Simplified Resting Metabolic Rate—Predicting Formulas for Normal‐Sized and Obese Individuals

Objective: Resting metabolic rate (RMR) is known to be proportional to body weight and to follow allometric scaling principles. We hypothesized that RMR can be predicted from an allometric formula with weight alone as an independent variable. Research Methods and Procedures: An allometric, power‐law scaling model was fit to RMR measurements obtained from a cohort of patients being treated for weight loss. This, as well as many of the commonly used RMR‐predicting formulas, was tested for RMR prediction ability against a large publicly available RMR database. Bland‐Altman analysis was used to determine the efficacy of the various RMR‐predicting formulas in obese and non‐obese subjects. Results: Power law modeling of the RMR—body weight relationship yielded the following RMR‐predicting equations: RMR_Women = 248 × Weight^0.4356 ? (5.09 × Age) and RMR_Men = 293 × Weight^0.4330 ? (5.92 × Age). Partial correlation analysis revealed that age significantly contributed to RMR variance and was necessary to include in RMR prediction formulas. The James, allometric, and Harris‐Benedict formulas all yielded reasonable RMR predictions for normal sized and obese subjects. Discussion: A simple power formula relating RMR to body weight can be a reasonable RMR estimator for normal‐sized and obese individuals but still requires an age term and separate formulas for men and women for the best possible RMR estimates. The apparent performance of RMR‐predicting formulas is highly dependent on the methodology employed to compare the various formulas.     

Quick Construction of Femoral Model Using Surface Feature Parameterization

To facilitate the modifying of femoral surface model, by dividing the femoral mesh into surface feature units bearing medical significance based on surface feature technology, a new approach of constructing femoral models using surface feature technology is proposed. Firstly, considering of femoral anatomy, the femoral triangle mesh model generated from the averaged point-clouds is divided into several specific regions, which are called feature regions; Secondly, feature parameters are defined and the constraints among them are set up, and feature surfaces are created by skinning the contours; Finally, the adjacent feature surfaces are connected by transition surfaces, and the parametric CAD surface model of femur is constructed. Experimental results show that, with the proposed method, the surface feature model can be intuitively constructed and edited with high-level parameters. Therefore, the proposed method provides a basic tool for the design of implants and the digital restoration of incomplete femurs.     

Towards Semantically Sensitive Text Clustering: A Feature Space Modeling Technology Based on Dimension Extension

The objective of text clustering is to divide document collections into clusters based on the similarity between documents. In this paper, an extension-based feature modeling approach towards semantically sensitive text clustering is proposed along with the corresponding feature space construction and similarity computation method. By combining the similarity in traditional feature space and that in extension space, the adverse effects of the complexity and diversity of natural language can be addressed and clustering semantic sensitivity can be improved correspondingly. The generated clusters can be organized using different granularities. The experimental evaluations on well-known clustering algorithms and datasets have verified the effectiveness of our approach.     

Accuracy of predicted resting metabolic rate and relationship between resting metabolic rate and cardiorespiratory fitness in obese men

[Purpose]

The purpose of this study is to examine that not only the relationship of the resting metabolic rate (RMR) and cardiorespiratory fitness(VO2peak), but also the comparison between measured and predicted results of RMR in obese men.

[Methods]

60 obese men (body fat>32%) were recruited for this study. They did not participate in regular exercising programs at least 6 months. The RMR was measured with indirect calorimetry and predicted RMR using Herris-Benedicte equation. The cardiorespiratory fitness was determined by directly measuring the oxygen consumption (VO2peak) during the exercise on the treadmill.

[Results]

The significance for the difference between the measured results and predicted result of RMR were tested by paired t-test. Correlation of measured date was obtained by Pearson correlation coefficient. The value of predicted RMR and measured RMR were significantly different in these obese subjects. (p < 0.001). The difference between RMR cardiorespiratory fitness and cardiorespiratory fitness showed significant correlation (r=0.67, p < 0.05).

