Flow quantification in valvular heart disease based on the integralof backscattered acoustic power using Doppler ultrasound

The noninvasive quantification of pathologic backflow, referred to as regurgitant flow, associated with valvular heart disease has been an elusive medical goal. To date, techniques based on ultrasound have been unsatisfactory due to weak assumptions and indirect estimations. Here, instead, we propose to estimate regurgitant flow directly from the Doppler spectrum of the backscattered ultrasound. Since backscattered spectral power is proportional to the sonified blood volume and spectral frequency is directly related to velocity, power times velocity should be proportional to flow. To date, however investigators have assumed this held only for laminar flow, not for regurgitant jets in which turbulence augments backscatter. We demonstrate that this challenge can be overcome by analyzing the Doppler spectrum at the origin of the regurgitant jet, where flow is laminar since turbulence has not yet developed. We present in vitro and in vivo data that demonstrate that there is a linear proportionality between regurgitant flow and the integral of Doppler power times velocity (PVI). Power measurements were also calibrated by applying a dual-beam technique, providing absolute values of flow rate and volume in vivo. In our work we demonstrate that in patients with valvular heart disease, this new PVI technique allows for the measurement of regurgitant flow directly and noninvasively for the first time, overcoming the limitations of current techniques     

Noninvasive estimation of cardiac output

A noninvasive method of measuring cardiac output is described. The method uses adaptive aorta models in conjunction with femoral and carotid pulse contour waveform measurements to calculate aortic flow. Results are presented from measurements on dogs using internal pressure recordings made with fluid-filled catheters and compared with electromagnetic flow measurements taken in the ascending aorta. Preliminary results using external pulse measurements on patients are also presented and compared with thermal dilution measurements.     

Simultaneous estimation of physiological parameters and the inputfunction - in vivo PET data

Dynamic imaging with positron emission tomography (PET) is widely used for the in-vivo measurement of the regional cerebral metabolic rate for glucose (rCMRGlc) with [¹⁸F]fluorodeoxy-D-glucose (FDG), and is used for the clinical evaluation of neurological diseases. However, in addition to the acquisition of dynamic images, continuous arterial blood sampling is the conventional method of obtaining the tracer time-activity curve in blood (or plasma) for the numerical estimation of rCMRGlc in mg glucose/100 g tissue/min. The insertion of arterial lines and the subsequent collection and processing of multiple blood samples are impractical for clinical PET studies because it is invasive, it has the remote (but real) potential for producing limb ischemia, and it exposes personnel to additional radiation and the risks associated with handling blood. Based on a method for extracting kinetic parameters from dynamic PET images, we developed a modified version (post-estimation method) to improve the numerical identifiability of the parameter estimates when we deal with data obtained from clinical studies. We applied both methods to dynamic neurological FDG PET studies in three adults. We found that the input function and parameter estimates obtained with our noninvasive methods agreed well with those estimated from the gold-standard method of arterial blood sampling and that rCMRGlc estimates were highly correlated. No significant difference was found between rCMRGlc estimated by our methods and the gold-standard method. We suggest that our proposed noninvasive methods may offer an advance over existing methods     

Tracking time-varying properties of the systemic vascular bed

The problem of tracking changes in viscoelastic properties of the systemic arterial bed is considered and a recursive estimation procedure, belonging to the class of output-error algorithms with adjustable compensator, is developed and discussed. By means of computer simulations, suitable values are determined for the key design variable which controls the tradeoff between tracking ability and noise sensitivity of the algorithm. In this way, the algorithm allows on-line estimation of arterial compliance, peripheral resistance, and characteristic impedance on the basis of aortic pressure and flow signals. Furthermore, the results obtained from data numerically simulated, as well as measured on a mock circulatory system, demonstrate that the dominant arterial time-constant can be tracked by the algorithm using only measurements of the aortic pressure during diastole.     

A Novel Estimation Method for Physiological Parameters in Dynamic Contrast-Enhanced MRI: Application of a Distributed Parameter Model Using Fourier-Domain Calculations

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a promising tool in the evaluation of tumor physiology. From rapidly acquired images and a model for contrast agent pharmacokinetics, physiological parameters are derived. One pharmacokinetic model, the tissue homogeneity model, enables estimation of both blood flow and vessel permeability together with parameters that describe blood volume and extracellular extravascular volume fraction. However, studies have shown that parameter estimation with this model is unstable. Therefore, several initial guesses are needed for accurate estimates, which makes the estimation slow. In this study a new estimation algorithm for the tissue homogeneity model, based on Fourier domain calculations, was derived and implemented as a Matlab program. The algorithm was tested with Monte-Carlo simulations and the results were compared to an existing method that uses the adiabatic approximation. The algorithm was also tested on data from a metastasis in the brain. The comparison showed that the new algorithm gave more accurate results on the 2.5th and 97.5th percentile levels, for instance the error in blood volume was reduced by 21%. In addition, the time needed for the computations was reduced with a factor 25. It was concluded that the new algorithm can be used to speed up parameter estimation while accuracy can be gained at the same time.      

