Biomechanics of Blood Vessels: Structure, Mechanics, and Adaptation

Matsumotο, Takeo; Sugita, Shukei; Yaguchi, Toshiyuki

doi:10.1007/978-3-662-46836-4_4

Cited by 11 publications

(13 citation statements)

References 51 publications

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“…The tube is assumed to be made of elastin, which is a highly elastic protein found in all vertebrates and is major constituent of arteries [18]. Here, along the lines of the work in [18, 85, 86], elastin is modeled as an isotropic linearly elastic solid with a constant Young's modulus of

E = 0.5

MPa and a Poisson ratio of

ν = 0.499

(i.e., a nearly incompressible material). The dimensions have been chosen to ensure that the assumptions of shallowness and slenderness are satisfied.…”

Section: Resultsmentioning

confidence: 99%

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

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A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross‐sectional area. The latter gives rise to a non‐constant pressure gradient in the flow‐wise direction and, hence, to a nonlinear flow rate–pressure drop relation (unlike the Hagen–Poiseuille law for a rigid tube). Many biofluids are non‐Newtonian, and are well approximated by generalized Newtonian (say, power‐law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a “generalized Hagen–Poiseuille law” for soft microtubes. We benchmark the mathematical predictions against three‐dimensional two‐way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow‐induced deformation of a blood vessel, which is featured in some textbooks.

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E = 0.5

MPa and a Poisson ratio of

ν = 0.499

(i.e., a nearly incompressible material). The dimensions have been chosen to ensure that the assumptions of shallowness and slenderness are satisfied.…”

Section: Resultsmentioning

confidence: 99%

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

View full text Add to dashboard Cite

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“…We therefore, divided it into five arbitrary equal sublayers in order to investigate which part of the media was under most stress. (VI) Finally, the arterial wall was assumed to be an elastic, anisotropic and inhomogeneous material (16,17) while the blood flow was assumed to be the standard K-epsilon (two equations) viscous model, with enhanced wall treatment, non-Newtonian Carreau viscosity modelling {Eq. [1]}, and incompressible fluid (18,19).…”

Section: Methodsmentioning

confidence: 99%

Stress distribution in the walls of major arteries: implications for atherogenesis

Mishani¹,

Belhoul-Fakir²,

Lagat³

et al. 2021

Quant Imaging Med Surg

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Background: There is a correlation between the sites of atheroma development and stress points in the arterial system. Generally, pulse pressure results in stresses acting on the vascular vessel, including longitudinal stress, radial or normal stress, tangential stress or hoop stress and shear stress. This paper explores the relationship between arterial wall shear stress and pulsatile blood pressure with the aim of furthering the understanding of atherogenesis and plaque progression. Methods:We computed the magnitude of the shear stresses within the carotid bifurcation geometry of a patient and calculated the increase in shear stress levels that would occur when the blood pressure and pulse pressures rise during exertion. We also determined in which layer of the artery wall the maximum shear stress is located, and computed the shear stress at different levels within the media. We used the theory of laminate analysis, (Classical Laminate Plate Theory), to analyse the stress distribution on the carotid artery wall. Computational Fluid Dynamics (CFD) analysis was used on anatomy based on a CT angiogram of the carotid bifurcation of a patient with a 90% stenosis on the right side and 10% on the left. The pulsatile non-Newtonian blood flow with a resting blood pressure of 120/80 mmHg and an exertion pressure of 200/100 mmHg was simulated and the resultant forces were transferred to an ANSYS Composite PrepPost (ACP) model for wall shear stress analysis. A multilayer elastic, anisotropic, and inhomogeneous arterial wall (intima, internal elastic lamina, media, external elastic lamina, and adventitial layers) was modelled and the shear stress magnitudes and change over time between the layers was calculated.Results: Shear stress in the individual composite layers is far greater than that acting on the endothelium (less than 5 Pa). At rest, the maximum variation of shear stress in the arterial wall occurs in the intima (138 Pa) and adventitia (135 Pa). The medial layer has the lowest variation of shear stress. Under severe exertion, the maximum shear stress magnitude in the intimal layer and the adjacent medial layer is near the ultimate stress level. The maximum/minimum shear stress ratios during the cardiac cycle vary most widely in the innermost part of the media, adjacent to the intima, with a four-fold ratio increase. This compares with a less than two-fold increase in all the other layers including the intima and adventitia, making the inner media the most vulnerable layer to mechanical injury.Conclusions: This study showed that the magnitude of exertion-induced shear stress approaches the ultimate stress limit in the intima and the immediate adjacent medial layer. The variation in stress is maximal in the inner layer of the media. These findings correlate the site of atheroma development with the most vulnerable site for injury in the media and emphasise the impact of pulse pressure. Further biological studies are required to ascertain whether this leads to injury that initiates atheroma that then precipitates an ...

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“…Three mechanisms can be proposed to explain the increase in BP caused by stretching, and they are related to the modulation of baroreflex sensitivity through mechanosensitive reflexes [44,45], the increase in sympathetic activity when the stretch is performed at high intensities [46], and finally, to a relative occlusion of the smaller peripheral vessels due to stretching [31]. It should be noted that blood vessels have an architectural arrangement that extends beyond the length of the sarcomere that prevents the vessels from collapsing during movement [11,47]. This functional arrangement is defined as tortuosity and changes in relation to the type of movement and muscle contraction [48].…”

Section: Discussionmentioning

confidence: 99%

Cardiovascular Responses to Muscle Stretching: A Systematic Review and Meta-analysis

et al. 2021

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The aim of this study will be to review the current body of literature to understand the effects of stretching on the responses of the cardiovascular system. A literature search was performed using the following databases: Scopus, NLM Pubmed and ScienceDirect. Studies regarding the effects of stretching on responses of the cardiovascular system were investigated. Outcomes regarded heart rate(HR), blood pressure, pulse wave velocity (PWV of which baPWV for brachial-ankle and cfPWV for carotid-femoral waveforms), heart rate variability and endothelial vascular function. Subsequently, the effects of each outcome were quantitatively synthetized using meta-analytic synthesis with random-effect models. A total of 16 studies were considered eligible and included in the quantitative synthesis. Groups were also stratified according to cross-sectional or longitudinal stretching interventions. Quality assessment through the NHLBI tools observed a “fair-to-good” quality of the studies. The meta-analytic synthesis showed a significant effect of d=0.38 concerning HR, d=2.04 regarding baPWV and d=0.46 for cfPWV. Stretching significantly reduces arterial stiffness and HR. The qualitative description of the studies was also supported by the meta-analytic synthesis. No adverse effects were reported, after stretching, in patients affected by cardiovascular disease on blood pressure. There is a lack of studies regarding vascular adaptations to stretching.

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Biomechanics of Blood Vessels: Structure, Mechanics, and Adaptation

Cited by 11 publications

References 51 publications

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Stress distribution in the walls of major arteries: implications for atherogenesis

Cardiovascular Responses to Muscle Stretching: A Systematic Review and Meta-analysis

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