3d Mechanical properties of the partially obstructed guinea pig small intestine

Background and aimsPartial obstruction of the small intestine results in severe hypertrophy of smooth muscle cells, dilatation and functional denervation. Hypertrophy of the small intestine is associated with alteration of the wall structure and the mechanical properties. The aims of this study were to determine three dimensional material properties of the obstructed small intestine in guinea pigs and to obtain the 3D stress–strain distributions in the small intestinal wall.MethodsPartial obstruction of mid-jejunum was created surgically in five guinea pigs that were euthanized 2 weeks after the surgery. Ten-cm-long segments proximal to the obstruction site were used for the stretch-inflation mechanical test using a tri-axial test machine. The outer diameter, longitudinal force and the luminal pressure during the test were recorded simultaneously. An anisotropic exponential pseudo-strain energy density function was used as the constitutive equation to fit the experimental loading curve and for computation of the stress–strain distribution.ResultsThe wall thickness and the wall area increased significantly in the obstructed jejunum (P<0.001). The pressure—outer radius curves in the obstructed segments were translated to the left of the normal segments, indicating wall stiffening after the obstruction. The circumferential stress and the longitudinal stress through the wall were higher in the obstructed segments (P<0.02). This was independent of whether the zero-stress state or the no-load states were used as the reference state.ConclusionThe mechanical behaviour of the obstructed small intestine can be described using a 3D constitutive model. The obstruction-induced biomechanical properties change was characterized by higher circumferential and longitudinal stresses in the wall and altered material constants in the 3D constitutive model.     

An Analysis and Comparison of Convergence and Uniqueness of Time-Independent Bone Adaptation Models

Several stimuli are proposed in the bone remodeling theory. It is not clear, if a unique solution exists and if the result is convergent using a certain stimulus. In this study, the strain stimulus, strain energy stimulus and the von Mises stress stimulus for bone remodeling are compared and applied to a square plate model using the finite element method. In the plane stress state, the remodeling equilibrium equations are transformed into functions of only the principal strains and the graphs of these functions are drawn in a diagram using the principal strains as the variables of two coordinate axes. The equation of the sum of principal strain squared equal to a constant is a circle in the diagram. The remodeling equilibrium equation of the strain stimulus is a quadrangle fitting into the circle, the remodeling equilibrium equation of the strain energy stimulus is an ellipse and the remodeling equilibrium equation of the von Mises stress stimulus is also an ellipse close to the principal strains circle when we take the same constants in the above equations. Using the finite element method, two models are performed with the uniform initial elastic properties and with the semi-random initial distribution of the elastic properties. The principal strains as the final finite element results converge within 2% of the objective constant for all the different stimuli. The obtained Young's moduli of two models as the adaptation object are different but in equilibrium, i.e. the equilibrium solution of adaptation model is not unique. The principal strains can not be used to examine the uniqueness of solution, since two different solutions can have the same results of principal strains. Using a certain stimulus, certain initial properties and a certain iterative equation, the solution is unique in equilibrium. The results using the model in this study show also that the same results can be obtained using any of the three stimuli when a proper constant in each remodeling equilibrium equation is chosen.     

Three-dimensional stress and strain distribution in a two-layer model of a coronary artery

For a right coronary artery, three-dimensional stress and strain distributions at a physiological intraluminal pressure and an axial extension ratio were computed on the basis of a two-layer elastic model. To validate the model, curves of external radius versus pressure and of axial force versus pressure were computed for three axial extension ratios. To analyze mechanical properties, stress-free configurations of media and adventitia, and the constitutive law of each layer in literature, were used. The present study showed that the peak circumferential stress and the peak axial stress appear in the media at the boundary between the media and adventitia. This result is due to the opening angle of the media being larger than π (rad) and the larger value of a material constant of the strain energy function for the media than for the adventitia. The circumferential stress and strain were discontinuous at the boundary. On the other hand, the radial stress was continuous at the boundary because of the boundary condition for stress. The circumferential stress and axial stress in the adventitia were almost uniformly distributed, and smaller than in the media. The residual stress and strain were also computed. The circumferential residual stress and strain were almost linearly distributed in each layer, although discontinuity appeared at the boundary between the two layers.     

