Due to the high individual differences in the anatomy and pathophysiology of patients, planning individualized treatment requires patient-specific diagnosis. Indeed, hemodynamic quantification can be immensely valuable for accurate diagnosis, however, we still lack precise diagnostic methods for numerous cardiovascular diseases including complex (and mixed) valvular, vascular, and ventricular interactions (C3VI) which is a complicated situation made even more challenging in the face of other cardiovascular pathologies. Transcatheter aortic valve replacement (TAVR) is a new less invasive intervention and is a growing alternative for patients with aortic stenosis. In a recent paper, we developed a non-invasive and Doppler-based diagnostic and monitoring computational mechanics framework for C3VI, called C3VI-DE that uses input parameters measured reliably using Doppler echocardiography. In the present work, we have developed another computational-mechanics framework for C3VI (called C3VI-CT). C3VI-CT uses the same lumped-parameter model core as C3VI-DE but its input parameters are measured using computed tomography and a sphygmomanometer. Both frameworks can quantify: (1) global hemodynamics (metrics of cardiac function); (2) local hemodynamics (metrics of circulatory function). We compared accuracy of the results obtained using C3VI-DE and C3VI-CT against catheterization data (gold standard) using a C3VI dataset (N = 49) for patients with C3VI who undergo TAVR in both pre and post-TAVR with a high variability. Because of the dataset variability and the broad range of diseases that it covers, it enables determining which framework can yield the most accurate results. In contrast with C3VI-CT, C3VI-DE tracks both the cardiac and vascular status and is in great agreement with cardiac catheter data.