A constituent-based model for the nonlinear viscoelastic behavior of ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.     

Arterial remodeling in response to increased blood flow using a constituent-based model

Previous theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the arterial wall remain unchanged during the remodeling process. According to experimental findings, however, remodeling due to increased flow is accompanied by alteration in the structural properties of elastin, which results in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling hypothesizing that the variation in mechanical properties of elastin is initiated and driven by the deviation of the intimal shear stress from its baseline value. Geometrical remodeling restores the wall stress distribution as it was under normal flow conditions. A constrained mixture approach is followed. Artery is modeled as a thick-walled cylindrical tube made of non-linear, elastic, anisotropic and incompressible material. Data for a rabbit thoracic aorta have been employed. At the final adapted state, the model predicts a non-monotonic dependence of arterial compliance on the magnitude of flow. This result is in agreement with available experimental data in the literature.     

Differences in nitric oxide production in porcine resistance arteries and epicardial conduit coronary arteries

The purpose of this study was to test the hypothesis that endothelial cells from resistance arteries and epicardial conduit coronary arteries differ in their expression of nitric oxide synthase (NOS) and calcium metabolism, and that these differences contribute to the mechanism underlying disparate physiological vasodilator responses observed between the two populations of vessels. The functional vasodilator responses of isolated resistance arteries and epicardial conduit coronary arteries were compared in vitro using both the receptor-independent agonist A23187 ionophore to increase intracellular calcium and the receptor-dependent agonist bradykinin. Constitutive NOS (cNOS) activity in monocultures of endothelial cells derived from resistance arteries and conduit arteries was assayed using a fibroblast-reporter cell method. Intracellular calcium concentration was assessed using fura-2 microfluorometry. Nitric oxide production was determined using a chemiluminescence technique, while cNOS protein was quantitated by Western blot analysis. A23187 was a less potent vasodilator of resistance arteries studied in vitro, compared to epicardial conduit arteries (EC₅₀ = 1.6 μM, resistance artery vs. EC₅₀ = 0.03 μM, conduit artery); however, bradykinin was more potent in resistance arteries (EC₅₀ = 0.3 nM, resistance artery vs. EC₅₀ = 2 nM, conduit artery). In pure monocultures of endothelium, nitric oxide production measured by chemiluminescence both basally and in response to A23187 was significantly less in resistance arteries (6.1 ± 0.5, basal vs. 10.80 ± 0.55, stimulated nmol/μg protein), compared to conduit arteries (7.7 ± 0.5, basal vs. 17.00 ± 1.52, stimulated nmol/μg protein; P < 0.05 resistance artery endothelium vs. conduit artery endothelium). cNOS enzyme activity assessed by cGMP production in reporter cell fibroblasts was also lower in resistance arteries compared to conduit arteries (0.17 ± 0.03 vs. 0.33 ± 0.05 fmol cGMP/μg protein, respectively; P < 0.05 resistance artery endothelium vs. conduit artery endothelium). Conduit arteries expressed 2.1 × more cNOS protein than resistance arteries, as assessed by Western blotting of cellular homogenates. No significant differences were found with microfluorimetry in either basal or ionophore-stimulated intracellular calcium concentrations. The results signified that porcine resistance arteries expressed less NOS and produced less nitric oxide than epicardial conduit arteries both basally and in response to an increase in intracellular calcium. This difference was reflected functionally as a decreased vasodilatory response to increased intracellular calcium in resistance arteries that could not be explained on the basis of differences in the metabolism of intracellular calcium. In contrast, the functional vasodilator response of intact vessels to a receptor-mediated agonist was enhanced in resistance arteries compared to conduit arteries, suggesting an important role of signal transduction mechanisms in specific physiological responses. Thus, the ability of the endothelium to regulate on a regional basis the expression of NOS and integrate receptor-mediated responses with these differences may provide a mechanism for diverse vasomotor responses in different populations of vessels. © 1996 Wiley-Liss, Inc.     

