Pulsatile spiral blood flow through arterial stenosis

Pulsatile spiral blood flow in a modelled three-dimensional arterial stenosis, with a 75% cross-sectional area reduction, is investigated by using numerical fluid dynamics. Two-equation k-ω model is used for the simulation of the transitional flow with Reynolds numbers 500 and 1000. It is found that the spiral component increases the static pressure in the vessel during the deceleration phase of the flow pulse. In addition, the spiral component reduces the turbulence intensity and wall shear stress found in the post-stenosis region of the vessel in the early stages of the flow pulse. Hence, the findings agree with the results of Stonebridge et al. (2004). In addition, the results of the effects of a spiral component on time-varying flow are presented and discussed along with the relevant pathological issues.     

Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.     

Cryopreservation procedure does not modify human carotid homografts mechanical properties: an isobaric and dynamic analysis

The viscoelastic and inertial properties of the arterial wall are responsible for the arterial functional role in the cardiovascular system. Cryopreservation is widely used to preserve blood vessels for vascular reconstruction but it is controversially suspected to affect the dynamic behaviour of these allografts. The aim of this work was to assess the cryopreservation's effects on human arteries mechanical properties. Common carotid artery (CCA) segments harvested from donors were divided into two groups: Fresh (n = 18), tested for 24–48 h after harvesting, and Cryopreserved (n = 18) for an average time of 30 days in gas-nitrogen phase, and finally defrosted. Each segment was tested in a circulation mock, and its pressure and diameter were registered at similar pump frequency, pulse and mean pressure levels, including those of normotensive and hipertensive conditions. A compliance transfer function (diameter/pressure) derived from a mathematical adaptive modelling was designed for the on line assessment of the arterial wall dynamics and its frequency response. Assessment of arterial wall dynamics was made by measuring its viscous (η), inertial (M) and elastic (E) properties, and creep and stress relaxation time constant (τ_C and τ_SR, respectively). The frequency response characterization allowed to evaluate the arterial wall filter or buffer function. Results showed that non-significant differences exist between wall dynamics and buffer function of fresh and cryopreserved segments of human CCA. In conclusion, our cryopreservation method maintains arterial wall functional properties, close to their fresh values.     

Influence of the distensibility of large arteries on the longitudinal impedance: application for the development of non-invasive techniques to the diagnosis of arterial diseases

Background

This study shows that the arterial longitudinal impedance constitutes a hemodynamic parameter of interest for performance characterization of large arteries in normal condition as well as in pathological situations. For this purpose, we solved the Navier?CStokes equations for an incompressible flow using the finite element analysis method and the Arbitrary Lagrangian Eulerian (ALE) formulation. The mathematical model assumes a two-dimensional flow and takes into account the nonlinear terms in the equations of fluid motion that express the convective acceleration, as well as the nonlinear deformation of the arterial wall. Several numerical simulations of the blood flow in large vessels have been performed to study the propagation along an arterial vessel of a pressure gradient pulse and a rate flow pulse. These simulations include various deformations of the wall artery leading to parietal displacements ranging from 0 (rigid wall) to 15% (very elastic wall) in order to consider physiological and pathological cases.

Results

The results show significant changes of the rate flow and the pressure gradient wave as a function of aosc, the relative variation in the radius of the artery over a cardiac cycle. These changes are notable beyond a critical value of aosc equal to 0.05. This critical value is also found in the evolution of the longitudinal impedance. So, above a variation of radius of 5%, the convective acceleration, created by the fluid-wall interactions, have an influence on the flow detectable on the longitudinal impedance.

Conclusions

The interpretation of the evolution of the longitudinal impedance shows that it could be a mean to test the performance of large arteries and can contribute to the diagnosis of parietal lesions of large arteries. For a blood vessel with a wall displacement higher than 5% similar to those of large arteries like the aorta, the longitudinal impedance is substantially greater than that obtained in the absence of wall displacement. This study also explains the effects of convective acceleration, on the shape of the decline of the pressure gradient wave and shows that they should not be neglected when the variation in radius is greater than 5%.     

