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

Flow-Based Coronary Artery Bypass Graft Patency Metrics: Uncertainty Quantification Simulations to Guide Development

PURPOSE

Over time, transit time flow measurement (TTFM) has proven itself as a simple and effective tool for intra-operative evaluation of coronary artery bypass grafts (CABGs). However, metrics used to screen for possible technical error show considerable spread, preventing the definition of sharp cut-off values to distinguish between patent, questionable, and failed grafts. The simulation study presented in this paper aims to quantify this uncertainty for commonly used patency metrics, and to identify the most important physiological parameters influencing it.

METHODS

Uncertainty quantification was performed on a realistic multiscale numerical model of the coronary circulation, guided by Morris screening sensitivity analysis of a simpler, lumped-parameter model. Simulation results were qualitatively verified against results of a recent clinical study.

RESULTS

Correspondence with clinical study data is reasonable, especially considering that the model was not fitted in any way. Stenosis severity was confirmed to be an influential parameter. However, also cardiac period and graft diameter were observed to be important, particularly for mean flow rate and pulsatility index.

CONCLUSION

Metrics quantifying the flow waveform's diastolic dominance show the highest sensitivity to graft stenosis, and seem to be least affected by autoregulation. Among these, the novel diastolic resistance index shows the strongest sensitivity to stenosis severity.

SIGNIFICANCE

The approach used in this study is expected to benefit the development of improved patency metrics, by allowing medical engineers to include sensitivity and uncertainty in assessing, in-silico, the potential of novel metrics, thus enabling them to provide better guidance in the design of clinical studies.

In silico data-based comparison of the accuracy and error source of various methods for noninvasively estimating central aortic blood pressure

BACKGROUND AND OBJECTIVES

The higher clinical significance of central aortic blood pressure (CABP) compared to peripheral blood pressures has been extensively demonstrated. Accordingly, many methods for noninvasively estimating CABP have been proposed. However, there still lacks a systematic comparison of existing methods, especially in terms of how they differ in the ability to tolerate individual differences or measurement errors. The present study was designed to address this gap.

METHODS

A large-scale 'virtual subject' dataset (n = 600) was created using a computational model of the cardiovascular system, and applied to examine several classical CABP estimation methods, including the direct method, generalized transfer function (GTF) method, n-point moving average (NPMA) method, second systolic pressure of periphery (SBP2) method, physical model-based wave analysis (MBWA) method, and suprasystolic cuff-based waveform reconstruction (SCWR) method. The errors of CABP estimation were analyzed and compared among methods with respect to the magnitude/distribution, correlations with physiological/hemodynamic factors, and sensitivities to noninvasive measurement errors.

RESULTS

The errors of CABP estimation exhibited evident inter-method differences in terms of the mean and standard deviation (SD). Relatively, the estimation errors of the methods adopting pre-trained algorithms (i.e., the GTF and SCWR methods) were overall smaller and less sensitive to variations in physiological/hemodynamic conditions and random errors in noninvasive measurement of brachial arterial blood pressure (used for calibrating peripheral pulse wave). The performances of all the methods worsened following the introduction of random errors to peripheral pulse wave (used for deriving CABP), as characterized by the enlarged SD and/or increased mean of the estimation errors. Notably, the GTF and SCWR methods did not exhibit a better capability of tolerating pulse wave errors in comparison with other methods.

CONCLUSIONS

Classical noninvasive methods for estimating CABP were found to differ considerably in both the accuracy and error source, which provided theoretical evidence for understanding the specific advantages and disadvantages of each method. Knowledge about the method-specific error source and sensitivities of errors to different physiological/hemodynamic factors may contribute as theoretical references for interpreting clinical observations and exploring factors underlying large estimation errors, or provide guidance for optimizing existing methods or developing new methods.

