Remodelling of the left anterior descending artery in a porcine model of supravalvular aortic stenosis

Changes of thoracic duct flow and morphology in an animal model of elevated central venous pressure

Objective: Investigation of lymph fluid dynamics in thoracic duct during central venous pressure elevation.

Background: Lymphatic flow is affected by elevated central venous pressure (CVP) in congestive heart failure. The changes of thoracic duct (TD) lymph flow have not been studied chronically in the setting of elevated CVP. This study is to investigate fluid dynamics and remodeling of the TD in the elevated CVP animal model.

Methods: A flow probe was implanted on the swine TD (n = 6) and tricuspid regurgitation (TR) was created by cutting tricuspid chordae percutaneously. Six swine were used as control group animals. The TD flow was measured for 2 weeks (baseline) before TR and 4 weeks postop-TR surgery. Arterial pressure and CVP were measured. The pressure and flow in the TD were measured percutaneously. Histological and morphological analyses were performed.

Results: TR resulted in an increase in CVP from 4.2 ± 2.6 to 10.1 ± 4.3 mmHg (p < 0.05). The lymph flow in the TD increased from 0.78 ± 1.06 before TR to 8.8 ± 4.8 ml/min (p < 0.05) 2 days post-TR and remained plateau for 4 weeks, i.e., the TD flow remained approximately 8–11 fold its baseline. Compared to the 8.1 ± 3.2 mmHg control group, the TD average pressures at the lymphovenous junction increased to 14.6 ± 5.7 mmHg in the TR group (p < 0.05). The TD diameter and wall thickness increased from 3.35 ± 0.37 mm and 0.06 ± 0.01 mm in control to 4.32 ± 0.57 mm and 0.26 ± 0.02 mm (p < 0.05) in the TR group, respectively.

Conclusion: The elevated CVP results in a significant increase in TD flow and pressure which causes the TD’s outward remodeling and thickening. Our study implicates that the outward remodeling may result in the TD valve incompetence due to failure coaptation of leaflets.

Epigenetic regulators of the revascularization response to chronic arterial occlusion

Peripheral arterial disease (PAD) is the leading cause of lower limb amputation and estimated to affect over 202 million people worldwide. PAD is caused by atherosclerotic lesions that occlude large arteries in the lower limbs, leading to insufficient blood perfusion of distal tissues. Given the severity of this clinical problem, there has been long-standing interest in both understanding how chronic arterial occlusions affect muscle tissue and vasculature and identifying therapeutic approaches capable of restoring tissue composition and vascular function to a healthy state. To date, the most widely utilized animal model for performing such studies has been the ischaemic mouse hindlimb. Despite not being a model of PAD per se, the ischaemic hindlimb model does recapitulate several key aspects of PAD. Further, it has served as a valuable platform upon which we have built much of our understanding of how chronic arterial occlusions affect muscle tissue composition, muscle regeneration and angiogenesis, and collateral arteriogenesis. Recently, there has been a global surge in research aimed at understanding how gene expression is regulated by epigenetic factors (i.e. non-coding RNAs, histone post-translational modifications, and DNA methylation). Thus, perhaps not unexpectedly, many recent studies have identified essential roles for epigenetic factors in regulating key responses to chronic arterial occlusion(s). In this review, we summarize the mechanisms of action of these epigenetic regulators and highlight several recent studies investigating the role of said regulators in the context of hindlimb ischaemia. In addition, we focus on how these recent advances in our understanding of the role of epigenetics in regulating responses to chronic arterial occlusion(s) can inform future therapeutic applications to promote revascularization and perfusion recovery in the setting of PAD.

Pressure overload changes mesenteric afferent nerve responses in a stress-dependent way in a fasting rat model

It is well known that overload changes the mechanical properties of biological tissues and fasting changes the responsiveness of intestinal afferents. This study aimed to characterize the effect of overload on mechanosensitivity in mesenteric afferent nerves in normal and fasted Sprague-Dawley rats. Food was restricted for 7 days in the Fasting group. Jejunal whole afferent nerve firing was recorded during three distensions, i.e., ramp distension to 80 cmH₂O luminal pressure (D1), sustained distension to 120 cmH₂O for 2 min (D2), and again to 80 cmH₂O (D3). Multiunit afferent recordings were separated into low-threshold (LT) and wide-dynamic-range (WDR) single-unit activity for D1 and D3. Intestinal deformation (strain), distension load (stress), and firing frequency of mesenteric afferent nerve bundles [spike rate increase ratio (SRIR)] were compared at 20 cmH₂O and 40 cmH₂O and maximum pressure levels among distensions and groups. SRIR and stress changes showed the same pattern in all distensions. The SRIR and stress were larger in the Fasting group compared to the Control group (P < 0.01). SRIR was lower in D3 compared to D1 in controls (P < 0.05) and fasting rats (P < 0.01). Total single units and LT were significantly lower in Fasting group than in Controls at D3. LT was significantly higher in D3 than in D1 in Controls. Furthermore, correlation was found between SRIR with stress (R = 0.653, P < 0.001). In conclusion, overload decreased afferent mechanosensitivity in a stress-dependent way and was most pronounced in fasting rats. Fasting shifts LT to WDR and high pressure shifts WDR to LT in response to mechanical stimulation.

Hepatic Hemangiomas Alter Morphometry and Impair Hemodynamics of the Abdominal Aorta and Primary Branches From Computer Simulations

Background: The formation of hepatic hemangiomas (HH) is associated with VEGF and IL-7 that alter conduit arteries and small arterioles. To our knowledge, there are no studies to investigate the effects of HH on the hemodynamics in conduit arteries. The aim of the study is to perform morphometric and hemodynamic analysis in abdominal conduit arteries and bifurcations of HH patients and controls.

