Biomodelling and 3D technologies: A novel technique for subungual glomus tumor evaluation.

Subungual glomus tumors often remain undiagnosed for several years with patients seeing an average of 2.5 dermatologists before the diagnosis is confirmed. We describe the use of biomodelling and 3D technologies that allows the detection of tumoral recurrences more easily, as well as providing supplementary information for the radiologist report, such as select anatomical structure analysis, images with 360° rotation and visualization in transparency mode for detailed anatomic analysis.

Analysis and modeling of human seat interaction with a focus on the upper body and backrest using biomechanics and contact mechanics.

BACKGROUND: This paper outlines a method to study the interaction between the human body and the aircraft seat concerning the seat comfort. METHOD: Firstly, the human body is modeled based on biomechanics and divided into a number of body segments connected by joints according to human anatomy. The angles between the body segments are obtained by curve fitting of the existing biomechanical research data. The contact forces between the human body and the seat are modeled using pairs of bi-lateral point forces. These forces are calculated and located through the analysis of the center of gravity of each body segment and average muscular structure of the human body. The geometry of the human and the seat is obtained from a 3D scan model or a CAD model. Secondly, the pressure distribution between the human body and the seat is modeled and calculated using the contact stress theory. The results of the two parts are combined to analyze the comfortability in relation to different postures, backrest recline angles and changing in shape and material. RESULTS: Simulations were performed and they are compared with experimental measurement and various FEM studies for validation. It is found that accuracy of this method is comparable with most FEM calculation. CONCLUSION: This method provides a new direction in cushion conform research. It is faster and convenient to use comparing to the FEM, and the result is reliable.

Retracted Article: Application of 3D printing technology in orthopedic medical implant - Spinal surgery as an example.

Additive manufacturing has been used in complex spinal surgical planning since the 1990s and is now increasingly utilized to produce surgical guides, templates, and more recently customized implants. Surgeons report beneficial impacts using additively manufactured biomodels as pre-operative planning aids as it generally provides a better representation of the patient's anatomy than on-screen viewing of computed tomography (CT) or magnetic resonance imaging (MRI). Furthermore, it has proven to be very beneficial in surgical training and in explaining complex deformity and surgical plans to patients/parents. This paper reviews the historical perspective, current use, and future directions in using additive manufacturing in complex spinal surgery cases. This review reflects the authors' opinion of where the field is moving in light of the current literature. Despite the reported benefits of additive manufacturing for surgical planning in recent years, it remains a high niche market. This review raises the question as to why the use of this technology has not progressed more rapidly despite the reported advantages - decreased operating time, decreased radiation exposure to patients intraoperatively, improved overall surgical outcomes, pre-operative implant selection, as well as being an excellent communication aid for all medical and surgical team members. Increasingly, the greatest benefits of additive manufacturing technology in spinal surgery are custom-designed drill guides, templates for pedicle screw placement, and customized patient-specific implants. In view of these applications, additive manufacturing technology could potentially revolutionize health care in the near future.

Experimental Models of Spinal Cord Injury in Laboratory Rats.

Pathologies associated with spinal cord injury are some of the leading diseases in the world. The search for new therapeutic agents and 3D biodegradable materials for the recovery of spinal cord functions is a topical issue. In this review, we have summarized the literature data on the most common experimental models of spinal cord injury in laboratory rats and analyzed the experience of using 3D biodegradable materials (scaffolds) in experimental studies of spinal trauma. The advantages and disadvantages of the described models are systematically analyzed in this review.

Stepwise construction of a metabolic network in Event-B: The heat shock response.

There is a high interest in constructing large, detailed computational models for biological processes. This is often done by putting together existing submodels and adding to them extra details/knowledge. The result of such approaches is usually a model that can only answer questions on a very specific level of detail, and thus, ultimately, is of limited use. We focus instead on an approach to systematically add details to a model, with formal verification of its consistency at each step. In this way, one obtains a set of reusable models, at different levels of abstraction, to be used for different purposes depending on the question to address. We demonstrate this approach using Event-B, a computational framework introduced to develop formal specifications of distributed software systems. We first describe how to model generic metabolic networks in Event-B. Then, we apply this method for modeling the biological heat shock response in eukaryotic cells, using Event-B refinement techniques. The advantage of using Event-B consists in having refinement as an intrinsic feature; this provides as a final result not only a correct model, but a chain of models automatically linked by refinement, each of which is provably correct and reusable. This is a proof-of-concept that refinement in Event-B is suitable for biomodeling, serving for mastering biological complexity.

