FUNCTIONAL IMAGING IN CONGENITAL HEART DISEASE WITH 3D CINE PHASE CONTRAST MRI. Elizabeth Janus Nett. Doctor of Philosophy.

Transcription

1 FUNCTIONAL IMAGING IN CONGENITAL HEART DISEASE WITH 3D CINE PHASE CONTRAST MRI by Elizabeth Janus Nett A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Medical Physics) at the UNIVERSITY OF WISCONSIN-MADISON 2013 Date of final oral examination: 12/19/12 The dissertation is approved by the following members of the Final Oral Committee: Oliver Wieben, Assistant Professor, Medical Physics Walter F. Block, Professor, Medical Physics Christopher J. François, Assistant Professor, Radiology Charles Mistretta, Professor, Medical Physics Scott B. Reeder, Professor, Radiology

2 ii FUNCTIONAL IMAGING IN CONGENITAL HEART DISEASE WITH 3D CINE PHASE CONTRAST MRI Elizabeth Janus Nett Under the supervision of Oliver Wieben, PhD At the University of Wisconsin-Madison Abstract Volumetric, time-resolved, phase contrast Magnetic Resonance Imaging (MRI) with three-directional velocity encoding (4D PC MRI) can provide both anatomical and hemodynamic information with high spatial resolution in clinically feasible scan times. This work focuses on the application of 4D PC MRI to congenital heart disease (CHD). Major and minor CHD defects occur in approximately nine defects per 1000 live births, of which about a quarter would be expected to require invasive treatment or result in death within the first year of life. Imaging modalities such as Doppler Ultrasound and CT have been used extensively in CHD patients. Despite several appealing properties, MRI use has

3 iii been limited clinically because current protocols for CHD are lengthy and require the use of sedation or general anesthesia in younger or uncooperative patients. Recent advances in MR hardware and data acquisition and reconstruction methodology have facilitated 4D PC MRI which can be used for comprehensive velocity and flow measurements, as well as the derivation of additional hemodynamic parameters such a trans-stenotic pressure gradients and wall shear stress. Therefore, 4D PC MRI could prove extremely useful for CHD diagnosis, surgery planning, and long-term monitoring. Our research focuses on improving the acquisition, reconstruction, and post-processing of 4D PC MRI for clinical use. We were able to extend the velocity range of 4D PC MRI while maintaining a high velocity-to-noise ration in order to optimize the acquisition for regions such as the thoracic vasculature with a wide range of flow velocities. Other aspects of this work focuses on improving the measurement of trans-stenotic pressure gradients. An in vitro study was conducted to validate 4D PC MRI pressure measurements in a stenotic phantom against computational fluid dynamics (CFD) and pressure probe measurements. We have also performed a feasibility study that demonstrates the utility of 4D PC MRI for quantifying vessel anatomy and 4D pressure gradients in both the aorta and pulmonary arteries.

4 iv Acknowledgements First, I would like to thank my advisor Dr. Oliver Wieben for his guidance, training, and encouragement throughout this endeavor. I truly appreciate the many hours he spent teaching me and working with me during the past five years. I would like to thank Dr. Kevin Johnson for all of the knowledge he shared with me and his help throughout my time in graduate school. The work in this thesis would not have been possible without him. I thank Dr. Chris François for his frequent guidance in the clinical aspects of my work. His explanations of pathologies and clinical perspective were invaluable. Many thanks to the other members of my thesis committee, Dr. Chuck Mistretta, Dr. Scott Reeder, and Dr. Wally Block for their helpful insights. Thank you to all of the members of the flow group, Ashley Anderson, Dr. Steve Kecskemeti, Mike Loecher, Leonardo Rivera, Eric Schrauben, and Dr. Andrew Wentland, for their help and collaboration over the years. I d like to thank Dr. Alejandro Roldán for his enthusiast work and helpful discussions. I had the pleasure of working with Dr. Alex Frydrychowicz during his time in Wisconsin and I appreciate the hours he spent scanning human volunteers with me. There are many other students in the medical physics program

5 v who have provided me with advice, support, and humor. I would especially like to thank Dr. Kitty Moran, Dr. Beth Hutchinson, and Dr. Rachel McKinsey for their friendship, intelligence, and understanding during this process. Finally, I would like to thank my family. My husband Brian has provided me with unwavering support throughout this entire process and I am incredibly grateful for everything he has done for me. I am so thankful for our son Bryce who has been the light of my life for the past eight months and has enriched my life in so many ways. And I am very appreciative of my parents, Myra and Lincoln, for the constant love and encouragement they have provided.

6 vi Abstract... ii Chapter 1: INTRODUCTION... 1 Chapter 2: BACKGROUND CONGENITAL HEART DISEASE Congenital Heart Disease Statistics in the United States Role of Imaging in CHD MRI Protocols for CHD PHASE CONTRAST MRI Phase Contrast Theory Phase Contrast Velocity Encoding Errors in Phase Contrast Three Directional Phase Encoding D PHASE CONTRAST MRI PC VIPR Acquisition D Phase Contrast MRI Validation and Reproducibility Tools for interactive analysis and exploration of hemodynamics from 4D PC MRI Chapter 3: FOUR-DIMENSIONAL PHASE CONTRAST MRI WITH ACCELERATED DUAL VELOCITY ENCODING ABSTRACT INTRODUCTION MATERIALS AND METHODS Dual Venc Theory MR Imaging RESULTS DISCUSSION Chapter 4: NONINVASIVE PRESSURE MEASUREMENTS IN PATIENTS WITH CONGENITAL HEART DISEASE USING 4D PHASE CONTRAST MRI ABSTRACT INTRODUCTION MATERIALS AND METHODS... 72

7 vii 4.4 RESULTS DISCUSSION Chapter 5: IN VITRO VALIDATION OF PC VIPR PRESSURE MEASUREMENTS IN A STENOTIC FLOW PHANTOM ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS DISCUSSION Chapter 6: SUMMARY AND RECOMMENDATIONS SUMMARY RECOMMENDATIONS... 98

8 Chapter 1 INTRODUCTION Current data suggest an incidence of congenital heart disease (CHD) of approximately 9 defects per 1000 live births. Of these, 2.3/1000 would be expected to require invasive treatment or result in death within the first year of life (1). CHD describes a number of different pathologies affecting the heart or great vessels, including bicuspid valves, atrial septal defects, transposition of the great vessels, and pulmonary artery stenosis. Medical imaging is used widely in congenital heart disease for diagnosis, patient monitoring and surgical planning. Imaging modalities such as Doppler Ultrasound and CT have been used extensively in these patients. Magnetic Resonance Imaging (MRI) can also be used for patients with CHD and has certain advantages over other modalities. MRI can provide a comprehensive cardiac exam that includes cardiac anatomy, function, perfusion, hemodynamics, and viability imaging without ionizing radiation and therefore, could prove

9 2 extremely useful for CHD diagnosis, surgery planning and long-term follow-up as is frequently required in these patients. However, the use of MRI has been limited clinically because current protocols for CHD are lengthy (> 1 hour) and require the use of sedation or general anesthesia in younger or uncooperative patients. The aim of this work was to develop novel MRI acquisition, reconstruction and data processing schemes that provide diagnostic and hemodynamic information for patients with CHD. Specifically, the use of 4D Phase Contrast MRI (4D PC MRI) with radial undersampling was investigated to drastically reduce exam times for these patients, provide detailed blood flow information and calculate additional hemodynamic parameters, and generally improve diagnosis and understanding of the disease process for patients with CHD. The development and presentation of this body of work in the following chapters is summarized below: Chapter 2: Background gives an introduction to congenital heart disease and an overview of phase contrast MRI and developments in 4D phase contrast MRI including data acquisition techniques, validation and data processing. Chapter 3: Noninvasive Pressure Measurements in Patients with Congenital Heart Disease Using Phase Contrast MRI focuses on the validation of a novel approach for accelerated four-dimensional phase contrast MR imaging (4D PC MRI) with an extended range of velocity sensitivity. 4D PC MRI data were acquired with a radially undersampled trajectory (PC VIPR). The theory of this technique and results from a phantom and human volunteer study are described.

10 3 Chapter 4: Noninvasive Pressure Measurements in Patients with Congenital Heart Disease Using 4D Phase Contrast MRI This study investigates the feasibility of noninvasively quantifying the percent stenosis and pressure differences in the pulmonary arteries and aorta using 4D PC MRI, specifically in patients with aortic coarctation (CoA) and pulmonary artery stenosis (PAS). We also evaluate different data analysis strategies for the assessment of spatial and temporal pressure differences derived from 4D PC MRI. Chapter 5: In Vitro Validation of PC VIPR Pressure Difference Measurements in a Stenotic Flow Phantom compares 4D Flow MRI pressure measurements in a stenosis phantom with pressure catheter measurements and computational fluid dynamics (CFD). Pressure gradients calculated from 4D PC MRI data in a stenosis phantom were comparable to those obtained from pressure probe and CFD. Pressures differences calculated using the Navier-Stokes and Bernoulli methods were also compared for 4D Flow and CFD data. Chapter 6: Summary and Recommendations summarizes the contributions of this thesis in the context of medical imaging research and recommends future work for use of PC MRI in congenital heart disease.

11 4 Chapter 2 BACKGROUND 1.1 CONGENITAL HEART DISEASE Congenital Heart Disease Statistics in the United States From 1940 to 2002, about 2 million patients with congenital cardiovascular defects were born in the United States: about 1 million with simple lesions and 0.5 million each with moderate and complex lesions (1). Common complex defects include: Tetralogy of Fallot (TOF) (9% to 14%) Transposition of the great arteries (10% to 11%) Atrioventricular septal defects (4% to 10%) Coarctation of the aorta (8% to 11%) Hypoplastic left heart syndrome (4% to 8%)

12 5 Ventricular septal defects (VSDs) (14% to 16%) Absent valve(s) Aortic regurgitation Mitral valve disease Coarctation of the aorta Pulmonary valve regurgitation Pulmonary valve stenosis The percentages above exclude bicuspid aortic valves, which are prevalent in about 2 million adults and 1 million children. Multiple defects are often present in one patient. A wide range of pathologies affect the heart chambers such as atrial and ventricular septal defects and ventricular hypertrophy. The right ventricles of patients with doublechambered right ventricle (DCRV) and stenotic right-ventricle-to-pulmonary-artery conduits, and the left ventricle of aortic stenosis patients all exhibit hypertrophy caused by pressure overload. The right ventricles of patients with atrial septal defects (ASD), pulmonary regurgitation (PR), and the left ventricles of aortic regurgitation patients display ventricular dilatation. CHD is the most common birth defect to result in death and accounts for almost 140,000 hospitalizations yearly (1). Management of most complicated CHD requires surgical procedures to restore cardiac circulation. Some conditions require redirection of blood flow and use of imaging has been crucial to understanding post-surgical outcomes. As a result of improvements in management of patients with CHD, the mortality rate related to CHD continues to decline. In addition, improvements in invasive and noninvasive cardiac imaging techniques have increased the detection of CHD in adults that were undiagnosed in

13 6 childhood. Unfortunately, CHD still accounts for a substantial number of lost life-years (approximately 195,000) before the age of 55 years, which is greater than those lost due to prostate cancer, Alzheimer s disease, and leukemia combined (1). The total hospital costs for CHD in 2004 was estimated to be $2.6 billion (2) Role of Imaging in CHD Cardiac imaging is critical in patients with congenital heart defects for delineating cardiovascular anatomy, therapeutic planning, and follow-up after therapy. Transthoracic and transesophageal echocardiography (TTE and TEE, respectively) are the primary modalities used for managing patients with CHD. TTE and TEE are widely available imaging options with inexpensive, mobile units and exams can be performed by a cardiologist without a referral to radiology. TTE involves very little patient discomfort and no risks are identified with the procedure. TTE can be used to assess: Valve function structure Aortic, pulmonary or mitral valve stenosis or regurgitation Chamber size Ventricular function including evaluating ejection fraction Ventricular structure including aneurysm, ventricular septal defect, and hypertrophy Pulmonary artery pressure Degree of aortic coarctation In TEE, the ultrasound transducer is passed into the esophagus and stomach which involves some discomfort. TEE is used in cases where the diagnostic information from TTE