Methods: Based on morphometry reconstructed from CT images, geometrical models were meshed with prismatic elements for the near wall region and tetrahedral and hexahedral elements for the core region. Simulations were performed for computation of the non-Newtonian blood flow using the Carreau-Yasuda model, based on which multiple hemodynamic parameters were determined.

Results: There was an increase of the lumen size, diameter ratio, and curvature in the abdominal arterial tree of HH patients as compared with controls. This significantly increased the surface area ratio of low time-averaged wall shear stress (i.e., SAR-TAWSS =Surface  areaTAWSS≤4 dynes·cm−2Total  surface  area× 100%) (24.1 ± 7.9 vs. 5 ± 6%, 11.6 ± 12.8 vs. < 0.1%, and 44.5 ± 9.2 vs. 21 ± 24% at hepatic bifurcations, common hepatic arteries, and abdominal aortas, respectively, between HH and control patients).

Conclusions: Morphometric changes caused by HH significantly deteriorated the hemodynamic environment in abdominal conduit arteries and bifurcations, which could be an important risk factor for the incidence and progression of vascular diseases.

Passive and Active Triaxial Wall Mechanics in a Two-Layer Model of Porcine Coronary Artery

Triaxial active and passive mechanical properties of coronary arteries are needed for understanding arterial mechanics in health and disease. The aim of the study was to quantify both active and passive strain energy functions in circumferential, axial and radial directions based on the experimental measurement. Moreover, a two-layer computational model was used to determine the transmural distribution of stresses and strains across the vessel wall. The first Piola-Kirchhoff stresses in the three normal directions had the approximate relationship as:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,{T}_{\theta \theta }\cong 2{T}_{zz}\cong 5|{T}_{rr}|$$\end{document}Tθθ≅2Tzz≅5|Trr|. The two-layer model showed that circumferential Cauchy stresses increased significantly from the intima layer to the interface between media and adventitia layers (from ~80 to 160 kPa), dropped abruptly at the interface (from ~160 to <5 kPa), and increased slightly towards the outer boundary of the adventitia layer. In contrast, absolute values of radial Cauchy stress decreased continuously from the inner to outer boundaries of the vessel wall (from ~11 kPa to zero). Smooth muscle cell contraction significantly increased the ratio of radial to circumferential Cauchy stresses at the intima-media layer, which had the highest values at the intima layer.

Molecular mechanisms of inherited thoracic aortic disease - from gene variant to surgical aneurysm

Aortic dissection is a catastrophic event that has a high mortality rate. Thoracic aortic aneurysms are the clinically silent precursor that confers an increased risk of acute aortic dissection. There are several gene mutations that have been identified in key structural and regulatory proteins within the aortic wall that predispose to thoracic aneurysm formation. The most common and well characterised of these is the FBN1 gene mutation that is known to cause Marfan syndrome. Others less well-known mutations include TGF-β1 and TGF-β2 receptor mutations that cause Loeys-Dietz syndrome, Col3A1 mutations causing Ehlers-Danlos Type 4 syndrome and Smad3 and-4, ACTA2 and MYHII mutations that cause familial thoracic aortic aneurysm and dissection. Despite the variation in the proteins affected by these genetic mutations, there is a unifying pathological end point of medial degeneration within the wall of the aorta characterised by vascular smooth muscle cell loss, fragmentation and loss of elastic fibers, and accumulation of proteoglycans and glycosaminoglycans within vascular smooth muscle cell-depleted areas of the aortic media. Our understanding of these mutations and their post-translational effects has led to a greater understanding of the pathophysiology that underlies thoracic aortic aneurysm formation. Despite this, there are still many unanswered questions regarding the molecular mechanisms. Further elucidation of the signalling pathways will help us identify targets that may be suitable modifiers to enhance treatment of this often fatal condition.

Two-layer model of coronary artery vasoactivity

Since vascular tone is regulated by smooth muscle cells in the media layer, a multilayer mechanical model is required for blood vessels. Here, we performed biaxial mechanical tests in the intima-media layer of right coronary artery to determine the passive and active properties in conjunction with the passive properties of adventitia for a full vessel wall model. A two-layer (intima-media and adventitia) model was developed to determine the transmural stress and stretch across the vessel wall. The mean ± SE values of the outer diameters of intima-media layers at transmural pressure of 60 mmHg in active state were 3.17 ± 0.16 and 3.07 ± 0.18 mm at axial stretch ratio of 1.2 and 1.3, respectively, which were significantly smaller than those in passive state (i.e., 3.62 ± 0.19 and 3.49 ± 0.22 mm, respectively, P < 0.05). The inner and outer diameters in no-load state of intima-media layers were 1.17 ± 0.09 and 2.08 ± 0.09 mm, respectively. The opening angles in zero-stress state had values of 159 ± 21° for intima-media layers and 98 ± 15° for adventitia layers, which suggests a residual strain between the two layers. There were slightly decreased active circumferential stresses (<10%), but significantly decreased active axial stresses (>25%) in the intima-media layer compared with those in the intact vessel. This suggests that the adventitia layer affects vascular contraction. The two-layer analysis showed that the intima-media layer bears the majority of circumferential tensions, in contrast to the adventitia layer, while contraction results in decreased stress and stretch in both layers.

Compensatory remodeling of coronary microvasculature maintains shear stress in porcine left-ventricular hypertrophy

BACKGROUND

Hypertension-induced left-ventricular hypertrophy (LVH) is generally accompanied with coronary neovascularization. The extent of vascular growth or rarefaction depends on many factors (e.g. age, duration of hypertension, degree of hypertrophy). Here, we hypothesize that there is a compensatory vascular growth that maintains uniform wall shear stress (WSS) in perfusion arterioles (diameters of 8-60 μm) in LVH of young porcine.

