Voxel Array Research Articles

Freehand three‐dimensional ultrasound to assess semitendinosus muscle morphology

In several neurological disorders and muscle injuries, morphological changes of the m. semitendinosus (ST) are presumed to contribute to movement limitations around the knee. Freehand three‐dimensional (3D) ultrasound (US), using position tracking of two‐dimensional US images to reconstruct a 3D voxel array, can be used to assess muscle morphology in vivo. The aims of this study were: (i) to introduce a newly developed 3D US protocol for ST; and (ii) provide a first comparison of morphological characteristics determined by 3D US with those measured on dissected cadaveric muscles. Morphological characteristics of ST (e.g. muscle belly length, tendon length, fascicle length and whole muscle volume, and volumes of both compartments) were assessed in six cadavers using a 3D US protocol. Subsequently, ST muscles were removed from the body to measure the same morphological characteristics. Mean differences between morphological characteristics measured by 3D US and after dissection were smaller than 10%. Intra‐class correlation coefficients (ICCs) were higher than 0.75 for all variables except for the lengths of proximal fascicles (ICC = 0.58). Measurement of the volume of proximal compartment by 3D US was not feasible, due to low US image quality proximally. We conclude that the presented 3D US protocol allows for reasonably accurate measurements of key morphological characteristics of ST muscle.

TH‐CD‐206‐01: Expectation‐Maximization Algorithm‐Based Tissue Mixture Quantification for Perfusion MRI

Purpose:To investigate the feasibility of estimating the tissue mixture perfusions and quantifying cerebral blood flow change in arterial spin labeled (ASL) perfusion MR images.Methods:The proposed perfusion MR image analysis framework consists of 5 steps: (1) Inhomogeneity correction was performed on the T1‐ and T2‐weighted images, which are available for each studied perfusion MR dataset. (2) We used the publicly available FSL toolbox to strip off the non‐brain structures from the T1‐ and T2‐weighted MR images. (3) We applied a multi‐spectral tissue‐mixture segmentation algorithm on both T1‐ and T2‐structural MR images to roughly estimate the fraction of each tissue type ‐ white matter, grey matter and cerebral spinal fluid inside each image voxel. (4) The distributions of the three tissue types or tissue mixture across the structural image array are down‐sampled and mapped onto the ASL voxel array via a co‐registration operation. (5) The presented 4‐dimensional expectation‐maximization (4D‐EM) algorithm takes the down‐sampled three tissue type distributions on perfusion image data to generate the perfusion mean, variance and percentage images for each tissue type of interest.Results:Experimental results on three volunteer datasets demonstrated that the multi‐spectral tissue‐mixture segmentation algorithm was effective to initialize tissue mixtures from T1‐ and T2‐weighted MR images. Compared with the conventional ASL image processing toolbox, the proposed 4D‐EM algorithm not only generated comparable perfusion mean images, but also produced perfusion variance and percentage images, which the ASL toolbox cannot obtain. It is observed that the perfusion contribution percentages may not be the same as the corresponding tissue mixture volume fractions estimated in the structural images.Conclusion:A specific application to brain ASL images showed that the presented perfusion image analysis method is promising for detecting subtle changes in tissue perfusions, which is valuable for the early diagnosis of certain brain diseases, e.g. multiple sclerosis.

Volume enhancement with externally controlled anisotropic diffusion

This paper proposes a method to enhance volumetric data using anisotropic diffusion controlled by another voxel array representing the same object with different physical quantities. The main application of this approach is to enhance volumetric functional data (obtained e.g. with PET or SPECT) based on anatomic (e.g. CT or MRI) information. Enhancement includes noise removal, sharpening and resolution upsampling. As different modalities measure different physical quantities that may or may not be correlated, enhancement must be carefully designed not to introduce spurious features that are present only in one modality. Forward diffusion working with non-negative diffusivity guarantees this kind of causality but also limits the potential of enhancement. To allow the preservation or even the increase of the dynamic range, diffusion should also go backwards. Therefore, we propose a forward---backward diffusion scheme for the enhancement where stability and the avoidance of spurious features are provided by the automatic determination of parameters controlling the diffusion process.