14 7 is incomplete because of a larger body, chest deformities, or an insufficient transthoracic acoustic window. TEE is used when TTE is inconclusive such as in cases of possible atrial or ventricular septal defects or in cases where there is a need to clarify pathology (3, 4). The major limitation of TTE and TEE is the inability of these modalities to sufficiently visualize the pulmonary arteries and veins beyond the hilum. In addition, TTE and TEE are limited in their ability to accurately quantify ventricular volumes and calculate flow parameters. A more complete assessment of the aorta, pulmonary arteries, and cardiac chambers is desirable. This is particularly true in patients with CHD lesions that affect the right ventricle and pulmonary vasculature (i.e. Tetralogy of Fallot, pulmonary stenosis, and partial anomalous venous return) and in older patients with CHD lesions affecting the ascending aorta and aortic arch (i.e. aortic coarctation, bicuspid aortic valves, interrupted aorta repairs). These assessments can be performed with catheter angiography, computed tomographic angiography (CTA), or MRI (5). Computed tomography provides 3D scans that can be acquired in a single breath-hold with excellent spatial resolution. Catheter angiography guided by fluoroscopy is often used in surgical planning. These techniques can be used in the morphologic evaluation of CHD, including: Aortic pathology Pulmonary artery anatomy Post-operative systemic to pulmonary shunt size Vascular stent imaging Additionally, imaging can be done in the presence of pacemakers, defibrillators, aneurysm clips, etc. Although catheter angiography, CTA, and MRI all provide similar information

15 8 regarding the vascular anatomy, MRI is the only of these three imaging modalities that can also be used to noninvasively assess hemodynamic and cardiac function parameters in patients with CHD. The other main disadvantage of CTA and catheterization compared with MR is the use of ionizing radiation. Many patients need repeated examinations and the risk from repeated exposure to ionizing radiation, especially in younger patients, could be substantial. Catheter angiography has other associated risks including arrhythmias, perforation, bleeding, etc. (6) MRI Protocols for CHD Cardiac MRI is a comprehensive, non-invasive diagnostic tool that can be used to asses cardiac anatomy, global and local myocardial function, perfusion, hemodynamics in the cardiac chambers and great vessels, and myocardial viability without ionizing radiation (7-11). CT and ultrasound are used much more extensively in this patient population; however MRI has emerged as a viable and robust alternative to these modalities. The availability of a comprehensive cardiac assessment without ionizing radiation makes MRI well suited as a method for long term monitoring of patients. The 2008 American College of Cardiology and American Heart Association guidelines for the management of adults with CHD (5) has listed the following types of CHD as appropriate indications for cardiac MRI based on currently available evidence: Aortic coarctation Subvalvular and supravalvular aortic stenosis Supravalvular, branch, peripheral pulmonary artery stenosis Coronary arteriovenous fistula

16 9 Pulmonary artery hypertension secondary to CHD Tetralogy of Fallot Baffle repair of d-tga Congenitally corrected TGA Figure 2.1 Sequence of MRI/MRA scans performed for CHD patients: (1) localization, (2) 2D cine bssfp, (3) 3D CE MRA, (4) 2D PC for flow analysis A representative imaging protocol for CHD patients is shown in Figure 2.1. Axial, coronal, and/or sagittal images are acquired as localizers. A cine gradient echo sequence is used for assessment of cardiac structure and local and global cardiac function. The preferred imaging sequence for superior imaging contrast is balanced steady state free precession (bssfp) (12), also known as truefisp, FIESTA, or balanced FFE, depending on the vendor. For quantification of left and right ventricular functional parameters, multiple consecutive cine 2D bssfp images are acquired with cardiac gating. The acquisition of a cine series for given slice position requires approximately 8-20 seconds and is completed during a breath hold to avoid artifacts from respiratory motion. For cardiac function analysis, contours are drawn along the endocardial and epicardial borders to determine ventricular volumes which are used to quantify various cardiac function parameters end-diastolic volume

17 10 (EDV), end-systolic volume (ESV), stroke volume (SV), ejection fraction (EF), and myocardial mass. These cine images can also be used to assess regional ventricular function qualitatively. For evaluation of right ventricular function, contiguous axial slices (typically slices) are acquired through the entire heart. For imaging of left ventricular function, several localizers are used to establish the double oblique orientation of the cardiac short and long axis and subsequently short axis scans are prescribed from base to apex. Other common views include four chamber, two chamber, and ventricular outflow tract cine series. Vascular anatomy is usually assessed with a 3D contrast enhanced MR angiogram (CE MRA) (13, 14) that requires the injection of a Gadolinium based contrast agent, proper synchronization of the bolus arrival with a breath hold and data sampling, and the acquisition of a pre-contrast volume for mask mode subtraction and an additional postcontrast acquisition. While the Gadolinium-based MRA contrast agents are considered very safe it has been recently shown that they are linked to the occurrence of nephrogenic systemic fibrosis (NSF) in patients with severely compromised kidney function (15-17), leading to the exclusion of such patients from CE MRA studies. 2D cine phase contrast (PC) images are used for blood flow quantification and part of practically every MRI exam of a CHD patient. Usually, 2D PC images are obtained in multiple orientations to assess flow through the regions of greatest interest. For example, to quantify shunt fraction, or difference between pulmonary (QP) and systemic (QS) flow (QP/QS), flow measurements must be obtained through the aorta and pulmonary artery. Other areas of interest include velocity measurements proximal and distal to valvular

18 11 disease, aortic coarctations and dilations. As with the cine bssfp acquisitions, the 2D PC measurements are obtained during suspended respiration. Due to the need for bipolar gradients for velocity encoding and a reference image to account for background phase contributions, these acquisitions take more than twice as long as bssfp acquisitions (approximately s scan time per slice). Although the amount of time it takes to acquire a single cine bssfp or PC slice is relatively quick, multiple slices are obtained in different orientations and each orientation requiring new localizers for proper alignment of the slice orientation with the patient specific anatomy. Therefore, the total amount of time required to image many locations in the heart can be quite long. Younger patients (typically < 10 years) must be under general anesthesia (GA) and for complex CHD cases, the total exam time can be up to 90 minutes. Breath holds of these patients are controlled by the anesthesiologist by switching the respirator on and off. Additional time is required between each slice to allow for the patient to recover from the breath hold and these patients must remain motionless throughout the examination to avoid slice misregistration. For many patients with CHD, the risks of GA outweigh the benefits of the information that could be obtained with cardiac MRI and other imaging modalities such as catheter based angiography or CTA are chosen by the referring clinician. CTA can be performed under sedation because the acquisition is much shorter. The requirement of GA in certain patient groups, long overall exam times, and the need for breath holds are major impediments to the greater use of MRI in CHD patients. The development of 4D Phase Contrast MRI techniques for imaging in CHD patients has the potential to reduce overall scan times and represents a major step to developing new

19 12 cardiac MRI sequences that will allow CHD studies to be performed without anesthesia in much less time. With new scan protocols, many more patients could be considered for this very valuable imaging modality, possibly saving them from repeated x-ray exposures and catheterizations as their disease state is regularly monitored throughout their life. 1.2 PHASE CONTRAST MRI Phase Contrast Theory Phase contrast (PC) MRI is an angiographic imaging technique that allows for velocity quantification on a voxel-by-voxel basis and was originally introduced by Moran et al. (18). In the presence of a magnetic field, magnetic moments or spins precess at a characteristic frequency that is proportional to the strength of the field: 2.1 where ω is the angular frequency also known as the Larmor frequency of the spin, γ is the gyromagnetic ratio and B is the magnitude of the magnetic field. The precession of the net magnetization vector ( ) can be described as 2.1 Where M is the magnetization, ω is the angular frequency, and t is time. In the rotating coordinate system, spins that precess at the Larmor frequency 0 appear stationary and spins that precess faster or slower accumulate additional phase. Moving spins or spins in different locations along a magnetic field gradient acquire different phases and this phase accumulation can be positive or negative depending on the location. For linear field gradients, the amount of phase shift acquired by moving spins is proportional to

20 13 the velocity of the spin (Figure 2.2). In phase contrast imaging, this property is used to encode velocity. If we consider a spin with an initial position xo, with a velocity v and acceleration a, the phase signal of a spin in MR can be written: 2.2 where γ is the gyromagnetic ratio and G(t) is the applied gradient in the direction of the motion. The terms of this equation can be separated and expressed in terms of the moments (M0,M1,M2) of the gradient pulse: 2.3 The first term represents spatial encoding, the second velocity encoding, and the third acceleration encoding.

21 14 Figure 2.2 A schematic showing the effect of a bipolar gradient on the phase of stationary and moving spins. A spin at a particular position x 0 experiences a particular field strength during the application of the positive lobe, causing it to process at a particular rate for the entire time the positive lobe is being applied. During the positive lobe, both the moving and stationary spins acquire a phase of Δ. When the negative lobe of the bipolar is applied, the stationary spin experiences a negative gradient of the same strength and accumulates a phase, - Δ. However, the moving spin is in a different location by the time the negative gradient is applied, and it experiences a different strength gradient and accumulates a smaller amount of phase, - Δ. This is a simplification because in reality, the moving spin is moving continuously during the first lobe of the bipolar but the end result is similar. A 2D phase contrast MRI sequence includes an additional velocity-encoding gradient or bipolar gradient. The effect of the bipolar gradient on stationary and moving spins is shown in Figure 2.2. This bipolar velocity-encoding gradient has no net effect on the phase of stationary spins because the net area under the gradient is zero (ΔM0=0). However,

22 15 because moving spins experience varying magnetic field strengths during the application of the bipolar gradient, those spins acquire a net phase. In phase contrast images, the phase is displayed as a grayscale value and is proportional to the spin velocity. Stationary spins have a velocity of zero so regions of stationary tissue have an intensity of zero. Slow moving spins accumulate a small amount of phase and have low signal intensity. Similarly, faster moving spins have higher signal intensity. The phase accumulation of a spin due to the application of a bipolar gradient can be described by the expression: 2.4 In the case of a rectangular bipolar gradient, the change in the gradient first moment is the area under one lobe of the bipolar times the time between the applications of the lobes of the bipolar gradient. Thus, phase accumulation can be increased by applying a larger gradient or increasing the gradient duration. One important consideration in phase contrast imaging is that phase is induced only by the component of velocity that is aligned with the axis of the bipolar gradients. Therefore, in order to detect motion in three directions, bipolar gradients must be applied along each gradient axis. Figure 2.3 shows magnitude and phase images from a 2D PC chest exam. Each voxel of the phase image represents its corresponding velocity and flow can be measured by integrating over the vessel area. Images are acquired with cardiac gating throughout the cardiac cycle.

23 16 Figure 2.3 Magnitude and phase images with through plane velocity encoding from a series of 2D phase contrast images collected throughout the cardiac cycle. Bright voxels in the phase images correspond to high, positive velocity and dark voxels correspond to high, negative velocity. Below the images is a flow waveform obtained by integrating velocity over the ascending aorta area at different time points in the cardiac cycle. The expression above for phase accumulation (eqn. 2.4) can be used to determine velocity as long as the accumulated phase is between π and +π. Once the phase accumulation is greater than π, phase wrapping occurs and velocity can no longer be measured accurately (Figure 2.4). The velocity corresponding to a phase accumulation of π is the velocity encoding or the Venc. Using equation 2.4, the Venc can be written:

24 Similarly, the velocity can be determined using the relationship: 2.6 Figure 2.4 Velocity and phase have a linear relationship. Phase wrapping and velocity aliasing occurs when the phase is greater than π and the velocity is greater than the V enc If the velocity in a voxel is greater than the chosen Venc, the accumulated phase will be greater than π and phase wrapping and velocity aliasing will occur. Ideally, a Venc is chosen that is equal to or just greater than the maximum velocity in a region of interest. However, there is a penalty for choosing a higher Venc. Because only the fastest spins acquire a phase of π, slowly moving spins acquire smaller phases. Therefore, at a higher Venc, slower moving spins accumulate less phase leading to smaller signals and a decrease in the velocity-to-noise (VNR) ratio of the image. The SNR of the phase image is given by: 2.7

25 18 where (SNR)mag is the SNR of the magnitude image, σ is the variance of the magnitude signal, and ρm is the magnitude signal. The SNR of the phase is directly proportional to the magnitude signal. The noise for the phase signal can be written as (19): 2.8 Using equations 2.6 the noise of the velocity can be expressed in terms of the noise of the phase: 2.9 Using this expression, the velocity-to-noise ratio can be written: 2.10 The VNR is inversely proportional to the Venc. If the Venc is too high, the VNR may not be sufficient to make accurate measurements in slow flow regions.

