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

Pressure drop and recovery in cases of cardiovascular disease: a computational study

The presence of disease in the cardiovascular system results in changes in flow and pressure patterns. Increased resistance to the flow observed in cases of aortic valve and coronary artery disease can have as a consequence abnormally high pressure gradients, which may lead to overexertion of the heart muscle, limited tissue perfusion and tissue damage. In the past, computational fluid dynamics (CFD) methods have been used coupled with medical imaging data to study haemodynamics, and it has been shown that CFD has great potential as a way to study patient-specific cases of cardiovascular disease in vivo, non-invasively, in great detail and at low cost. CFD can be particularly useful in evaluating the effectiveness of new diagnostic and treatment techniques, especially at early ‘concept’ stages. The main aim of this thesis is to use CFD to investigate the relationship between pressure and flow in cases of disease in the coronary arteries and the aortic valve, with the purpose of helping improve diagnosis and treatment, respectively. A transitional flow CFD model is used to investigate the phenomenon of pressure recovery in idealised models of aortic valve stenosis. Energy lost as turbulence in the wake of a diseased valve hinders pressure recovery, which occurs naturally when no energy losses are observed. A “concept” study testing the potential of a device that could maximise pressure recovery to reduce the pressure load on the heart muscle was conducted. The results indicate that, under certain conditions, such a device could prove useful. Fully patient-specific CFD studies of the coronary arteries are fewer than studies in larger vessels, mostly due to past limitations in the imaging and velocity data quality. A new method to reconstruct coronary anatomy from optical coherence tomography (OCT) data is presented in the thesis. The resulting models were combined with invasively acquired pressure and flow velocity data in transient CFD simulations, in order to test the ability of CFD to match the invasively measured pressure drop. A positive correlation and no bias were found between the calculated and measured results. The use of lower resolution reconstruction methods resulted in no correlation between the calculated and measured results, highlighting the importance of anatomical accuracy in the effectiveness of the CFD model. However, it was considered imperative that the limitations of CFD in predicting pressure gradients be further explored. It was found that the CFD-derived pressure drop is sensitive to changes in the volumetric flow rate, while bench-top experiments showed that the estimation of volumetric flow rate from invasively measured velocity data is subject to errors and uncertainties that may have a random effect on the CFD pressure result. This study demonstrated that the relationship between geometry, pressure and flow can be used to evaluate new diagnostic and treatment methods. In the case of aortic stenosis, further experimental work is required to turn the concept of a pressure recovery device into a potential clinical tool. In the coronary study it was shown that, though CFD has great power as a study tool, its limitations, especially those pertaining to the volumetric flow rate boundary condition, must be further studied and become fully understood before CFD can be reliably used to aid diagnosis in clinical practice.Open Acces

Validation of 4D Flow based relative pressure maps in aortic flows

While the clinical gold standard for pressure difference measurements is invasive catheterization, 4D Flow MRI is a promising tool for enabling a non-invasive quantification, by linking highly spatially resolved velocity measurements with pressure differences via the incompressible Navier–Stokes equations. In this work we provide a validation and comparison with phantom and clinical patient data of pressure difference maps estimators. We compare the classical Pressure Poisson Estimator (PPE) and the new Stokes Estimator (STE) against catheter pressure measurements under a variety of stenosis severities and flow intensities. Specifically, we use several 4D Flow data sets of realistic aortic phantoms with different anatomic and hemodynamic severities and two patients with aortic coarctation. The phantom data sets are enriched by subsampling to lower resolutions, modification of the segmentation and addition of synthetic noise, in order to study the sensitivity of the pressure difference estimators to these factors. Overall, the STE method yields more accurate results than the PPE method compared to catheterization data. The superiority of the STE becomes more evident at increasing Reynolds numbers with a better capacity of capturing pressure gradients in strongly convective flow regimes. The results indicate an improved robustness of the STE method with respect to variation in lumen segmentation. However, with heuristic removal of the wall-voxels, the PPE can reach a comparable accuracy for lower Reynolds’ numbers

4D Flow Patterns and Relative Pressure Distribution in a Left Ventricle Model by Shake-the-Box and Proper Orthogonal Decomposition Analysis

