Assessing micromechanical properties of cells with atomic force microscopy: importance of the contact point.

Mechanical properties are obtainable from atomic force microscopy (AFM) indentation force-depth curves, which are calculated from relationships between tip deflection and cantilever position, i.e. deflection curves. Indentation depth is the difference between tip deflections on a rigid and a soft material for the same amount of cantilever advancement, after contact is made. Since the contact point cannot be unequivocally identified from experimental data, there is some uncertainty in estimating material properties. Using simulations, this study examines some important issues related to the influence of contact point identification on estimated material properties. Simulations for linear materials using a typical stiffness for an AFM cantilever demonstrate that certain portions of the post-contact region of deflection curves for soft and very stiff materials can be approximated by quadratic and linear functions, respectively. Based on these findings, we first develop and verify an objective, automatic method to identify the contact point for materials with linear properties. We then assess the effect of misidentifying the contact point, with and without noise. If the contact point is missed by <50 nm, material properties for small indentations are erroneous but the error decreases asymptotically beyond 200 nm of indentation and the correct estimate of material stiffness is obtained. If the contact point is missed by >100 nm, however, the true material properties cannot be estimated accurately. Noise adds to uncertainty in material properties at small indentations but the combined effect of missing the contact point and noise is dominated by the former. Even though the algorithm was developed for linear materials, it is also suitable for certain nonlinear materials making it more generally applicable.

Functional correlates of central arterial geometric phenotypes.

We have assessed the functional correlates of common carotid artery (CCA) arterial geometry, derived by combining a measure of vascular mass (VM) with the wall-to-lumen (W/L) ratio in both untreated hypertensive (HT) and normotensive (NT; blood pressure <140/90 mm Hg) subjects of a broad age span (30 to 79 years) of both genders. Brachial systolic, diastolic, and pulse (SBP, DBP, PP) pressures; CCA SBP and PP; CCA diameter (D); intima-media thickness (IMT); relative distensibility; circumferential wall stress (MBPxW/L); fluid shear stress (FSS); strain; augmentation index (AGIh); and aortic pulse wave velocity (PWV) were measured in 680 NT and 635 untreated HT Taiwanese men and women. Carotid geometric phenotypes (CGPs) were derived from ultrasonographic measures of VM and W/L ratio. A normal CGP (CGP1) was defined as that within the 95th NT percentile of age- and gender-specific VM and W/L means. Three "deviant" CGPs were defined as follows: CGP2 or remodeling, ie, a normal VM coupled with an increased W/L; CGP3 or hypertrophy, ie, an increase in both VM and W/L; and CGP4 or hypertrophy with dilation, ie, an increased VM with normal W/L. The prevalence of specific CGPs in the total sample was 83.4% for CGP1, 5.5% for CGP2, 2.2% for CGP3, and 8.9% for CGP4. Compared with CGP1, all deviant CGPs had increased carotid resistance, had higher CCA circumferential wall stress, and varied in blood flow velocity. Compared with CGP1, CGP2 subjects were more likely to be women (69.3% versus 45.9%), were on average 10 years older, and had similar central and brachial BP levels, PWV, and AGIh but had increased strain, higher distensibility, lower flow, and a higher FSS. CGP3 subjects did not differ in age or gender but had a higher prevalence of HT; higher circumferential stress, PWV, and distensibility; and lower flow, as well as a trend toward higher SBP, PP, and AGIh and lower FSS. CGP4 subjects did not differ in age or gender but exhibited higher AGIh and aortic PWV, lower distensibility and FSS, and unchanged strain and flow. CGP4 was the only deviant CGP in which the average brachial or central arterial pressures were significantly increased. CGP4 subjects also had the highest prevalence of HT among all the CGPs (77.8% versus 45% in CGP1). CGPs exhibit some common mechanical or functional properties but each also exhibits a unique profile. Although differing quantitatively in NT and HT and at young and older age, the characteristic functional profile of a given CGP is preserved, regardless of age or BP status. A normal CGP is characterized by a low circumferential wall stress and high FSS. Each deviant CGP is characterized by a unique combination of increased circumferential wall stress, with variable FSS, strain, distensibility, central BP, and late pressure augmentation. The interplay among these factors, particularly circumferential wall and FSS, likely determines the CGP; conversely, the resultant CGP may modulate the FSS and wall stress for a given pressure and flow.

Specificity of endothelial cell reorientation in response to cyclic mechanical stretching.