In silico modelling of stroke volume, cardiac output and systemic vascular resistance in cardiovascular safety pharmacology studies by telemetry

The principle of proportionality of the systolic area of the central aortic pressure to stroke volume (SV) has been long known. The aim of the present work was to evaluate an in silico solution derived from this principle for modelling SV (iSV model) in cardiovascular safety pharmacology studies by telemetry. Blood pressure was measured in the abdominal aorta in accordance with standard practice. Central aortic pressure was modelled from the abdominal aortic pressure waveform using the N-point moving average (NPMA) method for beat-to-beat estimation of SV. First, the iSV was compared to the SV measured by ultrasonic flowmetry in the ascending aorta (uSV) after various pharmacological challenges in beagle dogs anaesthetised with etomidate/fentanyl. The iSV showed minimal bias (0.2 mL i.e. 2%) and excellent agreement with uSV. Then, previous telemetry studies including reference vasoactive and inotropic compounds were retrospectively reanalysed to model drug effects on stroke volume (iSV), cardiac output (iCO) and systemic vascular resistance (iSVR). Among them, the examples of nicardipine and isoprenaline highlight risks of erroneous or biased estimation of drug effects from the abdominal aortic pressure due to pulse pressure amplification. Furthermore, the examples of verapamil, quinidine and moxifloxacin show that iSV, iCO and iSVR are earlier biomarkers than blood pressure itself for predicting drug effect on blood pressure. This in silico modelling approach included in vivo telemetry safety pharmacology studies can be considered as a New Approach Methodology (NAM) that provides valuable additional information and contribute to improving non-clinical translational research to the clinic.

Central arterial pressure estimation based on two peripheral pressure measurements using one-dimensional blood flow simulation

Aortic pressure can be estimated using one-dimensional arterial flow simulations. This study demonstrates that two peripheral pressure measurements can be used to acquire the central pressure curve through the patient-specific optimization of a set of system parameters. Radial and carotid pressure measurements and parameter optimization were performed in the case of 62 patients. The two calculated aortic curves were in good agreement, Systolic and Mean Blood Pressures differed on average by 0.5 and -0.5 mmHg, respectively. Good agreement was achieved with the transfer function method as well. The effect of carotid clamping is demonstrated using one resulting patient-specific arterial network.

Optimization and validation of a suprasystolic brachial cuff-based method for noninvasively estimating central aortic blood pressure

Clinical studies have extensively demonstrated that central aortic blood pressure (CABP) has greater clinical significance in comparison with peripheral blood pressure. Despite the existence of various techniques for noninvasively measuring CABP, the clinical applications of most techniques are hampered by the unsatisfactory accuracy or large variability in measurement errors. In this study, we proposed a new method for noninvasively estimating CABP with improved accuracy and reduced uncertain errors. The main idea was to optimize the estimation of the pulse wave transit time from the aorta to the occluded lumen of the brachial artery under a suprasystolic cuff by identifying and utilizing the characteristic information of the cuff oscillation wave, thereby improving the accuracy and stability of the CABP estimation algorithms under various physiological conditions. The method was firstly developed and verified based on large-scale virtual subject data (n = 800) generated by a computational model of the cardiovascular system coupled to a brachial cuff, and then validated with small-scale in vivo data (n = 34). The estimation errors for the aortic systolic pressure were -0.05 ± 0.63 mmHg in the test group of the virtual subjects and -1.09 ± 3.70 mmHg in the test group of the patients, both demonstrating a good performance. In particular, the estimation errors were found to be insensitive to variations in hemodynamic conditions and cardiovascular properties, manifesting the high robustness of the method. The method may have promising clinical applicability, although further validation studies with larger-scale clinical data remain necessary.

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.

Central-to-peripheral blood pressure amplification: role of the recording site, technology, analysis approach, and calibration scheme in invasive and non-invasive data agreement

Background

Systolic blood pressure amplification (SBPA) and pulse pressure amplification (PPA) can independently predict cardiovascular damage and mortality. A wide range of methods are used for the non-invasive estimation of SBPA and PPA. The most accurate non-invasive method for obtaining SBPA and/or PPA remains unknown.

Aim

This study aims to evaluate the agreement between the SBPA and PPA values that are invasively and non-invasively obtained using different (1) measurement sites (radial, brachial, carotid), (2) measuring techniques (tonometry, oscillometry/plethysmography, ultrasound), (3) pulse waveform analysis approaches, and (4) calibration methods [systo-diastolic vs. approaches using brachial diastolic and mean blood pressure (BP)], with the latter calculated using different equations or measured by oscillometry.

Methods

Invasive aortic and brachial pressure (catheterism) and non-invasive aortic and peripheral (brachial, radial) BP were simultaneously obtained from 34 subjects using different methodologies, analysis methods, measuring sites, and calibration methods. SBPA and PPA were quantified. Concordance correlation and the Bland-Altman analysis were performed.