A model for the nonlinear elastic response of large arteries

The nonlinear elastic response of large arteries subjected to finite deformations due to action of biaxial principal stresses, is described by simple constitutive equations. Generalized measures of strain and stress are introduced to account for material nonlinearity. This also ensures the existence of a strain energy density function. The orthotropic elastic response is described via quasi-linear relations between strains and stresses. One nonlinear parameter which defines the measures of strain and stress, and three elastic moduli are assumed to be constants. The lateral strain parameters (equivalent to Poisson's ratios in infinitesimal deformations) are deformation dependent. This dependence is defined by empirical relations developed via the incompressibility condition, and by the introduction of a fifth material parameter. The resulting constitutive model compares well with biaxial experimental data of canine carotid arteries.     

Nonlinear elastic analysis of blood vessels

Based on the theory of Green and Adkins [9], a strain energy function is proposed to describe the nonlinear mechanical behavior of arteries. The arterial tissue is assumed to be a nonlinear elastic, incompressible material with local triclinicity and transverse isotropy. Although the arterial tissue shows viscous phenomena, experimental results have indicated that viscosity is only a second-order effect as compared to the nonlinear elasticity of the tissue. The advantage of the formulation presented herein is that it is relatively simple and results in an accurate stress-strain relation that can be used readily for the study of wave propagations in the blood vessels. For nonlinear finite strain elasticity of the order two, ten elastic constants are needed to describe the material nonlinearity of the arterial tissue. Based on the orthogonal, transverse isotropies and the incompressibility conditions, ten constraint equations may be established and the elastic constants can be uniquely determined by correlating with the experimental results. An example of calculating these elastic constants is made by using the experimental data of Patel, et al. [14-17] for the intercoastal arteries in living dogs. The predicted mechanical behavior of canine arteries is quite satisfactory as compared to the experimental data except when the longitudinal and the circumferential stretches exceed 1.60. However, such a strain magnitude may not be expected in in-vivo arteries because of the constraints of peripheral connecting tissues. Otherwise, the strain energy function including higher order strain terms should be used.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Stress and strain analysis of contractions during ramp distension in partially obstructed guinea pig jejunal segments

Previous studies have demonstrated morphological and biomechanical remodeling in the intestine proximal to an obstruction. The present study aimed to obtain stress and strain thresholds to initiate contraction and the maximal contraction stress and strain in partially obstructed guinea pig jejunal segments. Partial obstruction and sham operations were surgically created in mid-jejunum of male guinea pigs. The animals survived 2, 4, 7 and 14 days. Animals not being operated on served as normal controls. The segments were used for no-load state, zero-stress state and distension analyses. The segment was inflated to 10 cmH(2)O pressure in an organ bath containing 37°C Krebs solution and the outer diameter change was monitored. The stress and strain at the contraction threshold and at maximum contraction were computed from the diameter, pressure and the zero-stress state data. Young's modulus was determined at the contraction threshold. The muscle layer thickness in obstructed intestinal segments increased up to 300%. Compared with sham-obstructed and normal groups, the contraction stress threshold, the maximum contraction stress and the Young's modulus at the contraction threshold increased whereas the strain threshold and maximum contraction strain decreased after 7 days obstruction (P<0.05 and 0.01). In conclusion, in the partially obstructed intestinal segments, a larger distension force was needed to evoke contraction likely due to tissue remodeling. Higher contraction stresses were produced and the contraction deformation (strain) became smaller.     