[Metabolic and hormonal indices in rats with prolonged model of metabolic syndrome induced by high-carbohydrate and high-fat diet].

To develop the approaches for the prevention and treatment of metabolic syndrome (MS), a pathological state widespread in modern population, that involves a complex of metabolic and functional disorders, appropriate animal models of MS are required. One of these models is induced by the consumption of combined high-carbohydrate and high-fat (HC/HF) diet consisting of excess amount of easily digestible carbohydrates and saturated fats. At the same time, the character, temporal dynamics and severity of metabolic abnormalities in MS induced by HC/HF diet are still poorly understood. The aim of work was the characterization of metabolic changes in Wistar rats with MS induced by 10- and 15-week HC/HF diet that includes the consumption of 30% sucrose solution (instead of drinking water) and food rich in saturated fats. Rats that received HC/HF diet for 15 weeks had a number of features characteristic of MS, such as increased body weight and content of abdominal fat, hyperglycemia, hyperinsulinaemia, impaired glucose tolerance, insulin resistance, dyslipidemia, as well as the markers of impaired function of the cardiovascular system (hyperhomocysteinemia, the reduced level of vasodilator nitric oxide, the increased concentration of vasoconstrictor endothelin 1). In rats, which were on the diet for 10 weeks, the metabolic abnormalities were less pronounced, indicating an insufficiency of 10-week duration of HC/HF diet for MS induction. Thus, the model of MS induced by 15-week HC/HF diet has the characteristic features that allow for extrapolation of the obtained data to similar pathologic changes in human, and can be used to study the etiology and pathogenesis of MS and the search of effective ways of MS prevention and treatment.

Direct Bio-printing with Heterogeneous Topology Design.

Bio-additive manufacturing is a promising tool to fabricate porous scaffold structures for expediting the tissue regeneration processes. Unlike the most traditional bulk material objects, the microstructures of tissue and organs are mostly highly anisotropic, heterogeneous, and porous in nature. However, modelling the internal heterogeneity of tissues/organs structures in the traditional CAD environment is difficult and oftentimes inaccurate. Besides, the de facto STL conversion of bio-models introduces loss of information and piles up more errors in each subsequent step (build orientation, slicing, tool-path planning) of the bio-printing process plan. We are proposing a topology based scaffold design methodology to accurately represent the heterogeneous internal architecture of tissues/organs. An image analysis technique is used that digitizes the topology information contained in medical images of tissues/organs. A weighted topology reconstruction algorithm is implemented to represent the heterogeneity with parametric functions. The parametric functions are then used to map the spatial material distribution. The generated information is directly transferred to the 3D bio-printer and heterogeneous porous tissue scaffold structure is manufactured without STL file. The proposed methodology is implemented to verify the effectiveness of the approach and the designed example structure is bio-fabricated with a deposition based bio-additive manufacturing system.

Comparison of nonlinear models to describe growth in Blanco Orejinegro (BON) cattle / Comparación de modelos no lineales para describir el crecimiento en ganado Blanco Orejinegro (BON) / Comparação de modelos não lineares para descrever o crescimento em gado Blanco Orejinegro (BON)

BON cattle is an important genetic resource. It is necessary to describe the productive behavior of BON to improve the use of this breed. The objective of this study was to determine the model that best fit BON growth. Nonlinear models (Gompertz, logistic, Brody and von Bertalanffy) were compared to determine the one with the best fit and estimate the parameters for each model. Brody showed the best fit, with the lowest sum of squared errors (SQE) for both Akaike information criterion (AIC) and Bayesian information criterion (BIC). Brody parameters were β0 (mature weight: 590 kg) and β2 (maturity index: 0.00153 ± 0.0000042 kg/day). The maturity index was similar and in some cases higher to that found in some crosses of commercial beef cattle, highlighting the precocity of BON, which reaches about 52.9% maturity at 12 months. Additionally, the age BON reaches 75% maturity was approximately 708 days, which shows its precocity and growth potential. This results highlight the importance of this breed as a valuable genetic resource for cattle farming in the tropics.

