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Y C Fung

Publications and source records attributed to Y C Fung.

At least 19 recordsLinked to original sources
PubMed1995

Determination of the mechanical properties of the different layers of blood vessels in vivo.

The structure and materials of the blood vessel wall are layered. This article presents the principle of a method to determine the mechanical properties of the different layers in vivo. In vivo measurement begets in vivo data and avoids pitfalls of in vitro tests of dissected specimens. With the proposed method, we can measure vessels of diameters 100 microns and up and obtain data on vascular smooth muscles and adventitia. To derive the full constitutive equations, one must first determine the zero-stress state, obtain the morphometric data on the thicknesses of the layers, and make mechanical measurements in the neighborhood of the zero-stress state. Then eight small perturbation experiments are done on earth blood vessel in vivo to determine eight incremental elastic moduli of the two layers of the blood vessel wall. The calculation requires the morphometric data and the location of the neutral axis. The experiments are simple, the interpretation is definitive, but the analysis is somewhat sophisticated. The method will yield results that are needed to assess the stress and strain in the tissues of the blood vessel. The subject is important because blood vessels remodel themselves significantly and rapidly when their stress and strain deviate from their homeostatic values, and because cell proliferation, differentiation, adhesion, contraction, and locomotion depend on stress and strain in the tissue.

Animals↗
PubMed1995

Longitudinal strain of canine and porcine aortas.

The in situ longitudinal strain of canine and porcine aortas was investigated. Marks of black water-resistant ink were placed on the aortas and the axial lengths between the marks were measured in situ and in vitro. When the aortas were cut, the retraction was measured and described by the stretch ratio, which is defined as the length of a segment in situ divided by the length at no-load state. Results show that the stretch ratios of both porcine and canine aortas increase monotonically from 1.2 in the descending region to about 1.5 in abdominal region. Species differences are seen in the middle region. In both animals, the stretch ratio is correlated to the cross-sectional area of the vessel wall.

Animals↗
PubMed1995

Bending of blood vessel wall: stress-strain laws of the intima-media and adventitial layers.

In order to determine the stress-strain relationship of the inner (intima and media) and outer (adventitia) layers of blood vessels in the neighborhood of the zero-stress state, bending experiments were performed on aortic strips of rats. In the experiments, one end of a strip was clamped, and a force was applied on the other end. The deflection curves of the strips were measured. By regarding the aortic strip as a curved beam, the classical beam theory was employed to analyze the strain distribution from the experimental data. A computer program dealing with nonlinear equations and nonlinear least squares optimization was developed. Strains were referred to the zero-stress state. The load-deflection relationship was then used to determine the stress-strain relationship. Certain forms of the stress-strain laws were assumed. The linear laws fit the experimental data accurately, probably because the strains during bending are quite small, although the rotations are large. The Young's modulus of the inner layer, which consists of endothelial and smooth muscle cells and elastic lamina, was found to be three to four times larger than that of the outer layer which consists of collagen with a small amount of fibroblasts and elastin. The residual stresses and strains at the no-load state were calculated from the deduced stress-strain relationship. It is shown that large errors (up to 50 percent) in the values of the residual strains will occur if the wall material was treated as homogeneous, i.e., if the layered constitution was ignored.

Animals↗
PubMed1995

Biaxial mechanics of excised canine pulmonary arteries.

A new method has been developed for measuring the stress-strain relationship in excised canine pulmonary arteries. Segments of dog main right pulmonary arteries were isolated by making two transverse cuts at each end of a segment near the bifurcations, yielding short cylinders, which were then cut radially, relieving the residual stress, causing the cylindrical shells to spring open to approximately flat rectangular slabs with dimensions approximately 1.0 x 3.0 x 0.1 cm. The specimens were then tested using a biaxial tensile testing machine. The resulting data show an approximately linear relationship between Kirchhoff stress and Lagrangian strain with very little hysteresis. The following pseudostrain energy function serves as a practical approximation for pulmonary arteries subjected to physiological levels of stress and strain: rho 0W(2) = 1/2(a1E2xx + a2E2yy + 2 a4ExxEyy), where rho 0 is the density of the wall (mass per unit volume), W is the energy per unit mass [superscript "(2)" indicates this is a 2-dimensional strain energy function], E is strain, a1, a2, and a4 are material constants with units of stress, and the subscripts x and y refer to the circumferential and axial axes, respectively, of the artery. To assess the physiological level of strain in the main right pulmonary artery, vessels were perfused in situ at physiological pressure (26 cmH2O) with silicone elastomer. The arteries were then excised and marked with small ink spots. Photographs of the spots on four tangent planes of the excised artery indicate a maximum circumferential strain of 21.5% and a maximum axial strain of 36.5% relative to the zero-stress state. These values are within the range of strain used in the biaxial tests. The relationship between Kirchhoff stress and Green's strain is approximately linear within the physiological range. The stress levels required to cause tissue failure are at least 10 times greater than the estimated normal physiological level.

