Multi-parameter Representation Research Articles

Biopathologic Characterization and Grade Assessment of Breast Cancer With 3-D Multiparametric Ultrasound Combining Shear Wave Elastography and Backscatter Tensor Imaging

ObjectiveDespite recent improvements in medical imaging, the final diagnosis and biopathological characterization of breast cancers currently still requires biopsies. Ultrasound is commonly used for clinical examination of breast masses. B-mode and Shear Wave Elastography (SWE) are already widely used to detect suspicious masses and differentiate benign lesions from cancers. But additional ultrasound modalities such as Backscatter Tensor Imaging (BTI) could provide relevant biomarkers related to tissue organization. Here we present a 3D multiparametric ultrasound approach applied to breast carcinomas aiming to (i) validate the ability of BTI to reveal the underlying organization of collagen fibers and (ii) assess the complementarity of SWE and BTI to reveal biopathological features of diagnostic interest. Methods3D SWE and BTI were performed ex vivo on 64 human breast carcinoma samples using a linear ultrasound probe moved by a set of motors. In this paper, we present a 3D multiparametric representation of the breast masses and quantitative measurements combining B-mode, SWE and BTI. ResultsOur results show for the first time that BTI can capture the orientation of the collagen fibers around tumors. BTI was found to be a relevant marker for assessing cancer stages revealing a more tangent tissue orientation for in situ carcinomas than for invasive cancers. In invasive cases, the combination of BTI and SWE parameters allowed for classification of invasive tumors with respect to their grade with an accuracy of 95.7%. ConclusionOur results highlight the potential of 3D multiparametric ultrasound imaging for biopathological characterization of breast tumors.

Multiparameter representation and classification of blood cells based on phase map analysis

Morphological analysis and feature representation of whole blood cells (white blood cells, red blood cells and platelets) are of great importance in life science and clinical medicine. In order to obtain phases of cells, an experimental platform is used based on the principle of transport of intensity equation (TIE). To obtain the detailed information of the cells, five characteristic parameters of the measured phase including peak-valley difference, phase volume, phase surface area, perimeter and project area are introduced. At the same time, the corresponding characteristic values of erythrocytes, neutrophils and platelets are discussed. Moreover, a phase gradient method is proposed to analyze the interface of the cell and remove the halo in its phase map. Finally, combining with the threshold of the parameters and phase gradient of the cells, an identifying method is established so that three classification of whole blood cells can be realized. Experimental results demonstrate that the proposed method has a better accuracy and good feasibility. It provides a novel method and technical basis for the analysis and classification of blood cells based on quantitative phase imaging.

Designing double freeform surfaces for point source and extended sources using a construction, iteration and optimization process

In this paper, a construction-iteration-optimization method is developed to design a double freeform surface lens for point sources as well as extended sources to achieve uniform illuminance. In the construction process, the initial double freeform surfaces are first calculated by the variable separation method with preset source-target ray mapping to obtain the maximum utilization ratio with Fresnel loss. Then, the double freeform surfaces are fitted into a fourth-order XY polynomial surface considering both the coordinates and surface normals of the data points, which ensures the smoothness of freeform surfaces. To reduce the relative standard deviation of the illuminance distribution, an iteration process is required to reconstruct the two freeform surfaces by turns, and this process can be repeated several times to further decrease the deviation of the rays. The system after the construction-iteration process can be taken as a good starting point for further optimization with optical design software. Although the construction-iteration-optimization process is for a point source at first, with the advantage of multi-parameter representation of freeform surfaces we can further optimize the parameters for an extended source by replacing the point source. Simulation results for illuminance uniformity are demonstrated to verify the effectiveness of this method. The energy utilization ratios are above 86.5% and 82.3% with Fresnel loss, while the relative standard deviations of the illuminance distribution are less than 0.036 and 0.063 for a point source and an extended source, respectively.

Multi-parameter singular integral operators and representation theorem

We formulate a class of singular integral operators in arbitrarily many parameters using mixed type characterizing conditions. The main result we prove for this class of operators is a multi-parameter representation theorem stating that a generic operator in our class can be represented as an average of sums of dyadic shifts, which implies a new multi-parameter T 1 theorem as a byproduct. This extends the representation principles of Hytönen’s and Martikainen’s to the multi-parameter setting. Furthermore, equivalence between ours and Journé’s class of multi-parameter operators is established, whose proof requires the multiparameter T 1 theorem.

