Simplified single neuron model for robust local pulse wave velocity sensing using a tetherless bioimpedance device

Pulse arrival time (PAT), Pulse transit time (PTT), and Pulse Wave Velocity (PWV) have all been used as metrics for assessing a number of cardiovascular applications, including arterial stiffness and cuffless blood pressure monitoring. These have been measured using various sensing methods, including electrocardiogram (ECG) with photoplethysmogram (PPG), two PPG sensors, or two Bioimpedance (BioZ) sensors. Our study addresses the mathematical inaccuracies of previous bioimpedance approaches and incorporates PTT weights for the peak-peak (PTTpp), middle-middle (PTTmm), and foot-foot (PTTff) segments of the sensing signal into a single neuron model to determine a more accurate and stable PWV. In addition, we developed a tetherless bioimpedance device and compared our PTT estimation approaches, which yielded PWV across six subjects and two different arteries. Specifically, using our model, we found that the most reliable combination of weights corresponding to PTTpp, PTTmm, and PTTff was (0.260, 0.704, 0.036) for the brachial artery and (0.104, 0.858, 0.038) for radial artery. This model consistently yielded stable values across repetitions, with PWV values of 5.2 m/s, 5.3 m/s, and 5.9 m/s for the brachial artery and values of 5.8 m/s, 6.6 m/s, and 6.5 m/s for the radial artery. This system and model offer the possibility of obtaining higher reliability PTT and PWV values yielding better monitoring of cardiovascular health measures such as blood pressure and arterial stiffness.

The role of pulse wave analysis indexes for critically ill patients: a narrative review

Objective.Arterial pulse wave analysis (PWA) is now established as a powerful tool to investigate the cardiovascular system, and several clinical studies have shown how PWA can provide valuable prognostic information over and beyond traditional cardiovascular risk factors. Typically these techniques are applied to chronic conditions, such as hypertension or aging, to monitor the slow structural changes of the vascular system which lead to important alterations of the arterial PW. However, their application to acute critical illness is not currently widespread, probably because of the high hemodynamic instability and acute dynamic alterations affecting the cardiovascular system of these patients.Approach.In this work we propose a review of the physiological and methodological basis of PWA, describing how it can be used to provide insights into arterial structure and function, cardiovascular biomechanical properties, and to derive information on wave propagation and reflection.Main results.The applicability of these techniques to acute critical illness, especially septic shock, is extensively discussed, highlighting the feasibility of their use in acute critical patients and their role in optimizing therapy administration and hemodynamic monitoring.Significance.The potential for the clinical use of these techniques lies in the ease of computation and availability of arterial blood pressure signals, as invasive arterial lines are commonly used in these patients. We hope that the concepts illustrated in the present review will soon be translated into clinical practice.

Arterial pressure pulse wave separation analysis using a multi-gaussian decomposition model

OBJECTIVE

Methods for separating the forward-backward components from blood pulse waves rely on simultaneously measured pressure and flow velocity from a target artery site. Modelling approaches for flow velocity simplify the wave separation analysis (WSA), providing a methodological and instrumentational advantage over the former; however, current methods are limited to the aortic site. In this work, a multi-Gaussian decomposition (MGD) modelled WSA (MGDWSA) is developed for a non-aortic site asuch as the carotid artery. While the model is an adaptation of the existing wave separation theory, it does not rely on the information of measured or modelled flow velocity.

APPROACH

The proposed model decomposes the arterial pressure waveform using weighted and shifted multi-Gaussians, which are then uniquely combined to yield the forward (PF(t)) and backward (PB(t)) pressure wave. A study using the database of healthy (virtual) subjects was used to evaluate the performance of MGDWSA at the carotid artery and was compared against reference flow-based WSA methods.

MAIN RESULTS

The MGD modelled pressure waveform yielded a root-mean-square error (RMSE) < 0.35 mmHg. Reliable forward-backward components with a group average RMSE < 2.5 mmHg for PF(t) and PB(t) were obtained. When compared with the reference counterparts, the pulse pressures (ΔPF and ΔPB), as well as reflection quantification indices, showed a statistically significant strong correlation (r > 0.96, p < 0.0001) and (r > 0.83, p < 0.0001) respectively, with an insignificant (p > 0.05) bias.

