Search results for: Inverse Kinematics

Authors: Saeideh Soltanmohammadlou, Pilar M Guerrieri, Amir Kianfar, Sara Sadeghian, Yasaman Nafezi, Emily Irvin

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Architecture is rooted in the experiences of the residents in a place. Its foundations are based on needs and circumstances of each territory in terms of climate, available materials, economics and governmental policies, and cultural ideals and ideas of the people that live there. The architectural history of Iran echoes these architectural origins and has revealed certain trends reflecting this territory and culture. However, in recent years, new architectural patterns are developing that diverge from what has previously been considered classic forms of Iranian architecture. This article investigates architectural elements that make up the architecture created by religious minorities after the Safavid dynasty (one of the most significant ruling dynasties of Iran (from 1501 to 1736) in Iranian cities: Isfahan, Tabriz, Kerman, and Uremia. Similarities and differences are revealed between the architecture that composes neighborhoods of religious minorities in Iran and common national architectural trends in each era after this dynasty. This dynasty is specific as a point of reference in this article because Islam was identified as the state religion of Iran during this era. This decision changed the course of architecture in the country to incorporate religious motifs and meanings. The study associated with this article was conducted as a survey that sought to find links between architecture of religious minorities with Iranian national architecture. Interestingly, a merging of architectural forms and trends occur as immigrants interact with Iranian Islamic meanings. These observations are significant within the context of modern architecture around the world and within Western discourse because what are considered religious minorities in Iran are the dominant religions in Western nations. This makes Iran’s architecture particularly unique as it creates a kind of inverse relationship, than that of Western nations, to the ways in which religion influences architectural history.

Keywords: Architecture, ethnic architecture, national architecture, religion architecture.

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Authors: Mutuku Muvengei, John Kihiu

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This paper focuses on the development of bond graph dynamic model of the mechanical dynamics of an excavating mechanism previously designed to be used with small tractors, which are fabricated in the Engineering Workshops of Jomo Kenyatta University of Agriculture and Technology. To develop a mechanical dynamics model of the manipulator, forward recursive equations similar to those applied in iterative Newton-Euler method were used to obtain kinematic relationships between the time rates of joint variables and the generalized cartesian velocities for the centroids of the links. Representing the obtained kinematic relationships in bondgraphic form, while considering the link weights and momenta as the elements led to a detailed bond graph model of the manipulator. The bond graph method was found to reduce significantly the number of recursive computations performed on a 3 DOF manipulator for a mechanical dynamic model to result, hence indicating that bond graph method is more computationally efficient than the Newton-Euler method in developing dynamic models of 3 DOF planar manipulators. The model was verified by comparing the joint torque expressions of a two link planar manipulator to those obtained using Newton- Euler and Lagrangian methods as analyzed in robotic textbooks. The expressions were found to agree indicating that the model captures the aspects of rigid body dynamics of the manipulator. Based on the model developed, actuator sizing and valve sizing methodologies were developed and used to obtain the optimal sizes of the pistons and spool valve ports respectively. It was found that using the pump with the sized flow rate capacity, the engine of the tractor is able to power the excavating mechanism in digging a sandy-loom soil.

Keywords: Actuators, bond graphs, inverse dynamics, recursive equations, quintic polynomial trajectory.

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Authors: Ye. B. Utepov, A. S. Tulebekova, A. B. Kazkeyev

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Maturity sensors are used to determine concrete strength by the non-destructive method. The method of placement of the maturity sensors determines their number required for a certain frame of a monolithic building. This paper proposes a cheap prototype of an embedded wireless sensor for monitoring concrete structures, as well as an alternative strategy for placing sensors based on the transitional boundaries of the temperature distribution of concrete curing, which were determined by building a heat map of the temperature distribution, where unknown values are calculated by the method of inverse distance weighing. The developed prototype can simultaneously measure temperature and relative humidity over a smartphone-controlled time interval. It implements a maturity method to assess the in-situ strength of concrete, which is considered an alternative to the traditional shock impulse and compression testing method used in Kazakhstan. The prototype was tested in laboratory and field conditions. The tests were aimed at studying the effect of internal and external temperature and relative humidity on concrete's strength gain. Based on an experimentally poured concrete slab with randomly integrated maturity sensors, it the transition boundaries form elliptical forms were determined. Temperature distribution over the largest diameter of the ellipses was plotted, resulting in correct and inverted parabolas. As a result, the distance between the closest opposite crossing points of the parabolas is accepted as the maximum permissible step for setting the maturity sensors. The proposed placement strategy can be applied to sensors that measure various continuous phenomena such as relative humidity. Prototype testing has also revealed Bluetooth inconvenience due to weak signal and inability to access multiple prototypes simultaneously. For this reason, further prototype upgrades are planned in the future work.