Dominance of geometric overelastic factors in pulse transmission through arterial branching

The branching characteristic of the arterial system is such that blood pressure pulses propagate with minimum loss. This characteristic depends on the geometric and elastic properties of branching vessels. In the current investigation, mathematical relations of branching geometry and elastic properties are formulated and their relative contributions to pulse reflection at an arterial junction are analyzed. Results show that alteration of pulse transmission through the junction is more significantly affected by changes in branching vessel radii and wall thickness than by corresponding percentage changes in vessel wall elastic moduli.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is empolyed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to ‘normotensive’ hemodynamics, ‘hypertension’ simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the ‘hypertension’ simulations.The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to ‘hypertensive’ (vs ‘normotensive’) hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation

Mounting evidence suggests that the pulsatile character of blood pressure and flow within large arteries plays a particularly important role as a mechano-biological stimulus for wall growth and remodeling. Nevertheless, understanding better the highly coupled interactions between evolving wall geometry, structure, and properties and the hemodynamics will require significantly more experimental data. Computational fluid–solid-growth models promise to aid in the design and interpretation of such experiments and to identify candidate mechanobiological mechanisms for the observed arterial adaptations. Motivated by recent aortic coarctation models in animals, we used a computational fluid–solid interaction model to study possible local and systemic effects on the hemodynamics within the thoracic aorta and coronary, carotid, and cerebral arteries due to a distal aortic coarctation and subsequent spatial variations in wall adaptation. In particular, we studied an initial stage of acute cardiac compensation (i.e., maintenance of cardiac output) followed by early arterial wall remodeling (i.e., spatially varying wall thickening and stiffening). Results suggested, for example, that while coarctation increased both the mean and pulse pressure in the proximal vessels, the locations nearest to the coarctation experienced the greatest changes in pulse pressure. In addition, after introducing a spatially varying wall adaptation, pressure, left ventricular work, and wave speed all increased. Finally, vessel wall strain similarly experienced spatial variations consistent with the degree of vascular wall adaptation.     

Transmission characteristics of axial waves in blood vessels

The elastic behavior of blood vessels can be quantitatively examined by measuring the propagation characteristics of waves transmitted by them. In addition, specific information regarding the viscoelastic properties of the vessel wall can be deduced by comparing the observed wave transmission data with theoretical predictions. The relevance of these deductions is directly dependent on the validity of the mathematical model for the mechanical behavior of blood vessels used in the theoretical analysis. Previous experimental investigations of waves in blood vessels have been restricted to pressure waves even though theoretical studies predict three types of waves with distinctly different transmission characteristics. These waves can be distinguished by the dominant displacement component of the vessel wall and are accordingly referred to as radial, axial and circumferential waves. The radial waves are also referred to as pressure waves since they exhibit pronounced pressure fluctuations. For a thorough evaluation of the mathematical models used in the analysis it is necessary to measure also the dispersion and attenuation of the axial and circumferential (torsion) waves.

To this end a method has been developed to determine the phase velocities and damping of sinusoidal axial waves in the carotid artery of anesthetized dogs with the aid of an electro-optical tracking system. For frequencies between 25 and 150 Hz the speed of the axial waves was between 20 and 40 m/sec and generally increased with frequency, while the natural pressure wave travelled at a speed of about 10 m/sec. On the basis of an isotropic wall model the axial wave speed should however be approximately 5 times higher than the pressure wave speed. This discrepancy can be interpreted as an indication for an anisotropic behavior of the carotid wall. The carotid artery appears to be more elastic in the axial than in the circumferential direction.     

