A flow bio-reactor for studying the effects of haemodynamic forces on the morphology and rheology of cylindrically cultured endothelial cells.

This study reports on the development and validation of an integrated experimental system for quantitative monitoring of the effects of vascular dynamic and static forces on endothelial cells (ECs), in terms of their morphological remodelling and rheological properties. The system consists of a microscope-based flow bio-reactor which imposes controlled individual and combined haemodynamic forces on ECs cultured on the inner surface of cylindrical transparent substrate tubes. EC morphology is monitored by optical microscopy. Micro-rheological alterations are measured by optical magnetic twisting cytometry (OMTC) using ferromagnetic micro-beads adherent to the EC cytoskeleton. System validation tests ascertained the capability for imposing controlled flow conditions and for real-time monitoring of morphological and rheological changes.

Lumped flow modeling in dynamically loaded coronary vessels.

Most of the myriad (order of 10(9)) interconnected coronary vessels interact nonlinearly with their embedding contracting myocardium. Their dynamic flow can be simulated based on a nonlinear distributive segmental flow model involving highly nonlinear partial differential equations. Such network flow analysis, although of high accuracy, is computationally excessively complex. On the other hand, a corresponding nonlinear lumped analysis is significantly less demanding since it involves ordinary differential equations. This is, however, at the detriment of accuracy. In the present technical report, a nonlinear lumped representation of coronary segmental flow is presented and tested against predictions of the corresponding distributive analysis. The results suggest that under physiological conditions, the proposed lumped model achieves similar accuracy to the distributive one, yet with considerably higher computational speed.

Effects of contact-induced membrane stiffening on platelet adhesion.

The adhesion of platelets plays an essential role in thrombogenesis. Adhesion occurs at sites called focal adhesions (FA), where cell-membrane receptors bind specifically to substrate proteins and couple to each other and to the cytoskeleton via various cellular proteins. The resulting molecular structure suggests that the cortex stiffens at the FA, which likely affects platelet adhesion. This hypothesis is explored by structural analysis and parametric investigation. The cortex is modeled as a shell anchored to the substrate by adhesion forces and subjected to a detachment force. Equilibrium considerations result in a non-linear, two-point boundary value problem that is solved numerically. The results show that cortex stiffening significantly influences the force required for detachment as well as the cell-membrane internal stresses. The magnitude of these effects depends on the ratio of adhesion-to-bending energies and on the inclination of the detachment force. Because the cortex stiffening depends on cellular events, these results suggest a possible mechanism by which platelets can control their adhesion and protect themselves from damage.

Measuring principles of frictional coefficients in cartilaginous tissues and its substitutes.

The frictional properties of cartilaginous tissues, such as the hydraulic permeability, the electro-osmotic permeability, the diffusion coefficients of various ions and solutes, and the electrical conductance, are vital data to characterise the extracellular environment in which chondrocytes reside. This paper analyses one-dimensional measurement principles of these coefficients. Particular attention is given to the deformation dependence of them and the highly deformable nature of the tissues. A suggested strategy is the combination of a diffusion experiment using radiotracer methods, an electro-osmotic flow experiment and an electro-osmotic pressure experiment at low electric current.

Time-dependent mechanical behavior of sheep digital tendons, including the effects of preconditioning.

The time-dependent mechanical properties of sheep digital extensor tendons were studied by sequences of stress-relaxation tests. The results exhibited irreversible preconditioning and reversible viscoelasticity. Preconditioning effects were manifested by stress decay during consecutive stretch cycles to the same strain level, accompanied by elongation of the tendon's reference length. They intensified with increased strain level, and were reduced or became negligible as the strain decreased. The significance of intrinsic response mechanisms was studied via a structural model that includes viscoelasticity, preconditioning, and morphology of the tendon's collagen fibers. Model/data comparisons showed good agreement and good predictive power, suggesting that preconditioning can be integrated into comprehensive material characterization of tendons.

