Estimation of wall shear stress using 4D flow cardiovascular MRI and computational fluid dynamics

Electronic version of an article published as Journal of mechanics in medicine and biology, 0, 1750046 (2016), 16 pages. DOI:10.1142/S0219519417500464 © World Scientific Publishing CompanyIn the last few years, wall shear stress (WSS) has arisen as a new diagnostic indicator in patients with arterial disease. There is a substantial evidence that the WSS plays a significant role, together with hemodynamic indicators, in initiation and progression of the vascular diseases. Estimation of WSS values, therefore, may be of clinical significance and the methods employed for its measurement are crucial for clinical community. Recently, four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) has been widely used in a number of applications for visualization and quantification of blood flow, and although the sensitivity to blood flow measurement has increased, it is not yet able to provide an accurate three-dimensional (3D) WSS distribution. The aim of this work is to evaluate the aortic blood flow features and the associated WSS by the combination of 4D flow cardiovascular magnetic resonance (4D CMR) and computational fluid dynamics technique. In particular, in this work, we used the 4D CMR to obtain the spatial domain and the boundary conditions needed to estimate the WSS within the entire thoracic aorta using computational fluid dynamics. Similar WSS distributions were found for cases simulated. A sensitivity analysis was done to check the accuracy of the method. 4D CMR begins to be a reliable tool to estimate the WSS within the entire thoracic aorta using computational fluid dynamics. The combination of both techniques may provide the ideal tool to help tackle these and other problems related to wall shear estimation.Peer ReviewedPostprint (author's final draft

Respiratory organ motion in interventional MRI : tracking, guiding and modeling

Respiratory organ motion is one of the major challenges in interventional MRI, particularly in interventions with therapeutic ultrasound in the abdominal region. High-intensity focused ultrasound found an application in interventional MRI for noninvasive treatments of different abnormalities. In order to guide surgical and treatment interventions, organ motion imaging and modeling is commonly required before a treatment start. Accurate tracking of organ motion during various interventional MRI procedures is prerequisite for a successful outcome and safe therapy. In this thesis, an attempt has been made to develop approaches using focused ultrasound which could be used in future clinically for the treatment of abdominal organs, such as the liver and the kidney. Two distinct methods have been presented with its ex vivo and in vivo treatment results. In the first method, an MR-based pencil-beam navigator has been used to track organ motion and provide the motion information for acoustic focal point steering, while in the second approach a hybrid imaging using both ultrasound and magnetic resonance imaging was combined for advanced guiding capabilities. Organ motion modeling and four-dimensional imaging of organ motion is increasingly required before the surgical interventions. However, due to the current safety limitations and hardware restrictions, the MR acquisition of a time-resolved sequence of volumetric images is not possible with high temporal and spatial resolution. A novel multislice acquisition scheme that is based on a two-dimensional navigator, instead of a commonly used pencil-beam navigator, was devised to acquire the data slices and the corresponding navigator simultaneously using a CAIPIRINHA parallel imaging method. The acquisition duration for four-dimensional dataset sampling is reduced compared to the existing approaches, while the image contrast and quality are improved as well. Tracking respiratory organ motion is required in interventional procedures and during MR imaging of moving organs. An MR-based navigator is commonly used, however, it is usually associated with image artifacts, such as signal voids. Spectrally selective navigators can come in handy in cases where the imaging organ is surrounding with an adipose tissue, because it can provide an indirect measure of organ motion. A novel spectrally selective navigator based on a crossed-pair navigator has been developed. Experiments show the advantages of the application of this novel navigator for the volumetric imaging of the liver in vivo, where this navigator was used to gate the gradient-recalled echo sequence

