Academic literature on the topic 'Gompertz growth'

We compared the Gompertz model, the generalized Gompertz model, the Piantadosi model, the autostimulation model and the polynomials for the power to predict growth of multicellular tumor spheroids as paradigms of the prevascular phase of tumor growth. For the comparison of models we developed a criterion that established the Gompertz model as the model with the best prediction power. The prediction power of the remaining models was ranked in declining order: the generalized Gompertz model; the mutually indistinguishable Piantadosi model and the autostimulation model; and the polynomials. The ranking of models was not affected by the applied minimization criteria of weighted least squares, unweighted least squares and fitting to logarithmically transformed data, but the prediction power was affected by these criteria. The best predictions were obtained by weighted least squares, closely followed by fitting to logarithmically transformed data. The unweighted least-squares minimization was much less applicable for prediction (and description) of growth.

Growth curves of the Morada Nova sheep males and females were described using nonlinear models and the relationships between body weight and thoracic circumference were evaluated. Altogether 1516 repeated measures of body weight and thoracic circumference of the Morada Nova sheep (668 males and 848 females) taken since birth till 730 days of age were used. The Brody, Richards, von Bertalanffy, Gompertz, and Logistic models have been tested. The Fisher’s test (F) was used to verify the differences (P < 0.05) in growth curves between males and females. The Gompertz model presented a significant difference (P < 0.001) for growth curve parameters between males (asymptotic weight (A) = 40.5 kg and maturing rate (k) = 0.0043 kg/day) and females (A = 36.44 kg and k = 0.0028 kg/day). The relationships between body weight and thoracic circumference presented R² above 0.7 and a high significance (P < 0.0001) for all categories, showing that the thoracic circumference may be a good indicator of body weight. In addition, a significant effect (P < 0.05) of the relationship between thoracic circumference and prediction of animal’s body weight was verified using the models of linear, quadratic, and cubic regression. Among the models studied, the Gompertz model presented the best fit and biological interpretation. Furthermore, the Gompertz model indicated the need to separate animals by sex in order to properly meet nutritional requirements and determine adequate slaughter age. Thoracic circumference can be used to predict animal body weight with a high accuracy.

The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.

Soybean plants have limited growth with a planting period of 12 weeks, which causes the observed sample to be very small. A small sample of soybean plant growth observations can be bias causes in the conclusion of prediction results on soybean plant growth. The purpose this study is to apply the bootstrap resampling technique in Gompertz growth model which overcomes residual distribution with small samples, the research data was taken from soybean plant growth in four varieties with four spacing treatments, five replications and twelve weeks (long planting period). Gompertz growth model uses nonlinear least squares method in estimating parameters with Levenberg–Marquardt iteration. The value of the Gompertz model after resampling bootstrap has no significant difference. The adjusted R2 value of 0.96 is close to 1. This means that the total diversity of plant heights can be explained by the Gompertz model of 96 percent. Judging from the graph of predictions of soybean plant growth before resampling and after resampling coincide with each other it can also be seen in the initial growth values before resampling 14, 05 and 14.18, the maximum growth values are 55.13 and 55.60. Bootsrap resampling technique can overcome residual normality in the Gompertz growth model, but does not change the information in the initial data.

The objectives of this study were to adjust the Gompertz and logistic models to fit the fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars and indicate the model that best describes the growth in spring. Cultivars Ceres, Gloriosa, Grandes Lagos, and Rubinela were grown in protected environment and in soilless system, in the spring of 2016 and 2017. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters were weighed every four days until beginning of flowering. The Gompertz and logistic models were adjusted as a function of accumulated thermal sum. The parameters of the Gompertz and logistic models and their confidence intervals were estimated, the assumptions of the models were verified, the goodness-of-fit measures and critical points were calculated, and the parametric and intrinsic nonlinearities quantified. The logistic and Gompertz growth models fitted well to fresh and dry leaf and shoot matters of cultivars Ceres, Gloriosa, Grandes Lagos, and Rubinela, under spring conditions. The logistic model is the most suitable to describe the growth of lettuce cultivars.

