Optimal CT scanning plan for long-bone 3-D reconstruction

Digital computed tomographic (CT) data are widely used in three-dimensional (3-D) construction of bone geometry and density features for 3-D modelling purposes. During in vivo CT data acquisition the number of scans must be limited in order to protect patients from the risks related to X-ray absorption. The aim of this work is to automatically define, given a finite number of CT slices, the scanning plan which returns the optimal 3-D reconstruction of a bone segment from in vivo acquired CT images. An optimization algorithm based on a Discard-Insert-Exchange technique has been developed. In the proposed method the optimal scanning sequence is searched by minimizing the overall reconstruction error of a two-dimensional (2-D) prescanning image: an anterior-posterior (AP) X-ray projection of the bone segment. This approach has been validated in vitro on 3 different femurs. The 3-D reconstruction errors obtained through the optimization of the scanning plan on the 3-D prescanning images and on the corresponding 3-D data sets have been compared. 2-D and 3-D data sets have been reconstructed by linear interpolation along the longitudinal axis. Results show that direct 3-D optimization yields root mean square reconstruction errors which are only 4%-7% lower than the 2-D-optimized plan, thus proving that 2-D-optimization provides a good suboptimal scanning plan for 3-D reconstruction. Further on, 3-D reconstruction errors given by the optimized scanning plan and a standard radiological protocol for long bones have been compared. Results show that the optimized plan yields 20%-50% lower 3-D reconstruction errors     

Development and experimental verification of a two-dimensionalnumerical model of piezoelectrically induced threshold voltage shifts inGaAs MESFETs

The results of a combined experimental and analytical investigation of the effects of mechanical stress on DC electrical parameters, particularly threshold voltage, in MESFETs are reported. The theoretical aspect of this study involves a two-dimensional finite-element simulation of the device structure on which measurements were made. The substrate stresses and resultant piezoelectric charge distributions calculated in this study take into account the two-dimensional nature of the geometry of the gate. The experimental portion of this study involves measurement of DC parameters of devices using external mechanical loads that simulate mechanical stresses that arise during device processing. Measurements under applied loads of both signs and on devices of two different orientations confirm the existence of a piezoelectrically induced threshold voltage shift. A comparison between the approximate line load method of modeling substrate stress fields, and the finite-element method used in this study shows that the piezoelectric charge densities predicted by two models are substantially different. This results from the fact that the simplifying assumptions used to construct the line load model are inappropriate for accurately determining stress fields beneath micrometer and submicrometer gates. Good agreement was obtained between measured threshold voltage shifts and those predicted by the finite-element method model. The results show the need for accurate modeling of mechanical stresses when attempting to model piezoelectric effects     

An Integrated Segmentation and Analysis Approach for QCT of the Knee to Determine Subchondral Bone Mineral Density and Texture

We have developed a new integrated approach for quantitative computed tomography of the knee in order to quantify bone mineral density (BMD) and subchondral bone structure. The present framework consists of image acquisition and reconstruction, 3-D segmentation, determination of anatomic coordinate systems, and reproducible positioning of analysis volumes of interest (VOI). Novel segmentation algorithms were developed to identify growth plates of the tibia and femur and the joint space with high reproducibility. Five different VOIs with varying distance to the articular surface are defined in the epiphysis. Each VOI is further subdivided into a medial and a lateral part. In each VOI, BMD is determined. In addition, a texture analysis is performed on a high-resolution computed tomography (CT) reconstruction of the same CT scan in order to quantify subchondral bone structure. Local and global homogeneity, as well as local and global anisotropy were measured in all VOIs. Overall short-term precision of the technique was evaluated using double measurements of 20 osteoarthritic cadaveric human knees. Precision errors for volume were about 2-3% in the femur and 3-5% in the tibia. Precision errors for BMD were about 1-2% lower. Homogeneity parameters showed precision errors up to about 2% and anisotropy parameters up to about 4%.     