Enhancement of bone defect healing in old rats by TGF-beta and IGF-1.

Bone defects are often created in order to repair bone pathologies. In the aging population, the healing of such defects is very limited. Bone healing in aging depends on the availability of various hormone and growth factors. The ability of growth factors to enhance bone formation in femoral defects in old rats was tested. Bone defects were induced in femurs of old rats. A single dose of transforming growth factor-beta (TGF-beta), IGF-1, TGF-beta+IGF-1 or saline was inserted in the defect and bones were tested after 2 and 4 weeks. Radiology revealed that mineralization appeared in the 2 weeks group in defects treated with TGF-beta and in defects treated with TGF-beta, TGF-beta+IGF-1 in the 4 weeks groups. Computerized tomography (CT) coronal and axial images revealed that 4 weeks after treatment with TGF-beta+IGF-1, a complete bone bridge was observed. Morphology revealed that these defects were filled with trabecular bone. A less pronounced bone healing was observed after TGF-beta or IGF-1, while control specimens revealed partial healing of the bone defect. Biomechanical tests indicated that treatment with TGF-beta, IGF-1 or TGF-beta+IGF-1 resulted in a significant increase of bone bending rigidity compared to control in the 4 weeks group and that TGF-beta+IGF-1 was the most inductive in this respect. The ability to induce bone healing in aging by TGF-beta+IGF-1 is of a great clinical importance for restoration of bone strength and biomechanical properties of bone defects in aging.

Effects of strain level and proteoglycan depletion on preconditioning and viscoelastic responses of rat dorsal skin.

The mechanical response of rat dorsal skin was experimentally studied under cyclic uniaxial ramp stretches to various strain levels. Special emphasis was paid to the effects of the preconditioning protocol on the stress-strain relationship, and to the effects of ramp strain level and proteoglycan (PG) depletion, on viscoelasticity and preconditioning responses. The results show that preconditioning significantly reduced both the slope of the low strain stress-strain relationship, and the stress levels at consecutive stretch cycles. Following a short rest there was a significant partial recovery. Stress decay due to preconditioning was significant at all strain levels, and increased with strain. Stress relaxation was significant at all strain levels, but varied little with strain. Recovery following a 10 min rest was minor at all strain levels and varied little with strain. PG-depleted samples manifested similar response patterns. These results are consistent with the following notion: (1) skin consists of three mechanical components: elastin and proteoglycan which dominate the low strain response and are effected by preconditioning and (PG) depletion, and collagen which dominates the high strain response and is unaffected by preconditioning and PG depletion; (2) that the viscoelasticity of elastin and PG vs that of collagen are similar, so that rat dorsal skin can be regarded quasilinear viscoelastic.

Partition and diffusion of sodium and chloride ions in soft charged foam: the effect of external salt concentration and mechanical deformation.

The partition and diffusion characteristics of an acrylic acid/acrylamide hydrogel, copolymerized in the pores of a polyurethane foam with sodium and chloride ions, were studied by radiochemical methodologies. The hydrogel foam swells by 51%, 80%% and 260% relative to its raw state under bath salt concentrations of 2.0, 1.0, and 0.15 M, respectively. The corresponding partition coefficients are 1.13, 1.29, and 1.99 for sodium (Na+) and 0.89, 0. 85, and 0.65 for chloride (Cl-). The diffusion coefficients are independent of bath concentration and increase linearly with hydration towards their values in water. Deformation affects partition and diffusion solely by dilatation, which determines the swelling and hydration. Comparison of the hydrogel foam with cartilage and intervertebral disc shows considerable similarities and suggests that the same mechanisms control their function.

Tethering affects the mechanics of coronary capillaries.

