Many phenomenological models of cerebral aneurysm formation have been proposed. Such studies have focused on modeling the structural adaption of the arterial wall. However, further development is required to accurately represent the underlying mechanobiology during growth and remodeling processes. Here, we present a general framework for modeling the interplay of fluid dynamics, molecular signaling pathways and arterial wall mechanics.

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.

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.

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.

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. © 2001 Biomedical Engineering Society.

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.

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.

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.

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.

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.

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.

Mathematical model and numerical simulation are used to analyze optimal conditions of cardiovascular performance, with an emphasis on the effect of ventricular-arterial (VA) coupling. The following research questions were posed: Does the VA-coupling affect the cardiovascular system (CVS) performance in addition to the direct effects of the left ventricle and of the vascular load? Is there an optimal coupling state? Does the CVS in human subjects, either healthy or diseased, operate with optimal VA-coupling? and finally, is it possible to improve the CVS performance by controlling the VA-coupling? To answer these questions, a clinically oriented integral model of the CVS is introduced, based on the ventricular and arterial elastances. The main advantages of the model are its simplicity and the fact that all its variables can be measured non-invasively in the clinical practice. Traditionally, the optimal state of CVS operation was evaluated by two criteria — the energetic efficiencyof the left ventricle and the efficiency of energy transfer through the vascular system. In the present study a combined criterion of the total energetic efficiency is utilized — from the input metabolic energy consumed by the ventricle to the net energy available to the peripheral tissues. It is found that optimal coupling for maximal global efficiency depends in a complex, non-linear way on all the classical determinants of CVS performance — the preload, the myocardial contractility, the afterload and the heart rate. Response surfaces of the analyzed variables as function of two independent variables were generated by numerical simulation. Based on the analysis of the global efficiency as the optimization criterion, answers to the research questions were found: The VA-coupling affects the CVS performance in addition to the direct effects of its determinants; there is an optimal state of coupling which results in maximal efficiency; the CVS in healthy subject operates in the region of optimal coupling; during stress, changes in the state of coupling result in additional contribution to CVS performance; in patients with left ventricular dysfunction the efficiency is reduced and it further decreases during exercise. The model shows that there is, however, an optimal coupling which improves performance even in cases of severe heart failure. This optimal state can theoretically be approached by titrating the vascular resistance and the end-diastolic volume (the preload) to optimal levels. These results suggest, and lay the theoretical foundation for the notion, that vasodilator drugs can be used to optimize VA-coupling and CVS performance in heart failure patients.

Soft tissues are binary systems of fibers embedded in a fluid matrix. Their equilibrium response to external loading is the sum of the fibers’ stress and the matrix osmotic pressure. The present study examines the conditions under which the elastic response of isotropic tissues, as modeled by structural constitutive equations, is physically plausible. The analysis shows that plausibility is ensured if the fibers’ stretch force increases monotonically with the stretch and if the matrix osmotic pressure increases convexly with the concentration. Published data shows that both conditions prevail in soft tissues. It is thus concluded that structural modeling is compatible with physically plausible response.

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.

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.

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.

Technical Briefs The Orientation of an Intramyocardial Vessel Affects Its Mechanical Loading by the Surrounding Myocardium Y. Lanir, Y. Lanir The Julius Silver Institute-Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel Search for other works by this author on: This Site PubMed Google Scholar E. Nevo E. Nevo The Julius Silver Institute-Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information Y. Lanir The Julius Silver Institute-Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel E. Nevo The Julius Silver Institute-Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel J Biomech Eng. Aug 1993, 115(3): 327-328 (2 pages) https://doi.org/10.1115/1.2895493 Published Online: August 1, 1993 Article history Received: July 27, 1988 Revised: February 2, 1993 Online: March 17, 2008

The most important functions of connective tissues is to maintain structural integrity and allow transport of chemicals and water. This is achieved through their multiphase structure which consists primarily of solid components and fluid matrix.