SIGNIFICANCE

This study reports WSA for carotid pressure waveforms without assumptions on flow conditions. The proposed method has the potential to adapt and widen the vascular health assessment techniques incorporating pulse wave dynamics.

Separation of Forward-Backward Waves in the Arterial System using Multi-Gaussian Approach from Single Pulse Waveform

The arterial pulse waveform has an immense wealth of information in its morphology yet to be explored and translated to clinical practice. Wave separation analysis involves decomposing a pulse wave (pressure or diameter waveform) into a forward wave and a backward wave. The backward wave accumulates reflections due to arterial stiffness gradient, branching and geometric tapering of blood vessels across the arterial tree. The state-of-the-art wave separation analysis is based on estimating the input impedance of the target artery in the frequency/time domain, which requires simultaneously measured or modelled flow velocity and pressure waveform. We are proposing a new method of wave separation analysis using a multi-gaussian decomposition. The novelty of this approach is that it requires only a single pulse waveform at the target artery. Our method was compared against the triangular waveform-based impedance method. We successfully separated forward and backward waveform from the pressure waveform with maximum RMSE less than 5 mmHg and mean RMSE of 1.31 mmHg when compared against the triangular flow/impedance method. Results demonstrated a statistically significant correlation (r>0.66, p<0.0001) for Reflection Magnitude (RM) and Reflection Index (RI) for the multi-gaussian approach against the triangular flow method for 105 virtual subjects. The range of RM was from 0.35 to 0.97 (RI: 27.53% to 49.29%). This method proves to be a technique for evaluating reflection parameters if only a single pulse measurement is available from any artery.Clinical Relevance- This simulation study supplements the evidence for wave reflections. It provides a new method to study wave reflections using only a single pulse waveform without the need for any measured or modelled flow.

Evaluation of Nonlinear Wave Separation Method to Assess Reflection Transit Time: A Virtual Patient Study

Conventional methods to calculate reflection transit time (RTT) is based on pulse counter analysis. An alternative to this approach is separating forward and backward components from a pulse waveform to calculate the RTT. State-of-the-art in wave separation requires simultaneously measured pressure and flow velocity waveforms. Practically, getting a simultaneous measurement from a single arterial site has its limitations, and this has made the translation of wave separation methods to clinical practice difficult. We propose a new method of wave separation analysis that requires only a single pulse waveform measurement using a multi-Gaussian decomposition approach. The novelty of the method is that it does not require any measured or modelled flow velocity waveform. In this method, the pulse waveform is decomposed into the sum of Gaussians and reconstructed based on model criteria. RTT is calculated as the time difference between normalized forward and backward waveform. The method's feasibility in using RTT as a potential surrogate is demonstrated on 105 diverse selections of virtual subjects. The results were statistically significant and had a strong correlation (r>79, p<0.0001) against clinically approved artery stiffness markers such as Peterson's elastic modulus (Ep), pulse wave velocity (PWV), specific stiffness index (β), and arterial compliance (AC). Out of all the elasticity markers, a better correlation was found against AC.Clinical Relevance-This simulation study supplements the evidence for the dependence of pulse wave reflections on arterial stiffness. It provides a new method to study wave reflections using only a single pulse waveform.

Reconstruction of Continuous Brachial Arterial Pressure From Continuous Finger Arterial Pressure Using a Two-Level Optimization Strategy

OBJECTIVE

We attempt to reconstruct brachial arterial pressure (BAP) waves from finger arterial pressure waves measured using the vascular unloading technique without arm-cuff calibration. A novel method called two-level optimization (TOP) strategy is proposed as follows.

METHODS

We first derive a simplified transfer function (TF) based on a tube-load model with only two parameters to be estimated, a coefficient B and a time delay ∆t. Then, at level one, two minimization problems are formulated to estimate the optimal coefficient B^opt and time delay ∆t^opt. Then, we can derive an optimal TF h^opt(t). However, this derivation requires true (or reference) BAP waves. Therefore, at level two, we apply multiple linear regression (MLR) to further model the relationship between the derived optimal parameters and subjects' physiologic parameters. Hence, eventually, one can estimate coefficient B^MLR and time delay ∆t^MLR from subject's physiologic parameters to derive the MLR-based TF h^MLR(t) for the BAP reconstruction.

