Advanced maximum entropy approaches for medical and microscopy imaging

The maximum entropy framework is a cornerstone of statistical inference, which is employed at a growing rate for constructing models capable of describing and predicting biological systems, particularly complex ones, from empirical datasets.‎ In these high-yield applications, determining exact probability distribution functions with only minimal information about data characteristics and without utilizing human subjectivity is of particular interest. In this thesis, an automated procedure of this kind for univariate and bivariate data is employed to reach this objective through combining the maximum entropy method with an appropriate optimization method. The only necessary characteristics of random variables are their continuousness and ability to be approximated as independent and identically distributed. In this work, we try to concisely present two numerical probabilistic algorithms and apply them to estimate the univariate and bivariate models of the available data. In the first case, a combination of the maximum entropy method, Newton's method, and the Bayesian maximum a posteriori approach leads to the estimation of the kinetic parameters with arterial input functions (AIFs) in cases without any measurement of the AIF. ‎The results shows that the AIF can reliably be determined from the data of dynamic contrast enhanced-magnetic resonance imaging (DCE-MRI) by maximum entropy method. Then, kinetic parameters can be obtained. By using the developed method, a good data fitting and thus a more accurate prediction of the kinetic parameters are achieved, which, in turn, leads to a more reliable application of DCE-MRI. ‎ In the bivariate case, we consider colocalization as a quantitative analysis in fluorescence microscopy imaging. The method proposed in this case is obtained by combining the Maximum Entropy Method (MEM) and a Gaussian Copula, which we call the Maximum Entropy Copula (MEC). This novel method is capable of measuring the spatial and nonlinear correlation of signals to obtain the colocalization of markers in fluorescence microscopy images. Based on the results, MEC is able to specify co- and anti-colocalization even in high-background situations.‎ ‎The main point here is that determining the joint distribution via its marginals is an important inverse problem which has one possible unique solution in case of choosing an proper copula according to Sklar's theorem. This developed combination of Gaussian copula and the univariate maximum entropy marginal distribution enables the determination of a unique bivariate distribution. Therefore, a colocalization parameter can be obtained via Kendall’s t, which is commonly employed in the copula literature. In general, the importance of applying these algorithms to biological data is attributed to the higher accuracy, faster computing rate, and lower cost of solutions in comparison to those of others. The extensive application and success of these algorithms in various contexts depend on their conceptual plainness and mathematical validity. ‎ Afterward, a probability density is estimated via enhancing trial cumulative distribution functions iteratively, in which more appropriate estimations are quantified using a scoring function that recognizes irregular fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian criterion. Uncertainty induced by statistical fluctuations in random samples is reflected by multiple estimates for the probability density. In addition, as a useful diagnostic for visualizing the quality of the estimated probability densities, scaled quantile residual plots are introduced. Kullback--Leibler divergence is an appropriate measure to indicate the convergence of estimations for the probability density function (PDF) to the actual PDF as sample. The findings indicate the general applicability of this method to high-yield statistical inference.Die Methode der maximalen Entropie ist ein wichtiger Bestandteil der statistischen Inferenz, die in immer stärkerem Maße für die Konstruktion von Modellen verwendet wird, die biologische Systeme, insbesondere komplexe Systeme, aus empirischen Datensätzen beschreiben und vorhersagen können. In diesen ertragreichen Anwendungen ist es von besonderem Interesse, exakte Verteilungsfunktionen mit minimaler Information über die Eigenschaften der Daten und ohne Ausnutzung menschlicher Subjektivität zu bestimmen. In dieser Arbeit wird durch eine Kombination der Maximum-Entropie-Methode mit geeigneten Optimierungsverfahren ein automatisiertes Verfahren verwendet, um dieses Ziel für univariate und bivariate Daten zu erreichen. Notwendige Eigenschaften von Zufallsvariablen sind lediglich ihre Stetigkeit und ihre Approximierbarkeit als unabhängige und identisch verteilte Variablen. In dieser Arbeit versuchen wir, zwei numerische probabilistische Algorithmen präzise zu präsentieren und sie zur Schätzung der univariaten und bivariaten Modelle der zur Verfügung stehenden Daten anzuwenden. Zunächst wird mit einer Kombination aus der Maximum-Entropie Methode, der Newton-Methode und dem Bayes'schen Maximum-A-Posteriori-Ansatz die Schätzung der kinetischen Parameter mit arteriellen Eingangsfunktionen (AIFs) in Fällen ohne Messung der AIF ermöglicht. Die Ergebnisse zeigen, dass die AIF aus den Daten der dynamischen kontrastverstärkten Magnetresonanztomographie (DCE-MRT) mit der Maximum-Entropie-Methode zuverlässig bestimmt werden kann. Anschließend können die kinetischen Parameter gewonnen werden. Durch die Anwendung der entwickelten Methode wird eine gute Datenanpassung und damit eine genauere Vorhersage der kinetischen Parameter erreicht, was wiederum zu einer zuverlässigeren Anwendung der DCE-MRT führt. Im bivariaten Fall betrachten wir die Kolokalisierung zur quantitativen Analyse in der Fluoreszenzmikroskopie-Bildgebung. Die in diesem Fall vorgeschlagene Methode ergibt sich aus der Kombination der Maximum-Entropie-Methode (MEM) und einer Gaußschen Copula, die wir Maximum-Entropie-Copula (MEC) nennen. Mit dieser neuartigen Methode kann die räumliche und nichtlineare Korrelation von Signalen gemessen werden, um die Kolokalisierung von Markern in Bildern der Fluoreszenzmikroskopie zu erhalten. Das Ergebnis zeigt, dass MEC in der Lage ist, die Ko- und Antikolokalisation auch in Situationen mit hohem Grundrauschen zu bestimmen. Der wesentliche Punkt hierbei ist, dass die Bestimmung der gemeinsamen Verteilung über ihre Marginale ein entscheidendes inverses Problem ist, das eine mögliche eindeutige Lösung im Falle der Wahl einer geeigneten Copula gemäß dem Satz von Sklar hat. Diese neu entwickelte Kombination aus Gaußscher Kopula und der univariaten Maximum Entropie Randverteilung ermöglicht die Bestimmung einer eindeutigen bivariaten Verteilung. Daher kann ein Kolokalisationsparameter über Kendall's t ermittelt werden, der üblicherweise in der Copula-Literatur verwendet wird. Die Bedeutung der Anwendung dieser Algorithmen auf biologische Daten lässt sich im Allgemeinen mit hoher Genauigkeit, schnellerer Rechengesch windigkeit und geringeren Kosten im Vergleich zu anderen Lösungen begründen. Die umfassende Anwendung und der Erfolg dieser Algorithmen in verschiedenen Kontexten hängen von ihrer konzeptionellen Eindeutigkeit und mathematischen Gültigkeit ab. Anschließend wird eine Wahrscheinlichkeitsdichte durch iterative Erweiterung von kumulativen Verteilungsfunktionen geschätzt, wobei die geeignetsten Schätzungen mit einer Scoring-Funktion quantifiziert werden, um unregelmäßige Schwankungen zu erkennen. Dieses Kriterium verhindert eine Unter- oder Überanpassung der Daten als Alternative zur Verwendung des Bayes-Kriteriums. Die durch statistische Schwankungen in Stichproben induzierte Unsicherheit wird durch mehrfache Schätzungen für die Wahrscheinlichkeitsdichte berücksichtigt. Zusätzlich werden als nützliche Diagnostik zur Visualisierung der Qualität der geschätzten Wahrscheinlichkeitsdichten skalierte Quantil-Residuen-Diagramme eingeführt. Die Kullback-Leibler-Divergenz ist ein geeignetes Maß, um die Konvergenz der Schätzungen für die Wahrscheinlichkeitsdichtefunktion (PDF) zu der tatsächlichen PDF als Stichprobe anzuzeigen. Die Ergebnisse zeigen die generelle Anwendbarkeit dieser Methode für statistische Inferenz mit hohem Ertrag.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated-in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching ("method of moments"), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

