3D modeling of spatiotemporal distributions of metabolites in the structural and functional unit of the liver

Etezova F.M.1, Nartsissov Y.R.2, Mashkovtseva E.V.1

Institute of Cytochemistry and Molecular Pharmacology, Russia, 115404, Moscow, 6-ya Radialnaya Street 24, building 14, Тел.: +7 (495) 327-49-87, Email:

1Federal State Autonomous Educational Institution of Higher Education «N.I. Pirogov Russian National Research Medical University» of the Ministry of Health of the Russian Federation, Russia, Moscow, Ostrovityanova Street 1, building 7, Тел.: +7 (495) 434-22-66, E-mail:

2Biomedical Research Group, BiDiPharma GmbH, Bültbek 5, 22962 Siek, Email:

The liver is an important organ that performs many vital functions such as metabolic. Computer modeling is a promising approach to the comprehensive study of the distribution of metabolites in the liver in normal and pathological conditions, since it can help avoid long and expensive experiments and invasive procedures.

The vascular network of the hepatic lobule is a unique and complex system of interconnected vessels of different sizes and types [1], the features of which are not taken into account in any of the existing models [2]. This is due both to the complexity of the architecture itself and to the computer-intensive calculation.

We have constructed a 3D model of the functional unit of the liver in the form of a classical Kiernan lobule [1], [3] in accordance with its morphometric characteristics. The model includes all types of blood vessels supplying the lobule. Glucose serves as a source of energy for all cells of the body, but it is accumulated mainly in liver cells. It penetrates into hepatocytes via GLUT-2 transporter and becomes a substrate during glycogenesis in case of excess carbohydrates. Degradation of stored glycogen occurs in the case of carbohydrate deficiency, so these processes are in equilibrium and depend on the concentration of glucose in the blood and the body's need for it.

Modeling of blood flow was carried out solving the unsteady Navier-Stokes equation for the flow of an incompressible non-Newtonian fluid with dynamic viscosity corresponding to the Carro model [4], [5]. The spatiotemporal distribution of glucose in the liver parenchyma was modeled using boundary value problems for the reaction-diffusion equation.

Thus, we obtained the correct profile of blood flow rates in the vessels of the hepatic lobule and the spatiotemporal distribution of glucose in the volume of the liver parenchyma. The resulting highly detailed 3D model can be used to study the distribution of other metabolites that significantly affect the functioning of the organ in various pathological processes.


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