A model of bubble growth leading to xylem conduit embolism

The dynamics of a gas bubble inside a water conduit after a cavitation event was modeled. A distinction was made between a typical angiosperm conduit with a homogeneous pit membrane and a typical gymnosperm conduit with a torus-margo pit membrane structure. For conduits with torus-margo type pits pit membrane deflection was also modeled and pit aspiration, the displacement of the pit membrane to the low pressure side of the pit chamber, was found to be possible while the emboli was still small. Concurrent with pit aspiration, the high resistance to water flow out of the conduit through the cell walls or aspirated pits will make the embolism process slow. In case of no pit aspiration and always for conduits with homogeneous pit membranes, embolism growth is more rapid but still much slower than bubble growth in bulk water under similar water tension. The time needed for the embolism to fill a whole conduit was found to be dependent on pit and cell wall conductance, conduit radius, xylem water tension, pressure rise in adjacent conduits due to water freed from the embolising conduit, and the rigidity and structure of the pits in the case of margo-torus type pit membrane. The water pressure in the conduit hosting the bubble was found to occur almost immediately after bubble induction inside a conduit, creating a sudden tension release in the conduit, which can be detected by acoustic and ultra-acoustic monitoring of xylem cavitation.     

Phosphodiesterase 5 inhibition restores impaired ACh relaxation in hypertensive conduit pulmonary arteries

Responses to acetylcholine (ACh) and sodium nitroprusside (SNP) were compared in large (LPA) and small pulmonary artery (SPA) rings from normoxic and chronically hypoxic (CH) rats. In addition, the effects of a selective phosphodiesterase (PDE) 5 inhibitor, E-4021, on ACh-induced relaxation were evaluated. Chronic hypoxia markedly decreased both ACh- and SNP-induced relaxations in LPA but not in SPA rings. Pretreatment with E-4021 caused a much greater leftward shift of the concentration-response curve for ACh in hypoxic than in normoxic LPA rings, eliminating the difference in response to ACh between these two vessels. These results suggest that cGMP-dependent relaxation is impaired in the proximal but not in the distal pulmonary artery of CH rats and that increased PDE5 activity could be a mechanism responsible for this impaired responsiveness.     

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.     

Glucagon-like peptide-1 relaxes rat conduit arteries via an endothelium-independent mechanism

A lot of interest has engendered in glucagon-like peptide-1 (GLP-1) as an emerging new drug in the treatment of type 2 diabetes. GLP-1 exerts several effects that reduce glycemia in type 2 diabetes patients. We recently also demonstrated that GLP-1 ameliorates endothelial dysfunction in type 2 diabetes mellitus patients with established coronary heart disease, suggesting a new important cardioprotective role for GLP-1. Because hypertension is overrepresented in diabetes and is adversely influencing survival, we have now investigated direct GLP-1 effects on vascular beds in a rat organ bath model. It was found that GLP-1 relaxed femoral artery rings in a dose-response manner. The relaxant effect from GLP-1 was completely inhibited by the specific GLP-1 receptor antagonist, exendin(9-39). Neither the specific nitric oxide (NO) synthase inhibitor, N-nitro-L-arginine, nor removing of endothelium, affected the GLP-1 relaxant effect. In conclusion, we now report a direct vascular action of GLP-1, relaxing conduit vessels independently of NO and the endothelium.     

Influence of vascular dimension on gender difference in flow-dependent dilatation of peripheral conduit arteries

To assess the influence of initial diameter on the gender difference in flow-dependent dilatation (FDD) of the conduit artery, we measured radial artery internal diameter (echotracking), flow (Doppler) and total blood viscosity in 24 healthy (25 +/- 0.8 yr) men and women during reactive hyperemia (RH) and during a gradual hand skin heating (SH). At baseline, mean diameter (men, 2.76 +/- 0.09 vs. women, 2.32 +/- 0.07 mm, P < 0.05), flow (men, 21 +/- 4 vs. women, 10 +/- 1 ml/min, P < 0.05), and blood viscosity (men, 4.13 +/- 0.07 vs. women, 3.92 +/- 0.13 cP, P < 0.05) were higher in men but mean shear stress (MSS) was not different between groups. During RH, the percent increase in diameter was lower in men (men, 9 +/- 1 vs. women, 13 +/- 1%, P < 0.05). This difference was suppressed after correction for baseline diameter. During SH, the increase in diameter with flow was higher in women (P < 0.01). However, the increase in MSS was higher in women because of their smaller diameter at each level of flow (P < 0.01) and there was no difference between groups for the increase in diameter at each level of MSS. These results demonstrate in a direct manner that initial diameter influences the magnitude of FDD of conduit arteries in humans by modifying the value of the arterial wall shear stress at each level of flow and support the interest of the heating method in presence of heterogeneous groups.     

