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PubMed2006

Scale dependence of branching in arterial and bronchial trees.

Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verification of this dependence by comparison with data is uncommon. We compare measurements of bifurcation parameters of airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models based on minimization of pumping power and network volume. We find that the size dependence is more complex than existing theories based solely on energy and volume minimization explain, and suggest additional factors that may govern the branching at different scales.

Animals↗
PubMed1989

Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data.

In this paper, the computational and practical aspects of a realistically-shaped multilayer model for the conductivity geometry of the human head are discussed. A novel way to handle the numerical difficulties caused by the presence of the poorly conducting skull is presented. Using our method, both the potential on the surface of the head and the magnetic field outside the head can be computed accurately. The procedure was tested with the multilayer sphere model, for which analytical expressions are available. The method is then applied to a realistically-shaped head model, and it is numerically shown that for the computation of B, produced by cerebral current sources, it is sufficient to consider a brain-shaped homogeneous conductor only since the secondary currents on the outer interfaces give only a negligible contribution to the magnetic field outside the head. Comparisons with the sphere model are also included to pinpoint areas where the homogeneous conductor model provides essential improvements in the calculation of the magnetic field outside the head.

Brain↗
PubMed1989

Modified asymmetric T-tube model to infer arterial wave reflection at the aortic root.

A modified version of the T-tube model was constructed to represent the systemic arterial loading system as "seen" by the left ventricle (LV). This model consisted of two uniform tubes connected in parallel. It differs from the original T-tube model in that the transmission paths have no frictional losses and are terminated with complex impedances, rather than simple resistors. To estimate model parameters (load and tube compliances, tube inertances, characteristic impedances, and peripheral resistances) we measured ascending aortic pressure and flow in a group of five open-chest, anesthetized dogs. Parameter estimates were obtained by fitting experimental pressure to the pressure predicted by the model from experimental flow. To check the reliability of the model, an additional experiment was performed where flow in the upper descending thoracic aorta was measured in addition to ascending aorta pressure and flow. The fit between the experiment and model predicted ascending aortic pressure was satisfactory in all six dogs. This pressure was always characterized by the presence of a prominent diastolic oscillation. Our model showed that this oscillation is due to reflections from the lower body, the effective reflection site being most probably located at the level of middle to low abdominal aorta. The effective reflection site located in the upper body is closer to the heart. The related reflected wave affects pressure in late systole.

Analog-Digital Conversion↗
PubMed1995

Multiple sources of the impedance cardiogram based on 3-D finite difference human thorax models.

Two 3-D electrical models of the human thorax, each consisting of 216,000 control volumes, were constructed based upon MR images taken at end diastole and end systole. Using the finite difference method, the contributions of various sources to the impedance cardiogram were studied for the traditional band electrode configuration. The contributions were categorized into three areas: 1) the structural changes between end diastole and end systole, 2) the flow-induced blood resistivity changes in major arteries and veins, and 3) the lung resistivity variation due to the lung blood volume change. Based on the models, Zo and delta Z between end diastole and end systole were 24.4 omega and -0.132 omega, as compared with the measurements of 21.8 omega and -0.123 omega made on the same subject from whom the images were taken. Arterial and venous blood resistivity changes caused approximately 57% of the total impedance change. The lung resistivity change and the structural changes contributed 39% and 4%, respectively. The structural changes inside the thorax included the dimensional changes of blood vessels, the blood volume changes of the heart chambers, and heart movement. Although the net impedance change due to the structural changes was relatively small, the individual variation of various factors was large, with significant cancellation occurring. The results suggest that the thoracic impedance cardiographic signal is a mixed representation of many inseparable factors and may not be reliable for the stroke volume calculation. Also, the O-wave, which is clinically observed in various cardiac conditions, may be linked to the diastolic blood flow in the central veins.

Adult↗
PubMed1995

Optimization of cardiac defibrillation by three-dimensional finite element modeling of the human thorax.

The goal of this study was to determine the optimal electrode placement and size to minimize myocardial damage during defibrillation while rendering refractory a critical mass of cardiac tissue of 100%. For this purpose, we developed a 3-D finite element model with 55,388 nodes, 50,913 hexahedral elements, and simulated 16 different organs and tissues, as well as the properties of the electrolyte. The model used a nonuniform mesh with an average spatial resolution of 0.8 cm in all three dimensions. To validate this model, we measured the voltage across 3-cm2 Ag-AgCl electrodes when currents of 5 mA at 50 kHz were injected into a human subject's thorax through the same electrodes. For the same electrode placements and sizes and the same injected current, the finite element analysis produced results in good agreement with the experimental data. For the optimization of defibrillation, we tested 12 different electrode placements and seven different electrode sizes. The finite element analyses showed that the anterior-posterior electrode placement and an electrode size of about 90 cm2 offered the least chance of potential myocardial damage and required a shock energy of less than 350 J for 5-ms defibrillation pulses to achieve 100% critical mass. For comparison, the average cross-sectional area of the heart is approximately 48 cm2, about half of the optimal area. A second best electrode placement was with the defibrillation electrodes on the midaxillary lines under the armpits. Although this placement had higher chances of producing cardiac damage, it required less shock energy to achieve 100% critical mass.

