One of the most common acute and chronic cardiovascular disease conditions is aortic stenosis, a disease in which the aortic valve is damaged and can no longer function properly. Moreover, aortic stenosis commonly exists in combination with other conditions causing so many patients suffer from the most general and fundamentally challenging condition: complex valvular, ventricular and vascular disease (C3VD). Transcatheter aortic valve replacement (TAVR) is a new less invasive intervention and is a growing alternative for patients with aortic stenosis. Although blood flow quantification is critical for accurate and early diagnosis of C3VD in both pre and post-TAVR, proper diagnostic methods are still lacking because the fluid-dynamics methods that can be used as engines of new diagnostic tools are not well developed yet. Despite remarkable advances in medical imaging, imaging on its own is not enough to quantify the blood flow effectively. Moreover, understanding of C3VD in both pre and post-TAVR and its progression has been hindered by the absence of a proper non-invasive tool for the assessment of the cardiovascular function. To enable the development of new non-invasive diagnostic methods, we developed an innovative image-based patient-specific computational fluid dynamics framework for patients with C3VD who undergo TAVR to quantify metrics of: (1) global circulatory function; (2) global cardiac function as well as (3) local cardiac fluid dynamics. This framework is based on an innovative non-invasive Doppler-based patient-specific lumped-parameter algorithm and a 3-D strongly-coupled fluid-solid interaction. We validated the framework against clinical cardiac catheterization and Doppler echocardiographic measurements and demonstrated its diagnostic utility by providing novel analyses and interpretations of clinical data in eleven C3VD patients in pre and post-TAVR status. Our findings position this framework as a promising new non-invasive diagnostic tool that can provide blood flow metrics while posing no risk to the patient. The diagnostic information, that the framework can provide, is vitally needed to improve clinical outcomes, to assess patient risk and to plan treatment.