Formula For Volume Research Articles

Trends in Subcutaneous Tumour Height and Impact on Measurement Accuracy.

Tumour volume is typically calculated using only length and width measurements, using width as a proxy for height in a 1:1 ratio. When tracking tumour growth over time, important morphological information and measurement accuracy is lost by ignoring height, which we show is a unique variable. Lengths, widths, and heights of 9522 subcutaneous tumours in mice were measured using 3D and thermal imaging. The average height:width ratio was found to be 1:3 proving that using width as a proxy for height overestimates tumour volume. Comparing volumes calculated with and without tumour height to the true volumes of excised tumours indeed showed that using the volume formula including height produced volumes 36X more accurate (based off of percentage difference). Monitoring the height:width relationship (prominence) across tumour growth curves indicated that prominence varied, and that height could change independent of width. Twelve cell lines were investigated individually; the scale of tumour prominence was cell line-dependent with relatively less prominent tumours (MC38, BL2, LL/2) and more prominent tumours (RENCA, HCT116) detected. Prominence trends across the growth cycle were also dependent on cell line; prominence was correlated with tumour growth in some cell lines (4T1, CT26, LNCaP), but not others (MC38, TC-1, LL/2). When pooled, invasive cell lines produced tumours that were significantly less prominent at volumes >1200 mm3 compared to non-invasive cell lines (P < .001). Modelling was used to show the impact of the increased accuracy gained by including height in volume calculations on several efficacy study outcomes. Variations in measurement accuracy contribute to experimental variation and irreproducibility of data, therefore we strongly advise researchers to measure height to improve accuracy in tumour studies.

Analysis of Three Main Error Sources in Traditional Bladder Volume Formula and Development of a Computer Bladder Volume Calculation Program

Analysis of Three Main Error Sources in Traditional Bladder Volume Formula and Development of a Computer Bladder Volume Calculation Program

Assessment of Relationship between Clinical Manifestation of Chiari Malformation Type I and Volumetric Measurement of Cerebellar Tonsils Herniation within Foramen Magnum

Introduction: Chiari malformation type I (CMI) is diagnosis based on clinical and radiological measurement of cerebellar tonsils herniation of 5mm or more below the foramen magnum (FM). The aim of the study was to determine the relationship between clinical presentation of CMI and cerebellar tonsils herniation measured in 3dimensions (3D), cerebellar tonsils volume and T/F volume ratio (cerebellar tonsils volume/foramen magnum). Methods: The study included 96 patients with CMI based on study sample size and power calculation.3D measurement of cerebellar tonsils was made, the volume of cerebellar tonsils was calculated using ellipsoid volume formula. The transverse diameter of FM measured and the volume of FM calculated using sphere formula. We computed non-parametric statistical tests and hypothesis testing to analyze correlation and variation of cerebellar tonsils measurements, cerebellar tonsils volume, and T/F volume ratio in relation to severity of myelopathy using mJOA (modified Japanese Orthopedics association) score and headache severity using NRS (Numerical Rate Score). Results: The finding showed a correlation between myelopathy severity and the volume of herniated cerebellar tonsils as well as correlation between myelopathy severity and T/F volume ratio (Cerebellar tonsil volume/Foramen magnum volume). There was also correlation between headache severity and cerebellar tonsil volume as well as T/F volume ratio. Conclusion: Consideration of both clinical presentation and radiological measurement in assessment of CMI is crucial, rather than considering only cut off of 5 mm descent of cerebellar tonsils herniation in midsaggital view. Cerebellar tonsils volume and T/F volume ratio are the indicators of severity of myelopathy and headache severity as shown in the study

Assessment of Prostate Volume and Prostate-specific Antigen Density With the Segmentation Method on Magnetic Resonance Imaging.

