Intramuscular fat (IMF) content depends on sex, genotype and diet and varies with pig growth. The aim of the present work was to determine the evolution of IMF by genotype-sex, muscle and muscle location, to determine relationships between IMF content of different muscles and to predict IMF in live pigs with computed tomography (CT). For this purpose, 155 pigs of seven combinations of genotype-sex were CT scanned and slaughtered at 70, 100 and 120 kg. From the carcasses, fat thickness was measured at several locations along the midline. Loin samples from three anatomical positions (between the eighth and ninth last ribs, between the third and fourth last ribs and between the third and fourth lumbar vertebrae) and three ham muscles (biceps femoris, semimembranosus and gluteus medius) were extracted, weighed and IMF was determined with near-IR equipment. From CT images, the distribution of volume by Hounsfield value (unit related with the density) was obtained for each muscle and anatomical location. Marbling was evaluated in the three loin locations. The effects of genotype-sex and live weight and their interaction were included in the statistical model. For prediction of IMF with CT images, partial least square regression was used. The results show differences in IMF content by genotype-sex and muscle. In general, the most cranial part of the loin presented higher IMF content, as well as the biceps femoris muscle of the ham. Depending on the genotype-sex, IMF content increased during all growth or increased until 100 kg and then became constant. Correlation coefficients between IMF content by muscle/location were between 0.74 and 0.83 within loin locations and between 0.53 and 0.70 for ham muscles. Correlation coefficients between marbling and IMF content evaluated at the same location varied between 0.51 and 0.66. Prediction of IMF content from CT images is not accurate enough (residual predictive deviation statistical values lower than 1.3). Muscle weight increase with animal growth and allometric coefficients varied between 0.89 and 0.97 for the muscles evaluated. The conclusions of the present work are that IMF content differs between and within muscle, during growth and by genotype-sex and that prediction of IMF in CT images of live pigs is not accurate.

A general analytic approach is proposed for nonlinear eigenvalue problems governed by nonlinear differential equations with variable coefficients. This approach is based on the homotopy analysis method for strongly nonlinear problems. As an example, a beam with arbitrary variable cross section acted on by a compressive axial load is used to show its validity and effectiveness. This approach provides us with great freedom to transfer the original nonlinear buckling equation with variable coefficients into an infinite number of linear differential equations with constant coefficients that are much easier to solve. More importantly, it provides us with a convenient way to guarantee the convergence of solution series. As an example, the beam displacement and the critical buckling load can be obtained for arbitrary variable cross sections. The influence of nonuniformity of moment of inertia is investigated in detail and the optimal distributions of moment of inertia are studied. It is found that the critical buckling load of a beam with the optimal distribution of moment of inertia can be approximately 21–22% larger than that of a uniform beam with the same average moment of inertia. Mathematically, this approach is rather general and thus can be used to solve many other linear/nonlinear differential equations with variable coefficients.