Determination of the critical buckling pressure of blood vessels using the energy approach

Revealing anisotropic elasticity of endothelium under fluid shear stress

Endothelium lining interior surface of blood vessels experiences various physical stimulations in vivo. Its physical properties, especially elasticity, play important roles in regulating the physiological functions of vascular systems. In this paper, an integrated approach is developed to characterize the anisotropic elasticity of the endothelium under physiological-level fluid shear stress. A pressure sensor-embedded microfluidic device is developed to provide fluid shear stress on the perfusion-cultured endothelium and to measure transverse in-plane elasticities in the directions parallel and perpendicular to the flow direction. Biological atomic force microscopy (Bio-AFM) is further exploited to measure the vertical elasticity of the endothelium in its out-of-plane direction. The results show that the transverse elasticity of the endothelium in the direction parallel to the perfusion culture flow direction is about 70% higher than that in the direction perpendicular to the flow direction. Moreover, the transverse elasticities of the endothelium are estimated to be approximately 120 times larger than the vertical one. The results indicate the effects of fluid shear stress on the transverse elasticity anisotropy of the endothelium, and the difference between the elasticities in transverse and vertical directions. The quantitative measurement of the endothelium anisotropic elasticity in different directions at the tissue level under the fluid shear stress provides biologists insightful information for the advanced vascular system studies from biophysical and biomaterial viewpoints. STATEMENT OF SIGNIFICANCE: In this paper, we take advantage an integrated approach combining microfluidic devices and biological atomic force microscopy (Bio-AFM) to characterize anisotropic elasticities of endothelia with and without fluidic shear stress application. The microfluidic devices are exploited to conduct perfusion cell culture of the endothelial cells, and to estimate the in-plane elasticities of the endothelium in the direction parallel and perpendicular to the shear stress. In addition, the Bio-AFM is utilized for characterization of the endothelium morphology and vertical elasticity. The measurement results demonstrate the very first anisotropic elasticity quantification of the endothelia. Furthermore, the study provides insightful information bridging the microscopic sing cell and macroscopic organ level studies, which can greatly help to advance vascular system research from material perspective.

Analysis of sequential ultrasound frames for the measurement of hemodynamic stresses, critical bent buckling pressure, and critical buckling torque of human common carotid atherosclerosis

BACKGROUND

Structural properties of the arterial wall are important diagnostic parameters. The current study aimed at investigating the hemodynamic properties and intima-media thickness changes of the common carotid artery in human subjects with atherosclerosis in order to determine the relationships between these indices.

METHODS

This study presented methods to detect instantaneous changes in the lumen diameter, intima media thickness, longitudinal movement and acceleration, and velocity of the left side of common carotid artery. These parameters were measured in 155 male patients, categorized into control (n = 42), mild (n = 39), moderate (n = 37), and severe (n = 37) carotid stenosis groups by B-mode and Doppler ultrasonography. Extracted parameters were used to estimate the biomechanical properties of arteries, including radial strain, arterial stiffness index, Young's elastic modulus, circumferential stress, shear stress, axial stress, critical bent buckling pressure, and critical buckling torque.

FINDINGS

All biomechanical parameters of common carotid artery were significantly different in patients with mild, moderate, and severe stenosis, compared to the control group (P < 0.05). Moreover, the current results showed a significant correlation between intima media thickness and non-intima media thickness-based biomechanical indices including circumferential strain, stiffness index, and shear stress in different stenosis groups (P < 0.05).

INTERPRETATION

We concluded that the conventional and new indicators such as axial stress, critical bent buckling pressure, critical buckling torque could be useful for evaluating atherosclerosis development and also, may provide more information for physicians and interventional radiologists in designing strategies for decreasing risk in interventional treatment such as stent replacement and differentiation of vulnerable plaques.

Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (&lt;5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

Finite Element simulation of buckling-induced vein tortuosity and influence of the wall constitutive properties

The mechanisms giving rise to vein tortuosity, which is often associated with varicosis, are poorly understood. Recent works suggest that significant biological changes in the wall of varicose veins may precede the mechanical aspects of the disease. To test the hypothesis of tortuosity being a consequence of these changes, a Finite Element model was developed based on previous experimental work on vein buckling. The model was then used to evaluate the effect of alterations of the mechanical behavior of the wall on tortuosity onset and severity. The results showed that increasing anisotropy toward the circumferential direction promotes tortuosity. An increase in wall stiffness tends to decrease the level of tortuosity but interestingly, if the vein segment is little or not pre-stretched such increase will not prevent, or it will even promote, the onset of tortuosity. These results provide additional arguments supporting the hypothesis of tortuosity being the consequence of biologically-induced changes in the varicose vein wall. Based on a 3D model of the leg and in vivo identification of the material properties of varicose veins, a clinical validation of these findings is being developed.

Mechanical buckling of arterioles in collateral development

Collateral arterioles enlarge in both diameter and length, and develop corkscrew-like tortuous patterns during remodeling. Recent studies showed that artery buckling could lead to tortuosity. The objective of this study was to determine arteriole critical buckling pressure and buckling pattern during arteriole remodeling. Arterioles were modeled as elastic cylindrical vessels with an elastic matrix support and underwent axial and radial growth. Our results demonstrated that arteriole critical buckling pressure decreased with increasing axial growth ratio and radius growth ratio, but increased with increasing wall thickness. Arteriole buckling mode number increased (wavelength decreased) with increasing axial growth ratio, but decreased with increasing radius growth ratio and wall thickness. Our study suggests that axial growth in arterioles makes them prone to buckling and that buckling leads to tortuous collaterals. These results shed light on the mechanism of collateral arteriole tortuosity.