Automated segmentation of acetabulum and femoral head from 3-d CT images

This paper describes several new methods and software for automatic segmentation of the pelvis and the femur, based on clinically obtained multislice computed tomography (CT) data. The hip joint is composed of the acetabulum, cavity of the pelvic bone, and the femoral head. In vivo CT data sets of 60 actual patients were used in the study. The 120 (60 /spl times/ 2) hip joints in the data sets were divided into four groups according to several key features for segmentation. Conventional techniques for classification of bony tissues were first employed to distinguish the pelvis and the femur from other CT tissue images in the hip joint. Automatic techniques were developed to extract the boundary between the acetabulum and the femoral head. An automatic method was built up to manage the segmentation task according to image intensity of bone tissues, size, center, shape of the femoral heads, and other characters. The processing scheme consisted of the following five steps: 1) preprocessing, including resampling 3-D CT data by a modified Sine interpolation to create isotropic volume and to avoid Gibbs ringing, and smoothing the resulting images by a 3-D Gaussian filter; 2) detecting bone tissues from CT images by conventional techniques including histogram-based thresholding and binary morphological operations; 3) estimating initial boundary of the femoral head and the joint space between the acetabulum and the femoral head by a new approach utilizing the constraints of the greater trochanter and the shapes of the femoral head; 4) enhancing the joint space by a Hessian filter; and 5) refining the rough boundary obtained in step 3) by a moving disk technique and the filtered images obtained in step 4). The above method was implemented in a Microsoft Windows software package and the resulting software is freely available on the Internet. The feasibility of this method was tested on the data sets of 60 clinical cases (5000 CT images).     

Computer-Assisted Preoperative Planning for Reduction of Proximal Femoral Fracture Using 3-D-CT Data

This paper describes procedures for repositioning calculations of fractured bone fragments using 3-D-computed tomography (CT), aimed at preoperative planning for computer-guided fracture reduction of the proximal femur. Fracture boundaries of the bone fragments, as ldquofracture lines (FLs),rdquo and the mirror-transformed contralateral femur shape extracted from 3-D-CT were used for repositioning of the fragments. We first describe a method for extracting FLs based on 3-D curvature analysis and then formulate repositioning methods based on registration of bone fragments using the following three constraints: 1) contralateral (CL) femur shape; 2) FLs; and 3) both CL femur shape and fracture lines, as ldquoboth constraintsrdquo. We performed experiments using CT datasets from five simulated and four real patients with proximal femoral fracture. We evaluated the rotation error in reposition calculations and the contact ratio between repositioned fragment boundaries, which are crucial for the recovery of proper functional axes and bone adhesion of fragments, respectively. Experimental results showed that good accuracy and stability were attainable when registration using both constraints was performed after registration using the fracture-line constraint. On average, 6.0deg plusmn0.8deg in rotation error and 89% plusmn 3% in contact ratio were obtained without providing precise initial values.     

Trabecular Bone Analysis in CT and X-Ray Images of the Proximal Femur for the Assessment of Local Bone Quality

Currently, conventional X-ray and CT images as well as invasive methods performed during the surgical intervention are used to judge the local quality of a fractured proximal femur. However, these approaches are either dependent on the surgeon's experience or cannot assist diagnostic and planning tasks preoperatively. Therefore, in this work a method for the individual analysis of local bone quality in the proximal femur based on model-based analysis of CT- and X-ray images of femur specimen will be proposed. A combined representation of shape and spatial intensity distribution of an object and different statistical approaches for dimensionality reduction are used to create a statistical appearance model in order to assess the local bone quality in CT and X-ray images. The developed algorithms are tested and evaluated on 28 femur specimen. It will be shown that the tools and algorithms presented herein are highly adequate to automatically and objectively predict bone mineral density values as well as a biomechanical parameter of the bone that can be measured intraoperatively.     

