Reconciling PC-MRI and CFD: An in-vitro study

Imaging of Intracranial Aneurysms: A Review of Standard and Advanced Imaging Techniques

The treatment of intracranial aneurysms is dictated by its risk of rupture in the future. Several clinical and radiological risk factors for aneurysm rupture have been described and incorporated into prediction models. Despite the recent technological advancements in aneurysm imaging, linear length and visible irregularity with a bleb are the only radiological measure used in clinical prediction models. The purpose of this article is to summarize both the standard imaging techniques, including their limitations, and the advanced techniques being used experimentally to image aneurysms. It is expected that as our understanding of advanced techniques improves, and their ability to predict clinical events is demonstrated, they become an increasingly routine part of aneurysm assessment. It is important that neurovascular specialists understand the spectrum of imaging techniques available.

Aortic valve neocuspidization and bioprosthetic valves: Evaluating turbulence haemodynamics

Aortic valve disease is often treated with bioprosthetic valves. An alternative treatment is aortic valve neocuspidization which is a relatively new reparative procedure whereby the three aortic cusps are replaced with patient pericardium or bovine tissues. Recent research indicates that aortic blood flow is disturbed, and turbulence effects have yet to be evaluated in either bioprosthetic or aortic valve neocuspidization valve types in patient-specific settings. The aim of this study is to better understand turbulence production in the aorta and evaluate its effects on laminar and turbulent wall shear stress. Four patients with aortic valve disease were treated with either bioprosthetic valves (n=2) or aortic valve neocuspidization valvular repair (n=2). Aortic geometries were segmented from magnetic resonance images (MRI), and 4D flow MRI was used to derive physiological inlet and outlet boundary conditions. Pulsatile large-eddy simulations were performed to capture the full range of laminar, transitional and turbulence characteristics in the aorta. Turbulence was produced in all aortas with highest levels occurring during systolic deceleration. In the ascending aorta, turbulence production is attributed to a combination of valvular skew, valvular eccentricity, and ascending aortic dilation. In the proximal descending thoracic aorta, turbulence production is dependent on the type of arch-descending aorta connection (e.g., a narrowing or sharp bend) which induces flow separation. Laminar and turbulent wall shear stresses are of similar magnitude throughout late systolic deceleration and diastole, although turbulent wall shear stress magnitudes exceed laminar wall shear stresses between 27.3% and 61.1% of the cardiac cycle. This emphasises the significance of including turbulent wall shear stress to improve our comprehension of progressive arterial wall diseases. The findings of this study recommend that aortic valve treatments should prioritise minimising valvular eccentricity and skew in order to mitigate turbulence generation.

Assessing a heterogeneous model for accounting for endovascular devices in hemodynamic simulations of cerebral aneurysms

The heterogeneous model developed by Berod et al [Int J Numer Method Biomed Eng 38, 2021] for representing the hemodynamic effects of endovascular prostheses is applied to a series of 10 patient specific cerebral aneurysms, 6 being treated by flow diverters, 4 being equipped with WEBs. Two markers correlated with the medical outcome of the treatment are used to assess the potential of the model, namely the saccular mean velocity and the inflow rate at the neck of the aneurysm. The comparison with the corresponding wire-resolved simulations is very favorable in both cases, and the model-based simulations also retrieve the jetting-type flows generated downstream of the struts. Noteworthy, the very same model was used for representing the flow diverters and the WEBs, showing the versatility and robustness of the heterogeneous modeling of the devices.

Optimization of 4D Flow MRI Spatial and Temporal Resolution for Examining Complex Hemodynamics in the Carotid Artery Bifurcation

BACKGROUND

Three-dimensional, ECG-gated, time-resolved, three-directional, velocity-encoded phase-contrast MRI (4D flow MRI) has been applied extensively to measure blood velocity in great vessels but has been much less used in diseased carotid arteries. Carotid artery webs (CaW) are non-inflammatory intraluminal shelf-like projections into the internal carotid artery (ICA) bulb that are associated with complex flow and cryptogenic stroke.

PURPOSE

Optimize 4D flow MRI for measuring the velocity field of complex flow in the carotid artery bifurcation model that contains a CaW.