Evidence suggests that cellular responses to mechanical stimuli depend specifically on the type of stimuli imposed. For example, when subjected to fluid shear stress, endothelial cells align along the flow direction. In contrast, in response to cyclic stretching, cells align away from the stretching direction. However, a few aspects of this cell alignment response remain to be clarified: (1) Is the cell alignment due to actual cell reorientation or selective cell detachment? (2) Does the resulting cell alignment represent a response of the cells to elongation or shortening, or both? (3) Does the cell alignment depend on the stretching magnitude or rate, or both? Finally, the role of the actin cytoskeleton and microtubules in the cell alignment response remains unclear. To address these questions, we grew human aortic endothelial cells on deformable silicone membranes and subjected them to three types of cyclic stretching: simple elongation, pure uniaxial stretching and equi-biaxial stretching. Examination of the same cells before and after stretching revealed that they reoriented. Cells subjected to either simple elongation or pure uniaxial stretching reoriented specifically toward the direction of minimal substrate deformation, even though the directions for the two types of stretching differed by only about 20 degrees. At comparable stretching durations, the extent of cell reorientation was more closely related to the stretching magnitude than the stretching rate. The actin cytoskeleton of the endothelial cell subjected to either type of stretching was reorganized into parallel arrays of actin filaments (i.e., stress fibers) aligned in the direction of the minimal substrate deformation. Furthermore, in response to equi-biaxial stretching, the actin cytoskeleton was remodeled into a "tent-like" structure oriented out of the membrane plane-again towards the direction of the minimal substrate deformation. Finally, abolishing microtubules prevented neither the formation of stress fibers nor cell reorientation. Thus, endothelial cells respond very specifically to the type of deformation imposed upon them.

Evidence for stretch-induced resistance increase of proximal coronary microcirculation.

We investigated the influence of stretch on regional hemodynamic parameters of the septal circulation. We used a similar experimental setup and mathematical model, as described previously (14). Five ventricular septa were isolated from anesthetized dogs, sutured to a biaxial stretching apparatus, and perfused with an oxygenated perfluorochemical emulsion at maximal vasodilation. Under unloaded and biaxially stretched conditions, flow and septal thickness (to index vascular volume) were measured continuously. Pressure was varied sinusoidally at 30, 50, and 70 mmHg with amplitude of 7.5 mmHg over frequencies ranging between 0.015 and 7 Hz. Admittance (flow/pressure) and capacitance (thickness/pressure) transfer functions were calculated and interpreted in terms of a two-compartmental model with volume-dependent resistances. Parameter estimation showed that the proximal resistance and compliance were unaffected, whereas the resistance of the proximal part of the microcirculation, including the small arterioles, increased with stretch. The effect of stretch on the distal resistance and capacitance, however, could not be determined unequivocally.

Leukotrienes and tyrosine phosphorylation mediate stretching-induced actin cytoskeletal remodeling in endothelial cells.

We studied actin cytoskeletal remodeling and the role of leukotrienes and tyrosine phosphorylation in the response of endothelial cells to different types of cyclic mechanical stretching. Human aortic endothelial cells were grown on deformable silicone membranes subjected to either cyclic one-directional (strip) stretching (10%, 0.5 Hz), or biaxial stretching. After 1 min of either type of stretching, actin cytoskeletons of the stretched cells were already disrupted. After stretching for 10 and 30 min, the percentage of the stretched cells that had disrupted actin cytoskeletons were significantly increased, compared with control cells without stretching. Also, at these two time points, biaxial stretching consistently produced higher frequencies of actin cytoskeleton disruption. At 3 h, strip stretching caused the formation of stress fiber bundles, which were oriented nearly perpendicular to the stretching direction. With biaxial stretching, however, actin cytoskeletons in many stretched cells were remodeled into three-dimensional actin structures protruding outside the substrate plane, within which cyclic stretching was applied. In both stretching conditions, actin filaments were formed in the direction without substrate deformation. Moreover, substantially inhibiting either leukotriene production with nordihydroguaiaretic acid or tyrosine phosphorylation with tyrphostin A25 did not block the actin cytoskeletal remodeling. However, inhibiting both leukotriene production and tyrosine phosphorylation completely blocked the actin cytoskeletal remodeling. Thus, the study showed that the remodeling of actin cytoskeletons of the stretched endothelial cells include rapid disruption first and then re-formation. The resulting pattern of the actin cytoskeleton after remodeling depends on the type of cyclic stretching applied, but under either type of cyclic stretching, the actin filaments are formed in the direction without substrate deformation. Finally, leukotrienes and tyrosine phosphorylation are necessary for actin cytoskeletal remodeling of the endothelial cells in response to mechanical stretching.

