Multivariate Mathematical Model Research Articles

An efficient LBM-DEM simulation method for suspensions of deformable preformed particle gels

Because of the capacity of in-depth plugging and flowing diversion, the deformable preformed particle gel (PPG) is used as an effective solution to severe fluid channeling and low sweep efficiency in oil development. However, the transport, plugging and deformation of PPG are a complex issue that involves both general characteristics of particle suspension and special deformation process. In addition, the flow of deformable PPG in porous media cannot be simulated by the classical seepage flow theory based on continuum assumptions. Thus, the paper develops an efficient simulation method for suspensions of deformable PPG, which combines the discrete idea of immersed boundary (IB) for particle deformation, lattice Boltzmann method (LBM) for fluid flow, discrete element method (DEM) for particle contact and immersed moving boundary (IMB) method for the solid-fluid interaction. The improved method is first validated by matching of the transport, plugging and deformation of PPG in porous media between numerical simulations and microscopic visualization experiments. Next, the method is used to study the effect of the particle-throat diameter ratio and elastic modulus on the critical pressure gradient, which is the smallest pressure gradient for a given PPG to pass through a throat of the porous media. The results indicate that there is a good exponential relationship between the critical pressure gradient of the PPG and the particle-throat diameter ratio. The critical pressure gradient is also linearly related to the elastic modulus of PPG. Finally, a multivariate mathematical model is proposed to characterize the quantitative relationships among the critical pressure gradient, particle-throat diameter ratio and elastic modulus. The proposed model is validated by comparisons between simulation results and prediction results by the quantitative model. Thus, the model can be used as the most important parameter for macroscopic simulations of PPG flooding in large oilfield-scale projects.

Fasciola hepatica reinfection potentiates a mixed Th1/Th2/Th17/Treg response and correlates with the clinical phenotypes of anemia.

BackgroundFascioliasis is a severe zoonotic disease of worldwide extension caused by liver flukes. In human fascioliasis hyperendemic areas, reinfection and chronicity are the norm and anemia is the main sign. Herein, the profile of the Th1/Th2/Th17/Treg expression levels is analyzed after reinfection, correlating them with their corresponding hematological biomarkers of morbidity.Methodology/Principal findingsThe experimental design reproduces the usual reinfection/chronicity conditions in human fascioliasis endemic areas and included Fasciola hepatica primo-infected Wistar rats (PI) and rats reinfected at 8 weeks (R8), and at 12 weeks (R12), and negative control rats. In a cross-sectional study, the expression of the genes associated with Th1 (Ifng, Il12a, Il12b, Nos2), Th2 (Il4, Arg1), Treg (Foxp3, Il10, Tgfb, Ebi3), and Th17 (Il17) in the spleen and thymus was analyzed. After 20 weeks of primary infection, PI did not present significant changes in the expression of those genes when compared to non-infected rats (NI), but an increase of Il4, Arg1 and Ifng mRNA in the spleen was observed in R12, suggesting the existence of an active mixed Th1/Th2 systemic immune response in reinfection. Foxp3, Il10, Tgfb and Ebi3 levels increased in the spleen in R12 when compared to NI and PI, indicating that the Treg gene expression levels are potentiated in chronic phase reinfection. Il17 gene expression levels in R12 in the spleen increased when compared to NI, PI and R8. Gene expression levels of Il10 in the thymus increased when compared to NI and PI in R12. Ifng expression levels in the thymus increased in all reinfected rats, but not in PI. The clinical phenotype was determined by the fluke burden, the rat body weight and the hemogram. Multivariate mathematical models were built to describe the Th1/Th2/Th17/Treg expression levels and the clinical phenotype. In reinfection, two phenotypic patterns were detected: i) one which includes only increased splenic Ifng expression levels but no Treg expression, correlating with severe anemia; ii) another which includes increased splenic Ifng and Treg expression levels, correlating with a less severe anemia.Conclusions/SignificanceIn animals with established F. hepatica infection a huge increase in the immune response occurs, being a mixed Th2/Treg associated gene expression together with an expression of Ifng. Interestingly, a Th17 associated gene expression is also observed. Reinfection in the chronic phase is able to activate a mixed immune response (Th1/Th2/Th17/Treg) against F. hepatica but T and B proliferation to mitogens is strongly suppressed in all infected rats vs control in the advanced chronic phase independently of reinfection The systemic immune response is different in each group, suggesting that suppression is mediated by different mechanisms in each case. Immune suppression could be due to the parasite in PI and R8 rats and the induction of suppressive cells such as Treg in R12. This is the first study to provide fundamental insight into the immune profile in fascioliasis reinfection and its relation with the clinical phenotypes of anemia.

