A method for calculation of human systolic and diastolic blood pressures using an elastic reservoir theory of the systemic arterial system,and some clinical and physiological applications

Two equations have been developed that describe the interrelationship of the clinically measurable variables of the human systemic arterial system. An approximation method is given for their simultaneous solution for systolic and diastolic pressures in terms of heart rate, cardiac output, total peripheral resistance, and aortic distensibility. In this way, blood pressures were calculated for various clinically important and didactically useful situations. The effects on systolic and diastolic pressures due to changing either cardiac output or peripheral resistance or heart rate or aortic distensibility alone are shown. The effects on pulse pressure of varying cardiac output and peripheral resistance while holding mean arterial pressure constant are demonstrated. Compensatory mechanisms in hypertension and exercise are explored. Opinions and conclusions contained in this report are those of the author. They are not to be construed as necessarily reflecting the views or the endorsement of the Navy Department.     

Estimation of aortic distensibility and instantaneous left ventricular volume in living man

A method is presented in this paper for the estimation of aortic distensibility and instantaneous systolic left ventricular volume in living man in the absence of valvular regurgitation. The method is based on a simple, elastic-reservoir-theory, model of the circulatory system and requires no assumption concerning the geometry of the left ventricle. The input data required for this mathematical model consists of stroke volume, an aortic pressure record over an entire cardiac cycle and end diastolic ventricular volume. The procedure developed here for the estimation of aortic distensibility and instantaneous left ventricular volume is very practical from a computational point of view. It is believed that it will yield useful information concerning two clinically important quantities which cannot be measured directly in living man and will facilitate the study of correlations between these quantities and various physiological and pathological states. Results are presented in the paper for six cardiac patients. The requisite data in each case was obtained in the Cardiac Research Laboratory at the Peter Bent Brigham Hospital.     

Fluid dynamics of aortic root dilation in Marfan syndrome

Aortic root dilation and propensity to dissection are typical manifestations of the Marfan Syndrome (MS), a genetic defect leading to the degeneration of the elastic fibres. Dilation affects the structure of the flow and, in turn, altered flow may play a role in vessel dilation, generation of aneurysms, and dissection. The aim of the present work is the investigation in-vitro of the fluid dynamic modifications occurring as a consequence of the morphological changes typically induced in the aortic root by MS. A mock-loop reproducing the left ventricle outflow tract and the aortic root was used to measure time resolved velocity maps on a longitudinal symmetry plane of the aortic root. Two dilated model aortas, designed to resemble morphological characteristics typically observed in MS patients, have been compared to a reference, healthy geometry. The aortic model was designed to quantitatively reproduce the change of aortic distensibility caused by MS. Results demonstrate that vorticity released from the valve leaflets, and possibly accumulating in the root, plays a fundamental role in redirecting the systolic jet issued from the aortic valve. The altered systolic flow also determines a different residual flow during the diastole.     

Bicuspid aortic valve aortopathies: An hemodynamics characterization in dilated aortas

Bicuspid aortic valve (BAV) aortopathy remains of difficult clinical management due to its heterogeneity and further assessment of related aortic hemodynamics is necessary. The aim of this study was to assess systolic hemodynamic indexes and wall stresses in patients with diverse BAV phenotypes and dilated ascending aortas. The aortic geometry was reconstructed from patient-specific images while the aortic valve was generated based on patient-specific measurements. Physiologic material properties and boundary conditions were applied and fully coupled fluid-structure interaction (FSI) analysis were conducted. Our dilated aortic models were characterized by the presence of abnormal hemodynamics with elevated degrees of flow skewness and eccentricity, regardless of BAV morphotype. Retrograde flow was also present. Both features, predicted by flow angle and flow reversal ratios, were consistently higher than those reported for non-dilated aortas. Right-handed helical flow was present, as well as elevated wall shear stress (WSS) on the outer ascending aortic wall. Our results suggest that the abnormal flow associated with BAV may play a role in aortic enlargement and progress it further on already dilated aortas.     

An Elastic reservoir theory of the human systemic arterial system using current data on aortic elasticity

A review of the literature of aortic elasticity data leads to the conclusion that the pressure-volume curves of the human aorta can be reasonably well approximated by parabolas, while a straight line approximation proves inadequate. By using the above relationship and assuming flow through the peripheral vascular system to be directly proportional to the pressure difference across it, two equations are derived which relate systolic and diastolic blood pressures, cardiac output, pulse rate, peripheral resistance, and two constants of aortic elasticity. Pulsewave transmission phenomena are ignored. These two equations can be solved simultaneously for any two variables in terms of the others. When values computed from these equations are compared with experiment, the errors are usually less than 5 per cent, provided errors due to inaccurate measurements of the aortic elasticity constants are avoided.     