Computer Simulation↗
PubMed1996

Iterative refinement of the minimum norm solution of the bioelectric inverse problem.

Functional brain imaging based on the bioelectric scalp field depends on the solution of the inverse problem. The object is to estimate the current distribution in the cortex from a measured noisy scalp potential field. A minimum norm least squares solution is often used for this purpose. Although this approach leads to a unique solution, it represents only one of a set of feasible solutions. In particular, it leads to a solution in which current is found to be generated widely in the cortex. There are other feasible minimum norm solutions for which cortical current is generated only in a restricted region, and it is likely that in many cases, these solutions are of physiological importance. This study presents a method to uncover these solutions. It is based on the idea that a minimum norm solution can be used to define a region of interest, an ellipsoid, within which it is worthwhile to search for another feasible solution. The minimum norm approach is used iteratively and the ellipsoid shrinks. As it shrinks it provides evidence pointing to the location of the active cortical region. The method explicitly recognizes the role of measurement noise in defining feasible solutions. It is tested in a model of the human head that incorporates a realistic cortex in a three-shell sphere. The method improves the localization of cortical activity mimicking physiological processing.

Brain Mapping↗
PubMed1998

An ultrasonic approach to localization of fiducial markers for interactive, image-guided neurosurgery--Part I: Principles.

Fiducial markers are reference points used in the registration of image space(s) with physical (patient) space. As applied to interactive, image-guided surgery, the registration of image space with physical space allows the current location of a surgical tool to be indicated on a computer display of patient-specific preoperative images. This intrasurgical guidance information is particularly valuable in surgery within the brain, where visual feedback is limited. The accuracy of the mapping between physical and image space depends upon the accuracy with which the fiducial markers were located in each coordinate system. To effect accurate space registration for interactive, image-guided neurosurgery, the use of permanent fiducial markers implanted into the surface of the skull is proposed in this paper. These small cylindrical markers are composed of materials that make them visible in the image sets. The challenge lies in locating the subcutaneous markers in physical space. This paper presents an ultrasonic technique for transcutaneously detecting the location of these markers. The technique incorporates an algorithm based on detection of characteristic properties of the reflected A-mode ultrasonic waveform. The results demonstrate that ultrasound is an appropriate technique for accurate transcutaneous marker localization. The companion paper to this article describes an automatic, enhanced implementation of the marker-localization theory described in this article.

Adipose Tissue↗
PubMed1999

EEG and MEG: forward solutions for inverse methods.

A solution of the forward problem is an important component of any method for computing the spatio-temporal activity of the neural sources of magnetoencephalography (MEG) and electroencephalography (EEG) data. The forward problem involves computing the scalp potentials or external magnetic field at a finite set of sensor locations for a putative source configuration. We present a unified treatment of analytical and numerical solutions of the forward problem in a form suitable for use in inverse methods. This formulation is achieved through factorization of the lead field into the product of the moment of the elemental current dipole source with a "kernel matrix" that depends on the head geometry and source and sensor locations, and a "sensor matrix" that models sensor orientation and gradiometer effects in MEG and differential measurements in EEG. Using this formulation and a recently developed approximation formula for EEG, based on the "Berg parameters," we present novel reformulations of the basic EEG and MEG kernels that dispel the myth that EEG is inherently more complicated to calculate than MEG. We also present novel investigations of different boundary element methods (BEM's) and present evidence that improvements over currently published BEM methods can be realized using alternative error-weighting methods. Explicit expressions for the matrix kernels for MEG and EEG for spherical and realistic head geometries are included.

Electric Conductivity↗
PubMed1999

Impact of nonlinear heat transfer on temperature control in regional hyperthermia.

We describe an optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat transfer model based on temperature-dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral objective function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant-rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System.

Algorithms↗
PubMed1999

Estimating cortical potentials from scalp EEG's in a realistically shaped inhomogeneous head model by means of the boundary element method.

Cortical potentials are estimated from scalp potentials using a realistically shaped inhomogeneous head model, by means of the boundary element method (BEM). A new adaptive algorithm has been developed to achieve high accuracy to link directly the cortical potentials to the scalp potentials in a realistically shaped inhomogeneous head model including the thin low-conductivity skull layer. Computer simulations using a concentric three-spheres head model have tested this approach. The present study demonstrates that the cortical potentials can be directly estimated from the scalp potentials using the BEM in a realistically shaped inhomogeneous head model.

Algorithms↗
PubMed1999

Registration of three-dimensional cardiac catheter models to single-plane fluoroscopic images.

