The effect of collagenase on the critical buckling pressure of arteries

The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effects of collagen degradation on the mechanical stability of arteries are unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400 U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure of arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries.     

Effects of elastin degradation and surrounding matrix support on artery stability

Tortuous arteries are often associated with aging, hypertension, atherosclerosis, and degenerative vascular diseases, but the mechanisms are poorly understood. Our recent theoretical analysis suggested that mechanical instability (buckling) may lead to tortuous blood vessels. The objectives of this study were to determine the critical pressure of artery buckling and the effects of elastin degradation and surrounding matrix support on the mechanical stability of arteries. The mechanical properties and critical buckling pressures, at which arteries become unstable and deform into tortuous shapes, were determined for a group of five normal arteries using pressurized inflation and buckling tests. Another group of nine porcine arteries were treated with elastase (8 U/ml), and the mechanical stiffness and critical pressure were obtained before and after treatment. The effect of surrounding tissue support was simulated using a gelatin gel. The critical pressures of the five normal arteries were 9.52 kPa (SD 1.53) and 17.10 kPa (SD 5.11) at axial stretch ratios of 1.3 and 1.5, respectively, while model predicted critical pressures were 10.11 kPa (SD 3.12) and 17.86 kPa (SD 5.21), respectively. Elastase treatment significantly reduced the critical buckling pressure (P < 0.01). Arteries with surrounding matrix support buckled into multiple waves at a higher critical pressure. We concluded that artery buckling under luminal pressure can be predicted by a buckling equation. Elastin degradation weakens the arterial wall and reduces the critical pressure, which thus leads to tortuous vessels. These results shed light on the mechanisms of the development of tortuous vessels due to elastin deficiency.     

The Mechanical Buckling of Curved Arteries^*

Though tortuosity and kinking are often observed in various arteries and arterioles, little is known about the underlying mechanisms. This paper presents a biomechanical analysis of bent buckling in long arterial segments with a small initial curvature using a thick-walled elastic cylindrical arterial model. The critical buckling pressure was established as a function of wall stiffness, wall dimensions, and the axial tension (or axial stretch ratio). The effects of both wall dimensions and axial stretch ratio on the critical pressure, as well as the thin-walled approximation were discussed. The buckling equation sheds light on the biomechanical mechanism of artery tortuosity and provides guidance for the development of new techniques to treat and prevent artery tortuosity and kinking.     

A biomechanical model of artery buckling

The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using an elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young's modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (subphysiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that hypertension and aging are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

Artery buckling analysis using a four-fiber wall model

Artery bent buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery buckling behavior. To this end, the objectives of this study were to develop arterial buckling equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical buckling pressures than what the Fung model predicted. The buckling equation using the 4-fiber model captured the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies.     

Blood vessel buckling within soft surrounding tissue generates tortuosity

The stability of blood vessel under lumen pressure load is essential to the maintenance of normal arterial function. Previous mechanical models showed that blood vessels may buckle into a half sine wave but arteries and veins in vivo often demonstrate tortuous paths with multiple waves. The objective of this study was to analyze the buckling of blood vessels under lumen pressure with surrounding tissue support. Blood vessels were modeled as elastic cylindrical vessels within an elastic substrate. Buckling equations were established to determine the critical pressure and the wavelength. These equations and simulation results demonstrated that blood vessels do take higher order mode shapes when buckling inside an elastic substrate while they take the basal mode shape without the substrate. The wave number increases i.e. blood vessels take a higher mode shape, as the stiffness of the substrate increases. These results suggest that mechanical buckling is a possible mechanism for the development of tortuous blood vessels. The current model provides a powerful tool for further studying the tortuosity of arteries and veins.     

Age-related thermal stability and susceptibility to proteolysis of rat bone collagen.