This paper aims to solve the arterial input function (AIF) determination in dynamic contrast-enhanced MRI (DCE-MRI), an important linear ill-posed inverse problem, using the maximum entropy technique (MET) and regularization functionals. In addition, estimating the pharmacokinetic parameters from a DCE-MR image investigations is an urgent need to obtain the precise information about the AIF-the concentration of the contrast agent on the left ventricular blood pool measured over time. For this reason, the main idea is to show how to find a unique solution of linear system of equations generally in the form of y = Ax + b, named an ill-conditioned linear system of equations after discretization of the integral equations, which appear in different tomographic image restoration and reconstruction issues. Here, a new algorithm is described to estimate an appropriate probability distribution function for AIF according to the MET and regularization functionals for the contrast agent concentration when applying Bayesian estimation approach to estimate two different pharmacokinetic parameters. Moreover, by using the proposed approach when analyzing simulated and real datasets of the breast tumors according to pharmacokinetic factors, it indicates that using Bayesian inference-that infer the uncertainties of the computed solutions, and specific knowledge of the noise and errors-combined with the regularization functional of the maximum entropy problem, improved the convergence behavior and led to more consistent morphological and functional statistics and results. Finally, in comparison to the proposed exponential distribution based on MET and Newton's method, or Weibull distribution via the MET and teaching-learning-based optimization (MET/TLBO) in the previous studies, the family of Gamma and Erlang distributions estimated by the new algorithm are more appropriate and robust AIFs

