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The blood oxygenation level-dependent (BOLD) contrast mechanism allows the noninvasive monitoring of changes in deoxyhemoglobin content. As such, it is commonly used in functional magnetic resonance imaging (fMRI) to study brain activity since levels of deoxyhemoglobin are indirectly related to local neuronal activity through neurovascular coupling mechanisms. However, the BOLD signal is severely affected by physiological processes as well as motion. Due to this, several noise correction techniques have been developed to correct for the associated confounds. The present study focuses on cardiac pulsatility fMRI confounds, aiming to refine model-based techniques that utilize the photoplethysmograph (PPG) signal. Specifically, we propose a new technique based on convolution filtering, termed cardiac pulsatility model (CPM) and compare its performance with the cardiac-related RETROICOR (Card-RETROICOR), which is a technique commonly used to model fMRI fluctuations due to cardiac pulsatility. Further, we investigate whether variations in the amplitude of the PPG pulses (PPG-Amp) covary with variations in amplitude of pulse-related fMRI fluctuations, as well as with the systemic low frequency oscillations (SLFOs) component of the fMRI global signal (GS - defined as the mean signal across all gray matter voxels). Capitalizing on 3T fMRI data from the Human Connectome Project, CPM was found to explain a significantly larger fraction of the fMRI signal variance compared to Card-RETROICOR, particularly for subjects with larger heart rate variability during the scan. The amplitude of the fMRI pulse-related fluctuations did not covary with PPG-Amp; however, PPG-Amp explained significant variance in the GS that was not attributed to variations in heart rate or breathing patterns. Our results suggest that the proposed approach can model high-frequency fluctuations due to pulsation as well as low-frequency physiological fluctuations more accurately compared to model-based techniques commonly employed in fMRI studies.