METHODS

A 3D printed phantom model created from computed tomography angiography (CTA) of a subject with CaW was placed in a pulsatile flow loop within the MRI scanner. 4D Flow MRI images of the phantom were acquired with five different spatial resolutions (0.50-2.00  mm3) and four different temporal resolutions (23-96 ms) and compared to a computational fluid dynamics (CFD) solution of the flow field as a reference. We examined four planes perpendicular to the vessel centerline, one in the common carotid artery (CCA) and three in the internal carotid artery (ICA) where complex flow was expected. At these four planes pixel-by-pixel velocity values, flow, and time average wall shear stress (TAWSS) were compared between 4D flow MRI and CFD.

HYPOTHESIS

An optimized 4D flow MRI protocol will provide a good correlation with CFD velocity and TAWSS values in areas of complex flow within a clinically feasible scan time (~ 10 min).

RESULTS

Spatial resolution affected the velocity values, time average flow, and TAWSS measurements. Qualitatively, a spatial resolution of 0.50  mm3 resulted in higher noise, while a lower spatial resolution of 1.50-2.00  mm3 did not adequately resolve the velocity profile. Isotropic spatial resolutions of 0.50-1.00  mm3 showed no significant difference in total flow compared to CFD. Pixel-by-pixel velocity correlation coefficients between 4D flow MRI and CFD were > 0.75 for 0.50-1.00  mm3 but were < 0.5 for 1.50 and 2.00  mm3. Regional TAWSS values determined from 4D flow MRI were generally lower than CFD and decreased at lower spatial resolutions (larger pixel sizes). TAWSS differences between 4D flow and CFD were not statistically significant at spatial resolutions of 0.50-1.00  mm3 but were different at 1.50 and 2.00 mm3. Differences in temporal resolution only affected the flow values when temporal resolution was > 48.4 ms; temporal resolution did not affect TAWSS values.

CONCLUSION

A spatial resolution of 0.74-1.00  mm3 and a temporal resolution of 23-48 ms (1-2 k-space segments) provides a 4D flow MRI protocol capable of imaging velocity and TAWSS in regions of complex flow within the carotid bifurcation at a clinically acceptable scan time.

A Digital Twin Framework Embedded with POD and Neural Network for Flow Field Monitoring of Push-Plate Kiln

The push-plate kiln is a kind of kiln equipment widely used in the oxygen-free sintering of high-temperature alloy materials. Its flow field monitoring has an important application value for the manufacturing industry. However, traditional simulation methods cannot meet the requirements of real-time applications due to the high computational cost and being time-consuming. The rapid development of artificial intelligence technology will empower the traditional manufacturing industry. In this paper, we propose a data-driven digital twin framework for real-time flow field prediction by combining the CFD modeling simulation, IoT, and deep learning technologies. The framework integrates geometric, rule, physical, and neural network models to achieve the real-time simulation of physical and twin objects. The proper orthogonal decomposition (POD) and multiscale convolutional neural network (MCNN) are innovatively embedded into the framework. The POD is used to map high-dimensional data to low-dimensional features, and the MCNN is used to construct models predicting low-dimensional features for fast flow field prediction. The effectiveness of the proposed model is verified by the push-plate kiln case. The results show that the digital twin can quickly predict multi-physics fields based on the perceptual data to achieve the real-time evaluation of the operating state of the push-plate kiln.

Accelerated sequences of 4D flow MRI using GRAPPA and compressed sensing: A comparison against conventional MRI and computational fluid dynamics

PURPOSE

To evaluate hemodynamic markers obtained by accelerated GRAPPA (R = 2, 3, 4) and compressed sensing (R = 7.6) 4D flow MRI sequences under complex flow conditions.

METHODS

The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>L</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> <mml:annotation>$$ {L}_2 $$</mml:annotation></mml:semantics> </mml:math> -norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities.

RESULTS

4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation.

CONCLUSION

GRAPPA (R = 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

Impact of extra-anatomical bypass on coarctation fluid dynamics using patient-specific lumped parameter and Lattice Boltzmann modeling

