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

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.

Vascular ageing: moving from bench towards bedside

Prevention of cardiovascular disease (CVD) remains one of the largest public health challenges of our time. Identifying individuals at increased cardiovascular risk at an asymptomatic, sub-clinical stage is of paramount importance for minimizing disease progression as well as the substantial health and economic burden associated with overt CVD. Vascular ageing (VA) involves the deterioration in vascular structure and function over time and ultimately leads to damage in the heart, brain, kidney, and other organs. Vascular ageing encompasses the cumulative effect of all cardiovascular risk factors on the arterial wall over the life course and thus may help identify those at elevated cardiovascular risk, early in disease development. Although the concept of VA is gaining interest clinically, it is seldom measured in routine clinical practice due to lack of consensus on how to characterize VA as physiological vs. pathological and various practical issues. In this state-of-the-art review and as a network of scientists, clinicians, engineers, and industry partners with expertise in VA, we address six questions related to VA in an attempt to increase knowledge among the broader medical community and move the routine measurement of VA a little closer from bench towards bedside.

Impact of thoracic endovascular aortic repair following blunt traumatic thoracic aortic injury on blood pressure

BACKGROUND

Blunt traumatic thoracic aortic injuries (BTAIs) are associated with a high mortality rate. Thoracic endovascular aortic repair (TEVAR) is the most frequently used surgical strategy in patients with BTAI, as it offers good short- and middle-term results. Previous studies have reported an abnormally high prevalence of hypertension (HT) in these patients. This work aimed to describe the long-term prevalence of HT and provide a comprehensive evaluation of the biomechanical, clinical, and functional factors involved in HT development.

METHODS

Twenty-six patients treated with TEVAR following BTAI with no history of HT at the time of trauma were enrolled. They were matched with 37 healthy volunteers based on age, sex, and body surface area and underwent a comprehensive follow-up study, including cardiovascular magnetic resonance, 24-hour ambulatory blood pressure monitoring, and assessment of carotid-femoral pulse wave velocity (cfPWV, a measure of aortic stiffness) and flow-mediated vasodilation.

RESULTS

The mean patient age was 43.5 ± 12.9 years, and the majority were male (23 of 26; 88.5%). At a mean of 120.2 ± 69.7 months after intervention, 17 patients (65%) presented with HT, 14 (54%) had abnormal nighttime blood pressure dipping, and 6 (23%) high cfPWV. New-onset HT was related to a more proximal TEVAR landing zone and greater distal oversizing. Abnormal nighttime blood pressure was related to high cfPWV, which in turn was associated with TEVAR length and premature arterial aging.

CONCLUSIONS

HT frequently occurs otherwise healthy subjects undergoing TEVAR implantation after BTAI. TEVAR stiffness and length, the proximal landing zone, and distal oversizing are potentially modifiable surgical characteristics related to abnormal blood pressure.

Magnetic Resonance Imaging and Computed Tomography for the Noninvasive Assessment of Arterial Aging: A Review by the VascAgeNet COST Action

Magnetic resonance imaging and computed tomography allow the characterization of arterial state and function with high confidence and thus play a key role in the understanding of arterial aging and its translation into the clinic. Decades of research into the development of innovative imaging sequences and image analysis techniques have led to the identification of a large number of potential biomarkers, some bringing improvement in basic science, others in clinical practice. Nonetheless, the complexity of some of these biomarkers and the image analysis techniques required for their computation hamper their widespread use. In this narrative review, current biomarkers related to aging of the aorta, their founding principles, the sequence, and postprocessing required, and their predictive values for cardiovascular events are summarized. For each biomarker a summary of reference values and reproducibility studies and limitations is provided. The present review, developed in the COST Action VascAgeNet, aims to guide clinicians and technical researchers in the critical understanding of the possibilities offered by these advanced imaging modalities for studying the state and function of the aorta, and their possible clinically relevant relationships with aging.

