Estimating central blood pressure from aortic flow: development and assessment of algorithms

A new methodology for determining the central pressure waveform from peripheral measurement using Fourier-based machine learning

Radial applanation tonometry is a well-established technique for hemodynamic monitoring and is becoming popular in affordable non-invasive wearable healthcare electronics. To assess the central aortic pressure using radial-based measurements, there is an essential need to develop mathematical approaches to estimate the central pressure waveform. In this study, we propose a new Fourier-based machine learning (F-ML) methodology to transfer non-invasive radial pressure measurements to the central pressure waveform. To test the method, collection of tonometry recordings of the radial and carotid pressure measurements are used from the Framingham Heart Study (2640 individuals, 55 % women) with mean (range) age of 66 (40-91) years. Method-derived estimates are significantly correlated with the measured ones for three major features of the pressure waveform (systolic blood pressure, r=0.97, p < 0.001; diastolic blood pressure, r=0.99, p < 0.001; and mean blood pressure, r=0.99, p < 0.001). In all cases, the Bland-Altman analysis shows negligible bias in the estimations and error is bounded to 5.4 mmHg. Findings also suggest that the F-ML approach reconstructs the shape of the central pressure waveform accurately with the average normalized root mean square error of 5.5 % in the testing population which is blinded to all stages of machine learning development. The results show that the F-ML transfer function outperforms the conventional generalized transfer function, particularly in terms of reconstructing the shape of the central pressure waveform morphology. The proposed F-ML transfer function can provide accurate estimates for the central pressure waveform, and ultimately expand the usage of non-invasive devices for central hemodynamic assessment.

Development of a Personalized Multiclass Classification Model to Detect Blood Pressure Variations Associated with Physical or Cognitive Workload

Comprehending the regulatory mechanisms influencing blood pressure control is pivotal for continuous monitoring of this parameter. Implementing a personalized machine learning model, utilizing data-driven features, presents an opportunity to facilitate tracking blood pressure fluctuations in various conditions. In this work, data-driven photoplethysmograph features extracted from the brachial and digital arteries of 28 healthy subjects were used to feed a random forest classifier in an attempt to develop a system capable of tracking blood pressure. We evaluated the behavior of this latter classifier according to the different sizes of the training set and degrees of personalization used. Aggregated accuracy, precision, recall, and F1-score were equal to 95.1%, 95.2%, 95%, and 95.4% when 30% of a target subject's pulse waveforms were combined with five randomly selected source subjects available in the dataset. Experimental findings illustrated that incorporating a pre-training stage with data from different subjects made it viable to discern morphological distinctions in beat-to-beat pulse waveforms under conditions of cognitive or physical workload.

Patient-specific non-invasive estimation of the aortic blood pressure waveform by ultrasound and tonometry

BACKGROUND AND OBJECTIVE

Aortic blood pressure (ABP) is a more effective prognostic indicator of cardiovascular disease than peripheral blood pressure. A highly accurate algorithm for non-invasively deriving the ABP wave, based on ultrasonic measurement of aortic flow combined with peripheral pulse wave measurements, has been proposed elsewhere. However, it has remained at the proof-of-concept stage because it requires a priori knowledge of the ABP waveform to calculate aortic pulse wave velocity (PWV). The objective of this study is to transform this proof-of-concept algorithm into a clinically feasible technique.

METHODS

We used the Bramwell-Hill equation to non-invasively calculate aortic PWV which was then used to reconstruct the ABP waveform from non-invasively determined aortic blood flow velocity, aortic diameter, and radial pressure. The two aortic variables were acquired by an ultrasound system from 90 subjects, followed by recordings of radial pressure using a SphygmoCor device. The ABPs estimated by the new algorithm were compared with reference values obtained by cardiac catheterization (invasive validation, 8 subjects aged 62.3 ± 12.7 years) and a SphygmoCor device (non-invasive validation, 82 subjects aged 45.0 ± 17.8 years).