Enhancing magnetic resonance imaging with computational fluid dynamics

Quantitative assessment of haemodynamics has been utilised for better understanding of cardiac function and assisting diagnostics of cardiovascular diseases. To study haemodynamics, magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) are widely used because of their non-invasive nature. It has been demonstrated that the two approaches are complementary to each other with their own advantages and limitations. Four dimensional cardiovascular magnetic resonance (4D Flow CMR) imaging enables direct measurement of blood flow velocity in vivo while spatial and temporal resolutions as well as region of image acquisition are limited to achieve a detailed assessment of the haemodynamics. CFD, on the other hand, is a powerful tool that has the potential to expand the image-obtained velocity fields with some problem-specific assumptions such as rigid arterial walls. We suggest a novel approach in which 4D Flow CMR and CFD are integrated synergistically in order to obtain an enhanced 4D Flow CMRI (EMRI). The enhancement will consist in overcoming the spatial-resolution limitations of the original 4D Flow CMRI, which will enable more accurate quantification of flow dependent bio-mechanical quantities (e.g. endothelial shear stress) as well as non-invasive estimation of blood pressure. At the same time, it will reduce a number of assumptions in conventional haemodynamic CFD such as in/outflow conditions including the effect of valves, the impact of patient-specific vessel wall motion and the effect of the surrounding tissues. The approach was first tested on a 2D portion of a pipe, to understand the behaviour of the parameters of the model in this novel framework. Afterwards the methodology was tested on patient specific data, to apply it to the analysis of blood flow in a patient specific human aorta, in 2D. The outcomes of EMRI are assessed by comparing the computed velocities with the 4D Flow CMR one. A fundamental step to allow the translation to clinics of this methodology was the validation. The study was performed on an idealised-simplified model of the human aortic arch – a U bend – with a sinusoidal inflow applied by a pump. Firstly, phase resolved particle image velocimetry (PIV) (an experimental technique enables high spatial-temporal resolution) was performed in 5 different time points of the pump cycle, using a blood alike fluid with the same refractive index matched of the clear silicon phantom, and seeded with silver coated hollow glass spheres. Real time 4D Flow CMR was then performed on the phantom with MRI. Lastly using the pump flow rate and the phantom geometry, a computation of the flow through the U bend was conducted using Ansys CFX. The flow patterns obtained from the 3 methods were compared in the middle plane of the phantom. The methodology was then applied to study a patient specific aorta in 3D, and retrieve flow patterns and flow dependent parameters. Finally, the validated methodology was applied to study atherogenesis, and in particular to investigate the relation between EMRI retrieved flow quantities (e.g. wall shear stress (WSS)) and temperature heterogeneity. A carotid artery phantom was realised and studied with CFD, MRT and EMRI. All the results demonstrate that EMRI preserves flow structures while correcting for experimental noise. Therefore it can provide better insights of the haemodynamics of cardiovascular problems, overcoming the limitations of 4D Flow CMR and CFD, even when considering a small region of interest. These findings were supported by the validation experiment that showed how EMRI retrieved flow patterns were much more consistent with the one measured with high resolution PIV, compensating for 4D Flow CMR errors. These findings lead to the application to the atherogenesis problem, allowing higher resolution flow patterns, more suitable to be compared to the temperature distribution and highlighted how flow patterns exert an influence on the temperature distribution on the vessel wall. EMRI confirmed its potential to provide more accurate non-invasive estimation of flow derived and flow dependent quantities and become a novel diagnostic tool

Analysis of cardiac motion using MRI and nonrigid image registration

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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

Technological innovations in magnetic resonance for early detection of cardiovascular diseases

Most recent technical innovations in cardiovascular MR imaging (CMRI) are presented in this review. They include hardware and software developments, and novelties in parametric mapping. All these recent improvements lead to high spatial and temporal resolution and quantitative information on the heart structure and function. They make it achievable ambitious goals in the field of mapletic resonance, such as the early detection of cardiovascular pathologies. In this review article, we present recent innovations in CMRI, emphasizing the progresses performed and the solutions proposed to some yet opened technical problems

4D ultra-short TE (UTE) phase-contrast MRI for assessing stenotic flow and hemodynamics.

