Noninvasive estimation of central blood pressure through fluid-structure interaction modeling

Central blood pressure (cBP) is considered a superior indicator of cardiovascular fitness than brachial blood pressure (bBP). Even though bBP is easy to measure noninvasively, it is usually higher than cBP due to pulse wave amplification, characterized by the gradual increase in peak systolic pressure during pulse wave propagation. In this study, we aim to develop an individualized transfer function that can accurately estimate cBP from bBP. We first construct a three-dimensional, patient-specific model of the upper limb arterial system using fluid-structure interaction simulations, incorporating variable material properties and complex boundary conditions. Then, we develop an analytical brachial-aortic transfer function based on novel solutions for compliant vessels. The accuracy of this transfer function is successfully validated against numerical simulation results, which effectively reproduce pulse wave propagation and amplification, with key hemodynamic parameters falling within the range of clinical measurements. Further analysis of the transfer function reveals that cBP is a linear combination of bBP and aortic flow rate in the frequency domain, with the coefficients determined by vessel geometry, material properties, and boundary conditions. Additionally, bBP primarily contributes to the steady component of cBP, while the aortic flow rate is responsible for the pulsatile component. Furthermore, local sensitivity analysis indicates that the lumen radius is the most influential parameter in accurately estimating cBP. Although not directly applicable clinically, the proposed transfer function enhances understanding of the underlying physics-highlighting the importance of aortic flow and lumen radius-and can guide the development of more practical transfer functions.

Reconstruction of central arterial pressure waveform based on CBi-SAN network from radial pressure waveform

The central arterial pressure (CAP) is an important physiological indicator of the human cardiovascular system which represents one of the greatest threats to human health. Accurate non-invasive detection and reconstruction of CAP waveforms are crucial for the reliable treatment of cardiovascular system diseases. However, the traditional methods are reconstructed with relatively low accuracy, and some deep learning neural network models also have difficulty in extracting features, as a result, these methods have potential for further advancement. In this study, we proposed a novel model (CBi-SAN) to implement an end-to-end relationship from radial artery pressure (RAP) waveform to CAP waveform, which consisted of the convolutional neural network (CNN), the bidirectional long-short-time memory network (BiLSTM), and the self-attention mechanism to improve the performance of CAP reconstruction. The data on invasive measurements of CAP and RAP waveform were used in 62 patients before and after medication to develop and validate the performance of CBi-SAN model for reconstructing CAP waveform. We compared it with traditional methods and deep learning models in mean absolute error (MAE), root mean square error (RMSE), and Spearman correlation coefficient (SCC). Study results indicated the CBi-SAN model performed great performance on CAP waveform reconstruction (MAE: 2.23 ± 0.11 mmHg, RMSE: 2.21 ± 0.07 mmHg), concurrently, the best reconstruction effect was obtained in the central artery systolic pressure (CASP) and the central artery diastolic pressure(CADP) (RMSECASP: 2.94 ± 0.48 mmHg, RMSECADP: 1.96 ± 0.06 mmHg). These results implied the performance of the CAP reconstruction based on CBi-SAN model was superior to the existing methods, hopped to be effectively applied to clinical practice in the future.

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.

Aortic pressure waveform reconstruction using a multi-channel Newton blind system identification algorithm

BACKGROUND

Central aortic pressure (CAP) as the major load on the left heart is of great importance in the diagnosis of cardiovascular disease. Studies have pointed out that CAP has a higher predictive value for cardiovascular disease than peripheral artery pressure (PAP) measured by means of traditional sphygmomanometry. However, direct measurement of the CAP waveform is invasive and expensive, so there remains a need for a reliable and well validated non-invasive approach.

METHODS

In this study, a multi-channel Newton (MCN) blind system identification algorithm was employed to noninvasively reconstruct the CAP waveform from two PAP waveforms. In simulation experiments, CAP waveforms were recorded in a previous study, on 25 patients and the PAP waveforms (radial and femoral artery pressure) were generated by FIR models. To analyse the noise-tolerance of the MCN method, variable amounts of noise were added to the peripheral signals, to give a range of signal-to-noise ratios. In animal experiments, central aortic, brachial and femoral pressure waveforms were simultaneously recorded from 2 Sprague-Dawley rats. The performance of the proposed MCN algorithm was compared with the previously reported cross-relation and canonical correlation analysis methods.