[Conclusion]

The current formulas of predicted RMR have limited the evaluation of measured RMR for Korean obese men. Therefore, this study suggests that new formula should be designed for Korean in order to obtain more accurate results in obese.     

A novel cost function to estimate parameters of oscillatory biochemical systems

Oscillatory pathways are among the most important classes of biochemical systems with examples ranging from circadian rhythms and cell cycle maintenance. Mathematical modeling of these highly interconnected biochemical networks is needed to meet numerous objectives such as investigating, predicting and controlling the dynamics of these systems. Identifying the kinetic rate parameters is essential for fully modeling these and other biological processes. These kinetic parameters, however, are not usually available from measurements and most of them have to be estimated by parameter fitting techniques. One of the issues with estimating kinetic parameters in oscillatory systems is the irregularities in the least square (LS) cost function surface used to estimate these parameters, which is caused by the periodicity of the measurements. These irregularities result in numerous local minima, which limit the performance of even some of the most robust global optimization algorithms. We proposed a parameter estimation framework to address these issues that integrates temporal information with periodic information embedded in the measurements used to estimate these parameters. This periodic information is used to build a proposed cost function with better surface properties leading to fewer local minima and better performance of global optimization algorithms. We verified for three oscillatory biochemical systems that our proposed cost function results in an increased ability to estimate accurate kinetic parameters as compared to the traditional LS cost function. We combine this cost function with an improved noise removal approach that leverages periodic characteristics embedded in the measurements to effectively reduce noise. The results provide strong evidence on the efficacy of this noise removal approach over the previous commonly used wavelet hard-thresholding noise removal methods. This proposed optimization framework results in more accurate kinetic parameters that will eventually lead to biochemical models that are more precise, predictable, and controllable.     

Relationships between bone growth rate, body mass and resting metabolic rate in growing amniotes: a phylogenetic approach

We explored the factors that explain the variation in resting metabolic rates (RMR) in growing amniotes by using the phylogenetic comparative method. For this, we measured raw RMR (mL O₂ h⁻¹), body mass, body mass growth rate, and periosteal bone growth rate in a sample of 44 growing individuals belonging to 13 species of amniotes. We performed variation partitioning analyses, which showed that phylogeny explains a significant fraction of the variation of mass-specific RMR (mL O₂ h⁻¹ g⁻¹), and that the cost of growth is much higher than the cost of maintenance. Moreover, we tested the hypothesis of the independence of energy allocation, and found that maintenance metabolism and growth rates are not significantly related. Finally, we calculated the statistical parameters of the relationship between geometry-corrected RMR (mL O₂ h⁻¹ g^−0.67) and bone growth rate. This relationship could potentially be used in palaeobiology to infer RMR from bone tissue samples of fossil species by assuming Amprino's rule (according to which bone tissue types reflect bone growth rates). These estimates would be especially interesting for Mesozoic non-avian theropod dinosaurs and Permian and Triassic therapsids to investigate, respectively, the origin of avian and mammalian endothermy.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 92 , 63–76.     

XCSc: a novel approach to clustering with extended classifier system

In this paper, we propose a novel approach to clustering noisy and complex data sets based on the eXtend Classifier Systems (XCS). The proposed approach, termed XCSc, has three main processes: (a) a learning process to evolve the rule population, (b) a rule compacting process to remove redundant rules after the learning process, and (c) a rule merging process to deal with the overlapping rules that commonly occur between the clusters. In the first process, we have modified the clustering mechanisms of the current available XCS and developed a new accelerate learning method to improve the quality of the evolved rule population. In the second process, an effective rule compacting algorithm is utilized. The rule merging process is based on our newly proposed agglomerative hierarchical rule merging algorithm, which comprises the following steps: (i) all the generated rules are modeled by a graph, with each rule representing a node; (ii) the vertices in the graph are merged to form a number of sub-graphs (i.e. rule clusters) under some pre-defined criteria, which generates the final rule set to represent the clusters; (iii) each data is re-checked and assigned to a cluster that it belongs to, guided by the final rule set. In our experiments, we compared the proposed XCSc with CHAMELEON, a benchmark algorithm well known for its excellent performance, on a number of challenging data sets. The results show that the proposed approach outperforms CHAMELEON in the successful rate, and also demonstrates good stability.     