Animals↗
PubMed1994

On measuring the third dimension of cultured endothelial cells in shear flow.

The stress in the endothelial cells induced by blood flow depends on the waviness of the blood-endothelium interface and the slopes at the junctions of neighboring cells in the direction of flow. The height and slope in the third dimension of the living endothelial cells cannot be measured by ordinary optical and electron microscopy. Here we show that interference microscopy meets the challenge. We measured the geometry of cultured confluent human vascular endothelial cells in a flow, and we found that in a normal section parallel to the flow, the absolute values of the surface slopes at the cell junctions were 0.70 +/- 0.02 (SE) and 0.80 +/- 0.02 (SE) at the leading and trailing edges of the cells, respectively, in a culture medium of osmolarity 310 mosM with a shear stress of approximately 1 N/m2. A reversal of the flow direction led to a reversal of the slope pattern. An increase in medium osmolarity above 310 mosM induced an initial decrease in the slopes followed by a return to normal, whereas a decrease in the osmolarity had a reversed effect. These results, in light of our previous theoretical analyses, show that tensile stress exists in the endothelial cell membrane, and that the mechanism of tension accumulation is a reality. The accumulation is not 100% because the membranes are not smooth at the cell junctions.

Blood Viscosity↗
PubMed1994

New experiments on shear modulus of elasticity of arteries.

Although the mechanical properties of blood vessels have been studied extensively, the shear modulus of the blood vessel wall is still unknown. New data on the shear modulus of elasticity of rat arteries and its variation with axial stretch and blood pressure are presented. The data were obtained from a new instrument designed and constructed by us to perform simultaneous torsion, inflation, and longitudinal stretching tests. It was found under physiological conditions (pressure = 120 mmHg or 16 kPa; longitudinal stretch = 1.2 relative to zero-stress state), the shear modulus of normal rat thoracic aorta is G = 137 +/- 18 kPa. The difference of shear modulus at body temperature (37 degrees C) and room temperature (25 degrees C) is within 10%. The shear modulus varies significantly with changing longitudinal and circumferential strains in proportion to the strain energy due to these strains. A constitutive equation based on a pseudo strain energy function is proposed. The vessel wall is not transversely isotropic in the incremental sense. When the rat was subjected to high blood pressure due to constriction of its aorta, the shear modulus does not vary significantly with the length of time the animal was subjected to hypertension.

Animals↗
PubMed1994

Topology and dimensions of pig coronary capillary network.

To provide a morphometric basis for any mathematical modeling of the coronary vasculature, data on the network of coronary capillary blood vessels and the topology of the arteriolar supply and venular drainage relative to the capillaries are presented. The diameters, lengths, and branching patterns of the coronary capillary blood vessels in the right and left ventricles of four pigs were measured. The locations of the coronary arterioles and venules were identified, topological maps were constructed, and the mean functional length of capillaries connecting an arteriole to an adjacent venule was measured. The vasculature was fixed by perfusing the coronary vessels with a catalyzed polymer. After the polymer hardened, plugs of the myocardium were removed, sectioned, dehydrated, and cleared to render the capillary network visible in a light microscope. The capillaries then were traced by optical sectioning. We designated the capillaries as blood vessels of order number zero; we further designated the capillaries as those fed directly by arterioles (C0a), those drained directly into venules (C0v), and those capillary vessels connected to C0a and C0v. The capillaries are connected in patterns identified as Y, T, H, or hairpin and anastomosed through capillary cross-connections (Ccc). The Ccc vessels may connect adjacent capillaries or capillaries originating from different arterioles. The connection among the capillaries, arteries, and veins is presented in terms of a connectivity matrix. Combining the present data with those for the arterial and venous trees, we have obtained a complete set of statistical data of all the blood vessels of the heart of the pig. Such a data set will serve as the basis of coronary hemodynamics.

Anatomy, Comparative↗
PubMed1994

Morphometry of pig coronary venous system.