RESULTS

The results showed that the root mean square error of the measured and reconstructed CAP waveforms and less noise-sensitive using the MCN algorithm was smaller than those of the cross-relation and canonical correlation analysis approaches.

CONCLUSION

The MCN method can be exploited to reconstruct the CAP waveform. Reliable estimation of the CAP waveform from non-invasive measurements may aid in early diagnosis of cardiovascular disease.

Estimating Central Pulse Pressure From Blood Flow by Identifying the Main Physical Determinants of Pulse Pressure Amplification

Several studies suggest that central (aortic) blood pressure (cBP) is a better marker of cardiovascular disease risk than peripheral blood pressure (pBP). The morphology of the pBP wave, usually assessed non-invasively in the arm, differs significantly from the cBP wave, whose direct measurement is highly invasive. In particular, pulse pressure, PP (the amplitude of the pressure wave), increases from central to peripheral arteries, leading to the so-called pulse pressure amplification (ΔPP). The main purpose of this study was to develop a methodology for estimating central PP (cPP) from non-invasive measurements of aortic flow and peripheral PP. Our novel approach is based on a comprehensive understanding of the main cardiovascular properties that determine ΔPP along the aortic-brachial arterial path, namely brachial flow wave morphology in late systole, and vessel radius and distance along this arterial path. This understanding was achieved by using a blood flow model which allows for workable analytical solutions in the frequency domain that can be decoupled and simplified for each arterial segment. Results show the ability of our methodology to (i) capture changes in cPP and ΔPP produced by variations in cardiovascular properties and (ii) estimate cPP with mean differences smaller than 3.3 ± 2.8 mmHg on in silico data for different age groups (25-75 years old) and 5.1 ± 6.9 mmHg on in vivo data for normotensive and hypertensive subjects. Our approach could improve cardiovascular function assessment in clinical cohorts for which aortic flow wave data is available.

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.

Noninvasive Cardiac Output and Central Systolic Pressure From Cuff-Pressure and Pulse Wave Velocity

GOAL

We introduce a novel approach to estimate cardiac output (CO) and central systolic blood pressure (cSBP) from noninvasive measurements of peripheral cuff-pressure and carotid-to-femoral pulse wave velocity (cf-PWV).

METHODS

The adjustment of a previously validated one-dimensional arterial tree model is achieved via an optimization process. In the optimization loop, compliance and resistance of the generic arterial tree model as well as aortic flow are adjusted so that simulated brachial systolic and diastolic pressures and cf-PWV converge towards the measured brachial systolic and diastolic pressures and cf-PWV. The process is repeated until full convergence in terms of both brachial pressures and cf-PWV is reached. To assess the accuracy of the proposed framework, we implemented the algorithm on in vivo anonymized data from 20 subjects and compared the method-derived estimates of CO and cSBP to patient-specific measurements obtained with Mobil-O-Graph apparatus (central pressure) and two-dimensional transthoracic echocardiography (aortic blood flow).

RESULTS

Both CO and cSBP estimates were found to be in good agreement with the reference values achieving an RMSE of 0.36 L/min and 2.46 mmHg, respectively. Low biases were reported, namely -0.04 ± 0.36 L/min for CO predictions and -0.27 ± 2.51 mmHg for cSBP predictions.

SIGNIFICANCE

Our one-dimensional model can be successfully "tuned" to partially patient-specific standards by using noninvasive, easily obtained peripheral measurement data. The in vivo evaluation demonstrated that this method can potentially be used to obtain central aortic hemodynamic parameters in a noninvasive and accurate way.

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.

Estimation of echocardiogram parameters with the aid of impedance cardiography and artificial neural networks

The advent of cardiovascular diseases as a disease of mass catastrophy, in recent years is alarming. It is expected to spread as an epidemic by 2030. Present methods of determining the health of one's heart include doppler based echocardiogram, MDCT (Multi Detector Computed Tomography), among various other invasive and non-invasive hemodynamic monitoring techniques. These methods require expert supervision and costly clinical set-ups, and cannot be employed by a common individual to perform a self diagnosis of one's cardiac health, unassisted. In this work, the authors propose a novel methodology using impedance cardiography (ICG), for the determination of a person's cardio-vascular health. The recorded ICG signal helps in extraction of features which are used for estimating parameters for cardiac health monitoring. The proposed methodology with the aid of artificial neural network is able to determine Stroke Volume (SV), Left Ventricular End Systolic Volume (LVESV), Left Ventricular End Diastolic Volume (LVEDV), Left Ventricular Ejection Fraction (LVEF), Iso Volumetric Contraction Time (IVCT), Iso Volumetric Relaxation Time (IVRT), Left Ventricular Ejection Time (LVET), Total Systolic Time (TST), Total Diastolic Time (TDT), and Myocardial Performance Index (MPI), with error margins of ±8.9%, ±3.8%, ±1.4%, ±7.8%, ±16.0%, ±9.0%, ±9.7%, ±6.9%, ±6.2%, and ±0.9%, respectively. The proposed methodology could be used in screening of precursors to cardiac ailments, and to keep a check on the cardio-vascular health.