RESULTS

In the invasive comparison, there was good agreement between the estimated and directly measured pressures: the mean error in systolic blood pressure (SBP) was 1.4 ± 0.8 mmHg; diastolic blood pressure (DBP), 0.9 ± 0.8 mmHg; mean blood pressure (MBP), 1.8 ± 1.2 mmHg and pulse pressure (PP), 1.4 ± 1.1 mmHg. In the non-invasive comparison, the estimated and directly measured pressures also agreed well: the errors being: SBP, 2.0 ± 1.4 mmHg; DBP, 0.8 ± 0.1 mmHg; MBP, 0.1 ± 0.1 mmHg and PP, 2.3 ± 1.6 mmHg. The significance of the differences in mean errors between calculated and reference values for SBP, DBP, MBP and PP were assessed by paired t-tests. The agreement between the reference methods and those obtained by applying the new approach was also expressed by correlation and Bland-Altman plots.

CONCLUSION

The new method proposed here can accurately estimate ABP, allowing this important variable to be obtained non-invasively, using standard, well validated measurement techniques. It thus has the potential to relocate ABP estimation from a research environment to more routine use in the cardiac clinic.

SHORT ABSTRACT

A highly accurate algorithm for non-invasively deriving the ABP wave has been proposed elsewhere. However, it has remained at the proof-of-concept stage because it requires a priori knowledge of the ABP waveform to calculate aortic pulse wave velocity (PWV). This study aims to transform this proof-of-concept algorithm into a clinically feasible technique. We used the Bramwell-Hill equation to non-invasively calculate aortic PWV which was then used to reconstruct the ABP waveform. The ABPs estimated by the new algorithm were compared with reference values obtained by cardiac catheterization or a SphygmoCor device. The results showed that there was good agreement between the estimated and directly measured pressures. The new method proposed can accurately estimate ABP, allowing this important variable to be obtained non-invasively, using standard, well validated measurement techniques. It thus has the potential to relocate ABP estimation from a research environment to more routine use in the cardiac clinic.

Effect of TAVR commissural alignment on coronary flow: A fluid-structure interaction analysis

BACKGROUND AND OBJECTIVES

Coronary obstruction is a complication that may affect patients receiving Transcatheter Aortic Valve Replacement (TAVR), with catastrophic consequences and long-term negative effects. To enable healthy coronary perfusion, it is fundamental to appropriately position the device with respect to the coronary ostia. Nonetheless, most TAVR delivery systems do not control commissural alignment to do so. Moreover, no in silico study has directly assessed the effect of commissural alignment on coronary perfusion. This work aims to evaluate the effect of TAVR commissural alignment on coronary perfusion and device performance.

METHODS

A two-way computational fluid-structure interaction model is used to predict coronary perfusion at different commissural alignments. Moreover, in each scenario, hemodynamic biomarkers are evaluated to assess device performance.

RESULTS

Commissural misalignment is shown to reduce the total coronary perfusion by -3.2% and the flow rate to a single coronary branch by -6.8%. It is also observed to impair valvular function by reducing the systolic geometric orifice area by -2.5% and increasing the systolic transvalvular pressure gradients by +5.3% and the diastolic leaflet stresses by +16.0%.

CONCLUSIONS

The present TAVR patient model indicates that coronary perfusion, hemodynamic and structural performance are minimized when the prosthesis commissures are fully misaligned with the native ones. These results support the importance of enabling axial control in new TAVR delivery catheter systems and defining recommended values of commissural alignment in upcoming clinical treatment guidelines.

Haemodynamic effects of hypertension and type 2 diabetes: Insights from a 4D flow MRI-based personalized cardiovascular mathematical model