The growth patterns of two murine and eight human tumors, bilaterally implanted into subcutaneous tissue of groups of recipient mice, were studied. A Gompertz equation was fitted to experimental data for each individual implant and the Gompertz parameters were utilized as quantitative growth characteristics. The relative roles of the tumor-implanted flank (right versus left), of the individual host and of the tumor were analyzed by the paired t-test, simple linear regression model, one-way and two-way analysis of variance. Sixty pairs of Gompertz curves were obtained in seventy animals. Heterogeneity was the main characteristic of the growth pattern in all tumors under study, with a wide variability among the Gompertz parameters. Statistical analysis of experimental data showed that only the tumor systematically influenced the growth characteristics, whereas neither the tumor-implanted flank nor the individual host played a significant role. These results have both theoretical and practical implications.

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus while developing the simplest discrete fractional variational theory. Some applications of the theory to tumor growth are also studied. The first chapter is a brief introduction to discrete fractional calculus that presents some important mathematical functions widely used in the theory. The second chapter shows the main fractional difference and sum operators as well as their important properties. In the third chapter, a new proof for Leibniz formula is given and summation by parts for discrete fractional calculus is stated and proved. The simplest variational problem in discrete calculus and the related Euler-Lagrange equation are developed in the fourth chapter. In the fifth chapter, the fractional Gompertz difference equation is introduced. First, the existence and uniqueness of the solution is shown and then the equation is solved by the method of successive approximation. Finally, applications of the theory to tumor and bacterial growth are presented.

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Objetivou-se avaliar o efeito de diferentes nÃveis de fibra em detergente neutro (FDN) nas raÃÃes de frangas de duas linhagens comerciais de aves de postura, no perÃodo de 7 a 17 semanas de idade, sobre a curva de crescimento corporal e Ãssea e a deposiÃÃo de componentes na carcaÃa e nos ossos. Foram utilizadas 648 aves de cada linhagem, distribuÃdas em um delineamento experimental inteiramente casualizado, em esquema fatorial 3 x 2, composto de trÃs nÃveis de FDN (14,5; 16,5 e 18,5%) e duas linhagens (LOHMAN LSL e HY LINE BROWN), com quatro repetiÃÃes de 54 aves. Semanalmente, foram avaliados o peso corporal e das penas, peso e comprimento dos ossos (tÃbia e fÃmur) e a composiÃÃo corporal e dos ossos em proteÃna, cinzas e Ãgua. As curvas de crescimento e deposiÃÃo foram determinadas aplicando-se os dados na funÃÃo de Gompertz. NÃo houve interaÃÃo entre linhagem e nÃvel de FDN da raÃÃo, para os parÃmetros da equaÃÃo de Gompertz determinados, para todas as caracterÃsticas avaliadas. Os nÃveis de FDN da raÃÃo influenciaram significativamente nos parÃmetros da curva de crescimento para peso corporal e deposiÃÃo de Ãgua, de modo que o nÃvel de 14,5% de FDN possibilitou maior peso corporal e de deposiÃÃo de Ãgua à maturidade (Pm), maior idade de mÃximo crescimento (t*) e menor taxa de maturidade (b) que os demais nÃveis testados. Entretanto, os parÃmetros da curva de crescimento para o peso e o comprimento da tÃbia e do fÃmur, assim como, as estimativas dos parÃmetros para a deposiÃÃo de Ãgua nos ossos e as deposiÃÃes de proteÃna e matÃria mineral na carcaÃa e nos osso nÃo foram influencias significativamente pelo nÃvel de FDN da raÃÃo. Entre as linhagem, observou-se que as aves leves, apresentaram menor taxa de maturidade (b) e menor peso à maturidade (Pm), sem apresentar diferenÃas significativas na idade de mÃximo crescimento (t*). Os parÃmetros para a deposiÃÃo de proteÃna e cinzas na carcaÃa nÃo variaram significativamente, enquanto, as aves leves apresentaram menores estimativas de taxa de maturidade (b) para a deposiÃÃo de Ãgua corporal em relaÃÃo Ãs aves semipesadas. NÃo houve diferenÃa entre as linhagens para os parÃmetros estimados para o comprimento da tÃbia e do fÃmur, peso da tÃbia, deposiÃÃo de proteÃna e cinzas da tÃbia. Entretanto, para o peso do fÃmur, deposiÃÃo de proteÃna no fÃmur e deposiÃÃo de Ãgua na tÃbia, as aves leves apresentaram maior peso à maturidade (Pm) e valor da idade de mÃximo crescimento (t*) e menor valor na taxa de maturidade (b) em comparaÃÃo as aves semipesada, as quais apresentaram maior peso à maturidade (Pm) e valor da idade de mÃximo crescimento (t*) e menor valor na taxa de maturidade (b) em comparaÃÃo as aves leves para deposiÃÃo de Ãgua no fÃmur. Assim, o nÃvel de FDN da raÃÃo de recria pode ser utilizado para modificar a curva de crescimento das frangas leves e semipesadas, podendo-se controlar o ganho de peso corporal pelo aumento do seu nÃvel na raÃÃo em nÃvel superior a 14,5%, sem alterar o crescimento dos ossos e a deposiÃÃo de Ãgua, matÃria mineral e proteÃna na carcaÃa e nos ossos atà o nÃvel de 18,5%. Embora as poedeiras semipesadas da linhagem avaliada apresentem maior potencial de crescimento corporal e das penas em relaÃÃo Ãs leves, essa aves sÃo semelhantes quanto à proporÃÃo de proteÃna e matÃria mineral depositada na carcaÃa e divergem no desenvolvimento dos ossos quanto ao peso e deposiÃÃo de Ãgua e proteÃna no fÃmur.