METHOD

To test this hypothesis, we investigated LVH in young porcine after 5 weeks of supravalvular aortic stenosis (3 months of age). The morphometry (diameters, lengths, number and connectivity of vessels) of the entire left circumflex (LCx) arterial tree was determined and a hemodynamic network analysis was used to calculate the distribution of pressure, flow and WSS throughout the tree in the control and LVH groups.

RESULTS

It was found that the number of vessels and the weight of left ventricle (LV) in hypertrophy increased 1.5 and 1.2 times, respectively, and the length of the LCx main trunk increased by 3 cm (36% increase), as compared with those in control group. There were similar myocardial blood flows of 0.87 ± 0.24 and 0.94 ± 0.38 ml/min per g in control and LVH hearts, respectively. The compensatory remodeling in early LVH restores WSS in the smaller perfusion arterioles, but not in the larger epicardial branches.

CONCLUSION

The present findings quantify the structural and functional remodeling in the entire LCx arterial tree in response to LVH, which reflect heterogeneity in vascular morphometry and hemodynamics from small to large vessels. These conclusions enhance our understanding of compensatory vascular remodeling in LVH of pediatric heart.

Arterial pulse wave dynamics after percutaneous aortic valve replacement: fall in coronary diastolic suction with increasing heart rate as a basis for angina symptoms in aortic stenosis

BACKGROUND

Aortic stenosis causes angina despite unobstructed arteries. Measurement of conventional coronary hemodynamic parameters in patients undergoing valvular surgery has failed to explain these symptoms. With the advent of percutaneous aortic valve replacement (PAVR) and developments in coronary pulse wave analysis, it is now possible to instantaneously abolish the valvular stenosis and to measure the resulting changes in waves that direct coronary flow.

METHODS AND RESULTS

Intracoronary pressure and flow velocity were measured immediately before and after PAVR in 11 patients with unobstructed coronary arteries. Using coronary pulse wave analysis, we calculated the intracoronary diastolic suction wave (the principal accelerator of coronary blood flow). To test physiological reserve to increased myocardial demand, we measured at resting heart rate and during pacing at 90 and 120 bpm. Before PAVR, the basal myocardial suction wave intensity was 1.9±0.3×10(-5) W · m(-2) · s(-2), and this increased in magnitude with increasing severity of aortic stenosis (r=0.59, P=0.05). This wave decreased markedly with increasing heart rate (β coefficient=-0.16×10(-4) W · m(-2) · s(-2); P<0.001). After PAVR, despite a fall in basal suction wave (1.9±0.3 versus 1.1±0.1×10(-5) W · m(-2) · s(-2); P=0.02), there was an immediate improvement in coronary physiological reserve with increasing heart rate (β coefficient=0.9×10(-3) W · m(-2) · s(-2); P=0.014).

CONCLUSIONS

In aortic stenosis, the coronary physiological reserve is impaired. Instead of increasing when heart rate rises, the coronary diastolic suction wave decreases. Immediately after PAVR, physiological reserve returns to a normal positive pattern. This may explain how aortic stenosis can induce anginal symptoms and their prompt relief after PAVR. Clinical Trial Registration- URL: http://www.clinicaltrials.gov. Unique identifier: NCT01118442.

Subcoronary versus supracoronary aortic stenosis. An experimental evaluation

Background

Valvular aortic stenosis is the most common cause of left ventricular hypertrophy due to gradually increasing pressure work. As the stenosis develop the left ventricular hypertrophy may lead to congestive heart failure, increased risk of perioperative complications and also increased risk of sudden death. A functional porcine model imitating the pathophysiological nature of valvular aortic stenosis is very much sought after in order to study the geometrical and pathophysiological changes of the left ventricle, timing of surgery and also pharmacological therapy in this patient group.

Earlier we developed a porcine model for aortic stenosis based on supracoronary aortic banding, this model may not completely imitate the pathophysiological changes that occurs when valvular aortic stenosis is present including the coronary blood flow. It would therefore be desirable to optimize this model according to the localization of the stenosis.

Methods

In 20 kg pigs subcoronary (n = 8), supracoronary aortic banding (n = 8) or sham operation (n = 4) was preformed via a left lateral thoracotomy. The primary endpoint was left ventricular wall thickness; secondary endpoints were heart/body weight ratio and the systolic/diastolic blood flow ratio in the left anterior descending coronary. Statistical evaluation by oneway anova and unpaired t-test.

Results

Sub- and supracoronary banding induce an equal degree of left ventricular hypertrophy compared with the control group. The coronary blood flow ratio was slightly but not significantly higher in the supracoronary group (ratio = 0.45) compared with the two other groups (subcoronary ratio = 0.36, control ratio = 0.34).

Conclusions

A human pathophysiologically compatible porcine model for valvular aortic stenosis was developed by performing subcoronary aortic banding. Sub- and supracoronary aortic banding induce an equal degree of left ventricular hypertrophy. This model may be valid for experimental investigations of aortic valve stenosis but studies of left ventricular hypertrophy can be studied equally well by graduated constriction of the ascending aorta.

A model for left ventricular hypertrophy enabling non-invasive assessment of cardiac function

OBJECTIVE

To develop a porcine model for Left Ventricular Hypertrophy (LVH) in which cardiac performance could be quantified non-invasively by Doppler ultrasound.

DESIGN

Sixteen 5 kg piglets were divided into two groups. In the first group (n=12) we performed an aortic banding and in the second group (n=4) a sham-operation. Endpoints were echo-assessed left ventricular midseptal and free-wall thickness, heart/body-weight ratio and cardiac myocyte diameter.