El ganado BON constituye un recurso genético y ganadero de gran importancia, por lo que describir su comportamiento productivo es necesario para garantizar su utilización. El objetivo del presente trabajo fue determinar el modelo que mejor se ajustara al crecimiento del ganado BON, por lo que se compararon diferentes modelos no lineales (Gompertz, Logístico, de Brody y de Von Bertalanffy), con el fin de determinar el que mejor se ajusta y estimar los parámetros para cada uno. El modelo que mejor se ajustó al crecimiento del BON fue el de Brody, mostrando menores valores de sumatoria de cuadrados del error (SQE), de AIC y de BIC. Por otra parte, los parámetros hallados para el modelo de Brody fueron: β0 , interpretado como el peso maduro, de 590 kg y el parámetro β2 , correspondiente con el índice de madurez, de 0,00153 ± 0,0000042 kg/día. El índice de madurez fue similar y en algunos casos superior al encontrado en algunos cruces y ganados de carne comerciales, lo que resalta la precocidad que presenta el ganado BON, que alcanza aproximadamente 52,9% de madurez a los 12 meses. Adicionalmente, se encontró que la edad a la cual el BON alcanza el 75% de madurez fue de 708 días aproximadamente, lo que muestra su precocidad y capacidad de crecimiento. Lo expuesto anteriormente resalta la importancia del ganado BON como un recurso genético y productivo para los programas de producción bovina en el trópico.

O gado BON, constitui um recurso genético e de produção de grande importância, pelo qual, descrever seu comportamento e desempenho produtivo e mostrar suas fortalezas é necessário para garantir sua utilização. O objetivo do presente trabalho foi determinar o modelo que melhor tivesse ajuste não linear (Gompertz, Logístico, de Brody e de Von Bertalanffy), com o fim de determinar o modelo que melhor se ajustasse e estimar os parâmetros para cada um deles. O modelo que melhor se ajustou ao crescimento do gado BON foi o de Brody, apresentando menores valores na somatória de quadrados do erro (SQE), de AIC e de BIC. Por outro lado, os parâmetros encontrados para o modelo de Brody foram: β0, interpretado como o peso maduro, de 590 kg e o parâmetro β2, que corresponde com o índice de maturidade, de 0,00153 ± 0,0000042 kg/dia. O índice de maturidade foi similar e em alguns casos até superior ao encontrado em alguns cruzamentos e gados de corte não registrados, o que ressalta a precocidade que apresenta o gado BON, que consegue aproximadamente 52,9% de maturidade aos 365 dias (12 meses). Adicionalmente, encontrou-se que a idade na qual o gado BON consegue o 75% de maturidade foi de 708 dias (23,6 meses) aproximadamente, o que demostra sua precocidade e capacidade de crescimento. O exposto anteriormente ressalta a importância do gado BON como um recurso genético com boas qualidades produtivas e reprodutivas para os programas de produção bovina no tropico.

Comparison of two stretching methods and optimization of stretching protocol for the piriformis muscle.

Piriformis syndrome is an uncommon diagnosis for a non-discogenic form of sciatica whose treatment has traditionally focused on stretching the piriformis muscle (PiM). Conventional stretches include hip flexion, adduction, and external rotation. Using three-dimensional modeling, we quantified the amount of (PiM) elongation resulting from two conventional stretches and we investigated by use of a computational model alternate stretching protocols that would optimize PiM stretching. Seven subjects underwent three CT scans: one supine, one with hip flexion, adduction, then external rotation (ADD stretch), and one with hip flexion, external rotation, then adduction (ExR stretch). Three-dimensional bone models were constructed from the CT scans. PiM elongation during these stretches, femoral neck inclination, femoral head anteversion, and trochanteric anteversion were measured. A computer program was developed to map PiM length over a range of hip joint positions and was validated against the measured scans. ExR and ADD stretches elongated the PiM similarly by approximately 12%. Femoral head and greater trochanter anteversion influenced PiM elongation. Placing the hip joints in 115° of hip flexion, 40° of external rotation and 25° of adduction or 120° of hip flexion, 50° of external rotation and 30° of adduction increased PiM elongation by 30-40% compared to conventional stretches (15.1 and 15.3% increases in PiM muscle length, respectively). ExR and ADD stretches elongate the PiM similarly and therefore may have similar clinical effectiveness. The optimized stretches led to larger increases in PiM length and may be more easily performed by some patients due to increased hip flexion.