The objective was to evaluate the effect of using different levels of neutral detergent fiber (NDF) in diets for hens of two commercial layer-hen strains from 7 to 17 weeks of age on the growth curve and deposition of body components and bones. A total of 648 birds from each strain were distributed in a completely randomized design in a 3 Ã 2 factorial arrangement consisting of three levels of NDF and two strains, with four replicates of 54 birds. The tested NDF levels were 14.5, 16.5 and 18.5%. Additionally, live weight, feather weight, body composition of protein, ash and water, bones weight, bones length and bones composition of protein, ash and water were evaluated. Growth curves were determined by applying the data on Gompertz function. According to the results, there was no interaction among factors, strain and NDF levels for the parameters of the equation of Gompertz determined for all evaluated traits. The NDF levels of the diet affected the estimates of weight at maturity and water deposition in the carcass. The level of 14.5% NDF allowed for greater weight at maturity (Wm), greater age at maximum growth (t*) and lower maturity rate (b) than the other tested levels. There was no influence of NDF levels tested on the parameters of the growth curve for weight and length of the tibia and femur (P <0.05). There was no influence of NDF levels tested on the estimates of the parameters of the Gompertz equation for the composition of water, protein and ash of the tibia and fÃmur (P <0.05). The level of NDF in the ration of growing can be used to modify the growth curve of pullets, being able to control the body weight gain by increasing its level in the ration without changing the deposition of water, ash and protein in the carcass. Pullets fed diets containing up to 18.5% inclusion of NDF, during 7-17 weeks of age, showed no changes in the curves of growth and nutrient deposition in the tibia and femur.

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Modelos de crescimento podem servir como ferramenta de planejamento de plantios florestais para o serviço público, produtores e investidores. O presente trabalho utilizou o modelo de crescimento Gompertz para analisar e comparar curvas médias de crescimento em volume de madeira com casca e sem casca por árvore de dois clones distintos de Eucalyptus grandis x Eucalyptus urophylla em diferentes densidades de plantio: 1,5m x 1,5m, 3,0m x 0,75m, 3,0m x 1,0m, e 3,0m x 1,9m. Os dados foram coletados a partir de parcelas permanentes localizadas em plantios da empresa Duratex Florestal LTDA no município de Estrela do Sul - MG em quatro idades: 24, 36, 48 e 60 meses. As análises seguiram duas abordagens. A primeira abordagem foi pela curva de crescimento utilizando o modelo Gompertz, do qual foram ajustadas as curvas médias de crescimento. Os parâmetros estimados de interesse foram a velocidade máxima de crescimento no ponto de inflexão e a abscissa da inflexão. A segunda abordagem foi pela modelagem do máximo volume com e sem casca amostrais através de modelos lineares generalizados. O efeito de clone e espaçamento foi avaliado e as médias dos maiores volumes amostrais foram, também, comparadas entre tratamentos. Os dados observados de volume com e sem casca por árvore permitiram bons ajustes do modelo de Gompertz, com o objetivo de descrever o crescimento destas variáveis ao longo do tempo. Foi possível identificar as fases juvenil, que vai até o ponto de inflexão da curva e de maturidade, que vai do ponto de inflexão até o ponto de máxima tangência nas curvas projetadas para quase todos os tratamentos. Porém, o período de dados coletados não foi o suficiente para se modelar a curva de crescimento por árvore até a senescência da curva, mesmo para os espaçamentos mais adensados. As maiores médias de velocidade máxima de crescimento individual foram encontradas no espaçamento mais amplo, 3,0m x 1,9m, para ambos os clones, assim como as maiores médias dos volumes individuais máximos com e sem casca. O clone c1 apresentou maiores médias dos volumes individuais máximos com e sem casca por árvore observados que o clone c2. A idade do plantio se mostrou essencial na discussão sobre a produtividade de diferentes arranjos de plantio. Portanto, este estudo confirma a importância do uso de curvas de crescimentos em estudos na área florestal.
