This paper deals with modelling the tissue blood perfusion and focuses on the identification of the model parameters using the patient-specific data obtained using the standard CT, or MRI investigations. The research is aimed to develop a complex model which would assist in planning the liver surgery. Recently we proposed a multicompartment model of the blood perfusion in liver which serves as the feed back for simulations of dynamic CT investigation (Rohan, Jonášová, & Lukeš 2014). The flow can be characterized at several scales for which different models are used. Flow in larger branching vessels is described using a simple 1D model based of the Bernoulli equation with correction terms respecting the pressure losses due to the dissipation. This model is coupled through point sources/sinks with a 3D model describing multicompartment flows at the lower hierarchies of the perfusion trees penetrating to the parenchyma. The compartments in the liver tissue are associated with segments which confine the flow to subdomains within the organ, and hierarchies which reflect the flow complexity on branching vascular trees of the portal and hepatic veins. For simulations of the CT perfusion test, a model of the dynamic transport of the contrast fluid in the compartments was developed; the time-space distribution of the so-called tissue density can be computed and compared with the measured data obtained form the CT. To find suitable values of the perfusion model parameters, we formulate an optimization problem where the objective function expresses the difference between the standard CT images and the corresponding perfusion maps of the contrast agent concentration. This is computed by solving the perfusion problem to obtain a steady distribution of the blood pressure at all the compartments, and the transport problem describing the contrast fluid saturation. The optimization problem can be solved using a suitable gradient-based method. For this the sensitivity analysis formulae were derived using the adjoint system method. A simplified identification problem was implemented and solved numerically to show viability of the proposed approach.