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.

Multiscale mathematical modeling vs. the generalized transfer function approach for aortic pressure estimation: a comparison with invasive data

We aimed to evaluate the performance of a mathematical model and currently available non-invasive techniques (generalized transfer function (GTF) method and brachial pressure) in the estimation of aortic pressure. We also aimed to investigate error dependence on brachial pressure errors, aorta-to-brachial pressure changes and demographic/clinical conditions. Sixty-two patients referred for invasive hemodynamic evaluation were consecutively recruited. Simultaneously, the registration of the aortic pressure using a fluid-filled catheter, brachial pressure and radial tonometric waveform was recorded. Accordingly, the GTF device and mathematical model were set. Radial invasive pressure was recorded soon after aortic measurement. The average invasive aortic pressure was 141.3 ± 20.2/76 ± 12.2 mm Hg. The simultaneous brachial pressure was 144 ± 17.8/81.5 ± 11.7 mm Hg. The GTF-based and model-based aortic pressure estimates were 133.1 ± 17.3/82.4 ± 12 and 137 ± 21.6/72.2 ± 16.7 mm Hg, respectively. The Bland-Altman plots showed a marked tendency to pressure overestimation for increasing absolute values, with the exclusion of mathematical model diastolic estimations. The systolic pressure was increased from the aortic to radial locations (7.5 ± 19 mm Hg), while the diastolic pressure was decreased (3.8 ± 9.8 mm Hg). The brachial pressure underestimated the systolic and overestimated diastolic intra-arterial radial pressure. GTF errors were independently correlated with the variability in pulse pressure amplification and with the brachial error. Errors of the mathematical model were related to only demographic and clinical conditions. Neither a multiscale mathematical model nor a generalized transfer function device substantially outperformed the oscillometric brachial pressure in the estimation of aortic pressure. Mathematical modeling should be improved by including further patient-specific conditions, while the variability in pulse pressure amplification may hamper the performance of the GTF method in patients at the risk of coronary artery disease.

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.

Estimation of aortic systolic blood pressure from radial systolic and diastolic blood pressures alone using artificial neural networks

BACKGROUND

Current aortic SBP estimation methods require recording of a peripheral pressure waveform, a step with no consensus on method. This study investigates the possibility of aortic SBP estimation from radial SBP and DBP using artificial neural networks (ANN) with [ANNSBP.DBP.heart rate (HR)] and without HR (ANNSBP.DBP).

METHODS

Ten-fold cross validation was applied to invasive, simultaneously recorded aortic and radial pressure during rest and nitroglycerin infusion (n = 62 patients). The results of the ANN models were compared with an ANN model using additional waveform features (ANNwaveform), to an N-point moving average method (NPMA) and to existing, validated generalized transfer function (GTF).

RESULTS

Estimated aortic SBP for all methods was on average less than 1 mmHg away from measured aortic SBP with the exception of NPMA (difference 2.0 ± 3.5 mmHg, P = 0.62). Variability of the difference was significantly greater in ANNSBP.DBP.HR and ANNSBP.DBP (both SD of ± 5.9 mmHg, P < 0.001 compared with GTF, ± 4.0 mmHg, P < 0.001). Inclusion of waveform features decreased the variability (ANNwaveform ± 3.9 mmHg, P = 0.264). Estimated aortic SBP in all models was correlated with measured SBP, with ANN models providing statistically similar results to the GTF method, only the NPMA being statistically different (P = 0.031).

CONCLUSION

These findings indicate that use of radial SBP, DBP, and HR alone can provide aortic SBP estimation comparable with the GTF, albeit with slightly greater variance. Pending noninvasive validation, the technique provides plausible aortic SBP estimation without waveform analysis.

