Structural strain energy function applied to the ageing of the human aorta

Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch (lambda(z)) and residual strain (opening angle) in the biomechanical analysis. Both lambda(z) and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure-diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.     

A study on large radial motion of arteries in vivo

This study analyses the radial periodic motion of an artery which is modelled as a thin cylinder of uniform cross-section subjected to dynamic inner pressure using the theory of finite deformation of elastic materials. The arterial tissue properties (anisotropy, homogeneity and incompressibility) are taken into account in an analysis based on the use of the strain energy function. The validity of the mathematical analysis is illustrated through numerical computation applying the available in vivo data for elastic constants of the canine middle descending thoracic aorta to the expressions for the intramural pressure and circumferential stresses obtained by solving the necessary equation of motion together with the boundary conditions. Results obtained in this study indicate very low stresses which suggest that the arteriosclerosis resulting from high stress gradients is effectively ruled out in this model.     

Analysis of some effects of aortic smooth muscle on<Emphasis Type="Italic">in vivo</Emphasis> aortic pressure curves

When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.     

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.     

Passive elastic properties of the rat aorta

The passive anisotropic elastic properties of rat's aorta were studied in vitro by subjecting cylindrical segments of thoracic and abdominal aorta to a wide range of deformations. Using data on pressure, axial stretch, outer diameter, axial force and wall thickness, incremental moduli of elasticity in the circumferential, axial and radial directions were computed. Results indicate that while the elastic behavior of the aortic wall is globally anisotropic, there exists a state of deformation at which the vessel displays incremental isotropy. This state of deformation corresponds approximately to the loading conditions to which the aorta is exposed in situ. Values of the moduli, analyzed as a function of transmural pressure, show that the stiffness of the aortic wall is fairly constant at low pressures but raises steeply for pressures higher than physiological. For axial stretches as occurring in situ, the magnitudes of the circumferential and radial moduli do not differ significantly for the thoracic aorta; hence this vessel can be regarded as transversely isotropic over a wide range of pressures. The same observation is valid also for the abdominal aorta when pressures equal or smaller than physiological are considered. For both the thoracic and abdominal segments of the aorta, the circumferential and radial moduli are smaller than the axial modulus at low pressures, while the reverse is true for large pressures.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

Coupling between MRI-assessed regional aortic pulse wave velocity and diameters in patients with thoracic aortic aneurysm: a feasibility study

Aims

Thoracic aortic aneurysm (TAA) is potentially life-threatening and requires close follow-up to prevent aortic dissection. Aortic stiffness and size are considered to be coupled. Regional aortic stiffness in patients with TAA is unknown. We aimed to evaluate coupling between regional pulse wave velocity (PWV), a marker of vascular stiffness, and aortic diameter in TAA patients.

Methods

In 40 TAA patients (59 ± 13 years, 28 male), regional aortic diameters and regional PWV were assessed by 1.5 T MRI. The incidence of increased diameter and PWV were determined for five aortic segments (S1, ascending aorta; S2, aortic arch; S3, thoracic descending aorta; S4, suprarenal and S5, infrarenal abdominal aorta). In addition, coupling between regional PWV testing and aortic dilatation was evaluated and specificity and sensitivity were assessed.

Results

Aortic diameter was 44 ± 5 mm for the aortic root and 39 ± 5 mm for the ascending aorta. PWV was increased in 36 (19 %) aortic segments. Aortic diameter was increased in 28 (14 %) segments. Specificity of regional PWV testing for the prediction of increased regional diameter was ≥ 84 % in the descending thoracic to abdominal aorta and ≥ 68 % in the ascending aorta and aortic arch.

Conclusion

Normal regional PWV is related to absence of increased diameter, with high specificity in the descending thoracic to abdominal aorta and moderate results in the ascending aorta and aortic arch.     

Regional distribution of glutathione-related antioxidant defences in the normal rabbit aorta

In 6 normal rabbits, the aortic arch, the descending thoracic and the abdominal aorta were tested for non proteic thiol compounds, selenium-dependent and selenium-independent glutatione peroxidase, glutatione reductase, glutatione transferase and thiobarbituric acid reactive substances. The aortic arch showed the greatest content of non proteic thiol compounds and thiobarbituric acid reactive substances, associated to the highest activities of glutathione-related enzymes. However, not significant differences were detectable between aortic arch and descending thoracic aorta, except for the glutathione transferase activity (0.395 +/- 0.031 vs 0.330 +/- 0.053 U/mg protein, p less than 0.05). Furthermore, both aortic arch and descending thoracic aorta showed significantly higher values of non proteic thiol compounds (46.05 +/- 10.15% and 33 +/- 13.5%, p less than 0.05), selenium-dependent glutathione peroxidase activity (70.35 +/- 26% and 54.3 +/- 9.5%, p less than 0.05), glutathione reductase activity (25.4 +/- 7% and 18.4 +/- 4.5%, p less than 0.05) and thiobarbituric acid reactive substances (65.8 +/- 18% and 47.2 +/- 17%, p less than 0.05) with respect to the abdominal aorta. The selenium-independent glutathione peroxidase activity was not detectable. In conclusion, a biochemical gradient in glutathione-related antioxidant defences and thiobarbituric acid reactive substances proceeding from the proximal to the distal segments seems to exist in the normal rabbit aorta. These results could contribute to explain the non homogeneous distribution of experimental atherosclerosis in the rabbit aorta.     

