Estimation of Parameters of Parathyroid Glands Using Particle Swarm Optimization and Multivariate Generalized Gaussian Function Mixture

Abstract

Featured Application: The analyzed technique allows the estimation of parameters of small objects from SPECT volumes. Data analysis was based on Particle Swarm Optimization that reduces error between assumed model and measurements. Analysis by Synthesis was used for the estimation of parameters. Abstract: The paper introduces a fitting method for Single-Photon Emission Computed Tomography (SPECT) images of parathyroid glands using generalized Gaussian function for quantitative assessment of preoperative parathyroid SPECT/CT scintigraphy results in a large patient cohort. Parathyroid glands are very small for SPECT acquisition and the overlapping of 3D distributions was observed. The application of multivariate generalized Gaussian function mixture allows modeling, but results depend on the optimization algorithm. Particle Swarm Optimization (PSO) with global best, ring, and random neighborhood topologies were compared. The obtained results show benefits of random neighborhood topology that gives a smaller error for 3D position and the position estimation was improved by about 3% voxel size, but the most important is the reduction of processing time to a few minutes, compared to a few hours in relation to the random walk algorithm. Moreover, the frequency of obtaining low MSE values was more than two times higher for this topology. The presented method based on random neighborhood topology allows quantifying activity in a specific voxel in a short time and could be applied it in clinical practice.

Preoperative and Intraoperative Methods of Parathyroid Gland Localization and the Diagnosis of Parathyroid Adenomas

“…Several preoperative examinations of the PGs, including cervical ECT scanning, ultrasonography (USG) or 99mTc sestamibi scintigraphy (MIBI) are commonly used; however, these methods are often not entirely sufficient for identifying the proper localization of PGs [27]. However, the effectiveness of providing a proper localization of PGs was significantly increased by some intraoperative methods, which appeared to be more frequently used [28]. Establishing the most exact localization of PGs seems to hold many promising results in reducing the number of surgical complications, including excessive bleeding or the accidental injury of the recurrent laryngeal nerve [29,30].…”

The Analysis of WJ Distribution as an Extended Gaussian Function: Case Study

“…in Equation (7). Nevertheless, there is no general relation between σII1 and σIII1 except for the condition of α = β.…”

“…It should be adequate to point out that the list of non-Gaussian or skewed Gaussian distributions, including the Gaussian distribution and working well in practice, is truly long [1,35], encompassing the well-established Weibull distributions [23,35,36], Levy distributions [27,35], skew-normal and related families [37][38][39][40], Beta distributions [35], lognormal distributions [35], multivariate normal distributions [7,35], multidimensional normal distributions [7,35], gamma distributions [35], hypergeometric distributions [35] and Cauchy distributions [35] in addition to the above-mentioned models concerning extreme events and critical phenomena [13][14][15][16].…”

“…Due to its skewedness; however, a concern could arise about the legitimacy of applying the Gaussian function to it as a result of possible misinterpretation in the procedure. To resolve the issue and give more examples in practical application, we are going to present the data acquired from the same experiment [7], both with and without skewedness, to directly appraise the applicability of the WJ distribution and the Gaussian function in the following. The experiment reports a multidisciplinary fitting approach to improve the localization of parathyroid glands from their Single-Photon Emission Computed Tomography (SPECT) images using generalized Gaussian functions for quantitative assessment of preoperative parathyroid SPECT/CT (CT, Computed Tomography) scintigraphy results in a large patient cohort in combination with Particle Swarm Optimization (PSO) modeling and generates the distributions of several important parameters.…”

“…In probability statistics, both t-distribution and binomial distribution eventually trend to the Gaussian distribution, from which t-distribution and F-distribution are derivable. Multivariate and multidimensional methods involving generalized Gaussian functions have been developed for advanced applications [7]. In the field of communications, the Gaussian function is incurred to quantify the statistical behaviors of channel noises, bit error rates, image processing, and multimedia signal enhancement [8], as well as the response peak of chromatographic detection [9].…”