Central Blood Pressure Monitoring via a Standard Automatic Arm Cuff

Current oscillometric devices for monitoring central blood pressure (BP) maintain the cuff pressure at a constant level to acquire a pulse volume plethysmography (PVP) waveform and calibrate it to brachial BP levels estimated with population average methods. A physiologic method was developed to further advance central BP measurement. A patient-specific method was applied to estimate brachial BP levels from a cuff pressure waveform obtained during conventional deflation via a nonlinear arterial compliance model. A physiologically-inspired method was then employed to extract the PVP waveform from the same waveform via ensemble averaging and calibrate it to the brachial BP levels. A method based on a wave reflection model was thereafter employed to define a variable transfer function, which was applied to the calibrated waveform to derive central BP. This method was evaluated against invasive central BP measurements from patients. The method yielded central systolic, diastolic, and pulse pressure bias and precision errors of -0.6 to 2.6 and 6.8 to 9.0 mmHg. The conventional oscillometric method produced similar bias errors but precision errors of 8.2 to 12.5 mmHg (p ≤ 0.01). The new method can derive central BP more reliably than some current non-invasive devices and in the same way as traditional cuff BP.

Estimation of Pulse Transit Time From Radial Pressure Waveform Alone by Artificial Neural Network

OBJECTIVE

To validate the feasibility of the estimation of pulse transit time (PTT) by artificial neural network (ANN) from radial pressure waveform alone.

METHODS

A cascade ANN with ten-fold cross validation was applied to invasively and simultaneously recorded aortic and radial pressure waveforms during rest and nitroglycerin infusion () for the estimation of mean and beat-to-beat PTT. The results of the ANN models were compared to a multiple linear regression (LR) model when the features of radial arterial pressure waveform in time and frequency domains were used as the predictors of the models.

RESULTS

For the estimation of mean PTT and beat-to-beat PTT by ANN ( ), the correlation coefficient between the and the measured PTT () (mean: ; beat-to-beat: ) is higher than that between the PTT estimated by LR ( ) and (mean: ; beat-to-beat: ). The standard deviation (SD) of the difference between the and ( ; beat-to-beat: ) is significantly less than that between the and (; beat-to-beat: 10 ms), but no significant difference exists between their mean ( ). The lack of frequency features of radial pressure waveform caused obvious reduction in the correlation coefficient and SD of the difference between the and . The performance of the ANN was improved by increasing the sample number but not by increasing the neuron number.

CONCLUSION

ANN is a potential method of PTT estimation from a single pressure measurement at radial artery.

Diastolic Augmentation Index Improves Radial Augmentation Index in Assessing Arterial Stiffness

Arterial stiffness is an important risk factor for cardiovascular events. Radial augmentation index (AI_r) can be more conveniently measured compared with carotid-femoral pulse wave velocity (cfPWV). However, the performance of AI_r in assessing arterial stiffness is limited. This study proposes a novel index AI_rd, a combination of AI_r and diastolic augmentation index (AI_d) with a weight α, to achieve better performance over AI_r in assessing arterial stiffness. 120 subjects (43 ± 21 years old) were enrolled. The best-fit α is determined by the best correlation coefficient between AI_rd and cfPWV. The performance of the method was tested using the 12-fold cross validation method. AI_rd (r = 0.68, P < 0.001) shows a stronger correlation with cfPWV and a narrower prediction interval than AI_r (r = 0.61, P < 0.001), AI_d (r = −0.17, P = 0.06), the central augmentation index (AI_c) (r = 0.61, P < 0.001) or AI_c normalized for heart rate of 75 bpm (r = 0.65, P < 0.001). Compared with AI_r (age, P < 0.001; gender, P < 0.001; heart rate, P < 0.001; diastolic blood pressure, P < 0.001; weight, P = 0.001), AI_rd has fewer confounding factors (age, P < 0.001; gender, P < 0.001). In conclusion, AI_rd derives performance improvement in assessing arterial stiffness, with a stronger correlation with cfPWV and fewer confounding factors.

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.

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.