Results

(1) In general, SBPA and PPA levels obtained with non-invasive approaches were not associated with those recorded invasively. (2) The different non-invasive approaches led to (extremely) dissimilar results. In general, non-invasive measurements underestimated SBPA and PPA; the higher the invasive SBPA (or PPA), the greater the underestimation. (3) None of the calibration schemes, which considered non-invasive brachial BP to estimate SBPA or PPA, were better than the others. (4) SBPA and PPA levels obtained from radial artery waveform analysis (tonometry) (5) and common carotid artery ultrasound recordings and brachial artery waveform analysis, respectively, minimized the mean errors.

Conclusions

Overall, the findings showed that (i) SBPA and PPA indices are not "synonymous" and (ii) non-invasive approaches would fail to accurately determine invasive SBPA or PPA levels, regardless of the recording site, analysis, and calibration methods. Non-invasive measurements generally underestimated SBPA and PPA, and the higher the invasive SBPA or PPA, the higher the underestimation. There was not a calibration scheme better than the others. Consequently, our study emphasizes the strong need to be critical of measurement techniques, to have methodological transparency, and to have expert consensus for non-invasive assessment of SBPA and PPA.

Central arterial pressure and patient-specific model parameter estimation based on radial pressure measurements

One-dimensional arterial flow simulations are suitable to estimate the aortic pressure from peripheral measurements in a patient-specific arterial network. This study introduces a reduction of the system parameters, and a novel calculation method to estimate the patient-specific set and the aortic curve based on radial applanation tonometry. Peripheral and aortic pressure curves were measured in patients, optimization were carried out. The aortic pressure curves were reproduced well, with an overestimation of the measured Systolic and Mean Blood Pressures on average by 0.6 and 0.5 mmHg respectively, and the Root Mean Square Difference of the curves was 3 mmHg on average.

Aortic systolic and pulse pressure invasively and non-invasively obtained: Comparative analysis of recording techniques, arterial sites of measurement, waveform analysis algorithms and calibration methods

Background: The non-invasive estimation of aortic systolic (aoSBP) and pulse pressure (aoPP) is achieved by a great variety of devices, which differ markedly in the: 1) principles of recording (applied technology), 2) arterial recording site, 3) model and mathematical analysis applied to signals, and/or 4) calibration scheme. The most reliable non-invasive procedure to obtain aoSBP and aoPP is not well established. Aim: To evaluate the agreement between aoSBP and aoPP values invasively and non-invasively obtained using different: 1) recording techniques (tonometry, oscilometry/plethysmography, ultrasound), 2) recording sites [radial, brachial (BA) and carotid artery (CCA)], 3) waveform analysis algorithms (e.g., direct analysis of the CCA pulse waveform vs. peripheral waveform analysis using general transfer functions, N-point moving average filters, etc.), 4) calibration schemes (systolic-diastolic calibration vs. methods using BA diastolic and mean blood pressure (bMBP); the latter calculated using different equations vs. measured directly by oscillometry, and 5) different equations to estimate bMBP (i.e., using a form factor of 33% ("033"), 41.2% ("0412") or 33% corrected for heart rate ("033HR"). Methods: The invasive aortic (aoBP) and brachial pressure (bBP) (catheterization), and the non-invasive aoBP and bBP were simultaneously obtained in 34 subjects. Non-invasive aoBP levels were obtained using different techniques, analysis methods, recording sites, and calibration schemes. Results: 1) Overall, non-invasive approaches yielded lower aoSBP and aoPP levels than those recorded invasively. 2) aoSBP and aoPP determinations based on CCA recordings, followed by BA recordings, were those that yielded values closest to those recorded invasively. 3) The "033HR" and "0412" calibration schemes ensured the lowest mean error, and the "033" method determined aoBP levels furthest from those recorded invasively. 4) Most of the non-invasive approaches considered overestimated and underestimated aoSBP at low (i.e., 80 mmHg) and high (i.e., 180 mmHg) invasive aoSBP values, respectively. 5) The higher the invasively measured aoPP, the higher the level of underestimation provided by the non-invasive methods. Conclusion: The recording method and site, the mathematical method/model used to quantify aoSBP and aoPP, and to calibrate waveforms, are essential when estimating aoBP. Our study strongly emphasizes the need for methodological transparency and consensus for the non-invasive aoBP assessment.

