis and prediction of asymptomatic carotid artery stenosis progression. Based on results, the value of TAWSS at the stenosis in the stenotic Common Carotid Artery (CCA) is 46.68 Pa comparing to 19.24 Pa and 10.049 Pa in Internal Carotid Artery (ICA) and External Carotid Artery (ECA) respectively. Also, it was found that the maximum value of WSS in the healthy artery at the bifurcation with 3.829 Pa. However, in stenotic arteries the maximum value for WSS located at the stenosis throat which was found to be 102.158 Pa for CCA comparing to 46.859 Pa in ICA and 33.658 Pa in ECA.
动脉粥样硬化是一种以动脉壁增厚为特征的主要动脉疾病。颈动脉分叉处狭窄的发生影响局部血流动力学因素的变化。颈动脉动态因素:包括管壁剪切应力(WSS)、时间平均管壁剪切应力(TAWSS)和压力梯度影响狭窄进展速度。在具有现实边界条件的三维重建的患者特定几何形状中分析血流是估计血流动力学因素的必要条件。因此,建立了包含脉动血流条件下非牛顿血流的三维综合模型。利用计算流体动力学求解器和医学成像对该模型进行数值模拟,研究狭窄位置对其发展的影响。对数值预测的血流动力学因素进行了分析。发现血流动力学因素对无症状颈动脉狭窄进展的诊断和预测有重要影响。结果显示,狭窄的颈总动脉(CCA)狭窄处TAWSS值为46.68 Pa,颈内动脉(ICA)和颈外动脉(ECA)狭窄处TAWSS值分别为19.24 Pa和10.049 Pa。健康动脉在分叉处的WSS最大值为3.829 Pa。而在狭窄动脉中,WSS最大值位于狭窄喉部,CCA为102.158 Pa, ICA为46.859 Pa, ECA为33.658 Pa。
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引用次数: 2
Manufacturing Capability Index of 3D Printing Parts for Impact Applications 用于冲击应用的3D打印部件制造能力指数
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23123
A. Schmitz
Three-dimensional (3D) printing with high-resolution stereolithography (SLA) has grown in popularity for creating personalized medical devices. 3D printing is now starting to expand to weight-bearing components, e.g. prosthetic feet, as data on the dynamic properties impact and fatigue is published in the literature. The next step towards using 3D printing in impact applications is to assess the capability of the high-resolution SLA process to manufacture components of uniform impact resistance. Because impact testing is destructive, a surrogate measure to check a part’s viability for resisting an impact load also needs to be established. Thirteen notched Izod specimens were printed on a Form2 SLA printer using the manufacturer’s clear V4, photocurable resin. Once all the specimens were printed, washed in isopropyl alcohol, and cured with ultraviolet light, the impact resistance was quantified using a pendulum impact tester in a notched Izod configuration. Then, the hardness of the specimens was quantified using a HBW 10/250 scale. The impact resistance of the clear, SLA polymer was 0.59 ± 0.14 ft-lb/in. With an upper standard limit of 0.53 ft-lb/in, the process capability index was 0.133. Impact resistance and Brinell hardness were not correlated with a Spearman coefficient of r = −0.108, p = 0.73. Since the process capability index was less than one, 3D printing with SLA polymers is not a viable manufacturing process for creating parts of consistent impact resistance. The current technology would lead to too many rejected parts. Also, Brinell hardness and impact strength were not related. Therefore, there is no non-destructive method to spot-check these components before use.
高分辨率立体光刻(SLA)的三维(3D)打印在创建个性化医疗设备方面越来越受欢迎。3D打印现在开始扩展到承重部件,例如假肢脚,因为有关动态特性影响和疲劳的数据发表在文献中。在冲击应用中使用3D打印的下一步是评估高分辨率SLA工艺制造均匀抗冲击组件的能力。由于冲击试验是破坏性的,因此还需要建立一种替代措施来检查零件抵抗冲击载荷的可行性。13个缺口Izod标本在Form2 SLA打印机上使用制造商的透明V4光固化树脂打印。一旦所有的样品被打印出来,在异丙醇中洗涤,并在紫外光下固化,使用一个缺口Izod配置的摆锤冲击试验机对其抗冲击性进行量化。然后,采用HBW 10/250标尺对试样的硬度进行量化。透明的SLA聚合物的抗冲击性为0.59±0.14 ft-lb/in。标准上限为0.53 ft-lb/in,工艺能力指数为0.133。抗冲击性和布氏硬度与Spearman系数r = - 0.108, p = 0.73无关。由于工艺能力指数小于1,因此使用SLA聚合物进行3D打印并不是一种可行的制造工艺,无法制造出具有一致抗冲击性的部件。目前的技术会导致太多的不合格品。布氏硬度与冲击强度无显著相关性。因此,在使用前没有非破坏性的方法对这些部件进行抽查。
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引用次数: 0
How Does Physical Activity Affect Residual Limb Volume Change, Comfort and Gait Symmetry on Traumatic Transfemoral Amputees? 体育活动如何影响创伤性经股截肢者残肢体积变化、舒适度和步态对称性?
