Janusz Mroczka

Hybrid model of arm for analysis of regional blood oxygenation in non-invasive optical diagnostics

The paper presents a new comprehensive approach to modeling and analysis of processes occurring during the blood flow in the arm‟s small vessels as well as non-invasive measurement method of mixed venous oxygen saturation. During the work, a meta-analysis of available physiological data was performed and based on its result a hybrid model of forearm vascular tree was proposed. The model, in its structure, takes into account a classical nonlinear hydro-electric analogy in conjunction with light-tissue interaction. Several geometries of arm vascular tree obtained from magnetic resonance angiography (MRA) image were analyzed which allowed to proposed the structure of electrical analog network. Proposed model allows to simulate the behavior of forearm blood flow from the vascular tree mechanics point of view, as well as effects of the impact of cuff and vessel wall mechanics on the recorded photoplethysmographic signals. In particular, it allows to analyze the reaction and anatomical effects in small vessels and microcirculation caused by occlusive maneuver in selected techniques, what was of particular interest to authors and motivation to undertake research in this area. Preliminary studies using proposed model showed that inappropriate selection of occlusion maneuver parameters (e.g. occlusion time, cuff pressure etc.), cause dangerous turbulence of blood flow in the venous section of the vascular tree.

Dynamic Effects of Obstructed Airways Mechanics on the Forced Expiratory Curve

Spirometry is the most popular test of lung function. Its status arises from the effort-independence of the maximal expiratory flow-volume (MEFV) curve, its reproducibility for a given subject and simultaneous sensitivity to respiratory disorders. Previous trials have shown that the morphology-based, quasi-static models cannot reproduce characteristic swings in the MEFV curve, sometimes visible in the case of obstructive diseases. The aim of this work was to test the hypothesis that the aforementioned details in the MEFV curve are caused by dynamic phenomena occurring during forced expiration, and that they manifest particularly in obstructive diseases. To this end, the computational model for forced expiration including the fundamental physical phenomena in quasi-static conditions was further developed by including the dynamic phenomena: additional flows from narrowing airways, and gas compressibility and inertia. The MEFV curves simulated using the quasi-dynamic and quasi-static models were then compared for a variety of respiratory system states. For most simulated cases, the differences between forced expiratory curves computed with the models were negligible. Only implementing some specific conditions causing flow limitation in small airways yielded a visible alteration and the characteristic swing after the peak expiratory flow (PEF). Concluding, the dynamic effects of airway narrowing and gas compressibility and inertia modify the MEFV curve near the PEF slightly and only in specific cases. This finding justifies the general use of the quasi-static models as an adequate tool for forced expiration simulations.

Modeling the Impact of Heterogeneous Airway Narrowing on the Spirometric Curve

The respiratory system is one of the most complex human organs and deeper insight into the lung structure and function involves usually mathematical modeling. In this work we present a modification of the computational model for spirometry -- the most popular test of lung function -- by implementing the heterogeneous narrowing of airways at a chosen level of the bronchial tree. The stochastic nature of heterogeneity was achieved using the modified gamma distribution to generate random values of coefficients describing reduction of cross-section areas of chosen groups of airways. A sort of simulations mimicking the development of asthma were performed with different levels of airway narrowing and heterogeneity. The results demonstrate that the spirometric curve is very sensitive to modifications in a central airways narrowing pattern, and this may explain the observed between-visit variation of the test results. Moreover, interpretations based on a single spirometric curve may not be unambiguous. The simulations have also shown that changes associated with developing asthma lead to a general reduction of expiratory airflow, which becomes significantly smaller, justifying the popularity of spirometry in lung testing.

Tomographic image reconstruction via estimation of sparse unidirectional gradients

Since computed tomography (CT) was developed over 35 years ago, new mathematical ideas and computational algorithms have been continuingly elaborated to improve the quality of reconstructed images. In recent years, a considerable effort can be noticed to apply the sparse solution of underdetermined system theory to the reconstruction of CT images from undersampled data. Its significance stems from the possibility of obtaining good quality CT images from low dose projections. Among diverse approaches, total variation (TV) minimizing 2D gradients of an image, seems to be the most popular method. In this paper, a new method for CT image reconstruction via sparse gradients estimation (SGE), is proposed. It consists in estimating 1D gradients specified in four directions using the iterative reweighting algorithm. To investigate its properties and to compare it with TV and other related methods, numerical simulations were performed according to the Monte Carlo scheme, using the Shepp-Logan and more realistic brain phantoms scanned at 9-60 directions in the range from 0 to 179°, with measurement data disturbed by additive Gaussians noise characterized by the relative level of 0.1%, 0.2%, 0.5%, 1%, 2% and 5%. The accuracy of image reconstruction was assessed in terms of the relative root-mean-square (RMS) error. The results show that the proposed SGE algorithm has returned more accurate images than TV for the cases fulfilling the sparsity conditions. Particularly, it preserves sharp edges of regions representing different tissues or organs and yields images of much better quality reconstructed from a small number of projections disturbed by relatively low measurement noise.