Respective contribution of age, mean arterial pressure, and body weight on central arterial distensibility in SHR

In spontaneously hypertensive rats (SHR), carotid and aortic distensibilities measured at operational blood pressure (BP) are reduced. Increased body weight and mean arterial pressure (MAP) are both known to reduce distensibility independently. However, whether, after adjustment to body weight and mean BP, distensibility remains reduced in SHR has never been investigated. Carotid and abdominal aorta distensibilities were measured under anesthesia in SHR at 5, 12, 52, and 78 wk of age, and measurements were compared with age-matched normotensive Wistar rats. Each age group was composed of 9 or 10 animals. We determined distensibility using echo-tracking techniques of high resolution. Compared with Wistar rats, carotid and aortic distensibilities measured at operational MAP are reduced in SHR. This reduction is accentuated with age, particularly for the carotid artery. After adjustment to body weight and MAP, carotid and aortic distensibilities become identical in Wistar and SHR (or even slightly increased in SHR) but continue to be reduced with age, mainly for the carotid artery. In conclusion, in SHR, age and high BP do not have a parallel and similar influence on the reduction of arterial distensibility. Aging constantly reduces arterial distensibility, whereas MAP levels contribute to maintenance of arterial function.     

Effects of diabetes and gender on mechanical properties of the arterial system in rats: aortic impedance analysis

We determined the effects of diabetes and gender on the physical properties of the vasculature in streptozotocin (STZ)-treated rats based on the aortic input impedance analysis. Rats given STZ 65 mg/kg i.v. were compared with untreated age-matched controls. Pulsatile aortic pressure and flow signals were measured and were then subjected to Fourier transformation for the analysis of aortic input impedance. Wave transit time was determined using the impulse response function of the filtered aortic input impedance spectra. Male but not female diabetic rats exhibited an increase in cardiac output in the absence of any significant changes in arterial blood pressure, resulting in a decline in total peripheral resistance. However, in each gender group, diabetes contributed to an increase in wave reflection factor, from 0.47 +/- 0.04 to 0.84 +/- 0.03 in males and from 0.46 +/- 0.03 to 0.81 +/- 0.03 in females. Diabetic rats had reduced wave transit time, at 18.82 +/- 0.60 vs 21.34 +/- 0.51 msec in males and at 19.63 +/- 0.37 vs 22.74 +/- 0.57 msec in females. Changes in wave transit time and reflection factor indicate that diabetes can modify the timing and magnitude of the wave reflection in the rat arterial system. Meanwhile, diabetes produced a fall in aortic characteristic impedance from 0.023 +/- 0.002 to 0.009 +/- 0.001 mmHg/min/kg/ml in males and from 0.028 +/- 0.002 to 0.014 +/- 0.001 mmHg/min/kg/ml in females. With unaltered aortic pressure, both the diminished aortic characteristic impedance and wave transit time suggest that the muscle inactivation in diabetes may occur in aortas and large arteries and may cause a detriment to the aortic distensibility in rats with either sex. We conclude that only rats with male gender diabetes produce a detriment to the physical properties of the resistance arterioles. In spite of male or female gender, diabetes decreases the aortic distensibility and impairs the wave reflection phenomenon in the rat arterial system.     

The strength of the aortic media and its role in the propagation of aortic dissection

The elastic properties of the thoracic aorta are well known, but this is the first study of the inherent strength of the tunica media. The latter is crucial to understand how dissecting aneurysms occur. Pressure-volume (P-V) measurements were recorded as a dilute suspension of India ink was infused into the tunica media using a constant flow pump (0.21 or 0.88 ml min-1) attached to a 20 G needle inserted into the media. Tests done on 31 opened pig upper descending thoracic aortas showed the peak pressure to tear the media averaged 77.2 +/- 1.5 kPa (579 mm Hg). The initial slope of the P-V curve revealed the average distensibility of the media of 3.02 +/- 0.28 (MPa)-1. The work per unit area of tissue required to propagate a tear in the aorta was 15.9 +/- 0.9 mJ cm-2. These values were independent of the tear depth at the 95% confidence interval.     

