Data-driven lossy tube-load modeling of arterial tree: in-human study

Personalized aortic pressure waveform estimation from brachial pressure waveform using an adaptive transfer function

BACKGROUND AND OBJECTIVE

The aortic pressure waveform (APW) provides reliable information for the diagnosis of cardiovascular disease. APW is often measured using a generalized transfer function (GTF) applied to the peripheral pressure waveform acquired noninvasively, to avoid the significant risks of invasive APW acquisition. However, the GTF ignores various physiological conditions, which affects the accuracy of the estimated APW. To solve this problem, this study utilized an adaptive transfer function (ATF) combined with a tube-load model to achieve personalized and accurate estimation of APW from the brachial pressure waveform (BPW).

METHODS

The proposed method was validated using APWs and BPWs from 34 patients. The ATF was defined using a tube-load model in which pulse transit time and reflection coefficients were determined from, respectively, the diastolic-exponential-pressure-decay of the APW and a piece-wise constant approximation. The root-mean-square-error of overall morphology, mean absolute errors of common hemodynamic indices (systolic blood pressure, diastolic blood pressure and pulse pressure) were used to evaluate the ATF.

RESULTS

The proposed ATF performed better in estimating diastolic blood pressure and pulse pressure (1.63 versus 1.94 mmHg, and 2.37 versus 3.10 mmHg, respectively, both P < 0.10), and produced similar errors in overall morphology and systolic blood pressure (3.91 versus 4.24 mmHg, and 2.83 versus 2.91 mmHg, respectively, both P > 0.10) compared to GTF.

CONCLUSION

Unlike the GTF which uses fixed parameters trained on existing clinical datasets, the proposed method can achieve personalized estimation of APW. Hence, it provides accurate pulsatile hemodynamic measures for the evaluation of cardiovascular function.

Single measurement estimation of central blood pressure using an arterial transfer function

BACKGROUND

Central blood pressure (BP) better reflects the loading conditions on the major organs and is more closely correlated with future cardiovascular events. The increased invasiveness and risk of infection prevents the routine measurement of central BP. Arterial transfer functions can provide central BP estimates from clinically available peripheral measurements. However, current methods are either generalized, potentially lacking the ability to adapt to inter and intra subject variability, or individualized based on additional, clinically unavailable, pulse transit time measurements. This work proposes a novel, self-contained method for individualizing an arterial transfer function from a single peripheral pressure measurement, capable of accurately estimating central BP in a range of hemodynamic conditions.

METHODS

Pulse wave analysis of femoral BP waves was employed to formulate initial approximations of central BP and arterial inlet flow waveforms, to serve as objective functions for the identification of all model parameters. Root mean squared error (RMSE), and systolic and pulse pressure errors were assessed with respect to invasive aortic BP measurements in a seven (7) porcine endotoxin experiments. Systolic and pulse pressure errors were analysed using Bland-Altman analysis. Method accuracy is also compared with an idealized transfer function, derived using the measured aortic-femoral pulse transit time and minimizing the RMSE of model output pressure with respect to reference aortic pressure, a generalized transfer function model, and invasive femoral pressure measurements.

RESULTS

Mean bias and limits of agreement (95% CI) for the proposed method were 1.0(-4.6, 6.7)mmHg and -1.0(-6.6, 4.6)mmHg for systolic and pulse pressure, respectively, compared to 3.6(-0.9, 8.2)mmHg and 2.7(-1.8, 7.3)mmHg for the generalized transfer function model. Mean bias and limits of agreement for femoral pressure measurements were -6.4(-15.0, 2.3)mmHg and -9.4(-18.1, -0.8)mmHg, for systolic and pulse pressure, respectively. The pooled mean and standard deviation of the RMSE produced by the single measurement method, relative to reference aortic pressure, was 4.3(1.1)mmHg, consistent with estimates produced by the idealized transfer function, 3.9(1.2)mmHg, and improving of the generalized transfer function, 4.6(1.4)mmHg.

CONCLUSIONS

The proposed single measurement method provides accurate central BP estimates from routinely available peripheral pressure measurements, and nothing else. The method allows for the individualization of transfer functions on a per patient basis to better capture changes in patient condition during the progression of disease and subsequent treatment, at no additional clinical cost.

Observer-Based Deconvolution of Deterministic Input in Coprime Multichannel Systems With Its Application to Noninvasive Central Blood Pressure Monitoring

Estimating central aortic blood pressure (BP) is important for cardiovascular (CV) health and risk prediction purposes. CV system is a multichannel dynamical system that yields multiple BPs at various body sites in response to central aortic BP. This paper concerns the development and analysis of an observer-based approach to deconvolution of unknown input in a class of coprime multichannel systems applicable to noninvasive estimation of central aortic BP. A multichannel 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 deconvolution in coprime multichannel systems. We provided 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 were illustrated using a case study of estimating central aortic BP waveform from two noninvasively acquired peripheral arterial pulse waveforms. The UIO could reduce the root-mean-squared error (RMSE) associated with the central aortic BP by up to 27.5% and 28.8% against conventional inverse filtering (IF) and peripheral arterial pulse scaling techniques.