This study aimed to compare the prostate volume (PV) and prostate-specific antigen density (PSAD) obtained using the ellipsoid volume formula or segmentation methods on magnetic resonance imaging (MRI) and further predict prostate cancer (PCa). Retrospectively, the enrolled patients underwent prostate MRI and had PSA levels between 4 and 10 ng/ml. The PV was measured with both the ellipsoid volume formula (PVe) and the segmentation method (PVs). The transitional zone volume (TZV) was measured with the segmentation method. The PSADe, PSADs, and PSAD_TZV were calculated. Bland-Altman plots were used to compare the agreements. ROC curve analysis was used to compare the diagnostic accuracies to predict PCa. The results were also compared between the PCa and the no-PCa groups, and among tumors with different locations and different Gleason scores (GS). Seventy-six of the 117 enrolled patients were classified into the PCa group. There were high agreements between PVs and PVe as well as between PSADs and PSADe, while several outliers were mainly due to post-transurethral resection of the prostate changes and irregular hyperplastic nodules. The diagnostic accuracy of PSADe (AUC: 0.732) was slightly higher than that of PSADs (AUC: 0.729) and PSAD_TZV (AUC: 0.715). The PSADe and PSADs were not different among different tumor locations but were higher in GS ≥7 lesions (both p=0.006). The segmentation method can be an alternative method to measure PV and calculate PSAD before prostate biopsy, particularly in post-transurethral resection of the prostate patients or those with irregular hyperplastic nodules.

Prediction of weaning weight in Santa Inês lambs using the body volume formula

Weaning weight (WW) is one of the most important information within production systems, as it is a reflection of management during the breastfeeding phase and will influence the performance of animals in subsequent phases. This study aimed to develop and evaluate linear, quadratic, and exponential models to predict WW using the body volume (BV) formula in Santa Inês lambs for meat. Eighty-five lambs at 90days of age with WW 17.52 ± 3.79kg and BV 13.29 ± 2.86 dm3 were evaluated. The quality of fit of the models was evaluated using the coefficient of determination (R2), mean squared error (MSE), and root MSE (RMSE). For the external evaluation of the models, an independent dataset from 43 lambs at 90days of age was used. The first-degree linear model showed the lowest values of MSE (1.02) and RMSE (1.01). In the external evaluation, all models exhibited estimates of mean WW and standard deviation of this weight similar to the external dataset, as well as high values (above 0.89) for the R2 of predicted vs. observed data. Concordance correlation coefficient (CCC) analysis also revealed that all models showed accuracy and precision (CCC > 0.90). There was no difference between the models in terms of accuracy (P > 0.05). The comparison in terms of precision indicated that the linear model is more precise than the exponential model and that the quadratic model is as precise as the linear model. The first-degree linear model should be used due to its simplicity of interpretation and ease of estimation.

Non-Holomorphic Cycles and Non-BPS Black Branes

We study extremal non-BPS black holes and strings arising in M-theory compactifications on Calabi–Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural formula for the asymptotic volumes of connected, locally volume-minimizing representatives of non-holomorphic, even-dimensional homology classes in the threefold, without knowledge of an explicit metric. In the case of divisors we find examples where the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon $$AdS_3$$ limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles).