The evaluation of cortical bone remodeling with a new ultrasonictechnique

Total hip arthroplasty causes biomechanical changes in the normal femur including a redistribution and concentration of stress. These mechanical alterations in the femur cause local remodeling and resorption that affect the geometry and mechanical properties of the bone. Three complementary techniques were used to study the local adaptive remodeling of bone due to prosthesis implantation. A graphics package was used to obtain section geometrical information, an ultrasonic wave propagation technique to determine elastic properties, and a new scanning acoustic microscope (SAM) to map the acoustic impedance profile of each section. The effects of the implantation of two different types of hip prostheses were investigated, an uncemented bipolar prosthesis with an Austin-Moore type stem and a cemented Charnley prosthesis. Prosthesis implantation resulted in an increase in cortical area and mediolateral diameter and a decrease in anterio-posterior diameter. Both prostheses had a detrimental effect on local elastic properties as determined by acoustic velocity measurements. Finally, the SAM system provided information about local inhomogeneities in bone properties not obtainable by any other means. The acoustic impedance maps highlighted bone resorption and bone remodeling on a microstructural level.     

A new accurate and precise 3-D segmentation method for skeletal structures in volumetric CT data

We developed a highly automated three-dimensionally based method for the segmentation of bone in volumetric computed tomography (CT) datasets. The multistep approach starts with three-dimensional (3-D) region-growing using local adaptive thresholds followed by procedures to correct for remaining boundary discontinuities and a subsequent anatomically oriented boundary adjustment using local values of cortical bone density. We describe the details of our approach and show applications in the proximal femur, the knee, and the skull. The accuracy of the determination of geometrical parameters was analyzed using CT scans of the semi-anthropomorphic European spine phantom. Depending on the settings of the segmentation parameters cortical thickness could be determined with an accuracy corresponding to the side length of 1 to 2.5 voxels. The impact of noise on the segmentation was investigated by artificially adding noise to the CT data. An increase in noise by factors of two and five changed cortical thickness corresponding to the side length of one voxel. Intraoperator and interoperator precision was analyzed by repeated analysis of nine pelvic CT scans. Precision errors were smaller than 1% for trabecular and total volumes and smaller than 2% for cortical thickness. Intraoperator and interoperator precision errors were not significantly different. Our segmentation approach shows: 1) high accuracy and precision and is 2) robust to noise, 3) insensitive to user-defined thresholds, 4) highly automated and fast, and 5) easy to initialize.     

Numerical dispersion of higher order nodal elements in thefinite-element method

The discretization inherent in the finite-element method results in numerical dispersion. This dispersion is investigated for a time-harmonic plane wave propagating through an infinite, two-dimensional, finite-element mesh composed of uniform quadrilateral and triangular elements. The effects on the dispersion due to the propagation direction of the wave, the order of the elements, the node density, and the mesh geometry are studied. Results are given which can serve as a guide in selecting the appropriate element order, node density, and mesh geometry when applying the finite-element method     

Toward Strong and Tough Glass and Ceramic Scaffolds for Bone Repair

The need for implants to repair large bone defects is driving the development of porous synthetic scaffolds with the requisite mechanical strength and toughness in vivo. Recent developments in the use of design principles and novel fabrication technologies are paving the way to create synthetic scaffolds with promising potential for reconstituting bone in load‐bearing sites. Here, the state of the art in the design and fabrication of bioactive glass and ceramic scaffolds that have improved mechanical properties for structural bone repair is reviewed. Scaffolds with anisotropic and periodic structures can be prepared with compressive strengths comparable to human cortical bone (100?150 MPa), while scaffolds with an isotropic structure typically have strengths in the range of trabecular bone (2?12 MPa). However, the mechanical response of bioactive glass and ceramic scaffolds in multiple loading modes such as flexure and torsion—as well as their mechanical reliability, fracture toughness, and fatigue resistance—has received little attention. Inspired by the designs of natural materials such as cortical bone and nacre, glass‐ceramic and inorganic/polymer composite scaffolds created with extrinsic toughening mechanisms are showing potential for both high strength and mechanical reliability. Future research should include improved designs that provide strong scaffolds with microstructures conducive to bone ingrowth, and evaluation of these scaffolds in large animal models for eventual translation into clinical applications.     