Effects of longitudinal stretch on VSM tone and distensibility of muscular conduit arteries

With progressing age, large arteries diminish their longitudinal stretch, which in extreme cases results in tortuosity. Increased age is also associated with loss of vessel distensibility. We measured pressure-diameter curves from muscular porcine carotid arteries ex vivo at different longitudinal stretch ratios (lambda(z) = 1.4 and 1.8) and under different vascular smooth muscle (VSM) conditions (fully relaxed, normal VSM tone, and maximally contracted). Distensibility was found to be halved by decreasing longitudinal stretch from lambda(z) = 1.8 to 1.4 at physiological pressures. This counterintuitive observation is possible because highly nonlinear elastic modulus of the artery and anisotropic properties. Furthermore, a significantly larger basal VSM contraction was observed at lambda(z) = 1.8 than 1.4, although this was clearly not related to a myogenic response during inflation. This dependence of VSM tone to longitudinal stretch may have possible implications on the functional characteristics of the arterial wall.     

A linearized and incompressible constitutive model for arteries

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E? (circumferential), E? (axial), and E? (radial) are necessary to fit the data. The advantages and limitations of this model are discussed.     

Study of age-related changes in Middle ear transfer function

Abstract

Osteoporosis (OP) is common with advancing age. Several studies have shown a strong correlation between OP and otosclerosis. However, no studies have investigated OP of the malleus, incus or stapes in the human middle ear, its effect on middle ear transfer function. Here, we investigate whether these three ossicles develop OP, and how this affects middle ear transfer function. The effect of OP on middle ear transfer function was investigated in simulations based on a finite element (FE) method. First, the FE model used in our previous study was refined, and optimized by introducing viscoelastic properties to selected soft tissues of the middle ear. Then, the FE model was used to simulate OP of the three ossicles and assess its influence on middle ear transfer function. Other possible age-related changes, such as stiffness of the joints or ligaments in the middle ear, were also investigated. The results indicated that OP of the ossicles could increase the high frequency displacement of both the umbo and stapes footplate (FP). However, the stiffness of the middle ear soft tissue can lead to the decrease of middle ear gain at lower frequencies. Furthermore, loosening of these joints or ligaments could increase displacement of the umbo and stapes FP. In conclusion, although age-related hearing loss is most commonly conceived of as sensorineural hearing loss (SNHL), we found that age-related changes may also include OP and changes in joint stiffness, but these will have little effect on middle ear transfer function in elderly people.     

A study of age-related architectural changes that are most damaging to bones

Osteoporosis-related bone damage causes major socioeconomic problems. For efficient use of therapeutic agents, it is necessary to be able to reliably identify patients with high propensity for nontraumatic fracture. Age-related bone loss imposes several architectural changes in bone; one of the few ways to estimate damage due to individual changes, and hence determine the most serious types of damage, is via the analysis of suitable mathematical models. Anatomical sites such as the vertebral body, proximal femur, and distal radius are locations where most age-related fractures occur. The inner porous (or trabecular) bone from these sites, which resemble disordered cubic networks, play a significant role in load transmission at these sites. Analysis of a mathematical model of porous bone is used to show that perforation of elements of the network is the most damaging architectural change to a bone. We also show that an expression for bone strength, derived on this basis, can capture changes in strength caused by the inclusion of other features like thinning of trabecular bone and the anisotropy of the network. We finally argue that bone density, which is currently the most routinely used diagnostic, cannot be a reliable surrogate for bone strength.     

A novel scratching approach for measuring age-related changes in the in situ toughness of bone

A scratch test using a nanoindentation system was proposed in this study to assess the age-related changes in the in situ toughness of bone matrix at ultrastructural levels. A tissue removal energy density (u(r)) was defined and estimated as the work done by the scratch (U(T)) divided by the total volume of the scratch groove (u(s)). The value of u(s) was used as a relative measure of the in situ toughness of the tissue. Human cortical bone specimens obtained from middle-aged (between 49 and 59 years old) and elderly groups (over 69 years old) were tested using this technique. A significant difference in the estimated removal energy density (u(s)) in the secondary osteons was found between the middle-aged and elderly groups (5.49+/-0.696 vs. 4.09+/-1.30 N/mm(2), respectively).     