Keywords: Heat map, placement strategy, temperature and relative humidity, wireless embedded sensor.

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Authors: Audrey Heffron, Casserleigh, Jarrett Broder, Brad Skillman

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Traditionally, terror groups have been formed by ideologically aligned actors who perceive a lack of options for achieving political or social change. However, terrorist attacks have been increasingly carried out by small groups of actors or lone individuals who may be only ideologically affiliated with larger, formal terrorist organizations. The formation of these groups represents the inverse of traditional organizational growth, whereby structural de-evolution within issue-based organizations leads to the formation of small, independent terror cells. Ideological franchising – the bypassing of formal affiliation to the “parent" organization – represents the de-evolution of traditional concepts of organizational structure in favor of an organic, independent, and focused unit. Traditional definitions of dark networks that are issue-based include focus on an identified goal, commitment to achieving this goal through unrestrained actions, and selection of symbolic targets. The next step in the de-evolution of small dark networks is the miniorganization, consisting of only a handful of actors working toward a common, violent goal. Information-sharing through social media platforms, coupled with civil liberties of democratic nations, provide the communication systems, access to information, and freedom of movement necessary for small dark networks to flourish without the aid of a parent organization. As attacks such as the 7/7 bombings demonstrate the effectiveness of small dark networks, terrorist actors will feel increasingly comfortable aligning with an ideology only, without formally organizing. The natural result of this de-evolving organization is the single actor event, where an individual seems to subscribe to a larger organization-s violent ideology with little or no formal ties.

Keywords: Organizational de-evolution, single actor, small group, terrorism.

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Authors: Atefeh Bagherianziarat, Dana Hamplova

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The inverse social gradient in life satisfaction (LS) is a well-established research finding. Although objective aspects of inequality or individuals’ socioeconomic status are among the approved predictors of life satisfaction; however, less is known about the effect of subjective inequality and the interplay of these two aspects of inequality on life satisfaction. It is suggested that individuals’ perception of their socioeconomic status in society can moderate the link between their absolute socioeconomic status and life satisfaction. Nevertheless, this moderating link has not been affirmed to work likewise in societies with different welfare regimes associating with different levels of social inequality. In this study, we compared the moderative influence of subjective inequality on the link between objective inequality and LS. In particular, we focus on differences across welfare state regimes based on Esping-Andersen's theory. Also, we explored the moderative role of believing in the value of equality on the link between objective and subjective inequality on LS, in the given societies. Since our studied variables were measured at both individual and country levels, we applied a multilevel analysis to the European Social Survey data (round 9). The results showed that people in different regimes reported statistically meaningful different levels of LS that is explained to different extends by their household income and their perception of their income inequality. The findings of the study supported the previous findings of the moderator influence of perceived inequality on the link between objective inequality and LS. However, this link is different in various welfare state regimes. The results of the multilevel modeling showed that country-level subjective equality is a positive predictor for individuals’ LS, while the Gini coefficient that was considered as the indicator of absolute inequality has a smaller effect on LS. Also, country-level subjective equality moderates the confirmed link between individuals’ income and their LS. It can be concluded that both individual and country-level subjective inequality slightly moderate the effect of individuals’ income on their LS.