Accurate hemodynamic analysis is not only crucial for successful diagnosis of coarctation of the aorta (COA), but intervention decisions also rely on the hemodynamics assessment in both pre and post intervention states to minimize patient risks. Despite ongoing advances in surgical techniques for COA treatments, the impacts of extra-anatomic bypass grafting, a surgical technique to treat COA, on the aorta are not always benign. Our objective was to investigate the impact of bypass grafting on aortic hemodynamics. We investigated the impact of bypass grafting on aortic hemodynamics using a patient-specific computational-mechanics framework in three patients with COA who underwent bypass grafting. Our results describe that bypass grafting improved some hemodynamic metrics while worsened the others: (1) Doppler pressure gradient improved (decreased) in all patients; (2) Bypass graft did not reduce the flow rate substantially through the COA; (3) Systemic arterial compliance increased in patients #1 and 3 and didn't change (improve) in patient 3; (4) Hypertension got worse in all patients; (5) The flow velocity magnitude improved (reduced) in patient 2 and 3 but did not improve significantly in patient 1; (6) There were elevated velocity magnitude, persistence of vortical flow structure, elevated turbulence characteristics, and elevated wall shear stress at the bypass graft junctions in all patients. We concluded that bypass graft may lead to pseudoaneurysm formation and potential aortic rupture as well as intimal hyperplasia due to the persistent abnormal and irregular aortic hemodynamics in some patients. Moreover, post-intervention, exposures of endothelial cells to high shear stress may lead to arterial remodeling, aneurysm, and rupture.

Quality Control for 4D Flow MR Imaging

In recent years, 4D flow MRI has become increasingly important in clinical applications for the blood vessels in the whole body, heart, and cerebrospinal fluid. 4D flow MRI has advantages over 2D cine phase-contrast (PC) MRI in that any targeted area of interest can be analyzed post-hoc, but there are some factors to be considered, such as ensuring measurement accuracy, a long imaging time and post-processing complexity, and interobserver variability.Due to the partial volume phenomenon caused by low spatial and temporal resolutions, the accuracy of flow measurement in 4D flow MRI is reduced. For spatial resolution, it is recommended to include at least four voxels in the vessel of interest, and if possible, six voxels. In large vessels such as the aorta, large voxels can be secured and SNR can be maintained, but in small cerebral vessels, SNR is reduced, resulting in reduced accuracy. A temporal resolution of less than 40 ms is recommended. The velocity-to-noise ratio (VNR) of low-velocity blood flow is low, resulting in poor measurement accuracy. The use of dual velocity encoding (VENC) or multi-VENC is recommended to avoid velocity wrap around and to increase VNR. In order to maintain sufficient spatio-temporal resolution, a longer imaging time is required, leading to potential patient movement during examination and a corresponding decrease in measurement accuracy.For the clinical application of new technologies, including various acceleration techniques, in vitro and in vivo accuracy verification based on existing accuracy-validated 2D cine PC MRI and 4D flow MRI, as well as accuracy verification on the conservation of mass' principle, should be performed, and intraobserver repeatability, interobserver reproducibility, and test-retest reproducibility should be checked.

A heterogeneous model of endovascular devices for the treatment of intracranial aneurysms

Numerical computations of hemodynamics inside intracranial aneurysms treated by endovascular braided devices such as flow-diverters contribute to understanding and improving such treatment procedures. Nevertheless, these simulations yield high computational and meshing costs due to the heterogeneity of length scales between the dense weave of the fine struts of the device and the arterial volume. Homogeneous strategies developed over the last decade to circumvent this issue substitute local dissipations due to the wires with a global effect in the form of a pressure-drop across the device surface. However, these methods cannot accurately reproduce the flow-patterns encountered near the struts, the latter strongly dictating the intra-saccular flow environment. In this work, a versatile theoretical framework which aims at correctly reproducing the local flow heterogeneities due to the wires while keeping memory consumption, meshing and computational times as low as possible is introduced. This model reproduces the drag forces exerted by the device struts onto the fluid, thus producing local and heterogeneous effects on the flow. Extensive validation for various flow and geometric configurations using an idealized device is performed. To further illustrate the method capabilities, a real patient-specific aneurysm endovascularly treated with a flow-diverter is used, enabling quantitative comparisons with classical approaches for both intra-saccular velocities and computational costs reduction. The proposed heterogeneous model endeavors to bridge the gap between computational fluid dynamics and clinical applications and ushers in a new era of numerical treatment planning with minimally costing computational tools.