Differential effects of eNOS uncoupling on conduit and small arteries in GTP-cyclohydrolase I-deficient hph-1 mice

In the present study, we used the hph-1 mouse, which displays GTP-cyclohydrolase I (GTPCH I) deficiency, to test the hypothesis that loss of tetrahydrobiopterin (BH(4)) in conduit and small arteries activates compensatory mechanisms designed to protect vascular wall from oxidative stress induced by uncoupling of endothelial nitric oxide synthase (eNOS). Both GTPCH I activity and BH(4) levels were reduced in the aortas and small mesenteric arteries of hph-1 mice. However, the BH(4)-to-7,8-dihydrobiopterin ratio was significantly reduced only in hph-1 aortas. Furthermore, superoxide anion and 3-nitrotyrosine production were significantly enhanced in aortas but not in small mesenteric arteries of hph-1 mice. In contrast to the aorta, protein expression of copper- and zinc-containing superoxide dismutase (CuZnSOD) was significantly increased in small mesenteric arteries of hph-1 mice. Protein expression of catalase was increased in both aortas and small mesenteric arteries of hph-1 mice. Further analysis of endothelial nitric oxide synthase (eNOS)/cyclic guanosine monophosphate (cGMP) signaling demonstrated that protein expression of phosphorylated Ser(1177)-eNOS as well as basal cGMP levels and hydrogen peroxide was increased in hph-1 aortas. Increased production of hydrogen peroxide in hph-1 mice aortas appears to be the most likely mechanism responsible for phosphorylation of eNOS and elevation of cGMP. In contrast, upregulation of CuZnSOD and catalase in resistance arteries is sufficient to protect vascular tissue from increased production of reactive oxygen species generated by uncoupling of eNOS. The results of our study suggest that anatomical origin determines the ability of vessel wall to cope with oxidative stress induced by uncoupling of eNOS.     

Dietary modulation of age-related changes in cerebral pro-oxidant status.

It has been proposed that senescence may be associated with changes associated with oxidative damage to macromolecules. Levels of cerebellar nitric oxide synthase (NOS) and rates of generation of cortical reactive oxygen species (ROS), have been determined in mice of various ages. Both of these parameters were significantly reduced in mice aged 9 months relative to 3-month-old mice. In order to determine whether dietary manipulation can modulate these changes, the effect of exposure of mice to differing diets incorporating various antioxidants, was examined. These diets were given to 3-month-old mice for a total period of 6 further months. The presence of melatonin (40 ppm) in the basal diet restored both NOS and ROS levels to the corresponding values found in the younger (3-month-old) group of mice while lipoic acid (1650 ppm) also restored levels of NOS to those found in 3-month-old animals. Addition of coenzyme Q (ubiquinone), 200 ppm or alpha-tocopherol (1000 ppm) to the basal diet had no effect on either NOS levels or ROS generation. These data suggest that dietary supplementation may aid in delaying onset of metabolic changes characteristic of the older brain. In behavioral testing, older (9-month-old) animals exhibited reduced motor activity and diminished recall ability on the second day of exposure to the test paradigm. While no diet altered motor activity or improved recall of older animals, lipoic acid or tocopherol treatment adversely affected place recall familiarity.     

Effects of chronic irradiation on age-related biochemical changes in mice

Some of the biochemical indices relevant to the "free radical theory" of aging have been assessed in mice subjected to chronic low-dose whole-body irradiation. Radiation exposure results in enhanced accumulation of the lipofuscins in brain, heart, and intestine. In these animals, the degree of lipoperoxidation in liver was greatly increased, as were the free activities of acid phosphatase and cathespin, indicating damage to lysosomal membranes. The activity of SOD in brain and liver 20,000g post-mitochondrial supernatants was lower in the irradiated mice. All these changes arising from chronic whole-body irradiation are similar to those observed during aging and are effectively prevented by dietary supplementation with BHT. These observations lend considerable support to the "free radical theory" of aging.