Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus

Abutaleb, Ahmed S.; Waheed, Mohamed; Elhamy, Nermeen M.

doi:10.1155/2010/102581

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…Consequently, δ ( t ) is taken as the asymptotic identity in ( L 1 ; ∗) in the domain of generalized functions. Accordingly, the inverse of the conventional convolution discussed by, for instance, Mikusinski [112], Bracewell [115], Huang and Qiu [116], Abutaleb et al [117], Rhoads and Ekstrom [118], Todoeschuck and Jensen [119], and Moreau et al [120], exists because the necessary and sufficient condition that the inverse of an operation exists is that there exists the identity in that system, see, for example, Korn and Korn [121], Zhang [122], Riley et al [123], Bronshtein et al [124], and Stillwell [125], but it should be in the sense of generalized functions. As a matter of fact, the conventional convolution itself is in that sense, see, for example, Smith [126].…”

Section: Min-plus Algebra and Problem Statementmentioning

confidence: 99%

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Zhao

2012

Computational and Mathematical Methods in Medicine

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Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

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Section: Min-plus Algebra and Problem Statementmentioning

confidence: 99%

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Zhao

2012

Computational and Mathematical Methods in Medicine

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Model-Based Blind System Identification Approach to Estimation of Central Aortic Blood Pressure Waveform From Noninvasive Diametric Circulatory Signals

Ghasemi

Kim

Ginsberg

et al. 2017

Journal of Dynamic Systems, Measurement, and Control

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This paper presents a model-based blind system identification approach to estimation of central aortic blood pressure (BP) waveform from noninvasive diametric circulatory signals. First, we developed a mathematical model to reproduce the relationship between central aortic BP waveform and a class of noninvasive circulatory signals at diametric locations by combining models to represent wave propagation in the artery, arterial pressure–volume relationship, and mechanics of the measurement instrument. Second, we formulated the problem of estimating central aortic BP waveform from noninvasive diametric circulatory signals into a blind system identification problem. Third, we performed identifiability analysis to show that the mathematical model could be identified and its parameters determined up to an unknown scale. Finally, we illustrated the feasibility of the approach by applying it to estimate central aortic BP waveform from two diametric pulse volume recording (PVR) signals. Experimental results from ten human subjects showed that the proposed approach could estimate central aortic BP waveform accurately: the average root-mean-squared error (RMSE) associated with the central aortic BP waveform was 4.1 mm Hg (amounting to 4.5% of the underlying mean BP) while the average errors associated with central aortic systolic pressure (SP) and pulse pressure (PP) were 2.4 mm Hg and 2.0 mm Hg (amounting to 2.5% and 2.1% of the underlying mean BP). The proposed approach may contribute to the improved monitoring of cardiovascular (CV) health by enabling estimation of central aortic BP waveform from conveniently measurable diametric circulatory signals.

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Estimation of Central Aortic Blood Pressure From Non-Invasive Cuff Pressure Oscillation Signals via System Identification

Ghasemi

Kim

Ginsberg

et al. 2016

Volume 1: Advances in Control Design Methods, Nonlinear and Optimal Control, Robotics, and Wind Energy Systems; Aerospace Appli

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This paper presents a model-based system identification approach to estimation of central aortic blood pressure waveform from non-invasive cuff pressure oscillation signals. First, we developed a mathematical model that can reproduce the relationship between central aortic blood pressure waveform and non-invasive cuff pressure oscillation signals at diametric locations by combining models to represent wave propagation in the artery, arterial pressure-volume relationship, and mechanics of the occlusive cuff. Second, we formulated the problem of estimating central aortic blood pressure waveform from non-invasive cuff pressure oscillation signals into a system identification problem. Third, we showed the proof-of-concept of the approach using simulated central aortic blood pressure waveform and cuff pressure oscillation signals. Finally, we illustrated the feasibility of the approach using central aortic blood pressure waveform and cuff pressure oscillation signals collected from a human subject. We showed that the proposed approach could estimate central aortic blood pressure waveform with accuracy: the root-mean-squared error associated with the central aortic blood pressure waveform was 1.7 mmHg (amounting to 1.6 % of the underlying mean blood pressure) while the errors associated with central aortic systolic and pulse pressures were −0.4 mmHg and −1.5 mmHg (amounting to −0.3 % and −1.4 % of the underlying mean blood pressure).

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Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus

Cited by 3 publications

References 35 publications

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

Model-Based Blind System Identification Approach to Estimation of Central Aortic Blood Pressure Waveform From Noninvasive Diametric Circulatory Signals

Estimation of Central Aortic Blood Pressure From Non-Invasive Cuff Pressure Oscillation Signals via System Identification

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