A nonlinear model for mammary gland growth and regression in lactating sows

The objective was to propose an empirical mathematical model to describe mammary gland growth and regression in lactating sows. A nonlinear dynamic model based on the logistic function was constructed, and data from 61 sows were used to illustrate the model. Sows were fed four diets with two levels of energy and of protein during lactation, and individuals were slaughtered over a 30-d period to produce a cross sectional data set on weight and composition variables from suckled mammary glands. Data (y_x) were obtained for each day of lactation (x) and fitted by nonlinear regression. The logistic distribution function was modified for different durations of growth (f; days/gram of weight or composition) and regression (g; days/gram of weight or composition): where y_max is maximum weight or composition and X_max is day of lactation at maximum. Based on results for wet weight, for example, individually suckled mammary glands grow until between Day 21 and 28 of lactation and reach a maximum of about 500 to 600 g, depending on diet. Growth pattern of mammary glands can be described well with an asymmetric nonlinear model, using different durations for growth and regression. From this model, it was possible to estimate directly biologically important parameters: maximum weight or composition, day of lactation at maximum weight or composition, and durations of growth and regression. This model can be applied to describe mammary gland growth patterns for other species and to describe similar growth or production patterns.