EVOLUTION OF METHODOLOGICAL APPROACHES IN THE STUDY OF INTEREST GROUPS AND LOBBYING

Currently, lobbying is one of the important mechanisms of interaction between society and the state. The relevance of the study theoretical and empirical approaches to the study of lobbying as a phenomenon of group participation in politics due to the growing influence of pressure groups on the political process, creating new mechanisms of interaction between interest groups and organs of political power. Extension of the problem the study of lobbying, involves the study not only of theoretical and methodological bases of this phenomenon, but also its applied aspects,the development of new models and instruments of the study of lobbying as a mechanism to promote group interests. The objective of this article is to analyze the evolution of the main approaches to the study of such a complex and ambiguous phenomenon as interest groups in politics and lobbying as an institution and a way of realization of group interests. Neoinstitutional method, in our opinion, provides an opportunity to identify mechanisms and principles characteristic of the system of functional representation and lobbying, as its integral part. The application of multivariate models mathematical modeling to the analysis of modern lobbying practices will allow you to enter multiple variables and predict the probability of certain lobbying activities.

Seasonal variability and source apportionment of volatile organic compounds (VOCs) in the Paris megacity (France)

Abstract. Within the framework of air quality studies at the megacity scale, highly time-resolved volatile organic compound (C2–C8) measurements were performed in downtown Paris (urban background sites) from January to November 2010. This unique dataset included non-methane hydrocarbons (NMHCs) and aromatic/oxygenated species (OVOCs) measured by a GC-FID (gas chromatograph with a flame ionization detector) and a PTR-MS (proton transfer reaction – mass spectrometer), respectively. This study presents the seasonal variability of atmospheric VOCs being monitored in the French megacity and their various associated emission sources. Clear seasonal and diurnal patterns differed from one VOC to another as the result of their different origins and the influence of environmental parameters (solar radiation, temperature). Source apportionment (SA) was comprehensively conducted using a multivariate mathematical receptor modeling. The United States Environmental Protection Agency's positive matrix factorization tool (US EPA, PMF) was used to apportion and quantify ambient VOC concentrations into six different sources. The modeled source profiles were identified from near-field observations (measurements from three distinct emission sources: inside a highway tunnel, at a fireplace and from a domestic gas flue, hence with a specific focus on road traffic, wood-burning activities and natural gas emissions) and hydrocarbon profiles reported in the literature. The reconstructed VOC sources were cross validated using independent tracers such as inorganic gases (NO, NO2, CO), black carbon (BC) and meteorological data (temperature). The largest contributors to the predicted VOC concentrations were traffic-related activities (including motor vehicle exhaust, 15 % of the total mass on the annual average, and evaporative sources, 10 %), with the remaining emissions from natural gas and background (23 %), solvent use (20 %), wood-burning (18 %) and a biogenic source (15 %). An important finding of this work is the significant contribution from wood-burning, especially in winter, where it could represent up to ∼ 50 % of the total mass of VOCs. Biogenic emissions also surprisingly contributed up to ∼ 30 % in summer (due to the dominating weight of OVOCs in this source). Finally, the mixed natural gas and background source exhibited a high contribution in spring (35 %, when continental air influences were observed) and in autumn (23 %, for home heating consumption).