Nonlinear model of human descending thoracic aortic segments with residual stresses

The nonlinear static deformation of human descending thoracic aortic segments is investigated. The aorta segments are modeled as straight axisymmetric circular cylindrical shells with three hyperelastic anisotropic layers and residual stresses by using an advanced nonlinear shell theory with higher-order thickness deformation not available in commercial finite element codes. The residual stresses are evaluated in the closed configuration in an original way making use of the multiplicative decomposition. The model was initially validated through comparison with published numerical and experimental data for artery and aorta segments. Then, two different cases of healthy thoracic descending aorta segments were numerically simulated. Material data and residual stresses used in the models came from published layer-specific experiments for human aortas. The material model adopted in the study is the mechanically based Gasser–Ogden–Holzapfel, which takes into account collagen fiber dispersion. Numerical results present a difference between systolic and diastolic inner radii close to the data available in literature from in vivo measurements for the corresponding age groups. Constant length of the aortic segment between systolic and diastolic pressures was obtained for the material model that takes the dispersion of the fiber orientations into account.     

Biological aortic age derived from the arterial pressure waveform

Indexes for arterial stiffness are, by their nature, influenced by the ambient blood pressure due to the curvilinear nature of arterial compliance. We developed a new concept of the "Modelflow aortic age," which is, theoretically, not influenced by the ambient blood pressure and provides an easily understood context (biological vs. chronological age) for measures of arterial stiffness. The purpose of the present study was to validate this pressure-independent index for aortic stiffness in humans. Twelve sedentary elderly (65-77 yr), 11 Masters athletes (65-73 yr), and 12 sedentary young individuals (20-42 yr) were studied. Modelflow aortic ages were comparable with chronological ages in both sedentary groups, indicating that healthy sedentary individuals have age-appropriate aortas. In contrast, Masters athletes showed younger Modelflow aortic ages than their chronological ages. The coefficient of variation of sedentary subjects was three times smaller with the Modelflow aortic age (21%) than with other indexes, such as static systemic arterial stiffness (61%), central pulse wave velocity (61%), or carotid β-stiffness index (58%). The typical error was very small and two times smaller in the Modelflow aortic age (<7%) than in static systemic arterial stiffness (>13%) during cardiac unloading by lower body negative pressure. The Modelflow aortic age can more precisely and reliably estimate aortic stiffening with aging and modifiers, such as life-long exercise training compared with the pressure-dependent index of static systemic arterial stiffness, and provides a physiologically relevant and clinically compelling context for such measurements.     

The effect of the elongation of the proximal aorta on the estimation of the aortic wall distensibility

The compliance of the proximal aortic wall is a major determinant of cardiac afterload. Aortic compliance is often estimated based on cross-sectional area changes over the pulse pressure, under the assumption of a negligible longitudinal stretch during the pulse. However, the proximal aorta is subjected to significant axial stretch during cardiac contraction. In the present study, we sought to evaluate the importance of axial stretch on compliance estimation by undertaking both an in silico and an in vivo approach. In the computational analysis, we developed a 3-D finite element model of the proximal aorta and investigated the discrepancy between the actual wall compliance to the value estimated after neglecting the longitudinal stretch of the aorta. A parameter sensitivity analysis was further conducted to show how increased material stiffness and increased aortic root motion might amplify the estimation errors (discrepancies between actual and estimated distensibility ranging from − 20 to − 62%). Axial and circumferential aortic deformation during ventricular contraction was also evaluated in vivo based on MR images of the aorta of 3 healthy young volunteers. The in vivo results were in good qualitative agreement with the computational analysis (underestimation errors ranging from − 26 to − 44%, with increased errors reflecting higher aortic root displacement). Both the in silico and in vivo findings suggest that neglecting the longitudinal strain during contraction might lead to severe underestimation of local aortic compliance, particularly in the case of women who tend to have higher aortic root motion or in subjects with stiff aortas.

     

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.     