Evaluation and verification of patient-specific modelling of type B aortic dissection

Quantitative assessment of the complex hemodynamic environment in type B aortic dissection (TBAD) through computational fluid dynamics (CFD) simulations can provide detailed insights into the disease and its progression. As imaging and computational technologies have advanced, methodologies have been developed to increase the accuracy and physiological relevance of CFD simulations. This study presents a patient-specific workflow to simulate blood flow in TBAD, utilising the maximum amount of in vivo data available in the form of CT images, 4D-flow MRI and invasive Doppler-wire pressure measurements, to implement the recommended current best practice methodologies in terms of patient-specific geometry and boundary conditions. The study aimed to evaluate and verify this workflow through detailed qualitative and quantitative comparisons of the CFD and in vivo data. Based on data acquired from five TBAD patients, a range of essential model inputs was obtained, including inlet flow waveforms and 3-element Windkessel model parameters, which can be utilised in further studies where in vivo flow data is not available. Local and global analysis showed good consistency between CFD results and 4D-MRI data, with the maximum velocity in the primary entry tear differing by up to 0.3 m/s, and 80% of the analysed regions achieving moderate or strong correlations between the predicted and in vivo velocities. CFD predicted pressures were generally well matched to the Doppler-wire measurements, with some deviation in peak systolic values. Overall, this study presents a validated comprehensive workflow with extensive data for CFD simulation of TBAD.

Evaluation of Computational Methodologies for Accurate Prediction of Wall Shear Stress and Turbulence Parameters in a Patient-Specific Aorta

Background: Recent studies suggest that blood flow in main arteries is intrinsically disturbed, even under healthy conditions. Despite this, many computational fluid dynamics (CFD) analyses of aortic haemodynamics make the assumption of laminar flow, and best practices surrounding appropriate modelling choices are lacking. This study aims to address this gap by evaluating different modelling and post-processing approaches in simulations of a patient-specific aorta. Methods: Magnetic resonance imaging (MRI) and 4D flow MRI from a patient with aortic valve stenosis were used to reconstruct the aortic geometry and derive patient-specific inlet and outlet boundary conditions. Three different computational approaches were considered based on assumed laminar or assumed disturbed flow states including low-resolution laminar (LR-Laminar), high-resolution laminar (HR-Laminar) and large-eddy simulation (LES). Each simulation was ran for 30 cardiac cycles and post-processing was conducted on either the final cardiac cycle, or using a phase-averaged approach which utilised all 30 simulated cycles. Model capabilities were evaluated in terms of mean and turbulence-based parameters. Results: All simulation types, regardless of post-processing approach could correctly predict velocity values and flow patterns throughout the aorta. Lower resolution simulations could not accurately predict gradient-derived parameters including wall shear stress and viscous energy loss (largest differences up to 44.6% and 130.3%, respectively), although phase-averaging these parameters improved predictions. The HR-Laminar simulation produced more comparable results to LES with largest differences in wall shear stress and viscous energy loss parameters up to 5.1% and 11.6%, respectively. Laminar-based parameters were better estimated than turbulence-based parameters. Conclusion: Our findings suggest that well-resolved laminar simulations can accurately predict many laminar-based parameters in disturbed flows, but there is no clear benefit to running a HR-Laminar simulation over an LES simulation based on their comparable computational cost. Additionally, post-processing "typical" laminar simulation results with a phase-averaged approach is a simple and cost-effective way to improve accuracy of lower-resolution simulation results.

A novel MRI-based data fusion methodology for efficient, personalised, compliant simulations of aortic haemodynamics

We present a novel, cost-efficient methodology to simulate aortic haemodynamics in a patient-specific, compliant aorta using an MRI data fusion process. Based on a previously-developed Moving Boundary Method, this technique circumvents the high computational cost and numerous structural modelling assumptions required by traditional Fluid-Structure Interaction techniques. Without the need for Computed Tomography (CT) data, the MRI images required to construct the simulation can be obtained during a single imaging session. Black Blood MR Angiography and 2D Cine-MRI data were used to reconstruct the luminal geometry and calibrate wall movement specifically to each region of the aorta. 4D-Flow MRI and non-invasive pressure measurements informed patient-specific inlet and outlet boundary conditions. Luminal area closely matched 2D Cine-MRI measurements with a mean error of less than 4.6% across the cardiac cycle, while physiological pressure and flow distributions were simulated to within 3.3% of patient-specific targets. Moderate agreement with 4D-Flow MRI velocity data was observed. Despite lower peak velocity, an equivalent rigid-wall simulation predicted a mean Time-Averaged Wall Shear Stress (TAWSS) 13% higher than the compliant simulation. The agreement observed between compliant simulation results and MRI data is testament to the accuracy and efficiency of this MRI-based simulation technique.

