Characterization of arterial wall mechanical behavior and stresses from human clinical data

This paper demonstrates the feasibility of material identification and wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data: dynamical intraluminal pressure measured by applanation tonometry, and medial diameter and intimal-medial thickness measured by high-resolution ultrasound echotracking. The mechanical behavior was quantified assuming an axially pre-stretched, thick-walled, cylindrical artery subjected to dynamical blood pressure and perivascular constraints. The wall was further assumed to be three-dimensional and to consist of a nonlinear, hyperelastic, anisotropic, incompressible material with smooth muscle activity and residual stresses. Mechanical contributions by individual constituents-an elastin-dominated matrix, collagen fibers, and vascular smooth muscle-were accounted for using a previously proposed microstructurally motivated constitutive relation. The in vivo boundary value problem was solved semi-analytically to compute the inner pressure during a mean cardiac cycle. Using a nonlinear least-squares method, optimal model parameters were determined by minimizing differences between computed and measured inner pressures over a mean cardiac cycle. The fit-to-data from two healthy patients was very good and the predicted radial, circumferential, and axial stretch and stress fields were sensible. Hence, the proposed approach was able to identify complex geometric and material parameters directly from non-invasive in vivo human data.     

Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ～15% of global cell deformation in cell compression tests, or more than ～3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.     

Computational modeling of the arterial wall based on layer-specific histological data

Arterial walls typically have a heterogeneous structure with three different layers (intima, media, and adventitia). Each layer can be modeled as a fiber-reinforced material with two families of relatively stiff collagenous fibers symmetrically arranged within an isotropic soft ground matrix. In this paper, we present two different modeling approaches, the embedded fiber (EF) approach and the angular integration (AI) approach, to simulate the anisotropic behavior of individual arterial wall layers involving layer-specific data. The EF approach directly incorporates the microscopic arrangement of fibers that are synthetically generated from a random walk algorithm and captures material anisotropy at the element level of the finite element formulation. The AI approach smears fibers in the ground matrix and treats the material as homogeneous, with material anisotropy introduced at the constitutive level by enhancing the isotropic strain energy with two anisotropic terms. Both approaches include the influence of fiber dispersion introduced by fiber angular distribution (departure of individual fibers from the mean orientation) and take into consideration the dispersion caused by fiber waviness, which has not been previously considered. By comparing the numerical results with the published experimental data of different layers of a human aorta, we show that by using histological data both approaches can successfully capture the anisotropic behavior of individual arterial wall layers. Furthermore, through a comprehensive parametric study, we establish the connections between the AI phenomenological material parameters and the EF parameters having straightforward physical or geometrical interpretations. This study provides valuable insight for the calibration of phenomenological parameters used in the homogenized modeling based on the fiber microscopic arrangement. Moreover, it facilitates a better understanding of individual arterial wall layers, which will eventually advance the study of the structure–function relationship of arterial walls as a whole.     

Analysis of stresses in the wall of the urinary tract based on urographic data

Mathematical analysis has been performed from the position of the strength of material theory and the elasticity theory, taking into account forms of surfaces in various parts of the urinary pathways (UP). At an increased pressure in UP cavities the deformity degree of their walls is not similar and depends on expressiveness of positive or negative curvature of saddle-like surfaces. In its turn, according to changes of the curvature radii in UP contours in roentgenograms, it is possible to consider on an increased pressure in their lumen, depending on disturbances in UP conductivity.     

Effects of arterial wall stress on vasomotion

Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Many muscular vessels present vasomotion, i.e., rhythmic diameter oscillations caused by synchronous cytosolic calcium oscillations of the smooth muscle cells. Vasomotion has been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the wall thickness is increased. Our results are in agreement with experimental observations concerning a broad range of vessels.     

