Mathematical modeling of the heart using magnetic resonance imaging

A hybrid three-dimensional solid mathematical model of cardiac ventricular geometry developed using magnetic resonance (MR) images of an in vivo canine heart is discussed. The modeling techniques were validated using MR images of an ex vivo heart and direct measurements of cardiac geometry and mass properties. A spin-echo MR sequence with in-plane resolution of 1.0 mm was used to image the canine heart in eleven short-axis planes at contiguous 5-mm intervals. Contour points on the epicardial, left ventricle (LV), and right ventricle (RV) boundaries were selected manually at each slice level. A boundary representation geometric model was constructed by fitting third-order nonuniform rational B-spline surfaces through each set of surface points. Compared to the anatomic specimen (AS), volume errors of the ex vivo model were 0.3, 1.5, and 5.8% for the LV cavity, RV cavity, and total enclosed volumes, respectively. Comparison of cross-sectional areas of the AS and the model at ten levels demonstrated mean model errors of 4.1, 2.5, and 2.9% for the LV, RV, and epicardial boundaries, respectively     

LV shape and motion: B-spline-based deformable model and sequential motion decomposition.

In this paper, we extend a previous work by J. Park and propose a uniform framework to reconstruct left ventricle (LV) geometry/motion from tagged MR images. In our work, the LV is modeled as a generalized prolate spheroid, and its motion is decomposed into four components-global translation, polar radial/z-axis compression, twisting, and bending. By formulating model parameters as tensor products of B-splines, we develop efficient algorithms to quickly reconstruct LV geometry/motion from extracted boundary contours and tracked planar tags. Experiments on both synthesized and in vivo data are also reported.     

A comparison of measured and calculated intracavitary potentialsfor electrical stimuli in the exposed dog heart

The objective of this paper is to test the feasibility of using a multielectrode, intracavitary probe to solve a forward problem in which measured intracavitary potentials are compared to those calculated from subendocardial potentials and left ventricular (LV) cavity geometry. Intracavitary potentials and subendocardial potentials are measured simultaneously during electrical pacing stimuli from the LV apex, LV anterior base, LV posterior base, and right ventricular (RV) outflow tract of three exposed dog hearts. The LV cavity geometry is measured from postmortem magnetic resonance microscopy images of fixed hearts. Boundary integrals are approximated using a boundary element method and solved for intracavitary potentials. Correlation coefficients for LV apical pacing episodes are 0.989 +/- 0.002 while those for nonapical pacing episodes are 0.873 +/- 0.092. These results indicate that for electrical pacing from the apex, intracavitary stimulus potentials can be calculated with a high degree of accuracy. For nonapical pacing locations, the accuracy decreases since the calculations are more sensitive to errors in measuring probe position and LV cavity geometry near the septum. These results show that accurate geometric measurements of the intracavitary probe position and subendocardial surface are the primary concerns in solving future forward and inverse problems using an intracavitary probe.     

Reconstruction of time-varying 3-D left-ventricular shape from multiview X-ray cineangiocardiograms

This paper reports on the clinical application of a system for recovering the time-varying three-dimensional (3-D) left-ventricular (LV) shape from multiview X-ray cineangiocardiograms. Considering that X-ray cineangiocardiography is still commonly employed in clinical cardiology and computational costs for 3-D recovery and visualization are rapidly decreasing, it is meaningful to develop a clinically applicable system for 3-D LV shape recovery from X-ray cineangiocardiograms. The system is based on a previously reported closed-surface method of shape recovery from two-dimensional occluding contours with multiple views. To apply the method to "real" LV cineangiocardiograms, user-interactive systems were implemented for preprocessing, including detection of LV contours, calibration of the imaging geometry, and setting of the LV model coordinate system. The results for three real LV angiographic image sequences are presented, two with fixed multiple views (using supplementary angiography) and one with rotating views. 3-D reconstructions utilizing different numbers of views were compared and evaluated in terms of contours manually traced by an experienced radiologist. The performance of the preprocesses was also evaluated, and the effects of variations in user-specified parameters on the final 3-D reconstruction results were shown to be sufficiently small. These experimental results demonstrate the potential usefulness of combining multiple views for 3-D recovery from "real" LV cineangiocardiograms.     

