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A non-invasive method of measurement and analysis of the arterial input impedance of the carotid artery was applied to silicone models of the normal and stenosed carotid bifurcation. The experimental setup enabled the simulation of in vivo conditions. The experimental results were compared with impedance computed for a lumped element electrical model and a model containing transmission line elements. The stenosis resulted in increased impedance moduli and phase values. Similar phenomena were observed for both computational results. However, the transmission line model yielded phase plots closer to the experimental ones. The method of measurement and analysis of the arterial input impedance appears to be an efficient tool for the assessment of the properties of the carotid bifurcation.

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the carotid arteries in the time-frequency domain using the short time Fourier transform (STFT) and the Wigner–Ville distribution (WVD). This study is carried out in order to investigate the behavior of the spectral broadening index (SBI) derived from spectra obtained using these methods. The variations in the shape of the Doppler power spectra as a function of time are presented in the form of sonograms in order to determine the degree of primitive carotid artery stenosis. The obtained results show a qualitative improvement in the appearance of the sonograms generated using the WVD over the STFT. However, despite this qualitative improvement the WVD suffers from some drawbacks: the presence of the cross terms which are primarily due to its quadratic nature. The application of the Choi–Williams distribution (CWD) in this analysis shows a noticeable reduction of these cross terms, improving therefore the quality of the sonograms. From these generated sonograms, the ultrasound frequency envelopes are extracted. The maximum and the mean frequencies in these envelopes are used to determine the SBI. The magnitude of the CWD-SBI is significantly greater than that of the STFT-SBI. In addition, there is a correlation between the SBIs obtained using the STFT and the CWD and the degree of severity of stenosis measured by 2D Doppler imaging.

This study proposes the inverse problem algorithm (IPA) with five risk factors applied to the semi-quantitative analysis of carotid stenosis 272 patients with suspected ischemic stroke. The IPA is known to provide a substantiated machine learning-based prediction of the expected outcomes by solving an inverse matrix of variable coefficients. In case of carotid stenosis prediction, such risk factors as patient’s age, mean arterial pressure (MAP), glucose AC, low-density lipoprotein-cholesterol (LDL-C), and C-Reactive protein (CRP) were assessed for the main group of 217 patients. Their results were processed by the STATISTICA program with a customized loss function ($\mathrm{\Phi }$), yielding the first-order nonlinear semi-empirical formula with 16 terms. The loss function was calculated via the total mismatch between the theoretical predictions and true carotid stenosis cases (%) for all 217 patients. Thus, the carotid stenosis (%) compromised solution array [$16\times 1=16$] was optimized using $217\times 16=3488$ individual data points via the proposed algorithm. The results showed a complete regression with loss function $\mathrm{\Phi }$=2.3543, variance $s^2$=87.46%, and correlation coefficient $r^2=0.9352$. The reference group of 55 more patients with the same preliminary diagnosis and symptoms was selected to validate the method predictive feasibility, which was found quite satisfactory. The decreasing order of three dominant risk factors was as follows: CRP, glucose AC, and MAP, whereas age and LDL-C weakly influenced the program computation results. The IPA showed a strong convergence by its default characteristic. The reduction of the number of variables in computation deteriorated the prediction accuracy, exhibiting the algorithm’s high sensitivity to the number of variables.