Estimation of aortic distensibility and instantaneous left ventricular volume in living man

A method is presented in this paper for the estimation of aortic distensibility and instantaneous systolic left ventricular volume in living man in the absence of valvular regurgitation. The method is based on a simple, elastic-reservoir-theory, model of the circulatory system and requires no assumption concerning the geometry of the left ventricle. The input data required for this mathematical model consists of stroke volume, an aortic pressure record over an entire cardiac cycle and end diastolic ventricular volume. The procedure developed here for the estimation of aortic distensibility and instantaneous left ventricular volume is very practical from a computational point of view. It is believed that it will yield useful information concerning two clinically important quantities which cannot be measured directly in living man and will facilitate the study of correlations between these quantities and various physiological and pathological states. Results are presented in the paper for six cardiac patients. The requisite data in each case was obtained in the Cardiac Research Laboratory at the Peter Bent Brigham Hospital.     

The application of robust calibration to radioimmunoassay.

The minute concentrations of many biochemically and clinically important substances are currently estimated by radioimmunoassay (RIA). Traditionally, the most popular approaches to the statistical analysis of RIA data have been to linearize the data through transformation and fit the calibration curve using least squares or to directly fit a nonlinear calibration curve using least squares. Estimates of the hormone concentration in patients are then obtained using this curve. Unfortunately, the transformation is frequently unsuccessful in linearizing the data. Furthermore, the least squares fit can lead to erroneous results in both approaches since the many sources of error which exist in the RIA process often result in outlier observations. In this paper, an approach to the analysis of RIA data which incorporates robust estimation methods is described. An algorithm is presented for obtaining the M-estimates of nonlinear calibration curves. The curves to be fitted are modified hyperbolae based on 12 to 16 observations. A procedure, based on the application of the Bonferroni Inequality, is presented for obtaining tolerance-like interval estimates of the concentration of the hormone of interest in the patients. Results of simulations are cited to support the method of construction of confidence bands for the fitted calibration curve. Data obtained from the Veteran's Hospital, Buffalo, New York are used to illustrate the application of the algorithm which is presented.     

A theoretical description of blood flow through the mitral orifice

A nonlinear differential equation describing the Doppler velocity profile for blood flow through the mitral valve has been derived. This equation is based on fluid dynamics and a simple, but comprehensive model of atrial and ventricular mechanics. A numerical solution to the equation is described and provides excellent agreement with Doppler velocity curves obtained clinically. One important result of the theory is that in patients with mitral stenosis, the slope of the clinically observed straight-line descent of the velocity profile is proportional to the mitral orifice area and inversely proportional to the atrioventricular compliance.     

HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.     

A Three-Dimensional Analytical (Rheological) Model of the Human Left Ventricle in Passive-Active States: Nontraumatic Determination of the In Vivo Values of the Rheological Parameters

In this paper a three-dimensional continuum model of a mammalian left ventricle is formulated. The stresses in the model satisfy the conditions of zero stress on the outer (epicardial surface-representing) boundary. The strains of the model are obtained from the actual dynamic geometry measurements (obtained from cineangiocardiography). Since the left ventricular muscle is incompressible, the dilatational strain is zero and hence the (three-dimensional) deviatric stress components are related to the corresponding strain components by Maxwell and Voigt rheological model analogues of one-dimensional systems; the parameters of the model are series and parallel elastic (SE, PE) elements and the contractile element (CE) (representing the sarcomere). The incorporation of the rheological features of the cardiac muscle into the three-dimensional constitutive equations (for the three-dimensional continuum model of the left ventricle) is a feature of this paper. A procedure is presented to determine the parameters of the constitutive equations (i.e., the SE, PE, and the parameters of the force-velocity relation for the CE) for the left ventricle of a subject from data on the dimensions and chamber pressure of the left ventricle. The values of these parameters characterize the rheology of the left ventricular muscle of the subject. In order to demonstrate clinical application of the analyses, in vivo data of the subjects' left ventricular pressure and dimensions are obtained, and the analyses are applied to the data to determine (for each subject) the values and characteristics of the elastic elements and CEs.     

Modeling initial strain distribution in soft tissues with application to arteries

A general theory for computing and identifying the stress field in a residually stressed tissue is presented in this paper. The theory is based on the assumption that a stress free state is obtained by letting each point deform independently of its adjacent points. This local unloading represents an initial strain, and can be described by a tangent map. When experimental data is at hand in a specific situation, the initial strain field may be identified by stating a nonlinear minimization problem where this data is fitted to its corresponding model response. To illustrate the potential of such a method for identifying initial strain fields, the application to an in vivo pressure–radius measurement for a human aorta is presented. The result shows that the initial strain is inconsistent with the strain obtained with the opening-angle-method. This indicates that the opening-angle-method has a too restrictive residual strain parameterization, in this case     

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) < 0.75) during isovolumic relaxation and early filling; and 4) logarithmic regression is superior in estimating the fixed volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.     