Mechanical behavior of human aortas: Experiments,material constants and 3-D finite element modeling including residual stress

Segments of fresh human ascending, thoracic descending and abdominal aortas from eight male sexagenarians were pressurized under closed-end and free extension conditions. The median unpressurized inner radii for the ascending, thoracic and abdominal locations were 14.21, 9.67 and 7.16 mm, respectively. The median thickness was similar in the ascending and thoracic regions, at about 1.6 mm, while it was 1.2 mm in the abdominal region. The opening angle was not statistically different between regions, with a median of ?38°. Under 13.3 kPa pressure, the median circumferential stretch ratio was about 1.26 in all three aortic locations; the median longitudinal stretch ratio was similar in the ascending and thoracic regions, at about 1.13, while it was 1.05 in the abdominal region. Material constants for a three-dimensional hyperelastic anisotropic constitutive model were determined. Experimental, analytical and finite element results showed excellent agreement, validating the novel experimental approach and the numerical methods used. When residual stress was not taken into account, stresses were highest on the inside of the aorta, with a gradient across the wall of about 200 and 50 kPa in the circumferential and longitudinal directions, respectively. When residual stress was included as described by negative opening angles, stresses were highest on the outside of the aorta, with a gradient across the wall in excess of 400 kPa for the circumferential direction, and on the order of 150 kPa for the longitudinal direction. The mechanical consequences of negative opening angles had not been appreciated so far, and deserve further investigation.     

Mechanical characterisation of the human thoracic descending aorta: experiments and modelling

This work presents experiments and modelling aimed at characterising the passive mechanical behaviour of the human thoracic descending aorta. To this end, uniaxial tension and pressurisation tests on healthy samples corresponding to newborn, young and adult arteries are performed. Then, the tensile measurements are used to calibrate the material parameters of the Holzapfel constitutive model. This model is found to adequately adjust the material behaviour in a wide deformation range; in particular, it captures the progressive stiffness increase and the anisotropy due to the stretching of the collagen fibres. Finally, the assessment of these material parameters in the modelling of the pressurisation test is addressed. The implication of this study is the possibility to predict the mechanical response of the human thoracic descending aorta under generalised loading states like those that can occur in physiological conditions and/or in medical device applications.     

Theoretical Study of Stress-Modulated Growth in the Aorta

A theoretical model is presented for stress-modulated growth in the aorta. The model consists of a pseudoelastic tube composed of two layers representing the intima/media and the adventitia. Finite volumetric growth is included by letting the time-rate of change of the zero-stress dimensions of each volume element depends linearly on the local stresses. After analyzing the model, we examine its fundamental growth response under changes in loads, material properties, and growth parameters. The behaviour of the model is quite sensitive to changes in material nonlinearity and in the coefficients of the growth law. Next, growth of the aorta is simulated during development and maturity. For an appropriate choice of the parameters, the model exhibits patterns of growth that agree qualitatively with known characteristics of aortic growth. Comparison of model results with published experimental data during hypertension in the rat shows good agreement in the time course of the vessel radii and residual strain. Finally, the implications of the results are discussed in the context of deducing a general mechanical growth law for soft tissues. The proposed model should be useful in studies to determine the biomechanical factor that regulates growth.     

Wall shear in pulsatile flow

This paper deals with a mathematical attempt to determine the wall shear during normal flow of blood in the ascending and the descending thoracic aorta. A simple model is used, but the results obtained are in agreement with published experimental results for the descending thoracic aorta. It is suggested that the degree of fluctuation in the pressure gradient at a given station is the major factor in determining the level of wall shear at that point.     