Dynamics of flow, resistance, and intramural vascular volume in canine coronary circulation.

Varying coronary volume will vary vascular resistance and thereby have an effect on coronary hemodynamics. Six ventricular septa were isolated from anesthetized dogs, dispersed in a biaxial stretch apparatus at diastolic stress, and perfused artificially with an oxygenated perfluorochemical emulsion at maximal vasodilation. Flow and thickness were measured continuously by an electromagnetic flow probe and sonomicrometer. Pressure was varied sinusoidally around 30, 50, and 70 mmHg with an amplitude of 7.5 mmHg; frequencies ranged between 0.015 and 7 Hz. Bode plots of admittance (flow/pressure) and capacitance (scaled thickness/pressure) were constructed. A two-compartment model was used in which the resistances vary with volume. Realistic values of microvascular compliance ( approximately 0.3 ml x mmHg(-1) x 100 g(-1)) were found. Values 10 times higher were then found when resistances were forced to be constant. We concluded that volume dependence of resistances have to be taken into account when dynamic or static pressure-flow relations are studied and conceal the effect of a large intramyocardial compliance on arterial hemodynamics.

Contractility affects stress fiber remodeling and reorientation of endothelial cells subjected to cyclic mechanical stretching.

We studied the effect of contractility on stress fiber remodeling and orientation response of human aortic endothelial cells subjected to cyclic mechanical stretching. The cells were grown on silicone membranes subjected to 10% cyclic pure uniaxial stretching in the presence or absence of 2,3 butanedione monoxime (BDM), a proven inhibitor of cellular contractility. It was found that treatment of the cells with BDM (40 mM) abolished stress fibers and blocked cell reorientation in response to cyclic stretching, indicating that contractility is required for these two cellular responses. When cells were stretched in the presence of N-acetylcysteine (NAG, 20 mM), a hydrogen peroxide (H2O2) scavenger, stress fibers were still formed and the cells reoriented--but more slowly. Specifically, compared with untreated cells, NAG treated cells after 0.5, 1, and 3 h of 10% stretching had significantly (p<0.005) less skewed orientation distributions than those of untreated cells. After the cells were treated with both NAG (20 mM) and nordihydroguaiaretic acid (NDGA, 50 microM), another antioxidant, however, stress fibers were abolished and cell reorientation was completely blocked. These results indicate that reactive oxygen species (ROS), including H2O2, affect stress fiber remodeling and reorientation of endothelial cells in response to cyclic stretching. We suggest that the effect of ROS on stress fiber remodeling and cell reorientation is due to the ability of ROS to regulate cellular contractility, which is crucial for these cellular responses.

Effect of vasoconstriction on coronary artery resistance changes caused by stretching surrounding myocardial tissue.

We previously showed that deformation of the cardiac tissue surrounding a dilated coronary artery changes its hydraulic resistance depending on the direction of stretch. Stretch parallel, but not perpendicular, to the vessel axis increased the hydraulic resistance. This asymmetric dependence of resistance on the direction of stretch was found at a low perfusion pressure only, presumably because this was the state in which surrounding fibers were sufficiently stretched to be able to exert their effects. When the vessel is vasoconstricted and its diameter decreases, this might alter the coupling between tissue and vessel. On the other hand, the stiffer vessel wall would be more difficult to deform, making the coupling less evident. The aim of this study was to test the hypothesis that, at this low perfusion pressure, the asymmetric resistance response to strain differs between the vasodilated and vasoconstricted states. We compared how the hydraulic resistance of an in situ segment of a vasodilated and then vasoconstricted epicardial coronary artery was affected by stretching the surrounding tissue by 10% in a direction parallel and then perpendicular to the vessel axis. Vasoconstriction increased the unstretched resistance of the vessel, demonstrating that the vessel diameter was decreased. In both vasomotor states the relative resistance changes to parallel and perpendicular tissue stretches were found to be similar. Thus, the effects of subtle differences in vessel cross-sectional shape underlying the resistance changes to tissue stretch in the vasodilated state - that should have been altered by vasoconstriction - were seemingly counterbalanced by increased vessel wall stiffness that decreased the manifestation of coupling between the vessel and the surrounding tissue.

Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy.

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.

Which arterial and cardiac parameters best predict left ventricular mass?

