Towards a Digital Twin of the Human Kidney for Diagnosis of Renal Diseases

In this paper, we attempt to develop a digital twin of a human kidney based on patient-specific images, clinically measured data and mathematical models of the kidney tissue, the renal artery, and the renal vein. The aim is to have a sufficiently accurate model so that certain kidney diseases can be analyzed and surgical planning can be carried out virtually and collaboratively on remotely connected mixed reality headsets. To model the hemodynamics of the kidney, we first obtain the patient-specific renal vascular geometry from the CT images and a blood flow model is built with the incompressible NavierStokes equations with several patient-specific inflow and outflow conditions. The geometry of the kidney tissue is also obtained from the CT images, and to model the microvascular structure of the kidney with a rich capillary network, we employ the Darcy equations and treat the microvascular bed that cannot be resolved by the CT as a porous medium. For the coupling between the fluid and the porous medium models, we impose three interface conditions based on the conservation of mass, the balance of the normal force and the Beavers-Josepha-Saffman condition. The numerical simulations are implemented offline using a high-end computer cluster and the computational results are rendered online in several holographic headsets, through which doctors can view the hemodynamic details of selected fields collaboratively. Moreover, by connecting and integrating holographic headsets with a high-performance GPU-based workstation, we can compute morphologic and hemodynamic indicators online in real time, aiding in disease diagnosis and treatment planning. Several renal diseases are considered as test cases including renal artery stenosis, renal artery aneurysm as well as localized necrosis of the kidney tissue.