Real-time cardiac output estimation of the circulatory system underleft ventricular assistance

A method for indirect and real-time estimation of the cardiac output of the circulatory system supported by the left ventricular assist device (LVAD) is proposed. This method has low invasiveness and is useful for clinical applications of the LVAD since it needs only two measurements: the rate of blood outflow from the LVAD and the aortic pressure. The method is based on a system identification technique for the time-series model of the cardiovascular system and requires less computational time than other methods with similar estimation accuracy. Hence, the method could be implemented in a personal computer system and realize online, real-time estimation of the instantaneous outflow rate of the natural heart. Results obtained in vitro using a mock circulatory system and in vivo using an adult goat show that the method can yield a fairly high correlation coefficient between the true stroke volume of the natural heart and its estimate of more than 0.99 (in vitro) or 0.95 (in vivo). The estimation method thus appears suitable for clinical use     

Source parameter estimation in inhomogeneous volume conductors ofarbitrary shape

In this paper it is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of current sources inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the fields of bioelectricity (e.g., electrocardiography and electroencephalography).     

Tissue-specific compartmental analysis for dynamic contrast-enhanced MR imaging of complex tumors

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.     

Effective length of the arterial circulation determined in the dogby aid of a model of the systemic input impedance

By `effective length' it is meant that if the systemic arterial tree is represented by an equivalent tube with one terminal reflection site, the effective length is the distance from the aortic valve to this site. The purpose of the present study was to develop a reliable method to determine this distance. Aortic pressure and flow and aortic radius were measured in seven dogs during steady state. The arterial system was represented by a uniform elastic and frictionless equivalent tube loaded with a complex load. Load parameter and tube inertance and compliance were estimated by fitting pulsatile aortic flow with flow predicted by the model using pressure as input. The fit was good, and parameter estimates compared well to values reported in the literature. The tube length was calculated from estimates of the inertance and the inner aortic radius. The results confirmed that the quarter-wave formula traditionally used significantly overestimates the distance to the effective reflection site     

Correlation of esophageal conductance measurements with aortic and left ventricular diameters and stroke volume

Esophageal conductance measurements were correlated with hemodynamic events in 9 dogs chronically instrumented for measurement of left ventricular (LV) and aortic pressures, LV short axis and descending aortic diameters, and aortic blood flow. A four-electrode conductance catheter was positioned in the esophagus. Both an internal and an internal/external configuration were examined during anesthesia with hemodilution, pulmonary lavage and dobutamine infusion. LV stroke volume was altered by caval occlusion at each intervention. Stroke conductance was highly correlated to aortic or LV diameters and stroke volume over a range of diameters depending on the electrode configuration. Esophageal conductance measurements are directly influenced by local hemodynamic events adjacent to the site of measurement.     

Noninvasive measurement of regional cerebral blood flow change with H(2)(15)O and positron emission tomography using a mechanical injector and a standard arterial input function

To estimate changes in regional cerebral blood flow (rCBF) without arterial sampling in the study of functional-anatomical correlations in the human brain, using (15)O-labeled water and PET, a standard arterial input function was generated from the input function in 10 normal volunteers with dose calibration and peak time normalization. The speed and volume of injection were precisely controlled with a mechanical injector. After global normalization of each tissue activity image, the standard arterial input function was applied to obtain estimated CBF images. Relative changes in estimated rCBF to whole brain mean CBF(DeltaFest) and those in regional tissue activity (DeltaC) were compared with true relative rCBF changes (DeltaF) in 40 pairs of images obtained from 6 normal volunteers. DeltaFest correlated well with DeltaF, whereas DeltaC consistently underestimated DeltaF. This noninvasive method simplifies the activation studies and provides the accurate estimation of relative flow changes.     

Video-Based Measuring of Quality Parameters for Tricuspid Xenograft Heart Valve Implants

Defective heart valves are often replaced by implants in open-heart surgery. Both mechanical and biological implants are available. Among biological implants, xenograft ones—i.e., valves grafted from animals such as pigs, are widely used. Good implants should exhibit certain typical anatomical and functional characteristics to successfully replace the native tissue. Here, we describe a video-based system for measuring quality parameters of xenograft heart valve implants, including the area of the orifice and the fluttering of the valves' leaflets, i.e., their flaps (or cusps). Our system employs automatic methods that provide a precise and reproducible way to infer the quality of an implant. The automatic analysis of both a valve's orifice and the fluttering of its leaflets offers a more comprehensive quality assessment than current, mostly manual methods. We focus on valves with three leaflets, i.e., aortic, pulmonary, and tricuspid valves.      

