Placenta accreta: clinical risk factors, accuracy of antenatal diagnosis and effect on pregnancy outcome.

The aim of this study is to evaluate the clinical risk factors, accuracy of antenatal ultrasound for diagnosis, and the effect of these on pregnancy outcome. It is a retrospective study looking at cases which had hysterectomy following vaginal or caesarean section deliveries from 1993 to 2005. Data regarding the maternal demographic characteristics, number of previous CS, number of previous termination/curettage, antenatal scan findings (state features) and the gestation at which accreta was first suspected/diagnosed, MRI scan findings, pregnancy outcome (need for hysterectomy, amount of blood loss, amount of transfusion, length of ICU and hospital stay, other maternal complications, and neonatal outcome) were collected and evaluated. There were a total of 40 cases diagnosed to have abnormal placental attachment and majority of these were actually diagnosed antenatally by sonography. Visualisation of an absence or thinning of hypoechoic myometrial zone had the highest sensitivity to detect placenta accreta followed by intraplacental lacunae, focal mass tissue elevation and disruption of uterine serosal bladder wall.

Determination of membrane tension during balloon distension of intestine.

During the last decades, it has become increasingly common to make balloons distension in visceral organs in vivo. In particular this is true for studies of gastrointestinal motor function and biomechanics. Balloon distension is often used for assessment of small intestinal compliance and tension based on Laplace's law for cylindrical pressure pipes. This commonly used law is valid only when the balloon-distended intestine is cylindrical. Experimentally, it is seen that the diameter of the balloon-distended intestine is not a constant, but variable in the axial direction. Hence, it is necessary to improve Laplace's law for intestinal investigation. In this paper we develop the framework for determination of the tension distribution in circumferential and longitudinal direction during balloon distension. When the radii of curvature are measured from a photograph of the intestinal profile, then the membrane stress resultants can be computed everywhere in the intestine in contact with the balloon from the equations of equilibrium. The experimental data were obtained from small intestinal segments from five pigs and three guinea pigs. Papaverine was injected before the animals were sacrificed to relax the intestinal smooth muscle. The segments were immersed in a bath with calcium-free Krebs solution with dextran and EGTA. A balloon was distended in the lumen with pressures up to 15 cmH2O in the pigs and 10 cmH2O in the guinea pigs and radii were measured along the z-axis. The tension in circumferential direction had its maximum approximately 25% away from the middle of the balloon. The circumferential tension was 2-3 times higher than the longitudinal tension. In conclusion when we know the shape of the intestine, we can compute the circumferential and longitudinal components of tension. The large variation in tensions along the z axis must be considered when performing balloon distension studies in the gastrointestinal tract for studying physiological and pathophysiological problems in which loading conditions are important, e.g. intestinal mechanoreceptor studies in order to obtain accurate description of the biomechanics and the stimulus-response function.

The surface-tension-driven flow of blood from a droplet into a capillary tube.

In tissue, medical, or dental engineering, when blood comes into contact with a new artificial material, the flow may be influenced by surface tension between the blood and the surface of the material. The effect of surface tension on the flow of blood is significant, especially in microscale. The leading edge of the flowing blood is the triple point where the blood, the material surface, and a stationary gas orfluid meet. The movement of the triple point, i.e., the advancing front of the flow, is driven by surface tension, resisted by viscous shear stress, and balanced by the inertial force (-mass x acceleration). In this article, the dynamics is illustrated in detail in the case of blood flowing into a capillary tube by contact. The capillar, tube draws the blood into it. It is shown theoretically that initially the flow of blood in the capillary has a large acceleration, followed by a relatively large deceleration over the next short period of time, then the acceleration becomes small and oscillatory. The velocity history appears impulsive at first, then slows down. The history of the length of blood column appears smooth after integration. Existing solutions of the Navier-Stokes equation permit the analysis of simpler cases. Further fluid mechanics development is needed to meet the practical needs of bioengineering. The importance of experimental study of surface tension and contact angle over a biological surface or a man-made material as a future direction of research is pointed out.