This is a third part of tripartite morphometric data of the pig coronary blood vessels, giving a complete quantitative description of the arterial tree [Kassab et al., Am. J. Physiol. 265 (Heart Circ. Physiol. 34): H350-H365, 1993], capillary network [Kassab and Fung, Am. J. Physiol. 267 (Heart Circ. Physiol. 36): H319-H325, 1994], and venous tree (this article). Together they provide the quantitative anatomic foundation for coronary hemodynamics. The coronary venules have a unique morphology. Unlike coronary arterioles, which have cylindrical cross sections and a fairly constant diameter in each segment, the venules have approximately elliptical cross sections, are usually wavy in the longitudinal direction, and often converge like fingers to a hand. Measurements were made with the silicone elastomer casting method on five pig hearts. Data on smaller vessels were obtained from histological specimens by optical sectioning. Data on larger vessels were obtained from vascular casts. Arcading veins and anastomoses on the epicardial surface have a unique topology. Data on the number of vessels in each order, the major and minor axes, length, connectivity matrix, and the fractions of the vessels of a given order connected in series in all orders of vessels of the sinusal and thebesian veins are presented. It is shown that of the blood in the coronary blood vessels of a pig heart 27.4% is in the arteries (> 200 microns), 37.1% is in veins (> 200 microns), and 35.5% is in microcirculation (< 200 microns), of which 89.4% is in the capillaries.

Animals↗
PubMed1994

Diameter-defined Strahler system and connectivity matrix of the pulmonary arterial tree.

For modeling of a vascular tree for hemodynamic analysis, the well-known Weibel, Horsfield, and Strahler systems have three shortcomings: vessels of the same order are all treated as in parallel, despite the fact that some are connected in series; histograms of the diameters of vessels in the successive orders have wide overlaps; and the "small-twigs-on-large-trunks" phenomenon is not given a quantitative expression. To improve the accuracy of the hemodynamic circuit model, we made a distinction between vessel segments and vessel elements: a segment is a vessel between two successive nodes of bifurcation; an element is a union of a group of segments of the same order that are connected in series. In an equivalent circuit, all elements of the same order are considered as arranged in parallel. Then, we follow the ordering method of Horsfield and Strahler, with introduction of an additional rule for the assignment of order numbers. If Dn and SDn denote the mean and standard deviation of the diameters of vessels of order n, then our rule divides the gap between Dn--SDn and Dn--1 + SDn--1 evenly between orders n and n--1. Finally, we introduced a connectivity matrix with a component in the mth row and the nth column that is the average number of vessels of order m that grow out of the vessels of order n. This method was applied to the rat. We found that the rat pulmonary arterial tree has 11 orders of vessels and that the geometry is fractal within these orders. The ratios of diameters, lengths, and numbers of elements in successive orders are 1.58, 1.60, and 2.76, respectively. The connectivity matrix reveals interesting features beyond the fractal concept. New features are found in the variation of the total cross-sectional area of elements with order numbers.

Animals↗
PubMed1993

Material coefficients of the strain energy function of pulmonary arteries in normal and cigarette smoke-exposed rats.

The effect of cigarette smoke on the stress-strain relationship of pulmonary arteries was studied in 2- and 3-month smoke-exposed rats. The animals were exposed to cigarette smoke in a smoke-generating system 10 times daily with one cigarette each time. The smoke density and the puffing duration and frequency of the system were regulated in accordance with reference values measured from human smokers. The mechanical properties of the pulmonary arteries about 450 microns in external diameter (at zero pressure) were determined in vitro by inflation and deflation tests. The average stress and middle-wall strain of the selected pulmonary arteries were determined on the basis of experimental data including inflation and deflation pressures during loading and unloading processes, respectively, and vessel diameter and length at various pressure levels, and vessel circumferential and longitudinal lengths at zero-stress state. A constitutive equation for the pulmonary arteries was derived from an energy function depending on circumferential and longitudinal Green's strains. The coefficients of the strain energy function of the pulmonary arteries were determined in both the smoke-exposed and control rats by fitting the experimental stress-strain data with the constitutive equation. It was found that the wall stress of the pulmonary arteries at a given strain and most of the coefficients of the strain energy function were increased in both the 2- and 3-month smoke-exposed rats in comparison with those in the corresponding controls. These results indicated that cigarette smoke induced an increase in the wall stiffness of the pulmonary arteries in the rats.

Animals↗
PubMed1993

Remodeling of the constitutive equation while a blood vessel remodels itself under stress.

