Non-invasive estimation of relative pressure for intracardiac flows using virtual work-energy

Precise Estimation of Intravascular Pressure Gradients

This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier-Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) interleaved sequence with 2 ×12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields an R -square of 0.985 and an RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from -59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flow rate of 12.9 mL/s. The double cross-correlation approach revealed no improvement compared to a normal differential operator. The method's strength, thus, lies primarily in the ultrasound sequence, which allows precise and accurate velocity estimations, at which acceleration and pressure differences can be acquired.

Cerebrovascular super-resolution 4D Flow MRI - Sequential combination of resolution enhancement by deep learning and physics-informed image processing to non-invasively quantify intracranial velocity, flow, and relative pressure

The development of cerebrovascular disease is tightly coupled to regional changes in intracranial flow and relative pressure. Image-based assessment using phase contrast magnetic resonance imaging has particular promise for non-invasive full-field mapping of cerebrovascular hemodynamics. However, estimations are complicated by the narrow and tortuous intracranial vasculature, with accurate image-based quantification directly dependent on sufficient spatial resolution. Further, extended scan times are required for high-resolution acquisitions, and most clinical acquisitions are performed at comparably low resolution (>1 mm) where biases have been observed with regard to the quantification of both flow and relative pressure. The aim of our study was to develop an approach for quantitative intracranial super-resolution 4D Flow MRI, with effective resolution enhancement achieved by a dedicated deep residual network, and with accurate quantification of functional relative pressures achieved by subsequent physics-informed image processing. To achieve this, our two-step approach was trained and validated in a patient-specific in-silico cohort, showing good accuracy in estimating velocity (relative error: 15.0 ± 0.1%, mean absolute error (MAE): 0.07 ± 0.06 m/s, and cosine similarity: 0.99 ± 0.06 at peak velocity) and flow (relative error: 6.6 ± 4.7%, root mean square error (RMSE): 0.56 mL/s at peak flow), and with the coupled physics-informed image analysis allowing for maintained recovery of functional relative pressure throughout the circle of Willis (relative error: 11.0 ± 7.3%, RMSE: 0.3 ± 0.2 mmHg). Furthermore, the quantitative super-resolution approach is applied to an in-vivo volunteer cohort, effectively generating intracranial flow images at <0.5 mm resolution and showing reduced low-resolution bias in relative pressure estimation. Our work thus presents a promising two-step approach to non-invasively quantify cerebrovascular hemodynamics, being applicable to dedicated clinical cohorts in the future.

Multivariable Technique for the Evaluation of the Trans-stenotic Pressure Gradient

PURPOSE

This study establishes a reliable image-based multivariable technique for measuring the trans-stenotic pressure gradient.

METHODS

A self-made in vitro steady flow model based on adjustable velocities and stenotic properties were used as the experimental subject. The pre-stenotic flow velocity, severity, and length of the stenosis were used as the input variables. Based on equations used to fit the plots of the physically measured pressure gradient values versus each input variable, a multivariable formula for the pressure gradient measurement could then be derived. The flow model was scanned using velocity-encoded phase-contrast magnetic resonance imaging (PC-MRI) to validate the derived formula while simultaneously measuring the trans-stenotic pressure gradient. The correlation between the physically-measured pressure gradient values and the pressure gradient values calculated using the new formula were subsequently analyzed.

RESULTS

The results of linear regression analysis using the physically measured pressure gradient values for the new method were compared to values obtained using the simplified Bernoulli equation (R², 0.991, and 0.975, respectively). In a paired t-test, no statistically significant difference was found between the new method and the physical measurements.

CONCLUSIONS

The derived multivariable technique was found to reliably measure the trans-stenotic pressure gradient, with better performance than a traditional procedure based on the simplified Bernoulli equation.

Relative pressure estimation from 4D flow MRI using generalized Bernoulli equation in a phantom model of arterial stenosis

OBJECTIVE

Arterial stenosis is a significant cardiovascular disease requiring accurate estimation of the pressure gradients for determining hemodynamic significance. In this paper, we propose Generalized Bernoulli Equation (GBE) utilizing interpolated-based method to estimate relative pressures using streamlines and pathlines from 4D Flow MRI.

METHODS

4D Flow MRI data in a stenotic phantom model and computational fluid dynamics simulated velocities generated under identical flow conditions were processed by Generalized Bernoulli Equation (GBE), Reduced Bernoulli Equations (RBE), as well as the Simple Bernoulli Equation (SBE) which is clinically prevalent. Pressures derived from 4D flow MRI and noise corrupted CFD velocities were compared with pressures generated directly with CFD as well as pressures obtained using Millar catheters under identical flow conditions.

RESULTS

It was found that SBE and RBE methods underestimated the relative pressure for lower flow rates while overestimating the relative pressure at higher flow rates. Specifically, compared to the reference pressure, SBE underestimated the maximum relative pressure by 22[Formula: see text] for a pulsatile flow data with peak flow rate [Formula: see text] and overestimated by around 40[Formula: see text] when [Formula: see text]. In contrast, for GBE method the relative pressure values were overestimated by 15[Formula: see text] with [Formula: see text]and around 10[Formula: see text] with [Formula: see text].

CONCLUSION

GBE methods showed robust performance to additive image noise compared to other methods. Our findings indicate that GBE pressure estimation over pathlines attains the highest level of accuracy compared to GBE over streamlines, and the SBE and RBE methods.