Parameter Estimation in the Stenosed Coronary Circulatory System

In a stenosed coronary circulation, the following parameters were estimated from pressure measurements: coronary vascular resistances, transmural blood flow, and endocardial to epicardial (ENDO: EPI) flow ratio. This was done by modeling the hemodynamics of the coronary system with an analogous electrical circuit. The circuit topology consists of a nonlinear stenosis resistance and an endocardial branch in parallel with an epicardial branch. The unknown, linear endocardial and epicardial resistances were determined by a least-squares estimation method with three inputs: the left ventricular pressure (LVP), the aortic pressure (AP), and the distal coronary arterial pressure (DP). In this paper, computer simulations also show that the input DP may be replaced by a phasic arterial coronary flow synthesized from its mean systolic and diastolic values. In animal studies, DP may be measured directly while such pressure measurements are difficult to obtain clinically since it requires passing a catheter distal to a stenosis. However, mean systolic and diastolic coronary arterial flow have been obtained in humans via video densitometry. Thus, this method may potentially be useful in clinical situations. Validity of the method was tested with 23 animal studies using swine under a variety of physiological conditions. Linear regression analyses were made between the ENDO: EPI flow ratios estimated by the model and those measured by use of the radiolabeled microsphere technique.     

Spatial Velocity Distributions in the Ascending Aorta of Healthy Humans and Cardiac Patients

Blood velocity profiles in the human ascending aorta were assessed with the aid of ultrasonic Doppler echocardiography. To this end, the transducer was placed in the suprasternal notch, and the spatial velocity profiles along an axis passing through the center of the aortic cross section were recorded by a multigate Doppler instrument. The profiles are analyzed with respect to characteristics independent of the angle of incidence and the cross sectional area. Data from 10 healthy individuals, 10 patients with hypertrophic obstructive cardiomyopathy (HOCM), and 10 patients with severe aortic insufficiency (AI) are compared. Five instantaneous profiles recorded at different times during systole and the temporal average of all profiles recorded during the entire cardiac cycle at 16 ms intervals are examined. Considerable differences between the three groups of subjects are observed visually as well as quantitatively in terms of specific parameters. The representation of the velocity maps in the form of contour graphs is particularly incisive. The results demonstrate that the temporal velocity patterns measured depend, in general, on both the disease and the location of the sampling volume within the aortic lumen. Reliable aortic volume flow rate measurements may have to be based on a method which takes into account the velocity at every point of the entire vascular cross section of patients with HOCM or AI.     

An Activity-Subspace Approach for Estimating the Integrated Input Function and Relative Distribution Volume in PET Parametric Imaging

Dynamic positron emission tomography (PET) imaging technique enables the measurement of neuroreceptor distributions corresponding to anatomic structures, and thus, allows image-wide quantification of physiological and biochemical parameters. Accurate quantification of the concentration of neuroreceptor has been the objective of many research efforts. Compartment modeling is the most widely used approach for receptor binding studies. However, current compartment-model-based methods often either require intrusive collection of accurate arterial blood measurements as the input function, or assume the existence of a reference region. To obviate the need for the input function or a reference region, in this paper, we propose to estimate the input function. We propose a novel concept of activity subspace, and estimate the input function by the analysis of the intersection of the activity subspaces. Then, the input function and the distribution volume (DV) parameter are refined and estimated iteratively. Thus, the underlying parametric image of the total DV is obtained. The proposed method is compared with a blind estimation method, iterative quadratic maximum-likelihood (IQML) via simulation, and the proposed method outperforms IQML. The proposed method is also evaluated in a brain PET dataset.     

Estimation of Mechanical Parameters in Multicompartment Models Applied to Normal and Obstructed Lungs During Tidal Breathing

A technique is presented which allows quantitative assessment of the use of parallel compartment models for characterizing pulmonary mechanical function during tidal breathing. A model consisting of a conducting airway leading to two parallel parenchymal regions is used. Numerical simulation and sensitivity analysis indicated that a) the compliance of the conducting airway was not significant under the experimental conditions of interest and that b) estimates of the distribution of central and peripheral resistances would not be precise. The techniques were demonstrated using measurements of transpulmonary pressure, flow, and volume changes during tidal breathing obtained from a human subject with normal lungs and a human subject with obstructed lungs. Optimal estimates of the parameters were obtained by minimizing the difference between the model output and experimental data combined from two breathing frequencies. In the estimation procedure, the sum of the peripheral compliances was constrained to equal the independently measured static lung compliance. This constraint was critical for correct evaluation of nonuniform mechanical lung function. From the parameter estimates, the ratio of parenchymal time constants was about five in the subject with normal lungs and 60 in the subject with obstructed lungs. These results suggest that a full study with several normal and obstructed lung subjects is warranted.     