Phase-contrast (PC) MRI is a non-invasive technique to assess cardiovascular blood flow. However, this technique is not accurate in the case of atherosclerotic disease and vascular and valvular stenosis due to intravoxel dephasing secondary to disturbed blood flow, flow recirculation, and turbulence distal to the narrowing, resulting in flow-related artifacts. Previous studies have shown that reducing the echo time (TE) decreases the errors associated with phase incoherence due to random motions as observed in unsteady and turbulent flows. As part of this dissertation, a novel 3-D cine Ultra-Short (UTE)-PC imaging method has been developed, and implemented to measure the blood velocity using a UTE center-out radial k-space trajectory with short TE time compared to standard PC MRI sequences. 3D UTE characterizes flow in one direction in a 3D volume, resulting in a single component of the flow velocities. In order to obtain a comprehensive flow assessment in three directions, the 3D UTE sequence needs to be repeated three times, which can be inefficient and time consuming. 4-D flow MRI has been recently used for quantitative flow assessment and visualization of complex flow patterns resulting in more anatomical information and comprehensive assessment of blood flow. With 4D flow MRI method, all the flow information in three direction in a 3D volume though the time can be achieved as part of a single scan. In this dissertation, a novel 4D UTE flow MRI technique has also been designed and implemented which is capable of deriving the three orthogonal components of the velocity field in the flow in a single scan, while achieving very short echo times. In flow phantom studies, comprehensive investigation of several different flow rates revealed significant improvement in flow quantification and reduction of flow artifacts when compared to conventional 4D flow. Furthermore, a reduced TE 4D Spiral flow MRI method has also been implemented which reduces scan times when compared to conventional 4D flow MRI (as well as 4D UTE flow). Despite reduction of scan time as well as TE relative to conventional 4D flow, the achieved TE with the 4D spiral technique is indeed longer than 4D UTE flow. In order to assess clinical feasibility and in order to perform further validation of 4D UTE flow, in an IRB-approved study, twelve aortic stenosis (AS) patients underwent Doppler Ultrasound, conventional 4D flow, and 4D UTE flow scans for a 3 way comparison. 4D UTE flow displayed good correlation with Doppler Ultrasound in patients with moderately severe aortic stenosis, though with the added benefit of not having confounding factors encountered in Doppler Ultrasound (e.g., angle dependence, 2D measurement, and difficulty in locating a proper acoustic window). The proposed 4D UTE flow permits 4D visualization of flow and true 3D measurement of all flow quantities, not possible with Doppler. Further investigations will be required to test the technique in patients with severe or critical aortic stenosis wherein conventional 4D flow will be less accurate due to intravoxel dephasing and spin incoherence

