Nonlinear elastic analysis of blood vessels

Based on the theory of Green and Adkins [9], a strain energy function is proposed to describe the nonlinear mechanical behavior of arteries. The arterial tissue is assumed to be a nonlinear elastic, incompressible material with local triclinicity and transverse isotropy. Although the arterial tissue shows viscous phenomena, experimental results have indicated that viscosity is only a second-order effect as compared to the nonlinear elasticity of the tissue. The advantage of the formulation presented herein is that it is relatively simple and results in an accurate stress-strain relation that can be used readily for the study of wave propagations in the blood vessels. For nonlinear finite strain elasticity of the order two, ten elastic constants are needed to describe the material nonlinearity of the arterial tissue. Based on the orthogonal, transverse isotropies and the incompressibility conditions, ten constraint equations may be established and the elastic constants can be uniquely determined by correlating with the experimental results. An example of calculating these elastic constants is made by using the experimental data of Patel, et al. [14-17] for the intercoastal arteries in living dogs. The predicted mechanical behavior of canine arteries is quite satisfactory as compared to the experimental data except when the longitudinal and the circumferential stretches exceed 1.60. However, such a strain magnitude may not be expected in in-vivo arteries because of the constraints of peripheral connecting tissues. Otherwise, the strain energy function including higher order strain terms should be used.(ABSTRACT TRUNCATED AT 250 WORDS)     

Nonlinear mechanical property of tracheal cartilage: a theoretical and experimental study

BACKGROUND: Despite being the stiffest airway of the bronchial tree, the trachea undergoes significant deformation due to intrathoracic pressure during breathing. The mechanical properties of the trachea affect the flow in the airway and may contribute to the biological function of the lung. METHOD: A Fung-type strain energy density function was used to investigate the nonlinear mechanical behavior of tracheal cartilage. A bending test on pig tracheal cartilage was performed and a mathematical model for analyzing the deformation of tracheal cartilage was developed. The constants included in the strain energy density function were determined by fitting the experimental data. RESULT: The experimental data show that tracheal cartilage is a nonlinear material displaying higher strength in compression than in tension. When the compression forces varied from -0.02 to -0.03N and from -0.03 to -0.04N, the deformation ratios were 11.03+/-2.18% and 7.27+/-1.59%, respectively. Both were much smaller than the deformation ratios (20.01+/-4.49%) under tension forces of 0.02 to 0.01N. The Fung-type strain energy density function can capture this nonlinear behavior very well, whilst the linear stress-strain relation cannot. It underestimates the stability of trachea by exaggerating the displacement in compression. This study may improve our understanding of the nonlinear behavior of tracheal cartilage and it may be useful for the future study on tracheal collapse behavior under physiological and pathological conditions.     

Elasticity of passive blood vessels: a new concept

The mechanical properties of passive blood vessels are generally thought to depend on the parallel arrangement of elastin and collagen with linear elasticity and collagen recruitment depending on vessel strain [hook-on (HO) model]. We evaluated an alternative model [serial element (SE) model] consisting of the series arrangement of an infinite number of elements, each containing elastin with a constant elastic modulus and collagen that switches stepwise from slack (zero stress) to fully rigid (infinite stiffness) on ongoing element strain. Both models were implemented with Weibull distributions for collagen recruitment strain (HO model) and collagen tightening strain (SE model). The models were tested in experiments on rat mesenteric small arteries. Strain-tension relations were obtained before and after two rounds of digestion by collagenase. Both models fitted the data prior to digestion. However, for the HO model, this required unrealistically low estimates for collagen recruitment or elastic modulus and unrealistically high estimates for distension of collagen fibers. Furthermore, the data after digestion were far better predicted by the SE model compared with the HO model. Finally, the SE model required one parameter less (collagen elastic modulus). Therefore, the SE model provides a valuable starting point for the understanding of vascular mechanics and remodeling of vessels.     

Spermine-nucleic acid interactions: a theoretical study

The interaction of spermine with nucleic acids is simulated theoretically using refined semi-empirical energy formulae and an advanced minimization procedure. Various nucleic acids are considered: model homopolymeric DNA's, a dodecamer (CGCGAATTCGCG) of type B-DNA, as well as a transfer RNA, tRNA^Phe. The dominant role of electrostatic potential in determining the preferential binding sites of spermine is demonstrated in each of these cases and the role of counterions, nucleic acid structure, and base-pair sequence is analyzed.     

LUMENating blood vessels

The acquisition of a lumen is an essential step in vascular morphogenesis. In this issue of Developmental Cell, Xu et?al. (2011) show that the small GTPase Rasip is a critical regulator of cytoskeleton dynamics and cell adhesion, which together drive the emergence of vascular lumens.     

Mode of action of intercalators: a theoretical study

Mode of action of some intercalators has been theoretically investigated on the basis of quantum mechanical perturbation method. Energies of H-bond interaction between drug chromophore and base pairs have been calculated in all possible orientations. The stacking energy has also been calculated with the base pairs. The effect of these interactions on specific recognition has also been discussed. On the basis of these studies, a model for the interaction of these drugs has been proposed. This explains the relative activities of acridine intercalators and satisfies the experimental observations.     

Blunt trauma to large vessels: a mathematical study

Background  

Blunt trauma causes short-term compression of some or all parts of the chest, abdomen or pelvis and changes hemodynamics of the blood. Short-term compression caused by trauma also results in a short-term decrease in the diameter of blood vessels. It has been shown that with a sudden change in the diameter of a tube or in the direction of the flow, the slower-moving fluid near the wall stops or reverses direction, which is known as boundary layer separation (BLS). We hypothesized that a sudden change in the diameter of elastic vessel that results from compression may lead not only to BLS but also to other hemodynamic changes that can damage endothelium.     

