The Method of Tangent Modulus Factor for the Design of External Pressure Vessels

Chen, Dan Yang; Tong, Chang He; Liu, Kang Lin

doi:10.4028/www.scientific.net/amr.479-481.1578

Cited by 7 publications

(3 citation statements)

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“…Otherwise, it was considered a short cylindrical vessel. The formula for calculating the critical length is [43]:where D is the internal diameter of the vessel and δ e is the vessel’s thickness. For short cylindrical blood vessels, the Pamm formula, commonly used in engineering, was utilized to calculate the critical value of the external pressure for vascular instability.…”

Section: Methodsmentioning

confidence: 99%

“…For short cylindrical blood vessels, the Pamm formula, commonly used in engineering, was utilized to calculate the critical value of the external pressure for vascular instability. This formula is as follows [43]:where E is the Young’s modulus and L is the vessel’s length. For long cylindrical blood vessels, the formula of critical pressure for vascular instability is as follows [43]:where μ is Poisson’s ratio.…”

Section: Methodsmentioning

confidence: 99%

“…This formula is as follows [43]:where E is the Young’s modulus and L is the vessel’s length. For long cylindrical blood vessels, the formula of critical pressure for vascular instability is as follows [43]:where μ is Poisson’s ratio. Based on physiological parameters of the external iliac artery, femoral artery, popliteal artery and tibial artery in the lower body, as shown in Table 6, the critical pressure for vascular instability of each part can be calculated [44–46].…”

Section: Methodsmentioning

confidence: 99%

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Hemodynamic effects of enhanced external counterpulsation on cerebral arteries: a multiscale study

Wang

Mao

et al. 2019

BioMed Eng OnLine

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Background Enhanced external counterpulsation (EECP) is an effective method for treating patients with cerebral ischemic stroke, while hemodynamics is the major contributing factor in the treatment of EECP. Different counterpulsation modes have the potential to lead to different acute and long-term hemodynamic changes, resulting in different treatment effects. However, various questions about appropriate counterpulsation modes for optimizing hemodynamic effects remain unanswered in clinical treatment. Methods A zero-dimensional/three-dimensional (0D/3D) geometric multiscale model of the cerebral artery was established to obtain acute hemodynamic indicators, including mean arterial pressure (MAP) and cerebral blood flow (CBF), as well as localized hemodynamic details for the cerebral artery, which includes wall shear stress (WSS) and oscillatory shear index (OSI). Counterpulsation was achieved by applying pressure on calf, thigh and buttock modules in the 0D model. Different counterpulsation modes including various pressure amplitudes and pressurization durations were applied to investigate hemodynamic responses, which impact acute and long-term treatment effects. Both vascular collapse and cerebral autoregulation were considered during counterpulsation. Results Variations of pressure amplitude and pressurization duration have different impacts on hemodynamic effects during EECP treatment. There were small differences in the hemodynamics when similar or different pressure amplitudes were applied to calves, thighs and buttocks. When increasing pressure amplitude was applied to the three body parts, MAP and CBF improved slightly. When pressure amplitude exceeded 200 mmHg, hemodynamic indicators almost never changed, demonstrating consistency with clinical data. However, hemodynamic indicators improved significantly with increasing pressurization duration. For pressurization durations of 0.5, 0.6 and 0.7 s, percentage increases for MAP during counterpulsation were 1.5%, 23.5% and 39.0%, for CBF were 1.2%, 23.4% and 41.6% and for time-averaged WSS were 0.2%, 43.5% and 85.0%, respectively. Conclusions When EECP was applied to patients with cerebral ischemic stroke, pressure amplitude applied to the three parts may remain the same. Patients may not gain much more benefit from EECP treatment by excessively increasing pressure amplitude above 200 mmHg. However, during clinical procedures, pressurization duration could be increased to 0.7 s during the cardiac circle to optimize the hemodynamics for possible superior treatment outcomes.

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Section: Methodsmentioning

confidence: 99%