On inlet pressure boundary conditions for CT-based computation of fractional flow reserve: clinical measurement of aortic pressure

BACKGROUND AND OBJECTIVES

A quick calculation approach of steady-state fractional flow reserve (FFRss) based on computed tomography angiography (CTA) images is a reliable non-invasive way of calculate FFR, the assumptions used in the research should be study further to increase forecast accuracy. The effect of inlet and outlet boundary conditions on FFRss was investigated.

METHODS

15 patients who had been diagnosed with coronary artery disease were enrolled in this study. We investigated the sensitivity of calculating FFR to boundary circumstances, using invasive FFR as a benchmark. There are two types of inlet: (1) aortic pressure based on clinically measured. (2) mean pressure calculated based on physiological formula; we further studied the outlet changes of FFRss under different coronary vasodilation responses (24%, 48%, 72%).

RESULTS

According to the calculate FFR results of all patients, FFR_SST (based on the clinical experiment) and FFR_SSM (based on the physiological formula) {r = 0.99, [95% confidence interval (CI):0.0.94 to 1.14] (p < 0.001)}. Although the pressure difference between the two pressure boundary conditions is 15 mmHg, the calculated FFR result does not change significantly. The microcirculation resistance of the outlet gradually rose as the vasodilation state changed, and the computed FFR increased.

CONCLUSIONS

A numerical analysis of the effects of proximal and distal boundary constraints of computational models on computed CT-FFR is presented. The findings revealed that distal boundary circumstances (hyperemic vasodilation response of coronary micro-vessels) have a significant impact on FFR, providing evidence to guide the development and application of a computational model for estimating FFR.

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.

A predictive patient-specific computational model of coronary artery bypass grafts for potential use by cardiac surgeons to guide selection of graft configurations

Cardiac surgeons face a significant degree of uncertainty when deciding upon coronary artery bypass graft configurations for patients with coronary artery disease. This leads to significant variation in preferred configuration between different surgeons for a particular patient. Additionally, for the majority of cases, there is no consensus regarding the optimal grafting strategy. This situation results in the tendency for individual surgeons to opt for a “one size fits all” approach and use the same grafting configuration for the majority of their patients neglecting the patient-specific nature of the diseased coronary circulation. Quantitative metrics to assess the adequacy of coronary bypass graft flows have recently been advocated for routine intraoperative use by cardiac surgeons. In this work, a novel patient-specific 1D-0D computational model called “COMCAB” is developed to provide the predictive haemodynamic parameters of functional graft performance that can aid surgeons to avoid configurations with grafts that have poor flow and thus poor patency. This model has significant potential for future expanded applications.

Geometric, Biomechanic and Haemodynamic Aortic Abnormalities Assessed by 4D Flow Cardiovascular Magnetic Resonance in Patients Treated by TEVAR Following Blunt Traumatic Thoracic Aortic Injury

OBJECTIVE

Thoracic endovascular aortic repair (TEVAR) is widely used for the treatment of patients with blunt traumatic thoracic aortic injury (BTAI). However, aortic haemodynamic and biomechanical implications of this intervention are poorly investigated. This study aimed to assess whether patients treated by TEVAR following BTAI have thoracic aortic abnormalities in geometry, stiffness, and haemodynamics.

METHODS

Patients with BTAI treated by TEVAR at Vall d'Hebron Hospital between 1999 and 2019 were compared with propensity score matched healthy volunteers (HVs). All subjects underwent cardiovascular magnetic resonance (CMR) comprising a 4D flow CMR sequence. Spatially resolved aortic diameter, length, volume, and curvature were assessed. Pulse wave velocity, distensibility, and longitudinal strain (all measurements of aortic stiffness) were determined regionally. Moreover, advanced haemodynamic descriptors were quantified: systolic flow reversal ratio (SFRR), quantifying backward flow during systole, and in plane rotational flow (IRF), measuring in plane strength of helical flow.