Uniform strain hypothesis and thin-walled theory in arterial mechanics

The authors (1987), and Chuong and Fung (1986) have shown that the strain and stress distributions in the arterial wall should be more uniform than those calculated on the basis of the conventional assumption that there is no stress over the cross-section of the arterial wall when all external force is removed (zero initial stress hypothesis). Instead of this assumption, the authors have proposed a new hypothesis that the circumferential strain uniformly distributes through the wall thickness at a physiologically normal loading, and named it 'uniform strain hypothesis'. Their results suggest the validity of the thin-walled theory in the vascular mechanics. This paper shows that if the uniform strain hypothesis is applied, the thin-walled theory can be used to accurately determine the constants included in the strain energy density function which describes the mechanical properties of the arterial wall. There were, however, significant differences in the values of the constants between the thin-walled theory and the thick-walled theory if assuming the conventional zero initial stress hypothesis.     

Determining the mechanical properties of yeast cell walls

The intrinsic cell wall mechanical properties of Baker's yeast (Saccharomyces cerevisiae) cells were determined. Force-deformation data from compression of individual cells up to failure were recorded, and these data were fitted by an analytical model to extract the elastic modulus of the cell wall and the initial stretch ratio of the cell. The cell wall was assumed to be homogeneous, isotropic, and incompressible. A linear elastic constitutive equation was assumed based on Hencky strains to accommodate the large stretches of the cell wall. Because of the high compression speed, water loss during compression could be assumed to be negligible. It was then possible to treat the initial stretch ratio and elastic modulus as adjustable parameters within the analytical model. As the experimental data fitted numerical simulations well up to the point of cell rupture, it was also possible to extract cell wall failure criteria. The mean cell wall properties for resuspended dried Baker's yeast were as follows: elastic modulus 185 ± 15 MPa, initial stretch ratio 1.039 ± 0.006, circumferential stress at failure 115 ± 5 MPa, circumferential strain at failure 0.46 ± 0.03, and strain energy per unit volume at failure 30 ± 3 MPa. Data on yeast cells obtained by this method and model should be useful in the design and optimization of cell disruption equipment for yeast cell processing.     

Influence of tensile strain on smooth muscle cell orientation in rat blood vessels.

Blood vessels are subject to tensile stress and associated strain which may influence the structure and organization of smooth muscle cells (SMCs) during physiological development and pathological remodeling. This study focused on the influence of the major tensile strain on the SMC orientation in the blood vessel wall. Several blood vessels, including the aorta, the mesenteric artery and vein, and the jugular vein of the rat were used to observe the normal distribution of tensile strains and SMC orientation; and a vein graft model was used to observe the influence of altered strain direction on the SMC orientation. The circumferential and longitudinal strains in these blood vessels were measured by using a biomechanical technique, and the SMC orientation was examined by fluorescent microscopy at times of 10, 20, and 30 days. Results showed that the SMCs were mainly oriented in the circumferential direction of straight blood vessels with an average angle of approximately 85 deg between the SMC axis and the vessel axis in all observed cases. The SMC orientation coincided with the principal direction of the circumferential strain, a major tensile strain, in the blood vessel wall. In vein grafts, the major tensile strain direction changed from the circumferential to the longitudinal direction at observation times of 10, 20, and 30 days after graft surgery. This change was associated with a decrease in the angle between the axis of newly proliferated SMCs and that of the vessel at all observation times (43 +/- 11 deg, 42 +/- 10 deg, and 41 +/- 10 deg for days 10, 20, and 30, respectively), indicating a shift of the SMC orientation from the circumferential toward the longitudinal direction. These results suggested that the major tensile strain might play a role in the regulation of SMC orientation during the development of normal blood vessels as well as during remodeling of vein grafts.     

