On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.

A biomechanical model of sagittal tongue bending

The human tongue is a structurally complex and extremely flexible organ. In order to better understand the mechanical basis for lingual deformations, we modeled a primitive movement of the tongue, sagittal tongue bending. We hypothesized that sagittal bending is a synergistic deformation derived from co-contraction of the longitudinalis and transversus muscles. Our model of tongue bending was based on classical bimetal strip theory, in which curvature is produced when one muscle layer contracts more so than another. Contraction was modulated via mismatched thermal expansion coefficients and temperature change (to simulate muscular contraction). Our results demonstrated that synergistic contraction produced curvature and strain results which were in better correspondence to empirical results derived from tagging MRI than were the results of contraction of the longitudinalis muscle alone. This fundamental reliance of tongue bending on the synergistic contraction of its intrinsic fibers supports the muscular hydrostat theory of tongue function.

Neutrophil transit times through pulmonary capillaries: the effects of capillary geometry and fMLP-stimulation

The deformations of neutrophils as they pass through the pulmonary microcirculation affect their transit time, their tendency to contact and interact with the endothelial surface, and potentially their degree of activation. Here we model the cell as a viscoelastic Maxwell material bounded by constant surface tension and simulate indentation experiments to quantify the effects of (N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLP)-stimulation on its mechanical properties (elastic shear modulus and viscosity). We then simulate neutrophil transit through individual pulmonary capillary segments to determine the relative effects of capillary geometry and fMLP-stimulation on transit time. Indentation results indicate that neutrophil viscosity and shear modulus increase by factors of 3.4, for 10(-9) M fMLP, and 7.3, for 10(-6) M fMLP, over nonstimulated cell values, determined to be 30.8 Pa.s and 185 Pa, respectively. Capillary flow results indicate that capillary entrance radius of curvature has a significant effect on cell transit time, in addition to minimum capillary radius and neutrophil stimulation level. The relative effects of capillary geometry and fMLP on neutrophil transit time are presented as a simple dimensionless expression and their physiological significance is discussed.

Numerical analysis of blood flow through a stenosed artery using a coupled, multiscale simulation method

A global system model of the systemic circulation is combined with a local finite element solution to simulate blood flow in a stenosed coronary artery. Local fluid dynamic issues arise in connection with the detailed flow patterns within the stenosed coronary artery while the global system model is used to simulate the response of the rest of the circulation to the local perturbation. A PISO type finite element technique is employed to compute the local blood flow. The Navier-Stokes equations are solved with the assumption of viscous incompressible flow across the stenosed coronary artery. A detailed lumped parameter model simulates the characteristics of the coronary circulation and is imbedded in a coarse-grained lumped parameter model of the entire cardiovascular system. These two methods are coupled in that the lumped parameter calculations provide the time-dependent boundary conditions for the local finite element calculation. In turn, the local fluid dynamical computation provides estimates for the pressure drop across the stenosis, which is subsequently used to refine the lumped parameter calculation. Results are obtained for an axisymmetric coronary artery model with a stenosis of 90% area reduction over one cardiac cycle. Numerical results show that the flow rate and resistance are strongly coupled. Compared with the flow rate distribution computed from the global simulation with constant resistance, the coupled solution predicts a flow rate with only slight changes. The high flow rate during diastole increases the stenosis pressure drop and resistance. In turn, this increased resistance of the stenosis slightly reduces the flow rate computed in the lumped parameter simulation.

Mucosal folding in biologic vessels

A two-layer model is used to simulate the mechanical behavior of an airway or other biological vessel under external compressive stress or smooth muscle constriction sufficient to cause longitudinal mucosal buckling. Analytic andfinite element numerical methods are used to examine the onset of buckling. Post-buckling solutions are obtained by finite element analysis, then verified with large-scale physical model experiments. The two-layer model provides insight into how the stiffness of a vessel wall changes due to changes in the geometry and intrinsic material stiffnesses of the wall components. Specifically, it predicts that the number of mucosal folds in the buckled state is diminished most by increased thickness of the inner collagen-rich layer, and relatively little by increased thickness of the outer submucosal layer. An increase in the ratio of the inner to outer material stiffnesses causes an intermediate reduction in the number of folds. Results are cast in a simple form that can easily be used to predict buckling in a variety of vessels. The model quantitatively confirms that an increase in the thickness of the inner layer leads to a reduction in the number of mucosal folds, and further, that this can lead to increased vessel collapse at high levels of smooth muscle constriction.

