Pressure-area Relation Research Articles

Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS.

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical-property-preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure-area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure-area curves.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries.

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

Nonlinear lumped-parameter models for blood flow simulations in networks of vessels

To address the issue of computational efficiency related to the modelling of blood flow in complex networks, we derive a family of nonlinear lumped-parameter models for blood flow in compliant vessels departing from a well-established one-dimensional model. These 0D models must preserve important nonlinear properties of the original 1D model: the nonlinearity of the pressure-area relation and the pressure-dependent parameters characterizing the 0D models, the resistance R and the inductance L, defined in terms of a time-dependent cross-sectional area subject to pressure changes. We introduce suitable coupling conditions to join 0D vessels through 0D junctions and construct 0D networks preserving the original 1D network topology. The newly derived nonlinear 0D models are then applied to several arterial networks and the predicted results are compared against (i) the reference 1D results, to validate the models and assess their ability to reproduce good approximations of pressure and flow waveforms in all vessels at a much lower computational cost, measured in terms of CPU time, and (ii) the linear 0D results, to evaluate the improvement gained by including certain nonlinearities in the 0D models, in terms of agreement with the 1D results.

Controllable assembly of zeolite beta monolayers and bilayers on various substrates using the Langmuir–Blodgett technique

The Langmuir–Blodgett (L–B) technique was employed to fabricate the monolayers and bilayers of nano-sized beta (nano-beta) crystals, and the monolayers of micrometer-sized beta (micro-beta) crystals on various substrates including glass plate, α-Al2O3 disk, glass capillary tube, copper wire, stainless-steel tube and γ-Al2O3 tube. With respect to the methanol suspension of 1 wt.% nano-beta modified with cetyltrimethylammonium bromide (CTAB), a two-region surface pressure-area isotherm was obtained, leading to the formation of both nano-beta monolayers and bilayers with satisfactory degree of coverage (DOC) and close packing (DCP) under each transfer surface pressure. When nano-beta crystals were dealuminated, the surface pressure-area relation was reduced to the one-region isotherm, and the resulting L–B film contained aggregated areas. As for the assembly of micro-beta crystals, both methanol and sec-butanol were used as the dispersant. The resulting micro-beta monolayer was randomly oriented with the sedimentation of large truncated-square-bipyramid crystals on compression by using the methanol suspension. The use of sec-butanol as the dispersant resulted in the enhanced hydrophobicity of micro-beta crystals due to the chemical reaction of sec-butanol molecules with surface silanols, leading to the formation of c-oriented micro-beta monolayers over various substrates, and simultaneously the sedimentation of large truncated-square-bipyramid crystals did not occur. Under the structure direction of the c-oriented micro-beta monolayer in the seeded growth, the dense and preferentially c-oriented zeolite beta film could be fabricated, which could not be formed on either the nano-beta monolayer or the micro-beta monolayer with random orientation. Therefore, it would be concluded that the growth of beta crystals over the seed layer could be followed by the epitaxial growth mechanism.

Upper Airway Elasticity Estimation in Pediatric Down Syndrome Sleep Apnea Patients Using Collapsible Tube Theory.

Elasticity of the soft tissues surrounding the upper airway lumen is one of the important factors contributing to upper airway disorders such as snoring and obstructive sleep apnea. The objective of this study is to calculate patient specific elasticity of the pharynx from magnetic resonance (MR) images using a 'tube law', i.e., the relationship between airway cross-sectional area and transmural pressure difference. MR imaging was performed under anesthesia in children with Down syndrome (DS) and obstructive sleep apnea (OSA). An airway segmentation algorithm was employed to evaluate changes in airway cross-sectional area dilated by continuous positive airway pressure (CPAP). A pressure-area relation was used to make localized estimates of airway wall stiffness for each patient. Optimized values of patient specific Young's modulus for tissue in the velopharynx and oropharynx, were estimated from finite element simulations of airway collapse. Patient specific deformation of the airway wall under CPAP was found to exhibit either a non-linear 'hardening' or 'softening' behavior. The localized airway and tissue elasticity were found to increase with increasing severity of OSA. Elasticity based patient phenotyping can potentially assist clinicians in decision making on CPAP and airway or tissue elasticity can supplement well-known clinical measures of OSA severity.