Hemodynamic analysis based on biofluid models and MRI velocity measurements

Tesis para optar al grado de Doctor en Ciencias de la Ingeniería, Mención Fluidodinámica en cotutela con la Universidad de GroningenFor the diagnosis, treatment planning and post-surgical monitoring of cardiovascular disease (CVD), hemodynamic markers have proven to be of great utility. However, non-invasive assessment of the hemodynamics of a patient is still a challenge. Phase-contrast magnetic resonance imaging (PC-MRI) can measure the distribution of blood velocity along two-dimensional planes or in three-dimensional volumes and is limited in accuracy mainly by the image resolution and noise. The local variation in the blood pressure cannot be measured non-invasively, but is required in the clinical practice to evaluate CVD. Other hemodynamic quantities, such as the arterial wall stiffness or wall shear stress can also be relevant as diagnostic quantities and for understanding the onset of CVD, but are not observable with imaging techniques. This thesis approaches the topic of patient-specific hemodynamics on three different paths. In Chapter 2 of this thesis a method was presented to improve the accuracy of hemodynamic data recovery from partial 2D PC-MRI measurements by means of solving an inverse problem of the Navier–Stokes equations of fluid flow. Vessel geometries extracted from MRI or CT images are affected by errors due to noise, artifacts and limited image resolution. Small errors in the geometry propagate into the recovered data and lead to large errors in the solution when standard no-slip boundary conditions are used on inaccurately positioned walls. The core idea of this work was replacing no-slip boundary conditions at the arterial walls by slip/transpiration conditions with parameters which were estimated from velocity measurements. Numerical results of synthetic test cases showed an important improvement in accuracy of the estimated pressure differences and the reconstructed velocity fields. In Chapter 3 a comparison study of different direct pressure gradient estimation techniques was presented. These methods compute relative pressure fields directly from 3D PC-MRI data. The new Stokes estimation method (STE) by Švihlová et al. [Švi+16] was applied for the first time to real phantom and patient data. In comparison to the classical Poisson pressure estimation method (PPE), the STE method proved more accurate and more robust to noise and the image segmentation in most cases. Chapter 4 was dedicated to a numerical validation of the new MAPDD model [Ber+19] for a domain decomposition reduction of vascular networks. This approach considers the vessels as a network of thin pipes in which the flow has the shape of a Womersley flow, connected by arbitrary 3D junction domains where the flow is governed by the Navier–Stokes equations. In the MAPDD model, the thin pipes are replaced by coupling conditions on the junction domains. A strategy to easily implement the MAPDD model with the finite element method was presented and the theoretical results of Bertoglio et al. [Ber+19] were reproduced with numerical simulations in a simple test case. The method was shown to deliver accurate results even for moderately large Reynolds numbers, far from the regime where the theory is valid.Los indicadores hemodinámicos han demostrado gran utilidad para el diagnóstico, planificación y monitoreo post-operatorio de enfermedades cardiovasculares (CVD). Sin embargo, la evaluación hemodinámica en pacientes continúa siendo un desafío. La Resonancia Magnética de Contraste de Fase (PC-MRI) es capaz de medir la distribución de la velocidad sanguínea en planos 2D o volúmenes 3D, siendo mayormente limitada por la resolución de la imágen y el ruido. Por otro lado, las variaciónes locales en la presión sanguínea sólo pueden ser medidas invasivamente, siendo usualmente requeridas en clínica para la evaluación de las CVD. Otras cantidades hemodinámicas, tales como la rigidez arterial, pueden ser también relevantes para el diagnóstico y entendimiento del origen de las CVD, pero lamentablemente estas no son observables en las imágenes. Esta tesis aborda el tema de la hemodinámica en pacientes desde tres diferentes perspectivas. En el Capítulo 2, se presenta un método para mejorar la precisión en la reconstrucción de datos hemodinámicos, usando medidas 2D en PC-MRI. A partir de las ecuaciones de Navier-Stokes para un fluido, se plantea y resuelve un problema inverso. Además, las geometrías arteriales extraídas de imágenes MRI o CT, suelen ser afectadas por errores debidos al ruido, artefactos o propios de la limitación en la resolución espacial. Pequeños errores en la geometría son propagados en la reconstrucción, pudiendo generar mayores desviaciones en la solución, por ejemplo cuando condiciones de borde tipo no-slip son usadas en paredes mal mente posicionadas. La idea central de este trabajo es relajar las condiciones no-slip en las paredes por unas slip/transpiration, con parámetros a estimar de medidas de velocidad. Los resultados numéricos en casos sintéticos muestran mejoras en el cálculo de diferencias de presión y campo de velocidades. En el Capítulo 3 se presenta una comparación entre diferentes técnicas de estimación de presión. Estos métodos reconstruyen campos de presión directamente de medidas 3D en PC-MRI. Por primera vez el reciente estimador de Stokes (STE) Švihlová y col. [Švi+16] es aplicado en medidas a fantomas y pacientes. A diferencia del clásico estimador de Poisson (PPE), este estimador muestra, en la mayoría de los casos, menos error en la reconstrucción y ser más robusto al ruido y a la segmentación. El Capítulo 4 es dedicado a la validación numérica del nuevo modelo MAPDD Bertoglio y col. [Ber+19], para una descomposición reducida de redes vasculares. Este enfoque considera las venas como una red de delgadas tuberías, en donde el flujo tiene la forma de un flujo de Womersley, conectado por un dominio arbitrario 3D de uniones, en donde el flujo es gobernado por las ecuaciones de Navier-Stokes. En este modelo, las tuberías delgadas son reemplazadas acoplando distintas condiciones en el dominio de uniones. Aquí, se presenta una estrategia fácilmente de implementar usando elementos finitos. Se reproducen los resultados teóricos de Bertoglio y col. [Ber+19] además de simulaciones numéricas en un caso de prueba simple. El método muestra entregar buenos resultados incluso para números de Reynolds ligeramente grandes, excediendo los límites donde es válida la teória