Inverse problems in blood flow modeling: A review

Mathematical and computational modeling of the cardiovascular system is increasingly providing non-invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid-solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol.

Four-dimensional flow cardiac magnetic resonance assessment of left ventricular diastolic function

Left ventricular diastolic dysfunction is a major cause of heart failure and carries a poor prognosis. Assessment of left ventricular diastolic function however remains challenging for both echocardiography and conventional phase contrast cardiac magnetic resonance. Amongst other limitations, both are restricted to measuring velocity in a single direction or plane, thereby compromising their ability to capture complex diastolic hemodynamics in health and disease. Time-resolved three-dimensional phase contrast cardiac magnetic resonance imaging with three-directional velocity encoding known as '4D flow CMR' is an emerging technology which allows retrospective measurement of velocity and by extension flow at any point in the acquired 3D data volume. With 4D flow CMR, complex aspects of blood flow and ventricular function can be studied throughout the cardiac cycle. 4D flow CMR can facilitate the visualization of functional blood flow components and flow vortices as well as the quantification of novel hemodynamic and functional parameters such as kinetic energy, relative pressure, energy loss and vorticity. In this review, we examine key concepts and novel markers of diastolic function obtained by flow pattern analysis using 4D flow CMR. We consolidate the existing evidence base to highlight the strengths and limitations of 4D flow CMR techniques in the surveillance and diagnosis of left ventricular diastolic dysfunction.

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

On the numerical treatment of viscous and convective effects in relative pressure reconstruction methods

The mechanism of many cardiovascular diseases can be understood by studying the pressure distribution in blood vessels. Direct pressure measurements, however, require invasive probing and provide only single-point data. Alternatively, relative pressure fields can be reconstructed from imaging-based velocity measurements by considering viscous and inertial forces. Both contributions can be potential troublemakers in pressure reconstruction: the former due to its higher-order derivatives, and the latter because of the quadratic nonlinearity in the convective acceleration. Viscous and convective terms can be treated in various forms, which, although equivalent for ideal measurements, can perform differently in practice. In fact, multiple versions are often used in literature, with no apparent consensus on the more suitable variants. In this context, the present work investigates the performance of different versions of relative pressure estimators. For viscous effects, in particular, two new modified estimators are presented to circumvent second-order differentiation without requiring surface integrals. In-silico and in-vitro data in the typical regime of cerebrovascular flows are considered, allowing a systematic noise sensitivity study. Convective terms are shown to be the main source of error, even for flows with pronounced viscous component. Moreover, the conservation (often integrated) form of convection exhibits higher noise sensitivity than the standard convective description, in all three families of estimators considered here. For the classical pressure Poisson estimator, the present modified version of the viscous term tends to yield better accuracy than the (recently introduced) integrated form, although this effect is in most cases negligible when compared to convection-related errors.

False lumen pressure estimation in type B aortic dissection using 4D flow cardiovascular magnetic resonance: comparisons with aortic growth

BACKGROUND

Chronic type B aortic dissection (TBAD) is associated with poor long-term outcome, and accurate risk stratification tools remain lacking. Pressurization of the false lumen (FL) has been recognized as central in promoting aortic growth. Several surrogate imaging-based metrics have been proposed to assess FL hemodynamics; however, their relationship to enlarging aortic dimensions remains unclear. We investigated the association between aortic growth and three cardiovascular magnetic resonance (CMR)-derived metrics of FL pressurization: false lumen ejection fraction (FLEF), maximum systolic deceleration rate (MSDR), and FL relative pressure (FL ΔPmax).

METHODS

CMR/CMR angiography was performed in 12 patients with chronic dissection of the descending thoracoabdominal aorta, including contrast-enhanced CMR angiography and time-resolved three-dimensional phase-contrast CMR (4D Flow CMR). Aortic growth rate was calculated as the change in maximal aortic diameter between baseline and follow-up imaging studies over the time interval, with patients categorized as having either 'stable' (< 3 mm/year) or 'enlarging' (≥ 3 mm/year) growth. Three metrics relating to FL pressurization were defined as: (1) FLEF: the ratio between retrograde and antegrade flow at the TBAD entry tear, (2) MSDR: the absolute difference between maximum and minimum systolic acceleration in the proximal FL, and (3) FL ΔPmax: the difference in absolute pressure between aortic root and distal FL.

RESULTS

FLEF was higher in enlarging TBAD (49.0 ± 17.9% vs. 10.0 ± 11.9%, p = 0.002), whereas FL ΔPmax was lower (32.2 ± 10.8 vs. 57.2 ± 12.5 mmHg/m, p = 0.017). MSDR and conventional anatomic variables did not differ significantly between groups. FLEF showed positive (r = 0.78, p = 0.003) correlation with aortic growth rate whereas FL ΔPmax showed negative correlation (r = - 0.64, p = 0.026). FLEF and FL ΔPmax remained as independent predictors of aortic growth rate after adjusting for baseline aortic diameter.

CONCLUSION

Comparative analysis of three 4D flow CMR metrics of TBAD FL pressurization demonstrated that those that focusing on retrograde flow (FLEF) and relative pressure (FL ΔPmax) independently correlated with growth and differentiated patients with enlarging and stable descending aortic dissections. These results emphasize the highly variable nature of aortic hemodynamics in TBAD patients, and suggest that 4D Flow CMR derived metrics of FL pressurization may be useful to separate patients at highest and lowest risk for progressive aortic growth and complications.