Incorporation of a left ventricle finite element model defining infarction into the XCAT imaging phantom

The 4D extended cardiac-torso (XCAT) phantom was developed to provide a realistic and flexible model of the human anatomy and cardiac and respiratory motions for use in medical imaging research. A prior limitation to the phantom was that it did not accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). We overcame this limitation in a previous study by combining the phantom with a finite-element (FE) mechanical model of the left ventricle (LV) capable of more realistically simulating regional defects caused by ischemia. In the present work, we extend this model giving it the ability to accurately simulate motion abnormalities caused by myocardial infarction (MI), a far more complex situation in terms of altered mechanics compared with the modeling of acute ischemia. The FE model geometry is based on high resolution CT images of a normal male subject. An anterior region was defined as infarcted and the material properties and fiber distribution were altered, according to the bio-physiological properties of two types of infarction, i.e., fibrous and remodeled infarction (30% thinner wall than fibrous case). Compared with the original, surface-based 4D beating heart model of the XCAT, where regional abnormalities are modeled by simply scaling down the motion in those regions, the FE model was found to provide a more accurate representation of the abnormal motion of the LV due to the effects of fibrous infarction as well as depicting the motion of remodeled infarction. In particular, the FE models allow for the accurate depiction of dyskinetic motion. The average circumferential strain results were found to be consistent with measured dyskinetic experimental results. Combined with the 4D XCAT phantom, the FE model can be used to produce realistic multimodality sets of imaging data from a variety of patients in which the normal or abnormal cardiac function is accurately represented.     

Parameter distribution models for estimation of population based left ventricular deformation using sparse fiducial markers

We present a method to estimate left ventricular (LV) motion based on three-dimensional (3-D) images that can be derived from any anatomical tomographic or 3-D modality, such as echocardiography, computed tomography, or magnetic resonance imaging. A finite element mesh of the LV was constructed to fit the geometry of the wall. The mesh was deformed by optimizing the nodal parameters to the motion of a sparse number of fiducial markers that were manually tracked in the images through the cardiac cycle. A parameter distribution model (PDM) of LV deformations was obtained from a database of MR tagging studies. This was used to filter the calculated deformation and incorporate a priori information on likely motions. The estimated deformation obtained from 13 normal untagged studies was compared with the deformation obtained from MR tagging. The end systolic (ES) circumferential and longitudinal strain values matched well with a mean difference of 0.1 +/- 3.2% and 0.3 +/- 3.0%, respectively. The calculated apex-base twist angle at ES had a mean difference of 1.0 +/- 2.3 degrees. We conclude that fiducial marker fitting in conjunction with a PDM provides accurate reconstruction of LV deformation in normal subjects.     

Analysis of Left Ventricular Mechanics During Filling, Isovolumic Contraction, and Ejection

The left ventricle (LV) was modeled by two confocal ellipsoids truncated in a plane corresponding to the base of the LV. The ellipsoids were approximated by a series of cylindrical shells. During passive filling, the pressure within the ventricular chamber was determined from chamber volume and a stress-strain relationship for myocardium in the relaxed state. The rapid filling phase of diastole was not analyzed. During isovolumic contraction, the cylindrical shells assumed the properties of myocardium in active contraction. Contraction was sequential, beginning at the ventricular apex, and progressing toward the ventricular base. Geometric changes occurred in the LV model as a function of wall stress, material properties, and timing of myocardial activation. During ejection, viscous and inertial forces were determined as were model output pressure and flow waveforms.     

A Model of 60 GHz Indoor Radio Channel

A novel model of millimeter-wave (MMW) indoor radio channel is presented in this paper. The model is related the random properties of the MMW radio channel to the underlying geometry of the environment. The geometric simplicity of the MMW channel is allowed examining fundamental deterministic properties of the wave propagation behavior in environments of predefined randomness. The dimensions and properties of environments are described by various probability distributions. Stochastic influence on the radio channel is studied for the down-link of a wireless local area network at 60 GHz. Other related factors, such as amplitudes of path lengths, angles of departure, and amplitudes, as well as spatial power densities, average power of the direct paths are investigated.     

Evolution of a CMOS Based Lateral High Voltage Technology Concept

This work describes the evolution of a CMOS based lateral high voltage (HV) technology concept, where the HV part is integrated in a low voltage (LV) CMOS technology. The starting point is an existing substrate related state of the art 0.35 μm LV CMOS technology (C35) which is optimized for digital and analog applications. The technology covers two different gate oxide thicknesses which allow to control two LV logic levels with different gate voltages and drain voltages (max.V_GS=max.V_DS=3.3V, max.V_GS=max.V_DS=5.5 V). The key requirement for the HV integration is to preserve the LV design rules (DR) and the LV transistor parameters. Only in this case it is possible to reuse the digital and analog intellectual property (IP) blocks. The major challenge of this integration is to overcome the relatively high surface concentration of the 0.35 μm CMOS process which defines the threshold voltages and the short channel effects. Because the HV devices use the same channel formation like the LV devices, a process concept for the drift region connection to the channel is the key point in this integration approach. A benchmark for the process complexity is given by the mask count (low volume production) and the number of alignments (high volume production). Starting from a very simple approach n-channel HV transistors are described which can be integrated in the substrate related LV CMOS concept without adding additional masks. During the next steps the LV CMOS process is modified continuously using additional masks and alignment steps. From each step to step the new HV properties are explained and the trade-off between process complexity and device performance is discussed.     