26 19 Figure 2.5 Demonstration of phase wrapping for parabolic flow profile. (A) Is the phase profile across a vessel and (B) is the measured phase. Phase wrapping occurs when the accumulated phase exceeds ±π. When the phase accumulation of a spin exceeds ±π, the phase wrapping occurs and the measured phase differs from the actual phase by multiples of π (Figure 2.5): 2.11 where φm is the measured phase, φ is the actual phase accumulation and n is an integer. It is sometimes possible to correct phase aliasing using phase unwrapping algorithms. While one wrapped pixel is easily corrected by adding or subtracting multiples of π, determining which pixels are wrapped is challenging, particularly in the presence of noise. Phase unwrapping techniques are based on the flow information contained in adjacent pixels and assume that inter-pixel phase variation is less than π radians. Song et al. used this assumption to estimate the phase gradient and solve for the absolute phase using the least squares solution in the spatial domain (20). Phase unwrapping can be performed in the temporal domain by registering cardiac frames to each other (21). Phase unwrapping can

27 20 also be done using both spatial and temporal data (22). Robust phase-unwrapping for MR data is not trivial and in cases of severe wrapping, it may not be possible to correct phase errors Phase Contrast Velocity Encoding Phase images may contain significant phase contributions from sources other than motion including magnetic susceptibility, field inhomogeneities, eddy currents, gradient delays or other effects. In order to allow for velocity quantification with PC MRI, phase contributions which are unrelated to motion must be eliminated. Consider a single voxel containing both stationary and moving spins and assume all the moving spins move in the same direction with the same velocity. The signals from the static and moving spins are Ss and Sm respectively. In order to encode the spin velocity in a single direction, two measurements are necessary. Several velocity encoding strategies have been reported (23, 24) but the most common approach consists of a flow-compensated scan to measure the background phase and a subsequent velocity encoded scan with identical parameters to the flow-compensated scan (referenced encoding). Alternatively, the second scan image could be acquired with a bipolar gradient toggled in the opposite direction (balanced encoding). In the referenced encoding scheme, the first measurement, S1, is a referenced measurement with a first moment of zero to remove the effects of background phase. The second measurement, S2, is made with the first moment of the gradient ΔM1 in the velocity direction which causes the phase of the moving spins to shift by φm. The two measurements are:

28 These data can be used to calculate the phase difference on a voxel by voxel basis which can then be used to calculate a velocity map for the whole image Errors in Phase Contrast Several sources of inaccuracies in PC MR measurements can lead to significant errors in measured velocities if unaccounted for. Small velocity offsets can lead to much larger error in blood flow quantification because blood flow is calculated by integrating velocities within a vessel area (25, 26). The major sources of error include non-compensated eddy currents, gradient non-linearity, and concomitant gradient fields (27-29). Concomitant or Maxell gradient fields arise from Maxell's equations. It can be shown that within an imaging volume, when a linear magnetic field gradient is switched on, additional nonlinear magnetic field gradients are generated concurrently which cause artifacts in MR imaging. Concomitant gradient cross terms arise when the longitudinal gradient, Gz, is activated with a transverse gradient (Gx or Gy). Corresponding cross terms arise when the linear gradient is applied in (Gx or Gy). They result in phase errors which affect velocity measurements and increase with distance from the isocenter (30). These errors can be corrected in waveform design, which can increase the TE of the acquisition (31). Most commonly, a phase correction can be applied in the image domain during reconstruction. Concomitant field at a specified location can be calculated exactly for a given gradient waveform and therefore, phase correction factors can be derived given knowledge of the gradient waveforms (27).

29 22 Eddy currents are caused by changes in the gradient magnitude which results in changes in magnetic flux, thereby inducing eddy currents in conducting parts of the scanner hardware, which in turn affect the magnetic field inside the bore. Eddy currents distort the effective gradient waveforms. Modern MRI scanners have pre-emphasis systems to compensate for these errors by predicting the eddy current effects and compensating for them with adjusted gradient waveforms. However, eddy current effects with short time constants (< 5ms) remain mostly uncompensated and cause trajectory errors, phase errors, and more. In phase contrast MR, the different waveforms used for subsequent velocity encodes lead to different eddy current induced phase changes in the phase images of each velocity encoded acquisition. Therefore, subtraction of phase images does not eliminate eddy current errors. These phase errors can be compensated for in a number of ways. One way these errors can be estimated is by fitting the phase in stationary tissue to a polynomial and subtracting out the estimated phase (27). However, there may not be sufficient amounts of static tissue in the image for the phase estimation. Another way to compensate for offsets is to place an ROI in stationary tissue adjacent to the vessel of interest and assume any nonzero velocity in that tissue is due to background phase effects. This might be difficult, especially in the case where there is not suitable static tissue adjacent to most vessels. Alternatively, the phase-offset can be measured directly in a region of interest by repeating the scan in a stationary phantom. This technique requires additional scan time but provides reliable background phase correction (25). More recently, magnetic field monitoring has been suggested for measuring and correcting for background velocity offsets (29). Although, this technique is effective, it requires additional hardware with limited availability.

30 23 Ideal magnetic field gradients cause a linear change in the field over a large field-of-view, thereby causing the precession frequency to also vary linearly with position. However, this is only true in the central region close to the isocenter of the magnet. The gradients fall off as the distance from the isocenter increases. Errors in the strength and direction of local gradient affect the strength and direction of the gradient first moments and thus, the velocity encoding. Therefore, in phase contrast, gradient non-linearity causes errors both in the magnitude of encoded velocities and the velocity encoded direction (30, 32) as well as in spatial encoding. Errors can be corrected during reconstruction using a gradient field model by first correcting the spatial distortion and then correcting the first moment with local gradients. Correction of these errors is not often part of standard imaging reconstruction for commercial 2D PC MR Three Directional Phase Encoding In order to measure velocity components in three directions, velocity encoding gradients must be applied in each direction. The simplest method for three-directional phase encoding is a six-point method which uses three pairs of points (three reference and three velocity encoded) to measure the three velocity components. However, assuming similar imaging parameters, the imaging time is tripled compared to the two point method and six-fold over non velocity-encoded acquisitions (23). Scan time for an acquisition with three directional encoding can be reduced using a single phase referenced measurement shared among each of the phase encoded points. This method is referred to as a four-point referenced approach (23, 24). Three orthogonal directions are encoded independently with one reference flow compensated (ΔM1 = 0)

31 24 acquisition that is used to remove the unknown background phase for all encoding directions. Alternatively, shorter echo times and less intra-voxel dephasing can be achieved using a non-zero reference (23, 33). Balanced encoding schemes have a net first moment of zero over the number of encoding TR s. This 4-point balanced scheme is usually based on a Hadamard matrix and can be represented by four equidistant points in M1 space. In this type of encoding scheme, the reference direction is arbitrarily chosen and all measurements contribute to all velocity components. Because all of the phase measurements are coupled, velocity aliasing is also coupled to other directions, making unwrapping more difficult than with a 4-point referenced approach. A four-point balanced encoding scheme requires smaller gradient first moments compared to a four-point referenced encoding. Consequently, shorter TRs, shorter scan time, and improved temporal resolution can be achieved compared to reference encoding. The flow encoding matrices for both the balanced and referenced approaches are shown below. Velocity encoding schemes will be discussed further in Chapter 3. 3D Referenced D Balanced z y x v v v M z y x v v v M

32 D PHASE CONTRAST MRI The work in this thesis primarily focuses on volumetric phase contrast MR imaging with three directional velocity encoding, also referred to as 4D PC MRI or 4D flow MRI. 4D PC MRI holds the potential to be a comprehensive vascular imaging method providing high quality angiograms and quantitative velocity measurements in a single exam. While the potential for these acquisitions was conceived 20 years ago (31), only recent advances in MR hardware and sequence design have made it possible to acquire these data in clinically feasible scan times (34). Recently, it has been used for imaging the cerebral system (35, 36), great vessels (37-39), renal arteries (40, 41), the hepatic vasculature (42, 43), and peripheral vessels (44). Additional hemodynamic information can be obtained through post-processing the acquired anatomical and velocity data to provide velocity visualization and quantitative hemodynamic measures. Complex velocity fields can be visualized with flow vectors, streamlines, and particle traces. Quantitative flow measurements can be obtained by retrospectively segmenting vessels, reformatting analysis planes, and integrating measures over space and time. Additionally, hemodynamic parameters can be derived from the measured velocity fields such as pressure gradients (45, 46), pulse wave velocity (47-49), kinetic energy (50), turbulence (51, 52), wall shear stress(53, 54), vorticity (55, 56), and more.

33 26 Figure 2.6 4D flow thoracic data set acquired in a patient. In (A), axial slices in the chest from a 3D phase contrast data set with 3-directional velocity encoding: magnitude images and velocity images with x, y, and z velocity encodings are shown (B) 3D visualization of the complex difference images from the same patient with velocity stream lines in the aorta. Several hemodynamic parameters that can be derived from 4D flow data are known to play a significant role in cardiovascular disease and could be powerful tools for diagnosis, monitoring, and treatment planning in CHD. Pressure gradients (measured via catheters) are already used clinically to assess the hemodynamic significance of narrowed vessels and will be discussed further in Chapter 4 and Chapter 4. Pulse wave velocity (PWV) is the rate at which a bolus of blood pumped from the heart travels through the vasculature. This is an indirect measure of vascular stiffness which is known to increase with age and blood pressure (57). PWV changes are also associated with the development of atherosclerotic disease (58) and can possibly serve as an early indicator for plaque development. Turbulent blood flow is characterized by fast random temporal and spatial velocity fluctuations and appears to accompany many cardiovascular diseases. Changes in signal magnitude are related to the standard deviation of velocity within a voxel, which is related

34 27 to turbulence. Turbulence causes pressure drops across stenoses and may increase the risk of hemolysis (59) and blood clot formation (60). Wall shear stress (WSS) characterizes the frictional force from blood flow on a vessel wall and is thought to play a role in aneurysm formation and atherosclerotic disease (61). The derivation of these parameters from 4D flow MRI data can help quantify alterations in flow seen in CHD malformations and possibly identify new flow characteristics or risk factors in these patients as well as serve in risk assessment, understanding normal flow, surgical planning and follow-up PC VIPR Acquisition Scan times required to acquire 4D flow data sets are lengthy due to the combination of 3D spatial encoding, three-directional velocity encoding and cine acquisition. In order for 4D PC MRI to become a clinically viable tool, acceleration methods must be utilized in order to reduce scan times. This need has been addressed with different methods: parallel imaging (62, 63), constrained reconstructions such as k-t BLAST (64), and non-cartesian trajectories (65, 66). These methods, along with recent hardware advances, have made 4D flow MR scan time reductions possible and enabled its use in human imaging. Phase Contrast Vastly undersampled Isotropic PRojection imaging (PC VIPR) is a 4D PC MRI technique that utilizes 3D projection imaging with three directional velocity encoding (66, 67) for the acquisition of high resolution angiograms and velocity images in reduced scan times. In this work, we take advantage of the inherent acceleration potential of radial imaging through undersampling, as well as the opportunities it provides for cardiac and respiratory gating.