Comparison of methods to determine total edible meat in the male Holstein cattle carcass / Comparación de métodos para determinar el total de carne aprovechable en la canal de machos Holstein / Comparação de métodos para determinar o total de carne aproveitável na carcaça de bezerros holandeses

Background: the objective of beef cattle farming is to produce young animals with adequate proportions of meat, fat and bone. In many countries, including Colombia, research on carcass quality and performance has focused on Bos indicus, resulting in little information available on Bos taurus breeds, particularly Holstein. Objective: to compare several methods for determining total edible meat (TEM) in the carcass of intact Holstein males slaughtered at 330 kg and 26 months of age. Methods: the TEM was determined by the direct method (true-TEM), and also by two indirect methods based on equations. One equation involving carcass measurements was proposed by the Instituto de Ciencia y Tecnología de Alimentos (ICTA). The other equation is based on the muscle proportion between ribs 9-11. Results: variance analysis detected statistically significant difference (p<0.05) among all methods. The relationship between true-TEM and that estimated by indirect methods was high (r =0.9756). However, according to Bland-Altman interchangeability analysis, the direct method is not interchangeable with the prediction by ICTA. The TEM variability obtained by the three methods was similar (average CV = 18.15%). Conclusion: according to this study, the method based on the muscle proportion between ribs 9-11 is useful for estimating TEM in Holstein bull carcasses.

Antecedentes: el objetivo de la ganaderia de carne es producir animales jóvenes para sacrificio, con proporciones adecuadas de carne, hueso y grasa. En países como Colombia, las investigaciones sobre calidad y rendimiento en canal se han concentrado en ganado Bos indicus, existiendo muy poca información sobre razas Bos taurus, particularmente Holstein. Objetivo: comparar varios métodos para determinar el total de carne aprovechable (TEM) en la canal de machos Holstein enteros, sacrificados a un peso aproximado de 330 Kg y 26 meses de edad. Métodos: la determinación del TEM se realizó mediante el método directo (TEM real) y dos métodos indirectos basados en el empleo de ecuaciones, a saber, la ecuación propuesta por el Instituto de Ciencia y Tecnología de Alimentos (ICTA) utilizando mediciones realizadas en la canal, y la basada en la proporción de músculo presente en la sección comprendida entre las costillas 9 y 11. Resultados: el análisis de varianza permitió detectar diferencia estadística significativa (p<0,05) entre todos los métodos evaluados. La relación entre el TEM real y el estimado desde los métodos indirectos fue alta (r =0,9756). Sin embargo, el análisis de intercambiabilidad de Bland-Altman permitió concluir que el método directo no es intercambiable con la predicción realizada a partir del sistema ICTA. La variabilidad del TEM obtenido por los tres métodos fue similar (CV medio =18,15%). Conclusión: de acuerdo con este estudio, el método basado en la proporción de músculo entre las costillas 9 y 11 es útil para estimar el TEM en la canal de machos Holstein.