3D strain mapping in rocks using digital volumetric speckle photography technique

Speckle photography technique is a versatile displacement/deformation mapping technique that can be applied to almost any material. It has its genesis in the laser speckle interferometry technique whereby the natural speckles created by illuminating an optically rough surface using a coherent laser beam are used as displacement gauging elements. It evolves into the white light speckle photography technique whereby a random pattern of any type is used as a displacement measurement transducer. With the advent of digital cameras and ubiquitous usage of computers, the digital version of the technique is developed. Up to now, the technique is essentially limited to 2D applications. Recently, we extended the technique into the 3D domain by using the volumetric imaging capabilities of CT or MRI. In this paper, we apply this technique to measuring the internal deformation of rocks. It so happens that certain rocks have natural density variation at various places such that when imaged by CT these impurities can be treated as 3D speckles. The elements of volumetric speckle photography technique are as follows. A reference volumetric image of the rock is recorded by a micro-CT scan and stored as a reference. Under load, the deformed CT image of the rock is also recorded. Both volume images are divided into subsets of certain voxel arrays. Each corresponding pair of the subsets is “compared” via a two-step 3D Fourier transform analysis. The result is a 3D map of displacement vectors representing the collective displacement experienced by all the speckles within the subset of voxels. The strain distribution of the entire rock specimen can then be calculated using appropriate displacement strain relations. The application of this technique to strain mapping of red sandstone and argillite rocks is presented.

Echogenicity intensity of the medial gastrocnemius and tendon achilles in age matched CP and TD children

simultaneously track theUS probe, 4 rigidly attachedmarkerswere tracked by a motion analysis system, at 120Hz (Optitrack, USA). For both volume and distance, 3 acquisition repetitions were performed. An in-house developedPythonpackage [2,4] andMeVisLab (www.mevislab.de) were used to reconstruct the acquisition data, whereby volume [2] and lengths were then manually extracted from the resulting 3D voxel array reconstruction (VA). In addition, the US probe was also used as a spatial pointer (PaP) to visualize the cross-wire points, and measure the length. Each reconstructed volume and calculated length was compared to the known values, obtained with a weighing scale and tape measure. Each acquisition was processed 3 times by 2 raters. The acquisition and feature extraction comparisons were investigated by the intra-class correlation coefficients for intra-rater (3,1) and inter-rater (3,k), and the standard error of measurement (SEM). Results: The ICC and SEM reliability for all measures were greater than 0.99 and 0.98, and 2.2ml and 2.1mm, respectively (Table 1). For the validity, on average, 3DUS overestimates volumes by 1.6%, lengths by 1.3% (PAP) and 2.1% (VA). Discussion: This study demonstrates a high reliability for the 3DUS method to estimate volume and lengths. This efficient method can be translated into clinical practice, where the reported validity suggests adequate accuracy required for defining anatomically relevant structures, such as muscle and tendon.

Precise autofocus method employing normalized fluorescence image size in a two-photon polymerization nanofabrication system.

The autofocus method has been investigated to improve the precise positioning of a substrate surface at the center of the laser focal spot in two-photon polymerization (TPP) nanofabrication. For this purpose, we developed a novel autofocus method using normalized image size, which was calculated with the second momentum radius (SMR) of two-photon induced fluorescence (TPIF). The SMR of TPIF was theoretically analyzed and experimentally compared with the average intensity of TPIF for various input laser powers. The results show that the proposed method enhanced the precision and robustness of autofocus in TPP. Specifically, the experimental creation of ascending voxel arrays demonstrated both the method's immunity to input laser power change, and a high precision of ±0.045 μm. To test the practical feasibility of the proposed autofocus method, 300 μm×260 μm single-layer honey-comb structures were successfully fabricated with precompensation and dynamic compensation using the proposed autofocus method.

Interior 3D-Strain Mapping in Opaque Materials Using Digital Volumetric Speckle Photography and X-Ray Micro Computer Tomography

Developing a true 3D experimental stress analysis technique has been the holy grail of solid mechanics researchers since the genesis of the field. Combined the high-resolution x-ray computer tomography (Micro CT) with the 2D speckle photography technique developed by one of us (Chiang), we recently proposed a new 3D strain analysis technique called Digital Volumetric Speckle Photography (DVSP). The elements of DVSP technique are as follows. A reference volumetric image of the specimen is recorded by a Micro-CT scan and stored as a reference. Under load the deformed CT image of the specimen is also recorded. Both volume images are divided into subimages of certain voxel arrays. Each corresponding pair of the subimages are ‘compared’ via a two-step 3D Fourier Transform analysis. The result is a 3D map of displacement vectors representing the collective displacement experienced by all the speckles within the subset of voxels. Strain distribution of the entire specimen can then be calculated using appropriate displacement strain relations. Application of this technique to strain mapping of red sandstone and composite are presented.