Energy landscapes and properties of biomolecules

Thermodynamic and dynamic properties of biomolecules can be calculated using a coarse-grained approach based upon sampling stationary points of the underlying potential energy surface. The superposition approximation provides an overall partition function as a sum of contributions from the local minima, and hence functions such as internal energy, entropy, free energy and the heat capacity. To obtain rates we must also sample transition states that link the local minima, and the discrete path sampling method provides a systematic means to achieve this goal. A coarse-grained picture is also helpful in locating the global minimum using the basin-hopping approach. Here we can exploit a fictitious dynamics between the basins of attraction of local minima, since the objective is to find the lowest minimum, rather than to reproduce the thermodynamics or dynamics.     

Metabolic costs of egg production in the European starling (Sturnus vulgaris)

The energy cost of egg production in passerine birds has typically been estimated to be 45%-60% of basal metabolic rate (BMR), but this is based on theoretical models using data on energy content of eggs and reproductive tissue; there are still very few empirical data on egg production costs. In this study, we directly measured resting metabolic rate (RMR) in egg-laying female European starlings (Sturnus vulgaris) over 3 yr. We compared these data with RMR of nonbreeding and chick-rearing birds and with estimated energy expenditure generated from a typical energy content model by using empirically derived data from body composition analysis for this species. We found marked variation in RMR between years and between reproductive stages, which complicates comparisons among breeding stages for the assessment of relative egg production costs. On the basis of this method, RMR during egg laying varied from +74% to -13% of nonbreeding RMR and from +20% to -7% of chick-rearing RMR. We therefore used an alternate approach: measuring changes in RMR through the complete cycle of follicle development and ovulation. The increase in RMR from the beginning of prelaying to the six-follicle stage (before first ovulation) when birds have a complete developing follicle hierarchy was 22.4%. This value is still much lower than that estimated from our energy content model. We discuss conceptual problems associated with the theoretical energy content approach but also suggest, on the basis of earlier work done in our lab, that the measured increase in RMR might still underestimate the actual cost of egg production if birds reallocate energy between different physiological systems.     

Demonstration of the surface values of spheroid cell nuclei, determined in natural size order, in relation to the large and small diameters of the nuclear incision surface, as a measurement value; a further contribution to the statistics of nuclear variation

The paper explains how the formulas for calculating the surface area of the prolate spheroid, which a nucleus resembles, can be changed by suitable substitutions into formulas based on measured diameters l and k [mm] of the nucleus approach side surface, magnified 3.000 times, and on a mixed cyclometric function dependent on the axial ratio. Their values established for distinct axial ratios are compiled in a table. The values of the mixed cyclometric function are to be calculated for any other axial ratio according to a formula based on linear interpolation. The nucleus surface Omu is obtained in the natural order of magnitude [micron2]. In case of constant axial ratio, the surface area values form a second-order arithmetic progression, and a recursion formula has been developed to check the values of its terms. In case of nuclei of spherical shape or constant small diameter k, the surface area formulas may be simplified. Numeral examples serve for explanation. For all measured-value combinations involved, a second part, which is being prepared, will contain a complete table of function values, which is referred to in the Appendix and from which the values of the natural surface areas of spheroid nuclei can be gathered.     

Prostate segmentation on T2 MRI using Optimal Surface Detection

This paper deals with a T2 MRI prostate segmentation method. We assume to have an initial surface mesh obtained interactively or after a first rough segmentation. The surface of the prostate is then searched within the initial mesh neighborhood using the Optimal Surface Detection algorithm (OSD). This algorithm is based on the construction of a directed graph from the information obtained around the initial mesh. The optimal surface is then obtained by a graph cut. Three different cost functions for the graph have been explored, one based on the local gradient, another on a statistical model of shape and a third on a model of gradient profile. The parameters of this method have been tuned on 33 different T2 MRI volumes.     