Optical Trapping of a Single Molecule of Length Sub-1 nm in Solution

Optical Trapping of a Single Molecule of Length Sub-1 nm in Solution

Predição do peso vivo em novilhas de corte usando a fórmula do volume corporal

ABSTRACT The objective of this study was to develop and evaluate linear, quadratic, and allometric models to predict live weight (LW) using the body volume formula (BV) in crossbred heifers raised in southeastern Mexico. The LW (426.25±117.49kg) and BV (338.05±95.38 dm3) were measured in 360 heifers aged between 3 and 30 months. Linear and non-linear regression were used to construct prediction models. The goodness-of-fit of the models was evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), coefficient of determination (R2), mean squared error (MSE), and root MSE (RMSE). In addition, the developed models were evaluated through cross-validation (k-folds). The ability of the fitted models to predict the observed values was evaluated based on the RMSEP, R2, and mean absolute error (MAE). The quadratic model had the lowest values of AIC (2688.39) and BIC (2700.05). On the other hand, the linear model showed the lowest values of MSE (7954.74) and RMSE (89.19), and the highest values of AIC (2709.70) and BIC (2717.51). Despite this, all models presented the same R2 value (0.87). The cross-validation (k-folds) evaluation of fit showed that the quadratic model had better values of MSEP (41.49), R2 (0.85), and MAE (31.95). We recommend the quadratic model to predictive of the crossbred beef heifers' live weight using the body volume as the predictor.

Volumes of Polyhedra in Non-Euclidean Spaces of Constant Curvature

Computation of the volumes of polyhedra is a classical geometry problem known since ancient mathematics and retaining its importance until present time. Deriving volume formulas for 3-dimensional non-Euclidean polyhedra of a given combinatorial type is a very difficult problem. Nowadays, it is fully solved for a tetrahedron, the most simple polyhedron in the combinatorial sense. However, it is well known that for a polyhedron of a special type its volume formula becomes much simpler. This fact was noted by Lobachevskii who found the volume of the so-called ideal tetrahedron in hyperbolic space (all vertices of this tetrahedron are on the absolute). In this survey, we present main results on volumes of arbitrary non-Euclidean tetrahedra and polyhedra of special types (both tetrahedra and polyhedra of more complex combinatorial structure) in 3-dimensional spherical and hyperbolic spaces of constant curvature K = 1 and K = −1, respectively. Moreover, we consider the new method by Sabitov for computation of volumes in the hyperbolic space (described by the Poincaré model in the upper half-space). This method allows one to derive explicit volume formulas for polyhedra of arbitrary dimension in terms of coordinates of vertices. Considering main volume formulas for non-Euclidean polyhedra, we will give proofs (or sketches of proofs) for them. This will help the reader to get an idea of basic methods for computation of volumes of bodies in non-Euclidean spaces of constant curvature.

Determination of subdural hematoma volume: Comparative analysis of calculation methods

Background. Accurate calculation of the volume of subdural hematomas of traumatic, vascular, and other origins during diagnosis is complicated which leads to difficulties in selection of optimal tactics of neurosurgical treatment. Aim. To preform comparative analysis of accuracy of different methods of subdural hematoma volume calculations to increase the quality of evaluation of the results of radiological methods in selection of surgical tactics.Materials and methods. Data from preoperative computed tomography of 20 patients (15 men and 5 women between the ages of 20 and 60 years) with confirmed diagnosis of subdural hematoma who were examined and treated at the Neurosurgery Clinic of the Kirov Military Medical Academy were used. Four groups were formed based of the calculation method: two groups using formulas for volume of ellipsoid or convexo-concave lens (the shape most accurately representing the shape of subdural hematoma); electronic algorithm of volume calculation (Gamma MultiVox D2 software, Gammamed-Soft, Russia); control method (manual sectional calculation of areas of the formed structures with subsequent summation).Results. Deviations between the obtained values varied between +18 and -16 %. Deviations for calculations using ellipsoid volume formula were +46 and -19 %; using convexo-concave lens formula +38 and -35 %, respectively. Electronic calculation algorithm (Gamma MultiVox D2) showed the best accuracy compared to other methods including the control method.Conclusions. Comparative analysis of the accuracy of the studied methods of calculation of subdural hematoma volume showed that median results are statistically similar which allows for selection and use of these methods in accordance with the neurosurgeon's preferences.Study of the algorithm based on ellipsoid volume shows low specificity of this method, comparatively high deviations of the results from the true value with a trend toward overprediction.Calculation using volume of convexo-concave lens showed intermediate result if the shape of the hematoma corresponded to the ideal chape of a figure enclosed between two segments of a sphere. In cases where the shape did not correspond to the convexo-concave lens, both overprediction and underprediction of hematoma volume were observed.Calculations using the Gamma MultiVox D2 software showed the highest accuracy, lowest range of deviation from the control data, best versatility, independence from both the shape and location of the subdural hematoma, as well as selection of a section used in other algorithms for the measurements.It should be noted that accuracy of determination of subdural hematoma volume by the studied methods is directly proportional to time necessary for calculation.