A Chemical Display: Generating Animations by Controlled Diffusion from Porous Voxels

The concept of utilizing precisely patterned and chemically loaded 3D porous containers akin to chemical voxels to enable dynamic visual patterns via spatial and temporal control of both local and global chemical release is described. Using numerical simulations and experiments, it is shown how variations in porosity, volume, shape, and relative positioning of the chemical voxels can be used to control the types of images that are formed with control in both space and time. Moving images are generated via controlled chemical release from an array of voxels to create an animation of a running man thereby illustrating proof‐of‐concept for a chemical display.

Initial reconstruction results from a simulated adaptive small animal C shaped PET/MR insert.

Traditionally, most clinical and preclinical PET scanners, rely on full cylindrical geometry for whole body as well as dedicated organ scans, which is not optimized with regards to sensitivity and resolution. Several groups proposed the construction of dedicated PET inserts for MR scanners, rather than the construction of new integrated PET/MR scanners. The space inside an MR scanner is a limiting factor which can be reduced further with the use of extra coils, and render the use of non-flexible cylindrical PET scanners difficult if not impossible. The incorporation of small SiPM arrays, can provide the means to design adaptive PET scanners to fit in tight locations, which, makes imaging possible and improve the sensitivity, due to the closer approximation to the organ of interest. In order to assess the performance of such a device we simulated the geometry of a C shaped PET, using GATE. The design of the C-PET was based on a realistic SiPM-BGO scenario. In order reconstruct the simulated data, with STIR, we had to calculate system probability matrix which corresponds to this non standard geometry. For this purpose we developed an efficient multi threaded ray tracing technique to calculate the line integral paths in voxel arrays. One of the major features is the ability to automatically adjust the size of FOV according to the geometry of the detectors. The initial results showed that the sensitivity improved as the angle between the detector arrays increases, thus better angular sampling the scanner's field of view (FOV). The more complete angular coverage helped in improving the shape of the source in the reconstructed images, as well. Furthermore, by adapting the FOV to the closer to the size of the source, the sensitivity per voxel is improved.

A visual LISP program for voxelizing AutoCAD solid models

AutoCAD solid models are increasingly recognized in geological and geotechnical 3D modeling. In order to bridge the currently existing gap between AutoCAD solid models and the grid modeling realm, a Visual LISP program is presented that converts AutoCAD solid models into voxel arrays. Acad2Vox voxelizer works on a 3d-model that is made up of arbitrary non-overlapping 3D-solids. After definition of the target voxel array geometry, 3D-solids are scanned at grid positions and properties are streamed to an ASCII output file. Acad2Vox has a novel voxelization strategy that combines a hierarchical reduction of sampling dimensionality with an innovative use of AutoCAD-specific methods for a fast and memory-saving operation. Acad2Vox provides georeferenced, voxelized analogs of 3D design data that can act as regions-of-interest in later geostatistical modeling and simulation. The Supplement includes sample geological solid models with instructions for practical work with Acad2Vox.

Systematic misregistration and the statistical analysis of surface data

Spatial normalisation is a key element of statistical parametric mapping and related techniques for analysing cohort statistics on voxel arrays and surfaces. The normalisation process involves aligning each individual specimen to a template using some sort of registration algorithm. Any misregistration will result in data being mapped onto the template at the wrong location. At best, this will introduce spatial imprecision into the subsequent statistical analysis. At worst, when the misregistration varies systematically with a covariate of interest, it may lead to false statistical inference. Since misregistration generally depends on the specimen's shape, we investigate here the effect of allowing for shape as a confound in the statistical analysis, with shape represented by the dominant modes of variation observed in the cohort. In a series of experiments on synthetic surface data, we demonstrate how allowing for shape can reveal true effects that were previously masked by systematic misregistration, and also guard against misinterpreting systematic misregistration as a true effect. We introduce some heuristics for disentangling misregistration effects from true effects, and demonstrate the approach's practical utility in a case study of the cortical bone distribution in 268 human femurs.