BACKGROUND: Many cardiovascular and noncardiovascular parameters are thought to be determinants of left ventricular mass (LVM). Complicated interactions necessitate the simultaneous measurement and consideration of each to determine their individual and collective impact on LVM. We undertook such a comprehensive study. METHODS AND RESULTS: The influence of anthropometry, cardiac size and contractility, arterial structure and function, as well as indices of lifestyle, physical activity, and dietary salt intake on LVM (by two-dimensionally guided M-mode echocardiography) was analyzed in 1315 Chinese subjects who were either normotensive or had untreated hypertension. Effects of many cardiac and arterial factors were assessed. In univariate analysis, almost all measured noncardiovascular, cardiac, and arterial variables were significantly correlated with LVM. In multivariate linear regression analyses, when age, sex, body habitus, fasting serum C-peptide level, dietary salt, physical activity, and lifestyle were accounted for, the optimum multivariate linear regression main effects model had an adjusted model r2 of 0.740, with 98% of the model variance accounted for by the 5 independent determinants of LVM: stroke volume (49.6%), systolic blood pressure (30.7%), contractility (14.7%), body mass index (1.8%), and aortic root diameter (1.6%). Other proposed arterial indices were significant independent determinants of LVM only when blood pressure was removed from the model and, even then, these indices not only resulted in less powerful prediction but also accounted for only a very small percentage of the total variance of LVM. CONCLUSIONS: In a large population, we (1) confirmed that age, body habitus, and some indexes of arterial structure and function are independent determinants of LVM; (2) found aortic diameter to be an independent structural determinant of LVM; (3) demonstrated that the effects of the derived measures of arterial function were small and provided no better predictive power than blood pressure alone; and (4) showed that when the best measures of cardiac and vascular load were included, the single most potent predictor was an index of left ventricular size.

A constitutive law for mitral valve tissue.

Biaxial mechanical testing and theoretical continuum mechanics analysis are employed to formulate a constitutive law for cardiac mitral valve anterior and posterior leaflets. A strain energy description is formulated based on the fibrous architecture of the tissue, accurately describing the large deformation, highly nonlinear transversely isotropic material behavior. The results show that a simple three-coefficient exponential constitutive law provides an accurate prediction of stress-stretch behavior over a wide range of deformations. Regional heterogenity may be accommodated by spatially varying a single coefficient and incorporating collagen fiber angle. The application of this quantitative information to mechanical models and bioprosthetic development could provide substantial improvement in the evaluation and treatment of valvular disease, surgery, and replacement.

A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus.

The constitutive law of the material comprising any structure is essential for mechanical analysis since this law enables calculation of the stresses from the deformations and vice versa. To date, there is no constitutive law for actively contracting myocardial tissue. Using 2,3-butanedione monoxime to protect the myocardium from mechanical trauma, we subjected thin midwall slices of rabbit myocardium to multiaxial stretching first in the passive state and then during steady-state barium contracture or during tetani in ryanodine-loaded tissue. Assuming transverse isotropy in both the passive and active conditions, we used our previously described methods (Humphrey et al., 1990a) to obtain both passive and active constitutive laws. The major results of this study are: (1) This is the first multiaxial constitutive law for actively contracting mammalian myocardium. (2) The functional forms of the constitutive law for barium contracture and ryanodine-induced tetani are the same but differ from those in the passive state. Hence, one cannot simply substitute differing values for the coefficients of the passive law to describe the active tissue properties. (3) There are significant stresses developed in the cross-fiber direction (more than 40 percent of those in the fiber direction) that cannot be attributed to either deformation effects or nonparallel muscle fibers. These results provide the foundation for future mechanical analyses of the heart.

Experimental and numerical analyses of indentation in finite-sized isotropic and anisotropic rubber-like materials.

Indentation tests perpendicular to the major plane of a material have been proposed as a means to index some of its in-plane mechanical properties. We showed the feasibility of such tests in myocardial tissue and established its theoretical basis with a formulation of small indentation superimposed on a finitely stretched half-space of isotropic materials. The purpose of this study is to better understand the mechanics of indentation with respect to the relative effects of indenter size, indentation depth, and specimen size, as well as the effects of material properties. Accordingly, we performed indentation tests on slabs of silicone rubber fabricated with both isotropic, as well as transversely isotropic, material symmetry. We performed indentation tests in different thickness specimens with varying sizes of indenters, amounts of indentation, and amounts of in-plane stretch. We used finite-element method simulations to supplement the experimental data. The combined experimental and modeling data provide the following useful guidelines for future indentation tests in finite-size specimens: (i) to avoid artifacts from boundary effects, the in-plane specimen dimensions should be at least 15 times the indenter size; (ii) to avoid nonlinearities associated with finite-thickness effects, the thickness-to-radius ratio should be >10 and thickness to indentation depth ratio should be >5; and (iii) we also showed that combined indentation and in-plane stretch could distinguish the stiffer direction of a transversely isotropic material.