Optimization of a generalized radial-aortic transfer function using parametric techniques

The central aortic blood pressure (cBP) waveform, which is different to that of peripheral locations, is a clinically important parameter for assessing cardiovascular function, however the gold standard for measuring cBP involves invasive catheter-based techniques. The difficulties associated with invasive measurements have given rise to the development of a variety of noninvasive methods. An increasingly applied method for the noninvasive derivation of cBP involves the application of transfer function (TF) techniques to a non-invasively measured radial blood pressure (BP) waveform. The purpose of the current study was to investigate the development of a general parametric model for determination of cBP from tonometrically transduced radial BP waveforms. The study utilized simultaneously measured invasive central aortic and noninvasive radial BP waveform measurements. Data sets were available from 92 subjects, a large cohort for a study of this nature. The output error (OE) model was empirically identified as the most appropriate model structure. A generalized model was developed using a pre-specified derivation cohort and then applied to a validation data set to estimate the recognized features of the cBP waveform. While our results showed that many relevant BP parameters could be derived within acceptable limits, the estimated augmentation index (AI) displayed only a weak correlation compared to the invasively measured value, indicating that any clinical diagnosis or interpretation based on estimated AI should be undertaken with caution.

A Simple Adaptive Transfer Function for Deriving the Central Blood Pressure Waveform from a Radial Blood Pressure Waveform

Generalized transfer functions (GTFs) are available to compute the more relevant central blood pressure (BP) waveform from a more easily measured radial BP waveform. However, GTFs are population averages and therefore may not adapt to variations in pulse pressure (PP) amplification (ratio of radial to central PP). A simple adaptive transfer function (ATF) was developed. First, the transfer function is defined in terms of the wave travel time and reflection coefficient parameters of an arterial model. Then, the parameters are estimated from the radial BP waveform by exploiting the observation that central BP waveforms exhibit exponential diastolic decays. The ATF was assessed using the original data that helped popularize the GTF. These data included radial BP waveforms and invasive reference central BP waveforms from cardiac catheterization patients. The data were divided into low, middle, and high PP amplification groups. The ATF estimated central BP with greater accuracy than GTFs in the low PP amplification group (e.g., central systolic BP and PP root-mean-square-errors of 3.3 and 4.2 mm Hg versus 6.2 and 7.1 mm Hg; p ≤ 0.05) while showing similar accuracy in the higher PP amplification groups. The ATF may permit more accurate, non-invasive central BP monitoring in elderly and hypertensive patients.

Experimental feasibility study of estimation of the normalized central blood pressure waveform from radial photoplethysmogram

The feasibility of a novel system to reliably estimate the normalized central blood pressure (CBPN) from the radial photoplethysmogram (PPG) is investigated. Right-wrist radial blood pressure and left-wrist PPG were simultaneously recorded in five different days. An industry-standard applanation tonometer was employed for recording radial blood pressure. The CBP waveform was amplitude-normalized to determine CBPN. A total of fifteen second-order autoregressive models with exogenous input were investigated using system identification techniques. Among these 15 models, the model producing the lowest coefficient of variation (CV) of the fitness during the five days was selected as the reference model. Results show that the proposed model is able to faithfully reproduce CBPN (mean fitness = 85.2% ± 2.5%) from the radial PPG for all 15 segments during the five recording days. The low CV value of 3.35% suggests a stable model valid for different recording days.

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.

Comparative study on tube-load modeling of arterial hemodynamics in humans

In this paper, we assess the validity of two alternative tube-load models for describing the relationship between central aortic and peripheral arterial blood pressure (BP) waveforms in humans. In particular, a single-tube (1-TL) model and a serially connected two-tube (2-TL) model, both terminated with a Windkessel load, are considered as candidate representations of central aortic-peripheral arterial path. Using the central aortic, radial and femoral BP waveform data collected from eight human subjects undergoing coronary artery bypass graft with cardiopulmonary bypass procedure, the fidelity of the tube-load models was quantified and compared with each other. Both models could fit the central aortic-radial and central aortic-femoral BP waveform pairs effectively. Specifically, the models could estimate pulse travel time (PTT) accurately, and the model-derived frequency response was also close to the empirical transfer function estimate obtained directly from the central aortic and peripheral BP waveform data. However, 2-TL model was consistently superior to 1-TL model with statistical significance as far as the accuracy of the central aortic BP waveform was concerned. Indeed, the average waveform RMSE was 2.52 mmHg versus 3.24 mmHg for 2-TL and 1-TL models, respectively (p < 0.05); the r² value between measured and estimated central aortic BP waveforms was 0.96 and 0.93 for 2-TL and 1-TL models, respectively (p < 0.05). We concluded that the tube-load models considered in this paper are valid representations that can accurately reproduce central aortic-radial/femoral BP waveform relationships in humans, although the 2-TL model is preferred if an accurate central aortic BP waveform is highly desired.

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.