The study of hyoscyamine in oxidative stress of liver cells in male rat

Background and aims: Increased production of free radicals by endogenous systems and exogenous sources in cells leads to oxidative stress, which damages to the cells of various organs. Hyoscyamine is one of the important tropane alkaloid isolated from some Solanaceous species used to traditional medicine that they are used for their analgesic, anti-inflammatory, antipyretic, and anticonvulsant activities. The antioxidant and antiglycation properties of tropane alkaloids may represent a role in dealing with oxidative stress. The aim of this study was to investigate the antioxidant and antiglycation effects of hyoscyamine component on the liver cells in male rats. Methods: In this experimental- laboratory study, liver cells were isolated from male Sprague–Dawley rats. The cells cultured under standard conditions. Various concentrations of hyoscyamine (0-32 µM) were treated on rat liver cells. Then, the activity of glutathione peroxidase (GPX), superoxide dismutase (SOD) and catalase (CAT) as well as glyoxal and 2,2-diphenyl-1-picrylhydrazyl (DPPH) inhibition were measured by spectrophotometry. High-performance liquid chromatography (HPLC) was performed for measuring malondialdehyde (MDA) in liver cells. Results: CAT, SOD and GPX enzyme activities increased as the concentration of hyoscyamine increased. DPPH showed a strong inhibition on reactive oxygen species generation compared to control group. The amount of SOD, CAT and GPX enzyme activities in 8 micromolar concentration of hyoscyamine compared with the control group significantly increased as 10.33 and 8.6 and 6.3 units (P<0.05). Also, hyoscyamine (4µM) reduced the amount of MDA, glyoxylate and DPPH compared to the control group as 1.94, 2.26, and 2.33 times (P<0.05). Conclusion: Our findings indicated that hyoscyamine had considerable antioxidant and antiglycation activities on rat liver cells. This compound protects liver cells against the damaging effects of free radicals. The effects of this compound for the treatment of diseases associated with oxidative stress would be useful in the future

Valproic Acid Promotes Apoptosis and Cisplatin Sensitivity Through Downregulation of H19 Noncoding RNA in Ovarian A2780 Cells

Abstract Cisplatin resistance is one of the main limitations in the treatment of ovarian cancer, which is partly mediated by long noncoding RNAs (lncRNAs). H19 is a lncRNA involving in cisplatin resistance in cancers. Valproic acid (VPA) is a commonly used drug for clinical treatment of seizure disorders. In addition, this drug may display its effects through regulation of noncoding RNAs controlling gene expression. The aim of the present study was the investigation of VPA treatment effect on H19 expression in ovarian cancer cells and also the relation of the H19 levels with apoptosis and cisplatin resistance. Briefly, treatment with VPA not only led to significant increase in apoptosis rate, but also increased the cisplatin sensitivity of A2780/CP cells. We found that following VPA treatment, the expression of H19 and EZH2 decreased, but the expression of p21 and PTEN increased significantly. To investigate the involvement of H19 in VPA-induced apoptosis and cisplatin sensitivity, H19 was inhibited by a specific siRNA. Our results demonstrate that H19 knockdown by siRNA induced apoptosis and sensitized the A2780/CP cells to cisplatin-induced cytotoxicity. These data indicated that VPA negatively regulates the expression of H19 in ovarian cancer cells, which subsequently leads to apoptosis induction, cell proliferation inhibition, and overwhelming to cisplatin resistance. The implication of H19→EZH2→p21/PTEN pathway by VPA treatment suggests

Investigation of RFLP Haplotypes β-Globin Gene Cluster in Beta-Thalassemia Patients in Central Iran.