35 28 Radial Imaging: PC VIPR utilizes radial undersampling in order to accelerate the acquisition. In a 2D Cartesian acquisition, a frequency-encoding gradient is applied in one direction which causes the frequencies of spins to vary linearly. Phase-encoding gradients create a linear phase variation in a direction perpendicular to the frequency-encoding gradient. The size of the phase-encoding gradient is varied in order to vary the phase accumulation and for each value of the phase-encoding gradient, a new line in k-space is sampled. In theory, spatial encoding in a 2D Cartesian acquisition could be done by phaseencoding both directions; however phase-encoding is much less efficient than frequency encoding because an entire line in k-space needs to be acquired for each value of the phaseencoding gradient whereas with frequency-encoding, all the spatial frequency information can be acquired from one line in k-space. For a 3D Cartesian acquisition, a second phaseencoding is added on the slice selection axis, further increasing scan time. While k-space is most often sampled in a rectilinear fashion with the spinwarp acquisition (68), data can be collected with a non-cartesian trajectory. A Cartesian acquisition can be accelerated by increasing the rate of data acquisition by using faster gradients to reduce the time for spatial encoding during the frequency encoding and readout gradient pulses. However, gradient performance is limited by slew rates and peripheral nerve stimulation. K-space can be traversed in any number of ways and non- Cartesian trajectories including spirals (69, 70), radial (71, 72), propeller (73) and others have been proposed as alternatives to standard Cartesian acquisitions. These sequences have challenges associated with them including sensitivity to trajectory errors (74), gradient imperfections, and off-resonance frequencies which cause pixel blurring (75). There are also a number of advantages to non-cartesian acquisitions including diffuse

36 29 undersampling artifacts (76), high sampling efficiency, and low sensitivity to motion due to frequent sampling of the center of k-space. Figure 2.7 (A) A 2D radial trajectory and a (B) 3D radial trajectory. The sampling density is high at the center of k-space and a fully sampled radius exists at the center of k-space which grows as the number of projections increases. In this work, a 3D radial trajectory was utilized for data acquisition (Figure 2.7). To acquire radial lines in k-space, two (2D acquisitions) or three (3D acquisitions) gradients are played out simultaneously during the data acquisition and the readout direction is no longer constant but changes with each projection angle. This trajectory has a number of advantages: robust against sub-sampling, robust against motion, frequent k-space update provides a high temporal resolution, a minimum TE can be achieved with partial or half echoes, and auto-navigation is possible. In Cartesian imaging, undersampling leads to wrapping of the image in the phase-encoding direction because the supported Nyquist FOV is the same everywhere. However, in radial imaging, a fully sampled radius exists at the center of k-space which grows as the number of projections increases. Therefore, if projections are removed, aliasing only occurs at high frequencies (76, 77). This produces diffuse streak artifacts outside the aliasing free region which are often more tolerable than

37 30 Cartesian artifacts. Examples of Cartesian and radial undersampling are shown in Figure 2.8. Figure 2.8 (A) Cartesian undersampling. When k-space is undersampled by acquiring fewer phase encoding lines, ghosting or phase wrapping occurs. As undersampling increases, ghosting is worse. (B) Radial undersampling. When undersampling is increased, more

38 31 diffuse streak artifacts are present in the image (images courtesy of Frank Korosec, UW- Madison) Cardiac gating: Accurate depiction of cardiac motion is essential for quantifying flow and vessel anatomy with PC VIPR. In a PC VIPR acquisition, retrospective cardiac gating is accomplished by storing the location of each detected R-wave detected with ECG or a pulse oximeter during the acquisition, and during reconstruction, projections are sorted according their position within the cardiac cycle (78) as demonstrated in Figure 2.9. Since the cardiac gating is retrospective, this scheme is compatible with both ECG gating and pulse oximeter signals. Pulse oximeter gating is not always compatible with prospective gating because the systolic peak in locations close to the heart might be missed with a delayed trigger position from the plethysmograph at the finger whereas with retrospective gating, the entire cardiac cycle is imaged. Figure 2.9 The grouping of views in the retrospective cardiac gating scheme with respect to cardiac phases during the (a) acquisition and (b) reconstruction. Data are acquired throughout the cardiac cycle (a). During reconstruction, projections are sorted according to their position in the cardiac cycle (b). Respiratory gating: Long exams such as PC VIPR cannot be completed in a breath hold. Instead, they are acquired during free breathing over a number of minutes and therefore,

39 32 respiratory motion must be considered. Although radial trajectories are more robust towards motion artifacts than Cartesian sequences, acquisitions in the abdomen and chest require compensation for respiratory motion. This can be accomplished with respiratory gating which utilizes respiratory information from navigator echoes (79) or respiratory bellows. Generally, these techniques work by setting a threshold above which data is rejected due to respiratory motion. To maximize the efficiency of respiratory motion compensation in a PC VIPR acquisition, an adaptive thresholding technique is used. The respiratory bellows position is acquired from a tension sensor attached to an elastic band wrapped around the abdomen (bellow). During expiration, the diaphragm relaxes the ribcage and the rubber band stretches. The position reading is recorded every new projection angle and buffered for the last ten seconds and analyzed continuously to adjust for common baseline drifts in the signal. Those position readings are reformatted into a histogram and data are only acquired if the current position is below the position corresponding to the present percentage threshold in the histogram. This scheme adjusts to the patient s breathing pattern throughout the exam. It was recently shown that pressure changes in the chest during breathing can also affect the flow waveforms (80). However, this mostly affects veins and was not considered in the work presented here.

40 33 Figure 2.10 PC VIPR respiratory gating scheme with a 50% acceptance window (diagram courtesy Kevin Johnson). The last ten seconds of respiratory positions recorded from bellows are stored in a histogram. Data are acquired when the current respiratory position is below the threshold in the histogram. This threshold is updated every projection to account for change in a patient s breathing pattern. A threshold of 50% is commonly used for PC VIPR acquisitions and this threshold was determined empirically D Phase Contrast MRI Validation and Reproducibility Before quantitative 4D PC MRI sequences can be used in clinical practice, assessment of the accuracy and reproducibility of these techniques is essential. This task is non-trivial because no reliable gold standard for in vivo flow measurements exists. Validation can be performed with flow phantoms, however it can be difficult with these phantoms to mimic in vivo conditions and for direct comparison with 4D Flow MRI, the velocity field within the phantom would need to be known. Flow rates in phantoms can be validated with in-line flow probes; although these probes do not map velocity fields (see Chapter 4). In vitro velocity fields can be measured using ultrasound or particle image velocimetry (PVI). However, both of these techniques have challenges and errors associated with them. Phantom measurements with ultrasound require a phantom with walls and fluid that are compatible with an ultrasound probe. Additionally, ultrasound is not a perfect gold standard. PIV is an optical method of visualizing fluid flow in which small particles are

41 34 mixed with fluid and the motion of the particles is tracked using an illumination source (two laser lights) and an imaging device (a high speed camera). PIV requires a challenging experimental setup: the refraction index of the phantom wall and phantom fluid must match, particle tracers must be added to the fluid for measurements and the velocity component along the z-axis (toward/away from the camera) cannot be measured. However, stereoscopic PIV uses two cameras to measure velocity in three directions. Computation fluid dynamics (CFD) can also be used to validate 4D flow MRI. However, CFD suffers from limitations including incomplete model assumptions such Newtonian fluid, noslip surface, and incorrect boundary conditions. In vivo validation of 4D PC MRI is also challenging and there is no true gold standard to compare with 4D PC MRI velocity fields. Several 2D and 4D phase contrast validation studies have been conducted, specifically focusing on thoracic flow measurements. Recently, Gatehouse et al. (26) tested the accuracy of 2D PC MRI in a multi-center, multivendor trial by measuring velocity offsets in static gel phantoms up to 70 mm from the isocenter of the magnet. The measured velocity offsets ranged from 0.4 cm/s to 4.9 cm/s with an average of 2.7 cm/s. They noted that, a velocity offset error of 0.6 cm/s (with a maximum velocity of 150 cm/s) could potentially cause an error 5% in calculated cardiac output and a 10% error in shunt fraction when the error is integrated over space and time in the ROI analysis. This study highlights the need for background phase corrections in order to achieve reliable flow measurements. Studies have also compared PC MRI measurements at 1.5 T and 3 T, showing both systems provide the same accuracy precision with reduced noise in the 3 T data. SNR and VNR are both higher at 3T which is advantageous for measuring flow in small vessels or regions of flow where accuracy is limited by spatial resolution and/or noise (81).

42 35 4D PC MRI flow measurements have been compared with computational fluid dynamics (CFD), programmable flow pumps, Doppler ultrasound, and 2D phase contrast MRI in phantom and in vivo studies. Canstein et al. compared in vivo 4D PC MRI flow measurements in the thoracic aorta to CFD and 4D PC MRI in a rapid prototyped model of the aorta (82). Good qualitative agreement was found between pulsatile flow waveforms from in vivo, in vitro, and CFD data. However, lower flows and velocities were measured with CFD and in the in vitro model than in vivo. The authors attributed these differences to different in-flow boundary conditions, lack of vessel wall compliance, and an insufficient flow pump in rapid prototype model compared with in vivo experiments. It was found that CFD calculations agreed well with measurements in the rapid prototype model with 4D PC MRI. The authors did not find any clear advantage to using rapid prototyping in comparison to CFD. Nordmeyer et al. compared 4D PC flow measurements in the thoracic vessels with and without respiratory gating to 2D PC and found good agreement between all techniques (83). In a study by Stalder et al., low resolution 4D PC MRI segmented with a cubic differential B-spline function were compared with 2D PC (53). The reliability and reproducibility of the techniques were evaluated and it was found that 4D PC slightly underestimates peak flow and slightly overestimates the time to peak flow. The interobserver variability was higher for 4D PC compared to 2D PC (17% vs. 8%) as was error introduced by lumen segmentation between two observers. In 2010, Bock et al. tested the influence of standard and blood-pool contrast agents on SNR, PC-MRA quality, and 3D stream line visualization in the aorta. It was found that contrast agent generally improved image visualization and background suppression. However, the SNR in data with

43 36 contrast agents did show significantly higher variation than those without, probably due to different contrast agent concentrations. Acceleration techniques for 4D PC MRI have also been tested. Two studies compared acceleration with parallel imaging and k-t BLAST. Stadlbauer et al. compared measurements from MR with those from Doppler Ultrasound and found both 4D PC techniques tended to underestimate velocity compared with US. They also found k-t BLAST with high acceleration factors tended to more significantly underestimate peak velocity (84). In another study, Carlsson et al. compared parallel imaging and k-t BLAST at 1.5 T and 3 T with 2D-flow as a reference. It was found that 4D PC with SENSE was accurate at 1.5 T and 3 T but k-t BLAST yielded too high a bias for quantitative in vivo use in the heart (85). The accuracy and repeatability of PC VIPR flow measurements have also been investigated. PC VIPR flow measurements have been compared to a programmable flow pump as well as 2D phase contrast measurements. Preliminary validation studies were performed by Gu et al (67). They compared PC VIPR to average pump flow rates between 0.75 and 5 ml/s and found excellent correlation (R 2 =0.99) with a slope of 0.94 indicating that PC VIPR slightly underestimates flow. In vivo, PC VIPR flow measurements in the right internal carotid artery and basilar artery of six volunteers were compared with 2D PC and the correlation of the two methods was R 2 =0.97. Wentland et al. compared the repeatability and internal consistency of PC VIPR and 2D PC flow measurements in the renal vasculature in healthy volunteers (86) without prior contrast agent injection. It was found that 4D measurements tended to be more internally consistent than 2D measurements on average (12.4% vs. 18.0% error). Validation of PC VIPR has also been

44 37 performed in the thoracic system. In ten healthy volunteers, flow and velocity were measured in five vessels with PC VIPR and 2D PC, all without contrast agent: ascending aorta (AAO), descending aorta (DAO), main pulmonary artery (MPA), superior vena cava (SVC) and inferior vena cava (IVC). Compared with 2D PC, PC VIPR underestimated flow (- 5.27±13.75 ml) and peak velocity (-3.50±16.79 cm/s) on average across all vessels (87). This work is discussed in more detail in Chapter 3. Boncyk et al. (88) compared blood flows in the ascending aorta (AAO) and main pulmonary artery (MPA) measured with PC VIPR to 2D PC and 2D cine bssfp left ventricular and right ventricular stroke volumes in 12 patients with congenital heart disease. All scans in this study were done with a prior contrast injection. The results in this study were similar to the results obtained in healthy volunteers. As in other studies, it was found that PC VIPR underestimated flow compared with 2D PC ( ml ± ml in the AAO, -1.97±13.12 ml in the MPA). Similar results were obtained when comparing PC VIPR to 2D cine bssfp Tools for interactive analysis and exploration of hemodynamics from 4D PC MRI Recent developments have allowed for volumetric, cine PC MRI data with 3- directional velocity encoding to be acquired in reasonable scan times. While these data contain vast amounts of anatomical and functional information, tools for efficient display and analysis are necessary for these techniques to become clinically useful. Currently, there is no commercial software available that can be used to process 4D PC MRI data for clinical analysis.

