Residual stresses in oscillating thoracic arteries reduce circumferential stresses and stress gradients

Chaudhry, Hans; Bukiet, Bruce; Davis, A; Ritter, Arthur; Findley, Thomas

doi:10.1016/s0021-9290(97)81292-4

Cited by 40 publications

(41 citation statements)

References 19 publications

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“…Considering that the in vivo axial stretch ratio should not change significantly in the cardiac cycle, z is assumed to be constant (7,13). Therefore, the radius r(t) is determined merely by the inner radius r i(t), as shown in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…The mass density was taken to be 0.9 g/cm 3 , which has been used by Chaudhry et al (7). Since viscoelastic properties for rabbit thoracic artery in Ref.…”

Section: Methodsmentioning

confidence: 99%

“…The pseudoelastic formulation (i.e., loading and unloading follow different elastic stressstrain curves) has been widely utilized to investigate salient mechanical characteristics of blood vessels (e.g., Refs. 5,7,8,10,13). In more realistic analyses, the viscoelastic behavior of arterial walls has been studied by many researchers (4,10,12,20,21,23,24,27,29).…”

mentioning

confidence: 99%

“…The residual stress and strain in unloaded arteries can homogenize the wall stress and strain at physiological condition (7,8,25). The vascular smooth muscle tone plays a similar role to reduce the transmural gradients of arterial wall stress and strain (1,14,17,19).…”

mentioning

confidence: 99%

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Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

Zhang

Liu²,

Kassab³

2007

American Journal of Physiology-Heart and Circulatory Physiology

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Zhang W, Liu Y, Kassab GS. Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue. Am J Physiol Heart Circ Physiol 293: H2355-H2360, 2007. First published June 29, 2007; doi:10.1152/ajpheart.00423.2007.-The mechanical behavior of blood vessels is known to be viscoelastic rather than elastic. The functional role of viscoelasticity, however, has remained largely unclear. The hypothesis of this study is that viscoelasticity reduces the stresses and strains in the vessel wall, which may have a significant impact on the fatigue life of the blood vessel wall. To verify the hypothesis, the pulsatile stress in rabbit thoracic artery at physiological loading condition was investigated with a quasi-linear viscoelastic model, where the normalized stress relaxation function is assumed to be isotropic, while the stress-strain relationship is anisotropic and nonlinear. The artery was subjected to the same boundary condition, and the mechanical equilibrium equation was solved for both the viscoelastic and an elastic (which has a constant relaxation function) model. Numerical results show that, compared with purely elastic response, the viscoelastic property of arteries reduces the magnitudes and temporal variations of circumferential stress and strain. The radial wall movement is also reduced due to viscoelasticity. These findings imply that viscoelasticity may be beneficial for the fatigue life of blood vessels, which undergo millions of cyclic mechanical loadings each year of life.artery; cyclic loading; fatigue life; viscoelastic BIOLOGICAL SOFT TISSUES ARE known to have highly nonlinear stress-strain relations, strongly anisotropic mechanical properties, and significant viscoelastic features (10). Blood vessels are typical soft tissues, and their mechanical behavior is imperative for understanding vascular processes under physiological and pathological conditions. The pseudoelastic formulation (i.e., loading and unloading follow different elastic stressstrain curves) has been widely utilized to investigate salient mechanical characteristics of blood vessels (e.g., Refs. 5,7,8,10,13). In more realistic analyses, the viscoelastic behavior of arterial walls has been studied by many researchers (4,10,12,20,21,23,24,27,29). To reduce the mathematical complexity, the theory of quasi-linear viscoelasticity (10) has been applied to arteries and other living tissues (e.g., Refs. 3,6,11,15,26). One known merit of viscoelasticity in blood vessels is to reduce the wall stress and strain during a sudden increase of mechanical loading, such as in acute hypertension (1). Although this is an interesting protective acute mechanism, the functional role of viscoelasticity in blood vessels and other biological tissues has not been fully understood.From a mechanical point of view, the energy dissipation due to viscoelasticity may produce heat to maintain isothermal conditions in tissues, and the force-deformation hysteresis loop (or phase delay between stress and strain) caused by internal ...