Keywords: individual values, life satisfaction, multi-level analysis, objective inequality, subjective inequality, welfare regimes status

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Authors: Emre Kara, Ahmet F. Geylan, Kadir Koç, Şura Karakuzu, Metehan Demir, Halil Aykul

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The structures obtained with the use of sandwich technologies combine low weight with high energy absorbing capacity and load carrying capacity. Hence, there is a growing and markedly interest in the use of sandwiches with aluminum foam core because of very good properties such as flexural rigidity and energy absorption capability. In the current investigation, the static threepoint bending tests were carried out on the sandwiches with aluminum foam core and glass fiber reinforced polymer (GFRP) skins at different values of support span distances aiming the analyses of their flexural performance. The influence of the core thickness and the GFRP skin type was reported in terms of peak load and energy absorption capacity. For this purpose, the skins with two different types of fabrics which have same thickness value and the aluminum foam core with two different thicknesses were bonded with a commercial polyurethane based flexible adhesive in order to combine the composite sandwich panels. The main results of the bending tests are: force-displacement curves, peak force values, absorbed energy, collapse mechanisms and the effect of the support span length and core thickness. The results of the experimental study showed that the sandwich with the skins made of S-Glass Woven fabrics and with the thicker foam core presented higher mechanical values such as load carrying and energy absorption capacities. The increment of the support span distance generated the decrease of the mechanical values for each type of panels, as expected, because of the inverse proportion between the force and span length. The most common failure types of the sandwiches are debonding of the lower skin and the core shear. The obtained results have particular importance for applications that require lightweight structures with a high capacity of energy dissipation, such as the transport industry (automotive, aerospace, shipbuilding and marine industry), where the problems of collision and crash have increased in the last years.

Keywords: Aluminum foam, Composite panel, Flexure, Transport application.

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Authors: Mustafa M. Donma, Orkide Donma

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Zinc (Zn) is a vital element required for growth and development particularly in children. It exhibits some protective effects against cardiovascular diseases (CVDs). Zn may be a potential biomarker of cardiovascular health. High sensitive cardiac troponin T (hs-cTnT) and cardiac myosin binding protein C (cMyBP-C) are new generation markers used for prediagnosis, diagnosis and prognosis of CVDs. The aim of this study is to determine Zn as well as new generation cardiac markers’ profiles in children with normal body mass index (N-BMI), obese (OB), morbid obese (MO) children and children with metabolic syndrome (MetS) findings. The association among them will also be investigated. Four study groups were constituted. The study protocol was approved by the institutional Ethics Committee of Tekirdag Namik Kemal University. Parents of the participants filled informed consent forms to participate in the study. Group 1 is composed of 44 children with N-BMI. Group 2 and Group 3 comprised 43 OB and 45 MO children, respectively. 45 MO children with MetS findings were included in Group 4. World Health Organization age- and sex-adjusted BMI percentile tables were used to constitute groups. These values were 15-85, 95-99 and above 99 for N-BMI, OB and MO, respectively. Criteria for MetS findings were determined. Routine biochemical analyses including Zn were performed. hs-cTnT and cMyBP-C concentrations were measured by enzyme-linked immunosorbent assay. Data were analyzed by using SPSS software. p < 0.05 was accepted as significant. Four groups were matched for age and gender. Decreased Zn concentrations were measured in Groups 2, 3 and 4 compared to Group 1. Groups did not differ from one another in terms of hs-cTnT. There were statistically significant differences between cMyBP-C levels of MetS group and N-BMI as well as OB groups. There was an increasing trend going from N-BMI group to MetS group. There were statistically significant negative correlations between Zn and hs-cTnT as well as cMyBP-C concentrations in MetS group. In conclusion, inverse correlations detected between Zn and new generation cardiac markers (hs-TnT and cMyBP-C) have pointed out that decreased levels of Zn accompany increased levels of hs-cTnT as well as cMyBP-C in children with MetS. This finding emphasizes that both Zn and these new generation cardiac markers may be evaluated as biomarkers of cardiovascular health during severe childhood obesity precipitated with MetS findings and also suggested as the messengers of the future risk in the adulthood periods of children with MetS.

Keywords: Cardiac myosin binding protein-C, cardiovascular diseases, children, high sensitive cardiac troponin T, obesity.

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: Optimal control, ensemble Kalman Filter, topography reconstruction, data assimilation, shallow water equations.