线扫描视觉检测系统机械—成像综合误差建模

针对线扫描视觉检测系统精度易受机械结构误差影响且具体影响机制不明确的问题,建立并分析了机械误差对系统成像误差影响的数学模型。基于多体运动学与齐次坐标变换理论推导了线扫描视觉检测系统机械系统误差传递模型,并结合线扫描成像特点建立了系统误差综合模型,阐明了机械误差与系统输出图像误差间的对应关系。利用多元函数全微分方法对模型进行了误差灵敏度分析,明确了对系统输出图像x、y两个维度误差影响显著的误差源。针对实际线扫描视觉检测系统进行了误差源验证实验,实验结果表明:所建立的系统误差综合模型可以准确识别出对线扫描视觉检测系统输出图像影响最大的关键误差源;模型对于关键误差源在不同位置灵敏度数值预测与实际偏差不超过2.38%,可以实现对系统关键误差源灵敏度的准确预测。     

Nonlinear finite-element analysis and biomechanical evaluation of the lumbar spine

A finite-element analysis (FEA) model of an intact lumbar disc-body unit was generated. The vertebral body of the FEA model consisted of a solid tetrahedral core of trabecular bone surrounded by a cortical shell. The disc consisted of an incompressible nucleus surrounded by nonlinear annulus fibers embedded in a solid ground substance. The purpose was to create a FEA model suitable for clinical purposes as fracture assessment, instrumentation with pedicle screws, and bone remodeling. Testing of the FEA model was performed nonlinear for a number of loading conditions, and the results were compared with experimental data from the literature. The results showed good agreement. The formulation of the FEA model can be justified for the tested loading conditions.     

Extraction of sheet resistance from four-terminal sheet resistorsreplicated in monocrystalline films with nonplanar geometries

This paper describes limitations of conventional methods of extracting sheet resistance from four-terminal sheet resistors incorporated into electrical linewidth test structures that are patterned in (110) monocrystalline silicon-on-insulator (SOI) films. Nonplanar sections of these structures render the extraction of sheet resistance by conventional techniques subject to systematic errors. The errors are addressed here by algorithms incorporating the results of finite-element current flow analysis. The intended end application is to facilitate the use of the uniquely high repeatability and low cost of electrical critical dimension (CD) metrology as a secondary reference in a traceability path for CD-reference artifacts     

基于空间解析几何的锥束CT系统角度偏差测量

针对锥束CT系统中机械结构的几何参数偏差校正 问题,提出一种基于空间解析几何算法的锥 束CT系统角度偏差的测量方法。利用一种校准模板,仅通过采集单一投影角度对应的投 影数据即 可得到锥束CT系统的角度偏差。仿真和实验结果 表明,利 用本文方法可以有效地获得待测锥束CT系统的机械角度偏差,其测量精度可达到分度量级。 与平面 解析几何法测量结果的对比分析可知,本文测量方法可实现角度偏差参数的有效分离。本文 方法具有较高的可靠性和测量效率,无需模板多角度旋转投影,具有较好的实用性。     

Finite element simulation of package stress in transfer molded MEMS pressure sensors

The goal of this paper is to investigate the effect of residual packaging stress resulting from transfer molding of a micro electro mechanical system pressure sensor. A model of a silicon diaphragm micro electro mechanical system pressure sensor geometry was used to simulate the stresses developed during the molding process. The analyses were carried out with an assumption that the epoxy molding compound was a temperature dependent elastic material. Finite element analysis was used to calculate the residual packaging stress. The stress values were used to obtain the electrical output signal and sensitivity of the packaged sensor. In this way, a direct link was established between package stress and device performance.The calculated output signal and sensitivity were compared with experimental data to verify the simulated stress and hence determine the effect of the packaging process on the pressure sensor. Four different service temperatures were considered to examine the temperature effects on the output signal and the sensitivity for the packaged sensor.     