Fiber-reinforced computational model of the aortic root incorporating thoracic aorta and coronary structures

Cardiovascular diseases are still the leading causes of death in the developed world. The decline in the mortality associated with circulatory system diseases is accredited to development of new diagnostic and prognostic tools. It is well known that there is an inter relationship between the aortic valve impairment and pathologies of the aorta and coronary vessels. However, due to the limitations of the current tools, the possible link is not fully elucidated. Following our previous model of the aortic root including the coronaries, in this study, we have further developed the global aspect of the model by incorporating the anatomical structure of the thoracic aorta. This model is different from all the previous studies in the sense that inclusion of the coronary structures and thoracic aorta into the natural aortic valve introduces the notion of globality into the model enabling us to explore the possible link between the regional pathologies. The developed model was first validated using the available data in the literature under physiological conditions. Then, to provide a support for the possible association between the localized cardiovascular pathologies and global variations in hemodynamic conditions, we simulated the model for two pathological conditions including moderate and severe aortic valve stenoses. The findings revealed that malformations of the aortic valve are associated with development of low wall shear stress regions and helical blood flow in thoracic aorta that are considered major contributors to aortic pathologies.     

Altered tissue behavior of a non-aneurysmal descending thoracic aorta in the mouse model of Marfan syndrome

Aortic aneurysm is predominantly found in the ascending aorta in patients with Marfan syndrome (MFS). However, descending aortic disease has emerged as a problem since people are living longer because of improved medical and surgical management of the ascending aorta. Diagnostic procedures before disease onset and the mechanisms involved in the transition of normal aortic tissue to aneurysm remain unclear. We determined signs of descending aortic disease before disease onset in mice with a mutation in the fibrillin 1 gene (Fbn1(+/C1039G)), a validated mouse model of disease susceptibility and progression of aortic aneurysm of MFS. We analyzed a tubular unfixed non-aneurysmal descending thoracic aorta from 8-month-old wild-type and Fbn1(+/C1039G) mice by a tubular biaxial tester that works in conjunction with a two-photon nonlinear microscope. Fbn1(+/C1039G) mouse aorta was more compliant in the circumferential direction. Two-photon imaging showed defective organization of adventitial collagen fibers in the pressurized aortas of Fbn1(+/C1039G) mice. Moreover, disruption in the elastic lamina was noted in the absence of aneurysms in pressurized aortas but not unpressurized aortas of Fbn1(+/C1039G) mice. At the molecular level, this altered tissue behavior in non-aneurysmal descending aortas of Fbn1(+/C1039G) mice was accompanied by an increasing trend of canonical but not noncanonical, transforming growth factor-β (TGFβ) signaling. Finally, assays of in vitro collagen lattice formation in mouse wild-type and TGFβ1-deficient embryonic fibroblasts indicate that TGFβ1 can regulate collagen organization. The ability to reveal the presence of altered biomechanics and microstructure coupled with subtle changes in TGFβ signaling provides a novel surrogate measure of tissue susceptibility to aneurysm before disease onset.     

Mechano-biology in the thoracic aortic aneurysm: a review and case study

An aortic aneurysm is a permanent and localized dilatation of the aorta resulting from an irreversible loss of structural integrity of the aortic wall. The infrarenal segment of the abdominal aorta is the most common site of aneurysms; however, they are also common in the ascending and descending thoracic aorta. Many cases remain undetected because thoracic aortic aneurysms (TAAs) are usually asymptomatic until complications such as aortic dissection or rupture occurs. Clinical estimates of rupture potential and dissection risk, and thus interventional planning for TAAs, are currently based primarily on the maximum diameter and growth rate. The growth rate is calculated from maximum diameter measurements at two subsequent time points; however, this measure cannot reflect the complex changes of vessel wall morphology and local areas of weakening that underline the strong regional heterogeneity of TAA. Due to the high risks associated with both open and endovascular repair, an intervention is only justified if the risk for aortic rupture or dissection exceeds the interventional risks. Consequently, TAAs clinical management remains a challenge, and new methods are needed to better identify patients for elective repair. We reviewed the pathophysiology of TAAs and the role of mechanical stresses and mathematical growth models in TAA management; as a proof of concept, we applied a multiscale biomechanical analysis to a case study of TAA.     

An analysis of aortic pressure curves taking into account visco-elastic properties of the aorta and variations in peripheral resistance

The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.     

Finite element comparison of performance related characteristics of balloon expandable stents

Cardiovascular stents are commonly made from 316L stainless steel and are deployed within stenosed arterial lesions using balloon expansion. Deployment involves inflating the balloon and plastically deforming the stent until the required diameter is obtained. This plastic deformation induces static stresses in the stent, which will remain for the lifetime of the device. In order to determine these stresses, finite element models of the unit cells of geometrically different, commercially available balloon expandable stents have been created, and deployment and elastic recoil have been simulated. In this work the residual stresses associated with deployment and recoil are compared for the various stent geometries, with a view to establishing appropriate initial stress states for fatigue loading for the stents. The maximum, minimum, and mean stresses induced in the stent due to systolic/diastolic pressure are evaluated, as are performance measures such as radial and longitudinal recoil.     