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23418
Sara Salazar-Salgado, F. Valencia, A. Uribe, Elizabeth Rendón-Vélez
There is a considerable amount of young adults who become amputees due to war and violence. For this population, a successful adaptation to their prosthesis depends on the socket fit, which in turn is caused by the volume change of the residual limb during the day. The literature reports several investigations on this topic, most of which use subjects walking on a treadmill to simulate their daily activity. However, this studies are focused on transtibial amputees and do not mention the relationship between this physical activity and other variables such as comfort, volume changes and gait. Therefore, the objective of this paper is to determine the effect of physical activity on the volume of the residual limb, the comfort and the symmetry of gait in traumatic transfemoral amputees. Plaster positive molds of the residual limb, the comfort perception and the gait data of five individuals were obtained at the first time of the day and after three sessions of treadmill walking of 15, 30 and 45 minutes. The positive molds of each individual were scanned and then, the volume was calculated. The gait data was acquired using a marker-based motion capture system and processed to obtain spatio-temporal, kinematic and kinetic parameters, including the Gait Deviation Index (GDI). Based on the literature, specific points of the gait data were selected and the symmetry index was obtain for each of them. A short comfort test was used after each session of treadmill walking. Data was analyzed throughout the tests within each subject. Statistical analysis was performed for the volume and the gait variables to check for statistical significance. After physical activity, a tendency towards residual limb volume decrease was found on almost all subjects, although it was not significant. The percentage of volume change obtained on almost all subjects are within the range considered “good socket fit” according to previous authors. Our results suggest that transfemoral amputees may have smaller volume changes than transtibial after treadmill walking. Significant difference was found on the symmetry index of “Swing phase” between the baseline and the 45-minute test. The values of gait symmetry on the gait parameters were consistent with previous findings regarding transfemoral amputees. The difference that arise may be due to the sample difference (cause of amputation, difference in prosthetic elements and use of walking aids). The lowest symmetry was noticed on the ankle kinematics. The comfort did not significantly change with the selected amount of physical activity. In subsequent research, it is recommended to increase the intensity or time of physical activity and/or increase the number of participants. This results can help the understanding of how the socket/residual limb interface behaves which can improve the design and prescription of prosthetic components.
有相当多的年轻人因战争和暴力而截肢。对于这一人群来说,成功地适应他们的假肢取决于插槽的适合度,而这反过来又由残肢在白天的体积变化引起。文献报道了关于这一主题的几项调查,其中大多数使用受试者在跑步机上行走来模拟他们的日常活动。然而,这项研究主要集中在跨胫截肢者身上,并没有提到这种身体活动与其他变量(如舒适度、体积变化和步态)之间的关系。因此,本文的目的是确定体力活动对创伤性经股截肢者残肢体积、舒适性和步态对称性的影响。在每天第一次和在跑步机上行走15、30和45分钟后,分别获得5个人的残肢石膏阳性模型、舒适度感知和步态数据。对每个个体的阳性模具进行扫描,然后计算体积。步态数据采用基于标记的动作捕捉系统获取,并进行处理,获得时空、运动学和动力学参数,包括步态偏差指数(GDI)。在文献的基础上,选取步态数据的特定点,得到每个点的对称性指数。在每次跑步机行走后进行一个简短的舒适测试。在每个受试者的整个测试过程中分析数据。对体积和步态变量进行统计分析,检验有无统计学意义。在体力活动后,几乎所有受试者都有残肢体积减小的趋势,尽管这种趋势并不显著。根据以前的作者,几乎所有受试者的体积变化百分比都在“良好的插槽配合”范围内。我们的研究结果表明,经股骨截肢者在跑步机行走后的体积变化可能比经胫骨截肢者小。基线与45分钟测试在“摇摆期”对称性指标上存在显著差异。步态对称性对步态参数的影响值与先前关于经股截肢者的研究结果一致。产生的差异可能是由于样本差异(截肢的原因,假体元件的差异和助行器的使用)。踝关节运动学的对称性最低。舒适度并没有随着体力活动量的选择而显著改变。在随后的研究中,建议增加体力活动的强度或时间和/或增加参与者的数量。这一结果可以帮助理解窝/残肢界面的行为,从而改进假肢部件的设计和处方。
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引用次数: 0
Effect of Additional Weight on Lyapunov Exponents for Human Squat Exercise 额外重量对人体深蹲运动李雅普诺夫指数的影响
Pub Date : 2020-11-16 DOI: 10.1115/IMECE2020-23943
J. Galarza, D. Caruntu
This work deals with the stability of the dynamics of human squat exercise. This is a common exercise. The focus of this investigation is to analyze the knee angle time series and calculate the divergence for different weight added in the exercise. Experiments are conducted and motion capture used for each of the cases. Then the Lyapunov exponents of the time series of the knee joint angle are determined. Matlab software package is used for all calculations. Results are compared with data available in the literature. This work provides insight on the level of stability for added weight on the human squat exercise. This gives an insight on the level of safety of this exercise as weight is added to the human subject.
这项工作涉及人类深蹲运动的动力学稳定性。这是一个常见的练习。本研究的重点是分析膝关节角度的时间序列,并计算不同重量在运动中的发散度。对每种情况进行了实验和动作捕捉。然后确定膝关节角度时间序列的Lyapunov指数。所有计算均采用Matlab软件包。结果与文献资料进行了比较。这项工作为人类深蹲运动中增加重量的稳定性水平提供了见解。这让我们了解到,随着人体重量的增加,这项运动的安全程度。
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引用次数: 0
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