Analysis of the influence of modelling assumptions on the prediction of the elastic properties of cardiac fibres

Abstract

Although several numerical models of the human heart have been proposed in the literature, there are still several discrepancies among the results predicted by each model. These discrepancies can be attributed to the fact that each model has a number of assumptions and simplifications, which can limit the scope and precision of the numerical predictions obtained. Moreover, none of the works reported in the literature have assessed the influence of modelling assumptions on the predicted cardiac fiber elastic properties. In this paper a new passive mechanical model that combines the left ventricular (LV) pressure–volume in-vivo measurements with an indirect approach based on the finite element method (FEM), is proposed and used to analyze the influence of different modelling assumptions on the estimated elastic properties of the cardiac fiber. This analysis is carried out by varying modelling assumptions that are common to existing passive mechanical models. The results have shown that although the different modelling assumptions have a significant effect on the predicted value of the fiber elastic properties, they tend to lead to the same results. This suggests that simplified passive numerical models in combination with adjustment factors, are valid in comparison with more refined and complex LV passive models.     

A new electric method for non-invasive continuous monitoring of stroke volume and ventricular volume-time curves

ABSTRACT: BACKGROUND: In this paper a new non-invasive, operator-free, continuous ventricular stroke volume monitoring device (Hemodynamic Cardiac Profiler, HCP) is presented, that measures the average stroke volume (SV) for each period of 20 seconds, as well as ventricular volume-time curves for each cardiac cycle, using a new electric method (Ventricular Field Recognition) with six independent electrode pairs distributed over the frontal thoracic skin. In contrast to existing non-invasive electric methods, our method does not use the algorithms of impedance or bioreactance cardiography. Instead, our method is based on specific 2D spatial patterns on the thoracic skin, representing the distribution, over the thorax, of changes in the applied current field caused by cardiac volume changes during the cardiac cycle. Since total heart volume variation during the cardiac cycle is a poor indicator for ventricular stroke volume, our HCP separates atrial filling effects from ventricular filling effects, and retrieves the volume changes of only the ventricles. METHODS: In-vitro experiments on a post-mortem human heart have been performed to measure the effects of increasing the blood volume inside the ventricles in isolation, leaving the atrial volume invariant (which can not be done in-vivo). These effects have been measured as a specific 2D pattern of voltage changes on the thoracic skin. Furthermore, a working prototype of the HCP has been developed that uses these in-vitro results in an algorithm to decompose voltage changes, that were measured in-vivo by the HCP on the thoracic skin of a human volunteer, into an atrial component and a ventricular component, in almost real-time (with a delay of maximally 39 seconds). The HCP prototype has been tested in-vivo on 7 human volunteers, using G-suit inflation and deflation to provoke stroke volume changes, and LVot Doppler as a reference technique. RESULTS: The in-vitro measurements showed that ventricular filling caused a pattern over the thorax quite distinct from that of atrial filling. The in-vivo tests of the HCP with LVot Doppler resulted in a Pearson's correlation of R = 0.892, and Bland-Altman plotting of SV yielded a mean bias of -1.6 ml and 2SD = 14.8 ml. CONCLUSIONS: The results indicate that the HCP was able to track the changes in ventricular stroke volume reliably. Furthermore, the HCP produced ventricular volume-time curves that were consistent with the literature, and may be a diagnostic tool as well.     

Monitoring the Function of the Right Ventricle of the Heart When Correcting an Interventricular Septal Defect

A clinical study of intracardiac hemodynamics was conducted on 46 patients with an interventricular septal defect. The practical significance of determining the contractile state of the right ventricular myocardium was confirmed based on information obtained during the long-term catheterization of the right chambers of the heart, when constructing the right ventricular function curves, and analyzing the pressure–volume diagrams. This approach to the analysis of intracardiac hemodynamic parameters versus conventional hemodynamic monitoring allows the cardiac function to be assessed on a real-time basis, the causes of the development of a low cardiac output to be revealed, and optimal ways of the regulation of myocardial contractility to be elaborated.     

Nonlinear relativistic quantum theory of Cherenkov emission of longitudinal Langmuir waves in a plasma

A nonlinear relativistic quantum theory of stimulated Cherenkov emission of longitudinal waves by a relativistic monoenergetic electron beam in a cold isotropic plasma is presented. The theory makes use of a quantum model based on the Klein-Gordon equation. The instability growth rates are obtained in the linear approximation and are shown to go over to the familiar growth rates in the classical limit. The mechanisms for the nonlinear saturation of relativistic Cherenkov beam instabilities are described with allowance for quantum effects, and the corresponding analytic solutions are derived.     

A constituent-based model for the nonlinear viscoelastic behavior of ligaments

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67-76; Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306-312; Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908-214; Weiss et al., 2002, J. Biomech., 35, pp. 943-950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.     