Transvenous cardiac procedures require accurate positioning of catheters within the geometrically complex cavities of the heart. Recently, nonfluoroscopic catheter tracking technologies have been developed to quantitate the (degrees-of-freedom) three-dimensional positions of intracardiac catheters. This paper presents a projection-Procrustes method to register an animated three-dimensional (3-D) model of multiple intracardiac catheters with a single-plane fluoroscopic image. Applying the computed transformation to the catheter coordinates enables the animated 3-D model of the catheters to be viewed from the same perspective as the fluoroscopic image. Mathematical simulations show that the computed transformation parameters are sensitive to both the position errors in the 3-D catheter coordinates and to the spatial distribution of the catheter-mounted transducers. Simulations with a realistic geometric model of three catheters with four transducers per catheter showed an angular error of 1.91 degrees +/- 0.27 degree for 3-D catheter position errors of 2.0 mm. An in vitro experiment demonstrated the feasibility of the method using a water tank phantom of three catheters and fluoroscopic images taken over an 80 degrees range. The mean angular error was 0.61 degree +/- 0.48 degree. The results of this study indicate that the projection-Procrustes method is a useful tool for registering 3-D catheter tracking models to single-plane fluoroscopic images.

Algorithms↗
PubMed2000

Variability in EMF permittivity values: implications for SAR calculations.

Digital anatomical models of man and animals are available for use in numerical calculations to predict electromagnetic field (EMF)-induced specific absorption rate (SAR) values. To use these models, permittivity values are assigned to the various tissues for the EMF frequencies of interest. There is, as yet, no consensus on what are the best permittivity data. This study analyzed the variability in published permittivity data and investigated the effects of permittivity values that are proportional on SAR calculations. Whole-sphere averaged and localized SAR values along the diameter of a 4-cm sphere are calculated for EMF exposures in the radio frequency range of 1 MHz to 1 GHz. When the dimensions of a sphere are small compared to the wavelength (i.e., wavelength inside the material is greater than ten times the dimensions of the object), the whole-sphere averaged SAR is inversely proportional to the permittivity of the material composing the sphere. However, the localized SAR values generally do not have the same relation and, as a matter of fact, vary greatly depending on the location within the sphere. These results indicate that care must be taken in choosing the permittivity values used in calculating SAR values and some estimate of the dependence of the calculated SAR values on variability in permittivity should be determined.

Animals↗
PubMed2000

Estimation of current leakage in left and right ventricular conductance volumetry using a dynamic finite element model.

Leakage of electric current through cardiac structures surrounding the ventricle is a primary source of error during ventricular volume measurements using a conductance catheter. This error can be represented as a leakage volume, VL. VL is generally estimated by a saline-bolus method, and is assumed constant throughout the cardiac cycle. However, dynamic changes in ventricular volume and cardiac wall thickness could change VL. To estimate VL, a dynamic finite element model of the heart was developed based on MR images. Conductance measurements were simulated using a modeled conductance catheter, and true VL was calculated. VL varied from 22.7 ml (end-systole) to 26.4 ml (end-diastole) in the left ventricle and from 19.9 ml (end-systole) to 26.9 ml (end-diastole) in the right ventricle. The saline-bolus method underestimated VL in both the left (VL = 19.4 ml) and the right (VL = 4.1 ml) ventricular volume measurements. VL increased linearly with the ratio of blood to tissue resistivity, and changed minimally with catheter position. These results indicate that VL has to be estimated dynamically throughout the cardiac cycle to obtain accurate cardiac volume measurements. The results also show that the saline bolus method does not estimate current leakage accurately, especially in the right ventricular volume measurement.

Biomedical Engineering↗
PubMed1998

Beamformed nearfield imaging of a simulated coronary artery containing a stenosis.

This paper is concerned with the potential for the detection and location of an artery containing a partial blockage by exploiting the space-time properties of the shear wave field in the surrounding elastic soft tissue. As a demonstration of feasibility, an array of piezoelectric film vibration sensors is placed on the free surface of a urethane mold that contains a surgical tube. Inside the surgical tube is a nylon constriction that inhibits the water flowing through the tube. A turbulent field develops in and downstream from the blockage, creating a randomly fluctuating pressure on the inner wall of the tube. This force produces shear and compressional wave energy in the urethane. After the array is used to sample the dominant shear wave space-time energy field at low frequencies, a nearfield (i.e., focused) beamforming process then images the energy distribution in the three-dimensional solid. Experiments and numerical simulations are included to demonstrate the potential of this noninvasive procedure for the early identification of vascular blockages-the typical precursor of serious arterial disease in the human heart.

Amplifiers, Electronic↗
PubMed2002

Parameter space warping: shape-based correspondence between morphologically different objects.

This paper presents a novel and comprehensive method for the automated determination of correspondences between two morphologically different two-dimensional (2-D) or three-dimensional (3-D) objects. Correspondences are determined by warping parametric representations of the objects to be matched. The warp is guided by the minimization of a similarity criterion function that measures features related to structural correspondence, including Euclidian point-to-point distance and differences in normals and curvature. The method uses a continuous harmonic parameterization for both the object and the warp, which provides: 1) a high degree of computational efficiency; 2) robust extraction of differential features, not subject to discretization errors or noise amplification in differentiation; 3) direct formulation of constraints to avoid overlaps in the resulting correspondence set; and 4) a scale-space paradigm of object shape and warp. The new method does not search for individual landmarks, but operates with a complete, integrated representation of the object geometry. The method was tested on 2-D and 3-D objects with substantial shape differences. Results demonstrated substantial improvements of 2%-33% in correspondence accuracy and 15%-59% in correspondence quality compared with direct registration methods.

Algorithms↗