Estimation of cardiac stroke volume from radial pulse waveform by artificial neural network

BACKGROUND AND OBJECTIVES

Stroke volume (SV) and cardiac output (CO) are the key indicators for the evaluation of cardiac function and hemodynamic status during the perioperative period, which are very important in the detection and treatment of cardiovascular diseases. Traditional CO and SV measurement methods have problems such as complex operation, low precision and poor generalization ability.

METHODS

In this paper, a method for estimating stroke volume based on cascade artificial neural network (ANN) and time domain features of radial pulse waveform (SV_ANN) was proposed. The simulation datasets of 4000 radial pulse waveforms and stroke volume (SV_meas) were generated by a 55 segment transmission line model of the human systemic vasculature and a recursive algorithm. The ANN was trained and tested by 10-fold cross-validation, and compared with 12 traditional models.

RESULTS

Experimental results showed that the Pearson correlation coefficients and mean difference between SV_ANN and SV_meas (R=0.95, mean standard deviation (SD) = 0.00 ± 6.45) were better than the best results of the 12 traditional models. Moreover, as increasing the number of training samples, the performance improvement of the ANN (R=0.94(Δ + 0.04), mean ± SD = 0.00 ± 6.38(Δ± 2.02)) was better than the other best model, namely, multiple linear regression model (MLR) (R=0.93(Δ + 0.03), mean ± SD = 0.00 ± 6.99(Δ± 1.50)).

CONCLUSIONS

A method is proposed to estimate cardiac stroke volume by the ANN with time domain features of radial pulse wave. It avoids the complicated modeling process based on hemodynamics within traditional models, improves the estimation accuracy of SV, and has a good generalization ability.

Ultrasound-based method for individualized estimation of central aortic blood pressure from flow velocity and diameter

Central aortic blood pressure (CABP) is a better predictor for cardiovascular events than brachial blood pressure. However, direct CABP measurement is invasive. The objective of this paper is to develop an ultrasound-based method using individualized Windkessel (WK) models for non-invasive estimation of CABP. Three WK models (with two-, three- and four-element WK, named, WK2, WK3 and WK4, respectively) were created and the model parameters were individualized based on aortic flow velocity and diameter waveforms measured by ultrasound (US). Experimental data were acquired in 42 subjects aged 21-67 years. The CABP estimated by WK models was compared with the reference CABP obtained using a commercial system. The results showed that the overall performance of the WK3 and WK4 models was similar, outperforming the WK2 model. The estimated CABP based on WK3/WK4 model showed good agreement with the reference CABP: the absolute errors of systolic blood pressure (SBP), 2.4 ± 2.1/2.4 ± 2.0 mmHg; diastolic blood pressure (DBP), 1.4 ± 1.1/1.7 ± 1.5 mmHg; mean blood pressure (MBP), 1.3 ± 0.8/1.3 ± 0.8 mmHg; pulse pressure (PP), 3.0 ± 2.3/3.2 ± 2.6 mmHg; the root mean square error (RMSE) of the waveforms, 2.5 ± 1.0/2.6 ± 1.1 mmHg. Therefore, the proposed method can provide a non-invasive CABP estimation during routine cardiac US examination.

Simultaneous adaption of the gain and phase of a generalized transfer function for aortic pressure waveform estimation

GOAL

This paper proposes and validates a completely adaptive transfer function (CATF) based on an autoregressive exogenous (ARX) model which adjusts the gain and phase of a generalized transfer function (GTF) simultaneously to estimate the aortic pressure waveform from a brachial pressure waveform.

METHODS

Invasive aortic and brachial pressure waveforms were recorded from 34 subjects for the validation of the proposed method. Individual transfer functions (ITFs) were trained based on the pressure waveforms using an ARX model. The GTF was derived by averaging the ITFs. CATF was then obtained by adjusting both the gain and phase of the GTF using regression formulas calculated from the ITFs and brachial hemodynamic parameters. Meanwhile the quantitative contributions of the adaption of gain and phase of the GTF were investigated respectively. The root-mean-square-error of the total waveform and absolute errors of common hemodynamic indices including systolic and diastolic blood pressures (SBP and DBP, respectively), pulse pressure (PP) and augmentation index were used to evaluate the performance of the proposed method in the data divided into low, middle and high PP amplification groups.