Purpose: Intraventricular blood flow dynamics are associated with cardiac function. Accurate, noninvasive, and easy assessments of hemodynamic quantities (such as velocity, vortex, and pressure) could be an important addition to the clinical diagnosis and treatment of heart diseases. However, the complex time-varying flow brings many challenges to the existing noninvasive image-based hemodynamic assessments. The development of reliable techniques and analysis tools is essential for the application of hemodynamic biomarkers in clinical practice. Methods: In this study, a time-resolved particle tracking method, Shake-the-Box, was applied to reconstruct the flow in a realistic left ventricle (LV) silicone model with biological valves. Based on the obtained velocity, 4D pressure field was calculated using a Poisson equation-based pressure solver. Furthermore, flow analysis by proper orthogonal decomposition (POD) of the 4D velocity field has been performed. Results: As a result of the Shake-the-Box algorithm, we have extracted: (i) particle positions, (ii) particle tracks, and finally, (iii) 4D velocity fields. From the latter, the temporal evolution of the 3D pressure field during the full cardiac cycle was obtained. The obtained maximal pressure difference extracted along the base-to-apex was about 2.7 mmHg, which is in good agreement with those reported in vivo. The POD analysis results showed a clear picture of different scale of vortices in the pulsatile LV flow, together with their time-varying information and corresponding kinetic energy content. To reconstruct 95% of the kinetic energy of the LV flow, only the first six POD modes would be required, leading to significant data reduction. Conclusions: This work demonstrated Shake-the-Box is a promising technique to accurately reconstruct the left ventricle flow field in vitro. The good spatial and temporal resolutions of the velocity measurements enabled a 4D reconstruction of the pressure field in the left ventricle. The application of POD analysis showed its potential in reducing the complexity of the high-resolution left ventricle flow measurements. For future work, image analysis, multi-modality flow assessments, and the development of new flow-derived biomarkers can benefit from fast and data-reducing POD analysis.</p

Non-invasive detection and assessment of coronary stenosis from blood mean residence times.

Coronary artery stenosis is an abnormal narrowing of a coronary artery caused by an atherosclerotic lesion that reduces lumen space. Fractional flow reserve (FFR) is the gold standard method to determine the severity of coronary stenosis based on the determination of rest and hyperemic pressure fields, but requires an invasive medical procedure. Normal FFR is 1.0 and FFR RT, to account for varying volume and flow rate of individual segments. BloodRT was computed in 100 patients who had undergone the pressure-wire FFR procedure, and a threshold for BloodRT was determined to assess the physiological significance of a stenosis, analogous to the diagnostic threshold for FFR. The threshold exhibited excellent discrimination in detecting significant from non-significant stenosis compared to the gold standard pressure-wire FFR, with sensitivity of 98% and specificity of 96%. When applied to clinical practice, this could potentially allow practicing cardiologists to accurately assess and quantify the severity of coronary stenosis without resorting to invasive catheter-based techniques. The first 100 patient study required a clinically determined blood flow rate as a key model input. To create a more non-invasive process, a multiple linear regression approach was employed to determine blood flow rate entering a given artery segment. To validate this method, BloodRT was computed for a new set of 100 patients using the regression derived blood flow rate. The sensitivity and specificity were 95% and 97%, respectively, indicating similar discrimination compared to the clinically derived flow rate. The method was also applied to a succession of stenosis in series. When BloodRT of each individual stenosis was well above the threshold for significance, the cumulative effect of all stenoses led to an overall BloodRT below the threshold of hemodynamic significance

Comprehensive 4D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Phase contrast cardiovascular magnetic resonance (CMR) is able to measure all three directional components of the velocities of blood flow relative to the three spatial dimensions and the time course of the heart cycle. In this article, methods used for the acquisition, visualization, and quantification of such datasets are reviewed and illustrated.</p> <p>Methods</p> <p>Currently, the acquisition of 3D cine (4D) phase contrast velocity data, synchronized relative to both cardiac and respiratory movements takes about ten minutes or more, even when using parallel imaging and optimized pulse sequence design. The large resulting datasets need appropriate post processing for the visualization of multidirectional flow, for example as vector fields, pathlines or streamlines, or for retrospective volumetric quantification.</p> <p>Applications</p> <p>Multidirectional velocity acquisitions have provided 3D visualization of large scale flow features of the healthy heart and great vessels, and have shown altered patterns of flow in abnormal chambers and vessels. Clinically relevant examples include retrograde streams in atheromatous descending aortas as potential thrombo-embolic pathways in patients with cryptogenic stroke and marked variations of flow visualized in common aortic pathologies. Compared to standard clinical tools, 4D velocity mapping offers the potential for retrospective quantification of flow and other hemodynamic parameters.</p> <p>Conclusions</p> <p>Multidirectional, 3D cine velocity acquisitions are contributing to the understanding of normal and pathologically altered blood flow features. Although more rapid and user-friendly strategies for acquisition and analysis may be needed before 4D velocity acquisitions come to be adopted in routine clinical CMR, their capacity to measure multidirectional flows throughout a study volume has contributed novel insights into cardiovascular fluid dynamics in health and disease.</p