Akinetic myocardial infarcts must contain contracting myocytes: finite-element model study

Infarcted segments of myocardium demonstrate functional impairment ranging in severity from hypokinesis to dyskinesis. We sought to better define the contributions of passive material properties (stiffness) and active properties (contracting myocytes) to infarct thickening. Using a finite-element (FE) model, we tested the hypothesis that infarcted myocardium must contain contracting myocytes to be akinetic and not dyskinetic. A three-dimensional FE mesh of the left ventricle was developed with echocardiographs from a reperfused ovine anteroapical infarct. The nonlinear stress-strain relationship for the diastolic myocardium was anisotropic with respect to the local muscle fiber direction, and an elastance model for active fiber stress was incorporated. The diastolic stiffness (C) and systolic material property (isometric tension at longest sarcomere length and peak intracellular calcium concentration, T(max)) of the uninfarcted remote myocardium were assumed to be normal (C = 0.876 kPa, T(max) = 135.7 kPa). Diastolic and systolic properties of the infarct necessary to produce akinesis, defined as an average radial strain between -0.01 and 0.01, were determined by assigning a range of diastolic stiffnesses and scaling infarct T(max) to represent the percentage of contracting myocytes between 0% and 100%. As C was increased to 11 times normal (C = 10 kPa) the percentage of T(max) necessary for akinesis increased from 20% to 50%. Without contracting myocytes, C = 250 kPa was necessary to achieve akinesis. If infarct stiffness is <285 times normal, contracting myocytes are required to prevent dyskinetic infarct wall motion.     

Developmental changes in collagen and elastin biosynthesis in the porcine aorta

Elastin and collagen are the principal scleroproteins of the aortic wall, and they largely determine its physical and mechanical properties. During perinatal development of the aorta, elastin and collagen accumulate rapidly, being present as inverse gradients by the time of birth. Elastin is most prevalent in the thoracic aorta, decreasing distally, while collagen shows the opposite trend. The present studies have determined the relative and absolute rates of collagen and elastin synthesis in the porcine aorta between 60 days of fetal development (mid-gestation) and 110 days after birth. Although there was measurable elastin synthesis in the upper thoracic aorta at the earliest time evaluated, there was a fourfold increase in relative elastin synthesis (from 4 to 16% of total protein synthesis) between 60 fetal days and birth. Elastin synthesis was maximal in successively distal segments between 1 and 3 weeks after birth. Relative collagen synthesis progressively increased in distal aortic regions between 90 fetal days and 60 days postpartum. Greater than twofold increases over thoracic levels were measured. Both elastin and collagen synthesis largely subsided by 110 days of development. When expressed as absolute rates of protein synthesis, these scleroproteins were maximally expressed in the first 3 postnatal weeks. Elastin mRNA levels were determined with a cloned sheep gene fragment by molecular hybridization. Gradients of elastin message were present at 60 fetal days and at 4 and 14 days after birth, elastin mRNA levels being maximal in the upper thoracic aorta at 14 days after birth. The differentiation of the aortic wall thus follows discrete patterns of phenotypic change which may be coupled to the rheologic stresses accompanying development of the circulatory system.     

心肌带收缩率与急性心肌梗死患者左心室收缩功能关系

目的:急性前壁心肌梗死明显影响室间隔收缩率和左心室射血分数(left ventricular ejection fraction LVEF)。本文旨在探讨心肌带降段及升段收缩率与急性前壁心肌梗死患者LVEF的相关性。方法:收集2015年4月-2017年2月在心内科住院的急性前壁心肌梗死患者36例,正常对照组患者39例。所有患者取左心室长轴M型超声心动图,测量室间隔收缩率、升段收缩率及降段收缩率。心肌梗死左心室射血分数采用双平面Simpson's法计算。结果:与正常对照组相比,心肌梗死组患者舒张末期心肌带升段厚度没有统计学差异(P=0.69),收缩末期升段厚度(P=0.014)更薄、升段收缩率(P0.01)明显降低;心肌梗死组舒张末期降段厚度(P0.01)更薄、收缩末期降段厚度(P0.01)更薄、降段收缩率(P0.01)明显降低;心肌梗死组左心室射血分数与降段收缩率(r~2=0.13,P=0.026)、室间隔增厚率(r~2=0.19,P0.01)呈正相关,与升段收缩率没有相关性(P0.05)。正常对照组左心室射血分数与室间隔增厚率、降段增厚率及升段增厚率无相关性。经过相关分析,筛选出与心肌梗死LVEF的相关因素,进一步经逐步回归分析,得多元线性回归方程为LVEF=48.206+18.914*LVDD(cm)-25.414*LVSD(cm)。结论:急性前壁心肌梗死室间隔降段收缩率明显受损,与左心室射血分数降低有关。多元线性回归方程可估算前壁心肌梗死LVEF。