Weinberg's differential rule reconsidered

A central problem in research on twins is the estimation of the rates of monozygotic and dizygotic twin maternities. The estimation usually follows Weinberg's differential rule. According to this rule, the rate of dizygotic twinning is twice the rate of twin maternities in which the twins are of opposite sex. The monozygotic twinning rate is the difference between the rates of same-sex and opposite-sex twin sets. Weinberg's differential rule is implicitly based on the assumptions that the probability of a male equals the probability of a female and that the sexes in a dizygotic twin set are independent. Although Weinberg's differential rule has been the target of continuing discussions, the reliability of these assumptions has never been conclusively verified or rejected. In this study we present new variance formulas for the monozygotic and dizygotic twinning rates obtained using Weinberg's differential rule and stress that these new formulas have to be used. We analyze the accuracy of Weinberg's differential rule by considering alternative attempts. Especially, we build a general likelihood function and show that the maximum-likelihood estimates differ only slightly from the rates obtained using Weinberg's differential rule. In addition, our methods are applied to twinning data from Finland and Sweden. We compare our results with findings in the literature. In conclusion, our findings indicate that Weinberg's differential rule is rather robust and that despite its simplicity, it gives reliable results when official birth registers are analyzed.     

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.     

A Bayesian Estimator of the Optimum for a Single Factor Quadratic Response Model

Estimation of the location and magnitude of the optimum has long been considered an important problem in response surface methodology. In the industrial context, prior information accumulated by the subject matter specialist bears special significance. In this paper we use the Bayesian approach to estimating the optimum in a single factor quadratic regression model. Following the Bayesian general linear model development by Broemeling the normal/gamma conjugate prior is used. Explicit formulas for the generalized maximum likehood estimates of the characteristic parameters are obtained from the joint posterior distribution.     

Intraspecific Scaling of the Resting and Maximum Metabolic Rates of the Crucian Carp (Carassius auratus)

The question of how the scaling of metabolic rate with body mass (M) is achieved in animals is unresolved. Here, we tested the cell metabolism hypothesis and the organ size hypothesis by assessing the mass scaling of the resting metabolic rate (RMR), maximum metabolic rate (MMR), erythrocyte size, and the masses of metabolically active organs in the crucian carp (Carassius auratus). The M of the crucian carp ranged from 4.5 to 323.9 g, representing an approximately 72-fold difference. The RMR and MMR increased with M according to the allometric equations RMR = 0.212M ^0.776 and MMR = 0.753M ^0.785. The scaling exponents for RMR (b _r) and MMR (b _m) obtained in crucian carp were close to each other. Thus, the factorial aerobic scope remained almost constant with increasing M. Although erythrocyte size was negatively correlated with both mass-specific RMR and absolute RMR adjusted to M, it and all other hematological parameters showed no significant relationship with M. These data demonstrate that the cell metabolism hypothesis does not describe metabolic scaling in the crucian carp, suggesting that erythrocyte size may not represent the general size of other cell types in this fish and the metabolic activity of cells may decrease as fish grows. The mass scaling exponents of active organs was lower than 1 while that of inactive organs was greater than 1, which suggests that the mass scaling of the RMR can be partly due to variance in the proportion of active/inactive organs in crucian carp. Furthermore, our results provide additional evidence supporting the correlation between locomotor capacity and metabolic scaling.     

Implementation and clinical application of a deformation method for fast simulation of biological tissue formed by fibers and fluid

Background

The aim of this paper is to provide a general discussion, algorithm, and actual working programs of the deformation method for fast simulation of biological tissue formed by fibers and fluid. In order to demonstrate the benefit of the clinical applications software, we successfully used our computational program to deform a 3D breast image acquired from patients, using a 3D scanner, in a real hospital environment.