Подготовка данных для многофакторного анализа в медицине и биологии с помощью алгебраической модели конструктивной логики

An algebraic model of constructive logic is intended to build multivariate non-linear logical mathematical model and is widely used in analytical studies in medicine and biology. An important stage of its construction is the data preparation in accordance with the following requirements:
 ▪ The optimal choice of the analyzed factors with the following features: the pursuit of the researcher to involve the largest possible number of factors is a common mistake; factors must be independent; it is advisable to select only those factors that meet the research objectives; the ability of the algorithm to exclude certain fac-tors from the resulting mathematical model, it is observed, when the array of data input is sufficiently complete; the ability to use both continuous variables and discrete; the mathematical model is a more compact, if less factors are used, this model is easier to analyze and identify the characteristics of the test process.
 ▪ Verification of the data is the identification and correction of errors at the stage of entering the informa-tion into the database; using the built-in intelligent tools that facilitate the process of correct coding of medical information; additional data verification by using special techniques, such as the analytical testing method in the database records.
 ▪ Selecting of objective study with the following features: the goal can be represented not only two dis-crete (the goal is achieved or not achieved), but also a large number of them; the more discrete, the amount of base should be larger; possibility to use calculated target value by using various criteria.
 ▪ Presence of the necessary number of entries for a full analysis, it is necessary to ensure compliance with each of the target case (corresponding to the goal) at least two cases of non-target (not corresponding to the goal).
 ▪ Choice of software options is adequate available data.
 These requirements will allow to performing the analytical studies in accordance with the required relia-bility.

Estimating width of the stable channels using multivariable mathematical models

Predicting behavior and the geometry of the channels and alluvial rivers in which the erosion and sediment transport are in equilibrium is one of the most important topics in river engineering. Various researchers have proposed empirical equations to estimate stable river width (W). In this research, empirical equations were examined and tested with a comprehensive available data set consisting of 1644 points collected from 29 stable rivers in various parts of the world. The data set covers a wide range of flow conditions, river geometry, and bed sediments. This data set is classified in two groups (W < 600 m and W ≥ 600 m) for presenting the new models. The new linear and nonlinear multivariable equations were fitted to these two groups, and the best models were selected by preliminary tests and diagnostic determined for each group. The determination coefficient of these models ranged from 0.87 to 0.96. The results show that the models presented in this paper are more accurate with respect to the previously presented models. In the second part, “Artificial neural networks,” perceptron was used and a new methodology for estimating stable channel width was developed. Comparison of the statistical methods presented in this paper and the results of perceptron neural network revealed preferential recent method.

Multi-variable mathematical models for the air-cathode microbial fuel cell system

This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explain elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). Simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.

Prediction of Discharge Capacity over Two-Cycle Labyrinth Side Weir Using ANFIS

AbstractPhysical and mathematical models widely used in hydraulic engineering are not always effective in practice. Numerical methods such as the adaptive neuro fuzzy inference system (ANFIS) can be quite useful for estimating the key parameters, especially for complex and multivariate mathematical models. The aim of this study is to determine the discharge coefficients of labyrinth side weirs with two cycles using an experiment setup and ANFIS. Estimation of the discharge efficiency of the side weir has been achieved by using 285 laboratory data sets. The results of ANFIS functions and multiple nonlinear regression (MNLR) analysis were compared with experimental results. It is shown that two ANFIS functions, trimf and gbellmf, give the best estimations, and therefore this technique can be used effectively in practice.

Characterizing and quantifying the effects of breast cancer therapy using mathematical modeling.