Determining consumers' attitudes towards organic products by factor analysis: The example of organic product markets

This study was carried out in order to reveal the attitudes of consumers toward organic products in the provinces of Istanbul, where Turkey's first and largest organic product market is located, and Izmir, where organic production first started. For this purpose, face-to-face surveys were conducted with 271 consumers who went to the organic product market using the proportional sample volume formula. Frequency tables were used in the analysis of demographic data obtained from the questionnaires. The Factor Analysis method was used to measure consumers' behavior toward organic products. It was determined that the majority of organic product consumers who participated in the survey were women (60.1%), married (66.8%), university graduates (57.6%), and individuals with high income (89.6%). After removing the missing, outlier, and extreme values, 251 questionnaires and 13 statements were used in the Factor Analysis. Within the scope of the results obtained, it was determined that reliability, experience (comparison), research (cognitive) and health factors directly affect the consumption of organic products in the attitudes of consumers in Istanbul and Izmir provinces towards organic products. It has been determined that it is important to increase the number of organic product markets throughout the country and to develop public service announcements highlighting these characteristics of organic products to increase organic product consumption.

On the Goncharov depth conjecture and a formula for volumes of orthoschemes

We prove a conjecture of Goncharov, which says that any multiple polylogarithm can be expressed via polylogarithms of depth at most half of the weight. We give an explicit formula for this presentation, involving a summation over trees that correspond to decompositions of a polygon into quadrangles. Our second result is a formula for volume of hyperbolic orthoschemes, generalizing the formula of Lobachevsky in dimension three to an arbitrary dimension. We show a surprising relation between the two results, which comes from the fact that hyperbolic orthoschemes are parametrized by configurations of points on P 1 \mathbb {P}^1 . In particular, we derive both formulas from their common generalization.

Another look at the two Egyptian pyramid volume ‘formulas’ of 1850 BCE

This paper provides some methodological, didactical, and historiographical reflections on Egyptian pyramid volume formulas, responding to suggestions by Paul Shutler from 2009. These suggestions partly reiterate a historically documented proof by the Chinese Liu Hui (third century CE), although Lui Hui’s contribution was apparently unknown to Shutler. The latter came forward, in addition, with intuitive arguments which might have been used by the Egyptians to convince themselves of the correctness of their formula for the volume of the full pyramid. In a broad sense, the reflections in this paper may contribute to the use of history in the mathematical classroom. As a cautionary note: The paper is an abridged version of a longer manuscript that contains detailed explanations and discussions of historical secondary sources. Since the paper is somewhat outside the usual canon of mathematics historiography, I have deposited the longer manuscript on <arXiv.org>.

Exclusion volumes of convex bodies in high space dimensions: applications to virial coefficients and continuum percolation

Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume v ex(K) for a general convex body K that applies in any space dimension. While our main interests concern the rotationally-averaged exclusion volume of a convex body with respect to another convex body, we also describe some results for the exclusion volumes for convex bodies with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume v ex(K)/v(K) among all convex bodies, whether randomly oriented or uniformly oriented, for any d, where v(K) is the volume of K. When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any d with a large-d asymptotic scaling behavior of 22d /d 3/2, which is to be contrasted with the corresponding scaling of 2 d for the sphere. We present explicit formulas for quermassintegrals W 0(K), …, W d (K) for many different nonspherical convex bodies, including cubes, parallelepipeds, regular simplices, cross-polytopes, cylinders, spherocylinders, ellipsoids as well as lower-dimensional bodies, such as hyperplates and line segments. These results are utilized to determine the rotationally-averaged exclusion volume v ex(K) for these convex-body shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, we show that, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal v ex(K)/v(K) with a scaling behavior of 21.6618…d . Subsequently, we apply these results to determine the corresponding second virial coefficient B 2(K) of the aforementioned hard hyperparticles. Our results are also applied to compute estimates of the continuum percolation threshold η c derived previously by the authors for systems of identical overlapping convex bodies. We conjecture that overlapping spheres possess the maximal value of η c among all identical nonzero-volume convex overlapping bodies for d ⩾ 2, randomly or uniformly oriented, and that, among all identical, oriented nonzero-volume convex bodies, overlapping simplices have the minimal value of η c for d ⩾ 2.

On Application of Contemporary Proof of the Sforza Formula to Computation of Volumes of Hyperbolic Tetrahedra of Special Kind

In this paper, we use the contemporary proof (by Abrosimov and Mednykh) of the Sforza formula for volume of an arbitrary non-Euclidean tetrahedron to derive new formulas that express volumes of hyperbolic tetrahedra of special kind (orthoschemes and tetrahedra with the symmetry group S4) via dihedral angles.

Splenic Size and Volume Measurements in Patients with Chronic Lymphocytic Leukemia

To determine which methods of assessment of splenic size most accurately represent the actual spleen volume in patients with Chronic Lymphocytic Leukemia (CLL). The Abdominal Computed Tomography images of 48 patients with CLL enrolled on a phase 2 clinical trial at two time-points before and after 2-months of continuous acalabrutinib treatment were analyzed. Linear one-dimensional measurements of the spleen were taken in different planes. Two-dimensional and three-dimensional measurements were calculated from the linear measurements using mathematical formulae. The spleen volume was determined by manual segmentation as the ground truth. Data derived were analyzed using Pearson correlation and statistical significance was set at p < 0.05. Among the single-dimensional measurements, the strongest correlation with the segmented splenic volume was the sagittal long axis diameter (LAD) (r=0.89, p < 0.05), followed closely by Coronal LAD (r=0.87, p < 0.05) and cephalocaudal length (iwCLL) (r=0.84, p < 0.05). For the two-dimensional indices, the sum of LAD and short axis diameter (SAD) of the spleen in axial plane showed good correlation with the splenic volume (r=0.77, p < 0.05). Among the three-dimensional indices, the splenic index (0.523 x axial LAD x axial SAD x coronal height) and a formula for volume (30+0.58 x axial LAD x axial SAD x coronal height) had the strongest correlation (both r=0.92, p < 0.05) with the spleen volume. The three-dimensional formulae showed the strongest correlation with volumetric reference spleen measurement. Among unidimensional measurements, the sagittal LAD had the best correlation with the actual splenic volume. The two-dimensional calculation methods were less reliable.

Verification of Usability of Medical Image Data Using Projective Photography for Designing Clothing for Breast Cancer Patients.

Manufacturing a customized mastectomy bra, using medical images obtained for breast cancer treatment, could be suggested as an alternative instead of the anthropometric method. However, the breast shape of a medical image is deformed from the anthropometric method as the measurement posture is different between the anthropometric method for making clothes and the medical image. As a breast consists of adipose tissues and a few muscles without bones, there is a possibility that a bra can be manufactured if the volume is constant. Therefore, a hypothesis was established that the volume of the breast would be constant, even if the measurement methods were different. As a result of the comparison of 3D-SIM and PPM by MRI, 18 items could be measured simultaneously. Nine items showed differences according to the measurement method. The next step in the case of 3D-SIM was calculating the volume by separating the breast shape into a cone and a hemispherical shape; in the case of MRI, an ellipsoidal volume formula was applied. A t-test was performed on the results obtained, showing no significant difference. Therefore, it was proven that the volume of the breast does not change despite the difference in the measurement and the measurement method.