Growth models can serve as a tool for forest management plans for public service, producers and investors. The present work used the Gompertz growth model to analyze and compare individual volume growth curves of three distinct clones of Eucalyptus grandis x Eucalyptus urophylla at different planting densities. Four different spacings densities were evaluated, 3.0m x 0.75m, 1.5m x 1.5m, 3.0m x 1.9m and 3.0m x 1.0m, for each clone at two different sites, São Paulo and Minas Gerais General. The data were collected from permanent plots at four ages: 24, 36, 48 and 60 months. The analyzes followed two approaches. The first approach was to adjust the growth curve using the Gompertz model to the volume data. The estimated parameters of interest, analyzed later, were the maximum velocity of growth at the inflection point and the abscissa of the inflection point. For each estimated parameter, generalized linear models were adjusted to detect the effect of location, clone and spacing. Thus, the adjustment was made for each portion of the treatments and the means of the estimated parameters were compared. The second approach was the modeling of the largest volume observed through generalized linear models. The effect of site, clone and spacing were evaluated and the means of the largest sample volumes were compared between treatments. The observed data of volume with and without bark per tree allowed good adjustments of the Gompertz model, in order to describe the growth of these variables over time. It was possible to identify the juvenile phase, which goes from first years to the point of inflection, and the maturity phase, which goes from the point of inflection to the point of maximum tangency, for almost all treatments. However, the period of data collection was not sufficient to get the curves to the senescence phase, even for the denser spaces. The spacing density 3.0m x 1.9m resulted on the higher averages of maximum individual growth velocity and on the higher mean values of the observed volumes with and without bark. Clone c1 presented higher mean values of the observed volumes with and without bark per tree than clone c2. The stand age was shown to be essential in the discussion of a productivity of different densities arrangements. Therefore, this study confirms the importance of the use of growth curves in studies in forestry.

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A eficácia de um programa nutricional depende do conhecimento a respeito do potencial genético de crescimento da ave, por ser esta a forma racional de calcular as exigências nutricionais e predizer o consumo de alimento. Neste sentido, os modelos fatoriais integrados as curvas de crescimento de aves auxilia no estabelecimento ou avaliação de programas alimentares específicos. Por serem modelos dinâmicos, possibilitam calcular a ingestão de acordo com o padrão de crescimento da linhagem ao longo do tempo. Tradicionalmente, a avaliação da composição corporal é feita por abate comparativo que impossibilita o acesso rápido às informações e inviabiliza o estudo das variações das caraterísticas estudadas no decorrer do tempo no mesmo animal. Uma alternativa é a técnica de absorciometria por duplo feixe de raios-X (DXA) que permite avaliar in vivo a composição corporal das aves em tempo real sem a necessidade de sacrifica-la, conciliando interesses sociais e científicos. Com base nisso, objetivou-se neste trabalho descrever o potencial de crescimento do corpo e componentes corporais de poedeiras Dekalb e Lohmann (White e Brown) meio da função Gompertz, com a composição corporal tomado pela técnica DXA nas mesmas aves no decorrer do crescimento. Foram utilizadas 360 poedeiras das linhagens Lohmann e Dekalb distribuídas em delineamento inteiramente ao acaso, com quatro tratamentos (linhagens) e seis repetições com 15 aves. As aves foram alojadas em galpão experimental dotado de gaiolas em sistema piramidal, controle de temperatura automatizado, comedouro tipo calha e bebedouro nipple. O programa alimentar adotado foi ad libitum composto por cinco dietas segundo a idade formuladas de forma a atender as exigências nutricionais das linhagens, garantindo que não houvesse nenhum nutriente limitante. Para descrição do crescimento uma ave por unidade experimental foi tomada aleatoriamente, identificada, e avaliadas do 1º ao 126º dia de idade, nas idades 1, 14, 28, 56, 70, 77, 84, 98, 112 e 126 dias, foram escaneadas para estimar o conteúdo mineral ósseo, tecido