We designed a mathematical model to describe and quantify the mechanisms and dynamics of tumor growth, cell-kill and resistance as they affect durations of benefit after cancer treatment. Our aim was to explore how treatment efficacy may be related to primary tumor characteristics, with the potential to guide future trial design and appropriate selection of therapy. Assuming a log-normal distribution of both resistant disease and tumor doubling times generates disease-free survival (DFS) or invasive DFS curves with specific shapes. Using a multivariate mathematical model, both treatment and tumor characteristics are related to quantified resistant disease and tumor regrowth rates by allowing different mean values for the influence of different treatments or clinical subtypes on these two log-normal distributions. Application of the model to the CALGB 9741 adjuvant breast cancer trial showed that dose-dense therapy was estimated to achieve an extra 3/4 log of cell-kill compared to standard therapy, but only in patients with more rapidly growing ER-negative tumors. Application of the model to the AZURE trial of adjuvant bisphosphonate treatment suggested that the 5-year duration of zoledronic acid was adequate for ER-negative tumors, but may not be so for ER-positive cases, with increased recurrences after ceasing the intervention. Mathematical models can identify different effects of treatment by subgroup and may aid in treatment design, trial analysis, and appropriate selection of therapy. They may provide a more appropriate and insightful tool than the conventional Cox model for the statistical analysis of response durations.Electronic supplementary materialThe online version of this article (doi:10.1007/s10549-016-3684-4) contains supplementary material, which is available to authorized users.

Возможности медикаментозного лечения и психотерапии в потенцировании ремиссии у пациентов на ранних стадиях шизофрении

В статье определены критерии клинической ремиссии, которые используются на современном этапе для пациентов с шизофренией (международные критерии Andreasen N.C., 2005). Отмечено, что недостатком данных критериев является отсутствие среди них критериев, отражающих социальную адаптацию пациентов, уровень их функционирования в обществе. В статье проведено комплексное исследование 237 пациентов с первым манифестным приступом шизофрении и представлены результаты оценки исходов болезни за 2-летний период, включая клинический, социальный и личностный аспекты. Проведен сравнительный анализ исходов шизофрении в группе пациентов (122 человека), которые были включены в комплексную программу лечения, и в группе пациентов (115 человек), получавших стандартную терапию. Комплексное лечение включало медикаментозную терапию и разработанную автором систему психотерапевтической реабилитации, содержание которой тезисно представлено в данной статье. Выявлены положительные корреляционные связи между более высоким уровнем социального функционирования, качества жизни, когнитивного функционирования пациентов, степени осознания пациентами психической болезни и благоприятными клинико-социальными исходами шизофрении. Методом построения многофакторных математических моделей установлены значимые предикторы двухлетних исходов болезни. Среди них: особенности лечебно-реабилитационной тактики, длительность нелеченого заболевания, выраженность симптоматики в продромальном периоде психоза, клиническое состояние пациента после купирования острой продуктивной симптоматики, уровень качества жизни пациентов и степень осознания пациентами психической болезни. Установлено, что при стандартизации по всем значимым факторам риска применение комплексного лечения пациентов с использованием медикаментозной терапии и разработанной автором системы психотерапевтической реабилитации позволяет снизить риск неблагоприятного двухлетнего исхода болезни (p &lt; 0,001), отношение шансов равно 0,17 (95% доверительный интервал 0,06–0,45). Представлено клиническое наблюдение, которое демонстрирует то, как меняется прогноз болезни при использовании стандартного или комплексного лечения.

Программа для выделения главных результирующих составляющих в алгебраической модели конструктивной логики

The article presents the program to determine the principal components resulting in the algebraic model of constructive logic, which is designed for construction multivariate nonlinear mathematical models. The resulting mathematical model is represented by a set of resulting components as factors indicating the detection limits, combined mark of conjunction (indicating joint impact). Each resulting component is characterized by power, which is the essence of the number of rows in the table that match the specified detection limits factors in their joint action. The program provides two methods to determine the main result components. The first method is based on determining the minimum difference between increasing amounts of capacity resulting components of the top and bottom. The second method is based on the determination of the inflection point of the curve decreasing capacity of the resulting components. The authors give recommendations on the choice of allocation method the main result components. If the curve changes power has a dedicated point of inflection and more like a straight line, it is recommended to use method 1. If the curve changes power has a dedicated point of inflection, it is recommended to use method 2. The program should be used in the package of analytical programs&#x0D; algebraic model of constructive logic when performing complex analytical calculations in biophysics, medicine and biology.