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Section: Methodsmentioning

confidence: 99%

“…The mass density was taken to be 0.9 g/cm 3 , which has been used by Chaudhry et al (7). Since viscoelastic properties for rabbit thoracic artery in Ref.…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

Zhang

Liu²,

Kassab³

2007

American Journal of Physiology-Heart and Circulatory Physiology

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“…) is emerging as an important parameter in fatigue life studies in both biology (Chaudhry et al, 1997;Tardy et al, 1997;Mulholland et al, 1999) and engineering (Fouvry et al, 1998;Araujo et al, 2004). Notably, for multiaxial fatigue life, the familiar engineering parameter of stress is not an appropriate concept, although engineers typically use an adjustment such as the von Mises method to calculate a uniaxial stress that would create the same distortion energy as the actual combination of applied stresses on multiple axes.…”

Section: Robustness Of the Data: Comparisons With Divergentmentioning

confidence: 99%

Scaling of maximum net force output by motors used for locomotion

Marden¹

2005

Journal of Experimental Biology

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SUMMARY Biological and engineered motors are surprisingly similar in their adherence to two or possibly three fundamental regimes for the mass scaling of maximum force output (Fmax). One scaling regime (Group 1:myosin, kinesin, dynein and RNA polymerase molecules; muscle cells; whole muscles; winches; linear actuators) comprises motors that create slow translational motion with force outputs limited by the axial stress capacity of the motor, which results in Fmax scaling as motor mass0.67 (M0.67). Another scaling regime (Group 2: flying birds, bats and insects; swimming fish; running animals; piston engines; electric motors; jets) comprises motors that cycle rapidly, with significant internal and external accelerations, and for whom inertia and fatigue life appear to be important constraints. The scaling of inertial loads and fatigue life both appear to enforce Fmax scaling as M1.0 in these motors. Despite great differences in materials and mechanisms, the mass specific Fmax of Group 2 motors clusters tightly around a mean of 57 N kg-1, a region of specific force loading where there appears to be a common transition from high- to low-cycle fatigue. For motors subject to multi-axial stresses, the steepness of the load-life curve in the neighborhood of 50-100 N kg-1 may overwhelm other material and mechanistic factors, thereby homogenizing the mass specific Fmax of grossly dissimilar animals and machines. Rockets scale with Group 1 motors but for different mechanistic reasons; they are free from fatigue constraints and their thrust is determined by mass flow rates that depend on cross sectional area of the exit nozzle. There is possibly a third scaling regime of Fmax for small motors (bacterial and spermatazoan flagella; a protozoan spring) where viscosity dominates over inertia. Data for force output of viscous regime motors are scarce, but the few data available suggest a gradually increasing scaling slope that converges with the Group 2 scaling relationship at a Reynolds number of about 102. The Group 1 and Group 2 scaling relationships intersect at a motor mass of 4400 kg, which restricts the force output and design of Group 2 motors greater than this mass. Above 4400 kg, all motors are limited by stress and have Fmax that scales as M0.67; this results in a gradual decline in mass specific Fmax at motor mass greater than 4400 kg. Because of declining mass specific Fmax, there is little or no potential for biological or engineered motors or rockets larger than those already in use.

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On the numerical treatment of initial strains in biological soft tissues

Peña

Martı́nez

Calvo

et al. 2006

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible 'deformation gradient' field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them.

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Residual stresses in oscillating thoracic arteries reduce circumferential stresses and stress gradients

Cited by 40 publications

References 19 publications

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

Viscoelasticity reduces the dynamic stresses and strains in the vessel wall: implications for vessel fatigue

Scaling of maximum net force output by motors used for locomotion

On the numerical treatment of initial strains in biological soft tissues

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