Biomedical subjects

Y C Fung

Publications and source records attributed to Y C Fung.

At least 37 records · Page 2Linked to original sources

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

Development of a device for measuring adherence of skin grafts to the wound surface.

Adherence of a biological graft to the wound surface is the most important factor influencing the ultimate success of graft viability. A machine has been developed to test the adherence of biological graft materials to a substrate such as a wound surface. The peeling mode, which yields reproducible quantitative measurements of adherence, is a standard method for testing adhesives. The device is designed to continuously measure the force required to peel the graft from the substrate at a constant rate. This force is a function of the energy of adhesion per unit area of adhered surface. This device has been used to measure the peeling force of (2 x 2 cm) skin grafts which are applied to full-thickness wounds on mice. Results of tests on adherence of autografts on mice show that the peeling force increases significantly with time over the first 9 days of healing. Thus, this device is useful in quantitative comparison of various skin grafting techniques and artificial grafts.

Adhesiveness↗

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

Elementary mechanics of the endothelium of blood vessels.

The endothelium lining human arteries is a continuum of endothelial cells. The flowing blood imposes a shear stress on the endothelium. To compute the internal stress in the endothelium, we use two alternative hypotheses: 1) The cell content is fluid-like so that at steady-state it has no shear stress. 2) The cell content is solid-like. Under hypothesis No. 1, the membrane tension in the upper cell membrane grows in the direction opposite to the blood flow at a rate equal to the blood shear stress. At the junction of two neighboring cells the membrane tension in the downstream cell is transmitted partly to the basal lamina, and partly to the upstream cell. The transmission depends on the osmotic or static pressure difference between the cell and blood. If the static pressure difference is zero, the tension in the upper cell membrane will accumulate upstream. At other values of static pressure, the cell membrane tension may increase, decrease, or fluctuate along the vessel depending on the inclination of the side walls of the cells at the junctions. To determine the sidewall inclinations, we propose to use the complementary energy theorem. Under hypothesis No. 2, the cell content can bear shear, which tends to reduce the cell membrane tension; but the cell membrane tension accumulation phenomenon discussed above remains valid. These results are used to analyze the interaction of the cell membrane and cell nucleus; and the effect of turbulences in the flow on causing large fluctuations in cell membrane tension and vertical oscillations of the nuclei. The implication of tensile stress on the permeability of the cell membrane is discussed. We conclude that for the study of mass transport and stress fibers in the endothelial cells, one should consider the interaction of neighboring endothelial cells as a continuum, and shift attention from the shear stress in the blood to the principal stresses in the cells.

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↗

PubMed1993

Morphometry of pig coronary arterial trees.

To establish a mathematical model of the tree like arteries for the purpose of hemodynamic analysis, a complete set of morphometric data of pig coronary arteries is presented. For the purpose of mathematical modeling, three innovations in morphometry are introduced: 1) a rule for assigning the order numbers of the vessels on the basis of diameter ranges, 2) a connectivity matrix to describe asymmetric branching, and 3) a measurement of the fraction of vessel segments connected in series. The morphometric measurements were made with the silicone elastomer-casting method. Data on smaller vessels were obtained from histological specimens by optical sectioning. Data on larger vessels were obtained from vascular casts. The order number, diameter, length, connectivity matrix, and fractions of the vessels of a given order connected in series were measured for all orders of vessels of the right coronary artery and the left anterior descending and left circumflex branches. The data can be used to analyze the longitudinal distribution of blood pressure and volume and spatial distribution of perfusion in myocardium.

Animals↗

PubMed1993

Coronary arterial tree remodeling in right ventricular hypertrophy.

We investigated coronary vascular adaptations occurring in right ventricular hypertrophy (RVH). Six pigs had RVH induced by pulmonary artery stenosis for 5 wk. Three pigs served as controls. At autopsy we made silicone elastomer casts of the right coronary arteries (RCA) and collected morphometric data. We organized the segments and their diameters and lengths into a framework of a modified Strahler's ordering scheme in which the order number of an offspring is increased only if its diameter is greater than the diameters of its parents by a specific amount. The segments of the same order arranged in series are combined into elements. In RVH the total number of orders of vessels was larger than the control by 1; the total number of elements in each order increased greatly, whereas the diameters and lengths of each order decreased somewhat. The total RCA resistance decreased in RVH mainly because the total cross-sectional area (CSA) of every order was increased. Because the diameters of the resistance vessels decreased, this decrease in total RCA resistance was due to a numerical increase in resistance vessels. These findings indicate that new flow channels have been established. In contrast, the RCA was remodeled in that the lumen diameter increased. Pressure-flow curves showed a decrease of coronary resistance in RVH, in agreement with the morphometric findings. We conclude that there is significant remodeling of the coronary arterial vasculature in RVH, and any future analysis of coronary hemodynamics of the right ventricle in hypertrophy must take the morphometric remodeling into account.

Adaptation, Physiological↗

PubMed1993

Neutral axis location in bending and Young's modulus of different layers of arterial wall.

With few exceptions, experimental results on the blood vessel elasticity have been analyzed with the blood vessel wall treated as a homogeneous material, probably because the experiments have been limited to inflation and stretching. To advance the subject, we must evaluate the force-deformation relationship of different layers of the vessel. A key strategy to do this is to study nonaxisymmetric deformation of the vessel wall so that the different layers of the vessel may deform in different amounts at different places. One of the most effective nonaxisymmetric deformations that can be imposed on the vessel wall is bending. The first important question to ask about bending is, Where is the neutral axis? In this study, a method to determine the neutral axis is presented. We found that the neutral axis of the aorta of the pig lies in the medial layer about one-third of the wall thickness from the endothelium. We measured the strain distribution in the vessel wall by optical methods. Using the load-deflection relationship, we evaluated the Young's modulus of the intima-media layer and that of the adventitia. They differ by an order of magnitude. Our results show that the Young's modulus of the intima-media layer of the pig thoracic aorta is 43.2 +/- 15.8 kPa, whereas the Young's modulus of the adventitial layer is 4.70 +/- 1.72 kPa, in a linear range of the stress-strain relationship including the zero-stress state and the no-load state.

Animals↗

PubMed1993

Changes in the structure and mechanical properties of pulmonary arteries of rats exposed to cigarette smoke.

The effect of cigarette smoke on the structure and mechanical properties 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 per day 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 volume fractions of the cells, including smooth muscle cells and fibroblasts, and extracellular matrix components, including collagen, elastin, and remainder (components not specified in this study), of the pulmonary arteries of approximately 450 microns in external diameter (at zero pressure) were determined in smoke-exposed and control rats by using an electron microscopic method. It was found that the volume fractions of the fibroblasts, the collagenous bundles, and the elastic laminae of the pulmonary arteries were increased significantly, whereas those of the smooth muscle cells and the remainder were decreased significantly in both the 2- and 3-month smoke-exposed rats in comparison with those of the corresponding control rats. The mechanical properties of the pulmonary arteries were determined based on the in vitro dimensional measurement of the vessels at various inflation pressures and zero-stress state. An increase in the stiffness of the pulmonary arteries was found in both the 2- and 3-month smoke-exposed rats. We conclude that cigarette smoke can induce structural and mechanical remodeling in the pulmonary arteries of rats.

Animals↗

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↗