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Authors: Bimali Sanjeevani Weerakoon, Toshiaki Osuga, Takehisa Konishi

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Magnetic Resonance Imaging Contrast Agents (MRI-CM) are significant in the clinical and biological imaging as they have the ability to alter the normal tissue contrast, thereby affecting the signal intensity to enhance the visibility and detectability of images. Superparamagnetic Iron Oxide (SPIO) nanoparticles, coated with dextran or carboxydextran are currently available for clinical MR imaging of the liver. Most SPIO contrast agents are T2 shortening agents and Resovist (Ferucarbotran) is one of a clinically tested, organ-specific, SPIO agent which has a low molecular carboxydextran coating. The enhancement effect of Resovist depends on its relaxivity which in turn depends on factors like magnetic field strength, concentrations, nanoparticle properties, pH and temperature. Therefore, this study was conducted to investigate the impact of field strength and different contrast concentrations on enhancement effects of Resovist. The study explored the MRI signal intensity of Resovist in the physiological range of plasma from T2-weighted spin echo sequence at three magnetic field strengths: 0.47 T (r1=15, r2=101), 1.5 T (r1=7.4, r2=95), and 3 T (r1=3.3, r2=160) and the range of contrast concentrations by a mathematical simulation. Relaxivities of r1 and r2 (L mmol-1 Sec-1) were obtained from a previous study and the selected concentrations were 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 2.0, and 3.0 mmol/L. T2-weighted images were simulated using TR/TE ratio as 2000 ms /100 ms. According to the reference literature, with increasing magnetic field strengths, the r1 relaxivity tends to decrease while the r2 did not show any systematic relationship with the selected field strengths. In parallel, this study results revealed that the signal intensity of Resovist at lower concentrations tends to increase than the higher concentrations. The highest reported signal intensity was observed in the low field strength of 0.47 T. The maximum signal intensities for 0.47 T, 1.5 T and 3 T were found at the concentration levels of 0.05, 0.06 and 0.05 mmol/L, respectively. Furthermore, it was revealed that, the concentrations higher than the above, the signal intensity was decreased exponentially. An inverse relationship can be found between the field strength and T2 relaxation time, whereas, the field strength was increased, T2 relaxation time was decreased accordingly. However, resulted T2 relaxation time was not significantly different between 0.47 T and 1.5 T in this study. Moreover, a linear correlation of transverse relaxation rates (1/T2, s–1) with the concentrations of Resovist can be observed. According to these results, it can conclude that the concentration of SPIO nanoparticle contrast agents and the field strengths of MRI are two important parameters which can affect the signal intensity of T2-weighted SE sequence. Therefore, when MR imaging those two parameters should be considered prudently.

Keywords: Concentration, Resovist, Field strength, Relaxivity, Signal intensity.

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Authors: A. J. Al-Graitti, G. A. Khalid, P. Berthelson, A. Mason-Jones, R. Prabhu, M. D. Jones

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Motor vehicle related pedestrian road traffic collisions are a major road safety challenge, since they are a leading cause of death and serious injury worldwide, contributing to a third of the global disease burden. The auto rickshaw, which is a common form of urban transport in many developing countries, plays a major transport role, both as a vehicle for hire and for private use. The most common auto rickshaws are quite unlike ‘typical’ four-wheel motor vehicle, being typically characterised by three wheels, a non-tilting sheet-metal body or open frame construction, a canvas roof and side curtains, a small drivers’ cabin, handlebar controls and a passenger space at the rear. Given the propensity, in developing countries, for auto rickshaws to be used in mixed cityscapes, where pedestrians and vehicles share the roadway, the potential for auto rickshaw impacts with pedestrians is relatively high. Whilst auto rickshaws are used in some Western countries, their limited number and spatial separation from pedestrian walkways, as a result of city planning, has not resulted in significant accident statistics. Thus, auto rickshaws have not been subject to the vehicle impact related pedestrian crash kinematic analyses and/or injury mechanics assessment, typically associated with motor vehicle development in Western Europe, North America and Japan. This study presents a parametric analysis of auto rickshaw related pedestrian impacts by computational simulation, using a Finite Element model of an auto rickshaw and an LS-DYNA 50^th percentile male Hybrid III Anthropometric Test Device (dummy). Parametric variables include auto rickshaw impact velocity, auto rickshaw impact region (front, centre or offset) and relative pedestrian impact position (front, side and rear). The output data of each impact simulation was correlated against reported injury metrics, Head Injury Criterion (front, side and rear), Neck injury Criterion (front, side and rear), Abbreviated Injury Scale and reported risk level and adds greater understanding to the issue of auto rickshaw related pedestrian injury risk. The parametric analyses suggest that pedestrians are subject to a relatively high risk of injury during impacts with an auto rickshaw at velocities of 20 km/h or greater, which during some of the impact simulations may even risk fatalities. The present study provides valuable evidence for informing a series of recommendations and guidelines for making the auto rickshaw safer during collisions with pedestrians. Whilst it is acknowledged that the present research findings are based in the field of safety engineering and may over represent injury risk, compared to “Real World” accidents, many of the simulated interactions produced injury response values significantly greater than current threshold curves and thus, justify their inclusion in the study. To reduce the injury risk level and increase the safety of the auto rickshaw, there should be a reduction in the velocity of the auto rickshaw and, or, consideration of engineering solutions, such as retro fitting injury mitigation technologies to those auto rickshaw contact regions which are the subject of the greatest risk of producing pedestrian injury.