Antecedentes: o objetivo do sector pecuário é produzir animais jovens, que assegurem proporções adequadas de carne, osso e gordura no momento do abate. Na Colômbia, as pesquisas sobre qualidade e rendimento da carcaça têm-se centrado em gado Bos indicus, e pouca informação existe na raça Holstein. Objetivo: comparar vários métodos de determinação do total de carne aproveitável (TEM) na carcaça de bezerros não castrados Holstein, abatidos, aproximadamente, aos 330 Kg de peso e 26 meses de idade. Métodos: o TEM foi determinado através do método directo (TEM real) e de dois métodos indirectos baseados no uso de equações, a saber, a equação proposta pelo Instituto de Ciencia y Tecnología de Alimentos (ICTA) usando mensurações feitas na carcaça, e a equação baseada na proporção de músculo presente na secção entre a 9ª y 11ª costela. Resultados: a análise de variância permitiu detectar diferença estatisticamente significante (p<0,05) entre todos os métodos avaliados. A relação entre o TEM real e o predito desde os métodos indirectos foi elevada (r = 0,9756). No entanto, a análise de Bland-Altman permitiu concluir que o método directo não pode se substituir pela predição feita a partir do sistema ICTA. A variabilidade do TEM obtido desde os três métodos foi similar (média CV =18.15%). Conclusão: de acordo com este estudo, o método baseado na proporção de músculo entre a 9ª y 11ª costela é útil para estimar TEM na carcaça de machos Holstein.

Estimation of genetic parameters for test-day milk yield in first calving buffaloes / Estimación de parámetros genéticos para producción de leche en el día de control en búfalas de primer parto / Estimação de parâmetros genéticos para produção do leite no dia do controle em búfalas de primeiro parto

Background: the milk yield records measured along lactation provide an example of repeated measures; the random regression models are an appealing approach to model repeated measures and to estimate genetic parameters. Objective: to estimate the genetic parameters by modeling the additive genetic and the residual variance for test-day milk yield in first calving buffaloes. Methods: 3,986 test-day data from 1,246 first lactations of crossbred buffalo daughters of 23 sires and 391 dams between 1997 and 2008 from five farms were used. The model included the genetic and permanent environment additive as the random effect and the contemporary group (year, month of test-day) and age at calving as covariable (linear) fixed effects. The fixed (third order) and random (third to ninth order) regressions were obtained by Legendre polynomials. The residual variances were modeled with a homogeneous structure and various heterogeneous classes. The variance components were estimated using the WOMBAT statistical program (Meyer, 2006). Results: according to the likelihood ratio test, the best model included four variance classes, considering Legendre polynomials of the fourth order for permanent environment and additive genetic effects. The heritabilities estimates were low, varying from 0.0 to 0.14. The estimates of genetic correlations were high and positive among PDC1 and PDC8, except for PCD9, which was negative. This indicates that for any of the selection criteria adopted, the indirect genetic gain is expected for all lactation curves, except for PCD9. Conclusion: heterogeneity of residual variances should be considered in models whose goal is to examine the alterations of variances according to day of lactation.

Antecedentes: los registros de producción de leche medidos a lo largo de la lactancia son un ejemplo de medidas repetidas, los modelos de regresión aleatoria presentan un enfoque atractivo para modelar medidas repetidas y para estimar parámetros genéticos. Objetivo: estimar parámetros genéticos a través de la modelación de la varianza genética y residual para producción de leche en el día de control en búfalas de primer parto. Métodos: fueron analizados 3986 controles de producción de leche en la primera lactancia de 1246 búfalas, hijas de 391 hembras y 23 toros, durante los años 1997 hasta 2008 en 5 fincas. El modelo incluyó como efectos aleatorios genético aditivo y de ambiente permanente, como efectos fijos grupo contemporáneo compuesto por mes, año de control y la covariable de la edad de la búfala al parto (lineal). Las regresiones fijas (3er orden) y aleatorias (3er a 9no orden) fueron obtenidas mediante polinomios de Legendre. Las varianzas residuales fueron modeladas con una estructura homogénea y varias clases heterogéneas. Los componentes de varianza fueron estimados utilizando el programa WOMBAT. Resultados: de acuerdo con la prueba de la razón de verosimilitud, el mejor modelo fue con 4 clases de varianzas residuales, siendo considerado un polinomio de Legendre de cuarto orden para el efecto de ambiente permanente y genético aditivo. Las heredabilidades fueron bajas, variando desde 0,00 hasta 0,14. Las correlaciones genéticas fueron altas y positivas entre los PDC1 a PDC8, excepto en el PDC9 que fue negativo con respecto a los demás controles. Conclusiones: es necesario considerar la heterogeneidad de varianzas residuales en los modelos estudiados, con el fin de modelar los cambios en las variaciones respecto a los días en lactancia.