Cryopreservation of isolated blood vessels

Canine saphenous veins were immersed in fetal calf serum (FCS) containing various cryoprotective agents, slowly frozen and stored for several weeks at subzero temperatures. Pharmacological investigations of frozen/thawed tissues revealed considerable attenuation of the contractile force of frozen stored veins as compared to unfrozen veins. The best recovery after thawing of frozen stored canine veins was obtained on tissues which had been frozen slowly to -70 degrees C and stored in liquid nitrogen while being immersed in FCS containing 1.8 mol/l dimethyl sulfoxide (DMSO). Though the maximum response to noradranline of helical strips prepared from these veins was diminished to about 60% the evidence suggests that there may be a very good preservation of the main biochemical properties, such as monoamine oxidase activity, endogenous prostaglandin synthesis and neuronal uptake mechanism in veins stored under these conditions. The same method of cryopreservation was applied to store samples of human veins. Comparison of the pD2 values for various agonists and of the blocking activities of various antagonists of both 5-HT receptors and alpha-adrenoceptors yielded an excellent correlation between the parameters determined on frozen/thawed and unfrozen human veins. It is concluded that freezing isolated blood vessels may be considered an effective means of preserving and storing vascular tissues for pharmacological investigations.     

Sleep-induced periodic breathing and apnea: a theoretical study

To elucidate the mechanisms that lead to sleep-disordered breathing, we have developed a mathematical model that allows for dynamic interactions among the chemical control of respiration, changes in sleep-waking state, and changes in upper airway patency. The increase in steady-state arterial PCO2 accompanying sleep is shown to be inversely related to the ventilatory response to CO2. Chemical control of respiration becomes less stable during the light stage of sleep, despite a reduction in chemoresponsiveness, due to a concomitant increase in "plant gain" (i.e., responsiveness of blood gases to ventilatory changes). The withdrawal of the "wakefulness drive" during sleep onset represents a strong perturbation to respiratory control: higher magnitudes and rates of withdrawal of this drive favor instability. These results may account for the higher incidence of periodic breathing observed during light sleep and sleep onset. Periodic ventilation can also result from repetitive alternations between sleep onset and arousal. The potential for instability is further compounded if the possibility of upper airway occlusion is also included. In systems with high controller gains, instability is mediated primarily through chemoreflex overcompensation. However, in systems with depressed chemoresponsiveness, rapid sleep onset and large blood gas fluctuations trigger repetitive episodes of arousal and hyperpnea alternating with apneas that may or may not be obstructive. Between these extremes, more complex patterns can arise from the interaction between chemoreflex-mediated oscillations of shorter-cycle-duration (approximately 36 s) and longer-wavelength (approximately 60-80 s) state-driven oscillations.     

An electron microscopic study of the cerebral blood vessels of the opossum

Summary Blood vessels of the opossum brain are paired, artery and vein, and end in a closed loop. Both anatomically and physiologically they are true end-arteries. The two limbs are enclosed within a single basement membrane and are separated from each other by an intercapillary cell thought to be analogous to the usual capillary pericytes. The similarity of this vascular arrangement to that in the rabbit placenta and in the medulla of the kidney is discussed in relation to the counter-current multiplier system.This work was supported in part by the Beaumont-May Institute of Neurology and by a grant, B-425, from the United States Public Health Service.Research Fellow of the National Multiple Sclerosis Society.     

Relationship between chromaffin cells and blood vessels in the rat adrenal medulla: a transmission electron microscopic study combined with blood vessel reconstructions

The rat adrenal medulla architecture was examined using a combination of medullary blood vessel reconstructions and transmission electron microscopy. The peripheral radicles of the central vein and the medullary capillaries of the medullary arteries were thus precisely identified in the electron microscopic observations. The observations confirmed that the peripheral segments of the central vein were sinusoidal vessels with an attenuated and fenestrated endothelial wall. No ultrastructural differences were observed between segments lined by epinephrine-storing cells and those lined by norepinephrine-storing cells. The findings suggest that these peripheral segments of the adrenal central vein were sites of cortical hormonal effects on the adrenal medulla. The vessel structure does not support the hypothesis that medullary chromaffin-cell development is controlled by selective distribution of adrenal blood vessels.     

A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending

Local arterial haemodynamics has been associated with the pathophysiology of several cardiovascular diseases. The stable spiral blood-flows that were observed in vivo in several vessels, may play a dual role in vascular haemodynamics, beneficial since it induces stability, reducing turbulence in the arterial tree, and accounts for normal organ perfusion, but detrimental in view of the imparted tangential velocities that are involved in plaque formation and development. Being a spiral flow considered representative of the local blood dynamics in certain vessels, a method is proposed to quantify the spiral structure of blood flow. The proposed function, computed along a cluster of particle trajectories, has been tested for the quantitative determination of the spiral blood flow in a three-dimensional, s-shaped femoral artery numerical model in which three degrees of stenosis were simulated in a site prone to atherosclerotic development. Our results confirm the efficacy of the Lagrangian analysis as a tool for vascular blood dynamics investigation. The proposed method quantified spiral motion, and revealed the progression in the degree of stenosis, in the presented case study. In the future, it could be used as a synthetic tool to approach specific clinical complications.