Keywords: Auto Rickshaw, finite element analysis, injury risk level, LS-DYNA, pedestrian impact.

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Authors: Mahmoud M. S. Albattah

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In this paper, to optimize the “Characteristic Straight Line Method" which is used in the soil displacement analysis, a “best estimate" of the geodetic leveling observations has been achieved by taking in account the concept of 'Height systems'. This concept has been discussed in detail and consequently the concept of “height". In landslides dynamic analysis, the soil is considered as a mosaic of rigid blocks. The soil displacement has been monitored and analyzed by using the “Characteristic Straight Line Method". Its characteristic components have been defined constructed from a “best estimate" of the topometric observations. In the measurement of elevation differences, we have used the most modern leveling equipment available. Observational procedures have also been designed to provide the most effective method to acquire data. In addition systematic errors which cannot be sufficiently controlled by instrumentation or observational techniques are minimized by applying appropriate corrections to the observed data: the level collimation correction minimizes the error caused by nonhorizontality of the leveling instrument's line of sight for unequal sight lengths, the refraction correction is modeled to minimize the refraction error caused by temperature (density) variation of air strata, the rod temperature correction accounts for variation in the length of the leveling rod' s Invar/LO-VAR® strip which results from temperature changes, the rod scale correction ensures a uniform scale which conforms to the international length standard and the introduction of the concept of the 'Height systems' where all types of height (orthometric, dynamic, normal, gravity correction, and equipotential surface) have been investigated. The “Characteristic Straight Line Method" is slightly more convenient than the “Characteristic Circle Method". It permits to evaluate a displacement of very small magnitude even when the displacement is of an infinitesimal quantity. The inclination of the landslide is given by the inverse of the distance reference point O to the “Characteristic Straight Line". Its direction is given by the bearing of the normal directed from point O to the Characteristic Straight Line (Fig..6). A “best estimate" of the topometric observations was used to measure the elevation of points carefully selected, before and after the deformation. Gross errors have been eliminated by statistical analyses and by comparing the heights within local neighborhoods. The results of a test using an area where very interesting land surface deformation occurs are reported. Monitoring with different options and qualitative comparison of results based on a sufficient number of check points are presented.

Keywords: Characteristic straight line method, dynamic height, landslides, orthometric height, systematic errors.

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Authors: Mustafa M. Donma, Orkide Donma