Active and passive stresses in the myocardium

A mathematical approach that can be used to calculate the passive stress in the ventricular wall is presented. The active fiber stress (force/unit area) generated by the muscular fibers in the ventricular wall is expressed by means of body force (force/unit volume of the myocardium). It is shown that the total intramyocardial passive stress induced in the passive medium of the myocardium can be expressed as the sum of a passive stress induced by the left ventricular pressure and a passive stress induced by the active fiber stress. Applications to experimental data published in the literature are given. New results are presented that show the relation among those two components of the intramyocardial passive stress. New relations between the intramyocardial passive stress, the slope (elastance) of the pressure-volume relation, and the residual volume are also derived. The results obtained give a better understanding of some aspects of the mechanics of cardiac contraction and can provide a more detailed interpretation of clinical conditions.     

Estimation of changes in instantaneous aortic blood flow by the analysis of arterial blood pressure

The purpose of this study was to introduce and validate a new algorithm to estimate instantaneous aortic blood flow (ABF) by mathematical analysis of arterial blood pressure (ABP) waveforms. The algorithm is based on an autoregressive with exogenous input (ARX) model. We applied this algorithm to diastolic ABP waveforms to estimate the autoregressive model coefficients by requiring the estimated diastolic flow to be zero. The algorithm incorporating the coefficients was then applied to the entire ABP signal to estimate ABF. The algorithm was applied to six Yorkshire swine data sets over a wide range of physiological conditions for validation. Quantitative measures of waveform shape (standard deviation, skewness, and kurtosis), as well as stroke volume and cardiac output from the estimated ABF, were computed. Values of these measures were compared with those obtained from ABF waveforms recorded using a Transonic aortic flow probe placed around the aortic root. The estimation errors were compared with those obtained using a windkessel model. The ARX model algorithm achieved significantly lower errors in the waveform measures, stroke volume, and cardiac output than those obtained using the windkessel model (P < 0.05).     

Deformation of the diastolic left ventricle—II. Nonlinear geometric effects

A finite element model for the rat left ventricle has been developed which is based on finite deformation elasticity theory: i.e. the model is not limited by assumptions relating to the magnitudes of extensions, shears and angles of rotation which are inherent in the classical theory of elasticity. This model represents the ventricle as a heterogeneous, nonlinearly elastic, isotropic thick-wall solid of revolution. For the representation of myocardial elasticity used in this study, the model predicts overall ventricular stiffnesses at physiological pressures which are 20–30 per cent lower than those obtained with a model based on the classical theory. However, extentions predicted by the two theories differ by as much as 100 per cent in certain portions of the ventricular wall.     

Rationale of the REPARATOR study: A randomised trial with serial cardiac MRI follow-up testing the ability of atorvastatin to reduce reperfusion damage after primary PCI for acute MI

The REPARATOR study is a multicentre clinical trial in which the effect of 80 mg atorvastatin on microvascular (re)perfusion and late ventricular remodelling, and infarct size in patients presenting with an acute ST-elevation myocardial infarction is studied. Primary endpoint is end-systolic volume index at three months measured by quantitative cine magnetic resonance imaging (MRI). Secondary endpoints are cardiac MI (CMR) measurements of global and regional left ventricular function, MRI measurements of infarct size on admission, one week and three months as well as changes between MRI investigations, biochemical markers of infarct size, blush grade, and TIMI frame count. A total of 50 patients will be enrolled. Including three months follow-up, the study will last for six months.     

Influence of left bundle branch block on left ventricular volumes, ejection fraction and regional wall motion

Background. Left ventricular volumes, ejection fraction and regional wall motion are cardiac parameters which provide valuable information for patient management in a large variety of cardiac conditions. Differences in regional wall motion are of relevance in the field of cardiac resynchronisation therapy. We quantified three-dimensional echocardiographic measurements of left ventricular volumes, ejection and regional wall motion (e.g. expressed as systolic dyssynchrony index (SDI)) in two patient cohorts: patients with normal conduction and patients with complete left bundle branch block. Methods. Thirty-five patients scheduled for routine cardiac examination underwent three-dimensional echocardiography: 23 patients with normal conduction and 12 patients with a complete left bundle branch block. Full-volume datasets were analysed and end-systolic volume (ESV), end-diastolic volume (EDV) and ejection fraction (EF) were obtained. SDI was derived from the standard deviation of the measured times to reach minimal regional volume for each of the 16 segments of the left ventricle. Results. A significant difference was observed in left ventricular volumes, ejection fraction and SDI between the two groups. Patients with complete left bundle branch block showed higher EDV (p=0.025) and ESV (p<0.01) and a lower EF (p<0.01) than patients with normal conduction. SDI is significantly higher in patients with complete left bundle branch block (p=0.004) expressing a higher amount of ventricular dyssynchrony. Intraobserver variability showed excellent correlation coefficients: r=0.99 for EDV, ESV and SDI and r=0.98 for EF. Conclusion. Three-dimensional echocardiography is a feasible and reproducible method for the quantification of left ventricular volumes, left ventricular ejection fraction and regional wall motion. Differences can be assessed between normal patients and patients with left bundle branch block. (Neth Heart J 2007;15:89-94.)     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.