The influence of microlensing on the profiles of emission lines generated in a biconical geometry is discussed. Microlensing amplification in this anisotropic model is not directly related to the bicone's intrinsic size but, rather, depends on the orientation of the bicone axis and on the cone aperture. The orientation of the projected bicone with respect to the shear of the magnification pattern can induce very interesting effects, such as quasi-periodic enhancements of the red or blue part of the emission-line profile or a lack of correlation between the broad-line region (BLR) and continuum light curve for QSOs. The emission-line profiles of a BLR moving in a high caustic concentration exhibit sharp features that are well defined in wavelength. These features (spikes) correspond to a scanning of the kinematics of the BLR by the caustic clusters. The biconical model can qualitatively reproduce, with a transverse (with respect to the shear) movement of the BLR, the recurrent blue-wing enhancement detected in the emission-line profile of image A of the lensed quasar SDSS J1004+4112. The probability of observing such a repetitive event is almost 2% for a fraction of matter in stars of 5%. This result makes plausible the detection of the spectral variability in SDSS J1004+4112 under the hypothesis that it reflects the microlensing of a bicone.