Assessment of turbulent blood flow and wall shear stress in aortic coarctation using image-based simulations

In this study, we analyzed turbulent flows through a phantom (a 180[Formula: see text] bend with narrowing) at peak systole and a patient-specific coarctation of the aorta (CoA), with a pulsating flow, using magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). For MRI, a 4D-flow MRI is performed using a 3T scanner. For CFD, the standard [Formula: see text], shear stress transport [Formula: see text], and Reynolds stress (RSM) models are applied. A good agreement between measured and simulated velocity is obtained for the phantom, especially for CFD with RSM. The wall shear stress (WSS) shows significant differences between CFD and MRI in absolute values, due to the limited near-wall resolution of MRI. However, normalized WSS shows qualitatively very similar distributions of the local values between MRI and CFD. Finally, a direct comparison between in vivo 4D-flow MRI and CFD with the RSM turbulence model is performed in the CoA. MRI can properly identify regions with locally elevated or suppressed WSS. If the exact values of the WSS are necessary, CFD is the preferred method. For future applications, we recommend the use of the combined MRI/CFD method for analysis and evaluation of the local flow patterns and WSS in the aorta.

Analysis of Turbulence Effects in a Patient-Specific Aorta with Aortic Valve Stenosis

Blood flow in the aorta is often assumed laminar, however aortic valve pathologies may induce transition to turbulence and our understanding of turbulence effects is incomplete. The aim of the study was to provide a detailed analysis of turbulence effects in aortic valve stenosis (AVS).

METHODS

Large-eddy simulation (LES) of flow through a patient-specific aorta with AVS was conducted. Magnetic resonance imaging (MRI) was performed and used for geometric reconstruction and patient-specific boundary conditions. Computed velocity field was compared with 4D flow MRI to check qualitative and quantitative consistency. The effect of turbulence was evaluated in terms of fluctuating kinetic energy, turbulence-related wall shear stress (WSS) and energy loss.

RESULTS

Our analysis suggested that turbulence was induced by a combination of a high velocity jet impinging on the arterial wall and a dilated ascending aorta which provided sufficient space for turbulence to develop. Turbulent WSS contributed to 40% of the total WSS in the ascending aorta and 38% in the entire aorta. Viscous and turbulent irreversible energy losses accounted for 3.9 and 2.7% of the total stroke work, respectively.

CONCLUSIONS

This study demonstrates the importance of turbulence in assessing aortic haemodynamics in a patient with AVS. Neglecting the turbulent contribution to WSS could potentially result in a significant underestimation of the total WSS. Further work is warranted to extend the analysis to more AVS cases and patients with other aortic valve diseases.

Enhancement of cerebrovascular 4D flow MRI velocity fields using machine learning and computational fluid dynamics simulation data

Blood flow metrics obtained with four-dimensional (4D) flow phase contrast (PC) magnetic resonance imaging (MRI) can be of great value in clinical and experimental cerebrovascular analysis. However, limitations in both quantitative and qualitative analyses can result from errors inherent to PC MRI. One method that excels in creating low-error, physics-based, velocity fields is computational fluid dynamics (CFD). Augmentation of cerebral 4D flow MRI data with CFD-informed neural networks may provide a method to produce highly accurate physiological flow fields. In this preliminary study, the potential utility of such a method was demonstrated by using high resolution patient-specific CFD data to train a convolutional neural network, and then using the trained network to enhance MRI-derived velocity fields in cerebral blood vessel data sets. Through testing on simulated images, phantom data, and cerebrovascular 4D flow data from 20 patients, the trained network successfully de-noised flow images, decreased velocity error, and enhanced near-vessel-wall velocity quantification and visualization. Such image enhancement can improve experimental and clinical qualitative and quantitative cerebrovascular PC MRI analysis.

Numerical simulation of time-resolved 3D phase-contrast magnetic resonance imaging

A numerical approach is presented to efficiently simulate time-resolved 3D phase-contrast Magnetic resonance Imaging (or 4D Flow MRI) acquisitions under realistic flow conditions. The Navier-Stokes and Bloch equations are simultaneously solved with an Eulerian-Lagrangian formalism. A semi-analytic solution for the Bloch equations as well as a periodic particle seeding strategy are developed to reduce the computational cost. The velocity reconstruction pipeline is first validated by considering a Poiseuille flow configuration. The 4D Flow MRI simulation procedure is then applied to the flow within an in vitro flow phantom typical of the cardiovascular system. The simulated MR velocity images compare favorably to both the flow computed by solving the Navier-Stokes equations and experimental 4D Flow MRI measurements. A practical application is finally presented in which the MRI simulation framework is used to identify the origins of the MRI measurement errors.

