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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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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.more » « less
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This work is aimed to establish engineering theories of the coupled longitudinal and radial motion of the arterial wall. By treating the arterial wall as a piano string in the longitudinal direction and as a viscoelastic material in the circumferential direction, and considering pulsatile pressure and wall shear stress from axial blood flow in an artery, the fully-formed governing equations of the coupled motion of the arterial wall are obtained and are related to the engineering theories of axial blood flow for a unified engineering understanding of blood circulation in the cardiovascular (CV) system. The longitudinal wall motion and the radial wall motion are essentially a longitudinal elastic wave and a transverse elastic wave, respectively, traveling along the arterial tree, with their own propagation velocities dictated by the physical properties and geometrical parameters of the arterial wall. The longitudinal initial tension is essential for generating a transverse elastic wave in the arterial wall to accompany the pulsatile pressure wave in axial blood flow. Under aging and subclinical atherosclerosis, propagation of the two elastic waves and coupling of the two elastic waves weakens and consequently might undermine blood circulation.more » « less
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Introduction: Many studies in mice have demonstrated that cardiac-specific innate immune signaling pathways can be reprogrammed to modulate inflammation in response to myocardial injury and improve outcomes. While the echocardiography standard parameters of left ventricular (LV) ejection fraction, fractional shortening, end-diastolic diameter, and others are used to assess cardiac function, their dependency on loading conditions somewhat limits their utility in completely reflecting the contractile function and global cardiovascular efficiency of the heart. A true measure of global cardiovascular efficiency should include the interaction between the ventricle and the aorta (ventricular-vascular coupling, VVC) as well as measures of aortic impedance and pulse wave velocity. Methods: We measured cardiac Doppler velocities, blood pressures, along with VVC, aortic impedance, and pulse wave velocity to evaluate global cardiac function in a mouse model of cardiac-restricted low levels of TRAF2 overexpression that conferred cytoprotection in the heart. Results: While previous studies reported that response to myocardial infarction and reperfusion was improved in the TRAF2 overexpressed mice, we found that TRAF2 mice had significantly lower cardiac systolic velocities and accelerations, diastolic atrial velocity, aortic pressures, rate-pressure product, LV contractility and relaxation, and stroke work when compared to littermate control mice. Also, we found significantly longer aortic ejection time, isovolumic contraction and relaxation times, and significantly higher mitral early/atrial ratio, myocardial performance index, and ventricular vascular coupling in the TRAF2 overexpression mice compared to their littermate controls. We found no significant differences in the aortic impedance and pulse wave velocity. Discussion: While the reported tolerance to ischemic insults in TRAF2 overexpression mice may suggest enhanced cardiac reserve, our results indicate diminished cardiac function in these mice.more » « less
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