Changes in the mechanical properties of a blood vessel when it remodels itself under stress are reviewed. One of the recent findings about blood vessels is the rapidity of tissue remodeling when the blood pressure is changed. When the tissue structure and material composition remodel, the zero-stress state of the vessel changes. The mechanical properties change also in the remodeling process. If the elastic behavior is expressed in terms of a pseudo-elastic strain-energy function, then the constants in the function will change in the course of the remodeling. With all these changes taking place, the scope of constitutive equations broadens: it should now include a mass-and-structure growth-stress relationship as well as a stress-strain-relationship. To obtain the mass-and-structure growth-stress relationship, one must be able to determine the mechanical properties of the different layers of the vessel wall, as well as the chemical composition and morphology. For the blood vessels, new methods of mechanical testing must be introduced. A key thought is to use bending of the blood vessel wall. By bending, different layers of the vessel wall are subjected to different stresses, leading to equations that can be used to solve the inverse problem of determining the stress-strain law from measured stress and strain. In vitro and in vivo experiments and theoretical prospectives are presented.

Adaptation, Physiological↗
PubMed1992

Strain distribution in small blood vessels with zero-stress state taken into consideration.

The active and passive deformation of a blood vessel is related to the stress in it. Any analysis of stress and strain must begin with the zero-stress state. Recent reports on large blood vessels such as the aorta, pulmonary arteries, and vena cava have shown that, at zero-stress state, blood vessels are not tubes, but opens sectors. This report presents data on the zero-stress state of small blood vessels with lumen diameters down to approximately 50 microns. Zero-stress state of a vessel was obtained by cutting the vessel into rings and then the rings into sectors; each sector is characterized by an opening angle, alpha. In rat ileal and plantar arterioles, the opening angles are in the order of 100-250 degrees; those in the venules are in the order of 50-100 degrees. The effect of norepinephrine on the opening angle alpha is minor; it decreases alpha of the superior mesenteric artery, and increases alpha of the ileocecocolic and ileal arteries. EDTA has little effect on alpha of arteries greater than 100 microns in diameter, but decreases alpha of arteries less than 100 microns. The physiological meaning of the opening angle is demonstrated in terms of the residual strains in a vessel at the no-load state and homeostatic strains at normal blood pressure. The strains in real vessels are compared with those in hypothetical vessels having an opening angle of zero. It is shown that ignoring the opening angle will cause a large error in strain evaluation.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1992

Microscopic vs. macroscopic deformation of the pulmonary alveolar duct.

The stretch of the perimeters of alveolar ducts was measured at the surface of saline-filled specimens of human and dog lung parenchyma that were stretched biaxially. The microscopic stretch of these ducts was measured at several levels of isotropic biaxial macroscopic stretch of the parenchyma with stretch ratio (lambda x = lambda y) in the range of 1.20-1.40, which roughly corresponds to tidal breathing in humans and dogs. Alveolar walls were found to be load-carrying elements in the saline-filled lung, as seen by their straightness at all levels of stretch. Quantitatively, let l, A, L, and S denote, respectively, the duct perimeter length and area and the parenchymal target perimeter and area in the deformed state and lo, Ao, Lo, and So the corresponding variables in the undeformed state. The microscopic stretch ratio of the ducts (l/lo) was found to be approximately 4% larger than the macroscopic stretch ratio (L/Lo) in human lung and approximately 10% larger in dog lung. The microscopic area ratio of the ducts (A/Ao) was found to be approximately 10% larger than the macroscopic area ratio (S/So) in human lung and approximately 22% larger in dog lung. Ducts within human parenchyma were seen to be about twice as stiff as ducts within dog parenchyma over the range of macroscopic stretch studied. This correlates with the volume fractions of collagen and elastin being higher in the human lung than in dog lung. The observed nonuniformity in strain field at the microstructural level suggests the need to include a force balance between alveolar ducts and septal walls when modeling the mechanics of saline-filled parenchyma.

Animals↗
PubMed1992

Effect of temperature on the biaxial mechanics of excised lung parenchyma of the dog.