Antecedentes: os registros da produção do leite medidos ao longo da lactação, apresentam um exemplo de medidas repetidas. Os modelos de regressão aleatória apresentam abordagem atraente para modelar medidas repetidas e estimar parâmetros genéticos. Objetivo: estimar parámetros genéticos mediante a modelação das variâncias genéticas e residual da produção do leite no dia do controle em búfalas de primeiro parto. Métodos: foram analisados 3986 controles de produção de leite em primeiras lactações de 1246 búfalas, filhas de 391 fêmeas e 23 touros, entre 1997 e 2008 em 5 fazendas. No modelo foram incluídos como efeitos aleatórios o genético aditivo e ambiente permanente, e como fixos o grupo contemporâneo (mês e ano de controle) e a covariável a idade da búfala ao parto (Lineal). As regressões fixas (3° ordem) e aleatórias (3° a 9° ordem) foram obtidas mediante polinômios ortogonais de Legendre. As variâncias residuais foram modeladas mediante estruturas homogêneas e diferentes classes heterogêneas. Os componentes de variância foram estimadas mediante o software WOMBAT. Resultados: de acordo com a prova da máxima verossimilhança, o melhor modelo foi com 4 classes de variâncias residuais, sendo considerado polinômios de Legendre de quarto ordem para o efeito de ambiente permanente e genético aditivo. As herdabilidades foram baixas, variando desde 0,00 até 0,14. As correlações genéticas foram altas e positivas entre o PDC1 e PDC8, a exceção do PDC9 que apresentou valores negativos com respeito aos outros controles. Conclusões:é necessário considerar heterogeneidade de variâncias nos modelos estudados, tentando modelar as mudanças nas variações respeito aos dias em lactação.

Stereolithographic biomodeling of equine ovary based on 3D serial digitizing device

The 3D internal structure microscopy (3D-ISM) was applied to the equine ovary, which possesses peculiar structural characteristics. Stereolithography was applied to make a life-sized model by means of data obtained from 3D-ISM. Images from serially sliced surfaces contributed to a successful 3D reconstruction of the equine ovary. Photopolymerized resin models of equine ovaries produced by stereolithography can clearly show the internal structure and spatial localizations in the ovary. The understanding of the spatial relationship between the ovulation fossa and follicles and/or corpora lutea in the equine ovary was a great benefit. The peculiar structure of the equine ovary could be thoroughly observed and understood through this model.

Modelación de las funciones de crecimiento aplicadas a la producción animal / Modelação das funções do crescimento aplicadas a lá produção animal / Modeling of growth functions applied to animal production

El crecimiento animal es uno de los aspectos más importantes al momento de evaluar la productividad en las explotaciones dedicadas a la producción de carne y en algunos casos es usado como criterio de selección, sin embargo, debe tenerse en cuenta que el crecimiento no se debe exclusivamente a factores genéticos sino también, a efectos ambientales. Para medir el crecimiento animal se han usado diferentes modelos matemáticos lineales e no lineales, eligiéndolos por su bondad de ajuste y la facilidad de interpretación biológica de sus parámetros. Recientemente se han usado modelos mixtos en los que sus parámetros están compuestos de efectos fijos y efectos aleatorios, representando los valores esperados y la varianza de los primeros, respectivamente, lo que permite evaluar la variabilidad de las diferentes curvas entre los individuos de una población, así como la covarianza entre los parámetros. Los criterios más usados para elegir la curva que mejor ajusta a los datos son: el coeficiente de determinación, el porcentaje de curvas significativas y atípicas encontradas para cada función; además se pueden aplicar criterios como el criterio de información Akaike y el criterio de información Bayesiano. El objetivo del presente trabajo es indicarle al lector una aplicación de los modelos no lineales y no lineales mixtos en el análisis del crecimiento animal.