RESULTS

Free-wall thickness: 0.77+/-0.013 cm in the intervention group and 0.60+/-0.006 cm in the control group (p=0.015). Midseptal thickness: 0.79+/-0.015 cm in the intervention group and 0.58+/-0.010 cm in the control group (p=0.012). Heart/body-weight ratio: 7.73+/-0.970 in the intervention group and 6.23+/-0.430 in the control group (p=0.003). Cardiac myocyte diameter: 19.6+/-4.9 microm in the intervention group and 11.0+/-1.9 microm in the control group (p=0.000).

CONCLUSION

A chronic porcine model for LVH has been established in which Doppler ultrasound can be used to quantify cardiac function non-invasively.

Wall thickness of coronary vessels varies transmurally in the LV but not the RV: implications for local stress distribution

Since the right and left ventricles (RV and LV) function under different loading conditions, it is not surprising that they differ in their mechanics (intramyocardial pressure), structure, and metabolism; such differences may also contribute to differences in the coronary vessel wall. Our hypothesis is that intima-media thickness (IMT), IMT-to-radius (IMT-to-R) ratio, and vessel wall stress vary transmurally in the LV, much more than in the RV. Five normal Yorkshire swine were used in this study. The major coronary arteries were cannulated through the aorta and perfusion fixed with 6.25% glutaraldehyde and casted with a catalyzed silicone-elastomer solution. Arterial and venous vessels were obtained from different transmural locations of the RV and LV, processed for histological analysis, and measured with an imaging software. A larger transmural gradient was found for IMT, IMT-to-R ratio, and diastolic circumferential stress in vessels from the LV than the nearly zero transmural slope in the RV. The IMT of arterial vessels in the LV showed a slope of 0.7 +/- 0.5 compared with 0.3 +/- 0.3 of arterial vessels in the RV (P <or= 0.05). The slope for venous vessels in the LV was 0.14 +/- 0.14 vs. 0.06 +/- 0.05 in the RV. The present data reflect the local structure-function relation, where the significant gradient in intramyocardial pressure in the LV is associated with a significant gradient of IMT and IMT-to-R ratio, unlike the RV. This has important implications for local adaptation of transmural loading on the vessel wall and vascular remodeling when the loading is perturbed in cardiac hypertrophy or heart failure.

Right coronary artery becomes stiffer with increase in elastin and collagen in right ventricular hypertrophy

Changes in blood flow influence the structure, function, mechanical properties, and remodeling of arteries. The objective of the present study was to investigate the role of increased blood flow on the biaxial incremental elastic moduli of the porcine right coronary artery (RCA) and to determine the microstructural basis for the changes in moduli. We hypothesized that an increase in RCA flow will lead to increased stiffness in conjunction with remodeling of elastin and collagen in the vessel wall. The control and experimental groups consisted of five RCA vessels each. The RCA of the experimental group was exposed to 4 wk of flow-overload in right ventricular hypertrophy induced by pulmonary artery banding. Stress-strain relationships were determined and the incremental elastic moduli were derived in the circumferential, axial, and cross directions. The results show a significant increase in the elastic moduli in the circumferential (262.7 +/- 15.7 vs. 120.2 +/- 12.4 kPa; P < 0.001), axial (177.8 +/- 25.5 vs. 100.3 +/- 11.9 kPa; P = 0.025), and cross directions (104.8 +/- 8.2 vs. 68.2 +/- 8.6 kPa; P = 0.016) of the experimental RCA compared with controls. Multiphoton microscopy was used to assess the changes in elastin and collagen content in the media and adventitia of the vessel wall. We found a significant increase in elastin and collagen area fraction particularly in the adventitial layer. These data suggest stiffening of the vessel wall as a result of increased elastin and more predominantly collagen.

Remodeling of conduit arteries in hypertension and flow-overload obeys a minimum energy principle

Arterial remodeling is an important process in physiology and pathophysiology. Based on an energy minimization method, Murray's law predicts the optimal inner radius. Application of Darcy's law in the wall results in an optimal outer radius. The average wall stress is computed by the Laplace's law. Using these formulas, a large porcine coronary artery in hypertension is studied. The results reveal how wall thickness and average circumferential stress change after increasing blood pressure and volume flow rate. The theoretical predictions are in good qualitative agreement with experimental observations. The advantage and limitation of the current approach are discussed.

A Novel Time-Varying Poly Lactic-Co Glycolic Acid External Sheath for Vein Grafts Designed under Physiological Loading

Changes in dimensional and mechanical properties of degradable sheaths in poly lactic-co glycolic acid (PLGA) have been researched extensively. Composite PLGA having variable resorption rates in multiple layers under physiological loading has not been reported. Our novel design of a PLGA sheath is composed of 3 layers with different degradation rates (i.e., the innermost layer degrades the fastest, followed by the middle, while the outer layer degrades the slowest). In the presence of physiological luminal pressure, diameter is greater, thickness is less, resorption rate is greater, pore size is greater, and incremental modulus is greater than in nonpressurized sheaths. Furthermore, the ratio of the pore size to the sheath radius affects the dimensional changes of the sheath in the radial direction. In addition to changing the pore size-to-sheath radius ratio, the dimensional changes can be manipulated by choosing different glycolic and lactic acid ratios for the different layers. The application of this novel PLGA design for gradual arterialization of vein grafts is contemplated.