45 38 Figure 2.11 Flow chart of processing tools currently used to analyze PC VIPR data sets At the University of Wisconsin, our own post-processing solution combines several commercial packages and customized code development in C and Matlab to address several needs for advanced visualization and hemodynamic analysis. Figure 2.11 gives an overview of the steps currently used to process PC VIPR data. Initially, data is reconstructed offline from the acquired raw MR data and the corresponding gating files and then preprocessed for analysis. Because 4D PC images have such large anatomic coverage, a large range of velocities are present in the imaging volume and there is a risk of velocity aliasing in areas of higher velocities. In some cases, pre-processing strategies can be applied to correct phase errors in order to ensure accurate flow measurements (30, 89, 90). Although velocity aliasing can be easily corrected by adding or subtracting multiples of π, automatically determining which voxels are wrapped is a very challenging task in the presence of noise and without reference phase maps (20-22). A tool was designed in MevisLab (MeVis Medical Solutions,

46 39 Breman, German) for retrospective phase unwrapping by calculating the probability that an individual voxel is wrapped based on the immediate neighbors (91). This correction algorithm will work for mild or moderate wrapping but will fail in cases of extreme wrapping. The tool also allows for manual corrections in cases algorithms have failed. Ongoing efforts are aimed to further improve the automated correction for phase unwrapping (92). Complex difference angiograms are loaded into Mimics (Materialise, Leuven, Belgium) for vessel segmentation. Complex difference (CD) images are generated from magnitude and velocity data using the following equation: sin 2.1 where M is the magnitude signal, V is the velocity, and VA is set velocity threshold. Accurate vessel segmentation is essential for flow analysis as well as wall shear stress and pressure calculations. Once segmentation is performed and phase errors are corrected (if necessary), the data is loaded into a home built Matlab (The Mathworks, Natick, MA) tool for cropping, post-processing, quantitative measurements, and derivation of additional hemodynamic parameters. The workflow for this tool is shown in Figure First, the data is loaded into the segmentation tool and the mask generated in Mimics is used to crop the data set for more efficient processing. Next, the data can be loaded into the analysis plug-ins to (a) measure and visualize flow (93, 94), (b) derive pressure maps (40, 46, 95), or (c) calculate wall shear stress(95).

47 40 Figure 2.12 Matlab processing toolbox can be used to segment data, measure flow, and calculate pressure or WSS As part of this thesis work, an analysis plug-in to measure flow was developed (93, 94). In this tool, the analysis plane can be interactively placed and is then automatically aligned perpendicular to the vessel path. Flow measurements are derived by integration of the velocity vectors over time and vessel area, which can be defined either automatically with a threshold algorithm or manual selection. Velocity and flow measurements can be exported for further analysis and visualization or comparisons. To validate velocity and flow measurements, multiple PC VIPR data sets including flow phantom data and in vivo cardiac data were compared with standard 2D PC MR measurements prescribed perpendicular to the vessel orientation.

48 41 Figure 2.13 Flow analysis for a patient with congenital heart disease. The arrow points to the ROI box that can be automatically centered and aligned with the segmented vessels shown as a volume rendered display (a). 2D cine representations of the vessel under investigation are calculated and analyzed for through place velocities of flow rates based on ROIs (b) To facilitate the comparison of PC VIPR and 2D PC data, a Matlab plug-in was developed that reformats the PC VIPR data at an identical slice position as the 2D PC data were acquired. To accomplish this, the PC VIPR data is loaded into a GUI that uses the DICOM coordinates from the corresponding 2D PC data set acquired in the same patient to extract a slice in the same location from the PC VIPR data. Another Matlab GUI is then used for the flow analysis in the 2D PC and the reformatted PC VIPR slices. The ROIs and flow data from this GUI can be exported for further analysis. While the Matlab tools allow for simple visualizations of PC VIPR data, these data can also be exported for advanced visualization. We have adopted import/export routines to use in Ensight (CEI, Apex, NC), a commercial software package for complex data visualization. Ensight can be used to visualize blood flow in 4D PC MR data sets with streamlines, pathlines, particle traces, and such (Figure 2.14). Ensight can also be used to

49 42 place analysis planes and make flow and velocity measurements. Alternatively, analysis planes can be interactively placed in Ensight and then exported to a Matlab GUI (53) for 2D flow, velocity, and WSS analysis. This Matlab tool allows the user to manually segment the vessel and exports comprehensive hemodynamic information. Figure 2.14 Ensight visualizations (a-d) Pulmonary venoblar syndrome (PVR): (a) posterior view, (b) atrial defect: 1.34 L/min, (c) anomalous pulmonary venous return Scimitar Vein : 0.42 L/min, (d) abnormal systemic artery: flow to the right lung., (e-f) Double inlet left ventricle status post bidirectional Glenn particle traces and flow waveforms

50 43 Chapter 3 FOUR-DIMENSIONAL PHASE CONTRAST MRI WITH ACCELERATED DUAL VELOCITY ENCODING This work was published in the Journal of Magnetic Resonance in May of 2012: Nett EJ, Johnson KM, Frydrychowicz A, Del Rio AM, Schrauben E, Francois CJ, Wieben O. Fourdimensional phase contrast MRI with accelerated dual velocity encoding. J Magn. Reson. Imaging 35: (2012). Portions of this work were presented in the Proceedings of the 18 th Annual Meeting of the International Society for Magnetic Resonance in Medicine in Stockholm, Sweden 2010, the Proceedings of the 19 th Annual Meeting of the International Society for Magnetic Resonance in Medicine in Montreal, Canada 2011 and the Proceedings of the 23 rd Annual Meeting of the International Magnetic Resonance Angiography Working Group in Banff, Canada 2011 (Oral Presentation). 3.1 ABSTRACT This chapter focuses on the validation of a novel approach for accelerated fourdimensional phase contrast MR imaging (4D PC MRI) with an extended range of velocity sensitivity. This work addresses the need to provide a high velocity-to-noise ratio across arteries and veins of varying diameters in large imaging volumes. 4D PC MRI data were acquired with a radially undersampled trajectory (PC VIPR). A dual Venc (dvenc) processing algorithm was implemented to investigate the potential for scan time savings while

51 44 providing an improved velocity-to-noise-ratio. Flow and velocity measurements were compared to a calibrated flow pump flow pump in a phantom study and conventional 2D PC MR and single Venc 4D PC MRI in the chest of ten volunteers. Phantom measurements showed excellent agreement between accelerated dvenc 4D PC MRI and the pump flow rate (R 2.97 with a threefold increase in measured velocity-to-noise-ratio (VNR) and a 5% increase in scan time. In volunteers, reasonable agreement was found when combining 100% of data acquired with Venc=80 cm/s and 25% of the high Venc data, providing the VNR of a 80 cm/s acquisition with a wider velocity range of 160 cm/s at the expense of a 25% longer scan. This acquisition scheme is well suited for vascular territories with wide ranges of flow velocities such as present in congenital heart disease, the hepatic vasculature, and others. 3.2 INTRODUCTION Phase contrast MRI (PC MRI) can obtain quantitative blood flow, peak velocity and other hemodynamic indicators of cardiovascular dysfunction. These measurements can be used to grade the severity of stenoses, quantify valvular regurgitation, or calculate shunt fractions (96, 97). Traditionally, clinical use of PC MR has been limited to 2D cine imaging with one-directional (through plane) velocity encoding due to long imaging times for cardiac gated, volumetric (3D) PC acquisitions with three-directional velocity encoding. However, recent advances in hardware and imaging techniques have made such acquisitions, feasible in clinically relevant scan times of approximately minutes for cardiac scans (38, ). 4D PC MRI allows for comprehensive assessment of

52 45 cardiovascular function, providing volumetric anatomical and quantitative hemodynamic information throughout the cardiac cycle (38, 45, 66, 98, ). One challenge of phase contrast MR in general and 4D PC MRI in particular is the choice of the optimal velocity encoding setting (Venc). The Venc determines the dynamic range of the velocity map obtained from the acquisition. If the Venc is set too low, phase aliasing, also known as phase wrapping, occurs in regions of velocities exceeding the Venc, thereby rendering quantitative measurements difficult or impossible. If the Venc is set too high, the velocity-to-noise ratio (VNR), itself inversely proportional to the Venc setting, suffers. The increased noise will lead to erroneous velocity readings, particularly in regions of slow flow. Therefore, the Venc must be chosen close to but higher than the highest expected velocity of interest in the chosen imaging plane or volume. Optimal Venc settings are not generally predictable and can require multiple scans. They are particularly difficult to determine for acquisitions with volumetric coverage where a large range of velocities is expected. A single optimal Venc setting might not exist, especially in difficult situations imaging complex flow patterns or vascular territories, such as in arteriovenous malformations, surgical alteration after congenital heart disease, or the hepatic vasculature with its dual arterial and portal venous blood supply. Dynamic range issues could be addressed with the acquisition of two or more separate scans with different Venc settings. Multiple Venc encoding schemes extend the velocity encoding range of the scan and preserve high VNR for slow flow regions, but also significantly increase the scan time. For one directional flow encoding, two different Vencs can be acquired using 3 flow encodings (reference and two velocity encoded), which requires a 50% increase in scan time. For three-directional flow encoding, uni-directional

53 46 velocity encoding requires at least 4 acquisitions (a reference and 3 velocity encoded acquisitions) and each additional Venc requires at least 3 additional flow encodings and 4 flow encodings if a balanced velocity scheme is used. Further prolonging the scan time, the bipolar gradients of the velocity encoded scans extend the echo time (TE) and repetition time (TR) especially in cases of low velocity encoding setting, in which the required gradient area increases and the TR can almost double. The additional time required for multiple scans with different Vencs would often lead to prohibitively long imaging times for 4D PC MRI. Rather than acquiring multiple Vencs, phase errors in a scan with a too low Venc setting could be corrected with automatic phase unwrapping (22, 104) but these algorithms often fail in large aliased regions, areas of multiple wrapping, and in the presence of noise. In addition, velocities measured with lower Vencs are more susceptible to errors from intra-voxel dephasing (105) and longer TE. Due to scan time penalties and diminishing gains alternative velocity encoding schemes have been investigated ( ). One such encoding scheme, a 5-point balanced technique, was shown to improve VNR by 60% for a 25% increase in scan time. However, the ratio between the higher and lower velocity encoding are not flexible with this scheme and can therefore not be adjusted to specific imaging demands. In this study, a dual Venc (dvenc) reconstruction approach on the basis of Phase Contrast Vastly undersampled Isotropic Projection Reconstruction (PC VIPR) data was explored. PC VIPR is a 3D radially undersampled phase contrast sequence with threedirectional velocity encoding (66). Without modification, this dual Venc acquisition would double the scan time due to additional high Venc encoding steps and a Hadamard encoding

54 47 scheme. In order to minimize the scan time penalty from added encoding steps, the effect of additional radial undersampling applied to the high Venc acquisition has been explored, possibly introducing undersampling artifacts yet maintaining the spatial resolution (111). The aim of this study was twofold: i) To evaluate the accuracy of an accelerated dvenc PC VIPR acquisition and reconstruction in phantom experiments and ii) to study in vivo utility of dvenc PC VIPR in 10 healthy volunteers by evaluating the tradeoffs between savings in scan times, VNR, and velocity measurements. Specifically, we compared dvenc PC VIPR data with various acceleration factors to a standard single Venc PC VIPR acquisition and 2D phase contrast acquisitions as the intrinsic and clinical reference. The comparison included the VNR of the resulting image, the measured blood flow parameters peak velocity [cm/s] and flow volume [ml] in 5 locations of the thoracic vasculature, and the clinically relevant ratio of pulmonic (Qp) to systemic (Qs) blood flow. 3.3 MATERIALS AND METHODS Dual Venc Theory Dual Venc reconstruction algorithms combine data from high and low Venc acquisitions to reduce the tradeoffs between VNR and dynamic range. The high Venc is chosen high enough to avoid phase wrapping errors. Estimated velocities, vest, are obtained from the high Venc data set and can be used to identify phase aliasing in the low Venc image and calculate the number of phase wraps: n NI Av est 2 4.1

55 48 where NI is the nearest integer function and A is the matrix containing the first moment (Δm1) values for each encoding in rows. The unaliased phase in the low Venc data is calculated using n: 2 unaliased n 4.2 This unaliased phase can then be used to calculate the velocity. The relationship between phase and velocity is: 1 v A 4.3 where v is the vector of velocities. Since the nearest integer function is insensitive to small deviations, the noise in the final image is dominated by the low Venc, and without intravoxel dephasing errors, the VNR improvement is proportional to the high-to-low Venc ratio (112). In this study, in order to minimize the scan time penalty from added encoding steps, additional radial undersampling was applied to high Venc data before the dual Venc reconstruction. Although undersampling introduces errors in the high Venc acquisition, these errors in the estimated velocities need to be greater than the low Venc in order to cause errors in the final estimation MR Imaging Phantom and volunteer imaging was performed on a clinical 3T system (Discovery MR 750, GE Healthcare, Waukesha, WI) with a maximum gradient strength of 50 mt/m and a maximum slew rate of 200 mt/m/ms. Sequence details are summarized in Table 3.1. While a venously injected Gd-based contrast agent is frequently used to improve the SNR and VNR in 4D PC MRI, none was used here to characterize the performance of a true non-