Coronary capillaries are extensively tethered to adjacent myocytes by collagen fibers. The influence of this tethering in the beating heart is studied by structural mechanics as applied to the specific morphology of the capillary-myocyte system. The results show considerable effects of the tethering collagen fibers on the capillary deformation, especially during systole and in the deeper myocardial layers. The tethering fibers prevent total systolic collapse, being taut during systole but partially slack during diastole, in agreement with reported observations. At the deeper wall layers, the systolic/diastolic differences in capillary cross-sectional area are predicted to be more pronounced: about 30 and 50% area reduction in arterial and venous ends, respectively, compared with 10 and 20% increase of area in the subepicardial vessels. These predictions comply well with published, experimental data. A parametric investigation shows a variable effect of the capillary-myocyte distance on the dynamics of the capillary area, while the stiffnesses of both the fibers and wall membrane, and the extent of transmural transmission of intramyocardial pressure, have both considerable quantitative effects. These effects are found to be region dependent and vary along the capillary length and from diastole to systole. The results indicate that capillary tethering to the myocardial tissue has significant effect on its mechanics. Tethering should, therefore, be considered in analyzing the dynamics of coronary flow.

Effect of myocardial swelling on residual strain in the left ventricle of the rat.

Left ventricular (LV) residual strain in the unloaded state was shown previously to affect LV performance. The interrelationship between myocardial swelling and LV residual strain was studied, both experimentally and theoretically. Myocardial swelling was induced by retrograde perfusion of beating, nonworking, isolated rat hearts with perfusate of graded osmolarities (200-420 mosM). The opening angle (an index of residual strain), in radially cut equatorial cross-sectional slices, and their water content were measured in 40 arrested rat LV. Both water content and opening angle decreased significantly with osmolarity from 84.2 +/- 0.45% and 77.2 +/- 9.2 degrees at 200 mosM to 76.5 +/- 1.05% and 36.3 +/- 9.8 degrees at 420 mosM (P < 0.001, respectively). A morphologically based theoretical model was developed and yielded as swelling residual strain relationship, which agrees well with the data. Our results indicate that myocardial swelling is strongly related to LV residual strain, suggesting that swelling, through its effect on residual strain, can affect both LV function and its adaptation to varying loading conditions.

Plausibility of structural constitutive equations for swelling tissues--implications of the C-N and S-E conditions.

The mechanically important constituents of swelling tissues are fibers embedded in an osmotically active fluid. The tissues' response to external loading is the sum of contribution of the axial stresses in the fibers and of the fluid pressure. The fluid osmotic properties play a key role in determining its equilibrium response. The present study examines the conditions under which the elastic response of tissues as modeled by structural constitutive equations, is thermodynamically plausible. The analysis shows that plausibility is ensured if the fibers' axial force increases monotonically with stretch and if the fluid osmotic pressure increases convexly with concentration. Published data shows that both conditions prevail in swelling tissues. Plausibility considerations seem to pose no specific restrictions on the structure of the tissues' fibrous network. It is thus concluded that in swelling tissues, structural constitutive formulation is compatible with thermodynamically plausible response.

Optimal design of biaxial tests for structural material characterization of flat tissues.

A rational methodology is developed for optimal design of biaxial stretch tests intended for estimating material parameters of flat tissues. It is applied to a structural model with a variety of constitutive equations and test protocols, and for a wide range of parameter levels. The results show nearly identical optimal designs under all circumstances. Optimality is obtained with two uniaxial stretch tests at mutually normal directions inclined by 22.5 deg to the axes of material symmetry. Protocols which include additional equibiaxial tests provide superior estimation with lower variance of estimates. Tests performed at angles 0, 45, and 90 deg to the axes of material symmetry provide unreliable estimates. The optimal sampling is variable and depends on the protocols and model parameters. In conclusion, the results indicate that biaxial tests can be improved over presently common procedures and show that this conclusion applies for a variety of circumstances.

A new methodology for non-invasive clinical assessment of cardiovascular system performance and of ventricular-arterial coupling during stress.

