Geometric modeling of blood vessels

Geometric modeling of blood vessels


Cardiovascular diseases are the leading cause of death worldwide. Their prevention and treatment require accurate, noninvasive and personalized diagnostic techniques. At present, the leading technique is magnetic resonance (MR) tomography. It allows acquisition of three-dimensional images of blood filling the vessels and tissues, without use of contrast agents or X-ray radiation. Despite huge, still unexplored capabilities of this method, images accessible in clinics consist of elementary cuboids (voxels) of finite dimensions, e. g. 0,5x0,5x0,5 mm3. The intensity of each voxel is constant within its space, e. g. proportional to the amount of blood filling it. On the other hand, the diameter of the blood vessel branches takes values from a few centimeters for aorta (macroscopic scale) down to tens of micrometers for venules and arterioles (mesoscopic scale). The radius of most arteries and veins is comparable then to the length of voxel sides. This leads to the effect of voxelization – vessel regions are approximated by sets of cuboids (boxes). Smooth boundaries between the vessel and surrounding tissues take unnatural form of staircase surfaces. There is a need for development of algorithms for reconstruction of the original shape and dimensions of blood vessels for medical diagnosis, through numerical analysis of their severely distorted (due to the limited resolution) images. Moreover, the MR images feature random intensity fluctuations which are an additional source of uncertainty in finding the course of centerlines and measuring the diameter of vessels. The modeling algorithms should be robust to those (and other) distortions and noise, inherent to MR tomography. Comprehensive modelling of the processes of blood delivery to tissues has to account for the fact thin branches, of diameter smaller than the voxel side, are not visible in the image as separate regions, one can observe the net effect of their perfusion with blood only.

The project is aimed at development of mathematical description of the structure of blood vessels visualized in 3D magnetic resonance images. Such models offer objective, accurate geometrical information on the blood vessel trees and parameters of their branches – for detailed, personalized diagnosis of the circulatory system. They can be used for noninvasive simulation of blood flow, e. g. in critical regions such as stenoses and aneurysms. Geometric modeling allows for construction of vascular prostheses, e. g. via 3D printing, to restore patency of diseased branches.

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Analysis and visualization of heart rate variability (HRV)

A blue wooden human figure running on the ECG signal grid


Nowadays, a healthy, active lifestyle is more and more important to us. Many people use sports watches or fitness bands to plan their workouts. This type of devices usually collect data such as number of steps and heart rate. In the case of heart rate signal the accuracy of the data recorded from optical sensors is of key importance.

Conducted research include development of methods for preprocessing and analysis of heart rate signal recorded using of non-invasive techniques, as well as for the determination of time-frequency parameters. Another aspect concerns development of methods for visualization of patterns occurring in time series in relation to heart rate variability, which may carry important information about the patient's health.

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Institute Structure – Divisions

Medical Electronics Division

Head of the Division
prof. Piotr Szczypiński

Communications Division

Head of the Division
prof. Sławomir Hausman

Electronic Circuits and Thermography Division

Head of the Division
prof. Bogusław Więcek


Institute of Electronics
Lodz University of Technology
Al. Politechniki 10, B-9 building
93-590 Lodz, POLAND

Correspondence address

116 Żeromskiego Str.
PL 90-924 Lodz

VAT identification number: PL 727-002-18-95