magro e gordo, por meio da absorciometria por duplo feixe de Raios X (DXA), usando modelo Hologic-QDR®. Concomitantemente, fez-se um estudo para relacionar dados de composição obtidos pelo DXA e por análise química do corpo livre de penas (CLP), Esses dados foram submetidos à análise de variância (ANOVA), sendo constatadas diferenças na quantificação da composição corporal pelas diferentes técnicas. Devido à essas diferenças, foram ajustadas regressões para cada componente químico do corpo, assim foram gerados equações de correção dos dados obtidos pelo DXA em referencia ao método químico, usando para isso aves Dekalb Brown, seguindo as mesmas idades e procedimentos do estudo de crescimento. A função Gompertz foi utilizada para descrever o crescimento do corpo e componentes químicos para cada linhagem. A mensuração da composição corporal nas mesmas aves ao longo do tempo pelo DXA auxiliou na redução do erro na avaliação do crescimento de poedeiras. As linhagens avaliadas neste estudo apresentaram diferenças no crescimento do corpo, penas e componentes entre se. E os parâmetros de crescimento aqui descritos condizem com os encontrados na literatura, e auxiliará no aperfeiçoamento de modelos de calculo de exigências nutricionais, melhorando a eficácia de programas alimentares.
The efficacy of a nutritional program depends on knowledge about the bird's genetic potential for growth, since this is the rational way of calculating nutritional requirements and predicting food consumption. In this sense, the factorial models integrated the growth curves of birds assists in the establishment or evaluation of specific food programs. Because they are dynamic models, they make it possible to calculate the feed intake according to the growth pattern of the lineage over time. Traditionally the evaluation of the body composition is made by comparative slaughter, impossibility the quick access to the information and to study the variations of the characteristics studied in the course of time in the same animal. An alternative is the X-ray absorptiometry technique (DXA) that allows in vivo evaluation of the body composition of the birds without the need to sacrifice them reconciling social and scientific interests. Based on this, the objective of this work was to describe the growth potential of the body and body components of laying hens Dekalb and Lohmann (White and Brown) through of the Gompertz function, with the body composition taken by the DXA technique in the same birds during the growth. A total of 360 laying hens of the Lohmann and Dekalb strains were used in a completely randomized design, with four treatments (strains) and six replicates of 15 birds. The birds were housed in experimental shed with cages in pyramidal system and with automated temperature control. Diets were provides ad libitum and composed of five diets according to age formulated to meet the nutritional requirements of the strains, ensuring that there was no limiting nutrient. To describe the growth, one bird per experimental unit was randomly identified and evaluated from 1 to 126 days of age. In the ages 0, 14, 28, 56, 70, 77, 84, 98, 112 and 126 days, birds were scanned to estimate bone mineral content, lean and fat tissue by means of dual beam X-ray absorptiometry (DXA) using Hologic-QDR® model. At the same time, a study was performed to correlate composition data obtained by DXA and by chemical analysis of the feather free body (FFB). These data were submitted to analysis of variance (ANOVA), being verified differences in the quantification of the body composition by the different techniques. Due to these differences, regressions were adjusted for each chemical component of the body, thus generating correction equations of the data obtained by DXA in reference to the chemical method, using Dekalb Brown birds, following the same ages and procedures of the growth study. The Gompertz function was used to describe the growth of the body and chemical components for each strain. The measurement of body composition in the same birds over time by DXA assisted in the reduction of error in the evaluation of the growth of laying hens. The strains evaluated in this study showed differences in body growth, feathers and components among themselves. And the growth parameters described here are consistent with those found in the literature, and will aid in the improvement of models for calculating nutritional requirements, improving the effectiveness of feeding programs.