RESULTS

Twenty-one volunteers were recruited for the data collection. The mean ± standard deviation of the root mean square errors between the reference BAP waves and the BAP waves reconstructed by h^opt(t), h^MLR(t), and a generalized transfer function (GTF) were 3.46 ± 1.42 mmHg, 3.61 ± 2.28 mmHg, and 6.80 ± 3.73 mmHg (significantly larger with p < 0.01), respectively.

CONCLUSIONS

The proposed method can be considered as a semi-individualized TF which reconstructs significantly better BAP waves than a GTF.

SIGNIFICANCE

The proposed TOP strategy can potentially be useful in more general reconstruction of proximal BP waves.

Tapered vs. Uniform Tube-Load Modeling of Blood Pressure Wave Propagation in Human Aorta

In this paper, tapered vs. uniform tube-load models are comparatively investigated as mathematical representation for blood pressure (BP) wave propagation in human aorta. The relationship between the aortic inlet and outlet BP waves was formulated based on the exponentially tapered and uniform tube-load models. Then, the validity of the two tube-load models was comparatively investigated by fitting them to the experimental aortic and femoral BP waveform signals collected from 13 coronary artery bypass graft surgery patients. The two tube-load models showed comparable goodness of fit: (i) the root-mean-squared error (RMSE) was 3.3+/−1.1 mmHg in the tapered tube-load model and 3.4+/−1.1 mmHg in the uniform tube-load model; and (ii) the correlation was r = 0.98+/−0.02 in the tapered tube-load model and r = 0.98+/−0.01 mmHg in the uniform tube-load model. They also exhibited frequency responses comparable to the non-parametric frequency response derived from the aortic and femoral BP waveforms in most patients. Hence, the uniform tube-load model was superior to its tapered counterpart in terms of the Akaike Information Criterion (AIC). In general, the tapered tube-load model yielded the degree of tapering smaller than what is physiologically relevant: the aortic inlet-outlet radius ratio was estimated as 1.5 on the average, which was smaller than the anatomically plausible typical radius ratio of 3.5 between the ascending aorta and femoral artery. When the tapering ratio was restricted to the vicinity of the anatomically plausible typical value, the exponentially tapered tube-load model tended to underperform the uniform tube-load model (RMSE: 3.9+/−1.1 mmHg; r = 0.97+/−0.02). It was concluded that the uniform tube-load model may be more robust and thus preferred as the representation for BP wave propagation in human aorta; compared to the uniform tube-load model, the exponentially tapered tube-load model may not provide valid physiological insight on the aortic tapering, and its efficacy on the goodness of fit may be only marginal.

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.

Reconstruction of continuous brachial artery pressure wave from continuous finger arterial pressure in humans

Generalized transfer functions (GTFs) are available to compute the more relevant proximal blood pressure (BP) waveform from a more easily measured peripheral BP waveform. However, GTFs are based on the black box model. This paper presents a practical approach to reconstruct brachial artery pressure (BAP) distally from finger artery pressure (FAP). We assume that continuous BAP can be simply approximated by summing two halves of the continuous FAP shifted by the time delay. We firstly showed that the pressure wave in the finger artery can be considered twice as much as the forward/backward wave in the finger. A simplified individualized transfer function was then derived so as to estimate BAP from FAP. The effectiveness of the method was examined by experiment involving 26 healthy volunteers (26.7 ± 3.8 years old) in a resting state. By comparing with a reference BAP, we found that the proposed method can correct the FAP. The errors of the proposed method in estimating systolic and diastolic pressures are - 0.6 ± 6.0 and - 0.6 ± 3.7 mmHg, respectively. These results agree with the standard of Association for the Advancement of Medical Instrumentation (AAMI). We also found that the reconstructed BAP from FAP by terminal arterial occlusion technology (TAOT) is comparable to that of the artery occlusion technology (AOT). Our method or TAOT is promising in estimating continuous proximal blood pressure from peripheral blood pressure in practice.