Tissue remodeling of rat pulmonary artery in hypoxic breathing. II. Course of change of mechanical properties.

When cells and the matrix of a tissue remodel, the mechanical properties of the tissue do change. The mechanical properties are expressed by constitutive equations. In this article the remodeling of the constitutive equation of the pulmonary artery is studied. The remodeling was induced in a rat breathing a gas whose oxygen concentration was suddenly decreased as a step function of time and maintained constant (17.2%, 13.6%, or 10%) afterwards. Since the mathematical form of the constitutive equation has been identified in earlier papers, we need to determine only the elastic constants that change in the process of tissue remodeling. We consider arteries subjected to blood pressure and longitudinal stretch, and limit ourselves to two-dimensional problems involving only circumferential and longitudinal stress and strain. In the neighborhood of an in vivo state, the perturbations of stresses and strains are related by linear, anisotropic, tensor equations involving three elastic constants: the incremental Young's modulus in the circumferential direction Ythetaz, that in the longitudinal direction Yzz, and the cross modulus Ythetaz. Over a 24 h period, changes of Ythetatheta between 164 and 187 kN/m2, Yzz between 64 and 92 kN/m2, and Ythetaz between 61 and 88 kN/m2 are statistically insignificant.

Tissue remodeling of rat pulmonary artery in hypoxic breathing. I. Changes of morphology, zero-stress state, and gene expression.

The remodeling of the pulmonary arterial tissue in response to a step change of the oxygen concentration in the gas in which a rat lives was recorded as function of time and function of O2 concentration. Three steps of changing from 20.9% to 17.2%, 13.6%, and 10% O2 were imposed. Earlier work in our laboratory has shown that pulmonary arterial tissue remodeling is significant in the first 24 h after a step change of oxygen tension. Hence we made measurements in this period. Furthermore, data were obtained for tissue remodeling of circumferential and axial lengths of the pulmonary arteries. We recorded the activities of gene expressions in the lung tissues by microarray, determined the dose response curves of gene expression in the homogenized whole lungs with respect to four levels of O2 concentration, and obtained the time courses of gene expression in the lung parenchyma in 30 days after a step decrease of O2 concentration from 20.9% to 10%. We would like to suggest that the correlation of gene expression with physiological function parameters, i.e., time, O2 tension, blood pressure, opening angle, wall thicknesses, etc., is the way to narrow down the search for specific genes for specific physiological functions.

Correlation of gene expression with physiological functions: Examples of pulmonary blood vessel rheology, hypoxic hypertension, and tissue remodeling.

Microarray gene chip technology is a powerful invention looking for applications. A general principle is proposed here to direct the power of the technology toward physiology, medicine, and pharmacology. Our principle is to match quantitative measures of gene expression with the trend of mathematical parameters that describe biological functions. Mathematical parameterization is the heart. The procedure is illustrated by lung physiology, including the hypoxic hypertension, rheological properties of the tissues, and the remodeling of the pulmonary arterial wall under hypertensive stress. We show first how to reduce the experimental results on these physiological functions into mathematical formulas, and how the parameters of these formulas describe the functional trends precisely. Then under the assumption that the microarray reveals gene activities quantitatively, we match the trends of the gene activity with the trends of the functional parameters. Genes whose trends do match are interpreted as relevant to the functions. Those that do not match are considered irrelevant to the functions. The more functions we consider, the fewer will be the number of genes that are relevant to all functions. Thus we learn about the generality and specificity of the influence of genes on physiology.

Remodeling of the bifurcation asymmetry of right coronary ventricular branches in hypertrophy.