Computationally Efficient Fluid-Particle Dynamics Simulations of Arterial Systems

AbstractRealistic and accurate computer simulations of the particle-hemodynamics in arterial systems can be a valuable tool for numerous biomedical applications. Examples include optimal by-pass grafting and optimal drug-delivery, as well as best medical management concerning the cardio-vascular system. However, such numerical analyses require large computer resources which may become prohibitive for extended sets of arterial bifurcations. A remedy is to develop a hybrid model where the first few generations of the bifurcating arteries of interest are simulated in full 3-D, while a 1-D model is then coupled for subsequent bifurcations. Alternatively, a 1-D computer model can be directly employed to simulate fluid-particle transport in complex bifurcating networks.Relying on a representative axial velocity profile, a physiological 1-D model has been developed and validated, which is capable of predicting with reasonable accuracy arterial flow, pressure field and elastic wall interaction as well as particle transport. The usefulness of the novel 1-D simulation approach is demonstrated via a comparison to 3-D blood flow and microsphere transport in a hepatic artery system, featuring as outlets one major branch and four small daughter vessels. Compared to the 3-D simulation, the 1-D analysis requires only about 1% of computational time. The hybrid modeling approach would be also applicable to the human respiratory tract to evaluate the fate of inhaled aerosols.A simple and cost-effective way to simulate particle-hemodynamics is using a 1-D model for simulating arterial pressures and flow rates as well as microsphere transport, based on assumptions involving the use of a simple algebraic pressure-area relation, an exponential elasticity model for the vessels, and considering only unidirectional flow with a representative skewed velocity profile. In summary, the novel contributions are:• Particle tracking in arteries via 1-D fluid modeling and selection of an averaged, skewed velocity profile based on 3-D simulation results to provide more realistic friction and inertia term values for modeling a flow system with bifurcations.• The 1-D model can be coupled to a 3-D model so that simulations can be run for larger regions of vascular or lung-airway systems.

Design of offshore structures against accidental ship collisions

In this paper, we investigate the damage to offshore platforms subjected to ship collisions. The considered scenarios are bow and stern impacts against the column of a floating platform and against the jacket legs and braces. The effect of the ship–platform interaction on the distribution of damage is studied by modeling both structures using nonlinear shell finite elements. A supply vessel of 7500-ton displacement with bulbous bow is modeled. A comprehensive numerical analysis program is conducted, and the primary findings are described herein. The collision forces from the vessel are compared with the suggested force–deformation curves in the NORSOK code. For collisions with floating platforms we particularly focus on the crushing behavior and potential penetration of the bulbous bow and stern sections into the cargo tanks or void spaces of semi-submersible platforms. For fixed jacket platforms we investigate whether jacket braces can penetrate into the ship without being subjected to significant plastic bending or local denting.Adequate treatment of the relative strength between the interacting bodies is especially relevant for impacts with high levels of available kinetic energy, for which shared energy or strength design is aimed at. Simplifying one body as rigid quickly leads to overly conservative and/or costly solutions, and is in some cases non-conservative.The numerical analysis is used to develop a novel pressure–area relation for the deformation of the bulbous bow and stern corners of the supply vessel. Procedures for strength design of the stiffened panels are discussed. Refined methods and criteria are proposed for strength design of platforms, including both floating and jacket structures. The adequacy of the NORSOK design guidance for collisions against jacket legs is evaluated. The characteristic strength of a cylindrical column is used to develop a novel criterion for the resistance to local denting from stern corners and bulbous bows.