Ранняя диагностика и профилактика кардиоваскулярного риска у больных сахарным диабетом 2 типа

In the paper the relevance of research associated with a high incidence in the world diabetes type 2 diabetes, with often development in patients with early and late, micro - and macro-vascular complications leading to disability and mortality is justified. The results of study on the complex clinical and anamnestic, biochemical, metabolic, functional risk factors for cardiovascular diseases are presented. By means of multivariate mathematical modeling the most informative predictors of complications and their combinations, associated with increased susceptibility to the development of macro-angiopathies in the patients with diabetes mellitus type 2, were defined. The importance of lipid disorders, metabolic profile and homocysteine in the development of cardiovascular complications and their progression based on the study of the correlation between homocysteine with lipoproteins in various forms macro-angiopathies of patients with diabetes type 2, has been demonstrated. Timely correction of identified violations promotes positive dynamics of metabolic processes and on this background, to reduce the frequency of cardiovascular complications. The obtained data contribute to a better understanding of the mechanisms of formation, disposition, development, clinical course and outcome of diseases, identification of the population of persons with risk factors for the purpose of prevention activities.

Research on Inverse System Decoupling of Three-Axis Flight Simulator Based on the High-Speed Rotation Missile

This paper researches on the kinematics and dynamics of coupling for three-axis flight Simulator based on the high-speed rotation missile. Firstly, to define station body coordinate and the positive direction of rotation according to three-axis flight Simulator based on the high-speed rotation missile, and then the mathematical coupling model is established. Secondly, multivariable nonlinear mathematical model can be decoupling, while substituting the parameters quality attribute analysis solved by ProE into the mathematical model. Lastly, the decoupled linear equations and the decoupling solutions based on inverse system method were given, and then to finish the simulation and to analysis the simulation results.

Selecting the Rational Structures of the Usage of Tomato’s Production Factors

The use of mathematical models in financial and economic analysis of the impact offactors on agricultural productivity growth is a priority in the contemporary developmentsof the agricultural sector. The main purpose of this study is the selection of the beststructure for the use of production factors in the cultivation of four different varieties oftomato (Merit, Fine, Samos and Laura) in the greenhouses using a multivariatemathematical model. Hence, our research is focused in identifying and analyzing the mostimportant factors affecting the level of greenhouse tomato culture productivity in 16municipalities of Lushnja district. Based on the level of importance, the correlationanalysis listed those factors: manure (0.369), fertilizer (0.149), water (0.189), and liquidcrystalline fertilizer (0.096). Moreover, focusing on the actual levels of production factorsused by each municipality, we estimated the maximum yield (113q/are), and the mostlikely production that could be achieved (100q/are), based on a rational use of factors. Onthe basis of the obtained results, the maximum unused reserves were calculated for eachmunicipality in the district of Lushnja. The obtained results constitute a strong basis forbudgeting and forecasting activities not only for the tomato crop but also for otheragricultural cultures cultivated in other municipalities in the district of Lushnja and inAlbania.

Two Balanced Car LQR Algorithm Achieved Based on LabVIEW

Constructed of high-order, multi-variable mathematical model of two balanced car, and using LQR algorithm relies on the powerful LabVIEW Control Toolkit, through continuously adjust the weighting matrix Q and R, designed the optimal secondary controller,it is better to balance the system robust stability and reaction fast, and by drawing out of the system output response curve, verify the correctness and the effectiveness of the controller.