Receiver operating characteristic (ROC) curves have been widely used in evaluation of the goodness of the diagnostic method in many study fields, such as disease diagnosis in medicine. The area under the ROC curve (AUC) naturally became one of the most used variables in gauging the goodness of the diagnosis (Mossman, Somoza 1991). Since medical diagnosis often is not dichotomous, the ROC curve and AUC need to be generalized to a multi-dimensional case. The generalization of AUC to multi-class case has been studied by many researchers in the past decade. Most recently, Nakas & Yiannoutsos (2004) considered the ordered d classes ROC analysis by only considering the sensitivities of each class. Hence, their dimension is only d. Cha (2005) considered more types of mis-classification in the ordered multiple-class case, but reduced the dimension of Ferri, at.el. from d(d-1) to 2(d-1). In this dissertation we are trying to adjust and calculate the VUS for an ordered multipleclass with Cha’s 2(d-1)-dimension method. Our methodology of finding the VUS is introduced. We present the method of adjusting and calculating VUS and their statistical inferences for the 2(d-1)-dimension. Some simulation results are included and a real example will be presented. Intellectual outcomes in pediatric brain-tumor patients were investigated in a prospective longitudinal study. The Standard-Binet Intelligence Scale-Fourth Edition (SB-IV) Standard Age Score (SAS) and Composite intelligence quotient (IQ) score are examined as cognitive outcomes in pediatric brain-tumor patients. Treatment factors, patient factors and time since diagnosis are taken into account as the risk factors. Hierarchical linear/quadratic models and Gompertz based hierarchical nonlinear growth models were applied to build linear and nonlinear longitudinal curves. We use PRESS and Volume Under the Surface (VUS) as the criterions to compare these two methods. Some model interpretations are presented in this dissertation.

The goal of this thesis was to develop innovative adaptive design methods for enhancing the effectiveness of ecological monitoring. This was demonstrated for monitoring the health of our coral reefs where new statistical methods were developed to collect highly informative data at reduced sampling costs when compared to current survey practices. These new methods are expected to encourage adaptive design approaches for reef/ecological monitoring in the future.

Bones are multifunctional passive organs of movement that supports soft tissue and directly attached muscles. They also protect internal organs and are a reserve of calcium, phosphorus and magnesium. Each bone is covered with periosteum, and the adjacent bone surfaces are covered by articular cartilage. Histologically, the bone is an organ composed of many different tissues. The main component is bone tissue (cortical and spongy) composed of a set of bone cells and intercellular substance (mineral and organic), it also contains fat, hematopoietic (bone marrow) and cartilaginous tissue. Bones are a tissue that even in adult life retains the ability to change shape and structure depending on changes in their mechanical and hormonal environment, as well as self-renewal and repair capabilities. This process is called bone turnover. The basic processes of bone turnover are: • bone modeling (incessantly changes in bone shape during individual growth) following resorption and tissue formation at various locations (e.g. bone marrow formation) to increase mass and skeletal morphology. This process occurs in the bones of growing individuals and stops after reaching puberty • bone remodeling (processes involve in maintaining bone tissue by resorbing and replacing old bone tissue with new tissue in the same place, e.g. repairing micro fractures). It is a process involving the removal and internal remodeling of existing bone and is responsible for maintaining tissue mass and architecture of mature bones. Bone turnover is regulated by two types of transformation: • osteoclastogenesis, i.e. formation of cells responsible for bone resorption • osteoblastogenesis, i.e. formation of cells responsible for bone formation (bone matrix synthesis and mineralization) Bone maturity can be defined as the completion of basic structural development and mineralization leading to maximum mass and optimal mechanical strength. The highest rate of increase in pig bone mass is observed in the first twelve weeks after birth. This period of growth is considered crucial for optimizing the growth of the skeleton of pigs, because the degree of bone mineralization in later life stages (adulthood) depends largely on the amount of bone minerals accumulated in the early stages of their growth. The development of the technique allows to determine the condition of the skeletal system (or individual bones) in living animals by methods used in human medicine, or after their slaughter. For in vivo determination of bone properties, Abstract 