The shrinkage temperature (Ts) and the pepsin-solubilizability of collagen fibrils in bone matrix obtained from decalcified femur diaphysis from 2-, 5-, 15- and 25-month-old rats were found to decrease with age. Digestion with human fibroblast collagenase dissolved less than half of the collagen, whereas sequential treatment by pepsin followed by collagenase resulted in its complete dissolution. This result shows that collagenase and a telopeptide-cleaving enzyme, when acting in an appropriate sequence, have a great potential for the degradation of bone collagen. The 'melting' profile of the pepsin-solubilized collagen showed a biphasic transition with transition peak at 35.9 degrees C and 40.8 degrees C. With increasing age an increasing proportion of the collagen 'melted' in the transition peak at 35.9 degrees C (pre-transition), and the 'melting' temperature (Tm) of the collagen decreased in parallel with Ts in relation to age. Both Ts and Tm decreased by 3 degrees C in the age span investigated. The age-related change in Ts could therefore be accounted for by the decrease in molecular stability. The collagenase-cleavage products of the bone collagen obtained by the sequential treatment with pepsin and collagenase showed only one peak transition (at 35.1 degrees C), and the Tm for the products was independent of age. The results indicate that the pre-transition for the pepsin-solubilized collagen is due to an age-related decrease in thermal stability may have implications for the mechanical strength and turnover of the bone collagen. In contrast with bone collagen, soft-tissue collagen showed neither the age-dependency of thermal stability nor the characteristic biphasic 'melting' profile.     

On the Onset of Cracks in Arteries¹

We present a theoretical approach to study the onset of failure localization into cracks in arterial wall. The arterial wall is a soft composite comprising hydrated ground matrix of proteoglycans reinforced by spatially dispersed elastin and collagen fibers. As any material, the arterial tissue cannot accumulate and dissipate strain energy beyond a critical value. This critical value is enforced in the constitutive theory via energy limiters. The limiters automatically bound reachable stresses and allow examining the mathematical condition of strong ellipticity. Loss of the strong ellipticity physically means inability of material to propagate superimposed waves. The waves cannot propagate because material failure localizes into cracks perpendicular to a possible wave direction. Thus, not only the onset of a crack can be analyzed but also its direction. We use the recently developed constitutive theories of the arterial wall including 8 and 16 structure tensors to account for the fiber dispersion. We enhance these theories with energy limiters. We examine the loss of strong ellipticity in uniaxial tension and pure shear in circumferential and axial directions of the arterial wall. We find that the vanishing longitudinal wave speed predicts the appearance of cracks in the direction perpendicular to tension. We also find that the vanishing transverse wave speed predicts the appearance of cracks in the the direction inclined (non-perpendicular) to tension. The latter result is counter-intuitive yet it is supported by recent experimental observations.     

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.     

Role of proteolysis and apoptosis in regression of pulmonary vascular remodeling

Remodeled pulmonary arteries return to normal structural conditions after the increase in pulmonary artery flow resistance is reversed. We studied whether proteolysis of extracellular matrix proteins and apoptosis occur during reversal of remodeling produced by chronic hypoxia in the rat. Main pulmonary arteries were removed at different times during a 10-day period of exposure to 10% O2 and 14 days after return to air. Content and rates of degradation of collagen and elastin as well as immunoreactive collagenase in tissue and isolated mast cells were measured. Immunoblots for collagenase and tissue inhibitor of metalloproteinases (TIMP) were performed. Apoptosis was assessed by cleavage of DNA and TUNEL assay. Excess collagen and elastin present at 10 days of hypoxia decreased to near normal levels after 3-5 days of air. Transient increases in collagenolytic and elastolytic enzyme activities accompanied the rapid decrease in matrix proteins. Mast cells containing collagenase accumulated in remodeled pulmonary arteries, and the active form of collagenase appeared at the time of peak proteolytic activity. TIMP increased during remodeling. Apoptosis was maximal 3 days after return to air. Our results suggest that activation of enzymes, which degrade matrix proteins, and apoptosis play a role in resolution of vascular remodeling.     

Proteolytic activity of first trimester human placenta: localization of interstitial collagenase in villous and extravillous trophoblast

Summary In human placentation, events of implantation and early blastocyst development are mediated by fetal trophoblastic cells which penetrate into the maternal endometrium and myometrium. Although highly regulated in its biological behavior, trophoblast simulates a malignant neoplasm by virtue of invading the uterine wall and uterine spiral arteries and by embolizing throughout the systemic circulation. This process is at least in part dependant on the regulated production of proteolytic enzymes to degrade extracellular matrix. The most abundant extracellular protein is connective tissue type (interstitial) collagen. The uterine remodeling during the establishment of the embryo requires collagenase which catalyzes the intial step in the breakdown of collagen. This study demonstrates the presence of interstitial collagenase in villous and extravillous trophoblast of first trimester placenta using immunocytochemical methods on light microscopic and ultrastructural levels. Intracytoplasmic staining for interstitial collagenase was present in cyto- and syncytiotrophoblast covering the chorionic villi as well as in extravillous intermediate trophoblast invading spiral arteries in the placental bed. Furthermore, outgrowth cultures of chorionic villi were studied with the immunogold method. Gold labelling was associated with the cell surface of trophoblastic cells as well as with fibrillary collagen like proteins of newly synthesized extracellular matrix. We speculate that interstitial collagenase plays a role in the degradation of uterine collagen within the developing human placenta.     