Quantitative characterization and sorting of three-dimensional geometries: application to left ventricles in vivo

A procedure for automatic sorting of three-dimensional (3-D) shapes is proposed. The procedure is applied to sort into normal and abnormal categories, human left ventricles (LV) using in vivo data from 19 subjects (ten normal and nine abnormal LV's) studied by ultrafast tomography (Cine-CT). The procedure starts by utilizing a vector in a helical coordinate system to describe the spatial geometry of each individual LV cavity. This individual vector is then anatomically aligned and normalized to eliminate effects due to size, yielding a dimensionless vector, denoted as "geometrical cardiogram" (GCG). The GCG characterizes the instantaneous 3-D geometrical information of the individual LV. For the group of healthy subjects, the Karhunen-Loeve Transform (KLT) is then applied to compress the geometric information contained in their individuals' GCG vectors, at end diastole (ED) and end systole (ES), and yield a unique set of basis vectors. The "normal shape domain" is next defined as a truncated set of the KLT basis vectors from which a normal GCG can be reconstructed with a mean squared error (MSE) smaller than a defined threshold. The calculated MSE of any individual GCG reconstructed in this domain is then used as a criterion for sorting the 3-D shapes. Hearts which yield MSE greater than the threshold are considered abnormal. When applied to the study group of 19 subjects a significant difference (p less than 0.0001) between the MSE values obtained for the normal LV's, and those obtained for the abnormal LV's was detected, thus leading to a successful sorting of all the studied LV's. Finally, the KLT is applied to yield a compact representation of the 3-D geometry of any LV (normal or abnormal).     

Influence of Electric Field on Microstructures of Pentacene Thin‐Films in Field‐Effect Transistors

We report on electric‐field‐induced irreversible structural modifications in pentacene thin films after long‐term operation of organic field‐effect transistor (OFET) devices. Micro‐Raman spectroscopy allows for the analysis of the microstructural modifications of pentacene in the small active channel of OFET during device operation. The results suggest that the herringbone packing of pentacene molecules in a solid film is affected by an external electric field, particularly the source‐to‐drain field that parallels the a–b lattice plane. The analysis of vibrational frequency and Davydov splitting in the Raman spectra reveals a singular behavior suggesting a reduced separation distance between pentacene molecules after long‐term operations and, thus, large intermolecular interactions. These results provide evidence for improved OFET performance after long‐term operation, related to the microstructures of organic semiconductors. It is known that the application of large electric fields alters the semiconductor properties of the material owing to the generation of defects and the trapping of charges. However, we first suggest that large electric fields may alter the molecular geometry and further induce structural phase transitions in the pentacene films. These results provide a basis for understanding the improved electronic properties in test devices after long‐term operations, including enhanced field‐effect mobility, improved on/off current ratio, sharp sub‐threshold swing, and a slower decay rate in the output drain current. In addition, the effects of source‐to‐drain electric field, gate electric field, current and charge carriers, and thermal annealing on the pentacene films during OFET operations are discussed.     

一种改善VDMOSFET高频性能新结构的分析与研究

栅电荷是低压功率MOSFETs开关性能的一项很重要的参数。器件优值（Ron＊Qg）是常用来量化开关性能的指标。文中对传统结构和新结构的栅电荷特性进行了二维数值模拟,并推导出可用于计算栅电荷的解析模型。仿真结果表明新结构相对于常规结构,栅电荷降低42．93％,器件优值降低37．05％。最后对新结构进行了参数优化。     

Volume conduction in an anatomically based surface EMG model

A finite-element model to simulate surface electromyography (EMG) in a realistic human upper arm is presented. The model is used to explore the effect of limb geometry on surface-detected muscle fiber action potentials. The model was based on magnetic resonance images of the subject's upper arm and includes both resistive and capacitive material properties. To validate the model geometry, experimental and simulated potentials were compared at different electrode sites during the application of a subthreshold sinusoidal current source to the skin surface. Of the material properties examined, the closest approximation to the experimental data yielded a mean root-mean-square (rms) error of the normalized surface potential of 18% or 27%, depending on the site of the applied source. Surface-detected action potentials simulated using the realistic volume conductor model and an idealized cylindrical model based on the same limb geometry were then compared. Variation in the simulated limb geometry had a considerable effect on action potential shape. However, the rate of decay of the action potential amplitude with increasing distance from the fiber was similar in both models. Inclusion of capacitive material properties resulted in temporal low-pass filtering of the surface action potentials. This effect was most pronounced in the end-effect components of action potentials detected at locations far from the active fiber. It is concluded that accurate modeling of the limb geometry, asymmetry, tissue capacitance and fiber curvature is important when the specific action potential shapes are of interest. However, if the objective is to examine more qualitative features of the surface EMG signal, then an idealized volume conductor model with appropriate tissue thicknesses provides a close approximation.     