Some unusual considerations about vessel walls and wall stresses

The "zero-stress state" of blood vessels is usually defined with respect to the atmospheric pressure p(a) ( approximately 750 mmHg). As a consequence, circumferential and axial wall stresses due to a positive transmural pressure can only be positive and thus, by definition, only tensile. If the zero-stress state were defined with respect to vacuum pressure (0 mmHg), the compressive stress -p(a) generated by p(a) everywhere in the wall would, however, be included so that negative (=compressive) wall stresses would formally become possible. In order to examine the consequences this alternative definition would have for arteries, we have compared radial, circumferential, and axial stresses calculated "conventionally" to the values they take when the zero-stress state is defined "correctly" by reference to the vacuum pressure. It turns out that, under normal physiologic conditions, axial stress and perhaps also circumferential stress might well be compressive in many elastic and conductance arteries, contrary to the intuitive conviction of many people. Since the type of stresses a vessel wall is submitted to may be highly relevant for its structure and mechanical properties, this unconventional way of considering wall stresses may reveal unsuspected relationships between wall stresses on one side, and wall structure, vessel growth, adaptation and repair processes, atherosclerosis, angioplasty or stenting on the other side. Similar considerations might also prove useful with regard to cardiac hypertrophy.     

Isotropy and anisotropy of the arterial wall

The passive biomechanical response of intact cylindrical rat carotid arteries is studied in vitro and compared with the mechanical response of rubber tubes. Using true stress and natural strain in the definition of the incremental modulus of elasticity, the tissue wall properties are analyzed over wide ranges of simultaneous circumferential and longitudinal deformations. The type of loading chosen is 'physiological' i.e. symmetric: the cylindrical segments are subjected to internal pressure and axial prestretch without torsion or shear. Several aspects pertaining to the choice of parameters characterizing the material are discussed and the analysis pertaining to the deformational behavior of a hypothetical compliant tube with Hookean wall material is presented. The experimental results show that while rubber response can be adequately represented as linearly elastic and isotropic, the overall response of vascular tissue is highly non-linear and anisotropic. However, for states of deformation that occur in vivo, the elasticity of arteries is quite similar to that of rubber tubes and as such the arterial wall may be viewed as incrementally isotropic for the range of deformations that occur in vivo.     

Passive elastic wall stiffness of the left ventricle: A comparison between linear theory and large deformation theory

Assuming a spherical geometry for the left ventricle, passive elastic stiffness-stress relations have been obtained on the basis of linear elasticity theory and large deformation theory. Employing pressure-volume aata taken from rat hearts of various age groups, it is shown that young rat heart muscle (1 month) is stiffer than either adult (7 months) or old rat heart muscle (17 months). Although the qualitative results are similar for both elasticity theories, the large deformation theory gave results in closer agreement with those obtained from papillary muscle studies. These results imply that stiffness of muscleper se can be assessed from left ventricular pressure-volume data.     

Structural and functional analyses of the wheat genomes based on expressed sequence tags (ESTs) related to abiotic stresses.

To gain insights into the structure and function of the wheat (Triticum aestivum L.) genomes, we identified 278 ESTs related to abiotic stress (cold, heat, drought, salinity, and aluminum) from 7671 ESTs previously mapped to wheat chromosomes. Of the 278 abiotic stress related ESTs, 259 (811 loci) were assigned to chromosome deletion bins and analyzed for their distribution pattern among the 7 homoeologous chromosome groups. Distribution of abiotic stress related EST loci were not uniform throughout the different regions of the chromosomes of the 3 wheat genomes. Both the short and long arms of group 4 chromosomes showed a higher number of loci in their distal regions compared with proximal regions. Of the 811 loci, the number of mapped loci on the A, B, and D genomes were 258, 281, and 272, respectively. The highest number of abiotic stress related loci were found in homoeologous chromosome group 2 (142 loci) and the lowest number were found in group 6 (94 loci). When considering the genome-specific ESTs, the B genome showed the highest number of unique ESTs (7 loci), while none were found in the D genome. Similarly, considering homoeologous group-specific ESTs, group 2 showed the highest number with 16 unique ESTs (58 loci), followed by group 4 with 9 unique ESTs (33 loci). Many of the classified proteins fell into the biological process categories associated with metabolism, cell growth, and cell maintenance. Most of the mapped ESTs fell into the category of enzyme activity (28%), followed by binding activity (27%). Enzymes related to abiotic stress such as beta-galactosidase, peroxidase, glutathione reductase, and trehalose-6-phosphate synthase were identified. The comparison of stress-responsive ESTs with genomic sequences of rice (Oryza sativa L.) chromosomes revealed the complexities of colinearity. This bin map provides insight into the structural and functional details of wheat genomic regions in relation to abiotic stress.     