A simple method for reconstruction of continuous brachial artery pressure from continuous digital artery pressure in humans

This paper presents a practical approach to reconstruct brachial artery pressure (BAP) distally from digital artery pressure (DAP). We hypothesize that continuous BAP can simply be approximated by sum of two halves of the continuous DAP shifted by the time delay. In order to test it, we enrolled 30 healthy volunteers for two experiments. We firstly showed that the pressure wave in the digital artery can be considered twice as much as the forward/backward wave in the finger. A simplified individualized transfer function was then derived so as to estimate BAP from DAP. Finally, by comparing with a reference BAP, we found that the proposed method can correct the DAP. The errors of the proposed method in estimating systolic and diastolic pressures are 2.82±3.58 and -2.32±4.06 mmHg, respectively. These results agree with the standard of Association for the Advancement of Medical Instrumentation (AAMI). Our method is therefore promising in estimating continuous proximal blood pressure from peripheral blood pressure in practice.

Estimation of Pulse Transit Time as a Function of Blood Pressure Using a Nonlinear Arterial Tube-Load Model

OBJECTIVE

pulse transit time (PTT) varies with blood pressure (BP) throughout the cardiac cycle, yet, because of wave reflection, only one PTT value at the diastolic BP level is conventionally estimated from proximal and distal BP waveforms. The objective was to establish a technique to estimate multiple PTT values at different BP levels in the cardiac cycle.

METHODS

a technique was developed for estimating PTT as a function of BP (to indicate the PTT value for every BP level) from proximal and distal BP waveforms. First, a mathematical transformation from one waveform to the other is defined in terms of the parameters of a nonlinear arterial tube-load model accounting for BP-dependent arterial compliance and wave reflection. Then, the parameters are estimated by optimally fitting the waveforms to each other via the model-based transformation. Finally, PTT as a function of BP is specified by the parameters. The technique was assessed in animals and patients in several ways including the ability of its estimated PTT-BP function to serve as a subject-specific curve for calibrating PTT to BP.

RESULTS

the calibration curve derived by the technique during a baseline period yielded bias and precision errors in mean BP of 5.1 ± 0.9 and 6.6 ± 1.0 mmHg, respectively, during hemodynamic interventions that varied mean BP widely.

CONCLUSION

the new technique may permit, for the first time, estimation of PTT values throughout the cardiac cycle from proximal and distal waveforms.

SIGNIFICANCE

the technique could potentially be applied to improve arterial stiffness monitoring and help realize cuff-less BP monitoring.

Quantification of wave reflection using peripheral blood pressure waveforms

This paper presents a novel minimally invasive method for quantifying blood pressure (BP) wave reflection in the arterial tree. In this method, two peripheral BP waveforms are analyzed to obtain an estimate of central aortic BP waveform, which is used together with a peripheral BP waveform to compute forward and backward pressure waves. These forward and backward waves are then used to quantify the strength of wave reflection in the arterial tree. Two unique strengths of the proposed method are that 1) it replaces highly invasive central aortic BP and flow waveforms required in many existing methods by less invasive peripheral BP waveforms, and 2) it does not require estimation of characteristic impedance. The feasibility of the proposed method was examined in an experimental swine subject under a wide range of physiologic states and in 13 cardiac surgery patients. In the swine subject, the method was comparable to the reference method based on central aortic BP and flow. In cardiac surgery patients, the method was able to estimate forward and backward pressure waves in the absence of any central aortic waveforms: on the average, the root-mean-squared error between actual versus computed forward and backward pressure waves was less than 5 mmHg, and the error between actual versus computed reflection index was less than 0.03.

