We propose an efficient computational method to obtain the fractional derivative of a digital signal. e proposal consists of a new interpretation of the Grünwald-Letnikov differintegral operator where we have introduced a finite Cauchy convolution with the Grünwald-Letnikov dynamic kernel. e method can be applied to any signal without knowing its analytical form. In the experiments, we have compared the proposed Grünwald-Letnikov computational fractional derivative method with the Riemman-Louville fractional derivative approach for two well-known functions. e simulations exhibit similar results for both methods; however, the Grünwald-Letnikov method outperforms the other approach in execution time. Finally, we show an application of how our proposal can be useful to find the fractional relationship between two well-known biomedical signals.
Cardiovascular diseases represent the leading cause of death worldwide. Thus, cardiovascular rehabilitation programs are crucial to mitigate the deaths caused by this condition each year, mainly in patients with coronary artery disease. COVID-19 was not only a challenge in this area but also an opportunity to open remote or hybrid versions of these programs, potentially reducing the number of patients who leave rehabilitation programs due to geographical/time barriers. This paper presents a method for building a cardiovascular rehabilitation prediction model using retrospective and prospective data with different features using stacked machine learning, transfer feature learning, and the joint distribution adaptation tool to address this problem. We illustrate the method over a Chilean rehabilitation center, where the prediction performance results obtained for 10-fold cross-validation achieved error levels with an NMSE of 0.03±0.013 and an R2 of 63%±19%, where the best-achieved performance was an error level with a normalized mean squared error of 0.008 and an R2 up to 92%. The results are encouraging for remote cardiovascular rehabilitation programs because these models could support the prioritization of remote patients needing more help to succeed in the current rehabilitation phase.
Blood Pressure (BP) waveform is a result of the response of the arteries to the blood ejection produced by the heart and, therefore, it is an important indicator of the state of the cardiovascular system. Currently, its measurement is performed invasively in critically ill patients who need a continuous and real time monitoring of their treatment response, however, it is possible to measure the BP, continuously and non-invasively, in non-critical patients to detect, monitor and control possible hypertensive events. Nevertheless, current non-invasive techniques can cause discomfort in patients and they are not used in critically ill patients. Consequently, non-Invasive and minimally-Intrusive methodologies (nImI) are required to estimate BP and its waveform. In the current study, the performance of machine learning algorithms, specifically the Extreme Learning Machine (ELM) algorithm, is evaluated to estimate both Blood Pressure and its waveform from the Photoplethysmography (PPG) signal and its first derivative's (VPG) waveforms. A total of 15 healthy volunteers participated in this study. They performed two handgrips, which is isometric maneuver to induce controlled BP rises. The first handgrip is used to train ELM and the second handgrip is used to test the ELM. Our results show that there are high correlation performances (0.98) between the estimated and measured BP waveforms, and a relative error of 3.3 ± 1.4%. An arterial volume-clamp at the middle finger is used as the gold-standard measurement. Meanwhile, BP extreme values estimations, Systolic BP (SBP) and Diastolic BP (DBP), are also performed. ELMs have a performance with an average RMSE of 5.9 ± 2.7 mmHG for SBP and 4.8 ± 2.0 mmHg for DBP and, an average relative error of 5.0 ± 2.7% for SBP and 7.0 ± 4.0% for DBP.
Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.
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