56 49 contrast-enhanced (NCE) MRA acquisition. For each exam, three separate single Venc PC VIPR scans were acquired for both phantom and volunteer experiments: a high Venc and two low Vencs all with four-point balanced (Hadamard) flow encoding and the same number of acquired projection angles. To simulate accelerated dual Venc, high Venc images were retrospectively reconstructed with varying degrees of additional radial undersampling. Dual Venc images were generated by unwrapping each low Venc image with the high Venc images. A schematic diagram of the in vivo accelerated dual Venc reconstruction is shown in Figure 3.1. Different high and low Vencs settings were chosen for in vitro and in vivo scans to best match the velocities in those studies. Table 3.1 Protocol parameters for velocity encoded MR acquisitions in a flow phantom and volunteer study for a volumetric, radially undersampled acquisition (PC VIPR) and the conventional 2D PC acquisition. For in vivo PC VIPR acquisitions, respiratory gating was used which resulted in scan time increases of about a factor of two over a non-gated acquisition. In Vitro PC In Vivo PC In Vivo 2D PC VIPR VIPR Repetition time (ms) Echo time (ms) Flip angle (degrees) Bandwidth (khz) Field of view (cm) 24x24 32x32 35x35 Slice thickness (mm) Matrix size 256x256x x256x x160 No. of projections 10,000 15,000 NA Acquisition length 5-6 min min 22 heart beats Velocity encodings (cm/s) 40,80,160 40,80, Undersampling Factor 10 7 NA

57 50 Figure 3.1 Schematic of acquisition and dual Venc reconstruction. The parameters shown are those that were used in volunteers. Three, minute PC VIPR data sets are acquired with three Vencs: one high Venc (160 cm/s) and two low Vencs (80, 40 cm/s). Dual Venc images are reconstructed with a low Venc data set and difference percentages of the high Venc dataset. The undersampled high Venc reconstruction mimics acquiring less high Venc data. In Vitro Study Study Design Accelerated dual Venc PC VIPR was validated using a MR compatible flow pump (CompuFlow 1000 MR, Shelley Medical Imaging Technologies, London, ON, CA) placed in the center of a quadrature head coil. The flow phantom consisted of one tube with an inner diameter of 7.9 mm and was looped in the bore such that two tube segments with opposing flows were within the coil. Each of these tube segments was permanently surrounded by a closed plastic pipe-like structure filled with doped water to minimize susceptibility artifacts and increase the coil loading. The tube was filled with blood-mimicking fluid (Shelley Medical Imaging Technologies, London, ON, CA) and connected to the flow pump. Flow was only measured in one of the tubes. Flow rates were chosen to match the

58 51 observed in vivo range of venous and arterial blood flow velocities: flow rates of 8 ml/s, 12 ml/s, 18 ml/s, and 24 ml/s (mean velocities of ~16 cm/s, 24 cm/s, 36 cm/s, and 48 cm/s, maximum velocities of ~30, 60, 68, and 120 cm/s) in the tube. Three PC VIPR data sets were acquired with Vencs of 30 cm/s, 60 cm/s, and 120 cm/s. At a pump flow rate of 12 ml/s, each acquisition was repeated for a subsequent velocity-to-noise (VNR) analysis. This analysis was performed at a single flow rate because the VNR ratios we compared can be expected to be on the same order at all the tested flow rates. Reconstruction Phantom data were acquired during constant flow and thus, three time-averaged, PC VIPR balanced-encoded data sets were reconstructed. Then, a dual Venc reconstruction was accomplished by combing low Venc (30 cm/s, 60 cm/s) and high Venc (120 cm/s) acquisitions with the goal of generating aliasing free dual Venc data. The phantom data were acquired with an undersampling factor of 10 with respect to radial Nyquist sampling and high Venc data (120 cm/s) were reconstructed with 100%, 50%, 25%, 12%, 5%, and 2% of the acquired projections to mimic acquisitions of reduced scan times from a single data set. Each of the radially undersampled high Venc data were used to correct each of the low Venc (30 cm/s, 60 cm/s) images, hence, for each flow rate, there were a total of 12 dual Venc PC VIPR images (six undersampling rates times two high and low Venc combinations). Flow and velocity measurements were made by placing identical ROIs over all data using Matlab (Mathworks, Natick, MA) to guarantee comparable measurements. For the repeated experiments at 12 ml/s, VNR was calculated over an ROI as the ratio of the average velocity to the standard deviation in the subtracted image:

59 52 2 VNR 2std v 1 v2 v v where and are the velocities in identical ROIs. VNR efficiency was calculated for each reconstructed dual Venc image as the ratio of the VNR to the scan time relative to a standard four-point balanced-encoded PC VIPR image. Statistical Analysis The accuracy, VNR efficiency, and phase unwrapping of the dual Venc PC reconstruction were tested. Linear regression analysis was used to assess the accuracy of dual Venc PC VIPR by comparing measured and set pump flow rates. Marginal hypothesis tests of the null that the intercept and slope equaled 0 and 1 respectively were obtained. P < 0.05 (twosided) was the criterion for statistical significance. In Vivo Study Study Design Ten by case history healthy volunteers (27 ± 3 years old, range 22-31; 75 ± 10 kg body weight, range 54-82; 8 men, 2 women) were scanned after approval of the local institutional review board (IRB) and obtaining written informed consent. Volunteer data were acquired with a 32 channel phased-array torso coil (NeoCoil, Pewaukee, WI). Bellow readings were performed for an acquisition gated to the breathing motion. The acceptance window was set to 50% (expiratory plateau).

60 53 Three separate balanced, time-resolved velocity-encoded PC VIPR data sets were acquired with the Vencs: 160cm/s, 80cm/s, and 40cm/s. Each in vivo data set was acquired with an undersampling factor of approximately 7 with respect to radial Nyquist sampling. Each data set was reconstructed with approximately 20 time frames resulting in an undersampling factor of approximately 140 each time frame with respect to Nyquist. Figure 3.2 shows the locations of prospectively gated, breath-hold, 2D PC acquisitions performed as intrinsic flow references: perpendicular to the ascending and descending aorta (AAO, DAO, respectively) at the level of the pulmonary artery (Venc = 160cm/s), main pulmonary artery (MPA) (Venc =120cm/s), and superior and inferior vena cava (SVC, IVC) (Venc =80cm/s). Following the recommendations of Chernobelsky et al., all 2D PC acquisitions were repeated in a static phantom to correct for residual phase errors (25). Figure 3.2 Slice locations analyzed in the comparison study. Volume rendering of the phase contrast angiogram derived from a PC VIPR exam shows large coverage and isotropic spatial resolution but was not part of the analysis. Arterial (red) and venous (blue) system have been segmented to facilitate orientation. Velocity and flow measurements were made in the ascending and descending aorta (AAO and DAO), main pulmonary artery (MPA), and superior and inferior vena cava (SVC and IVC). The left and right atrium (LA, RA) and ventricles (LV, RV) are labeled for reference.

61 54 Reconstruction Retrospectively gated, time-resolved PC VIPR data were reconstructed using a temporal filter (113, 114) as described for time-resolved contrast enhanced MRA with a 3D radial acquisition in (115). At the center of k-space, PC VIPR data were reconstructed with a time resolution similar to 2D PC (~40ms). At the edge of k-space, view sharing of the higher spatial frequencies represents a temporal resolution of 20 TRs (~120ms). In vivo high Venc (160 cm/s) data were reconstructed with 100%, 50%, and 25% of the acquired projections resulting in undersampling factors for individual time frames of approximately 140, 280, and 560 with respect to Nyquist. Velocity and Flow Measurements PC VIPR images were reformatted into 2D slices in the exact locations of the 2D PC acquisitions with a home-built Matlab tool. Vessels boundaries were manually segmented on individual time frames using complex difference angiogram images to enable flow and velocity measurements. Statistical Analysis The RR intervals were recorded as part of the retrospective gating scheme and subsequently analyzed for average and standard deviation for each Venc acquisition (outliers from missed beats were excluded). This analysis was conducted to provide information on the variation of the RR interval throughout the long cardiac gated scan. Bland-Altman analysis was used to compare the flow volume, peak velocity, and the ratio of pulmonary to systemic blood flow (Qp/Qs) measured by all techniques. The Bland-Altman

62 55 window was set to ± 2SD of the observed differences of the compared values. 2D PC was used as an internal reference and pair-wise comparisons were generated to compare individual PC VIPR data with 2D PC results. A single observer was used in this study. 3.4 RESULTS In Vitro Study Phantom experiments demonstrated the accuracy and VNR gains achievable with dual Venc PC VIPR. Results from linear regression and VNR analysis are summarized in Figure 3.3, Figure 3.4, and Table 3.2. Phase wraps in low Venc image are corrected with only 12% of the acquired high Venc data. When only 5% and 2% of the high Venc data are used in the reconstruction, more phase errors are introduced, particularly at the edge of the vessels. Statistical Results Linear regression analysis showed excellent accuracy for flow rates measured with dual Venc PC VIPR. The flow rates measured with all PC VIPR techniques correlated extremely well with the programmed pump flow rate (R 2.97; P. 6 for both slope and intercept. Table 3.2 and Figure 3.3 summarize these results comparing flow rates measured with PC VIPR to the programmed pump flow rate. Overall, PC VIPR methods somewhat underestimated the flow rate but in most cases, flow rates measured agreed well with the programmed flow rates.

63 56 Table 3.2 Results from linear regression analysis comparing programmed pump flow with PC VIPR measurements. The P-values and standard errors associated with the intercept and slope are also reported, in all cases indicating that the null hypothesis (intercept = 0, slope = 1) cannot be disproven (p > 0.05). All flow measurements correlated extremely well with the pump flow rate. Intercept P-value Standard Error Slope P-value Standard Error PCVIPR V80_100p V80_50p V80_25p V80_12p V80_5p V40_100p V40_50p V40_25p V40_12p V40_5p R^2 Figure 3.3 Flow rates measured with high V enc PC VIPR and dual V enc PC VIPR in a flow phantom programmed to deliver constant flow. Scatter was added around the set pump flow rates to allow for a better appreciation of the data. The dashed line marks the identity line. Overall, PC VIPR methods somewhat underestimated the flow rate but in most cases, flow rates measured agreed well with the programmed flow rates.

64 57 In Figure 3.4, the gains in VNR efficiency achieved with dual Venc PC VIPR are displayed. With a dual Venc reconstruction, it is possible to achieve a higher VNR efficiency than with single Venc PC VIPR. VNR efficiency increases with higher undersampling until velocity errors from the high Venc acquisition cause errors in the phase unwrapping. VNR efficiencies are lower for a high-to-low Venc ratio of 2 to 1 than 4 to 1. With a high-to-low Venc ratio of 4 to 1, it is possible to obtain a 3-fold gain in VNR with a 5% increase in scan time. With a high-to-low Venc ratio of 2 to 1, a 2 fold increase in VNR can be obtained at the cost of only 2% increase in scan time. Figure 3.4 Relative gains in VNR efficiency of dual V enc in comparison to a single/high V enc PC VIPR phantom scan. A marked increase in VNR efficiency can be achieved by decreasing undersampling expressed by relative scan times. With a 5% increase in scan time, the VNR efficiency can be increased from 26.7% to 77% (factor of 2.88) using a 4:1 ratio of high-tolow V enc scan during the reconstruction. When only 2% of the high V enc data is used to correct the low V enc scan, the VNR plummets due to phase unwrapping errors.