Open-target sparse sensing of biological agents using DNA microarray

BackgroundCurrent biosensors are designed to target and react to specific nucleic acid sequences or structural epitopes. These 'target-specific' platforms require creation of new physical capture reagents when new organisms are targeted. An 'open-target' approach to DNA microarray biosensing is proposed and substantiated using laboratory generated data. The microarray consisted of 12,900 25 bp oligonucleotide capture probes derived from a statistical model trained on randomly selected genomic segments of pathogenic prokaryotic organisms. Open-target detection of organisms was accomplished using a reference library of hybridization patterns for three test organisms whose DNA sequences were not included in the design of the microarray probes.ResultsA multivariate mathematical model based on the partial least squares regression (PLSR) was developed to detect the presence of three test organisms in mixed samples. When all 12,900 probes were used, the model correctly detected the signature of three test organisms in all mixed samples (mean(R2)) = 0.76, CI = 0.95), with a 6% false positive rate. A sampling algorithm was then developed to sparsely sample the probe space for a minimal number of probes required to capture the hybridization imprints of the test organisms. The PLSR detection model was capable of correctly identifying the presence of the three test organisms in all mixed samples using only 47 probes (mean(R2)) = 0.77, CI = 0.95) with nearly 100% specificity.ConclusionsWe conceived an 'open-target' approach to biosensing, and hypothesized that a relatively small, non-specifically designed, DNA microarray is capable of identifying the presence of multiple organisms in mixed samples. Coupled with a mathematical model applied to laboratory generated data, and sparse sampling of capture probes, the prototype microarray platform was able to capture the signature of each organism in all mixed samples with high sensitivity and specificity. It was demonstrated that this new approach to biosensing closely follows the principles of sparse sensing.

Análise da relação entre crescimento econômico e gastos públicos nas maiores cidades da região Sul do Brasil

Estudos que analisam os impactos da política fiscal sobre o crescimento econômico de países, estados e municípios são recorrentes. As questões de pesquisa mais comumente consideradas levam a investigar se os gastos públicos podem elevar o crescimento econômico com o aumento da produtividade do setor privado. Neste sentido, o objetivo deste estudo é investigar a relação existente entre o crescimento econômico, considerando o Produto Interno Bruto (PIB), e as variáveis que compõem os gastos públicos das maiores cidades da região Sul do Brasil. Trata-se de uma pesquisa descritiva com abordagem quantitativa e de corte seccional. Para tal, o artigo apresenta um modelo matemático não linear multivariável que é avaliado empiricamente por meio de uma aplicação para os gastos públicos das maiores cidades da região Sul do Brasil. A partir da utilização do modelo, estimou-se o PIB para as cidades e comparou-se com os valores reais do PIB. Os resultados mostram um erro de estimação de 22,45% para uma confiabilidade de 85,16%. Conclui-se que os gastos dos governos locais têm um importante papel no crescimento econômico.

Systems parasitology: effects of Fasciola hepatica on the neurochemical profile in the rat brain

We characterize the integrated response of a rat host to the liver fluke Fasciola hepatica using a combination of 1H nuclear magnetic resonance spectroscopic profiles (liver, kidney, intestine, brain, spleen, plasma, urine, feces) and multiplex cytokine markers of systemic inflammation. Multivariate mathematical models were built to describe the main features of the infection at the systems level. In addition to the expected modulation of hepatic choline and energy metabolism, we found significant perturbations of the nucleotide balance in the brain, together with increased plasma IL-13, suggesting a shift toward modulation of immune reactions to minimize inflammatory damage, which may favor the co-existence of the parasite in the host. Subsequent analysis of brain extracts from other trematode infection models (i.e. Schistosoma mansoni, and Echinostoma caproni) did not elicit a change in neural nucleotide levels, indicating that the neural effects of F. hepatica infection are specific. We propose that the topographically extended response to invasion of the host as characterized by the modulated global metabolic phenotype is stratified across several bio-organizational levels and reflects the direct manipulation of host–nucleotide balance.

