Abstract A tube-load model is used to reconstruct aortic pressure waveform from peripheral pressure waveform. Yet, the reconstructed aortic pressure waveform is greatly affected by load impedance used. In this work, a vibrating-string model for closed-loop wave transmission and reflection between the aorta and periphery is developed to examine the roles of all the parameters involved in aortic pressure waveform. The arterial pulsatile wave theory gives rise to the standard one-dimensional wave equation for a vibrating string. A vibrating-string model based on radial displacement of the arterial wall is developed to relate aortic pressure waveform to peripheral pressure waveform, relate load impedance to input impedance, and derive theoretical expressions for associated clinical indices. The vibrating-string model is extended to incorporate blood velocity and is further connected to the left ventricle (LV) to study the role of the LV in aortic pressure waveform. The difference between the vibrating-string model and the tube-load model is also examined. Load impedance is identified as an indispensable independent parameter for reconstruction of aortic pressure waveform with accuracy, and its physiologically realistic harmonic dependence can only be obtained from the measured input impedance. The derived expressions for clinical indices interpret some clinical findings and underscore the role of harmonics in clinical indices. Some misconceptions in the tube-load model are revealed, including load impedance and characteristic impedance. This work clarifies the role of harmonics-dependence of load impedance and harmonics of aortic pressure waveform in determining clinical indices.
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Observer-Based De-Convolution of Deterministic Input in Coprime Multi-Channel Systems with Its Application to Non-Invasive Central Blood Pressure Monitoring
Estimating central aortic blood pressure is important for cardiovascular health and risk prediction purposes. Cardiovascular system is a multi-channel dynamical system that yields multiple blood pressures at various body sites in response to central aortic blood pressure. This paper concerns the development and analysis of an observer-based approach to de-convolution of unknown input in a class of coprime multi-channel systems applicable to non-invasive estimation of central aortic blood pressure. A multi-channel system yields multiple outputs in response to a common input. Hence, the relationship between any pair of two outputs constitutes a hypothetical input-output system with unknown input embedded as a state. The central idea underlying our approach is to derive the unknown input by designing an observer for the hypothetical input-output system. In this paper, we developed an unknown input observer (UIO) for input de-convolution in coprime multi-channel systems. We provide a universal design algorithm as well as meaningful physical insights and inherent performance limitations associated with the algorithm. The validity and potential of our approach was illustrated using a case study of estimating central aortic blood pressure waveform from two non-invasively acquired peripheral arterial pulse waveforms. The UIO could reduce the root-mean-squared error associated with the central aortic blood pressure by up to 27.5% and 28.8% against conventional inverse filtering and peripheral arterial pulse scaling techniques.
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- Award ID(s):
- 1431672
- PAR ID:
- 10145593
- Date Published:
- Journal Name:
- Journal of dynamic systems measurement and control
- ISSN:
- 1528-9028
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Left ventricular assist devices (LVADs) have been used for end-stage heart failure patients as a therapeutic option. The aortic valve plays a critical role in heart failure and its treatment with a LVAD. The cardiovascular-LVAD model is often used to investigate the physiological demands required by patients and predict the hemodynamic of the native heart supported with a LVAD. As it is a “ bridge-to-recovery ” treatment, it is important to maintain appropriate and active dynamics of the aortic valve and the cardiac output of the native heart, which requires that the LVAD pump be adjusted so that a proper balance between the blood contributed through the aortic valve and the pump is maintained. In this paper, we investigate how the pump power of the LVAD pump can affect the dynamic behaviors of the aortic valve for different levels of activity and different severities of heart failure. Our objective is to identify a critical value of the pump power (i.e., breakpoint ) to ensure that the LVAD pump does not take over the pumping function in the cardiovascular-pump system and share the ejected blood with the left ventricle to help the heart to recover. In addition, the hemodynamic often involves variability due to patients’ heterogeneity and the stochastic nature of the cardiovascular system. The variability poses significant challenges to understanding dynamic behaviors of the aortic valve and cardiac output. A generalized polynomial chaos (gPC) expansion is used in this work to develop a stochastic cardiovascular-pump model for efficient uncertainty propagation, from which it is possible to rapidly calculate the variance in the aortic valve opening duration and the cardiac output in the presence of variability. The simulation results show that the gPC-based cardiovascular-pump model is a reliable platform that can provide useful information to understand the effect of the LVAD pump on the hemodynamic of the heart.more » « less
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Abstract Based on a one-dimensional (1D) uniform model of the arterial tree, various machine-learning techniques have been explored to reconstruct aortic pressure waveform (APW) from peripheral pressure waveform (PPW). This study aims to examine the feasibility of such reconstruction. Based on a 1D uniform vibrating-string model, transfer function (TF) of PPW to APW contains four harmonics-dependent parameters: value and phase of reflection coefficient (i.e., load impedance) at periphery and transmission parameter and transmission loss in the aorta-periphery section. Pressure waveforms and blood velocity waveforms at the ascending aorta (AA), the carotid artery (CA), and the radial artery (RA) of virtual health subjects at different ages in a prevalidated database are analyzed to calculate (1) reflection coefficient at the CA and the RA as two peripheries, (2) TF for the AA-CA and AA-RA sections, and (3) transmission parameter and transmission loss in the two sections. Harmonics-dependence of the four parameters varies with aging in both sections, and arterial nonuniformity makes it unpractical to configure any mathematical model for their harmonics-dependence. Instead of fluid-loading, arterial nonuniformity greatly affects transmission loss. Compared with higher harmonics, transmission loss dramatically alters reconstructed APW. A 1D uniform model allows accurate reconstruction of APW from PPW, with a caveat that baseline values of the four parameters at different harmonics under different cardiovascular (CV) conditions need to be established a priori. Alternatively, based on the baseline values, PPW can be directly utilized for inferring CV conditions.
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Accepted Manuscript1.0
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