In Vitro Model of Physiological and Pathological Blood Flow with Application to Investigations of Vascular Cell Remodeling

Vascular disease is a common cause of death within the United States. Herein, we present a method to examine the contribution of flow dynamics towards vascular disease pathologies. Unhealthy arteries often present with wall stiffening, scarring, or partial stenosis which may all affect fluid flow rates, and the magnitude of pulsatile flow, or pulsatility index. Replication of various flow conditions is the result of tuning a flow pressure damping chamber downstream of a blood pump. Introduction of air within a closed flow system allows for a compressible medium to absorb pulsatile pressure from the pump, and therefore vary the pulsatility index. The method described herein is simply reproduced, with highly controllable input, and easily measurable results. Some limitations are recreation of the complex physiological pulse waveform, which is only approximated by the system. Endothelial cells, smooth muscle cells, and fibroblasts are affected by the blood flow through the artery. The dynamic component of blood flow is determined by the cardiac output and arterial wall compliance. Vascular cell mechano-transduction of flow dynamics may trigger cytokine release and cross-talk between cell types within the artery. Co-culture of vascular cells is a more accurate picture reflecting cell-cell interaction on the blood vessel wall and vascular response to mechanical signaling. Contribution of flow dynamics, including the cell response to the dynamic and mean (or steady) components of flow, is therefore an important metric in determining disease pathology and treatment efficacy. Through introducing an in vitro co-culture model and pressure damping downstream of blood pump which produces simulated cardiac output, various arterial disease pathologies may be investigated.     

Effects of Viscosity and Constraints on the Dispersion and Dissipation of Waves in Large Blood Vessels: II. Comparison of Analysis with Experiments

The theoretical predictions described in part I of this study are compared with in vivo data from anesthetized dogs. It is shown that the observed attenuation of the pressure and axial waves cannot be accounted for by fluid viscosity alone. For large values of the frequency parameter α = √ρωR²₀/μ, the analysis of part I is extended to include the effects of viscoelasticity of the vessel wall. The results indicate that the speeds of both types of waves are essentially not affected by a realistic viscoelasticity model while the attenuation per wavelength is significantly increased and becomes frequency independent. The application of this analysis to in vivo data from the carotid arteries of anesthetized dogs demonstrates partial agreement between theory and experiment and suggests that the carotid arteries are anisotropically viscoelastic.     

黑龙江苹果亚科5属14种植物导管分子形态结构研究

利用扫描电子显微镜对黑龙江苹果亚科5属14种植物导管分子的管腔微形态结构特征进行了比较研究。结果显示:(1)该亚科植物导管分子的管腔长度、宽度及端壁斜度角有较大的差别。(2)孔纹导管在该亚科植物种中均存在,网纹导管和螺纹导管仅见于苹果属和花楸属中。(3)导管分子管壁除苹果属及山楂属中的毛山楂、辽宁山楂外均有螺纹加厚。(4)纹孔的排列方式为互列式、对列式及互列、对列同时存在。(5)在所观察的植物中花楸、山荆子、无毛山楂导管端壁具单穿孔板和梯状穿孔板,其余种的导管端壁仅具单穿孔板。(6)导管纹孔膜残留现象普遍存在。研究表明,导管分子管腔的微形态结构特征,可为该亚科植物的系统演化提供形态学依据;导管分子微形态结构特征与其所处的环境存在一定的适应性。     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

Coordination between ventilatory pressure oscillations and venous return in the cephalopod <Emphasis Type="Italic">Sepia officinalis</Emphasis> under control conditions,spontaneous exercise and recovery