RESULTS

Twenty-six BTAI patients treated by TEVAR were included and matched with 26 HVs. They did not differ in terms of age, sex, and body surface area. Patients with TEVAR had a larger and longer ascending aorta (AAo) and marked abnormalities in local curvature. Aortic stiffness was greater in the aortic segments proximal and distal to TEVAR compared with controls. Moreover, TEVAR patients presented strongly altered flow dynamics compared with controls: a reduced IRF from the distal AAo to the proximal descending aorta and an increased SFRR in the whole thoracic aorta. These differences persisted adjusting for cardiovascular risk factors and were independent of time elapsed since TEVAR implantation.

CONCLUSION

At long term follow up, previously healthy patients who underwent TEVAR implantation following BTAI had increased diameter, length and volume of the ascending aorta, and increased aortic stiffness and abnormal flow patterns in the whole thoracic aorta compared with matched controls. Further studies should address whether these alterations have clinical implications.

Central pulse pressure is inversely associated with proximal aortic remodelling

OBJECTIVES

Hypertension leads to aortic stiffening and dilatation but unexpected data from the Framingham Heart Study showed an inverse relationship between brachial pulse pressure and aortic diameter. Aortic dilatation would not only lead to lower pulse pressure but also to a worse prognosis (cardiac events, heart failure). Invasive pressure may be more informative but data are lacking.

AIM

This study evaluated the relationship between invasively measured central blood pressure and proximal aortic diameter.

METHODS

In 71 consecutive patients referred to invasive haemodynamic study, proximal aortic remodelling was evaluated in terms of Z-score, comparing diameters measured at the sinus of Valsalva to the diameter expected according to patients' age, sex and body height. Pressures were recorded directly in the proximal aorta by means of a catheter before coronary assessment.

RESULTS

The mean invasive aortic SBPs and DBPs were 146 ± 23 and 78 ± 13 mmHg, respectively, giving a central pulse pressure (cPP inv) of 68 ± 21 mmHg. Proximal aortic diameter was 34.9 ± 19.4 mm, whereas Z-score was -0.3 ± 1.7. Patients with higher cPPinv showed a significantly lower Z-score (-0.789 vs. 0.155, P = 0.001). cPPinv was inversely related to Z-score (R = -0.271, P = 0.022) independently from age, mean blood pressure and heart rate (β = -0.241, P = 0.011).

CONCLUSION

Aortic root Z-score is inversely associated with invasively measured central pulse pressure in a cohort of patients undergoing invasive coronary assessment. Remodelling at the sinuses of Valsalva may be a compensatory mechanism to limit pulse pressure.

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

Central blood pressure (cBP) is a highly prognostic cardiovascular (CV) risk factor whose accurate, invasive assessment is costly and carries risks to patients. We developed and assessed novel algorithms for estimating cBP from noninvasive aortic hemodynamic data and a peripheral blood pressure measurement. These algorithms were created using three blood flow models: the two- and three-element Windkessel (0-D) models and a one-dimensional (1-D) model of the thoracic aorta. We tested new and existing methods for estimating CV parameters (left ventricular ejection time, outflow BP, arterial resistance and compliance, pulse wave velocity, and characteristic impedance) required for the cBP algorithms, using virtual (simulated) subjects (n = 19,646) for which reference CV parameters were known exactly. We then tested the cBP algorithms using virtual subjects (n = 4,064), for which reference cBP were available free of measurement error, and clinical datasets containing invasive (n = 10) and noninvasive (n = 171) reference cBP waves across a wide range of CV conditions. The 1-D algorithm outperformed the 0-D algorithms when the aortic vascular geometry was available, achieving central systolic blood pressure (cSBP) errors≤2.1 ± 9.7mmHg and root-mean-square errors (RMSEs)≤6.4 ± 2.8mmHg against invasive reference cBP waves (n = 10). When the aortic geometry was unavailable, the three-element 0-D algorithm achieved cSBP errors ≤ 6.0 ± 4.7mmHg and RMSEs ≤ 5.9 ± 2.4mmHg against noninvasive reference cBP waves (n = 171), outperforming the two-element 0-D algorithm. All CV parameters were estimated with mean percentage errors ≤ 8.2%, except for the aortic characteristic impedance (≤13.4%), which affected the three-element 0-D algorithm’s performance. The freely available algorithms developed in this work enable fast and accurate calculation of the cBP wave and CV parameters in datasets containing noninvasive ultrasound or magnetic resonance imaging data.

