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.

Doctor of Philosophy

dissertationExpanded Polystyrene (EPS) geofoam has become a preferred material in various construction applications due to its light weight. Application of EPS accelerates the projects particularly on soft soils. The focus of this research is on the application of the EPS in embankments and its behavior mainly under harmonic vibration. The goal of this study was to investigate dynamic characteristics of freestanding vertical EPS geofoam embankment and address potential seismic issues that result from the distinguished dynamic behavior of such systems due to the layered and discrete block structure. A series of experimental studies on EPS 19 and a commercially available adhesive was conducted. Two-dimensional numerical analyses were performed to replicate the response of EPS geofoam embankment to horizontal and vertical harmonic motions. The results of the analyses have shown that for some acceleration amplitude levels interlayer sliding is expected to occur in EPS geofoam embankments almost immediately after the start of the base excitation; however, as a highly efficient energy dissipation mechanism sliding ceases rapidly. Shear keys and adhesive may be used to prevent interlayer sliding if they cover the proper extent of area of the embankment. EPS blocks placed in the corners of the embankment and at the edges of the segment prohibited from sliding may experience high stress concentrations. The embankment may show horizontal sway and rocking once sliding is prevented

Entinociceptive effects of Euphorbia helioscopia extract on Balb/c mice

Background and aims: Euphorbia helioscopia has multiple pharmacological activities, such as antibacterial, antiviral, antifungal,anticancer and/or antitumor, allelopathic, anti-allergic and anti-asthmatic, antioxidant, antinociceptive effect. The aim of the study was to evaluate the antinociceptive activities of Euphorbia helioscopia extract in Balb/c mice, as well as the total flavonoids, phenolic contents, and antioxidant activities of the extract. Methods: In this study, 90 Balb/c mice were randomly designated into 9 groups. Group 1 received normal saline, groups 2 to 7 received different doses of the E. helioscopia hydroethanolic extract (i.e., 0.05, 0.1, 0.2, 0.4, 2, & 8 mg/kg, i.p.).In addition, groups 8 and 9 received naloxone (1 mg/kg) and extract (8 mg/kg) plus naloxone (1 mg/kg), respectively (Naloxone was injected 15 minutes after extract administration). Then, pain response was evaluated for 30 minutes after the injection of 20 µL formalin (1.5%) in the plantar surface of the mice foot. Further, the beta-carotene-linoleate method was used for measuring antioxidant capacity. Finally, total phenolic and flavonoid content were measured based on Folin-Ciocalteu colorimetric and aluminum chloride colorimetric methods, respectively. Results: Total phenol and flavonoid content were 49.43 ± 1.8 mg GAE/g dried extract and 30.19 ± 1.96 mg rutin/g dried extract, respectively. Our results showed that during the first 5 minutes (the acute pain step), a significant difference (P<0.05) was observed between the control group and the group which received the E. helioscopia hydroethanolic extract (8 mg/kg). In the next 25 minutes (the chronic pain step), a significant difference (P<0.05) was found between the control group and the group which received 0.1 and 8 mg/kg doses of the extract. Based on the results, naloxone was unable to reverse the antinociceptive effects of the extract and the maximum antioxidant activity of the extract was 1.641 mg/g of rutin equivalent. Conclusion: In general, this study supports the use of the E. helioscopia extract in folk medicine as the analgesic agent and calls for further investigations regarding elucidating its mechanism of action. Eventually, our findings revealed that the extract of E. helioscopia possessed either antinociceptive or anti-oxidative activities. Keywords: Euphorbia helioscopia, Pain, Mice, Formalin test, Antioxidant activit

The effect of 8-week resistance training on IRS-1 gene expression in gastrocnemius muscle and glycemic profile in diabetes rats

Background: The insulin receptor substrate-1 (IRS-1) has an important role in insulin signaling pathways in the target tissue of obese or insulin-resistant individuals. This study aimed to assess the effect of resistance training on fasting glucose, insulin resistance, and IRS-1 gene expression in gastrocnemius muscle in male Wister rats with type 2 diabetes (T2D). Materials and Methods: For this purpose, T2D induced by high- fat diet (8 weeks) and STZ in fourteen male Wistar rats (220 ± 10 g) and then assigned into exercise (resistance training, 8 weeks, 5 days/weekly, n = 7) and control (no-training, n = 7) by randomly. Fasting blood samples were obtained for measuring glucose, insulin, and calculating insulin resistance (HOMA-IR).&nbsp; Also, the IRS-1 gene expression in gastrocnemius muscle was measured 48 hours after the last training session of both cases and controls. Results: Compared to control, IRS-1 gene expression in gastrocnemius muscle increased significantly by resistance training in exercise groups (p = 0.001). Fasting glucose (p &lt; 0.001) and insulin resistance (p = 0.007) were reduced in the exercise rats compared to the control group. Conclusion: Based on the results, improved fasting glucose and insulin function after resistance training in T2D diabetes could be attributed to enhancing IRS-1 expression in gastrocnemius muscle by training