To document the remodeling of the asymmetric branching pattern of the coronary right ventricular branches (RVBs) in right ventricular hypertrophy (RVH), we computed an asymmetry ratio, S, for the diameters and lengths of all vessels, defined as the ratio of the daughter diameters and lengths, respectively. We have previously induced RVH in pigs by pulmonary stenosis for five weeks. At autopsy, silicone elastomer casts of the right coronary arteries were made and the morphometric data on the branching pattern and vascular geometry of the RVB were collected. Data on smaller vessels were obtained from histological specimens while data on larger vessels were obtained from vascular casts. The results show that the diameter asymmetry ratio was significantly decreased in RVH hearts. The asymmetry ratios of diameters and lengths were used to compute the asymmetry ratios for vascular resistance and flow of the various daughter vessels. It was found that the degree of asymmetry of the resistance and flow were decreased, which implies that the flow heterogeneity at a bifurcation is decreased in the RVH hearts.

The zero-stress state of the gastrointestinal tract: biomechanical and functional implications.

The stresses and strains that remain in an organ when the external load is removed (the no-load state) are called residual stresses and strains. They can be relieved by cutting up the organ to obtain the zero-stress configuration. This phenomenon was demonstrated more than 15 years ago in cardiovascular research but until recently it was not realized by the gastrointestinal research community. The function of the gastrointestinal tract is to propel food by peristaltic motion, which is a result of the interaction of the tissue forces in the wall and the hydrodynamic forces in the food bolus. To understand the tissue forces, it is necessary to know the stress-strain relationships of the tissues that must be measured in reference to the zero-stress state. It has become clear that the zero-stress configuration of the gastrointestinal tract is very different from that of the no-load condition and that the zero-stress state is sensitive to structural and mechanical remodeling. The purpose of this review is to describe the basic theory and experiments of residual stress and to explore its physiological and pathophysiological implications in the gastrointestinal system.

A hemodynamic analysis of coronary capillary blood flow based on anatomic and distensibility data.

An understanding of cardiac health and disease requires knowledge of the various factors that control coronary capillary blood flow. An analysis of coronary capillary blood flow based on a complete set of actual data on the capillary anatomy and elasticity does not exist. Previously, a complete set of data on the branching pattern and the vascular geometry of the pig coronary capillary network were obtained in our laboratory. In the present study, we obtained distensibility data on the coronary capillary blood vessels on the epicardial surface in the form of a pressure-diameter relationship using intravital microscopy. A mathematical model of the coronary capillary blood flow was then constructed on the basis of measured anatomic and elasticity data of the coronary capillary network, rheology of blood, physical laws governing blood flow, and appropriate boundary conditions. The constructed model was used to examine the heterogeneity of the spatial distribution of coronary blood flow, which is an important issue in coronary physiology. One interesting result of the model is that the dispersions of pressure and flow are significantly reduced in the presence of capillary cross-connections, and the resistance to flow is reduced as well. Finally, we found that the compliance of the epicardial surface capillary vessels is so small that its effect on the blood pressure drop is negligible in the diastolic state. However, the compliance of the intramyocardial capillaries remains unknown, and the interaction of the muscle contraction and blood vessel elasticity in systole remains to be studied.

Strain distribution in the layered wall of the esophagus.

The function of the esophagus is to move food by peristaltic motion, which is the result of the interaction of the tissue forces in the esophageal wall and the hydrodynamic forces in the food bolus. To understand the tissue forces in the esophagus, it is necessary to know the zero-stress state of the esophagus, and the stress-strain relationships of the tissues. This article is addressed to the first topic: the representation of zero-stress state of the esophagus by the states of zero stress-resultant and zero bending moment of the mucosa-submucosa and the muscle layers. It is shown that at the states of zero stress-resultant and zero bending moment, these two layers are not tubes of smaller radii but are open sectors whose shapes are approximately cylindrical and more or less circular. When the sectors are approximated by circular sectors, we measured their radii, opening angles, and average thickness around the circumference. Data on the radii, thickness-to-radius ratios, and the opening angles of these sectors are presented. Knowing the zero-stress state of these two layers, we can compute the strain distribution in the wall at any in vivo state, as well as the residual strain in the esophageal wall at the no-load state. The results of the in vivo states are compared to those obtained by a conventional approach, which treats the esophageal wall as a homogeneous material, and to another popular simplification, which ignores the residual strains completely. It is shown that the errors caused by the homogeneous wall assumption are relatively minor, but those caused by ignoring the residual strains completely are severe.

Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia.

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (DeltapO2) in the breathing gas. For a step change of DeltapO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and DeltapO2, which can be written as P(t-t1 | DeltapO2). An effective method does not exist to examine the nonlinear function P(t-t1 | DeltapO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.

Use of intrinsic modes in biology: examples of indicial response of pulmonary blood pressure to +/- step hypoxia.

Recently, a new method to analyze biological nonstationary stochastic variables has been presented. The method is especially suitable to analyze the variation of one biological variable with respect to changes of another variable. Here, it is illustrated by the change of the pulmonary blood pressure in response to a step change of oxygen concentration in the gas that an animal breathes. The pressure signal is resolved into the sum of a set of oscillatory intrinsic mode functions, which have zero "local mean," and a final nonoscillatory mode. With this device, we obtain a set of "mean trends," each of which represents a "mean" in a definitive sense, and together they represent the mean trend systematically with different degrees of oscillatory content. Correspondingly, the oscillatory content of the signal about any mean trend can be represented by a set of partial sums of intrinsic mode functions. When the concept of "indicial response function" is used to describe the change of one variable in response to a step change of another variable, we now have a set of indicial response functions of the mean trends and another set of indicial response functions to describe the energy or intensity of oscillations about each mean trend. Each of these can be represented by an analytic function whose coefficients can be determined by a least-squares curve-fitting procedure. In this way, experimental results are stated sharply by analytic functions.

Engineering analysis of biological variables: an example of blood pressure over 1 day.

Almost all variables in biology are nonstationarily stochastic. For these variables, the conventional tools leave us a feeling that some valuable information is thrown away and that a complex phenomenon is presented imprecisely. Here, we apply recent advances initially made in the study of ocean waves to study the blood pressure waves in the lung. We note first that, in a long wave train, the handling of the local mean is of predominant importance. It is shown that a signal can be described by a sum of a series of intrinsic mode functions, each of which has zero local mean at all times. The process of deriving this series is called the "empirical mode decomposition method." Conventionally, Fourier analysis represents the data by sine and cosine functions, but no instantaneous frequency can be defined. In the new way, the data are represented by intrinsic mode functions, to which Hilbert transform can be used. Titchmarsh [Titchmarsh, E. C. (1948) Introduction to the Theory of Fourier Integrals (Oxford Univ. Press, Oxford)] has shown that a signal and i times its Hilbert transform together define a complex variable. From that complex variable, the instantaneous frequency, instantaneous amplitude, Hilbert spectrum, and marginal Hilbert spectrum have been defined. In addition, the Gumbel extreme-value statistics are applied. We present all of these features of the blood pressure records here for the reader to see how they look. In the future, we have to learn how these features change with disease or interventions.

Changes in the organization of the smooth muscle cells in rat vein grafts.

Mechanical tensile stress in vein grafts increases suddenly under the influence of arterial blood pressure. In this study, we examined the influence of increased tensile stress on the organization of the smooth muscle cells (SMCs) in the neointima and media of the rat vein grafts. An autogenous jugular vein was grafted into the abdominal aorta of the rat, and changes in the organization of the vein graft SMCs were studied by observing the distribution of SMC actin filaments and nuclei at 3 min and 1, 5, 10, and 30 days after surgery. In a normal jugular vein, the average wall circumferential tensile stress was approximately 3 kPa at an internal pressure of 3 mm Hg. The SMCs, that contained long, slender actin filamentous bundles, were oriented mainly in the circumferential direction of the vessel, and constituted a 2- to 3-cell-thick medial layer underneath the endothelium. In a vein graft, the wall circumferential tensile stress suddenly increased by approximately 140 times compared with the control level. In response to this suddenly increased stress, the SMC layer was stretched into a structure with scattered pores and disrupted SMC actin filamentous bundles within 3 min. This initial change was followed by a rapid reduction in the density of the SMC nuclei and actin filaments within 1 day and progressive SMC proliferation, that was associated with medial thickening and a change in the SMC orientation from 5 to 30 days. Further studies showed that a local inflation of normal jugular veins to 120 mm Hg for 3 min induced a similar change as found in the vein grafts, whereas the organization of the SMCs was not significantly changed in vein-vein grafts, that did not experience a change in tensile stress. These results suggested that increased tensile stress contributed to the initial damage of the SMCs and played a role in the regulation of medial SMC remodeling in vein grafts.