Smooth muscle cell contraction increases the critical buckling pressure of arteries

Recent in vitro experiments demonstrated that arteries under increased internal pressure or decreased axial stretch may buckle into the tortuous pattern that is commonly observed in aging or diseased arteries in vivo. It suggests that buckling is a possible mechanism for the development of artery tortuosity. Vascular tone has significant effects on arterial mechanical properties but its effect on artery buckling is unknown. The objective of this study was to determine the effects of smooth muscle cell contraction on the critical buckling pressure of arteries. Porcine common carotid arteries were perfused in an ex vivo organ culture system overnight under physiological flow and pressure. The perfusion pressure was adjusted to determine the critical buckling pressure of these arteries at in vivo and reduced axial stretch ratios (1.5 and 1.3) at baseline and after smooth muscle contraction and relaxation stimulated by norepinephrine and sodium nitroprusside, respectively. Our results demonstrated that the critical buckling pressure was significantly higher when the smooth muscle was contracted compared with relaxed condition (97.3mmHg vs 72.9mmHg at axial stretch ratio of 1.3 and 93.7mmHg vs 58.6mmHg at 1.5, p<0.05). These results indicate that arterial smooth muscle cell contraction increased artery stability.

Artery buckling: new phenotypes, models, and applications

Arteries are under significant mechanical loads from blood pressure, flow, tissue tethering, and body movement. It is critical that arteries remain patent and stable under these loads. This review summarizes the common forms of buckling that occur in blood vessels including cross-sectional collapse, longitudinal twist buckling, and bent buckling. The phenomena, model analyses, experimental measurements, effects on blood flow, and clinical relevance are discussed. It is concluded that mechanical buckling is an important issue for vasculature, in addition to wall stiffness and strength, and requires further studies to address the challenges. Studies of vessel buckling not only enrich vascular biomechanics but also have important clinical applications.

Cerebrovascular geometry in the anterior circulation: an analysis of diameter, length and the vessel taper

BACKGROUND

A study was undertaken to determine the typical length, diameter and taper of vessels in the anterior cerebral circulation.

METHODS

The sample size was calculated at 100 patients based on similar measurements in the literature and divided into cohorts based on gender and side. These patients were consecutively collected from a population that had undergone CT angiography and did not have any vascular abnormality. The arterial diameter was measured at the proximal cavernous internal carotid artery (ICA), the ICA terminus, the middle cerebral artery (MCA) origin and an M2 origin. The length between these endpoints was calculated along the center line. The vessel taper was calculated for the ICA as the change in caliber per unit length.

RESULTS

The mean length of the ICA from the proximal cavernous segment to the ICA terminus was 33.1 ± 6.1 mm. The mean diameter at the cavernous ICA and the ICA terminus was 5 ± 0.6 mm and 3.6 ± 0.4 mm, respectively. The mean ICA taper was 0.04 ± 0.02 mm/1 mm. For the MCA, the diameter at the MCA and M2 origins measured 3.1 ± 0.4 mm and 2.4 ± 0.4 mm, respectively. The mean MCA length was 22.5 ± 8.1 mm. There was no significant difference based on gender or between right and left sides. Patients aged >60 years had longer ICAs (p=0.02), larger cavernous ICA (p=0.003), ICA terminus (p<0.0001) and MCA origin (p=0.01) diameters than those aged 40-60 years. The ICA vessel taper did not change with age.

CONCLUSION

ICA and MCA vessel size did not change based on gender or side. Older patients had more redundant vessels based on diameter and length. The ICA has a gentle taper from its proximal cavernous segment to the ICA terminus. This information can be important in planning interventions or designing endovascular devices.

Mechanical buckling of artery under pulsatile pressure

Tortuosity that often occurs in carotid and other arteries has been shown to be associated with high blood pressure, atherosclerosis, and other diseases. However the mechanisms of tortuosity development are not clear. Our previous studies have suggested that arteries buckling could be a possible mechanism for the initiation of tortuous shape but artery buckling under pulsatile flow condition has not been fully studied. The objectives of this study were to determine the artery critical buckling pressure under pulsatile pressure both experimentally and theoretically, and to elucidate the relationship of critical pressures under pulsatile flow, steady flow, and static pressure. We first tested the buckling pressures of porcine carotid arteries under these loading conditions, and then proposed a nonlinear elastic artery model to examine the buckling pressures under pulsatile pressure conditions. Experimental results showed that under pulsatile pressure arteries buckled when the peak pressures were approximately equal to the critical buckling pressures under static pressure. This was also confirmed by model simulations at low pulse frequencies. Our results provide an effective tool to predict artery buckling pressure under pulsatile pressure.

[Patient education in chronic polyarthritis. 3. Intermediate results of a prospective, controlled study of the effectiveness and side effects of patient seminars for polyarthritis patients]

Efficacy and possible negative side effects of a patient education program for rheumatoid arthritis were evaluated in a controlled, prospective study over 3 months. 34 outpatients were educated over a total of 8 h in three groups within a patient-centred design. Before the program the knowledge of the disease depended only on the formal grade of education but not on disease-related variables such as disease duration or disability. Probably due to its individualizing method, the program improved the knowledge of all patients to the same extent, regardless of their intellectual and social prerequisites. The increased cognitive knowledge did not result in negative side effects like increased pain or depression. The pain score remained unchanged. Depression decreased after the education. The group sessions made us suppose that the participants may have represented a selected group of active, psychologically stable patients, who cope well with rheumatoid arthritis. In contrast, we felt that non-participation was the response of the inactive, fatalistic patients with rheumatoid arthritis, who live in social isolation and especially need our care. Therefore, future efforts must particularly focus on the problem of motivation and on an increase in the rate of participation.