Endothelial nitric oxide production during in vitro simulation of external limb compression

External pneumatic compression (EPC) is effective in preventing deep vein thrombosis (DVT) and is thought to alter endothelial thromboresistant properties. We investigated the effect of EPC on changes in nitric oxide (NO), a critical mediator in the regulation of vasomotor and platelet function. An in vitro cell culture system was developed to simulate flow and vessel collapse conditions under EPC. Human umbilical vein endothelial cells were cultured and subjected to tube compression (C), pulsatile flow (F), or a combination of the two (FC). NO production and endothelial nitric oxide synthase (eNOS) mRNA expression were measured. The data demonstrate that in the F and FC groups, there is a rapid release of NO followed by a sustained increase. NO production levels in the F and FC groups were almost identical, whereas the C group produced the same low amount of NO as the control group. Conditions F and FC also upregulate eNOS mRNA expression by a factor of 2.08 +/- 0.25 and 2.11 +/- 0.21, respectively, at 6 h. Experiments with different modes of EPC show that NO production and eNOS mRNA expression respond to different time cycles of compression. These results implicate enhanced NO release as a potentially important factor in the prevention of DVT.

Model-based assessment of cardiovascular health from noninvasive measurements

Cardiovascular health is currently assessed through a variety of hemodynamic parameters, many of which can only be determined by invasive measurement often requiring hospitalization. A noninvasive method of evaluating several of these parameters such as systemic vascular resistance (SVR), maximum left ventricular elasticity (E(LV)), end diastolic volume (VED), and cardiac output, is presented. The method has three elements: (1) a distributed model of the human cardiovascular system (Ozawa et aL, Ann. Biomed. Eng. 29:284-297, 2001) to generate a solution library that spans the anticipated range of parameter values, (2) a method for establishing the multidimensional relationship between features computed from the arterial blood pressure and/or flow traces (e.g., mean arterial pressure, pulse amplitude, mean flow velocity) and the critical hemodynamic parameters, and (3) a parameter estimation method that yields the best fit between measured and computed data. Sensitivity analyses were used to determine the critical parameters, and the influence of fixed model parameters. Using computer-generated brachial pressure and velocity profiles (which can be measured noninvasively), the error associated with this method was found to be less than 3% for SVR, and less than 10% for E(LV) and V(ED). Simulations were also performed to test the ability of the approach to predict changes in SVR and E(LV) from an initial base line state.

Three-dimensional cellular deformation analysis with a two-photon magnetic manipulator workstation

The ability to apply quantifiable mechanical stresses at the microscopic scale is critical for studying cellular responses to mechanical forces. This necessitates the use of force transducers that can apply precisely controlled forces to cells while monitoring the responses noninvasively. This paper describes the development of a micromanipulation workstation integrating two-photon, three-dimensional imaging with a high-force, uniform-gradient magnetic manipulator. The uniform-gradient magnetic field applies nearly uniform forces to a large cell population, permitting statistical quantification of select molecular responses to mechanical stresses. The magnetic transducer design is capable of exerting over 200 pN of force on 4.5-microm-diameter paramagnetic particles and over 800 pN on 5.0-microm ferromagnetic particles. These forces vary within +/-10% over an area 500 x 500 microm2. The compatibility with the use of high numerical aperture (approximately 1.0) objectives is an integral part of the workstation design allowing submicron-resolution, three-dimensional, two-photon imaging. Three-dimensional analyses of cellular deformation under localized mechanical strain are reported. These measurements indicate that the response of cells to large focal stresses may contain three-dimensional global deformations and show the suitability of this workstation to further studying cellular response to mechanical stresses.

Computational model of cardiovascular function during orthostatic stress

Orthostatic intolerance following spaceflight remains a critical problem in the current life-science space program. The study presented in this paper is part of an ongoing effort to use mathematical models to investigate the effects of gravitational stresses on the cardiovascular system of normals and microgravity adapted individuals. We employ a twelve compartment lumped parameter representation of the hemodynamic system coupled to set-point models of the arterial baroreflex and the cardiopulmonary reflex to investigate the transient response of heart rate to orthostatic stress. We simulate current hypotheses concerning the mechanisms underlying post-spaceflight orthostatic intolerance over a range of physiologically reasonable values and compare the simulations to astronaut stand-test data pre- and post-flight. Furthermore, we explore the effects of a potential countermeasure.

Computational modeling of cardiovascular response to orthostatic stress

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance.