A six-degrees-of-freedom numerical model for level ice–ship interaction

Abstract A new numerical model simulating ship–ice interaction is proposed in this paper. Since icebreaking is in its nature a three-dimensional nonlinear dynamic problem, the numerical model is developed to look into the intricate interaction process by considering ship motions in 6 degrees of freedom (DOFs). The effect on the icebreaking pattern and ship's performance of ship motions in heave, roll and pitch is investigated. Moreover, pressure–area relation is included in calculating the contact force. Semi-empirical method is used in developing the numerical model and the results are validated by comparing with full-scale data from an icebreaker.

AN IMPROVED MODEL FOR REDUCED-ORDER PHYSIOLOGICAL FLUID FLOWS

An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.

Effects of Preemptive Enoximone on Left Ventricular Diastolic Function After Valve Replacement for Aortic Stenosis

Left ventricular (LV) hypertrophy is associated with increased diastolic chamber stiffness early after aortic valve replacement for valve stenosis. Enoximone, a phosphodiesterase III inhibitor, has been shown to improve myocardial contractility and relaxation when administered as a single dose after cardiac surgery. The present study investigated, by analysis of transmitral flow velocity patterns and end-diastolic pressure-area relations, whether enoximone administered before aortic valve surgery has an effect on LV diastolic properties. Prospective, randomized study. Referral center for cardiothoracic surgery at a university hospital. Thirty-four patients undergoing aortic valve replacement for aortic stenosis. Patients in the enoximone group (n = 17) received a bolus dose of 0.35 mg/kg (0.15 mg/kg before aortic cross-clamping and 0.2 mg/kg added to the cardioplegic solution). Individual pressure-area relations (pulmonary capillary wedge pressure v left ventricular end-diastolic area) were obtained by using volume loading by leg elevation before and after surgery with closed chest. The pressure-area relation on the pressure-area plot was shifted to the left after surgery, indicating decreased LV diastolic distensibility in the enoximone and control groups and providing evidence of decreased LV diastolic function. Indices of LV diastolic chamber stiffness, LV operating stiffness (K(LV)) derived from the deceleration time of early ventricular filling, and the constant of chamber stiffness (beta) derived from pressure-area relations were not different after enoximone treatment. Systolic LV function was unaltered after cardiac surgery in both groups. Analysis of changes in transmitral flow patterns identified an increased atrial filling fraction in enoximone-treated patients, suggesting increased atrial systolic function. The unaltered systolic pulmonary venous flow velocity compared with the decrease in the control group after volume loading further supports preservation of left atrial reservoir function with enoximone in the absence of evidence for decreased LV stiffness. Preemptive enoximone did not change LV diastolic function based on diastolic filling patterns or LV stiffness indices (K(LV) and beta) derived from Doppler early filling deceleration time and pressure-area relations. Doppler data suggested improvement of left atrial systolic function and preservation of left atrial reservoir function with enoximone.

Theoretical analysis of the effects of viscous losses and abdominal straining on urinary outlet function.

The aim of this study was to theoretically explore the relationship between the tube law (TL) of the urethra and the pressure-flow (p-Q) relationship during micturition. The understanding of this relation is important for the evaluation of outlet obstruction by urodynamic interpretation of p-Q plots. We simulated the outlet function by a lumped theoretical model, and suggested how the TL can be used to quantitatively predict the p-Q relationship of the system. Our analysis considered the relation between the TL and the steady state p-Q plot for various TLs including the hysteresis of the pressure-area relationship. The inclusion of pressure losses distal to the flow controlling zone and experimentally measured p-A relations of the urethra in the model lead to the predictions that flow in the flow controlling zone is not always critical but is often in the sub-critical range, that an increase in abdominal pressure can increase the flow under certain conditions, and that hysteresis in the pressure-area relation is correlated to the hysteresis in the p-Q plot.