The influence of temperature on the mechanical properties of excised saline-filled lung parenchyma of the dog was studied at low lung volume. The motivation of this study was to determine whether lung tissue material without the influence of surface tension undergoes a phase transition in the 20-40 degrees C range, as does synthetic elastin studied by Urry in 1984-1986. Dynamic biaxial and uniaxial tensile tests were done, and strain vs. Lagrangian stress curves were recorded during slow cooling and heating between 40 and 10 degrees C. To emphasize the effects of elastin, strains (defined as stretch ratio minus one) were kept below 30%. A slight decrease in compliance occurred with cooling over the entire temperature range. This effect may be attributed to collagen. It was accompanied by a gradual increase in length as the tissue cooled, an effect that may be attributed to elastin. This process was partially reversible with reheating. However, this effect is in contrast with the sudden drastic change in mechanical properties of synthetic elastin described by Urry. Hysteresis, creep, and stress relaxation were small at these low strains. Possible causes of these effects are discussed.

Animals↗
PubMed1992

Influence of STZ-induced diabetes on zero-stress states of rat pulmonary and systemic arteries.

Zero-stress states of the main pulmonary arteries and aorta and small systemic arteries were determined in 22 nondiabetic and 29 streptozocin (STZ)-induced diabetic rats. The zero-stress state of each vessel was obtained by cutting the vessel transversely into a series of short rings, then cutting each ring radially, which caused the ring to spring open into a sector. Each sector can be characterized by its opening angle. The opening angle has strong regional dependence. In some regions of rat arteries, the opening angle can be greater than 360 degrees. Rats were studied 5, 10, 20, 30, and 40 days after an injection of 75 mg/kg body wt i.v. STZ. During diabetes development, the opening angles in general increased and reached a plateau in approximately 30 days. The maximum change of opening angle over normal lies in the range of 18-105 degrees, depending on location. The pulmonary arteries were affected by diabetes as much as the systemic arteries. The course of change of the opening angle during diabetogenesis was different from those of the serum glucose level and blood pressure. Blood pressure in carotid, external iliac, and pulmonary arteries did not change significantly in diabetogenesis. To clarify the physiological meaning of the opening angle, we measured the circumferential strain in the blood vessel wall in homeostatic condition and the residual strain at the no-load state, with both strains referred to the zero-stress state. We calculated the corresponding stresses in the vessel wall. The circumferential stress in the vessel wall was greatly increased by diabetes; great errors will result if the opening angle is ignored.

Animals↗
PubMed1991

What are the residual stresses doing in our blood vessels?

We show that the residual strain and stress in the blood vessels are not zero, and that the zero-stress state of a blood vessel consists of open-sector segments whose opening angles vary along the longitudinal axis of the vessel. When the homeostatic state of the blood vessel is changed, e.g., by a sudden hypertension, the opening angle will change. The time constant of the opening angle change is a few hours (e.g., in the pulmonary artery) or a few days (e.g., in the aorta). From a kinematic point of view, a change of opening angle is a bending of the blood vessel wall, which is caused by a nonuniformly distributed residual strain. From a mechanics point of view, changes of blood pressure and residual strain cause change of stress in the blood vessel wall. Correlating the stress with the change of residual strain yields a fundamental biological law relating the rate of growth or resorption of tissue with the stress in the tissue. Thus, residual stresses are related to the remodeling of the blood vessel wall. Our blood vessel remodels itself when stress changes. The stress-growth law provides a biomechanical foundation for tissue engineering.

Animals↗
PubMed1991

Residual strains in porcine and canine trachea.

Residual strains exist in canine and porcine tracheas. They are revealed by cutting the trachea first perpendicular to its axis into rings, then radially into sectors. Each sector is characterized by an opening angle which is defined as the angle subtended between two radii joining the middle point of the inner wall to the tips of the inner wall. The trachea being non-axisymmetric, the opening angle depends on the position of the radial cut. The trachea being also nonuniform in the axial direction, the opening angle varies along the length of the trachea. In the dog, the opening angle of the trachea cut at the anterior position (cartilaginous) is about 100 degrees at the larynx; it increases fairly linearly to 180 degrees midway down the trachea; then increases slowly to about 200 degrees at the lower end where the trachea bifurcates into the main bronchi. Dog trachea cut in the posterior (muscular) position have an opening angle of about 50 degrees at the larynx, which increases to about 70 degrees three-quarters of the way down the trachea, then drops to 60 degrees at the lower end. In the pig, the opening angle of the trachea is much smaller, the values at anterior and posterior cuts are similar (without significant difference), and their mean value decreases from about 15 degrees at the laryngeal end to about 5 degrees at the lower end. These species and regional differences are discussed in relation to tracheal geometry and structure.(ABSTRACT TRUNCATED AT 250 WORDS)

Age Factors↗