Effects of myocardial constraint on the passive mechanical behaviors of the coronary vessel wall

The large epicardial coronary arteries and veins span the surface of the heart and gradually penetrate into the myocardium. It has recently been shown that remodeling of the epicardial veins in response to pressure overload strongly depends on the degree of myocardial support. The nontethered regions of the vessel wall show significant intimal hyperplasia compared with the tethered regions. Our hypothesis is that such circumferentially nonuniform structural adaptation in the vessel wall is due to nonuniform wall stress and strain. Transmural stress and strain are significantly influenced by the support of the surrounding myocardial tissue, which significantly limits distension of the vessel. In this finite-element study, we modeled the nonuniform support by embedding the left anterior descending artery into the myocardium to different depths and analyzed deformation and strain in the vessel wall. Circumferential wall strain was much higher in the untethered than tethered region at physiological pressure. On the basis of the hypothesis that elevated wall strain is the stimulus for remodeling, the simulation results suggest that large epicardial coronary vessels have a greater tendency to become thicker in the absence of myocardial constraint. This study provides a mechanical basis for understanding the local growth and remodeling of vessels subjected to various degrees of surrounding tissue.

Capillary Perfusion and Wall Shear Stress Are Restored in the Coronary Circulation of Hypertrophic Right Ventricle

It has been shown that right ventricle (RV) hypertrophy involves significant compensatory vascular growth and remodeling. The objective of the present study was to determine the functional implications of the vascular growth and remodeling through a full flow analysis of arterial tree down to first capillary segments. A computer reconstruction of RV branches including the proximal right coronary artery to the posterior descending artery was established based on measured morphometric data in arrested, vasodilated porcine heart. The flows were computed throughout the reconstructed trees based on conservation of mass and momentum and appropriate pressure boundary conditions. It was found that the flow rate was significantly increased in large epicardial coronary arteries in hypertrophic as compared with control hearts but normalized in the intramyocardial coronary arteries and smaller vessels in RV hypertrophy primarily because of the significant increase in number of arterioles. Furthermore, the wall shear stress was restored to nearly homeostatic levels throughout most of the vasculature after 5 weeks of RV hypertrophy. The compensatory remodeling in RV hypertrophy functionally restores the perfusion at the arteriolar and capillary level and wall shear stress in most of larger vessels. This is the first full analysis of coronary arterial tree, with millions of vessels, in cardiac hypertrophy that reveals the compensatory adaptation of structure to function.

Biomechanics of the cardiovascular system: the aorta as an illustratory example

Biomechanics relates the function of a physiological system to its structure. The objective of biomechanics is to deduce the function of a system from its geometry, material properties and boundary conditions based on the balance laws of mechanics (e.g. conservation of mass, momentum and energy). In the present review, we shall outline the general approach of biomechanics. As this is an enormously broad field, we shall consider a detailed biomechanical analysis of the aorta as an illustration. Specifically, we will consider the geometry and material properties of the aorta in conjunction with appropriate boundary conditions to formulate and solve several well-posed boundary value problems. Among other issues, we shall consider the effect of longitudinal pre-stretch and surrounding tissue on the mechanical status of the vessel wall. The solutions of the boundary value problems predict the presence of mechanical homeostasis in the vessel wall. The implications of mechanical homeostasis on growth, remodelling and postnatal development of the aorta are considered.

BIOMECHANICAL CONSIDERATIONS IN THE DESIGN OF GRAFT: THE HOMEOSTASIS HYPOTHESIS

Since its inception in the 1960s, coronary artery bypass graft (CABG) evolved as one of the most common, best documented, and most effective of all major surgical treatments for ischemic heart disease. Despite its widespread use, however, the outcome is not always completely satisfactory. The objective of this review is to highlight the physical determinants of biomechanical design of CABG so that future procedures would have prolonged patency and better outcome. Our central axiom postulates the existence of a mechanical homeostatic state of the blood vessel, i.e., the variation in vessel wall stresses and strains are relatively small under physiological conditions. Any perturbation of mechanical homeostasis leads to growth and remodeling. In this sense, stenosis and failure of a graft may be viewed as an adaptation process gone awry. We outline the principles of engineering design and discuss the biofluid and biosolid mechanics principles that may have the greatest bearing on mechanical homeostasis and the long-term outcome of CABG.

Nonuniformity of axial and circumferential remodeling of large coronary veins in response to ligation

The pressure-induced remodeling of coronary veins is important in coronary venous retroperfusion. Our hypothesis is that the response of the large coronary veins to pressure overload will depend on the degree of myocardial support. Eleven normal Yorkshire swine from either sex, weighing 31–39 kg, were studied. Five pigs underwent ligation of the left anterior descending (LAD) vein, and six served as sham-operated controls. The ligation of the coronary vein caused an increase in pressure intermediate to arterial and venous values. After 2 wk of ligation, the animals were euthanized and the coronary vessels were perfusion-fixed with glutaraldehyde. The LAD vein was sectioned, and detailed morphometric measurements were made along its length from the point of ligation near the base down to the apex of the heart. The structural remodeling of the vein was circumferentially nonuniform because the vein is partially embedded in the myocardium; it was also axially nonuniform because it is tethered to the myocardium to different degrees along its axial length. The wall area was significantly larger in the experimental group, whereas luminal area in the proximal LAD vein was significantly smaller in the same group compared with sham-operated controls. The wall thickness-to-radius ratio was also significantly larger in the experimental group in proportion to the increase in pressure. The major conclusion of this study is that the response of the vein depends on the local wall stress, which is, in part, determined by the surrounding tissue. Furthermore, the geometric remodeling of the coronary vein restores the circumferential stress to the homeostatic value.