RESULTS

The CATF achieved lower errors for DBP and PP in the low PP amplification group (1.79 versus 2.10 mmHg and 5.08 versus 6.23 mmHg, respectively, both P < 0.05) and PP in the middle amplification group (1.43 versus 1.92 mmHg, P < 0.05) compared with the GTF.

SIGNIFICANCE

The proposed method provides a step towards the development of an improved and clinically useful non-invasive approach for estimating the aortic pressure waveform from a peripheral pressure waveform.

Physiological and clinical insights from reservoir-excess pressure analysis

There is a growing body of evidence indicating that reservoir-excess pressure model parameters provide physiological and clinical insights above and beyond standard blood pressure (BP) and pulse waveform analysis. This information has never been collectively examined and was the aim of this review. Cardiovascular disease is the leading cause of mortality worldwide, with BP as the greatest cardiovascular disease risk factor. However, brachial systolic and diastolic BP provide limited information on the underlying BP waveform, missing important BP-related cardiovascular risk. A comprehensive analysis of the BP waveform is provided by parameters derived via the reservoir-excess pressure model, which include reservoir pressure, excess pressure, and systolic and diastolic rate constants and Pinfinity. These parameters, derived from the arterial BP waveform, provide information on the underlying arterial physiology and ventricular-arterial interactions otherwise missed by conventional BP and waveform indices. Application of the reservoir-excess pressure model in the clinical setting may facilitate a better understanding and earlier identification of cardiovascular dysfunction associated with disease. Indeed, reservoir-excess pressure parameters have been associated with sub-clinical markers of end-organ damage, cardiac and vascular dysfunction, and future cardiovascular events and mortality beyond conventional risk factors. In the future, greater understanding is needed on how the underlying physiology of the reservoir-excess pressure parameters informs cardiovascular disease risk prediction over conventional BP and waveform indices. Additional consideration should be given to the application of the reservoir-excess pressure model in clinical practice using new technologies embedded into conventional BP assessment methods.

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.

Estimation of wave reflection in aorta from radial pulse waveform by artificial neural network: a numerical study

BACKGROUND AND OBJECTIVE

Wave reflection in aorta has been shown to have incremental value for predicting cardiovascular events. However, its estimation by wave separation analysis (WSA) is complex.

METHODS

In this study, a novel method was proposed based on a cascade artificial neural network (ANN) for wave reflection estimation by the frequency features of radial pressure waveform alone. The simulation database of 4000 samples was generated by a 55-segment transmission line model of human arterial tree and was used for evaluating the ANN with 10-fold cross validation for the estimation of reflection magnitude (RM_ANN) and reflection index (RI_ANN) of wave reflection in aorta. RM and RI also were estimated by the WSA with a triangle waveform of aortic flow (RM_WSA and RI_WSA) and with a real aortic flow waveform (RM_Ref and RI_Ref) as reference values.

RESULTS

The results showed the correlation coefficient and mean difference between RM_ANN and RM_Ref (R² = 0.92, mean ± standard deviation (SD) = 0.0 ± 0.02) and those between RI_ANN and RI_Ref (R² = 0.91, mean ± SD = 0.0 ± 0.01) were better than those between RM_WSA and RM_Ref (R² = 0.51, mean ± SD = 0.01 ± 0.07) and those between RI_WSA and RI_Ref (R² = 0.50, mean ± SD = 0.0 ± 0.02). As the sample diversity in the simulation database was increased but the total number of samples keeps constant, the advantage of the ANN, though decreased slightly, became more significant than those of WSA (RM_ANN VS. RM_Ref and RI_ANN VS. RI_Ref: R² = 0.88 and 0.88, mean ± SD = 0.0 ± 0.05 and 0.0 ± 0.05; RM_WSA VS. RM_Ref and RI_WSA VS. RI_Ref: R² = 0.24 and 0.24, mean ± SD = 0.07 ± 0.24 and 0.02 ± 0.08, respectively). In addition, the ANN can achieve better results than the traditional method WSA even only two hidden neurons are used.

CONCLUSIONS

ANN is a potential method for the estimation of wave reflection in aorta by a single radial pulse waveform, but further validation of this method in clinic trials is needed.