10 double energy X-ray absorptiometry or computed tomography scanning techniques are used. Both methods allow the quantification of mineral content and bone mineral density. The most important property from a practical point of view is the bone’s bending strength, which is directly determined by the maximum bending force. The most important factors affecting bone strength are: • age (growth period), • gender and the associated hormonal balance, • genotype and modification of genes responsible for bone growth • chemical composition of the body (protein and fat content, and the proportion between these components), • physical activity and related bone load, • nutritional factors: – protein intake influencing synthesis of organic matrix of bone, – content of minerals in the feed (CA, P, Zn, Ca/P, Mg, Mn, Na, Cl, K, Cu ratio) influencing synthesis of the inorganic matrix of bone, – mineral/protein ratio in the diet (Ca/protein, P/protein, Zn/protein) – feed energy concentration, – energy source (content of saturated fatty acids - SFA, content of polyun saturated fatty acids - PUFA, in particular ALA, EPA, DPA, DHA), – feed additives, in particular: enzymes (e.g. phytase releasing of minerals bounded in phytin complexes), probiotics and prebiotics (e.g. inulin improving the function of the digestive tract by increasing absorption of nutrients), – vitamin content that regulate metabolism and biochemical changes occurring in bone tissue (e.g. vitamin D3, B6, C and K). This study was based on the results of research experiments from available literature, and studies on growing pigs carried out at the Kielanowski Institute of Animal Physiology and Nutrition, Polish Academy of Sciences. The tests were performed in total on 300 pigs of Duroc, Pietrain, Puławska breeds, line 990 and hybrids (Great White × Duroc, Great White × Landrace), PIC pigs, slaughtered at different body weight during the growth period from 15 to 130 kg. Bones for biomechanical tests were collected after slaughter from each pig. Their length, mass and volume were determined. Based on these measurements, the specific weight (density, g/cm3) was calculated. Then each bone was cut in the middle of the shaft and the outer and inner diameters were measured both horizontally and vertically. Based on these measurements, the following indicators were calculated: • cortical thickness, • cortical surface, • cortical index. Abstract 11 Bone strength was tested by a three-point bending test. The obtained data enabled the determination of: • bending force (the magnitude of the maximum force at which disintegration and disruption of bone structure occurs), • strength (the amount of maximum force needed to break/crack of bone), • stiffness (quotient of the force acting on the bone and the amount of displacement occurring under the influence of this force). Investigation of changes in physical and biomechanical features of bones during growth was performed on pigs of the synthetic 990 line growing from 15 to 130 kg body weight. The animals were slaughtered successively at a body weight of 15, 30, 40, 50, 70, 90, 110 and 130 kg. After slaughter, the following bones were separated from the right half-carcass: humerus, 3rd and 4th metatarsal bone, femur, tibia and fibula as well as 3rd and 4th metatarsal bone. The features of bones were determined using methods described in the methodology. Describing bone growth with the Gompertz equation, it was found that the earliest slowdown of bone growth curve was observed for metacarpal and metatarsal bones. This means that these bones matured the most quickly. The established data also indicate that the rib is the slowest maturing bone. The femur, humerus, tibia and fibula were between the values of these features for the metatarsal, metacarpal and rib bones. The rate of increase in bone mass and length differed significantly between the examined bones, but in all cases it was lower (coefficient b <1) than the growth rate of the whole body of the animal. The fastest growth rate was estimated for the rib mass (coefficient b = 0.93). Among the long bones, the humerus (coefficient b = 0.81) was characterized by the fastest rate of weight gain, however femur the smallest (coefficient b = 0.71). The lowest rate of bone mass increase was observed in the foot bones, with the metacarpal bones having a slightly higher value of coefficient b than the metatarsal bones (0.67 vs 0.62). The third bone had a lower growth rate than the fourth bone, regardless of whether they were metatarsal or metacarpal. The value of the bending force increased as the animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. The rate of change in the value of this indicator increased at a similar rate as the body weight changes of the animals in the case of the fibula and the fourth metacarpal bone (b value = 0.98), and more slowly in the case of the metatarsal bone, the third metacarpal bone, and the tibia bone (values of the b ratio 0.81–0.85), and