65 58 In Vivo Study Results of the volunteer study demonstrated the feasibility of dual Venc PC VIPR reconstruction on in vivo acquired data. Results from statistical analysis comparing dual Venc PC VIPR, balanced-encoded PC VIPR and 2D PC are summarized in Figure 3.5 and Figure 3.6. Example balanced-encoded and reconstruction dual Venc PC VIPR images are shown in Figure 3.7. Statistical Results Figure 3.5 summarizes the results of Bland-Altman analysis comparing average flow volume and peak velocity measurements with 95% confidence intervals measured with high Venc PC VIPR and dual Venc PC VIPR with 2D PC. Flow volume was measured in the AAO, DAO, MPA, SVC, and IVC. Peak velocity was only measured in the arterial system (AAO, DAO, and MPA) because peak venous velocities are often difficult to define. Biases between and ml, with a mean bias of ml were found for total flow measured with dual Venc PC VIPR. 95% confidence intervals for total flow measurements were between ±25.02 and ±29.80 ml with a mean of ±28.66 ml. Similarly, the mean bias for peak velocity comparisons was cm/s with biases ranging between and cm/s. The 95% confidence intervals for these measurements were between ±14.64 and ±20.39 cm/s with a mean of ±17.30 cm/s. The smallest biases on average were produced with the combination of a low Venc of 80 corrected with 50 percent of the high Venc acquisition. On average, the peak velocities and total flow measured by dual Venc PC VIPR were lower than those measured with 2D PC. This is most likely a result of the temporal filtering used in the PC VIPR reconstruction.

66 59 Figure 3.5 Summary of the results from Bland-Altman analysis comparing average (A) flow volume and (B) peak velocity measurements with 95% confidence intervals in high V enc PC VIPR and dual V enc PC VIPR with 2D PC. Flow volume [ml] was measured in the AAO, DAO, MPA, SVC, and IVC. Peak velocity was only measured in the arterial system (AAO, DAO, and MPA) because peak venous velocities are often difficult to define. The flow volumes and peak velocities measured with PC VIPR techniques are lower than those measured by 2D PC in most cases. This is most likely a result of the temporal filtering used in the PC VIPR reconstruction. Figure 3.6 shows the average ratio of pulmonary to systemic flow (Qp/Qs) measured across all volunteers by each technique with standard deviations. The pulmonary flow is

67 60 higher than the systemic flow because the flow in the coronary arteries is not included in Qs. This ratio in normal volunteers is 1.03 ± 0.03 on average (116). Most of the techniques slightly underestimate Qp/Qs; however the average value is within 10% of the expected value. Figure 3.6 Measured average Q p/q s ratios with error bars indicating ±1 standard deviation. The expected value of 1.03 ± 0.03 for normal volunteers is indicated by the solid line with the grey box representing 1 SD (21). Most techniques slightly underestimate Q p/q s on average; however, all average values are within 10% of the expected Q p/q s. For all techniques, the expected value of Q p/q s is within ±1 standard deviation. Figure 3.7 shows example high, low and dual Venc PC VIPR images acquired in a healthy volunteer. The dual Venc PC VIPR images have the same dynamic range as the high Venc PC VIPR images but appear to have increased VNR compared to the high Venc images. Phase errors are still present in most of the dual Venc images but the number of phase errors decrease as scan time is increased. With a high-to-low Venc ratio of 2:1, 25% of the high Venc data is sufficient to remove aliasing. However, with a high-to-low Venc ratio of 4:1,

68 61 significant phase errors remain in the vessels when only 25% of the high Venc data is used for unwrapping. Figure 3.7 Example high, low and dual V enc PC VIPR images. The inlay in each image shows the descending aorta. Black arrows point to locations of uncorrected velocity aliasing. Each column of images is labeled with the relative scan time, increasing from left to right (100% for a single V enc PC VIPR acquisition). The dual V enc PC VIPR images have the same dynamic range as high V enc PC VIPR but with increased VNR. Phase errors decrease in dual V enc PC VIPR when the scan time is increased. Example AAO and SVC flow waveforms are shown in Figure 3.8. The ascending aorta waveforms agree well, although the peak flows are somewhat different. More discrepancy is seen between the IVC waveforms, however they similarly agree well. The velocities in the IVC are low and therefore, closer to the noise floor of the higher Venc measurements.

69 62 Figure 3.8 Representative flow waveforms acquired in (a) ascending aorta (AAO) and (b) superior vena cava (SVC) with 2D PC, balanced encoded PC VIPR and two dual V enc acquisitions. The ascending aorta waveforms agree extremely well across all techniques. There is more variation between the waveforms acquired in the SVC, most likely due to slower blood flows in the venous system. Note, the 2D PC waveforms cover a smaller time interval because the 2D PC acquisition is prospectively gated and the PC VIPR acquisitions are retrospectively gated. Based on the RR interval analysis, it was found that the heart beat durations vary 5% in average and 11% at most within each acquisition. The heart rate was found to be stable throughout the scan session as the average heart rates of the scans varied by less than 4% between the scans and 6% the most.

70 63 In two volunteers, the ascending aorta flow waveforms measured with 2D PC were missing the peak systolic flow so ascending aorta flow measurements were not compared in those two volunteers. Prospective gating was used for 2D PC acquisitions so early systole can be missed when subjects have a fast heart rate because of the trigger delay inherent to this acquisition. Similarly, two IVC waveforms measured with 2D PC were missing significant portions of the waveform so those volunteers were excluded from IVC analysis. In these cases, the missing portion of the waveform made it impossible to reliably compare the 2D PC and PC VIPR measurements. One volunteer moved during the PC VIPR scan with Venc = 80cm/s so that data was excluded from analysis as well. All other measurements were used for evaluation. 3.5 DISCUSSION In this work, we have presented a thorough analysis of dual Venc PC VIPR acquisition and reconstruction technique that allows for a large gain in VNR with a modest increase in scan time for 4D PC MRI. The addition of a high Venc scan to an existing phase contrast scan led to a substantial increase in the velocity range over a scan with a single Venc while maintaining the higher VNR of the low Venc acquisition. Because the high Venc scan was only used to correct phase errors in the low Venc, this scan can be highly undersampled to reduce overall scan time. In time averaged phantom scans, large gains in VNR were achieved with small increases in scan time using a dvenc acquisition and reconstruction. The measured VNR in a phantom was increased by a factor of three with only 5% additional scan time. In volunteers, the VNR gains achieved were less substantial than in phantoms due to complex aliasing patterns, noise, and a sparser signal distribution in phantoms. In vivo, we found a

71 64 reasonable compromise between accuracy and scan time when combining Venc=80 cm/s with 25% of the high Venc data, providing the VNR of a 80 cm/s acquisition while increasing the velocity range 100%. For this study, we implemented a dual Venc acquisition with eight velocity encodes: four high Venc and four low Venc. In theory, only seven-points are required for a 4D-PC dvenc acquisition: a velocity compensated reference, three low Venc and three high Venc points. However, PC VIPR data were acquired with a 4-point balanced (Hadamard) flow encoding which requires smaller 1st moments compared to 4-point referenced encoding (23). Consequently, shorter TRs, shorter scan time, and improved temporal resolution can be achieved. However, Hadamard encoding is incompatible with a 7-point acquisition scheme. Depending on the Venc setting, the possible advantage of time savings with 7-point reference encoding would be insignificant compared with an 8-point Hadamard encoding. Another possible implementation for a dual Venc acquisition would be to interleave the high and low Venc scans. However, despite distinct benefits, there are costs associated with that approach as well. With an interleaved scan, the acquisition of the low Venc data would have extended over a longer duration (up to twice as long), thereby possibly leading to greater errors from patient motion and physiological variation. Because the high Venc scan is only used for phase unwrapping, these errors are much less likely to propagate to the final velocity estimation. Additionally, for a dual Venc scheme, this would results in a decreased temporal resolution because 7 or 8 TRs are needed for a single phase encode (or unique radial projection) instead of 4 with the proposed implementation. Therefore, this scheme would result in a decreased temporal resolution leading to decreased accuracy in quantitative flow measurements.

72 65 A potential alternative to dual Venc is the five-point encoding approach (107). A fivepoint encoding strategy corresponds to a balanced four-point acquisition with an added flow-compensated measurement. Johnson and Markl have reported 60% increase in VNR with a scan time increase of 25% by using a non-accelerated five-point acquisition. Acceleration can also be applied to a five-point acquisition, and a 60% increase in VNR can be obtained with only a 1% increase in scan time. Thereby, a five-point velocity encoding approach allows for a shorter scan time than a dual Venc acquisition. However, the gain in dynamic range is fixed and cannot be adjusted as it can be with a dual Venc approach. With a dual Venc approach, the VNR gain and scan time can be adjusted to specific applications. In addition, several other methods have been proposed that could be used in conjunction with dual Venc phase contrast to decrease phase unwrapping errors. Herment et al. used spatial smoothness information from velocity images and magnitude signal for velocity estimation in dual Venc 2D PC (117). The standard deviation over the cardiac cycle of the phase contrast image has been used as an indicator of which voxels to correct (89). Methods such as these could be used to improve VNR in dual Venc images or reduce intermittent unwrapping errors at high undersampling rates. The maximum VNR achievable in a dual Venc acquisition is limited by various factors. As the low Venc is lowered, the unwrapping becomes more sensitive to velocity noise in the high Venc acquisition. This will result in phase unwrapping errors when the high Venc image has errors from noise and/or undersampling. The achievable high Venc undersampling rate decreases with an increasing high-to-low Venc ratio. In time-resolved in vivo scans, we found an undersampling factor of 25% acceptable for a high-to-low Venc ratio of 2 to 1. In time-averaged phantom scans, accurate results were achieved with a high-to-low Venc ratio

73 66 of 4 to 1 with a minimal increase scan time of 5%. Our data show that the achievable high Venc undersampling factor is much higher for the phantom scans. This is due to the presence of more undersampling artifacts in the in vivo images from (i) using fewer projections by reconstructing individual time frames instead of an time average and (ii) a sparser signal distribution in the phantom. Another factor that limits the effectiveness of a dual Venc acquisition is errors in the low Venc images. Since the low Venc image is acquired with a large first moment, requiring large flow encoding gradients, it is more sensitive to intravoxel dephasing, acceleration errors, and signal loss from turbulent or unsteady flow. This can lead to errors in regions with large velocity dispersion, such as near vessel walls or distal to a stenosis. These effects limit the high-to-low Venc ratio that can be achieved. In addition, lower high-to-low Venc ratios decrease the sensitivity of the phase unwrapping to errors in high Venc acquisition caused by undersampling and noise. In this study, we found a high-to-low Venc ratio of 2 to 1 provides a suitable balance between increased VNR and phase unwrapping errors. With this Venc ratio, we were able to achieve an increase of 100% in velocity range of the low Venc scan with only a 25% increase in scan time. There are other potential limitations to this work. Phase errors could also arise from intra-scan patient motion. In most volunteers, the high Venc and low Venc scans were done at least minutes apart to maximize efficiency of the exam, and therefore, some patient movement or physiological variation between the acquisitions is likely. In our cohort of volunteers, we found that variations in R-R intervals between scans were similar to variations of R-R intervals within single scans and therefore, we believe patient heart rate variation did not affect the accuracy of results. In the clinical setting, much greater

74 67 variability is expected due to pathology and patient disposition. The ultimate goal of an efficient dual Venc acquisition is a single scan with back-to-back high and low V enc encodings where the high Venc data are undersampled for time savings yet do not reduce the accuracy of flow measurements. However, in this work the acquisition was accomplished in three subsequent scans to investigate the optimal high-to-low Venc ratio and high Venc undersampling of a dual Venc 4D PC MRI acquisition. If we had acquired all the possible combinations of these factors with separate dual Venc scans, the scan time would be excessive. In this study, parameters for a dual Venc PC VIPR cardiac acquisition were investigated for imaging of the greater vessels in the chest. In future studies, the necessity to adapt settings to specific body regions has to be addressed. For instance, different scan field of view sizes could affect results because of variable inflow effects. Other factors such as vessel orientation and the presence of turbulent flows might also affect results. In conclusion, we investigated an accelerated dual Venc velocity reconstruction for 4D PC MRI with radial sampling. With this approach, it is possible to increase VNR with modest increases in scan time. The efficacy and limitations of this acquisition were demonstrated in both, phantoms and volunteers. This approach is suitable to 4D MR flow measurements in vascular territories where quantitative flow analysis of vessels with a wide range of flow velocities are of interest as shown here for imaging in congenital heart disease. Other potential clinical applications include the hepatic and portal venous system, arteriovenous malformations (AVM), aneurysms with jets and slow flow regions, and others. When adopting dual Venc acquisitions to other vascular beds, the achievable acceleration might differ due to the vessel size, SNR, image contrast, and other factors.