Venous blood flow was measured for the first time in a cephalopod. Blood velocity was determined in the anterior vena cava (AVC) of cuttlefish S. officinalis with a Doppler, while simultaneously, ventilatory pressure oscillations were recorded in the mantle cavity. In addition, magnetic resonance imaging (MRI) was employed to investigate pulsatile flow in other major vessels. Blood pulses in the AVC are obligatorily coupled to ventilatory pressure pulses, both in frequency and phase. AVC peak blood velocity (v_AVC) in animals of 232 (± 30 SD) g wet mass at 15°C was found to be 14.2 (± 7.1) cm s⁻¹, AVC stroke volume (SV_AVC) was 0.2 (± 0.1) ml stroke⁻¹, AVC minute volume (MV_AVC) amounted to 5.5 (± 2.8) ml min⁻¹. Intense exercise bouts of 1–2 min resulted in 2.2-fold increases in MV_AVC, enabled by 1.6-fold increments in both, AVC pulse frequency (f _AVC) and v_AVC. As increases in blood flow occurred delayed in time by 1.7 min with regard to exercise periods, we concluded that it is not direct mantle cavity pressure conveyance that drives venous return in this cephalopod blood vessel. However, during jetting at high pressure amplitude (> 1 kPa), AVC blood flow and mantle cavity pressure pulse shapes completely overlap, suggesting that under these conditions, blood transport must be driven passively by mantle cavity pressure. MRI measurements at 15°C also revealed that under resting conditions, f _AVC and ventilation frequency (f _V) match at 31.6 (± 2.1) strokes min⁻¹. In addition, rates of pulsations in the cephalic artery and in afferent branchial vessels did not significantly differ from f _AVC and f _V. It is suggested that these adaptations are beneficial for high rates of oxygen extraction observed in S. officinalis and the energy conserving mode of life of the cuttlefish ecotype in general.     

Physical properties of resistance vessel wall in peripheral blood flow regulation--I. Mathematical model

A mathematical model is introduced to investigate the influence of the physical properties of the resistance vessel wall on the metabolic and myogenic mechanisms. The resistance vessel wall is assumed to have an elastic property and the elastic modulus to be a function of pressure (myogenic) and flow (metabolic). Blood is Poiseuille's flow. The resulting mathematical equations for pressure-flow, pressure-diameter, pressure-wall tension and pressure-wall elastic modulus relationships introduced obey Laplace's law. Poiseuille's law and Hooke's law. In comparison with the experimental data (pressure diameter), the mathematical model is confirmed to explain well the dynamic behavior of the resistance vessel wall in vivo.     

Echolocation sounds and hearing of the greater Japanese horseshoe bat (Rhinolophus ferrumequinum nippon)

Summary The relationship between the orientation sounds and hearing sensitivity in the greater Japanese horseshoe bat,Rhinolophus ferrumequinum nippon was studied.An orientation pulse consisted of a constant frequency (CF) component followed by a short downward frequency-modulated (FM) component. Sometimes, an initial upward FM component preceded the CF component. Duration of pulses was about 30 ms and the CF of resting pulses (RF) averaged 65.5 kHz. The best frequency (BF) at the lowest threshold in audiograms as measured by the pinna reflex averaged 66.1 kHz. Audiograms showed remarkable sharp cut-offs on both sides near the BF. The frequency difference between the BF and the RF was about 0.6 kHz, and the RF was always below the BF. The values of RF and BF were characteristically different from those of the European subspecies,Rhinolophus ferrumequinum ferrumequinum.Abbreviations BF best frequency - CF constant frequency - FM frequency modulated - RF resting frequency     

Effects of glucanase treatment on the structure and mechanical properties of cell walls in the giant‐celled xanthophycean alga Vaucheria frigida

The cell wall of the tip‐growing cells of the giant‐cellular xanthophycean alga Vaucheria frigida is mainly composed of cellulose microfibrils (CMFs) arranged in random directions and the major matrix component into which the CMFs are embedded throughout the cell. The mechanical properties of a cell‐wall fragment isolated from the tip‐growing region, which was inflated by artificially applied pressure, were measured after enzymatic removal of the matrix component by using a protease; the results showed that the matrix component is involved in the maintenance of cell wall strength. Since glucose and uronic acid are present in the matrix component of Vaucheria cell walls, we measured the mechanical properties of the cell wall after treatment with endo‐1,3‐ß‐glucanase and observed the fine structures of its surfaces by atomic force microscopy. The major matrix component was partially removed from the cell wall by glucanase, and the enzyme treatment significantly weakened the cell wall strength without affecting the pH dependence of cell wall extensibility. The enzymatic removal of the major matrix component by using a protease released polysaccharide containing glucose and glucuronic acid. This suggests that the major matrix component of the algal cell walls contains both proteins (or polypeptides) and polysaccharides consisting of glucose and glucuronic acid as the main constituents.     