The objective of the study was to develop a non-invasive method for the quantitative evaluation of cardiovascular performance and ventricular-arterial (VA) coupling during varying physiological states. VA-coupling was represented by the ratio between the arterial and ventricular elastances-Ea/Ees. Approximate indices of the relative change of Ees and VA-coupling during stress were developed and tested. These indices can be evaluated directly from non-invasive measurements of ejection fraction values (for VA-coupling) and measurements of stroke volumes and systolic and diastolic arterial pressures (for Ees). Additional relative indices can be evaluated from these data (e.g., stroke work, cardiac output) to yield a complete representation of the cardiovascular response to stress. The present methodology was applied to assess the exercise stress response in healthy subjects (H, n = 8) and in patients with left ventricular dysfunction (n = 24). Left ventricular volumes were determined by nuclear angiography and arterial pressures were measured non-invasively by a new, validated method. Using published data obtained invasively, we found that the relative indices of Ees and VA-coupling showed a high correlation with the invasive ones (r > 0.8, P < 0.01). The patients were subgrouped by their maximal exercise capacitance (P2-50W, P3-75W). At rest, the two patient groups had similar ejection fraction values (45 +/- 15% and 48 +/- 16%), which were significantly different from those of the healthy subjects (66 +/- 7%, P < 0.05). During stress, a larger increase in stroke work and cardiac output was found in the healthy subjects. All three groups showed similar relative increases in Ees and heart rate, but relative Ea increased in P2 and decreased in H, while the opposite was found for the end-diastolic volume. The relative VA-coupling index in P2 was significantly larger than that in P3 and H (P < 0.05). The present non-invasively based indices can be used to quantitatively monitor the individual cardiovascular response to stress testing or drug interventions and to evaluate the importance of VA-coupling in the clinical setting.

The effect of residual strain on the diastolic function of the left ventricle as predicted by a structural model.

The unloaded heart is not stress-free. It is subjected to residual stress and strain. Their extent and influence on the global performance of the left ventricle and on local phenomena in the ventricular wall are studied by model simulation. The analysis focuses on the equatorial region of the ventricle, with an approximate thick-walled cylindrical geometry. The in vivo myocardium is considered to be incompressible, consisting of fibers embedded in a fluid matrix, with transmurally varying anisotropic microstructure in accordance with morphological characteristics. The results show that residual strain is transmurally distributed with a pattern and magnitude which agree well with measurements. The calculated residual strains are within mean +/- one standard deviation of the measured ones. Their magnitude was found to increase with increasing opening angle and with increasing wall thickness. The residual strain was found to have several effects on ventricular function: At volumes higher than the reference one it gives rise to more uniform transmural distributions of stress and intramyocardial pressure; it causes about 50% increase in the ventricular compliance at high volumes and doubles the suction of atrial blood at low volumes, thus facilitating the diastolic filling. In addition, residual strains cause bias of in vivo measured strains from their true values. This may significantly affect physiological interpretation of measured ventricular deformations. In conclusion, the present structural analysis predicts that residual strain has favorable effect on left-ventricular diastolic performance, and gives rise to more uniform ventricular stress distribution.

Mathematical model of blood flow in a coronary capillary.

The coronary capillary flow is analyzed theoretically based on continuum mechanics. The capillary is a long, elastic, and permeable vessel loaded externally by tissue pressure, and it is subject to possible periodic length changes, together with adjacent myocytes. Capillary flow is driven by arteriolar-venular pressure difference. Ultrafiltration due to transmural hydrostatic and osmotic gradients is included, and consideration of mass conservation leads to a nonlinear flow equation. The results show that under physiological conditions ultrafiltration is of minor importance, and the analysis predicts regional differences in capillary flow. In regions with high tissue pressure (subendocardium), capillaries undergo significant periodic volume changes, giving rise to intramyocardial pumping. In those regions, capillary wall elasticity is of major importance. In regions with low tissue pressure (subepicardium), the possible periodic capillary length changes are predominant. The predicted flow patterns are in good qualitative agreement with measured epicardial phasic flow. In conclusion, the methodological advantage of a distributive analysis is demonstrated by its ability to elucidate and evaluate the role of flow determinants and their complex interactions.