Feasibility testing of a pre-clinical coded aperture phase contrast imaging configuration using a simple fast Monte Carlo simulator

A simple method of simulating possible coded aperture phase contrast X-ray imaging apparatus is presented. The method is based on ray tracing, with the rays treated ballistically within a voxelized sample and with the phase-shift-induced angular deviations and absorptions applied at a plane in the middle of the sample. For the particular case of a coded aperture phase contrast configuration suitable for small animal pre-clinical imaging we present results obtained using a high resolution voxel array representation of a mathematically-defined 'digital' mouse. At the end of the article a link to the software is supplied.

Monte Carlo simulation based study of a proposed multileaf collimator for a telecobalt machine

The objective of the present work was to propose a design of a secondary multileaf collimator (MLC) for a telecobalt machine and optimize its design features through Monte Carlo simulation. The proposed MLC design consists of 72 leaves (36 leaf pairs) with additional jaws perpendicular to leaf motion having the capability of shaping a maximum square field size of 35 × 35 cm(2). The projected widths at isocenter of each of the central 34 leaf pairs and 2 peripheral leaf pairs are 10 and 5 mm, respectively. The ends of the leaves and the x-jaws were optimized to obtain acceptable values of dosimetric and leakage parameters. Monte Carlo N-Particle code was used for generating beam profiles and depth dose curves and estimating the leakage radiation through the MLC. A water phantom of dimension 50 × 50 × 40 cm(3) with an array of voxels (4 × 0.3 × 0.6 cm(3) = 0.72 cm(3)) was used for the study of dosimetric and leakage characteristics of the MLC. Output files generated for beam profiles were exported to the PTW radiation field analyzer software through locally developed software for analysis of beam profiles in order to evaluate radiation field width, beam flatness, symmetry, and beam penumbra. The optimized version of the MLC can define radiation fields of up to 35 × 35 cm(2) within the prescribed tolerance values of 2 mm. The flatness and symmetry were found to be well within the acceptable tolerance value of 3%. The penumbra for a 10 × 10 cm(2) field size is 10.7 mm which is less than the generally acceptable value of 12 mm for a telecobalt machine. The maximum and average radiation leakage through the MLC were found to be 0.74% and 0.41% which are well below the International Electrotechnical Commission recommended tolerance values of 2% and 0.75%, respectively. The maximum leakage through the leaf ends in closed condition was observed to be 8.6% which is less than the values reported for other MLCs designed for medical linear accelerators. It is concluded that dosimetric parameters and the leakage radiation of the optimized secondary MLC design are well below their recommended tolerance values. The optimized design of the proposed MLC can be integrated into a telecobalt machine by replacing the existing adjustable secondary collimator for conformal radiotherapy treatment of cancer patients.

Computationally-Optimized Bone Mechanical Modeling from High-Resolution Structural Images

Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging.

한국인 기준여성 체적소형 모의체 개발

The objective of this study is for development of the reference Korean female phantom, HDRK-Woman. The phantom was constructed by adjusting a Korean woman voxel phantom to the Reference Korean data. The Korean woman phantom had been developed based on the high-resolution color slice images obtained from an adult Korean female cadaver. There were a total of 39 organs including the 27 organs specified in ICRP 103 for effective dose calculation. The voxel resolution of the phantom was and the voxel array size is in the x, y and z directions. Then, the voxel resolution was changed to for adjustment of the height and total bone mass of the phantom to the Reference Korean data. Finally, the internal organs and tissue were adjusted using in-house software program developed for 3D volume adjustment of the organs and tissue. The effective dose values of HDRK phantoms were calculated for broad parallel photon beams using MCNPX Monte Carlo code and compared with those of ICRP phantoms.

A Variable-Resolution Probabilistic Three-Dimensional Model for Change Detection

Given a set of high-resolution images of a scene, it is often desirable to predict the scene's appearance from viewpoints not present in the original data for purposes of change detection. When significant 3-D relief is present, a model of the scene geometry is necessary for accurate prediction to determine surface visibility relationships. In the absence of an a priori high-resolution model (such as those provided by LIDAR), scene geometry can be estimated from the imagery itself. These estimates, however, cannot, in general, be exact due to uncertainties and ambiguities present in image data. For this reason, probabilistic scene models and reconstruction algorithms are ideal due to their inherent ability to predict scene appearance while taking into account such uncertainties and ambiguities. Unfortunately, existing data structures used for probabilistic reconstruction do not scale well to large and complex scenes, primarily due to their dependence on large 3-D voxel arrays. The work presented in this paper generalizes previous probabilistic 3-D models in such a way that multiple orders of magnitude savings in storage are possible, making high-resolution change detection of large-scale scenes from high-resolution aerial and satellite imagery possible. Specifically, the inherent dependence on a discrete array of uniformly sized voxels is removed through the derivation of a probabilistic model which represents uncertain geometry as a density field, allowing implementations to efficiently sample the volume in a nonuniform fashion.