Cardiovascular deconditioning during long-term spaceflight through multiscale modeling

Human spaceflight has been fascinating man for centuries, representing the intangible need to explore the unknown, challenge new frontiers, advance technology, and push scientific boundaries further. A key area of importance is cardiovascular deconditioning, that is, the collection of hemodynamic changes-from blood volume shift and reduction to altered cardiac function-induced by sustained presence in microgravity. A thorough grasp of the 0G adjustment point per se is important from a physiological viewpoint and fundamental for astronauts' safety and physical capability on long spaceflights. However, hemodynamic details of cardiovascular deconditioning are incomplete, inconsistent, and poorly measured to date; thus a computational approach can be quite valuable. We present a validated 1D-0D multiscale model to study the cardiovascular response to long-term 0G spaceflight in comparison to the 1G supine reference condition. Cardiac work, oxygen consumption, and contractility indexes, as well as central mean and pulse pressures were reduced, augmenting the cardiac deconditioning scenario. Exercise tolerance of a spaceflight traveler was found to be comparable to an untrained person with a sedentary lifestyle. At the capillary-venous level significant waveform alterations were observed which can modify the regular perfusion and average nutrient supply at the cellular level. The present study suggests special attention should be paid to future long spaceflights which demand prompt physical capacity at the time of restoration of partial gravity (e.g., Moon/Mars landing). Since spaceflight deconditioning has features similar to accelerated aging understanding deconditioning mechanisms in microgravity are also relevant to the understanding of aging physiology on the Earth.

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.

Estimation of central arterial pressure from the radial artery in patients undergoing invasive neuroradiological procedures

Backgrounds

Central arterial pressure can be derived from analysis of the peripheral artery waveform. The aim of this study was to compare central arterial pressures measured from an intra-aortic catheter with peripheral radial arterial pressures and with central arterial pressures estimated from the peripheral pressure wave using a pressure recording analytical method (PRAM).

Methods

We studied 21 patients undergoing digital subtraction cerebral angiography under local or general anesthesia and equipped with a radial arterial catheter. A second catheter was placed in the ascending aorta for central pressure wave acquisition. Central (AO) and peripheral (RA) arterial waveforms were recorded simultaneously by PRAM for 90–180 s. During an off-line analysis, AO pressures were reconstructed (AO_rec) from the RA trace using a mathematical model obtained by multi-linear regression analysis. The AO_rec values obtained by PRAM were compared with the true central pressure value obtained from the catheter placed in the ascending aorta.

Results

Systolic, diastolic and mean pressures ranged from 79 to 180 mmHg, 47 to 102 mmHg, and 58 to 128 mmHg, respectively, for AO, and 83 to 174 mmHg, 47 to 107 mmHg, and 60 to 129 mmHg, respectively, for RA. The correlation coefficients between AO and RA were 0.86 (p < 0.01), 0.83 (p < 0.01) and 0.86 (p < 0.01) for systolic, diastolic and mean pressures, respectively, and the mean differences − 0.3 mmHg, 2.4 mmHg and 1.5 mmHg. The correlation coefficients between AO and AO_rec were 0.92 (p < 0.001), 0.87 (p < 0.001) and 0.92 (p < 0.001), for systolic, diastolic and mean pressures, respectively, and the mean differences 0.01 mmHg, 1.8 mmHg and 1.2 mmHg.

Conclusions

PRAM can provide reliable estimates of central arterial pressure.

Electronic supplementary material

The online version of this article (10.1186/s12871-019-0844-1) contains supplementary material, which is available to authorized users.