Type 2 diabetes (T2D) and hypertension increase the risk of cardiovascular diseases mediated by whole-body changes to metabolism, cardiovascular structure and haemodynamics. The haemodynamic changes related to hypertension and T2D are complex and subject-specific, however, and not fully understood. We aimed to investigate the haemodynamic mechanisms in T2D and hypertension by comparing the haemodynamics between healthy controls and subjects with T2D, hypertension, or both. For all subjects, we combined 4D flow magnetic resonance imaging data, brachial blood pressure and a cardiovascular mathematical model to create a comprehensive subject-specific analysis of central haemodynamics. When comparing the subject-specific haemodynamic parameters between the four groups, the predominant haemodynamic difference is impaired left ventricular relaxation in subjects with both T2D and hypertension compared to subjects with only T2D, only hypertension and controls. The impaired relaxation indicates that, in this cohort, the long-term changes in haemodynamic load of co-existing T2D and hypertension cause diastolic dysfunction demonstrable at rest, whereas either disease on its own does not. However, through subject-specific predictions of impaired relaxation, we show that altered relaxation alone is not enough to explain the subject-specific and group-related differences; instead, a combination of parameters is affected in T2D and hypertension. These results confirm previous studies that reported more adverse effects from the combination of T2D and hypertension compared to either disease on its own. Furthermore, this shows the potential of personalized cardiovascular models in providing haemodynamic mechanistic insights and subject-specific predictions that could aid in the understanding and treatment planning of patients with T2D and hypertension. KEY POINTS: The combination of 4D flow magnetic resonance imaging data and a cardiovascular mathematical model allows for a comprehensive analysis of subject-specific haemodynamic parameters that otherwise cannot be derived non-invasively. Using this combination, we show that diastolic dysfunction in subjects with both type 2 diabetes (T2D) and hypertension is the main group-level difference between controls, subjects with T2D, subjects with hypertension, and subjects with both T2D and hypertension. These results suggest that, in this relatively healthy population, the additional load of both hypertension and T2D affects the haemodynamic function of the left ventricle, whereas each disease on its own is not enough to cause significant effects under resting conditions. Finally, using the subject-specific model, we show that the haemodynamic effects of diastolic dysfunction alone are not sufficient to explain all the observed haemodynamic differences. Instead, additional subject-specific variations in cardiac and vascular function combine to explain the complex haemodynamics of subjects affected by hypertension and/or T2D.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models

PURPOSE

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model.

METHOD

The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation.

RESULTS

The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress.

CONCLUSION

Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

Central Aortic Blood Pressure Waveform Estimation with a Temporal Convolutional Network

A novel temporal convolutional network (TCN) model is utilized to reconstruct the central aortic blood pressure (aBP) waveform from the radial blood pressure waveform. The method does not need manual feature extraction as traditional transfer function approaches. The data acquired by the SphygmoCor CVMS device in 1,032 participants as a measured database and a public database of 4,374 virtual healthy subjects were used to compare the accuracy and computational cost of the TCN model with the published convolutional neural network and bi-directional long short-term memory (CNN-BiLSTM) model. The TCN model was compared with CNN-BiLSTM in the root mean square error (RMSE). The TCN model generally outperformed the existing CNN-BiLSTM model in terms of accuracy and computational cost. For the measured and public databases, the RMSE of the waveform using the TCN model was 0.55 ± 0.40 mmHg and 0.84 ± 0.29 mmHg, respectively. The training time of the TCN model was 9.63 min and 25.51 min for the entire training set; the average test time was around 1.79 ms and 8.58 ms per test pulse signal from the measured and public databases, respectively. The TCN model is accurate and fast for processing long input signals, and provides a novel method for measuring the aBP waveform. This method may contribute to the early monitoring and prevention of cardiovascular disease.

Cardiac contractility is a key factor in determining pulse pressure and its peripheral amplification

Background

Arterial stiffening and peripheral wave reflections have been considered the major determinants of raised pulse pressure (PP) and isolated systolic hypertension, but the importance of cardiac contractility and ventricular ejection dynamics is also recognised.

Methods

We examined the contributions of arterial compliance and ventricular contractility to variations in aortic flow and increased central (cPP) and peripheral (pPP) pulse pressure, and PP amplification (PPa) in normotensive subjects during pharmacological modulation of physiology, in hypertensive subjects, and in silico using a cardiovascular model accounting for ventricular-aortic coupling. Reflections at the aortic root and from downstream vessels were quantified using emission and reflection coefficients, respectively.

Results

cPP was strongly associated with contractility and compliance, whereas pPP and PPa were strongly associated with contractility. Increased contractility by inotropic stimulation increased peak aortic flow (323.9 ± 52.8 vs. 389.1 ± 65.1 ml/s), and the rate of increase (3193.6 ± 793.0 vs. 4848.3 ± 450.4 ml/s2) in aortic flow, leading to larger cPP (36.1 ± 8.8 vs. 59.0 ± 10.8 mmHg), pPP (56.9 ± 13.1 vs. 93.0 ± 17.0 mmHg) and PPa (20.8 ± 4.8 vs. 34.0 ± 7.3 mmHg). Increased compliance by vasodilation decreased cPP (62.2 ± 20.2 vs. 45.2 ± 17.8 mmHg) without altering d P / d t , pPP or PPa. The emission coefficient changed with increasing cPP, but the reflection coefficient did not. These results agreed with in silico data obtained by independently changing contractility/compliance over the range observed in vivo.

