It has recently been shown that both high-frequency and low-frequency cardiac and respiratory noise sources exist throughout the entire brain and can cause significant signal changes in fMRI data. It is also known that the brainstem, basal forebrain and spinal cord areas are problematic for fMRI because of the magnitude of cardiac-induced pulsations at these locations. In this study, the physiological noise contributions in the lower brain areas (covering the brainstem and adjacent regions) are investigated and a novel method is presented for computing both low-frequency and high-frequency physiological regressors accurately for each subject. In particular, using a novel optimization algorithm that penalizes curvature (i.e. the second derivative) of the physiological hemodynamic response functions, the cardiac- and respiratory-related response functions are computed. The physiological noise variance is determined for each voxel and the frequency-aliasing property of the high-frequency cardiac waveform as a function of the repetition time (TR) is investigated. It is shown that for the brainstem and other brain areas associated with large pulsations of the cardiac rate, the temporal SNR associated with the low-frequency range of the BOLD response has maxima at subject-specific TRs. At these values, the high-frequency aliased cardiac rate can be eliminated by digital filtering without affecting the BOLD-related signal.