Improved pulse wave velocity estimation using an arterial tube-load model

Pulse wave velocity (PWV) is the most important index of arterial stiffness. It is conventionally estimated by noninvasively measuring central and peripheral blood pressure (BP) and/or velocity (BV) waveforms and then detecting the foot-to-foot time delay between the waveforms wherein wave reflection is presumed absent. We developed techniques for improved estimation of PWV from the same waveforms. The techniques effectively estimate PWV from the entire waveforms, rather than just their feet, by mathematically eliminating the reflected wave via an arterial tube-load model. In this way, the techniques may be more robust to artifact while revealing the true PWV in absence of wave reflection. We applied the techniques to estimate aortic PWV from simultaneously and sequentially measured central and peripheral BP waveforms and simultaneously measured central BV and peripheral BP waveforms from 17 anesthetized animals during diverse interventions that perturbed BP widely. Since BP is the major acute determinant of aortic PWV, especially under anesthesia wherein vasomotor tone changes are minimal, we evaluated the techniques in terms of the ability of their PWV estimates to track the acute BP changes in each subject. Overall, the PWV estimates of the techniques tracked the BP changes better than those of the conventional technique (e.g., diastolic BP root-mean-squared errors of 3.4 versus 5.2 mmHg for the simultaneous BP waveforms and 7.0 versus 12.2 mmHg for the BV and BP waveforms (p <; 0.02)). With further testing, the arterial tube-load model-based PWV estimation techniques may afford more accurate arterial stiffness monitoring in hypertensive and other patients.

Pulse arrival time is not an adequate surrogate for pulse transit time in terms of tracking diastolic pressure

We compared pulse arrival time (PAT) and pulse transit time (PTT) in terms of their ability to track diastolic pressure (DP). We performed the comparison using high fidelity, invasive arterial waveforms recorded from six dogs during multiple interventions. On average, DP ranged from 40 to 106 mmHg and therefore varied widely. PAT and PTT were able to predict DP with average root-mean-squared-errors of 9.8 ± 5.8 mmHg and 5.7 ± 2.0 mmHg (p = 0.02). Thus, even though PAT is simpler to measure, we can only recommend using PTT for tracking DP.

Tube-load model parameter estimation for monitoring arterial hemodynamics

A useful model of the arterial system is the uniform, lossless tube with parametric load. This tube-load model is able to account for wave propagation and reflection (unlike lumped-parameter models such as the Windkessel) while being defined by only a few parameters (unlike comprehensive distributed-parameter models). As a result, the parameters may be readily estimated by accurate fitting of the model to available arterial pressure and flow waveforms so as to permit improved monitoring of arterial hemodynamics. In this paper, we review tube-load model parameter estimation techniques that have appeared in the literature for monitoring wave reflection, large artery compliance, pulse transit time, and central aortic pressure. We begin by motivating the use of the tube-load model for parameter estimation. We then describe the tube-load model, its assumptions and validity, and approaches for estimating its parameters. We next summarize the various techniques and their experimental results while highlighting their advantages over conventional techniques. We conclude the review by suggesting future research directions and describing potential applications.

Pulse arrival time is not an adequate surrogate for pulse transit time as a marker of blood pressure

Pulse transit time (PTT) is a proven, simple to measure, marker of blood pressure (BP) that could potentially permit continuous, noninvasive, and cuff-less BP monitoring (after an initial calibration). However, pulse arrival time (PAT), which is equal to the sum of PTT and the pre-ejection period, is gaining popularity for BP tracking, because it is even simpler to measure. The aim of this study was to evaluate the hypothesis that PAT is an adequate surrogate for PTT as a marker of BP. PAT and PTT were estimated through the aorta using high-fidelity invasive arterial waveforms obtained from six dogs during wide BP changes induced by multiple interventions. These time delays and their reciprocals were evaluated in terms of their ability to predict diastolic, mean, and systolic BP (DBP, MBP, and SBP) per animal. The root mean squared error (RMSE) between the BP parameter predicted via the time delay and the measured BP parameter was specifically used as the evaluation metric. Taking the reciprocals of the time delays tended to reduce the RMSE values. The DBP, MBP, and SBP RMSE values for 1/PAT were 9.8 ± 5.2, 10.4 ± 5.6, and 11.9 ± 6.1 mmHg, whereas the corresponding values for 1/PTT were 5.3 ± 1.2, 4.8 ± 1.0, and 7.5 ± 2.2 mmHg (P < 0.05). Thus tracking BP via PAT was not only markedly worse than via PTT but also unable to meet the FDA BP error limits. In contrast to previous studies, our results quantitatively indicate that PAT is not an adequate surrogate for PTT in terms of detecting challenging BP changes.