Morphometry and strain distribution in guinea pig duodenum with reference to the zero-stress state.

The aim of the present study is to determine the distribution of residual circumferential strains along the duodenum in anesthetized guinea pigs. A silicone elastomer was allowed to harden in the duodenal lumen under a pressure of 0.7 kPa. The duodenum was excised with the cast and photographed. The zero-stress state was obtained by cutting rings of duodenum radially. The geometric configuration at the zero-stress state is of fundamental importance, because it is the basic state with respect to which the physical stresses and strains are defined. A basic piece of information is the way the tangent vector rotates from one end of the circumference to the other. In the duodenum at zero-stress state, the total rotation of the tangent from one tip to the other is -500 to -850 , with the lowest absolute value in the proximal duodenum. In other words, the duodenum usually turns itself inside out on changing from a loaded state to the zero-stress state. The serosal circumference, the duodenal wall thickness, and the ratio of wall thickness to mucosal circumference decreased in the distal direction. In the pressurized state, the serosal Cauchy strain was tensile and increased in the distal direction; the mucosal Cauchy strain was compressive in the proximal half of the duodenum and tensile in the distal half. The large circumferential residual strains must be taken into account in a study of physiological problems in which the stresses and strains are important, e.g., the bolus transport function.

Analysis of pig's coronary arterial blood flow with detailed anatomical data.

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: one asymmetric model satisfies all anatomical data (including the mean connectivity matrix) and the other, a symmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.

The degree of nonlinearity and anisotropy of blood vessel elasticity.

Blood vessel elasticity is important to physiology and clinical problems involving surgery, angioplasty, tissue remodeling, and tissue engineering. Nonlinearity in blood vessel elasticity in vivo is important to the formation of solitons in arterial pulse waves. It is well known that the stress-strain relationship of the blood vessel is nonlinear in general, but a controversy exists on how nonlinear it is in the physiological range. Another controversy is whether the vessel wall is biaxially isotropic. New data on canine aorta were obtained from a biaxial testing machine over a large range of finite strains referred to the zero-stress state. A new pseudo strain energy function is used to examine these questions critically. The stress-strain relationship derived from this function represents the sum of a linear stress-strain relationship and a definitely nonlinear relationship. This relationship fits the experimental data very well. With this strain energy function, we can define a parameter called the degree of nonlinearity, which represents the fraction of the nonlinear strain energy in the total strain energy per unit volume. We found that for the canine aorta, the degree of nonlinearity varies from 5% to 30%, depending on the magnitude of the strains in the physiological range. In the case of canine pulmonary artery in the arch region, Debes and Fung [Debes, J. C. & Fung, Y. C.(1995) Am. J. Physiol. 269, H433-H442] have shown that the linear regime of the stress-strain relationship extends from the zero-stress state to the homeostatic state and beyond. Both vessels, however, are anisotropic in both the linear and nonlinear regimes.

Longitudinal position matrix of the pig coronary vasculature and its hemodynamic implications.