Calculation of the required minimum of a motor oil level on cylinder-piston group moving surfaces of the automotive diesel

BACKGROUND: Theme of this article is actual because issues of the reliable and cost-effective opera-tion of augmented automotive piston engines are still not solved. An important aspect of solving the problem is rational oil supply of the cylinder-piston group.&#x0D; AIMS: The purpose of this work is the required minimum motor oil level estimation for the hydrodynamic lubrication of the cylinder-piston skirt pair. There were set and solved the tasks of determining the volume of motor oil capable of filling: 1) cavities of the flat-topped surface of the cylinder; 2) a raised surface of the piston skirt and 3) the piston skirt clearance. The object of study is an automotive diesel.&#x0D; METHODS: Three types of analytical determination of the total volume of the cavities of the rough surface and the piston skirt clearance were used as methods for estimation of a motor oil level.&#x0D; RESULTS: It was found, that the estimation with the well known formula for oil volume (a method 1) gives the overevaluated result of oil level estimation, in comparison with methods 2 and 3, which taking into account the real geometry of cavities and roughness parameters. The advantage of method 3 was determened by criteria of generalization and of simplicity to apply. Using the method 3, the estimated volume of motor oil ensured the hydrodynamic lubrication mode of the cylinder piston skirt pair of the object of study was obtained.&#x0D; CONCLUSION: The analytical expressions obtained by method 3 can be recommended to optimize the piston engine lubrication systems for reducing the friction and wear losses as well as to minimize a risk of oil starvation and increased oil consumption through burning.

Predição do peso vivo de ovelhas deslanadas em crescimento usando a fórmula do volume corporal

ABSTRACT Due to the conditions in which traditional sheep production systems operate, the evaluation of animal growth from live weight (LW) is limited by the high cost of the livestock scale as well as the sophisticated maintenance required. In this scenario, in recent years, biometric measurements have been investigated as an accurate indirect method to predict the LW of farm animals. Therefore, the present study was undertaken to examine different models for predicting the body weight of growing lambs using the body volume (BV) formula. Body volume, heart girth (HG) and body length (BL) data of 290 lambs aged between two and eight months were recorded. Body volume was calculated from HG and BL data using a formula that calculates the volume of a cylinder. The estimation of LW from the BV formula was achieved through regression equations using three mathematical models (linear, quadratic and exponential). The mean values of LW, HG, BL and BV of the lambs were 29.12±12.04kg, 70.00±11.69cm, 38.40±6.43cm and 23.93±9.90dm3, respectively. The correlation coefficient between LW and BV was r = 0.96 (P&lt;0.001). The quadratic model showed the highest coefficient of determination (0.93) and the lowest prediction error (3.29kg). Under the experimental conditions adopted in this study, it is possible to predict the live weight of growing lambs using the body volume formula.

Path integrals in JT gravity and Virasoro constraints

In this paper, we examine the large-[Formula: see text] asymptotic Weil–Petersson volume formulas deduced in the previous literature. The volume formulas have application to computing the partition functions and the correlation functions in Jackiw–Teitelboim gravity. We utilize two approaches to assess the validity of the formulas. The first approach is to examine the asymptotic volume formulas from the perspective of the Witten conjecture. If the volume formulas are correct, the generating function of the intersection indices deduced from the asymptotic volume formulas would satisfy constraints that are analogous to the Virasoro constraints. We confirmed that the intersection indices computed from the large-[Formula: see text] asymptotic volume formulas satisfy variants of the string and dilaton equations. This implies that the generating function of the intersection indices deduced from the asymptotic volume formulas indeed satisfies constraints analogous to first two of the Virasoro constraints. As another approach, we also examined the asymptotic volume formulas by studying the behavior of the higher-order spectral form factors. Our analyses suggest that the large-[Formula: see text] asymptotic Weil–Petersson volume formulas yield plausible estimations.