Prospective validation of a nomogram predictive of a positive initial prostate biopsy

IntroductionUltrasound-guided transrectal prostate biopsy is currently an indispensable test for diagnosing prostate cancer. Many variables have been related to the presence of cancer in the biopsy (e.g. digital rectal examination [DRE], serum levels of prostatespecific antigen [PSA], free PSA fraction [PSAI/PSAt]). Multivariate mathematical models integrating these variables (nomograms, artificial network models) and improving the capacity to predict tests results are currently available. ObjectiveTo develop a nomogram for predicting the probability of a positive prostate biopsy in patients in whom this test is requested, and to use such nomogram in subsequent patients to assess its predictive ability. Material and methodsA total of 410 consecutive patients undergoing biopsy due to a suspicious digital rectal examination or two serum PSA values higher than 4ng/mL were enrolled into the study. Ten cores were taken in the prostate biopsy. Patients with both PSA levels >20ng/ml and prior biopsies were excluded. The following variables were recorded in each patient: age, total PSA, free PSA fraction, prostate volume, transition zone volume, PSA density, PSA density adjusted by transition zone volume, digital rectal examination, and findings suggesting cancer during transrectal ultrasound (hypoechogenic nodules). Prospective external validation was performed with 185 patients who met the same inclusion criteria.Statistical analysis consisted of four phases: a univariate study, a multivariate logistic regression study which was used to develop the nomogram, internal validation, and prospective external validation. S-Plus® Programme Design and SPSS 12.0® software was used for the procedure. ResultsVariables found to be independently and significantly associated to the presence of cancer included age, digital rectal examination, trnsition zone volume, PSA density, and the presence of hypoechogenic nodules during transrectal ultrasound. Such variables were therefore used to develop the nomogram. The goodness-of-fit of the nomogram was 84%. Validation with an external sample showed a 73% concordance index. ConclusionA nomogram having a satisfactory predictive ability and fit that allows for predicting the prostate biopsy result with a high accuracy rate was developed.

Validación prospectiva de un nomograma predictivo de la presencia de cáncer de próstata en pacientes que se someten a biopsia transrectal ecodirigida de 10 cilindros

IntroductionUltrasound-guided transrectal prostate biopsy is currently an indispensable test for diagnosing prostate cancer. Many variables have been related to the presence of cancer in the biopsy (e.g. digital rectal examination [DRE], serum levels of prostatespecific antigen [PSA], free PSA fraction [PSAI/PSAt]). Multivariate mathematical models integrating these variables (nomograms, artificial network models) and improving the capacity to predict tests results are currently available. ObjectiveTo develop a nomogram for predicting the probability of a positive prostate biopsy in patients in whom this test is requested, and to use such nomogram in subsequent patients to assess its predictive ability. Material and methodsA total of 410 consecutive patients undergoing biopsy due to a suspicious digital rectal examination or two serum PSA values higher than 4 ng/mL were enrolled into the study. Ten cores were taken in the prostate biopsy. Patients with both PSA levels >20 ng/ml and prior biopsies were excluded. The following variables were recorded in each patient: age, total PSA, free PSA fraction, prostate volume, transition zone volume, PSA density, PSA density adjusted by transition zone volume, digital rectal examination, and findings suggesting cancer during transrectal ultrasound (hypoechogenic nodules). Prospective external validation was performed with 185 patients who met the same inclusion criteria.Statistical analysis consisted of four phases: a univariate study, a multivariate logistic regression study which was used to develop the nomogram, internal validation, and prospective external validation. S-Plus#r Programme Design and SPSS 12.0#r software was used for the procedure. ResultsVariables found to be independently and significantly associated to the presence of cancer included age, digital rectal examination, trnsition zone volume, PSA density, and the presence of hypoechogenic nodules during transrectal ultrasound. Such variables were therefore used to develop the nomogram. The goodness-of-fit of the nomogram was 84%. Validation with an external sample showed a 73% concordance index. ConclusionA nomogram having a satisfactory predictive ability and fit that allows for predicting the prostate biopsy result with a high accuracy rate was developed.