Multi-parametric representation of voxel-based quantitative magnetic resonance imaging.

The aim of the study was to explore the possibilities of multi-parametric representations of voxel-wise quantitative MRI data to objectively discriminate pathological cerebral tissue in patients with brain disorders. For this purpose, we recruited 19 patients with Multiple Sclerosis (MS) as benchmark samples and 19 age and gender matched healthy subjects as a reference group. The subjects were examined using quantitative Magnetic Resonance Imaging (MRI) measuring the tissue structure parameters: relaxation rates, R and R, and proton density. The resulting parameter images were normalized to a standard template. Tissue structure in MS patients was assessed by voxel-wise comparisons with the reference group and with correlation to a clinical measure, the Expanded Disability Status Scale (EDSS). The results were visualized by conventional geometric representations and also by multi-parametric representations. Data showed that MS patients had lower R and R, and higher proton density in periventricular white matter and in wide-spread areas encompassing central and sub-cortical white matter structures. MS-related tissue abnormality was highlighted in posterior white matter whereas EDSS correlation appeared especially in the frontal cortex. The multi-parameter representation highlighted disease-specific features. In conclusion, the proposed method has the potential to visualize both high-probability focal anomalies and diffuse tissue changes. Results from voxel-based statistical analysis, as exemplified in the present work, may guide radiologists where in the image to inspect for signs of disease. Future clinical studies must validate the usability of the method in clinical practice.

Recent developments in multi-parametric three-dimensional stress field representation in plates weakened by cracks and notches

The paper deals with the three-dimensional nature and the multi-parametric representation of the stress field ahead of cracks and notches of different shape. Finite thickness plates are considered, under different loading conditions. Under certain hypotheses, the three-dimensional governing equations of elasticity can be reduced to a system where a bi-harmonic equation and a harmonic equation have to be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, the latter provides the solution of the corresponding out-of-plane shear notch problem. The analytical frame is applied to some notched and cracked geometries and its degree of accuracy is discussed comparing theoretical results and numerical data from 3D FE models.

Multi-parameter Burau representations

We consider the multi-parameter representation of Artin's braid group introduced by D. D. Long and J. P. Tian, namely $\alpha: B_{n}\rightarrow GL_{m}(C)$, where $m=n!n$ . First, we show that there exists a complex specialization of the multi-parameter representation that does not arise from any Hecke algebra. Second, we find conditions under which the images of the generators of the braid group on three strings under the multi-parameter representation are unitary relative to a nonsingular hermitian matrix.

Higher Dimensional Irreducible Representations of the Pure Braid Group

The reduced Gassner representation is a multi-parameter representation of $%P_{n},$ the pure braid group on n strings. Specializing the parameters $%t_{1},t_{2},...,t_{n}$ to nonzero complex numbers $x_{1},x_{2},...,x_{n}$gives a representation $G_{n}(x_{1},\ldots ,x_{n}):P_{n}\rightarrowGL(\mathbb{C}^{n-1})$ which is irreducible if and only if $x_{1}\ldotsx_{n}\neq 1$. In a previous work, we found a sufficient condition for theirreducibility of the tensor product of two irreducible Gassnerrepresentations. In our current work, we find a sufficient condition that guarantees the irreducibility of the tensor product of three Gassner representations. Next, a generalization of our result is given by considering the irreducibility of the tensor product of $k$ representations (\;$k \geq 3\;$).

Using Block-based Multiparameter Representation to Detect Tumor Features on T2-weighted Brain MRI Images

The objective of this paper is to present an analytical method for digitized images to detect tumors or lesions in a medical decision support system. The authors have developed a simple method of tumor detection using three parameter values: edge (E), gray (G), and contrast (H). The method proposed here first studied the VHD (Visible Human Dataset) input brain feature using EGH parameters that divided the input image into fixed-size blocks (templates). The EGH parameters for the feature blocks were calculated and parameterized to detect the occurrences of abnormalities. These abnormal blocks were then marked for interpretation. Measurements of the following medical dataset were performed: 1) different time-interval images from the same dataset, 2) different brain disease images from multiple datasets, and 3) multiple slice images from multiple datasets. Our experimental results illustrate the ability of our proposed technique to detect tumor blocks with conceptual simplicity and computational efficiency. In this paper, we present output examples from our prototype system, comparing detection accuracy and system performance.