The effects of left ventricular stretch versus cavity pressure on intramyocardial pressure.

OBJECTIVE: Since muscles, vessels and interstitial spaces are in close physical proximity in the heart wall, interstitial (i.e., intramyocardial) pressure (IMP) should be affected by the stresses of the vessels and/or the muscular tissue surrounding the interstitial spaces. Thus, we tested the hypothesis that increasing the stresses (or stiffness) of the surrounding tissues by muscle contraction or stretching--produced externally by stretching the LV cavity or internally by increasing coronary perfusion pressure--has a greater effect than LV cavity pressure per se on IMP. METHODS: In isolated rabbit hearts we measured IMP with small (< 10 microns diam) glass micropipettes while stretching the vessels (by changing coronary perfusion pressure) and the wall (by inflating a balloon in the left ventricle) during the passive state as well as during barium contracture. RESULTS: With LV cavity pressure equal to 0 (balloon open to air) or equal to 30 mmHg, a 20 mmHg increase in perfusion pressure increased IMP by 3.6 and 5 mmHg, respectively, in the passive state and by 7.6 and 7.9 mmHg, respectively, in the contracted state. This 30 mmHg increase in LV pressure produced a significant but small (3-5 mmHg) increase in IMP in the passive state but no effect in the contracture state. CONCLUSIONS: These results can be explained by a unifying concept in which stretching of the tissues surrounding the intestinal spaces--produced externally by increasing ventricular cavity size or internally by pressurizing vessels--but not LV cavity pressure per se is the major determinant of IMP.

Effects of contraction, perfusion pressure, and length on intramyocardial pressure in rat papillary muscle.

If intramyocardial pressure (IMP) is the pressure that causes coronary flow to stop, i.e., "backpressure," then it should be equal to the zero-flow perfusion pressure intercept (Pzf). Therefore we determined Pzf and IMP at zero flow (IMPzf) in papillary muscles suspended isometrically in a bath, superfused with a well-oxygenated Tyrode solution (27 degrees C), and perfused with Tyrode solution via the septal artery. For the IMP (servo-null) measurements, we used unbeveled glass micropipettes with a tip diameter of 3-4 microns. During diastolic arrest and systolic contracture (2 mM Ba21), perfusion pressure steps were applied, and the corresponding flow and IMP values were recorded. Fitting of the relationships, yielded Pzf and IMPzf. In the diastolically arrested muscle, perfusion pressure affected IMP. Pzf was much higher in systolically contracted muscle than in diastolically arrested muscle. The IMPzf in both conditions was significantly smaller than Pzf. Thus, even in this preparation with no ventricular pressure, IMP increases during contraction. We conclude that IMP arises from contraction per se but is not the pressure that causes the flow to stop.

Estimation of central aortic pressure waveform by mathematical transformation of radial tonometry pressure. Validation of generalized transfer function.

BACKGROUND: Central aortic pressures and waveform convey important information about cardiovascular status, but direct measurements are invasive. Peripheral pressures can be measured noninvasively, and although they often differ substantially from central pressures, they may be mathematically transformed to approximate the latter. We tested this approach, examining intersubject and intrasubject variability and the validity of using a single averaged transformation, which would enhance its applicability. METHODS AND RESULTS: Invasive central aortic pressure by micromanometer and radial pressure by automated tonometry were measured in 20 patients at steady state and during hemodynamic transients (Valsalva maneuver, abdominal compression, nitroglycerin, or vena caval obstruction). For each patient, transfer functions (TFs) between aortic and radial pressures were calculated by parametric model and results averaged to yield individual TFs. A generalized TF was the average of individual functions. TFs varied among patients, with coefficients of variation for peak amplitude and frequency at peak amplitude of 24.9% and 16.9%, respectively. Intrapatient TF variance with altered loading (> 20% variation in peak amplitude) was observed in 28.5% of patients. Despite this, the generalized TF estimated central arterial pressures to < or = 0.2 +/- 3.8 mm Hg error, arterial compliance to 6 +/- 7% accuracy, and augmentation index to within -7% points (30 +/- 45% accuracy). Individual TFs were only marginally superior to the generalized TF for reconstructing central pressures. CONCLUSIONS: Central aortic pressures can be accurately estimated from radial tonometry with the use of a generalized TF. The reconstructed waveform can provide arterial compliance estimates but may underestimate the augmentation index because the latter requires greater fidelity reproduction of the wave contour.