On the transmission of external pressure fluctuations to the cerebrospinal fluid

A theory has been formulated to explain the manner in which external pressure fluctuations are transmitted to the cerebrospinal fluid (CSF). The theory is based upon a three-compartment model which consists of the cerebral ventricles, the basal cisterns and spinal subarachnoid space, and the cortical subarachnoid space. The external pressure disturbance is represented by a Fourier series summed over the frequency ω. The mathematical analysis leads to a time constant τ which depends upon the compliances of the spinal region and sources of external pressure fluctuations, the rate of CSF absorption and the rate of fluid transfer between compartments. For arterial pulsations where ωτ ? 1, the theory is in accord with the experimental observations that (i) the arterial and CSF pulse waves are nearly identical in shape, and (ii) the amplitude of the CSF pulse wave increases with intracranial pressure. Moreover, it predicts that the amplitude of the wave will be larger in the spinal region than in the ventricles. The theory also accounts for the observation of one per minute pulse waves observed in hydrocephalic patients with decreased absorption rates.     

Noninvasive pressure pulse waveform analysis of flow-mediated vasodilation evoked by post-occlusive reactive hyperemia maneuver

Post-occlusive reactive hyperemia (PORH) assesses flow-mediated vasodilation at microvascular level due to bioactivity of endothelial-derived factors. Ordinary augmentation index that quantifies endothelial response is based on an ensemble-averaged waveform that limits its short-time application. This study proposes a mathematical model and two corresponding indices to evaluate arterial pressure response after blood flow restoration. Radial pressure pulse waveforms were acquired by a 12 bits acquisition board at a sampling rate of 1.0 kHz using a piezoelectric transducer. Signals were stored during 30 s at baseline condition and 60 s after 5-min occlusion using an arm-cuff placed over the brachial artery. In both conditions, the pressure pulse waveform presents systolic and diastolic phases with progressive and regressive pulse waveforms, respectively. Changes in pulse wave morphology were also observed and comprised attenuation of the pulse pressure amplitude (markedly first and second systolic peaks). This characteristic of the pulse pressure was described by the time-domain summation of two pairs of Gaussian-like waveforms (representing independent progressive and regressive components) with parameters related to amplitude, time lag, and duration for each component. A steepest descent optimization routine was used to fit the model parameters to experimental data of normotensive and subjects with hypertension. The optimized parameters were used to calculate two indices, RIx_1,2 (second-to-first systolic peak ratio) and RIx_1,3 (first diastolic-to-first systolic ratio). The observed responses between groups suggest that RIx_1,2 is related to an endothelial response to the ischemic process and could be used as a clinical tool to assess endothelial function in hypertension.     

A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.

     

Influence of pressure on the low‐frequency vibrational modes of lysozyme and water: A complementary inelastic neutron scattering and molecular dynamics simulation study

We performed complementary inelastic neutron scattering (INS) experiments and molecular dynamics (MD) simulations to study the influence of pressure on the low‐frequency vibrational modes of lysozyme in aqueous solution in the 1 atm–6 kbar range. Increasing pressure induces a high‐frequency shift of the low‐frequency part (<10 meV = 80 cm^?1) of the vibrational density of states (VDOS), g(ω), of both lysozyme and water that reveals a stiffening of the interactions ascribed to the reduction of the protein and water volumes. Accordingly, high pressures increase the curvature of the free energy profiles of the protein quasiharmonic vibrational modes. Furthermore, the nonlinear influence of pressure on the g(ω) of lysozyme indicates a change of protein dynamics that reflects the nonlinear pressure dependence of the protein compressibility. An analogous dynamical change is observed for water and stems from the distortion of its tetrahedral structure under pressure. Moreover, our study reveals that the structural, dynamical, and vibrational properties of the hydration water of lysozyme are less sensitive to pressure than those of bulk water, thereby evidencing the strong influence of the protein surface on hydration water. Proteins 2013. © 2012 Wiley Periodicals, Inc.