Experimental Investigation of 3D Velocity by Tomographic Particle Image Velocimetry (Tomo-PIV) in a Short Riser Section

The measurement of instantaneous velocity field with high spatial resolution makes the Tomo-PIV (tomographic particle image velocimetry) technique attractive for the study of complex flows in circulating beds. The Tomo-PIV technique is employed for obtaining the velocity field of the fluid phase in three dimensions using tracer particles which follow the fluid. They are immersed in the fluid and illuminated by a source of pulsed light (laser) within a three-dimensional region. Images of the particles are recorded in the focus of several viewing directions using CCD (Charge-Coupled Device) sensors. The distribution of light intensity is discretized into a 3D array of voxels and then analyzed by interrogation of cross-correlation in three dimensions. The information field is returned in the form of instantaneous velocities of the measurement volume. This paper aims to present an experimental setup for an initial investigation of the velocity field of the particulate phase of a riser section of a circulating bed. The calibration errors were between 0.209 and 0.066 pixels and after the self-calibration errors were below 0.097 pixels. The volume investigated was 82 x 100 x 10 mm 3 with a resolution of 1571 x 897 x 113 voxels. The reconstructed volumes were processed using 3D cross-correlation with a volume interrogation size of 110 voxels decreasing to a final size of 16 voxels with a 75% overlap between adjacent interrogation volumes. The velocity field produced has 224 x 393 x 28 voxels.

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented.

Statistically reconstructing continuous isotropic and anisotropic two-phase media while preserving macroscopic material properties

We propose a method to generate statistically similar reconstructions of two-phase media. As with previous work, we initially characterize the microstructure of the material using two-point correlation functions (a subset of spatial correlation functions) and then generate numerical reconstructions using a simulated annealing method that preserves the geometric relationships of the material's phase of interest. However, in contrast to earlier contributions that consider reconstructions composed of discrete arrays of pixels or voxels alone, we generate reconstructions based on assemblies of continuous, three-dimensional, interpenetrating objects. The result is a continuum description of the material microstructure (as opposed to a discretized or pixelated description), capable of efficiently representing large disparities in scale. Different reconstruction methods are considered based on distinct combinations of two-point correlation functions of varying degrees of complexity. The quality of the reconstruction methods are evaluated by comparing the total pore fraction, specific surface area of the percolating cluster, pore fraction of the percolating cluster, tortuosity, and permeability of the reconstructions to those of a set of reference assemblies. Elsewhere it has been proposed that two-phase media could be statistically reproduced with only two spatial correlation functions: the two-point probability function (the probability that two points lie within the same phase) and the lineal path function (the probability that a line between two points lies entirely within the same phase). We find that methods employing the two-point probability function and lineal path function are improved if the percolating cluster volume is also considered in the reconstruction. However, to reproduce more complicated geometric assemblies, we find it necessary to employ the two-point probability, two-point cluster, and lineal path function in addition to the percolating cluster volume to produce a generally accurate statistical reconstruction.

Free Path Sampling in High Resolution Inhomogeneous Participating Media

Abstract This paper presents efficient algorithms for free path sampling in heterogeneous participating media defined either by high‐resolution voxel arrays or generated procedurally. The method is based on the concept of mixing ‘virtual’ material or particles to the medium, augmenting the extinction coefficient to a function for which the free path can be sampled in a straightforward way. The virtual material is selected such that it modifies the volume density but does not alter the radiance. We define the total extinction coefficient of the real and virtual particles by a low‐resolution grid of super‐voxels that are much larger than the real voxels defining the medium. The computational complexity of the proposed method depends just on the resolution of the super‐voxel grid and does not grow with the resolution above the scale of super‐voxels. The method is particularly efficient to render large, low‐density, heterogeneous volumes, which should otherwise be defined by enormously high resolution voxel grids and where the average free path length would cross many voxels.