Synchrony between circular and longitudinal muscle contractions during peristalsis in normal subjects

The current understanding is that longitudinal muscle contraction begins before and outlasts circular muscle contraction during esophageal peristalsis in normal subjects. The goal of our study was to reassess the relationship between the contractility of two muscle layers using novel ways to look at the muscle contraction. We studied normal subjects using synchronized high-frequency ultrasound imaging and manometry. Swallow-induced peristalsis was recorded at 5 and 10 cm above the lower esophageal sphincter (LES). Ultrasound (US) images were analyzed for muscle cross-sectional area (CSA) and circularity index of the esophagus during various phases of esophageal contraction. A plot of the M mode US image, muscle CSA, and esophageal circularity index was developed to assess the temporal correlation between various parameters. The muscle CSA wave began before and lasted longer than the contraction pressure wave at both 5 and 10 cm above the LES. M mode US images revealed that the onset of muscle CSA wave was temporally aligned with the onset of lumen collapse. The peak muscle CSA occurred in close proximity with the peak pressure wave. The esophagus started to become more circular (decrease in circularity index) with the onset of the muscle CSA wave. The circularity index and muscle CSA returned to the baseline at approximately the same time. In conclusion, the onset of lumen collapse and return of circularity index of the esophagus are likely to be the true markers of the onset and end of circular muscle contraction. Circular and longitudinal muscle layers of the esophagus contract in a precise synchronous fashion during peristalsis in normal subjects.

Scaling laws of vascular trees: of form and function

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.

Functional hierarchy of coronary circulation: direct evidence of a structure-function relation

The heart muscle is nourished by a complex system of blood vessels that make up the coronary circulation. Here we show that the design of the coronary circulation has a functional hierarchy. A full anatomic model of the coronary arterial tree, containing millions of blood vessels down to the capillary vessels, was simulated based on previously measured porcine morphometric data. A network analysis of blood flow through every vessel segment was carried out based on the laws of fluid mechanics and appropriate boundary conditions. Our results show an abrupt change in cross-sectional area that demarcates the transition from epicardial (EPCA) to intramyocardial (IMCA) coronary arteries. Furthermore, a similar pattern of blood flow was observed with a corresponding transition from EPCA to IMCA. These results suggest functional differences between the two types of vessels. An additional abrupt change occurs in the IMCA in relation to flow velocity. The velocity is fairly uniform proximal to these vessels but drops significantly distal to those vessels toward the capillary branches. This finding suggests functional differences between large and small IMCA. Collectively, these observations suggest a novel functional hierarchy of the coronary vascular tree and provide direct evidence of a structure-function relation.

Oesophageal wall stress and muscle hypertrophy in high amplitude oesophageal contractions

Excessive wall stress is a known stimulus for muscle growth. We recently reported a thickened muscularis propria in patients with high amplitude oesophageal contractions (HAEC). The goal of this study was to determine oesophageal wall stress in normal subjects and patients with HAEC. A manometry catheter equipped with a high frequency ultrasound (US) transducer was used to record pressure and US images simultaneously in 10 healthy subjects and 11 patients with HAEC. Recordings were obtained at 2 and 10 cm above the lower oesophageal sphincter during water swallows. The changes in circumferential wall stress during oesophageal contraction in both groups are relatively small because of an increase in the wall thickness-to-radius ratio during contraction. Patients show a greater muscle thickness than normal subjects at rest and at the peak of contraction. The wall stress in patients is elevated at the 2 cm but not at the 10-cm level as compared to normal subjects. Wall strain is not different between the two groups. Increase in wall thickness during oesophageal contraction maintains low wall stress. A greater wall stress in patients with HAEC may be a stimulus for the increased wall thickness.

Estrogen modulates the mechanical homeostasis of mouse arterial vessels through nitric oxide

We have recently shown that estrogen causes vessel dilation through receptor-mediated stimulation of nitric oxide (NO) production. Here, we hypothesize that estrogen modulates the mechanical homeostasis in the blood vessel wall through NO production. The mechanical properties of female ovariectomized (ovx) mice, female mice lacking the gene for endothelial NO synthase (eNOS(-/-)), and control female and male mice were studied to test the hypothesis. The femoral and carotid arteries and aorta were cannulated in situ and mechanically distended. The stress, strain, elastic modulus, and wall thickness of vessels in ovx and eNOS(-/-) mice, as well as intact female and male mice, were determined. Western blot and immunohistochemistry were used to assess eNOS protein expression in the aorta. Moreover, NO by-products of the femoral and carotid artery were determined by measuring the levels of nitrite and nitrate. Our results show that ovariectomy and eNOS(-/-) significantly decrease the strain in all arteries. Furthermore, the eNOS protein was significantly reduced in ovx mice. Finally, the NO metabolites were significantly decreased both in ovx and eNOS(-/-) mice. We found statistically significant correlations between the structural (wall thickness), mechanical (stress, strain, and elastic modulus), and biochemical parameters (NO by-products). These novel results connect NO to the structural and mechanical properties of the vessel wall. Hence, the effect of endogenous estrogen on the arterial mechanical properties is mediated by the regulation of NO derived from eNOS.

Axial nonuniformity of geometric and mechanical properties of mouse aorta is increased during postnatal growth

The hemodynamic conditions of aorta are relatively uniform prenatally and become more heterogeneous postnatally. Our objective was to quantify the heterogeneity of geometry and mechanical properties during growth and development. To accomplish this objective, we obtained a systematic set of data on the geometry and mechanical properties along the length of mouse aorta during postnatal development. C57BL/6 mice of ages 1-33 days were studied. The ascending aorta was cannulated in situ and preconditioned with several cyclic changes in pressure. We investigated the axial variations of geometry (diameter and length) and mechanical properties (stress-stain relation, elastic modulus and compliance) of the mouse aorta from the aortic valve to the common iliac. Our results show that the arterial blood pressure of mice increased from approximately 30 to 80 mmHg during the first 2 wk of life. The stretch ratio, diameter, wall (intima-media) thickness, and total lumen volume of mouse aorta increased with age. The aorta was transformed from a cylindrical tube at birth to a tapered structure during growth. Furthermore, we found the mechanical properties were fairly uniform along the length of the aorta at birth and become more nonuniform with age. We conclude that the rapid change of blood pressure and blood flow after birth alter the geometric and mechanical properties differentially along the length of the aorta. Hence, the axial nonuniformity of the aorta increases as the organ becomes more specialized during growth and development.