A maximum likelihood approach to parallel imaging with coil sensitivity noise

Parallel imaging is a powerful technique to speed up magnetic resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sensitivity maps of the coils are noiseless while the only errors are in coil outputs. In practice, however, sensitivity maps are subject to a wide variety of errors. At first glance, sensitivity noise appears to result in an errors-in-variables problem of the kind that is typically solved using total least squares (TLSs). However, existing TLS algorithms are in general inappropriate for the specific type of block structure that arises in parallel imaging. In this paper, we take a maximum likelihood approach to the problem of parallel imaging in the presence of independent Gaussian sensitivity noise. This results in a quasi-quadratic objective function, which can be efficiently minimized. Experimental evidence suggests substantial gains over conventional SENSE, especially in nonideal imaging conditions like low signal-to-noise ratio (SNR), high g-factors and large acceleration, using sensitivity maps suffering from misalignment, ringing, and random noise.     

Establishment of a knee-joint coordinate system from helical axes analysis--a kinematic approach without anatomical referencing

This study establishes a functional knee-joint coordinate system (FCS) derived from active motion. The scale invariant properties of helical axes were used in order to avoid inter-observer errors associated with the traditional anatomical referencing techniques. The algorithm was tested with six cadaveric specimens in a knee-joint motion and loading apparatus. To determine the FCS sensitivity to variable loading, rotational moments were applied to the tibia while extending and flexing the knee. Each derived FCS was compared with the clinically derived anatomical coordinate system (ACS). The FCS was reproducible when the loading condition was the same. Changing the rotational moments from internal to external affected the orientations and the positions of the FCS. The largest displacement of 20.8 mm in average occurred in the medio/lateral direction. The FCS corresponded with the ACS for all specimens and loading conditions. The origin was always located within the femur along the transepicondylar line. The orientations differed less than 16.6 degrees in average, thus allowing the use of clinical terminology. These findings suggest that the FCS might improve the ability to clinically assess kinematic alterations provided that the reference motion is reproducible.     

用投影算子改善信号子空间方向估计算法的稳健性

基于信号子空间的超分辨方法一般对接收器阵列误差非常敏感。本文提出的投影变换法利用目标方向的初始估计和阵列流形的先验知识，可以显著减小信号子空间方法的误差灵敏度。文中给出了数值仿真和实际阵列数据测试的结果。     

Microwave imaging using the finite-element method and a sensitivity analysis approach

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.     

3-D FEM Modeling and Fabrication of Circular Photonic Crystal Microcavity

In this paper, we study an unconventional kind of quasi-three-dimensional (3-D) photonic crystal (PhC) with circular lattice pattern: it consists of air holes in a GaAs material $({rm n}=3.408)$ along circular concentric lines. This particular PhC geometry has peculiar behavior if compared with the traditional square and triangular lattices, but it is difficult to model by using conventional numerical approaches such as wave expansion method. The resonance and the radiation aspects are analyzed by the 3-D finite-element method (FEM). The model, based on a scattering matrix approach, considers the cavity resonance frequency and evaluates the input–output relationship by enclosing the photonic crystal slab (PhCS) in a black box in order to define the responses at different input–output ports. The scattering matrix method gives important information about the frequency responses of the passive 3-D crystal in the 3-D spatial domain. A high sensitivity of the scattering parameters to the variation of the geometrical imperfection is also observed. The model is completed by the quality factor (Q-factor) estimation. We fabricated the designed circular photonic crystal over a slab membrane waveguide embedding InAs/GaAs quantum dots emitting around 1.28 $mu{hbox{m}}$. Good agreement between numerical and experimental results was found, thus validating the 3-D FEM full-wave investigation.