A constrained mixture model for developing mouse aorta

Mechanical stresses influence the structure and function of adult and developing blood vessels. When these stresses are perturbed, the vessel wall remodels to return the stresses to homeostatic levels. Constrained mixture models have been used to predict remodeling of adult vessels in response to step changes in blood pressure, axial length and blood flow, but have not yet been applied to developing vessels. Models of developing blood vessels are complicated by continuous and simultaneous changes in the mechanical forces. Understanding developmental growth and remodeling is important for treating human diseases and designing tissue-engineered blood vessels. This study presents a constrained mixture model for postnatal development of mouse aorta with multiple step increases in pressure, length and flow. The baseline model assumes that smooth muscle cells (SMCs) in the vessel wall immediately constrict or dilate the inner radius after a perturbation to maintain the shear stress and then remodel the wall thickness to maintain the circumferential stress. The elastin, collagen and SMCs have homeostatic stretch ratios and passive material constants that do not change with developmental age. The baseline model does not predict previously published experimental data. To approximate the experimental data, it must be assumed that the SMCs dilate a constant amount, regardless of the step change in mechanical forces. It must also be assumed that the homeostatic stretch ratios and passive material constants change with age. With these alterations, the model approximates experimental data on the mechanical properties and dimensions of aorta from 3- to 30-day-old mice.     

Biaxial elastic material properties of porcine coronary media and adventitia

The importance of mechanical stresses and strains has become well recognized in vascular physiology and pathology. To compute the stress and strain on the various components of the vessel wall, we must know the constitutive equations for the different layers of the vessel wall. The objective of the present study is to determine the constitutive equation of the coronary artery treated as a two-layer composite: intima-media and adventitial layers. Twelve hearts were obtained from a local slaughterhouse, and the right coronary artery and left anterior descending artery were dissected free from the myocardium. The vessel wall was initially mechanically tested biaxially (inflation and axial extension) as a whole (intact wall) and subsequently as intima-media or adventitial layer. A Fung-type exponential strain energy function was used to curve fit the experimental data for the intact wall and individual layers for the right coronary artery and left anterior descending artery. Two methods were used for the determination of material constants, including the Marquardt-Levenberg nonlinear least squares method and the genetic algorithm method. Our results show that there were no statistically significant differences in the material constants obtained from the two methods and that either set of elastic constants results in good fit of the data. Furthermore, at an in vivo value of axial stretch ratio, we find that the stiffness is as follows: intima-media > intact > adventitia. These results underscore the composite nature of coronary arteries with different material properties in each layer. The present results are necessary for analysis of coronary artery mechanics and to provide a fundamental understanding of vessel physiology.     

Nonlinear Anisotropic Elastic Properties of the Canine Aorta

A nonlinear theory of large elastic deformations of the aortic tissue has been developed. The wall tissue has been considered to be incompressible and curvilinearly orthotropic. The strain energy density function for the tissue is expressed as a polynomial in the circumferential and longitudinal Green-St. Venant strains. Limiting application to states of strains wherein the geometric axes are the principal axes and truncating the energy expression to include terms with highest degrees 2, 3, and 4, three expressions with 3, 7, and 12 constitutive constants are obtained. Results of application of these expressions to data from three series of in vitro and in vivo experiments involving 31 dogs have been presented. Whereas all the three expressions are found to be applicable to various degrees, the third-degree expression for the strain energy density function with seven constitutive constants is particularly recommended for general use.     

Adaptation of passive rat left ventricle in diastolic dysfunction.

This article deals with providing a theoretical explanation for quantitative changes in the geometry, the opening angle and the deformation parameters of the rat ventricular wall during adaptation of the passive left ventricle in diastolic dysfunction. A large deformation theory is applied to analyse transmural stress and strain distribution in the left ventricular wall considering it to be made of homogeneous, incompressible, transversely isotropic, non-linear elastic material. The basic assumptions made for computing stress distributions are that the average circumferential stress and strain for the adaptive ventricle is equal to the average circumferential stress and strain in the normotensive ventricle, respectively.All the relevant parameters, such as opening angle, twist per unit length, axial extension, internal and external radii and others, in the stress-free, unloaded and loaded states of normotensive, hypertensive and adaptive left ventricle are determined. The circumferential stress and strain distribution through the ventricular wall are also computed. Our analysis predicts that during adaptation, wall thickness and wall mass of the ventricle increase. These results are consistent with experimental findings and are the indications of initiation of congestive heart failure.     