Zero-stress state of intra- and extraparenchymal airways from human, pig, rabbit, and sheep lung

Alterations in airway wall anatomic properties and the consequential effects on airway narrowing have been assessed by use of computational models. In these models, it is generally assumed that at zero transmural pressure the airway wall exists in a zero-stress state. Many studies have shown that this is often not the case, as evidenced by a nonzero opening angle. In this study, we measured the opening angle of airway rings at zero transmural pressure to test this assumption. The airway tree was dissected from human, pig, sheep, and rabbit lungs. Airways were excised from the tree, and the opening angle was measured. There were obvious species and regional differences in opening angle. Rabbit airways from both extraparenchymal and intraparenchymal sites exhibited marked opening angles (7-82 degrees). Extraparenchymal airways from sheep had large opening angles (up to 50 degrees), but ovine intraparenchymal airways had small opening angles. Measurable opening angles were rarely observed in human and porcine airways of any size. The assumption of a stable zero-stress state at zero transmural pressure is therefore valid for human and porcine, but not rabbit and sheep, airways.

Computational models of cardiovascular function for analysis of post-flight orthostatic intolerance

The work presented in this paper is part of an ongoing effort to use mathematical models to investigate the effects of microgravity on the cardiovascular system. In particular, a thirteen compartment lumped parameter representation of the cardiovascular system is used to simulate some of the current hypotheses concerning the mechanism of post-flight orthostatic intolerance. Simulations are compared to astronaut stand test data pre - and post-flight in an effort to quantitatively evaluate alternative hypotheses.

Self-assembly of a beta-sheet protein governed by relief of electrostatic repulsion relative to van der Waals attraction

Using a synthetic oligopeptide, n-FKFEFKFEFKFE-c (KFE12), representative of a class of peptides that can undergo self-assembly into a three-dimensional matrix biomaterial, we show that the self-assembly occurs when solution conditions reduce intermolecular electrical double-layer repulsion below van der Waals attraction in accord with DLVO theory. This theory predicts that a critical coagulation concentration of counterions should be required to allow assembly and that this concentration should be inversely proportional to the valence of the counterion raised to the sixth power. Our experimental results show that KFE12, at low pH, exhibits critical coagulation concentrations in each of three different salt solutions, KCl, K2SO4, and K3Fe(CN)6, and that the relative values of these critical concentrations follow the predicted dependence upon anion valence. The theory further predicts that self-assembly should occur when the oligopeptide is electrically neutral even in the absence of exogenous salt. Our experimental results show that KFE12 indeed forms gels when neutralized with NaOH. Thus, we have gained fundamental theoretical understanding of how to control the assembly of this class of oligopeptide-based biomaterials.

Airway wall mechanics

The dimensions, composition, and stiffness of the airway wall are important determinants of airway cross-sectional area during dynamic collapse in a forced expiration or when airway smooth muscle is constricted. Under these circumstances, airway caliber is determined by an interaction between the forces acting to open the airway (parenchymal tension and wall stiffness) and those acting to close it (smooth-muscle force and surface tension at the inner gas-liquid interface). Experimental measurements and theoretical models of the airway tube law (relationship between cross-sectional area and transmural pressure) are presented. Data are presented for the elastic properties of the wall tissue. Simulations of airway constriction in normal and asthmatic airways are discussed. To the extent possible, comparisons are presented between the various models and existing experimental data.

Cellular fluid mechanics

The coupling of fluid dynamics and biology at the level of the cell is an intensive area of investigation because of its critical role in normal physiology and disease. Microcirculatory flow has been a focus for years, owing to the complexity of cell-cell or cell-glycocalyx interactions. Noncirculating cells, particularly those that comprise the walls of the circulatory system, experience and respond biologically to fluid dynamic stresses. In this article, we review the more recent studies of circulating cells, with an emphasis on the role of the glycocalyx on red-cell motion in small capillaries and on the deformation of leukocytes passing through the microcirculation. We also discuss flows in the vicinity of noncirculating cells, the influence of fluid dynamic shear stress on cell biology, and diffusion in the lipid bi-layer, all in the context of the important fluid-dynamic phenomena.

Control of self-assembling oligopeptide matrix formation through systematic variation of amino acid sequence

In order to elucidate design principles for biocompatible materials that can be created by in situ transformation from self-assembling oligopeptides, we investigate a class of oligopeptides that can self-assemble in salt solutions to form three-dimensional matrices. This class of peptides possesses a repeated sequence of amino acid residues with the type: hydrophobic/negatively-charged/hydrophobic/positively-charged. We systematically vary three chief aspects of this sequence type: (1) the hydrophobic side chains: (2) the charged side-chains: and (3) the number of repeats. Employing a rheometric assay to judge matrix formation, we determine the critical concentration of NaCl salt solution required to drive transformation from viscous state to gel state. We find that increasing side-chain hydrophobicity decreases the critical salt concentration in accord with our previous validation of DLVO theory for explaining this self-assembly phenomenon Caplan et al. (Biomacromolecules 1 (2000) 627). Further, we find that increasing the number of repeats yields a biphasic dependence-first decreasing, then increasing, the critical salt concentration. We believe that this result is likely due to an unequal competition between a greater hydrophobic (favorable) effect and a greater entropic (unfavorable) effect as the peptide length is increased. Finally, we find that we can use this understanding to rationally alter the charged side-chains to create a self-assembling oligopeptide sequence that at pH 7 remains viscous in the absence of salt but gels in the presence of physiological salt concentrations, a highly useful property for technological applications.