Influence of ageing on the in vivo mechanics of the skin.

The response of the skin to common in vivo tests (in-plane uniaxial stretch, torsion, indentation and levarometry) is analyzed in terms of their suitability for ageing studies. The analysis suggests that low-load indentation and small deformation levarometry are well suited for ageing studies since the skin response under these tests can be directly related to its structure and constituent properties (known to be affected by ageing). The measured forehead skin response under these tests in 'young' (20-26 years) and 'old' (64-80 years) subjects is presented and compared with predictions of corresponding models. The results show that levarometry is more sensitive to ageing than indentometry.

Modeling of coronary capillary flow.

The coronary capillary flow is analyzed theoretically based on the laws of continuum mechanics. The capillary is considered as a long, elastic and permeable vessel loaded externally by tissue pressure. It is subjected to periodic length changes, together with adjacent myocytes. Capillary flow is driven by arteriolar-venular pressure differences. Ultrafiltration due to transmural hydrostatic and osmotic pressure gradients is included in the model. Consideration of mass conservation leads to a nonlinear flow equation. The results show that under stable physiological conditions ultrafiltration is of minor importance. The analysis of untethered capillaries predicts regional differences in capillary flow. In all regions, but more so in the subendocardium, capillaries undergo significant periodic volume changes, giving rise to intramyocardial pumping. In the deeper layers, capillary wall elasticity is of major importance. In the subepicardium, the possible capillary length-changes with adjacent myocytes tend to enhance systolic/diastolic volume differences. The predicted patterns of the overall capillary flow in the left ventricular (LV) wall are in good qualitative agreement with measured coronary phasic flow, showing systolic retrograde arterial inflow, accelerated venal outflow, and diastolic rapid filling accompanied by venal retrograde flow. Analysis of the flow in tethered capillary shows significant effect of the collagen attachments between the surrounding myocytes and the capillary wall. The advantage of the continuum analysis is demonstrated in the present study by its ability to elucidate and evaluate the role of flow controlling mechanisms and their complex interactions.

In-vivo indentation of human skin.

Indentation tests were carried out on the forehead skin of volunteers under loading pressures of 0-5 KPa. The indentation was found to increase asymptomatically with loading pressure. In an attempt to develop a quantitative index for aging of the skin, its response to indentation loading was analyzed in reference to its glycosaminoglycan (GAG) containing ground substance and fibers' network microstructure. An analytic model that considers the skin as an incompressible solid-fluid mixture was developed and utilized to simulate the skin's indentation response. Following parameter fitting, the predicted results are in close agreement with the data. The model can thus serve as a tool for evaluating the effect of changes in the dermis components which accompany aging.

Structural finite deformation model of the left ventricle during diastole and systole.

A model of left ventricular function is developed based on morphological characteristics of the myocardial tissue. The passive response of the three-dimensional collagen network and the active contribution of the muscle fibers are integrated to yield the overall response of the left ventricle which is considered to be a thick wall cylinder. The deformation field and the distributions of stress and pressure are determined at each point in the cardiac cycle by numerically solving three equations of equilibrium. Simulated results in terms of the ventricular deformation during ejection and isovolumic cycles are shown to be in good qualitative agreement with experimental data. It is shown that the collagen network in the heart has considerable effect on the pressure-volume loops. The particular pattern of spatial orientation of the collagen determines the ventricular recoil properties in early diastole. The material properties (myocardial stiffness and contractility) are shown to affect both the pressure-volume loop and the deformation pattern of the ventricle. The results indicate that microstructural consideration offer a realistic representation of the left ventricle mechanics.