the slowest femur, humerus and rib (value of b = 0.60–0.66). Bone stiffness increased as animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. Abstract 12 The rate of change in the value of this indicator changed at a faster rate than the increase in weight of pigs in the case of metacarpal and metatarsal bones (coefficient b = 1.01–1.22), slightly slower in the case of fibula (coefficient b = 0.92), definitely slower in the case of the tibia (b = 0.73), ribs (b = 0.66), femur (b = 0.59) and humerus (b = 0.50). Bone strength increased as animals grew. Regardless of the growth point tested, bone strength was as follows femur > tibia > humerus > 4 metacarpal> 3 metacarpal> 3 metatarsal > 4 metatarsal > rib> fibula. The rate of increase in strength of all examined bones was greater than the rate of weight gain of pigs (value of the coefficient b = 2.04–3.26). As the animals grew, the bone density increased. However, the growth rate of this indicator for the majority of bones was slower than the rate of weight gain (the value of the coefficient b ranged from 0.37 – humerus to 0.84 – fibula). The exception was the rib, whose density increased at a similar pace increasing the body weight of animals (value of the coefficient b = 0.97). The study on the influence of the breed and the feeding intensity on bone characteristics (physical and biomechanical) was performed on pigs of the breeds Duroc, Pietrain, and synthetic 990 during a growth period of 15 to 70 kg body weight. Animals were fed ad libitum or dosed system. After slaughter at a body weight of 70 kg, three bones were taken from the right half-carcass: femur, three metatarsal, and three metacarpal and subjected to the determinations described in the methodology. The weight of bones of animals fed aa libitum was significantly lower than in pigs fed restrictively All bones of Duroc breed were significantly heavier and longer than Pietrain and 990 pig bones. The average values of bending force for the examined bones took the following order: III metatarsal bone (63.5 kg) <III metacarpal bone (77.9 kg) <femur (271.5 kg). The feeding system and breed of pigs had no significant effect on the value of this indicator. The average values of the bones strength took the following order: III metatarsal bone (92.6 kg) <III metacarpal (107.2 kg) <femur (353.1 kg). Feeding intensity and breed of animals had no significant effect on the value of this feature of the bones tested. The average bone density took the following order: femur (1.23 g/cm3) <III metatarsal bone (1.26 g/cm3) <III metacarpal bone (1.34 g / cm3). The density of bones of animals fed aa libitum was higher (P<0.01) than in animals fed with a dosing system. The density of examined bones within the breeds took the following order: Pietrain race> line 990> Duroc race. The differences between the “extreme” breeds were: 7.2% (III metatarsal bone), 8.3% (III metacarpal bone), 8.4% (femur). Abstract 13 The average bone stiffness took the following order: III metatarsal bone (35.1 kg/mm) <III metacarpus (41.5 kg/mm) <femur (60.5 kg/mm). This indicator did not differ between the groups of pigs fed at different intensity, except for the metacarpal bone, which was more stiffer in pigs fed aa libitum (P<0.05). The femur of animals fed ad libitum showed a tendency (P<0.09) to be more stiffer and a force of 4.5 kg required for its displacement by 1 mm. Breed differences in stiffness were found for the femur (P <0.05) and III metacarpal bone (P <0.05). For femur, the highest value of this indicator was found in Pietrain pigs (64.5 kg/mm), lower in pigs of 990 line (61.6 kg/mm) and the lowest in Duroc pigs (55.3 kg/mm). In turn, the 3rd metacarpal bone of Duroc and Pietrain pigs had similar stiffness (39.0 and 40.0 kg/mm respectively) and was smaller than that of line 990 pigs (45.4 kg/mm). The thickness of the cortical bone layer took the following order: III metatarsal bone (2.25 mm) <III metacarpal bone (2.41 mm) <femur (5.12 mm). The feeding system did not affect this indicator. Breed differences (P <0.05) for this trait were found only for the femur bone: Duroc (5.42 mm)> line 990 (5.13 mm)> Pietrain (4.81 mm). The cross sectional area of the examined bones was arranged in the following order: III metatarsal bone (84 mm2) <III metacarpal bone (90 mm2) <femur (286 mm2). The feeding system had no effect on the value of this bone trait, with the exception of the femur, which in animals fed the dosing system was 4.7% higher (P<0.05) than in pigs fed ad libitum. Breed differences (P<0.01) in the coross sectional area were found only in femur and III metatarsal bone. The value of this indicator was the highest in Duroc pigs, lower in 990 animals and the lowest in Pietrain pigs. The cortical index of individual bones was in the following order: III metatarsal bone (31.86) <III metacarpal bone (33.86) <femur (44.75). However, its value did not significantly depend on the intensity of feeding or the breed of pigs.