Imaging and Diagnostic Testing: Diastolic dysfunction after coronary artery bypass grafting: a frequent finding of clinical significance not influenced by intravenous calcium

BackgroundDiastolic dysfunction is common immediately after coronary artery bypass surgery (CABG). The duration of this phenomenon is unknown. Intravenous calcium is frequently administered during separation from cardiopulmonary bypass (CPB). We sought to determine whether intravenous calcium influences perioperative diastolic function and whether diastolic dysfunction persists into the postoperative period. Methods and resultsPatients undergoing first-time elective CABG (n = 29) were randomly assigned to receive intravenous calcium chloride (n = 13) or placebo (n = 16) during separation from CPB. Diastolic function was assessed by the pressure-area relation with transesophageal echocardiography and pulmonary capillary wedge pressure (PCWP) measured simultaneously. Left ventricular end-diastolic area (LVEDA) and Doppler indexes were measured at comparable PCWP (within 2 mm Hg) at baseline, after separation from CPB, after sternal closure, and 3 hours after surgery. After CABG, both groups had a significant decrease in LVEDA and mitral E-wave deceleration time that persisted at 3 hours. Because there were no significant differences between the calcium and control groups at any time point, the data for the entire study cohort was analyzed. The LVEDA decreased (stiffness increased) progressively from 16.9 ± 3.4 cm2 at baseline to 15.8 ± 2.9 cm2 after CPB, 14.9 ± 2.5 cm2 after sternal closure, and 14.3 ± 3.1 cm2 at 3 hours after surgery (P < .0001). The mitral E-wave deceleration time measured at the same time points was 168 ± 47 ms, 136 ± 25 ms, 137 ± 36 ms, and 111 ± 44 ms (P = .0001). ConclusionsAn increase in left ventricular diastolic chamber stiffness is nearly universal after CABG, and it persists for at least 3 hours after surgery. An intravenous bolus of calcium chloride given during separation from CPB has no measurable negative effect on diastolic function. In the setting of increased chamber stiffness, the PCWP alone does not adequately reflect the volume status and effective preload of the left ventricle.

Instantaneous end diastolic stiffness (IEDS): A simple, load independent measurement of left ventricular diastolic function in patients undergoing cardiac surgery

The end-diastolic pressure-volume relation is a load-independent measurement of diastolic function. However, its clinical utility is limited because of its complexity. Instantaneous end-diastolic stiffness (IEDS) is a simple to perform, single-point, measurement of ventricular stiffness. We have validated it against the end-diastolic pressure-area relation (EDPAR) in patients undergoing cardiac surgery. EDPARs were analyzed before and after cardiopulmonary bypass in 29 patients and compared with IEDS. Data was collected in an additional 69 patients in order to estimate the range of values of IEDS. End-diastolic area (EDA) measured by transesophageal echocardiography (TEE) was substituted for end-diastolic volume, and pulmonary capillary wedge pressure (PWCP) was substituted for end-diastolic pressure. IEDS = 100 x (log10 PWCP)/EDA. Comparison of the methods was done by ordinary least products regression analysis. Agreement between EDPAR and IEDS was identified by the absence of fixed and proportional bias. The maximal range of corresponding values identified by 95% confidence intervals was within +/- 16% of the mean indicating satisfactory agreement. The geometric mean and 95% confidence intervals (CI) for IEDS were 8. 7 mmHg/dm2 (8.1 to 9.4) and for IEDS indexed to body surface area were 17.2 mmHg/dm(2)/m2 (16.0 to 18.6). IEDS is a load independent index of left ventricular stiffness.

Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state

Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure–area relation for collapsible tubes.The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method.Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.