Nonlinear buckling of blood vessels: a theoretical study

Tortuosity and kinking often occur in arteries and veins but the underlying mechanisms are poorly understood. It has been suggested recently that long arteries may buckle and become tortuosity due to reduced axial tension or hypertensive pressure, but very few studies have been done to establish the biomechanical basis for artery buckling. Here we developed the arterial buckling equation using a nonlinear elastic thick-walled cylindrical model with residual stress. Our results demonstrated that arteries may buckle due to high blood pressure or low axial tension and that residual stress in the arteries increases the buckling pressure. These results are in general agreement with the previous linear elastic model. The buckling equation provides a useful tool for studying artery tortuosity and kinking.     

Twist buckling behavior of arteries

Arteries are often subjected to torsion due to body movement and surgical procedures. While it is essential that arteries remain stable and patent under twisting loads, the stability of arteries under torsion is poorly understood. The goal of this work was to experimentally investigate the buckling behavior of arteries under torsion and to determine the critical buckling torque, the critical buckling twist angle, and the buckling shape. Porcine common carotid arteries were slowly twisted in vitro until buckling occurred while subjected to a constant axial stretch ratio (1.1, 1.3, 1.5 (in vivo level) and 1.7) and lumen pressure (20, 40, 70 and 100 mmHg). Upon buckling, the arteries snapped to form a kink. For a group of six arteries, the axial stretch ratio significantly affected the critical buckling torque (\(p<0.002\)) and the critical buckling twist angle (\(p<0.001\)). Lumen pressure also significantly affected the critical buckling torque (\(p<0.001\)) but had no significant effect on the critical twist angle (\(p=0.067\)). Convex material constants for a Fung strain energy function were determined and fit well with the axial force, lumen pressure, and torque data measured pre-buckling. The material constants are valid for axial stretch ratios, lumen pressures, and rotation angles of 1.3–1.5, 20–100 mmHg, and 0–270\(^\circ \), respectively. The current study elucidates the buckling behavior of arteries under torsion and provides new insight into mechanical instability of blood vessels.     

Mechanical buckling of artery under pulsatile pressure

Tortuosity that often occurs in carotid and other arteries has been shown to be associated with high blood pressure, atherosclerosis, and other diseases. However the mechanisms of tortuosity development are not clear. Our previous studies have suggested that arteries buckling could be a possible mechanism for the initiation of tortuous shape but artery buckling under pulsatile flow condition has not been fully studied. The objectives of this study were to determine the artery critical buckling pressure under pulsatile pressure both experimentally and theoretically, and to elucidate the relationship of critical pressures under pulsatile flow, steady flow, and static pressure. We first tested the buckling pressures of porcine carotid arteries under these loading conditions, and then proposed a nonlinear elastic artery model to examine the buckling pressures under pulsatile pressure conditions. Experimental results showed that under pulsatile pressure arteries buckled when the peak pressures were approximately equal to the critical buckling pressures under static pressure. This was also confirmed by model simulations at low pulse frequencies. Our results provide an effective tool to predict artery buckling pressure under pulsatile pressure.     

Origin of axial prestretch and residual stress in arteries

The structural protein elastin endows large arteries with unique biological functionality and mechanical integrity, hence its disorganization, fragmentation, or degradation can have important consequences on the progression and treatment of vascular diseases. There is, therefore, a need in arterial mechanics to move from materially uniform, phenomenological, constitutive relations for the wall to those that account for separate contributions of the primary structural constituents: elastin, fibrillar collagens, smooth muscle, and amorphous matrix. In this paper, we employ a recently proposed constrained mixture model of the arterial wall and show that prestretched elastin contributes significantly to both the retraction of arteries that is observed upon transection and the opening angle that follows the introduction of a radial cut in an unloaded segment. We also show that the transmural distributions of elastin and collagen, compressive stiffness of collagen, and smooth muscle tone play complementary roles. Axial prestresses and residual stresses in arteries contribute to the homeostatic state of stress in vivo as well as adaptations to perturbed loads, disease, or injury. Understanding better the development of and changes in wall stress due to individual extracellular matrix constituents thus promises to provide considerable clinically important insight into arterial health and disease.     

Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal,proteoglycan depleted and collagen degraded articular cartilage

Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (-64+/-28%) and a minor decrease of the fibril network modulus (-11+/-9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (-69+/-5%) and a decrease of the drained porous matrix modulus (-44+/-18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.     

Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model

Arteries display a nonlinear anisotropic behavior dictated by the elastic properties and structural arrangement of its main constituents, elastin, collagen, and vascular smooth muscle. Elastin provides for structural integrity and for the compliance of the vessel at low pressure, whereas collagen gives the tensile resistance required at high pressures. Based on the model of Zulliger et al. (Zulliger MA, Rachev A, Stergiopulos N. Am J Physiol Heart Circ Physiol 287: H1335-H1343, 2004), which considers the contributions of elastin, collagen, and vascular smooth muscle cells (VSM) in an explicit form, we assessed the effects of enzymatic degradation of elastin on biomechanical properties of rabbit carotids. Pressure-diameter curves were obtained for controls and after elastin degradation, from which elastic and structural properties were derived. Data were fitted into the model of Zulliger et al. to assess elastic constants of elastin and collagen as well as the characteristics of the collagen engagement profile. The arterial segments were also prepared for histology to visualize and quantify elastin and collagen. Elastase treatment leads to a diameter enlargement, suggesting the existence of significant compressive prestresses within the wall. The elastic modulus was more ductile in treated arteries at low circumferential stretches and significantly greater at elevated circumferential stretches. Abrupt collagen fiber recruitment in elastase-treated arteries leads to a much stiffer vessel at high extensions. This change in collagen engagement properties results from structural alterations provoked by the degradation of elastin, suggesting a clear interaction between elastin and collagen, often neglected in previous constituent-based models of the arterial wall.     

Acute and specific collagen type I degradation increases diastolic and developed tension in perfused rat papillary muscle

Collagen degradation is suggested to be responsible for long-term contractile dysfunction in different cardiomyopathies, but the effects of acute and specific collagen type I removal (main type in the heart muscle) on tension have not been studied. We determined the diastolic and developed tension length relations in isometric contracting perfused rat papillary muscles (perfusion pressure 60 cmH(2)O) before and after acute and specific removal of small collagen struts with the use of purified collagenase type I. At 95% of the maximal length (95%L(max)), diastolic tension increased 20.4 +/- 8.1% (P < 0.05, n = 6) and developed tension increased 15.0 +/- 6.7% after collagenase treatment compared with time controls. Treatment increased the diastolic muscle diameter by 7.1 +/- 3.4% at 95%L(max), whereas the change in diameter due to contraction was not changed. Diastolic coronary flow and normalized coronary arterial flow impediment did not change after collagenase treatment. Electron microscopy revealed that the number of small collagen struts, interconnecting myocytes, and capillaries was reduced to approximately 32% after treatment. We conclude that removal of the small collagen struts by acute and specific collagen type I degradation increases diastolic and developed tension in perfused papillary muscle. We suggest that diastolic tension is increased due to edema, whereas developed tension is increased because the removal of the struts poses a lower lateral load on the cardiac myocytes, allowing more myocyte thickening.     

An in vitro model for the pathological degradation of articular cartilage in osteoarthritis

The objective of this study was to develop an in vitro cartilage degradation model that emulates the damage seen in early-stage osteoarthritis. To this end, cartilage explants were collagenase-treated to induce enzymatic degradation of collagen fibers and proteoglycans at the articular surface. To assess changes in mechanical properties, intact and degraded cartilage explants were subjected to a series of confined compression creep tests. Changes in extracellular matrix structure and composition were determined using biochemical and histological approaches. Our results show that collagenase-induced degradation increased the amount of deformation experienced by the cartilage explants under compression. An increase in apparent permeability as well as a decrease in instantaneous and aggregate moduli was measured following collagenase treatment. Histological analysis of degraded explants revealed the presence of surface fibrillation, proteoglycan depletion in the superficial and intermediate zones and loss of the lamina splendens. Collagen cleavage was confirmed by the Col II–3/4C_short antibody. Degraded specimens experienced a significant decrease in proteoglycan content but maintained total collagen content. Repetitive testing of degraded samples resulted in the gradual collapse of the articular surface and the compaction of the superficial zone. Taken together, our data demonstrates that enzymatic degradation with collagenase can be used to emulate changes seen in early-stage osteoarthritis. Further, our in vitro model provides information on cartilage mechanics and insights on how matrix changes can affect cartilage's functional properties. More importantly, our model can be applied to develop and test treatment options for tissue repair.