Conclusions

Ventricular contractility plays a key role in raising and amplifying PP, by altering aortic flow wave morphology.

Hemodynamic profiles of arterial hypertension with ambulatory blood pressure monitoring

Blood pressure (BP) measurements obtained during a twenty-four-hour ambulatory blood pressure monitoring (24 h ABPM) have not been reliably applied to extract arterial hemodynamics. We aimed to describe the hemodynamic profiles of different hypertension (HT) subtypes derived from a new method for total arterial compliance (C_t) estimation in a large group of individuals undergoing 24 h ABPM. A cross-sectional study was conducted, which included patients with suspected HT. Cardiac output, C_t, and total peripheral resistance (TPR) were derived through a two-element Windkessel model without having a pressure waveform. Arterial hemodynamics were analyzed according to HT subtypes in 7434 individuals (5523 untreated HT and 1950 normotensive controls [N]). The individuals mean age was 46.2 ± 13.0 years; 54.8% were male, and 22.1% were obese. In isolated diastolic hypertension (IDH), the cardiac index (CI) was greater than that in normotensive (N) controls (CI: IDH vs. N mean difference 0.10 L/m/m²; CI 95% 0.08 to 0.12; p value <0.001), with no significant clinical difference in C_t. Isolated systolic hypertension (ISH) and divergent systolic-diastolic hypertension (D-SDH) had lower C_t values than nondivergent HT subtype (C_t: divergent vs. nondivergent mean difference -0.20 mL/mmHg; CI 95% -0.21 to -0.19 mL/mmHg; p value <0.001). Additionally, D-SDH displayed the highest TPR (TPR: D-SDH vs. N mean difference 169.8 dyn*s/cm^-5; CI 95% 149.3 to 190.3 dyn*s/cm^-5; p value <0.001). A new method is provided for the simultaneous assessment of arterial hemodynamics with 24 h ABPM as a single diagnostic tool, which allows a comprehensive assessment of arterial function for hypertension subtypes. Main hemodynamic findings in arterial HT subtypes with regard to C_t and TPR. The 24 h ABPM profile reflects the state of C_t and TPR. Younger individuals with IDH present with a normal C_t and frequently increased CO. Patients with ND-SDH maintain an adequate C_t with a higher TPR, while subjects with D-SDH present with a reduced C_t, high PP and high TPR. Finally, the ISH subtype occurs in older individuals with significantly reduced C_t, high PP and a variable TPR proportional to the degree of arterial stiffness and MAP values. There was an observed increase in PP with age in relation to the changes in C_t (see also text). SBP: systolic blood pressure; DBP: diastolic blood pressure; MAP: mean arterial pressure; PP: pulse pressure; N: normotension; HT: hypertension; IDH: isolated diastolic hypertension; ND-SDH: nondivergent systole-diastolic hypertension; D-SDH: divergent systolic-diastolic hypertension; ISH: isolated systolic hypertension; C_t: total arterial compliance; TPR: total peripheral resistance; CO: cardiac output; 24 h ABPM: 24 h ambulatory blood pressure monitoring.

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.

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.

Human Hypertension Blood Flow Model Using Fractional Calculus

The blood flow dynamics in human arteries with hypertension disease is modeled using fractional calculus. The mathematical model is constructed using five-element lumped parameter arterial Windkessel representation. Fractional-order capacitors are used to represent the elastic properties of both proximal large arteries and distal small arteries measured from the heart aortic root. The proposed fractional model offers high flexibility in characterizing the arterial complex tree network. The results illustrate the validity of the new model and the physiological interpretability of the fractional differentiation order through a set of validation using human hypertensive patients. In addition, the results show that the fractional-order modeling approach yield a great potential to improve the understanding of the structural and functional changes in the large and small arteries due to hypertension disease.

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.

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.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.