Animal growth is one of the most important aspect for evaluating animal productivity in beef cattle enterprises and in some cases it is used as a criterion of selection, nevertheless, the fact that animal growth is not exclusively due to genetic factors but also, to environmental effects must be keep in mind. Measurement of animal growth have been performed by lineal and no-lineal mathematical models, choosing they for their fitness of adjustment and the feasibility for biological interpretation of their parameters. Recently the mixed models have been used in which their parameters are composed of fixed and random effects representing the expected values and variance of the fixed ones, respectively, which permits to evaluate the variability of different curves between individuals of a population, as well as the covariance between parameters. The most used criteria for selection of the curve that best fit data are: determination coefficient and the percent of significant and atypical curves found for each function. In addition, other models as the Akaike information criteria and Bayesian information criteria can also be applied. The objective of the present review is to provide the criteria for application of linear and non linear models in analyzing animal growth.

O crescimento animal é um dos aspectos mais importantes no momento de avaliar a produtividade nos sistemas de produção dedicados á produção de carne. Em alguns dos casos é usado como critério de seleção, mais é necessário ter em conta que depende de fatores ambientais e genéticos. Para medir o crescimento animal tem-se utilizado diferentes modelos matemáticos lineares e não lineares, entre outros, os quais a escolha do melhor modelo é realizada pela qualidade do ajuste e da interpretação biológica de seus parâmetros. Recentemente, tem-se utilizado modelos mistos nos quais os parâmetros estão compostos por efeitos fixos e aleatórios, representando os valores esperados e a variância dos primeiros, respectivamente, o que permite avaliar a variabilidade das diferentes curvas entre os indivíduos de uma população, assim como a covariância entre os parâmetros. Os critérios mais utilizados para escolher a curva que melhor ajuste os dados são: o coeficiente de determinação, a porcentagem de curvas significativas e atípicas encontradas para cada função; alem do mais, podem-se aplicar critérios como o critério de informação de Akaike e o critério de informação Bayesiano. O objetivo do presente trabalho foi indicar-lhe ao leitor uma aplicação dos modelos não lineares e não lineares mistos na análise do crescimento animal.

Modelación de funciones de crecimientoaplicadas a la producción animal / Modeling of growth functions applied to animal production

El crecimiento animal es uno de los aspectos más importantes al momento de evaluar la productividaden las explotaciones dedicadas a la producción de carne y en algunos casos es usado como criterio deselección, sin embargo, debe tenerse en cuenta que el crecimiento no se debe exclusivamente a factoresgenéticos sino también, a efectos ambientales. Para medir el crecimiento animal se han usado diferentesmodelos matemáticos lineales, no lineales y logarítmicos, entre otros, eligiéndolos por su bondad de ajustey la facilidad de interpretación biológica de sus parámetros. Recientemente se han usado modelos mixtosen los que sus parámetros están compuestos de efectos fijos y efectos aleatorios, representando los valoresesperados y la varianza de los primeros, respectivamente, lo que permite evaluar la variabilidad de lasdiferentes curvas entre los individuos de una población, así como la covarianza entre los parámetros. Loscriterios más usados para elegir la curva que mejor ajusta a los datos son: el coeficiente de determinación,el porcentaje de curvas significativas y atípicas encontradas para cada función; además se pueden aplicarcriterios como el criterio de información Akaike y el criterio de información Bayesiano. El objetivo delpresente trabajo es indicarle al lector una aplicación de los modelos no lineales y no lineales mixtos en elanálisis del crecimiento animal.

Animal growth is one of the most important aspect for evaluating animal productivity in beef cattleenterprises and in some cases it is used as a criterion of selection, nevertheless, the fact that animalgrowth is not exclusively due to genetic factors but also, to environmental effects should be keep inmind. Measurement of animal growth have been performed by several logarithmic, not lineal, lineal, andmathematical models, having as selection criteria its fitness of adjustment and the feasibility for biologicalinterpretation of their parameters. Recently the mixed models have been used in which their parametersare composed of fixed and random effects representing the expected values and variance of the fixedones, respectively, which permits to evaluate the variability of different curves between individuals of apopulation, as well as the covariance between parameters. The most used criteria for selection of the curvethat best fit data are: determination coefficient and the percent of significant and atypical curves foundfor each function. In addition, other models as the Akaike information criteria and Bayesian informationcriteria can also be applied. The objective of the present review is to provide the criteria for application oflinear and non linear models when analyzing animal growth.