Results

The method implements a quasi-static solution for elastic global deformations of objects. Each pair of vertices of the surface is connected and defines an elastic fiber. The set of all the elastic fibers defines a mesh of smaller size than the volumetric meshes, allowing for simulation of complex objects with less computational effort. The behavior similar to the stress tensor is obtained by the volume conservation equation that mixes the 3D coordinates. Step by step, we show the computational implementation of this approach.

Conclusions

As an example, a 2D rectangle formed by only 4 vertices is solved and, for this simple geometry, all intermediate results are shown. On the other hand, actual implementations of these ideas in the form of working computer routines are provided for general 3D objects, including a clinical application.

     

Resting metabolic rate and its adjustments as predictors of risk protein-energy wasting in hemodialysis patients

Background: The purpose of the present study was to explore the association between resting metabolic rate (RMR) and protein-energy wasting (PEW) risk in Chinese hemodialysis patients by age and gender subgroup.Methods: RMR and body composition (body cell mass (BCM) and fat mass) of 774 patients undergoing hemodialysis were estimated by bio-electrical impedance analysis (BIA). Anthropometric data were collected by a standard measurement protocol, and the upper arm muscle circumference (AMC) was calculated. Biochemical nutritional and dialysis parameters were obtained. Linear regression analysis was used to analyze the relationship among RMR, body composition and nutritional factors.Results: The mean age was 54.96 ± 15.78 years. RMR level in patients was 1463.0 (1240.5, 1669.0) kcal/d. In multiple linear regression models, BCM, left calf circumference (LCC), fat mass were the determinants association with RMR (P<0.001). Among the patients in the sample, 133 (17.2%) had been diagnosed with PEW per International Society of Renal Nutrition and Metabolism (ISRNM) criteria and 363 (46.9%) were being at risk PEW. The area under the receiver-operating characteristic curve (AUC) of RMR for predicting risk PEW was greater than RMR/BCM and RMR/body surface area (BSA). When the cutoff of RMR was 1481 kcal/d it had the higher sensitivity and specificity (82 and 42%), and the AUC was 0.68 in elderly maintenance hemodialysis (MHD) patients (P<0.001). After adjustment for potential confounders, lowest RMR quartile level (<1239) increased the risk of PEW (OR = 4.71, 95% CI: 1.33–16.64, P=0.016) in all patients.Conclusions: Older patients with PEW have a lower RMR reduction. RMR and RMR/BCM may play the role in objective screening to detect risk PEW in MHD patients, especially in males.     

Adaptive generation of multimaterial grids from imaging data for biomedical Lagrangian fluid–structure simulations

Spatial discretization of complex imaging- derived fluid–solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid–solid mesh of the mouse heart. An MRI dataset of a perfusion-fixed mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue, and background. Subsequently a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid–structure interaction computations will tend to have relative error equilibrated over the whole mesh.     

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.     

A novel approach to decoy set generation: designing a physical energy function having local minima with native structure characteristics

We suggest a new approach to the generation of candidate structures (decoys) for ab initio prediction of protein structures. Our method is based on random sampling of conformation space and subsequent local energy minimization. At the core of this approach lies the design of a novel type of energy function. This energy function has local minima with native structure characteristics and wide basins of attraction. The current work presents our motivation for deriving such an energy function and also tests the derived energy function.Our approach is novel in that it takes advantage of the inherently rough energy landscape of proteins, which is generally considered a major obstacle for protein structure prediction. When local minima have wide basins of attraction, the protein's conformation space can be greatly reduced by the convergence of large regions of the space into single points, namely the local minima corresponding to these funnels. We have implemented this concept by an iterative process. The potential is first used to generate decoy sets and then we study these sets of decoys to guide further development of the potential. A key feature of our potential is the use of cooperative multi-body interactions that mimic the role of the entropic and solvent contributions to the free energy.The validity and value of our approach is demonstrated by applying it to 14 diverse, small proteins. We show that, for these proteins, the size of conformation space is considerably reduced by the new energy function. In fact, the reduction is so substantial as to allow efficient conformational sampling. As a result we are able to find a significant number of near-native conformations in random searches performed with limited computational resources.