N-Point Moving Average: A Special Generalized Transfer Function Method for Estimation of Central Aortic Blood Pressure

OBJECTIVE

N-point moving average (NPMA) is a simplified method of central aortic systolic pressure (CASP) estimation in comparison with the generalized transfer function (GTF). The fundamental difference or similarity between the methods is not established. This study investigates theoretical properties of NPMA relative to GTF and explores the integer and fractional denominator for the averaging process in the NPMA.

METHODS

Convolution of a specified square wave and the radial (or brachial) blood pressure waveform constituted the NPMA . A single uniform tube model-based TF (MTF) was employed to investigate potential physiological meaning of NPMA. In experimental analysis, invasive, simultaneously recorded aortic and radial pressure waveforms were obtained in 62 subjects under control conditions and following nitroglycerin administration. CASP was estimated by NPMA (), GTF ( ), and MTF (CASP _MTF) from radial waveforms by tenfold cross validation.

RESULTS

Theoretical analysis showed that NPMA was an inversed constant TF. Its spectrum matched that of MTF in low frequency (<4 Hz for radial and <5 Hz for brachial) by optimizing reflection coefficient and propagation time. Experiment results showed the NPMA optimized fractional denominator of K = 4.4 significantly decreased the mean difference between CASP_NPMA and measured CASP to 0.0 ± 4.7 mmHg from -1.8 ± 4.6 mmHg for integer denominator of K = 4. CASP_NPMA correlated with CASP_MTF and CASP _GTF (r² = 0.99 and 0.97, mean difference: -0.3 ± 1.8 and 0.5 ± 2.7 mmHg).

CONCLUSION

This study demonstrated that NPMA is similar in nature to the GTF.

A review on low-dimensional physics-based models of systemic arteries: application to estimation of central aortic pressure

The physiological processes and mechanisms of an arterial system are complex and subtle. Physics-based models have been proven to be a very useful tool to simulate actual physiological behavior of the arteries. The current physics-based models include high-dimensional models (2D and 3D models) and low-dimensional models (0D, 1D and tube-load models). High-dimensional models can describe the local hemodynamic information of arteries in detail. With regard to an exact model of the whole arterial system, a high-dimensional model is computationally impracticable since the complex geometry, viscosity or elastic properties and complex vectorial output need to be provided. For low-dimensional models, the structure, centerline and viscosity or elastic properties only need to be provided. Therefore, low-dimensional modeling with lower computational costs might be a more applicable approach to represent hemodynamic properties of the entire arterial system and these three types of low-dimensional models have been extensively used in the study of cardiovascular dynamics. In recent decades, application of physics-based models to estimate central aortic pressure has attracted increasing interest. However, to our best knowledge, there has been few review paper about reconstruction of central aortic pressure using these physics-based models. In this paper, three types of low-dimensional physical models (0D, 1D and tube-load models) of systemic arteries are reviewed, the application of three types of models on estimation of central aortic pressure is taken as an example to discuss their advantages and disadvantages, and the proper choice of models for specific researches and applications are advised.

Investigation of Viscoelasticity in the Relationship Between Carotid Artery Blood Pressure and Distal Pulse Volume Waveforms

We investigated the relationship between carotid artery blood pressure (BP) and distal pulse volume waveforms (PVRs) via subject-specific mathematical modeling. We conceived three physical models to define the relationship: a tube-load model augmented with a gain (TLG), Voigt (TLV), and standard linear solid (TLS) models. We compared these models using PVRs measured via BP cuffs at an upper arm and an ankle as well as carotid artery tonometry waveform collected from 133 subjects. At both upper arm and ankle, PVR was related to carotid artery tonometry by TLV and TLS models better than by TLG model; when root-mean-squared over all the subjects, the systolic and diastolic BP errors between measured carotid artery tonometry waveform and the one estimated from distal PVR reduced from 4.3 mmHg and 4.6 mmHg (TLG) to 1.1 mmHg and 1.0 mmHg (TLS) for the upper arm (p < 0.0167), and from 2.1 mmHg and 1.7 mmHg (TLG) to 2.1 mmHg and 1.5 mmHg (TLV) for the ankle. Further, TLV and TLS models exhibited superior Akaike's Information Criterion (AIC) in both locations than TLG model. However, the difference between TLG versus TLV and TLS models associated with the ankle was not large. Therefore, the relationship of central arterial BP to arm PVR arises from both wave reflection and viscoelasticity while the relationship to ankle PVR mainly arises from wave reflection. These findings may imply that an effective subject-specific transfer function for estimating accurate central arterial BP from an arm PVR should account for the impact of viscoelasticity.

Toward Ubiquitous Blood Pressure Monitoring via Pulse Transit Time: Theory and Practice

Ubiquitous blood pressure (BP) monitoring is needed to improve hypertension detection and control and is becoming feasible due to recent technological advances such as in wearable sensing. Pulse transit time (PTT) represents a well-known potential approach for ubiquitous BP monitoring. The goal of this review is to facilitate the achievement of reliable ubiquitous BP monitoring via PTT. We explain the conventional BP measurement methods and their limitations; present models to summarize the theory of the PTT-BP relationship; outline the approach while pinpointing the key challenges; overview the previous work toward putting the theory to practice; make suggestions for best practice and future research; and discuss realistic expectations for the approach.