Receptor-based differences in human aortic smooth muscle cell membrane stiffness

Cells respond to mechanical stimuli with diverse molecular responses. The nature of the sensory mechanism involved in mechanotransduction is not known, but integrins may play an important role. The integrins are linked to both the cytoskeleton and extracellular matrix, suggesting that probing cells via integrins should yield different mechanical properties than probing cells via non-cytoskeleton-associated receptors. To test the hypothesis that the mechanical properties of a cell are dependent on the receptor on which the stress is applied, human aortic smooth muscle cells were plated, and magnetic beads, targeted either to the integrins via fibronectin or to the transferrin receptor by use of an IgG antibody, were attached to the cell surface. The resistance of the cell to deformation ("stiffness") was estimated by oscillating the magnetic beads at 1 Hz by use of single-pole magnetic tweezers at 2 different magnitudes. The ratio of bead displacements at different magnitudes was used to explore the mechanical properties of the cells. Cells stressed via the integrins required approximately 10-fold more force to obtain the same bead displacements as the cells stressed via the transferrin receptors. Cells stressed via integrins showed stiffening behavior as the force was increased, whereas this stiffening was significantly less for cells stressed via the transferrin receptor (P<0.001). Mechanical characteristics of vascular smooth muscle cells depend on the receptor by which the stress is applied, with integrin-based linkages demonstrating cell-stiffening behavior.

Mechanical stress is communicated between different cell types to elicit matrix remodeling

Tissue remodeling often reflects alterations in local mechanical conditions and manifests as an integrated response among the different cell types that share, and thus cooperatively manage, an extracellular matrix. Here we examine how two different cell types, one that undergoes the stress and the other that primarily remodels the matrix, might communicate a mechanical stress by using airway cells as a representative in vitro system. Normal stress is imposed on bronchial epithelial cells in the presence of unstimulated lung fibroblasts. We show that (i) mechanical stress can be communicated from stressed to unstressed cells to elicit a remodeling response, and (ii) the integrated response of two cell types to mechanical stress mimics key features of airway remodeling seen in asthma: namely, an increase in production of fibronectin, collagen types III and V, and matrix metalloproteinase type 9 (MMP-9) (relative to tissue inhibitor of metalloproteinase-1, TIMP-1). These observations provide a paradigm to use in understanding the management of mechanical forces on the tissue level.

Numerical simulation of enhanced external counterpulsation

Enhanced external counterpulsation (EECP) is a noninvasive, counterpulsative method to provide temporary aid to the failing heart by sequentially inflating cuffs on the lower extremity out-of-phase with the left ventricle. Optimization of the method necessitates consideration of the hemodynamics created by EECP and the mode of action providing patient benefit. A computational model based on the governing one-dimensional equations is developed that simulates cardiovascular hemodynamics during EECP. The model includes a 30-element arterial system including the left ventricle, bifurcations, and peripheral arterial vessels. Effects of vessel collapse as external pressure is applied, arterial refilling on pressure release, changes in aortic pressure, and shear stress generated in the arteries are each investigated. Device parameters are systematically varied to determine their effect on system performance. Results show the potential for significant collapse and shear augmentation throughout the arteries of the lower extremity. Performance is strongly influenced by the mean level of external pressurization and the timing of cuff inflation, but less so by the relative timing and pressure differences between cuff segments.

The impact of calcification on the biomechanical stability of atherosclerotic plaques

BACKGROUND

Increased biomechanical stresses in the fibrous cap of atherosclerotic plaques contribute to plaque rupture and, consequently, to thrombosis and myocardial infarction. Thin fibrous caps and large lipid pools are important determinants of increased plaque stresses. Although coronary calcification is associated with worse cardiovascular prognosis, the relationship between atheroma calcification and stresses is incompletely described.