CFD validation using in-vitro MRI velocity data - Methods for data matching and CFD error quantification

Predicting blood flow velocities in patient-specific geometries with Computational Fluid Dynamics (CFD) can provide additional data for diagnosis and treatment planning but the solution can be inaccurate. Therefore, it is crucial to understand the simulation errors and calibrate the numerical model. In-vitro velocity-encoded MRI is a versatile tool to validate CFD. The comparison between CFD and in-vitro MRI velocity data, and the analysis of the simulation error are the objectives of this study. A three-step routine is presented to validate medical CFD data. First, a properly scaled model of the patient-specific geometry is fabricated to achieve high relative resolution in the MRI experiment. Second, the measured flow geometry is matched with the CFD data using one of two algorithms, Coherent Point Drift and Iterative Closest Point. The aligned data sets are then interpolated onto a common grid to enable a point-to-point comparison. Third, the global and local deviations between CFD and MRI velocity data are calculated using different algorithms to reliably estimate the simulation error. The routine is successfully tested with a patient-specific model of a cerebral aneurysm. In conclusion, the methods presented here provide a framework for CFD validation using in-vitro MRI velocity data.

Towards quantitative evaluation of wall shear stress from 4D flow imaging

Wall shear stress (WSS) is a relevant hemodynamic indicator of the local stress applied on the endothelium surface. More specifically, its spatiotemporal distribution reveals crucial in the evolution of many pathologies such as aneurysm, stenosis, and atherosclerosis. This paper introduces a new solution, called PaLMA, to quantify the WSS from 4D Flow MRI data. It relies on a two-step local parametric model, to accurately describe the vessel wall and the velocity-vector field in the neighborhood of a given point of interest. Extensive validations have been performed on synthetic 4D Flow MRI data, including four datasets generated from patient specific computational fluid dynamics simulations on carotids. The validation tests are focused on the impact of the noise component, of the resolution level, and of the segmentation accuracy concerning the vessel position in the context of complex flow patterns. In simulated cases aimed to reproduce clinical acquisition conditions, the WSS quantification performance reached by PaLMA is significantly higher (with a gain in RMSE of 12 to 27%) than the reference one obtained using the smoothing B-spline method proposed by Potters et al. (2015) method, while the computation time is equivalent for both WSS quantification methods.

Towards multi-modal data fusion for super-resolution and denoising of 4D-Flow MRI

4D-Flow magnetic resonance imaging (MRI) has enabled in vivo time-resolved measurement of three-dimensional blood flow velocities in the human vascular system. However, its clinical use has been hampered by two main issues, namely, low spatio-temporal resolution and acquisition noise. While patient-specific computational fluid dynamics (CFD) simulations can address the resolution and noise issues, its fidelity is impacted by accuracy of estimation of boundary conditions, model parameters, vascular geometry, and flow model assumptions. In this paper a scheme to address limitations of both modalities through data-fusion is presented. The solutions of the patient-specific CFD simulation are characterized using proper orthogonal decomposition (POD). Next, a process of projecting the 4D-Flow MRI data onto the POD basis and projection coefficient mapping using generalized dynamic mode decomposition (DMD) enables simultaneous super-resolution and denoising of 4D-Flow MRI. The method has been tested using numerical phantoms derived from patient-specific aneurysmal geometries and applied to in vivo 4D-Flow MRI data.

Numerical simulation of deformable particles in a Coulter counter

In Coulter counters, cells counting and volumetry are achieved by monitoring their electrical print when they flow through a sensing zone. However, the volume measurement may be impaired by the cell dynamics, which may be difficult to control. In this paper, numerical simulations of the dynamics and electrical signature of red blood cells in a Coulter counter are presented, accounting for the deformability of the cells. In particular, a specific numerical pipeline is developed to overcome the challenge of the multi-scale nature of the problem. It consists in segmenting the whole computation of the cell dynamics and electrical response in a series of dedicated computations, with a saving of one order of magnitude in computational time. This numerical pipeline is used with rigid spheres and deformable red blood cells in an industrial Coulter counter geometry, and compared with experimental measurements. The simulations not only reproduce electrical signatures typical of those measured experimentally, but also allow an analysis of the electrical signature in terms of the heterogeneity of the electrical field and dynamics of the particles in the measurement zone. This study provides a methodology for computing the sizing of rigid or deformable particles by Coulter counters, opening the way to a better understanding of cells signatures in such devices.