Effect of surrounding tissue on vessel fluid and solid mechanics

There is no doubt that atherosclerosis is one of the most important health problems in the Western Societies. It is well accepted that atherosclerosis is associated with abnormal stress and strain conditions. A compelling observation is that the epicardial arteries develop atherosclerosis while the intramural arteries do not. Atherosclerotic changes involving the epicardial portion of the coronary artery stop where the artery penetrates the myocardium. The objective of the present study is to understand the fluid and solid mechanical differences between the two types of vessels. A finite element analysis was employed to investigate the effect of external tissue contraction on the characteristics of pulsatile blood flow and the vessel wall stress distribution. The sequential coupling of fluid-solid interaction (FSI) revealed that the changes of flow velocity and wall shear stress, in response to cyclical external loading, appear less important than the circumferential stress and strain reduction in the vessel wall under the proposed boundary conditions. These results have important implications since high stresses and strains can induce growth, remodeling, and atherosclerosis; and hence we speculate that a reduction of stress and strain may be atheroprotective. The importance of FSI in deformable vessels with pulsatile flow is discussed and the fluid and solid mechanics differences between epicardial and intramural vessels are highlighted.

Asynchrony between the circular and the longitudinal muscle contraction in patients with nutcracker esophagus

BACKGROUND & AIMS

The increases in intraluminal pressure and muscle cross-sectional area (CSA) during esophageal contraction are markers of circular and longitudinal muscle contractions. The goal of our study was to determine temporal synchrony between circular and longitudinal muscle contraction in healthy subjects and patients with nutcracker esophagus.

METHODS

Pressure and high-frequency intraluminal ultrasound (HFIUS) images were recorded simultaneously in healthy subjects and patients with nutcracker esophagus at 2 and 10 cm above the lower esophageal sphincter during wet swallow. HFIUS images were digitized and analyzed for the muscle CSA. The time interval (delta-t) between the peak muscle CSA and the peak pressure was determined.

RESULTS

In healthy subjects, a close temporal correlation existed between the peak contraction pressure and the peak muscle CSA with a maximum delta-t of 0.5 seconds at the 2- and 10-cm levels (0-0.5 seconds). On the other hand, the patient group had a median delta-t of 1.25 seconds (0.75-3.5 seconds) at the 2-cm level and 0.75 seconds (0-2.0 seconds) at the 10-cm level. Ninety-eight of 103 contractions in patients showed a delta-t >0.5 seconds. There was a significant correlation between delta-t and the amplitude of pressure wave, the duration of pressure wave, and the peak muscle CSA. The duration of pressure wave but not the duration of CSA wave was longer in patients with nutcracker esophagus as compared with healthy subjects.

CONCLUSIONS

Patients with nutcracker esophagus show temporal asynchrony between the contractions of circular and longitudinal muscle layers.

Novel method for measurement of medium size arterial lumen area with an impedance catheter: in vivo validation

There is no doubt that the transformation of a cardiac catheter into a conductance catheter that allows reliable and accurate assessment of lumen cross-sectional area (CSA) will provide a powerful diagnostic and treatment tool for the invasive cardiologist. The objective of this study was to develop a method based on the impedance catheter that allows accurate and reproducible measurements of CSA for medium size vessels (e.g., coronary, femoral, and carotid arteries). Two solutions of NaCl (0.5% and 1.5%) with known conductivities were injected directly into the lumen of the artery in eight swine. We showed that the CSA can be determined analytically from two Ohm's law-type algebraic equations that account for the parallel conductance of the current into the surrounding tissue. Excellent agreement was found between the conductance catheter with the proposed two-injection method and B-mode ultrasound (US). The root mean square error for the impedance measurements was 4.8% of the mean US diameter. The repeatability of the technique was assessed with duplicate measurements. The mean of the difference between the two measurements was nearly zero, and the repeatability coefficient was within 2.4% of the mean of the two measurements. The validated method was used to assess the degree of acute vasodilatation of the vessel in response to flow overload.

Transmural strain distribution in the blood vessel wall

The transmural distributions of stress and strain at the in vivo state have important implications for the physiology and pathology of the vessel wall. The uniform transmural strain hypothesis was proposed by Takamyzawa and Hayashi (Takamizawa K and Hayashi K. J Biomech 20: 7–17, 1987; Biorheology 25: 555–565, 1988) as describing the state of arteries in vivo. From this hypothesis, they derived the residual stress and strain at the no-load condition and the opening angle at the zero-stress state. However, the experimental evidence cited by Takamyzawa and Hayashi ( J Biomech 20: 7–17, 1987; and Biorheology 25: 555–565, 1988) to support this hypothesis was limited to arteries whose opening angles (θ) are <180°. It is well known, however, that θ > 180° do exist in the cardiovascular system. Our hypothesis is that the transmural strain distribution cannot be uniform when θ is >180°. We present both theoretical and experimental evidence for this hypothesis. Theoretically, we show that the circumferential stretch ratio cannot physically be uniform across the vessel wall when θ exceeds 180° and the deviation from uniformity will increase with an increase in θ beyond 180°. Experimentally, we present data on the transmural strain distribution in segments of the porcine aorta and coronary arterial tree. Our data validate the theoretical prediction that the outer strain will exceed the inner strain when θ > 180°. This is the converse of the gradient observed when the residual strain is not taken into account. Although the strain distribution may not be uniform when θ exceeds 180°, the uniformity of stress distribution is still possible because of the composite nature of the blood vessel wall, i.e., the intima-medial layer is stiffer than the adventitial layer. Hence, the larger strain at the adventitia can result in a smaller stress because the adventitia is softer at physiological loading.