Effects of pacing-induced and balloon coronary occlusion ischemia on left atrial function in patients with coronary artery disease

OBJECTIVESThe aim of this study was to compare left atrial (LA) function in 16 patients with distal left anterior descending (LAD) and in 16 patients with proximal left circumflex (LCx) coronary artery stenosis at rest and immediately after pacing-induced tachycardia (LAD-pacing [P] and LCx-P) or coronary occlusion (LAD-CO and LCx-CO).BACKGROUNDDuring left ventricular (LV) ischemia, compensatory augmentation of LA contraction enhances LV filling and performance. The left atrium is supplied predominantly by branches arising from the LCx. Therefore, we hypothesized that one mechanism for the loss of atrial contraction may be ischemic LA dysfunction.METHODSLeft ventricular and LA pressure–area relations were derived from simultaneous double-tip micromanometer pressure recordings and automatic boundary detection echocardiograms.RESULTSImmediately after pacing or after coronary occlusion, LV end-diastolic pressure, LV relaxation, LA mean pressure and LV stiffness significantly increased in all patients. However, the area of the A loop of the LA pressure–area relation, representing the LA pump function, significantly decreased in groups LCx-P and LCx-CO (from 14 ± 3 to 9 ± 2, and from 16 ± 4 to 9 ± 2 mm Hg·cm2, respectively, p < 0.05), whereas it increased in groups LAD-P and LAD-CO (from 12 ± 3 to 54 ± 10, and from 16 ± 3 to 49 ± 8 mm Hg·cm2, respectively, p < 0.001).CONCLUSIONSIn patients with LAD stenosis, LV supply or demand ischemia is associated with enhanced LA pump function. However, in patients with proximal LCx stenosis who develop the same type and degree of ischemia, LA branches might have been affected, rendering the LA ischemic and unable to increase its booster pump function.

Assessment of the mechanical properties of coronary arteries using intravascular ultrasound: an in vivo study.

The pressure-area relation of coronary arteries provides important information about the mechanical properties of these vessels. In human subjects methodological limitations have precluded measurement of instantaneous compliance and coronary stress in vivo. The purpose of this study was to assess a new method for measuring instantaneous values of coronary artery compliance and wall stress utilizing simultaneously acquired pressure and intravascular ultrasound measurements of vessel area. Ten subjects with coronary artery disease had intravascular ultrasound studies of the proximal left anterior descending or circumflex coronary arteries. Coronary luminal area was measured with a 30-MHz (3F or 3.5F) intravascular ultrasound catheter and simultaneous coronary pressure measured with a 2F micromanometer-tipped catheter. Using this technique the nonlinear pressure-area relation and mean circumferential wall stress were determined over the physiological pressure range. Coronary artery compliance at 100 mmHg ranged from 0.010 to 0.052 mm2/mmHg (mean +/- SD, 0.020+/-0.012 mm2/mmHg). Peak systolic circumferential stress ranged from 0.52 to 2.03 x 10(6) dyn/cm2 (1.09+/-0.42 x 10(6) dyn/cm2). This study describes a new method of determining coronary artery mechanical properties over the physiological pressure range. This technique may be useful in further studies of coronary artery mechanics.

Evaluation of the Left Atrial Performance Using Acoustic Quantification.

In most clinical studies, evaluation of left atrial (LA) function evolved from estimation of LA size on chest radiograph, electrocardiographic P wave abnormalities, LA diameter determined at fluoroscopy or by echocardiography, LA pressure recordings, blood flow velocity with Doppler echocardiography, and measurements of LA volume based on echocardiographic, cineangiographic, radionuclide, and magnetic resonance imaging techniques. The recent development of real-time two-dimensional echocardiographic acoustic quantification (AQ) suggests that LA dimensions can be measured instantaneously to provide online assessment of its systolic and diastolic functions. By means of AQ echocardiography and simultaneous recordings of LA pressure, the LA pressure-area relation can be obtained. LA pressure-area relation consisted of two loops: the A loop, representing the LA pump function, and the V loop, representing LA reservoir and passive emptying functions. The importance of LA function has been demonstrated in congestive heart failure, atrial fibrillation, hypertension, and ischemic heart disease and during pacing or dobutamine infusion.