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Vitamin deficiencies are common in obese individuals. Particularly, the status of vitamin B12 and its association with vitamin B9 (folate) and vitamin D is under investigation in recent time. Vitamin B12 is closely related to many vital processes in the body. In clinical studies, its involvement in fat metabolism draws attention from the obesity point of view. Obesity, in its advanced stages and in combination with metabolic syndrome (MetS) findings, may be a life-threatening health problem. Pediatric obesity is particularly important, because it may be a predictor of the severe chronic diseases during adulthood period of the child. Due to its role in fat metabolism, vitamin B12 deficiency may disrupt metabolic pathways of the lipid and energy metabolisms in the body. The association of low B12 levels with obesity degree may be an interesting topic to be investigated. Obesity indices may be helpful at this point. Weight- and fat-based indices are available. Of them, body mass index (BMI) is in the first group. Fat mass index (FMI), fat-free mass index (FFMI) and diagnostic obesity notation model assessment-II (D2I) index lie in the latter group. The aim of this study is to clarify possible associations between vitamin B12 status and obesity indices in pediatric population. The study comprises a total of 122 children. 32 children were included in the normal-body mass index (N-BMI) group. 46 and 44 children constitute groups with morbid obese children without MetS and with MetS, respectively. Informed consent forms and the approval of the institutional ethics committee were obtained. Tables prepared for obesity classification by World Health Organization were used. MetS criteria were defined. Anthropometric and blood pressure measurements were taken. BMI, FMI, FFMI, D2I were calculated. Routine laboratory tests were performed. Vitamin B9, B12, D concentrations were determined. Statistical evaluation of the study data was performed. Vitamin B9 and vitamin D levels were reduced in MetS group compared to children with N-BMI (p > 0.05). Significantly lower values were observed in vitamin B12 concentrations of MetS group (p < 0.01). Upon evaluation of blood pressure as well as triglyceride levels, there exist significant increases in morbid obese children. Significantly decreased concentrations of high-density lipoprotein cholesterol were observed. All of the obesity indices and insulin resistance index exhibit increasing tendency with the severity of obesity. Inverse correlations were calculated between vitamin D and insulin resistance index as well as vitamin B12 and D2I in morbid obese groups. In conclusion, a fat-based index, D2I, was the most prominent body index, which shows strong correlation with vitamin B12 concentrations in the late stage of obesity in children. A negative correlation between these two parameters was a confirmative finding related to the association between vitamin B12 and obesity degree. 

Keywords: Body mass index, children, D2I index, fat mass index, obesity.

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Authors: Mustafa M. Donma, Orkide Donma

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Metabolisms of macrominerals, those of calcium, phosphorus and magnesium, are closely associated with the metabolism of vitamin D. Particularly magnesium, the second most abundant intracellular cation, is related to biochemical and metabolic processes in the body, such as those of carbohydrates, proteins and lipids. The status of each mineral was investigated in obesity to some extent. Their products and ratios may possibly give much more detailed information about the matter. The aim of this study is to investigate possible relations between each macromineral and some obesity-related parameters. This study was performed on 235 children, whose ages were between 06-18 years. Aside from anthropometric measurements, hematological analyses were performed. TANITA body composition monitor using bioelectrical impedance analysis technology was used to establish some obesity-related parameters including basal metabolic rate (BMR), total fat, mineral and muscle masses. World Health Organization body mass index (BMI) percentiles for age and sex were used to constitute the groups. The values above 99^th percentile were defined as morbid obesity. Those between 95^th and 99^th percentiles were included into the obese group. The overweight group comprised of children whose percentiles were between 95 and 85. Children between the 85^th and 15^th percentiles were defined as normal. Metabolic syndrome (MetS) components (waist circumference, fasting blood glucose, triacylglycerol, high density lipoprotein cholesterol, systolic pressure, diastolic pressure) were determined. High performance liquid chromatography was used to determine Vitamin D status by measuring 25-hydroxy cholecalciferol (25-hydroxy vitamin D₃, 25(OH)D). Vitamin D values above 30.0 ng/ml were accepted as sufficient. SPSS statistical package program was used for the evaluation of data. The statistical significance degree was accepted as p < 0.05. The important points were the correlations found between vitamin D and magnesium as well as phosphorus (p < 0.05) that existed in the group with normal BMI values. These correlations were lost in the other groups. The ratio of phosphorus to magnesium was even much more highly correlated with vitamin D (p < 0.001). The negative correlation between magnesium and total fat mass (p < 0.01) was confined to the MetS group showing the inverse relationship between magnesium levels and obesity degree. In this group, calcium*magnesium product exhibited the highest correlation with total fat mass (p < 0.001) among all groups. Only in the MetS group was a negative correlation found between BMR and calcium*magnesium product (p < 0.05). In conclusion, magnesium is located at the center of attraction concerning its relationships with vitamin D, fat mass and MetS. The ratios and products derived from macrominerals including magnesium have pointed out stronger associations other than each element alone. Final considerations have shown that unique correlations of magnesium as well as calcium*magnesium product with total fat mass have drawn attention particularly in the MetS group, possibly due to the derangements in some basic elements of carbohydrate as well as lipid metabolism.

Keywords: Macrominerals, metabolic syndrome, pediatric obesity, vitamin D.

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