Biaxial incremental homeostatic elastic moduli of coronary artery: two-layer model

The detailed mechanical properties of various layers of the coronary artery are important for understanding the function of the vessel. The present article is focused on the determination of the incremental modulus in different layers and directions in the neighborhood of the in vivo state. The incremental modulus can be defined for any material subjected to a large deformation if small perturbations in strain lead to small perturbations of stresses in a linear fashion. This analysis was applied to the porcine coronary artery, which was treated as a two-layered structure consisting of an inner intima-media layer and an outer adventitia layer. We adopted a theory based on small-perturbation experiments at homeostatic conditions for determination of incremental moduli in circumferential, axial, and cross directions in the two layers. The experiments were based on inflation and axial stretch. We demonstrate that under homeostatic conditions the incremental moduli are layer- and direction dependent. The incremental modulus is highest in the circumferential direction. Furthermore, in the circumferential direction, the media is stiffer than the whole wall, which is stiffer than the adventitia. In the axial direction, the adventitia is stiffer than the intact wall, which is stiffer than the media. Hence, the coronary artery must be treated as a composite, nonisotropic body. The data acquire physiological relevance in relation to coronary artery health and disease.

Distribution of stress and strain along the porcine aorta and coronary arterial tree

The existence of a homeostatic state of stresses and strains has been axiomatic in the cardiovascular system. The objective of this study was to determine the distribution of circumferential stress and strain along the aorta and throughout the coronary arterial tree to test this hypothesis. Silicone elastomer was perfused through the porcine aorta and coronary arterial tree to cast the arteries at physiological pressure. The loaded and zero-stress dimensions of the vessels were measured. The aorta (1.8 cm) and its secondary branches were considered down to 1.5 mm diameter. The left anterior descending artery (4.5 mm) and its branches down to 10 microm were also measured. The Cauchy mean circumferential stress and midwall stretch ratio were calculated. Our results show that the stretch ratio and Cauchy stress were lower in the thoracic than in the abdominal aorta and its secondary branches. The opening angle (theta) and midwall stretch ratio (lambda) showed a linear variation with order number (n) as follows: theta = 10.2n + 63.4 (R(2) = 0.989) and lambda = 4.47 x 10(-2)n + 1.1 (R(2) = 0.995). Finally, the stretch ratio and stress varied between 1.2 and 1.6 and between 10 and 150 kPa, respectively, along the aorta and left anterior descending arterial tree. The relative uniformity of strain (50% variation) from the proximal aorta to a 10-microm arteriole implies that the vascular system closely regulates the degree of deformation. This suggests a homeostasis of strain in the cardiovascular system, which has important implications for mechanotransduction and for vascular growth and remodeling.

Indicial response functions of growth and remodeling of common bile duct postobstruction

Biliary duct obstruction is an important clinical condition that stems from cholelithiasis, the neoplasm in the wall or, most commonly, gallbladder stones. The objective of this study is to understand the structural and mechanical remodeling of the common bile duct (CBD) postobstruction. Porcine CBD was ligated near the duodenum that increased the duct's pressure from 6.4 to 18.3 cmH(2)O in the first 12 h and to 30.7 cmH(2)O after 32 days. The remodeling process was studied after 3 h, 12 h, 2 days, 8 days, and 32 days (n = 5 in each group) after obstruction. One additional animal in each group was sham operated. At each scheduled time, the time course of change of morphometry (diameter, length, wall thickness, etc.) and mechanical properties (stress, strain, etc.) was documented. It was found that the diameter increased by about threefold and the wall thickness of the CBD doubled in the 32-day group compared with the sham group (P < 0.001). The stress and strain increased initially with increase in pressure but recovered to near the control values by day 32 due to the structural and mechanical adaptations. Hence, the net effect of the structural and mechanical remodeling is to restore the stress and strain to their homeostatic values. Furthermore, the strain recovers more rapidly and more completely than stress. Finally, the remodeling data were expressed mathematically in terms of indicial response functions (IRF), i.e., change of a particular feature of a CBD in response to a unit step change of the pressure. The IRF approach provides a quantitative description of the remodeling process in the CBD.

Variation of mechanical properties along the length of the aorta in C57bl/6 mice

The objective of the present study is to obtain a systematic set of data on the mechanical properties along the entire length of the mouse aorta. The ascending aorta of seven mice was cannulated near the aortic valve, and the aorta was preconditioned with several cyclic changes in pressure. The perfusion pressure was then increased in 30-mmHg increments from 0 to 150 mmHg. Cab-O-Sil, colloidal silica, was mixed into the perfusate to prevent flow through the microvessels and hence attain zero-flow distensions. Our results show that the residual circumferential strain leads to a uniformity of transmural strain of the aorta in the loaded state along the entire length of the aorta. This uniformity is attained in the range of 60–120 mmHg. At pressures <60 mmHg, the outer strain is greater than the inner strain, whereas at pressures >120 mmHg, the converse is true. Furthermore, we found that the circumferential and longitudinal stress-strain relationships are linear in the pressure range of 30–120 mmHg. Finally, the circumferential modulus is greatest (most rigid) near the diaphragm, and the majority of volume compliance (85%) is in the thoracic compared with the abdominal aorta. These findings are important for an understanding of the hemodynamics of the cardiovascular system of the normal mouse and will serve as a reference state for the study of various diseases in knock-in and knock-out models of this species.