Relaxin regulates vascular wall remodeling and passive mechanical properties in mice

Administration of recombinant human relaxin (rhRLX) to conscious rats increases global arterial compliance, and small renal arteries (SRA) isolated from these rats demonstrate increased passive compliance. Here we characterize relaxin-induced vascular remodeling and examine its functional relevance. SRA and external iliac arteries (EIA) were examined in rhRLX-treated (1.0 μg/h for 5 days) and relaxin knockout mice. Arterial geometric remodeling and compositional remodeling were quantified using immunohistochemical and biochemical techniques. Vascular mechanical properties were quantified using an ex vivo preparation wherein pressure-diameter data were obtained at various axial lengths. Compared with vehicle-treated mice, SRA from rhRLX-treated mice showed outward geometric remodeling (increased unstressed wall area and wall-to-lumen area ratio), increased smooth muscle cell (SMC) density, reduction in collagen-to-total protein ratio, and unchanged elastin-to-tissue dry weight ratio. Compared with wild-type mice, relaxin knockout mice exhibited the opposite pattern: decreased unstressed wall area and wall-to-lumen area ratio, decreased SMC density, and increased collagen-to-total protein ratio. Although tissue biaxial strain energy of SRA was not different between rhRLX- and vehicle-treated groups at low-to-physiological circumferential and axial strains, it was lower for the rhRLX-treated group at the highest circumferential strain. In contrast to SRA, relaxin administration was not associated with any vascular remodeling or changes in passive mechanics of EIA. Thus relaxin induces both geometric and compositional remodeling in vessel-specific manner. Relaxin-induced geometric remodeling of SRA is responsible for the increase in passive compliance under low-to-physiological levels of circumferential and axial strains, and compositional remodeling becomes functionally relevant only under high circumferential strain.     

Flow-induced shear strain in intima of porcine coronary arteries.

The in vivo circumferential strain has a small variation throughout the vascular system (aorta to arterioles). The axial strain has also been shown to be nearly the same as the circumferential strain under physiological loading. Since the endothelium is mechanically much softer than the media-adventitia in healthy arteries, the porcine intima was considered as a mechanically distinct layer from the media-adventitia in a two-layer computational model. Based on the simulation result, we hypothesize that the flow-induced shear strain in intima can be of similar value as the pressure-induced circumferential strain in healthy coronary arteries, even though the shear stress is orders of magnitude smaller than the circumferential stress. The nearly isotropic deformation (circumferential, axial, and shear strains) may have important implications for mechanical homeostasis of endothelial cells, mechanotransduction, growth, and remodeling of blood vessels.     

A study on large radial motion of arteries in vivo

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

Uniform stress state in bone structure with residual stress.

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.     

Changes in the rheological properties of blood vessel tissue remodeling in the course of development of diabetes.

Rheological properties of blood vessels are expected to change in disease process if the structure of the vessel wall changes. This is illustrated in diabetes, which can be induced in rat by a single injection of Streptozocin. One of the rheological properties of the blood vessel is the stress-strain relationship. The nonlinear stress-strain relationship of arteries is best expressed as derivations of a strain-energy function. In this paper, the stress-strain relations are measured and the coefficients in the strain energy function of arteries are determined for diabetic and control rats. The meaning of these coefficients are explained. The influence of diabetes on the elastic property of the arteries is expressed by the changes of these coefficients. A point of departure of the present paper from all other blood vessel papers published so far is that all strains used here are referred to the zero-stress state of the arteries, whereas all other papers refer strains to the no-load state. The existence of a large difference between the zero-stress state and no-load state of arteries is one of our recent findings. We have explained that the use of zero-stress state as a basis of strain measurements reveals that the in vivo circumferential stress distribution is quite uniform in the vessel wall at the homeostatic condition. It also makes the strain energy function much more accurate than those in which the residual stress is ignored. Using these new results, the stress and strain distribution in normal and diabetic arteries are presented.