A vibration-based approach to quantifying the dynamic elastance of the superficial arterial wall

Wang, Jia‐Jung; Liu, Shing‐Hong; Su, Hung‑Mao; Chang, Steven Y.; Tseng, Wei‐Kung

doi:10.1186/s12938-016-0147-4

Cited by 3 publications

(8 citation statements)

References 27 publications

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“…New applications can also emerge from this work regarding the assessment of the dynamic elastance of superficial arterial walls (see for example, Wang et al . [ 37 ]).…”

Section: Discussionmentioning

confidence: 99%

The Effect of Strain Hardening on the Dynamic Response of Human Artery Segments

Charalambous¹,

Roussis²,

Giannakopoulos³

2017

TOBEJ

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Background:When subjected to time-dependent blood pressure, human arteries undergo large deformations, exhibiting mainly nonlinear hyperelastic type of response. The mechanical response of arteries depends on the health of tissues that comprise the artery walls. Typically, healthy arteries exhibit convex strain hardening under tensile loads, atherosclerotic parts exhibit stiffer response, and aneurysmatic parts exhibit softening response. In reality, arterial dynamics is the dynamics of a propagating pulse, originating in heart ventricle, propagating along aorta, bifurcating, etc. Artery as a whole cannot be simulated as a lump ring, however its cross section can be simulated as a vibrating ring having a phase lag with respect to the other sections, creating a running pressure wave. A full mathematical model would require fluid-solid interaction modeling continuity of blood flow in a compliant vessel and a momentum equation. On the other hand, laboratory testing often uses small-length arteries, the response of which is covered by the present work. In this way, material properties that change along the artery length can be investigated.Objective:The effect of strain hardening on the local dynamic response of human arteries (excluding the full fluid-structure interaction) is examined through appropriate hyperelastic models related to the health condition of the blood vessel. Furthermore, this work aims at constituting a basis for further investigation of the dynamic response of arteries accounting for viscosity.Method:The governing equation of motion is formulated for three different hyperelastic material behaviors, based on the constitutive law proposed by Skalak et al., Hariton, and Mooney-Rivlin, associated with the hardening behavior of healthy, atherosclerotic, and aneurysmatic arteries, respectively. The differences between these modelling implementations are caused by physiology, since aneurysmatic arteries are softer and often sclerotic arteries are stiffer than healthy arteries. The response is investigated by proper normalization of the involved material parameters of the arterial walls, geometry of the arteries, load histories, time effects, and pre-stressing. The effect of each problem parameter on the arterial response has been studied. The peak response of the artery segment is calculated in terms of radial displacements, principal elongations, principal stresses, and strain-energy density. The validity of the proposed analytical models is demonstrated through comparison with previous studies that investigate the dynamic response of arterial models.Results:Important metrics that can be useful to vascular surgery are the radial deformation and the maximum strain-energy density along with the radial resonance frequencies. These metrics are found to be influenced heavily by the nonlinear strain-hardening characteristics of the model and the longitudinal pre-stressing.Conclusion:The proposed formulation permits a systematic and generalizable investigation, which, together with the low computational cost ...

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“…New applications can also emerge from this work regarding the assessment of the dynamic elastance of superficial arterial walls (see for example, Wang et al . [ 37 ]).…”

Section: Discussionmentioning

confidence: 99%

The Effect of Strain Hardening on the Dynamic Response of Human Artery Segments

Charalambous¹,

Roussis²,

Giannakopoulos³

2017

TOBEJ

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“…Figure 2 shows the relation between F T /D and ω 2 at a specific time, T m , when F T /D and ω 2 are considered as the dependent and independent variables. The procedures for measuring the wall elastance (E multiple ) with the multiple-frequency vibration were introduced in our previous study [ 17 ]. In this section, we briefly describe the related process.…”

Section: Methodsmentioning

confidence: 99%

“…Many physical parameters of arterial stiffness have been proposed to assess the global arterial stiffness, such as the pulse pressure [ 7 ], pulse wave velocity [ 8 ], the capacity compliance of the aorta [ 9 ], augmentation index [ 10 ], carotid intima-media thickness [ 11 ], and β variable [ 12 ]. In addition, various indices have been submitted to appraise the local arterial stiffness, such as the compliance of brachial artery [ 13 ], arterial distensibility [ 14 ], spring constant of the arterial wall [ 15 ], Young’s elastic modulus [ 16 ], and arterial wall elastance [ 17 ]. These techniques for measuring arterial stiffness commonly have their own advantages and disadvantages.…”

Section: Introductionmentioning

confidence: 99%

“…Most of the techniques mentioned above can roughly provide an index of arterial stiffness for either an arterial segment or a whole arterial system. However, the arterial characteristics, especially in terms of arterial compliance and wall elastance, are not constant in essence but time-varying and dependent on the transmural pressure [ 8 , 17 , 22 ]. The Voigt and Maxwell model has been used to measure the time-varying arterial wall elastance with a multiple-frequency vibrator approach [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

“…However, the arterial characteristics, especially in terms of arterial compliance and wall elastance, are not constant in essence but time-varying and dependent on the transmural pressure [ 8 , 17 , 22 ]. The Voigt and Maxwell model has been used to measure the time-varying arterial wall elastance with a multiple-frequency vibrator approach [ 17 ]. Because our method measures the time-varying arterial wall elastance with a simplified Voigt and Maxwell model [ 25 ], the measured elastances were compared with those obtained using the multiple-frequency vibration approach.…”

Section: Introductionmentioning

confidence: 99%

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Noninvasive Measurement of Time-Varying Arterial Wall Elastance Using a Single-Frequency Vibration Approach

Wang

Liu

Tseng

et al. 2020

Sensors

Self Cite

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The arterial wall elastance is an important indicator of arterial stiffness and a kind of manifestation associated with vessel-related disease. The time-varying arterial wall elastances can be measured using a multiple-frequency vibration approach according to the Voigt and Maxwell model. However, such a method needs extensive calculation time and its operating steps are very complex. Thus, the aim of this study is to propose a simple and easy method for assessing the time-varying arterial wall elastances with the single-frequency vibration approach. This method was developed according to the simplified Voigt and Maxwell model. Thus, the arterial wall elastance measured using this method was compared with the elastance measured using the multiple-frequency vibration approach. In the single-frequency vibration approach, a moving probe of a vibrator was induced with a radial displacement of 0.15 mm and a 40 Hz frequency. The tip of the probe directly contacted the wall of a superficial radial artery, resulting in the arterial wall moving 0.15 mm radially. A force sensor attached to the probe was used to detect the reactive force exerted by the radial arterial wall. According to Voigt and Maxwell model, the wall elastance (Esingle) was calculated from the ratio of the measured reactive force to the peak deflection of the displacement. The wall elastances (Emultiple) measured by the multiple-frequency vibration approach were used as the reference to validate the performance of the single-frequency approach. Twenty-eight healthy subjects were recruited in the study. Individual wall elastances of the radial artery were determined with the multiple-frequency and the single-frequency approaches at room temperature (25 °C), after 5 min of cold stress (4 °C), and after 5 min of hot stress (42 °C). We found that the time-varying Esingle curves were very close to the time-varying Emultiple curves. Meanwhile, there was a regression line (Esingle = 0.019 + 0.91 Emultiple, standard error of the estimate (SEE) = 0.0295, p < 0.0001) with a high correlation coefficient (0.995) between Esingle and Emultiple. Furthermore, from the Bland–Altman plot, good precision and agreement between the two approaches were demonstrated. In summary, the proposed approach with a single-frequency vibrator and a force sensor showed its feasibility for measuring time-varying wall elastances.

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