Left atrial energy in normal subjects, in patients with symptomatic mitral stenosis, and in patients with advanced heart failure

In a population consisting of 45 subjects (15 patients with mitral stenosis, 15 patients with heart failure, and 15 normal subjects), the left atrial (LA) pressure-area relation was assessed and the correlations between LA stroke work, LA kinetic energy, and LA ejection force were studied. The area of the counterclockwise A loop expressing the LA external work was measured. LA kinetic energy was obtained from the formula: 1 2 · stroke volume · 1.06 · v 2, where v = transmitral Doppler A velocity. An excellent correlation was found between LA stroke work index and LA kinetic energy when data from all patients were plotted together (r = 0.95, p < 0.001). The Pearson's correlation similarity coefficient between LA ejection force and kinetic energy as well as between LA ejection force and stroke work index was r = 0.54 (p < 0.001). The r value of 0.54 was significantly lower than r = 0.95 (p < 0.03). LA kinetic energy extends the use of transmitral flow Doppler data to include assessment of LA work. LA work can be obtained noninvasively with a high degree of accuracy.

Noninvasive measurement of the human brachial artery pressure-area relation in collapse and hypertension.

A noninvasive method to obtain pressure-lumen area (P-A) measurements of the human brachial artery is introduced. The data obtained from this method are analyzed using a mathematical model of the relationship between vessel pressure and lumen area including vessel collapse and hypertension. An occlusive arm cuff is applied to the brachial artery of ten normal subjects. The cuff compliance is determined continuously by means of a known external volume calibration pump. This permits the computation of the P-A curve of the brachial artery under the cuff. A model is applied to analyze the P-A relation of each subject. The results show that the lumen area varies considerably between subjects. The in vivo resting P-A curve of the brachial artery possesses features similar to that of in vitro measurements. A primary difference is that the buckling pressure is higher in vivo, presumably due to axial tension, as opposed to in vitro where it is near zero or negative. It is found that hypertension causes a shift in the P-A curve towards larger lumen areas. Also, the compliance-pressure curve is shown to shift towards higher transmural pressures. Increased lumen area provides an adaptive mechanism by which compliance can be maintained constant in the face of elevated blood pressure, in spite of diminished distensibility.

Effects of balloon mitral valvuloplasty on left atrial function in mitral stenosis as assessed by pressure–area relation

Objectives. This study sought to investigate the changes induced on the pressure–area relation of the left atrium in patients with mitral stenosis after percutaneous balloon mitral valvuloplasty.Background. Left atrial (LA) function is influenced by changes in LA afterload. The latter is increased in mitral stenosis as a result of increased resistance to blood flow imposed by the stenotic mitral valve.Methods. We studied the effects of acute alterations of LA afterload induced by retrograde nontransseptal balloon mitral valvuloplasty (RNBMV) on LA function in patients with mitral stenosis. LA pressure–area relations were obtained in 15 patients with mitral stenosis (8 with sinus rhythm, 7 with atrial fibrillation) before and after valvuloplasty, as well as in 15 normal subjects. LA pressure was recorded by a catheter-tipped micromanometer introduced retrogradely into the left atrium while LA area was recorded simultaneously using acoustic quantification. The areas of the A and V loops of the pressure–area relation as well as the LA chamber stiffness constant were calculated.Results. Balloon valvuloplasty resulted in a significant increase in mitral valve area (p < 0.001) and a substantial reduction of the mean transmitral pressure gradient (p < 0.001) and mean LA pressure (p < 0.001). The area of the A loop in patients with sinus rhythm and the area of the V loop in those with atrial fibrillation increased significantly after completion of the procedure (p < 0.001). Furthermore, LA stiffness decreased in both groups.Conclusions. After RNBMV, there is a significant increase in LA pump function in patients with sinus rhythm, a significant increase in LA reservoir function in patients with atrial fibrillation and a significant reduction in LA stiffness in all patients. Marked alterations of the configuration of the LA pressure–area relation occur immediately after successful RNBMV in patients with mitral stenosis.