Introduction: Beta-thalassemia is one of the most prevalent inherited blood diseases among Iranians. The aim of this study was to elucidate the chromosomal background of beta-thalassemia mutations in Esfahan province, Iran. Materials and Methods: In this study, we investigated three frequent mutations (c.315+1G>A, c.93-21G>A and c.92+5G>C in β-globin gene, the frequency of RFLP haplotypes, and LD between markers at β-globin gene cluster) in 150 beta-thalassemia patients and 50 healthy individuals. The molecular and population genetic investigations were performed on RFLP markers HindIII in the c.315+1G>A of Gγ (HindIIIG) and Aγ (HindIIIA) genes, AvaII in the c.315+1G>A of β-globin gene and BamHI 3' to the β-globin gene. All statistical analyses were performed using Power Marker software and SISA server. Results: Fifty percent of beta-thalasemia patients were associated with these mutations. Haplotype I was the most prevalent haplotype among beta-thalassemia patients (39.33%) and normal individuals (46%). The commonest c.315+1G>A mutation in our population was tightly linked with haplotype III (43.75%) and haplotype I (31.25%). The second prevalent mutation, c.92+5G>C, was 90%, 6.66%, and 3.33% in linkage disequilibrium with haplotypes I, VII, and III, respectively. The c.93-21G>A mutation indicated a strong association with haplotype I (80%). Conclusion: Our study participants like beta-thalassemia patients from Kermanshah province was found to possess a similar haplotype background for common mutations. The emergence of most prevalent mutations on chromosomes with different haplotypes can be explained by gene conversion and recombination. High linkage of a mutation with specific haplotype is consistent with the hypothesis that chromosomes carrying beta-thalassemia mutations experienced positive selection pressure, probably because of the protection against malaria experienced by beta-thalassemia carriers. KEYWORDS: Beta-thalassemia; Haplotype; c.315+1G>A; c.92+5G>C; c.93-21G>

Effect of valproic acid on cisplatin-resistant ovarian cancer cell lines

Background and aims: Platinum resistance has been one of the most important problems in the management of ovarian cancer. The effects of various chemotherapeutic agents are limited in patients with platinum resistance. Therefore, developing new anticancer drugs that can improve the effect of currently used cytostatics is critical. The current study investigated the effects of valproic acid (VPA) alone and in combination with cisplatin on ovarian cancer cells. Methods: In this experimental study, the human ovarian cancer cell lines (A2780-S and A2780-CP) were grown in RPMI-1640 medium in appropriate culture conditions. The cells were treated with various concentrations of cisplatin (0.15-400 µg/mL) or VPA (10-2000 µg/mL) and were incubated for 24, 48, and 72 hours. Moreover, A2780 cells were co-treated with different concentrations of cisplatin and VPA for 48 hours. Afterward, cell viability was investigated using MTT assay. GraphPad Prism statistical software was used for the data analysis and ANOVA and Duncan’s test were conducted. Results: A dose- and time-dependent reduction was observed in cell viability following the treatment with cisplatin or VPA. Moreover, cotreatment of the A2780 cells with cisplatin and VPA resulted in a significantly greater inhibition of cell viability compared to the treatment with either agent alone. Conclusion: Overall, it can be argued that VPA does not only cause inhibition of proliferation and induction of apoptosis in ovarian cancer cells but also helps to enhance the antiproliferative effects of cisplatin and results in the increased susceptibility to cisplatin in resistant cells. VPA may therefore be used to treat cancer in the future. Keywords: Ovarian cancer, Cisplatin, Valproic acid, Platinum resistance, Antiproliferative effec

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated&mdash;in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (&ldquo;method of moments&rdquo;), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters

An investigation into geometric ratios of the sunken courtyards in traditional Iranian houses (a field study on Yazd and Kashan)

In Iranian architecture, the emphasis on the use of geometric ratios such as human scale and modularization, caused beauty and harmony. Unfortunately, in contemporary architecture, the use of these scales has been forgotten, and their presence has been diminished. Therefore, the main goal of the present study was to analyze and evaluate the geometry and proportions used in six remaining traditional Iranian sunken courtyards in Yazd and Kashan. For each house, the length, width, height and the ratio between these dimensions were measured for the sunken courtyard, courtyard and earth of the case studies. Then, to find out which kind of proportions were used in these sunken courtyards, we proposed some statistical tests to compare our measurements with the traditional proportions used. In the end, the results showed that the proportions used in the design of the sunken courtyard, courtyard, and earth of the case studies are related and the traditional Iranian sunken courtyards have been designed mostly based on the use of Gereh (a unit of measurement), which was the most appropriate and most widely used scale in housing architecture.&nbsp