Earlier accumulation of calcium, phosphorus, and magnesium in the coronary artery in comparison with the ascending aorta, aortic valve, and mitral valve

To explore reasons for a high accumulation of Ca and P occurring in the coronary artery of Thai with aging, the authors investigated age-related changes of elements in the coronary artery, ascending aorta near the heart, and cardiac valves in single individuals, and the relationships in the elements between the coronary artery and either the ascending aorta or cardiac valves. After an ordinary dissection by medical students at Chiang Mai University was finished, the anterior descending arteries of the left coronary artery, ascending aortas, mitral valves, and aortic valves were resected from the subjects. The subjects consisted of 17 men and 9 women, ranging in age from 46 to 76 yr. The element content was analyzed by inductively coupled plasma-atomic emission spectrometry. The average content of Ca and P was the highest in the coronary artery and decreased in the order aortic valve, ascending aorta, and mitral valve. The Ca, P, and Mg content increased in the coronary artery in the fifties and in the ascending aorta, aortic valve, and mitral valve in the sixties. It should be noted that the accumulation of Ca, P, and Mg occurred earlier in the coronary artery than in the ascending aorta, aortic valve, and mitral valve. It was found that with respect to the Ca, P, Mg, and Na contents, the coronary artery correlated well with both the aortic valve and ascending aorta, especially with the aortic valve, but it did not correlate with the mitral valves. This finding suggests that the accumulation of Ca, P, Mg, and Na occurs in the coronary artery together with the aortic valve and ascending aorta, but not together with the mitral valve. Because regarding the accumulation of Ca, P, and Mg, the ascending aorta and aortic valve are preceded by the coronary artery, it is unlikely that the accumulation of Ca, P, and Mg spreads from the ascending aorta or aortic valve to the coronary artery.     

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.     

In-vitro analysis of normal and aneurismal human ascending aortic tissues using FT-IR microspectroscopy

FTIR microspectroscopy has shown to be a proven tool in the investigation of many tissue types. We have used this spectroscopic approach to analyse structural differences between normal and aneurismal aortic tissues and also aortas from patients with congenital anomalies like aortic bicuspid valves. Spectral analysis showed important variations in amide I and II regions, related to changes in alpha-helix and beta-sheet secondary structure of proteins that seem to be correlated to structural modifications of collagen and elastin. These proteins are the major constituents of the aortic wall associated to smooth muscular cells. The amide regions have thus been identified as a marker of structural modifications related to these proteins whose modifications can be associated to a given aortic pathological situation. Both univariate (total absorbance image and band ratio) and multivariate (principal components analysis) analyses of the spectral information contained in the infrared images have been performed. Differences between tissues have been identified by these two approaches and allowed to separate each group of aortic tissues. However, with univariate band ratio analysis, the pathological group was found to be composed of samples from aneurismal aortas associated or not with an aortic bicuspid valve. In contrast, PCA was able to separate these two types of aortic pathologies. For other groups, PCA and band ratio analysis can differentiate between normal, aneurismal, and none dilated aortas from patients with a bicuspid aortic valve.     

In-vitro analysis of normal and aneurismal human ascending aortic tissues using FT-IR microspectroscopy

FTIR microspectroscopy has shown to be a proven tool in the investigation of many tissue types. We have used this spectroscopic approach to analyse structural differences between normal and aneurismal aortic tissues and also aortas from patients with congenital anomalies like aortic bicuspid valves. Spectral analysis showed important variations in amide I and II regions, related to changes in alpha-helix and beta-sheet secondary structure of proteins that seem to be correlated to structural modifications of collagen and elastin. These proteins are the major constituents of the aortic wall associated to smooth muscular cells. The amide regions have thus been identified as a marker of structural modifications related to these proteins whose modifications can be associated to a given aortic pathological situation. Both univariate (total absorbance image and band ratio) and multivariate (principal components analysis) analyses of the spectral information contained in the infrared images have been performed. Differences between tissues have been identified by these two approaches and allowed to separate each group of aortic tissues. However, with univariate band ratio analysis, the pathological group was found to be composed of samples from aneurismal aortas associated or not with an aortic bicuspid valve. In contrast, PCA was able to separate these two types of aortic pathologies. For other groups, PCA and band ratio analysis can differentiate between normal, aneurismal, and none dilated aortas from patients with a bicuspid aortic valve.     

Methylprednisolone Stiffens Aortas in Lipopolysaccharide-Induced Chronic Inflammation in Rats

Introduction

Glucocorticoids are commonly used as therapeutic agents in many acute and chronic inflammatory and auto-immune diseases. The current study investigated the effects of methylprednisolone (a synthetic glucocorticoid) on aortic distensibility and vascular resistance in lipopolysaccharide-induced chronic inflammation in male Wistar rats.