METHODS AND RESULTS

To test the hypothesis that calcification impacts biomechanical stresses in human atherosclerotic lesions, we studied 20 human coronary lesions with techniques that have previously been shown to predict plaque rupture locations accurately. Ten ruptured and 10 stable lesions derived from post mortem coronary arteries were studied using large-strain finite element analysis. Maximum stress was not correlated with percentage of calcification, but it was positively correlated with the percentage of lipid (P:=0.024). When calcification was eliminated and replaced with fibrous plaque, stress changed insignificantly; the median increase in stress for all specimens was 0.1% (range, 0% to 8%; P:=0.85). In contrast, stress decreased by a median of 26% (range, 1% to 78%; P:=0.02) when lipid was replaced with fibrous plaque.

CONCLUSIONS

Calcification does not increase fibrous cap stress in typical ruptured or stable human coronary atherosclerotic lesions. In contrast to lipid pools, which dramatically increase stresses, calcification does not seem to decrease the mechanical stability of the coronary atheroma.

Computational modeling of RBC and neutrophil transit through the pulmonary capillaries

A computational model of the pulmonary microcirculation is developed and used to examine blood flow from arteriole to venule through a realistically complex alveolar capillary bed. Distributions of flow, hematocrit, and pressure are presented, showing the existence of preferential pathways through the system and of large segment-to-segment differences in all parameters, confirming and extending previous work. Red blood cell (RBC) and neutrophil transit are also analyzed, the latter drawing from previous studies of leukocyte aspiration into micropipettes. Transit time distributions are in good agreement with in vivo experiments, in particular showing that neutrophils are dramatically slowed relative to the flow of RBCs because of the need to contract and elongate to fit through narrower capillaries. Predicted neutrophil transit times depend on how the effective capillary diameter is defined. Transient blockage by a neutrophil can increase the local pressure drop across a segment by 100--300%, leading to temporal variations in flow and pressure as seen by videomicroscopy. All of these effects are modulated by changes in transpulmonary pressure and arteriolar pressure, although RBCs, neutrophils, and rigid microspheres all behave differently.

Computational modeling of RBC and neutrophil transit through the pulmonary capillaries

A computational model of the pulmonary microcirculation is developed and used to examine blood flow from arteriole to venule through a realistically complex alveolar capillary bed. Distributions of flow, hematocrit, and pressure are presented, showing the existence of preferential pathways through the system and of large segment-to-segment differences in all parameters, confirming and extending previous work. Red blood cell (RBC) and neutrophil transit are also analyzed, the latter drawing from previous studies of leukocyte aspiration into micropipettes. Transit time distributions are in good agreement with in vivo experiments, in particular showing that neutrophils are dramatically slowed relative to the flow of RBCs because of the need to contract and elongate to fit through narrower capillaries. Predicted neutrophil transit times depend on how the effective capillary diameter is defined. Transient blockage by a neutrophil can increase the local pressure drop across a segment by 100--300%, leading to temporal variations in flow and pressure as seen by videomicroscopy. All of these effects are modulated by changes in transpulmonary pressure and arteriolar pressure, although RBCs, neutrophils, and rigid microspheres all behave differently.

Dynamic behavior of lung surfactant

We have previously developed an adsorption-limited model to describe the exchange of lung surfactant and its fractions to and from an air-liquid interface in oscillatory surfactometers. Here we extend this model to allow for diffusion in the liquid phase. Use of the model in conjunction with experimental data in the literature shows that diffusion-limited transport i.s important for characterizing the transient period from the start of oscillations to the achievement of steady-state conditions. Matching previous data shows that upon high levels of film compression, large changes occur in adsorption rate, desorption rate, and diffusion constant, consistent with what one might expect if the subsurface region was greatly enriched in DPPC. Collapse of the surfactant film that occurs during compression leads to a .significant elevation of surfactant concentration immediately heneath the interface, consistent with the subsurface depot of surfactant that has heen postulated by other investigators. Modeling studies also uncovered a phenomenon of surfactant behavior in which the interfacial tension remains constant at its minimum equilibrium value while the film is compressed, hut without collapse of the film. The phenomenon was due to desorption of surfactant from the interface and termed "pseudo-film collapse.'' The new model also gave improved agreement with steady-state oscillatory cycling in a pulsating bubble surfactometer.

Model-based parameter estimation using cardiovascular response to orthostatic stress

This paper presents a cardiovascular model that is capable of simulating the short-term (< or approximately equal to 3 min) transient hemodynamic response to gravitational stress and a gradient-based optimization method that allows for the automated estimation of model parameters from simulated or experimental data. We perform a sensitivity analysis of the transient heart rate response to determine which parameters of the model impact the heart rate dynamics significantly. We subsequently include only those parameters in the estimation routine that impact the transient heart rate dynamics substantially. We apply the estimation algorithm to both simulated and real data and showed that restriction to the 20 most important parameters does not impair our ability to match the data.