Acquisition of a great number of energy-filtered images in a TEM (EFTEM) around the characteristic signal with a low energy-selecting slit allows display of the electron energy loss (EEL)-spectrum of regions of interest (ROIs) of a sample. These EEL-spectra can be submitted to the different treatments already in use for electron energy loss spectroscopy (EELS). In particular, it is possible to fit the experimental background with different mathematical models, using images acquired below and above a characteristic ionization edge. After this fitting, elemental maps can be computed by subtraction of the extrapolated/interpolated background from the characteristic images. In this work, we compared two mathematical models for background fitting-the Egerton power law and the log-polynomial law. We studied the low-energy region (40-150 eV) and a higher-energy region (350-600 eV) with the aid of software for interactive processing of EFTEM image series that we developed. The analyzed elements were the constitutive elements: iron, phosphorus, nitrogen, and oxygen in several biological materials. Two analytical TEMs, one equipped with a post-column and the other with an in-column spectrometer, were used. Our experimental results confirm that the power law is very sensitive to the value of the energy loss of the pre-edge images when the background is computed by extrapolation. The log-polynomial model is less sensitive than the power law model to the value of the energy loss of the pre-edge images in the low energy region. For the oxygen K edge at 535 eV, it gives the best fit when it is combined with the interpolation method. The use of programs that facilitate the handling of EFTEM image series, and the controlled calculation of the background under the characteristic images, represent a step forward in the generation of elemental maps.