Methods

Chronic inflammation was induced by implanting a subcutaneous slow-release ALZET osmotic pump (1 mg kg⁻¹ day⁻¹ lipopolysaccharide) for either 2 or 4 weeks. Arterial wave transit time (τ) was derived to describe the elastic properties of aortas using the impulse response function of the filtered aortic input impedance spectra.

Results

Long-term lipopolysaccharide challenge enhanced the expression of advanced glycation end products (AGEs) in the aortas. Lipopolysaccharide also upregulated the inducible form of nitric oxide synthase to produce high levels of nitric oxide (NO), which resulted in vasodilation, as evidenced by the fall in total peripheral resistance (R_p). However, lipopolysaccharide challenge did not influence the elastic properties of aortas, as shown by the unaltered τ. The NO-mediated vascular relaxation may counterbalance the AGEs-induced arterial stiffening so that the aortic distensibility remained unaltered. Treating lipopolysaccharide-challenged rats with methylprednisolone prevented peripheral vasodilation because of its ability to increase R_p. However, methylprednisolone produced an increase in aorta stiffness, as manifested by the significant decline in τ. The diminished aortic distensibility by methylprednisolone paralleled a significant reduction in NO plasma levels, in the absence of any significant changes in AGEs content.

Conclusion

Methylprednisolone stiffens aortas and elastic arteries in lipopolysaccharide-induced chronic inflammation in rats, for NO activity may be dominant as a counteraction of AGEs.     

Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. Although exact causes and mechanisms of AV calcification are unclear, previous studies suggest that mechanical forces play a role. Since calcium deposits occur almost exclusively on the aortic surfaces of AV leaflets, it has been hypothesized that adverse patterns of fluid shear stress on the aortic surface of AV leaflets promote calcification. The current study characterizes AV leaflet aortic surface fluid shear stresses using Laser Doppler velocimetry and an in vitro pulsatile flow loop. The valve model used was a native porcine valve mounted on a suturing ring and preserved using 0.15% glutaraldehyde solution. This valve model was inserted in a mounting chamber with sinus geometries, which is made of clear acrylic to provide optical access for measurements. To understand the effects of hemodynamics on fluid shear stress, shear stress was measured across a range of conditions: varying stroke volumes at the same heart rate and varying heart rates at the same stroke volume. Systolic shear stress magnitude was found to be much higher than diastolic shear stress magnitude due to the stronger flow in the sinuses during systole, reaching up to 20 dyn/cm² at mid-systole. Upon increasing stroke volume, fluid shear stresses increased due to stronger sinus fluid motion. Upon increasing heart rate, fluid shear stresses decreased due to reduced systolic duration that restricted the formation of strong sinus flow. Significant changes in the shear stress waveform were observed at 90 beats/min, most likely due to altered leaflet dynamics at this higher heart rate. Overall, this study represents the most well-resolved shear stress measurements to date across a range of conditions on the aortic side of the AV. The data presented can be used for further investigation to understand AV biological response to shear stresses.     

Effects of aortic irregularities on blood flow

Anatomic aortic anomalies are seen in many medical conditions and are known to cause disturbances in blood flow. Turner syndrome (TS) is a genetic disorder occurring only in females where cardiovascular anomalies, particularly of the aorta, are frequently encountered. In this study, numerical simulations are applied to investigate the flow characteristics in four TS patient- related aortic arches (a normal geometry, dilatation, coarctation and elongation of the transverse aorta). The Quemada viscosity model was applied to account for the non-Newtonian behavior of blood. The blood is treated as a mixture consisting of water and red blood cells (RBC) where the RBCs are modeled as a convected scalar. The results show clear geometry effects where the flow structures and RBC distribution are significantly different between the aortas. Transitional flow is observed as a jet is formed due to a constriction in the descending aorta for the coarctation case. RBC dilution is found to vary between the aortas, influencing the WSS. Moreover, the local variations in RBC volume fraction may induce large viscosity variations, stressing the importance of accounting for the non-Newtonian effects.     

Echocardiographically documented acute aortic insufficiency induced by Amplatz left guide catheter

This paper examines a case of sudden systolic pressure fall, tachycardia, low pulse pressure, and high pulmonary artery wedge pressure due to acute aortic insufficiency which was induced by an Amplatz left (AL-1) guide catheter used for better guide support during percutaneous transluminal coronary angioplasty of the right coronary artery. AL guide catheters can cause acute aortic insufficiency, of which practitioners should be aware when sudden hemodynamic collapse occurs.