Compressibility of perfused passive myocardium.

In most theoretical analyses of the heart, the tissue has been assumed to be incompressible. Because the myocardium is extensively perfused with distensible vessels, increasing the stiffness of the surrounding tissue, as with contraction or passive stretching, should decrease the volume of fluid in these vessels. Using a digital subtraction angiographic method, we quantified the amount of vascular volume extruded from six passive, perfused canine interventricular septa during cyclic biaxial loading from 300 to 900 g force. At pressures from 0 to 120 mmHg the amount of fluid extruded during a loading cycle varied from 2 to 4 ml/100 g tissue at 0 and 120 mmHg, respectively. This volume change increased with perfusion pressure and was significantly greater at 120 than at 0, 30, or 60 mmHg. The amount of fluid extruded was on the same order as that estimated during active contraction or with a 60-mmHg change in perfusion pressure. The finding that perfused myocardium is compressible implies that results from existing analyses of the heart assuming incompressibility are not realistic. Such analyses must account for compressibility with, e.g., mixture theory or other similar approaches.

The need to account for residual strains and composite nature of heart wall in mechanical analyses.

We studied 19 excised, passive rabbit left ventricular walls to delineate the forms of the strain-energy functions (W) for myocardium and epicardium, to quantify residual strains across the wall, and to investigate whether the mechanical behavior of the intact wall can be predicted by accounting for the above properties. The unloaded dimensions and the stress-strain responses to equibiaxial and uniaxial loadings were obtained first for the intact wall and then individually for the epicardium and myocardium. Results show that the previously proposed W for canine myocardium and epicardium are suitable. The unloaded intact wall has residual strains: the epicardium is stretched and the myocardium shrunk from their respective isolated, unloaded states. The predicted mechanical responses of the intact wall to biaxial loadings were inaccurate when the residual strains were not taken into account. Accounting for these, however, yielded reasonable predictions. Thus information on the unloaded reference state and properties of each portion is needed to accurately predict the behavior of the intact wall.

Comparison of biaxial mechanical properties of excised endocardium and epicardium.

A complete understanding of cardiac mechanics requires knowledge of the mechanical properties of each of the tissues that comprise the heart, Data and constitutive relations are available for the nonlinear multiaxial behavior of epicardium and noncontracting myocardium, but there have been no comparable results for endocardium. In this paper, we present biaxial mechanical data for endocardium and epicardium excised from the same bovine hearts. The data reveal that these two membranes behave differently; endocardium exhibits a greater stiffness in the low-strain range. Moreover, quantification of endocardial behavior requires a seven-parameter, polynomial-exponential pseudostrain-energy function w, whereas epicardium can be described by a four-parameter exponential w. Comparison of our current findings with previous results on canine epicardium reveals further that canine and bovine epicardium behave similarly, although the latter is more extensible. Thus there appear to be marked species differences.

Coronary artery resistance changes depend on how surrounding myocardial tissue is stretched.

Deforming the tissue surrounding a coronary artery may change its hydraulic resistance. In excised blocks of dog left ventricular walls we examined how resistance (R) of a maximally dilated branch of a circumflex coronary artery was affected by 10% stretching of the tissue from its unloaded state, first parallel then perpendicular to the vessel axis (with the orthogonal dimension held constant) and finally biaxially. At 30 mmHg transmural pressure (Ptm) R per segment length (mmHg.min.ml-1.cm-1) increased significantly from the unloaded value of 0.0233 +/- 0.0031 (means +/- SE) to 0.0445 +/- 0.0073 and 0.0505 +/- 0.0090 during parallel and biaxial stretch, respectively. At Ptm of 80 mmHg unloaded R decreased to 0.0111 +/- 0.0016 mmHg.min.ml-1.cm-1 but did not change further with stretching. Stretching an isolated circular vessel 10% does not produce nearly this large an increase in R. A finite-element model simulating an epicardial vessel under our experimental conditions qualitatively predicted our results and demonstrated the combined roles of size and shape changes. Simulating a midwall arteriole surrounded by tissue predicted qualitatively similar results as for an epicardial vessel. Thus mechanical interaction between a coronary artery and surrounding tissue depends on both transmural pressure and the direction of stretching.