Constrained detection of left ventricular boundaries from cine CT images of human hearts

Detection of the left ventricular (LV) endocardial (inner) and epicardial (outer) boundaries in cardiac images, provided by fast computer tomography (cine CT), magnetic resonance (MR), or ultrasound (echocardiography), is addressed. The automatic detection of the LV boundaries is difficult due to background noise, poor contrast, and often unclear differentiation of the tissue characteristics of the ventricles, papillary muscles, and surrounding tissues. An approach to the automatic ventricular boundary detection that employs set-theoretic techniques, and is based on incorporating a priori knowledge of the heart geometry, its brightness, spatial structure, and temporal dynamics into the boundaries detection algorithm is presented. Available knowledge is interpreted as constraint sets in the functional space, and the consistent boundaries are considered to belong to the intersection of all the introduced sets, thus satisfying the a priori information. An algorithm is also suggested for the simultaneous detection of the endocardial and epicardial boundaries of the LV. The procedure is demonstrated using cine CT images of the human heart.     

多形态稀疏性正则化的图像超分辨率算法

 如何设计更加高效并能保持图像几何和纹理结构的多幅图像超分辨模型和算法是目前该领域有待解决的难点问题.针对图像的几何、纹理结构形态,分别建立符合类内强稀疏而类间强不相干的几何结构和纹理分量稀疏表示子成份字典,形成图像的多形态稀疏表示模型,进而提出一种新的基于多形态稀疏性正则化的多帧图像超分辨凸变分模型,模型中的正则项刻画了理想图像在多成份字典下的稀疏性先验约束,保真项度量其在退化模型下与观测信号的一致性,采用交替迭代法对该多变量优化问题进行数值求解,每一子问题采用前向后向的算法分裂法进行快速求解.针对可见光与红外图像序列进行了数值仿真,实验结果验证了本文模型与数值算法的有效性.     

Finite-element modeling of bones from CT data: sensitivity to geometry and material uncertainties

The aim of this paper is to analyze how the uncertainties in modelling the geometry and the material properties of a human bone affect the predictions of a finite-element model derived from computed tomography (CT) data. A sensitivity analysis, based on a Monte Carlo method, was performed using three femur models generated from in vivo CT datasets, each subjected to two different loading conditions. The geometry, the density and the mechanical properties of the bone tissue were considered as random input variables. Finite-element results typically used in biomechanics research were considered as statistical output variables, and their sensitivity to the inputs variability assessed. The results showed that it is not possible to define a priori the influence of the errors related to the geometry definition process and to the material assignment process on the finite-element analysis results. The errors in the geometric representation of the bone are always the dominant variables for the stresses, as was expected. However, for all the variables, the results seemed to be dependent on the loading condition and to vary from subject to subject. The most interesting result is, however, that using the proposed method to build a finite-element model of a femur from a CT dataset of the quality typically achievable in the clinical practice, the coefficients of variation of the output variables never exceed the 9%. The presented method is hence robust enough to be used for investigating the mechanical behavior of bones with subject-specific finite-element models derived from CT data taken in vivo.     

Exploratory analysis of the spatio-temporal deformation of the myocardium during systole from tagged MRI

Myocardial contractile function is, with perfusion, one of the main affected factors in ischemic heart diseases. In this paper, we propose an original framework based on functional data analysis for the quantitative study of spatio-temporal parameters related to the myocardial contraction mechanics. The mechanical strains in the left-ventricular (LV) myocardium are computed from tagged magnetic resonance imaging cardiac sequences. A statistical functional model of the normal contractile function of the LV is build from the study of eight examinations on healthy subjects. We show that it is possible to detect abnormal strain patterns comparatively to this model, by generating distance maps at rest and under pharmacological stress. We demonstrate the consistency of the results for the circumferential deformation parameter on healthy and pathological data sets.     

A Simple Interior Decomposition Model: Its Development And Application

A simple interior decomposition model composed of the product of two terms, a shielding-effectiveness term and a coupling- effectiveness term, has been developed that bounds the measured wire responses within a simple generic test object. A variety of modest to strong perturbations to the test object geometry and composition changed the response trend downward by at most 12 dB and typically only by 3-6 dB. Thus the model, called shielding effectiveness × coupling effectiveness (SEXCE), serves as a reasonable characterization of a broad range of generic geometries. It is useful in understanding the interior coupling response behavior and can be used as a predictive tool.