Non-invasive estimation of relative pressure for intracardiac flows using virtual work-energy

Intracardiac blood flow is driven by differences in relative pressure, and assessing these is critical in understanding cardiac disease. Non-invasive image-based methods exist to assess relative pressure, however, the complex flow and dynamically moving fluid domain of the intracardiac space limits assessment. Recently, we proposed a method, vWERP, utilizing an auxiliary virtual field to probe relative pressure through complex, and previously inaccessible flow domains. Here we present an extension of vWERP for intracardiac flow assessments, solving the virtual field over sub-domains to effectively handle the dynamically shifting flow domain. The extended vWERP is validated in an in-silico benchmark problem, as well as in a patient-specific simulation model of the left heart, proving accurate over ranges of realistic image resolutions and noise levels, as well as superior to alternative approaches. Lastly, the extended vWERP is applied on clinically acquired 4D Flow MRI data, exhibiting realistic ventricular relative pressure patterns, as well as indicating signs of diastolic dysfunction in an exemplifying patient case. Summarized, the extended vWERP approach represents a directly applicable implementation for intracardiac flow assessments.