Measurement of wall motion and wall shear in a compliant arterial cast

Initial measurements of the time-varying wall shear rate at two sites in a compliant cast of a human aortic bifurcation are presented. The shear rates were derived from flow velocities measured by laser Doppler velocimetry (LDV) near the moving walls of the cast. To derive these shear rate values, the distance from the velocimeter sampling volume to the cast wall must be known. The time variation of this distance was obtained from LDV measurements of the velocity of the wall itself.     

Influence of hypertension and of antihypertensive drugs on the arterial wall

This paper reviews some of the experimental data regarding the effects of hypertension and antihypertensive drugs on the arterial wall. Hypertension induces major changes in both the arterial media and intima. Experimental studies from our own and other laboratories have demonstrated that medial smooth muscle cells in several forms of hypertension in the rat undergo hypertrophy and nuclear polyploidy which contribute, along with connective tissue alterations, to a large increase in medial mass. Our studies in the deoxycorticosterone/salt-hypertensive rat indicate that such changes may be difficult to regress, despite prolonged control of the hypertension. In the arterial intima, major alterations in the endothelium are induced by hypertension in association with increase in arterial permeability. Marked enhancements of adherence of circulating white blood cells to the endothelium can also be demonstrated along with penetration of blood monocytes and their accumulation in the subendothelial space. Hypertension also appears to stimulate the migration and proliferation of smooth muscle cells in the intima, and evidence is beginning to accumulate that endogenous growth factors within the artery may be involved in this process. Essentially all of the intimal changes which we have observed as a result of arterial hypertension are also present with cholesterol feeding although intimal accumulation of lipid and formation of atherosclerotic plaques do not occur with hypertension alone. On the other hand, in hypercholesterolemic animals, hypertension appears to act as a promoter of atherogenesis. Several antihypertensive drugs may influence the atherosclerotic process. The experimental data regarding the effects of beta blockers and calcium antagonists in the cholesterol-fed rabbit are discussed. Though of considerable interest, the clinical relevance of the findings remains uncertain.     

A new method for isolating large quantities of Arabidopsis trichomes for transcriptome, cell wall and other types of analyses

A new procedure has been developed for the isolation of wild-type and mutant Arabidopsis trichomes. The isolated trichomes maintained enzymatic activity and were used for DNA, protein, and RNA isolation. The RNA was used to generate probes suitable for Affymetrix analysis. The validity of the Affymetrix results was confirmed by quantitative PCR analysis on a subset of genes that are preferentially expressed in trichomes or leaves. Sufficient quantities of trichomes were isolated to probe the biochemical nature of trichome cell walls. These analyses provide evidence for the presence of lignin in Arabidopsis trichome cell walls. The monosaccharide analysis and positive staining with ruthenium red indicates that the walls also contain a large portion of pectin. The 2.23-fold ratio of pectin-related sugars compared with potential cellulosic glucose suggests that the polysaccharides of the trichome cell walls are more like those of typical primary walls even though the wall becomes quite thick. Overall, these analyses open the door to using the Arabidopsis trichome cell wall as an excellent model to probe various questions concerning plant cell wall biosynthesis.     

Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions

We developed a methodology to assess and compare the prediction quality of cardiovascular models for patient-specific simulations calibrated with uncertainty-hampered measurements. The methodology was applied in a one-dimensional blood flow model to estimate the impact of measurement uncertainty in wall model parameters on the predictions of pressure and flow in an arterial network. We assessed the prediction quality of three wall models that have been widely used in one-dimensional blood flow simulations. A 37-artery network, previously used in one experimental and several simulation studies, was adapted to patient-specific conditions with a set of three clinically measurable inputs: carotid–femoral wave speed, mean arterial pressure and area in the brachial artery. We quantified the uncertainty of the predicted pressure and flow waves in eight locations in the network and assessed the sensitivity of the model prediction with respect to the measurements of wave speed, pressure and cross-sectional area. Furthermore, we developed novel time-averaged sensitivity indices to assess the contribution of model parameters to the uncertainty of time-varying quantities (e.g., pressure and flow). The results from our patient-specific network model demonstrated that our novel indices allowed for a more accurate sensitivity analysis of time-varying quantities compared to conventional Sobol sensitivity indices.