Hemodynamic analysis of coronary blood flow must be based on a statistically valid geometric model of the coronary vasculature. We have previously developed a diameter-defined Strahler model for the arterial and venous trees and a network model for the capillaries. A full set of data describing the geometric properties of the porcine coronary vasculature was given. The order number, diameter, length, connectivity matrix [m,n] (CM), and parallel-series features were measured for all orders of vessels of the right coronary artery (RCA), left anterior descending artery (LAD), left circumflex artery (LCX), and coronary venous system. The purpose of the present study is to present another feature of the branching pattern of the coronary vasculature: the longitudinal position matrix [m,n] (LPM), whose component in row m and column n is the fractional longitudinal position of the branch point on vessels of order n at which vessels of order m branch off (m < or = n). The LPM of the pig RCA, LAD and LCX arterial trees, as well as the coronary sinusal and thebesian venous trees, are presented. The hemodynamic implications of the LPM are illustrated by comparing two kinds of circuits: one, the CM + LPM model, simulates the mean data on the morphology (diameters, lengths, and numbers), CM, and LPM of vessels, whereas the other, the CM model, simulates the mean data on the morphology and CM without considering the LPM. We found that the LPM affects the hemodynamics of coronary blood flow especially with regard to the nonuniformity or dispersion of flow distribution.

Indicial functions of arterial remodeling in response to locally altered blood pressure.

We investigated the effect of locally altered blood pressure on the remodeling processes of the cells and extracellular matrices of the splenic and ileal arteries and used an indicial function approach to quantitatively analyze the relationship between the altered blood pressure and the remodeling processes. Blood pressure in these arteries was locally modulated by constricting the aorta at a location between the celiac and mesenteric bifurcations, resulting in a higher blood pressure at the splenic arteries then at the ileal arteries, After the pressure changes, the cross-sectional areas and the fractions of the cells and extracellular matrices of the splenic and ileal arteries were examined by electron microscopy at 2, 6, 10, 20, and 30 days. We found that both arteries remodeled, but the splenic arteries (higher blood pressure) remodeled more rapidly and to a larger degree than the ileal arteries (lower pressure compared with the splenic arteries) of the same animal. To verify whether an identical change in the blood pressure at the splenic and ileal arteries leads to the same remodeling process in these arteries, we created another model by constricting the aorta at a location between the mesenteric and renal bifurcations, resulting in hypertension of the same level at both splenic and ileal arteries. We found that the remodeling processes of the cells and matrices were almost identical in the arteries with similar changes in blood pressure. Thus we conclude that the remodeling processes of cells and matrices of the splenic and ileal arteries are dependent on the local blood pressure in aorta constriction-induced hypertension, and the indicial analysis is a useful approach in the description of the relationship between the blood pressure and the arterial remodeling processes.

Direct measurement of transverse residual strains in aorta.

Residual strains were measured in the porcine aorta. Segments were cut from the aorta perpendicular to its longitudinal axis. Microdots of water-insoluble black ink were sprinkled onto the transverse sectional surface of the segments in the no-load state. The segments were then cut radially, and sectional zero-stress states were approached. The coordinates of selected microdots (2-20 microns) were digitized from photographs taken in the no-load state and the zero-stress state. Residual strains in the transverse section were calculated from the displacement of the microdots. The circumferential residual strains on the inner wall and outer wall were calculated from the circumferential lengths in the no-load state and the zero-stress state. Results show that the circumferential residual strain is negative (compressive) in the inner layer of the aortic wall and positive (tensile) in the outer layer, whereas the radial residual strain is tensile in the inner layer and compressive in the outer layer. This residual strain distribution reduces the stress concentration in the aorta under physiological load. The experimental results compared well with theoretical estimations of a cylindrical model. Regional difference of the residual strain exists and is significant (P < 0.01), e.g., the circumferential residual strains on the inner wall of the ascending, descending thoracic, and abdominal regions of the aorta are -0.133 +/- 0.019, -0.074 +/- 0.020, and -0.046 +/- 0.017 (mean +/- SD), respectively. More radial cuts of a segment produced no significant additional strains. This means that an aortic segment after one radial cut can be considered as the zero-stress state.