Estimation of dense image flow fields in fluids

The estimation of flow fields from time sequences of satellite imagery has a number of important applications. For visualization of cloud or sea ice movements in sequences of crude temporal sampling, a satisfactory nonblurred temporal interpolation can be performed only when the flow field or an estimate thereof is known. Estimated flow fields in weather satellite imagery might also be used on an operational basis as inputs to short-term weather prediction. The authors describe a method for the estimation of dense flow fields. Local measurements of motion are obtained by analysis of the local energy distribution, which is sampled by using a set of three-dimensional (3D) spatio-temporal filters. The estimated local energy distribution also allows the authors to compute a confidence measure of the estimated local normal flow. The algorithm, furthermore, utilizes Markovian random fields in order to integrate the local estimates of normal flows into a dense flow field by using measures of spatial smoothness. To obtain smoothness, the authors will constrain first-order derivatives of the flow field. The performance of the algorithm is illustrated by the estimation of the flow fields corresponding to a sequence of Meteosat thermal images. The estimated flow fields are used in a temporal interpolation scheme     

Estimation of number of independent brain electric sources from the scalp EEGs

In electromagnetic source analysis, many source localization strategies require the number of sources as an input parameter (e.g., spatio-temporal dipole fitting and the multiple signal classification). In the present study, an information criterion method, in which the penalty functions are selected based on the spatio-temporal source model, has been developed to estimate the number of independent dipole sources from electromagnetic measurements such as the electroencephalogram (EEG). Computer simulations were conducted to evaluate the effects of various parameters on the estimation of the source number. A three-concentric-spheres head model was used to approximate the head volume conductor. Three kinds of typical signal sources, i.e., the damped sinusoid sources, sinusoid sources with one frequency band and sinusoid sources with two separated frequency bands, were used to simulate the oscillation characteristics of brain electric sources. The simulation results suggest that the present method can provide a good estimate of the number of independent dipole sources from the EEG measurements. In addition, the present simulation results suggest that choosing the optimal penalty function can successfully reduce the effect of noise on the estimation of number of independent sources. The present study suggests that the information criterion method may provide a useful means in estimating the number of independent brain electrical sources from EEG/MEG measurements.     

Parameter estimation in chaotic noise

The problem of parameter estimation in chaotic noise is considered in this paper. Since a chaotic signal is inherently deterministic, a new complexity measure called the phase space volume (PSV) is introduced for estimation instead of using the conventional probabilistic measures. We show that the unknown parameters of a signal embedded in chaotic noise ran be obtained by minimizing the PSV (MPSV) of the output of an inverse filter of the received signal in a reconstructed phase space. Monte Carlo simulations are carried out to analyze the efficiency of the MPSV method for parameter estimation in chaotic noise. To illustrate the usefulness of the MPSV technique in solving real-life problems, the problem of sinusoidal frequency estimation in real radar clutter (unwanted radar backscatters) is considered. Modeling radar clutter as a chaotic process, we apply the MPSV technique to estimate the sinusoidal frequencies by estimating the coefficients of an autoregressive (AR) spectrum. The results show that the frequency estimates generated by the MPSV method are more accurate than those obtained by the standard least square (LS) technique     

Optimal image sampling schedule for both image-derived input and output functions in PET cardiac studies

Optimal sampling schedule (OSS) design for both image-derived input and output functions in tracer kinetic modeling with positron emission tomography (PET) is investigated. This problem is very important in noninvasive PET dynamic cardiac studies where both the input function, i.e., the plasma time-activity curve (PTAC), and the output function, i.e., the tissue time-activity curve (TTAC), are obtained simultaneously from the same sequence of PET images. The integral PET measurement is used in this study. The spillover correction for the cross contaminations in cardiac studies is incorporated into the OSS design procedure. A new target function based on the D-optimal criterion involving both the input and output sensitivity functions is proposed. The fluorodeoxyglucose (FDG) model and a six-parameter PTAC model are used to illustrate the simultaneous OSS design for both the PTAC and TTAC. An OSS design consisting of six different scanning intervals is derived. Computer simulations are performed based on the estimated parameters from real studies to evaluate the effectiveness of the OSS. The double modeling approach is used in parameter estimation to simultaneously estimate the parameters involved. The results have shown that, for a wide range of parameter variations, the OSS is as effective as a conventional sampling schedule (CSS) and comparable parameter estimates can be obtained. Compared with the use of the CSS, the use of the OSS leads to an approximately 70% reduction in the storage space and data processing time.