75 68 Chapter 4 NONINVASIVE PRESSURE MEASUREMENTS IN PATIENTS WITH CONGENITAL HEART DISEASE USING 4D PHASE CONTRAST MRI Portions of this work were presented at the Proceedings of the 15 th Annual Meeting of the Society for Cardiovascular Magnetic Resonance in Orlando, FL and 20 th Annual Meeting of the International Society for Magnetic Resonance in Medicine in Melbourne, Australia. 4.5 ABSTRACT In this study, we investigate the feasibility of non-invasively quantifying the percent stenosis and pressure differences in the pulmonary arteries and aorta using 4D PC MRI, specifically in patients with aortic coarctation (CoA) and pulmonary artery stenosis (PAS). Relative pressure differences were calculated from three-directional, time resolved pressure gradients derived from 3-dimensional, time-resolved MR measured velocity fields calculated using the Navier-Stokes equation. Time resolved 3D pressure gradients were evaluated in twelve patients: seven with aortic coarctations (AoC) and five with pulmonary

76 69 artery stenosis (PAS). We developed and tested potential strategies for robustly measuring pressure differences across a vessel narrowing in these regions. The results from PC VIPR were compared with pressure differences estimated from Doppler ultrasound. Pressure differences calculated in this patient population showed reasonable correlation with Doppler ultrasound (R=0.75 in CoA patients and R=0.87 in PAS patients). However, in previous studies, PC VIPR pressure difference measurements were compared with intravascular pressure probes and much better correlation was found (R > 0.95). This study demonstrates the feasibility of using PC VIPR to calculate pressures in these vessels. 4.6 INTRODUCTION Pulmonary artery stenosis is the second most common congenital heart disease. It accounts for 8-12% of all CHD and 50% of CHD include pulmonary stenosis as a component of the defect. Aortic coarctation (CoA) accounts for about 6% of all congenital heart disease, either as an isolated finding or in conjunction with a bicuspid aortic valve(5). Grading the severity of a vascular stenosis is frequently conducted as an anatomical measurement based on the percentage of narrowing. However, this is often insufficient to judge the hemodynamic significance of the narrowed segment, specifically when the stenosis is moderate to severe. However, the pressure gradient across a stenosis is more representative of the hemodynamic severity of the lesion. Clinically, the criteria for intervention in aortic coarctations and PAS are based on the peak pressure gradient across the coarctation and anatomic evidence of significant narrowing. Invasive catheter pressure measurements are considered the gold standard for quantifying the pressure differences. Pressure gradients can also be estimated noninvasively from Doppler ultrasound (US) or

77 70 2D phase contrast (PC) MRI using a simplified Bernoulli equation (118). However, pressure gradients estimated with the Bernoulli equation can be inaccurate because of measurement errors and several assumptions that might not be accurate. For example, pressure recovery distal to the stenosis is not accounted for which can lead to overestimation of pressure gradients for more severe stenoses. Turbulence after the stenosis can cause pressure loss which is also not accounted for, possible leading to underestimation of pressure gradients. Furthermore, the shape of the stenosis can cause errors because the shape can affect pressure recovery and turbulence intensity (118). Additionally, thoracic US measurements are not always possible. Results obtained using the Bernoulli equation are highly sensitive to the maximum velocity observed, can be user dependent and error prone, and do not provide information regarding temporal and spatial variations of pressure gradients. Tyszka et al. developed an approach to estimate pressure gradients from PC MR flow data using the Navier-Stokes equations. In this implementation, three adjacent 2D slices with three-directional velocity encoding were acquired to derive pressure gradients for the central slice (103). 4D PC MRI with dynamic, three-directional velocity encoding can be used to derive the spatial and temporal distribution of pressure gradients noninvasively (66) as well as other hemodynamic parameters in addition to providing high resolution angiograms. In recent work, we have shown that PC VIPR pressure measurements correlate well with invasive catheter based measurements in the carotid, iliac, and renal arteries in swine models (40, 46). Lum et al. calculated transstenotic pressure gradients (TSPG) from the PC VIPR velocity vector field as well as invasively acquired TSPG in carotid and iliac arteries in

78 71 swine. PC VIPR pressure differences were obtained by recording the difference between the mean pressure 1 cm proximal and 1 cm distal to the center of the stenosis. These values correlated very well with the catheter-based measurements (R 2 = 90.6%). This study showed poor correlation in TSPG measurements of renal artery stenosis because of uncompensated respiratory motion. Subsequently, an adaptive respiratory gating scheme based of the bellows signal was implemented. Bley et al then compared PC VIPR pressure measurements in 12 swine with surgically created renal artery stenosis with mean and peak endovascular pressure measurements while applying respiratory gating with 50% efficiency (46). Excellent correlation was found for mean (R 2 = 95.4%) and peak (R 2 = 82.6%) pressure gradients measured invasively and with PC VIPR. It was found that PC VIPR pressure measurements tended to be slightly lower than catheter measurements. This could be attributed to the lower temporal resolution of the MR flow data and the guide wires, one of which crosses the stenosis and possibly increases the measured pressure gradient. A more recent study by Bock et al. explored 4D PC MRI aorta pressure mapping in a stenosis phantom and in vivo, in volunteers and aortic coarctation patients (119). In phantoms, pressure differences were calculated using the modified and simplified Bernoulli equations and the Navier-Stokes equation using 4D PC MRI data identical to the studies described above. Good agreement was found between all methods. In vivo, MRIbased peak mean pressure gradients calculated with the Navier-Stokes equation underestimated pressure differences compared with US by 60.1 ± 17.8% with no significant correlation. However, when the maximum pressure along all paths across the stenosis was used, it was found that MR measurements correlated well with

79 72 Echocardiography (r = 0.96, P < 0.05) in six aortic coarctation patients with underestimation of 14.7 ± 15.5%. Here we are investigating the use of pressure mapping based on PC VIPR data for the first time in humans. Particularly, this study included the challenging area of the pulmonary arteries. Stenoses in this region tend to be less well defined that in other regions, making the assessment of pressure gradients difficult. 4.7 MATERIALS AND METHODS Seven subjects (5M, 2F, mean age 22.7 years) with aortic coarctations and five subjects (3M, 3F, mean age 7.2 years) with pulmonary artery stenosis were enrolled according to an IRB approved, HIPAA-compliant protocol. Three CoA patients were imaged before repair and four after. Echocardiography: Data from routine, clinical transthoracic echocardiography (TTE) was also available in all CoA and four PAS patients to derive estimates of pressure gradients. Doppler values were recorded as maximum velocity. Pressure gradients at the aortic coarctations and pulmonary stenoses were derived from Doppler ultrasound using peak velocities and the simplified Bernoulli equation for all twelve patients. During echocardiography, peak velocities were recorded by the operator but the full velocity-time curves were not available for retrospective analysis. MRI: All patients were scanned on clinical 1.5T and 3T systems. Contrast-enhanced (CE)- MRA was performed as part of the routine clinical MRI prior to the volumetric PC MRI scan. In each patient, 4D PC MRI data were acquired with a radial trajectory (dual-echo PC VIPR [4]) with respiratory and retrospective cardiac gating. Representative parameters include

80 mm 3 isotropic spatial resolution, BW 5 khz, TR 6. ms, flip, volume: 3 cm x 32 cm x 20 cm, 12,000 dual echoes, scan time= ~13 min, Venc = 160 cm/s, reconstructed with time frames per R-R interval. Anatomic Vessel Measurements: The anatomical severity of the aortic coarctations and pulmonary artery stenoses were quantified from CE-MR angiograms and PC VIPR complex difference images. In CoA patients, the percent stenosis was defined from double-oblique vessel diameter measurements proximal to and at the area of greatest narrowing. In PAS patients, the percent stenosis was defined from measurements and the widest and narrowest areas in the vessel. In both patient populations, the percent stenosis was defined as the percent stenosis by diameter. Anatomical measurements made from PC VIPR and CE MRA data sets were compared in all patients. All vessel measurements were done using Vitrea software (Vital Image, Minnetonka, MN). Pressure Measurements: Pressure drops across the stenosis in each patient were first calculated from maximum velocities using the simplified Bernoulli equation. Maximum velocities from PC VIPR data were measured in three ways: distal to the stenosis, in the entire stenotic vessel segment, and along a centerline through the stenosis. Pressure differences were calculated from these maximum velocities using the simplified Bernoulli equation as it is used in clinical routine for ultrasound and MRI: 6.1 where vmax represents the peak velocity in the stenosis. These pressure gradients were compared to those measured with Doppler ultrasound. Next, a pressure difference map was calculated in all patients. In order to estimate pressure differences, a reliable identification of the vessel lumen is required. A vessel mask

81 74 of either the aorta or pulmonary arteries was created for pressure difference calculations for each patient from complex difference images using Mimics software (Materialise, Leuven, Belgium). Time resolved 3D pressure difference maps were derived from PC VIPR data using an iterative method based on the Navier-Stokes equation [5]. PC VIPR 3D visualizations and pressure measurements were accomplished in EnSight (CEI, Apex, NC). Pressure was measured from PC VIPR data using five separate methods (Figure 4.1): (1) Maximum difference in mean pressure between two planes, (2) maximum pressure difference in the stenotic vessel segment (a 'cylinder'), (3) the maximum pressure difference along a centerline, and the maximum pressure difference between either (4) mean or (5) maximum pressure in multiple planes along a centerline through the vessel. In previous studies, PC VIPR pressure differences (PD) were defined as the difference in mean pressures measured in two planes distal and proximal to the stenosis to mimic catheter measurements. However, in patients with PAS and CoA, stenoses are often not as well defined as in other vascular territories and in this study, the additional methods listed above were developed and tested to assess whether they provide more accurate and robust pressure estimations. We compared pressure differences measured with PC VIPR methods to those measured with ultrasound. 4.8 RESULTS Anatomic Vessel Measurements: In both sets of patients, excellent correlation was found between CE-MRA and PC VIPR vessel measurements (R > 0.93). In patients with pulmonary artery stenosis, PC VIPR underestimated vessel size compared to contrast enhanced MRA by about 15%.

82 75 Figure 4.1 PC VIPR pressure differences were measured with five different methods: (A) maximum pressure difference between two planes proximal and distal to the stenosis, (B) maximum pressure difference in a cylinder around the stenosis, (C) maximum pressure difference along a centerline, and (D) differences in mean and maximum pressures measured in planes along a spline. Pressure Difference Measurements Simplified Bernoulli Pressure Differences: Pressure differences measured with PC VIPR and ultrasound using the simplified Bernoulli equation are compared using a box plot in Figure 4.2. There was one outlier for each of the PC VIPR measurements that was much higher than the pressure measured with ultrasound. These outlier measurements belong to the same patient.

83 76 The pressure differences measured with PC VIPR using the modified Bernoulli equation were not significantly different from ultrasound (P > 0.15). Linear regression analysis was also performed on the data and only moderate correlation between US and PC VIPR pressure differences calculated with the simplified Bernoulli equation. For those measured in a cylinder around the stenosis, R = 0.57, distal to the stenosis, R = 0.48, and in a centerline through the stenosis, R = Figure 4.2 Box plot for pressure differences calculated with the simplified Bernoulli equation using maximum velocities from ultrasound and three PC VIPR measurement techniques in twelve patients with aortic coarctation or pulmonary artery stenosis. Navier-Stokes Pressure Differences: Pressure difference maps calculated in an aortic coarctation patient and a pulmonary artery stenosis patient are shown in Figure 4.3 and Figure 4.4.

84 77 Figure month old patient with an aortic coarctation. (A) Angiogram, (B) velocity map, and (C) pressure map generated from the PC VIPR data set. A velocity jet after the coarctation can been seen (B) and a pressure drop across the stenosis was also calculated (C)

85 78 Figure 4.4 Velocity (A) and pressure difference (B) maps measured in a 3 year old patient with narrowing in the MPA and LPA. The locations of these stenoses are indicated by the white arrows. PDs calculated with ultrasound and different PC VIPR techniques are grouped by patient. Pressure differences measured in aortic coarctation patients are show in Figure 4.5. In CoA patients, pressure differences calculated along a centerline had the highest correlation with ultrasound pressures (R=0.75) and with anatomical percent stenosis measurements (R=0.69).

86 79 Figure 4.5 Pressure differences measured with Doppler Ultrasound and different PC VIPR methods in Aortic Coarctation Patients Pressure difference results for all pulmonary artery stenosis patients are shown in Figure 4.6. In patients with PAS, pressure difference measured by taking the difference in maximum pressure between two planes had the greatest correlation with Doppler Ultrasound pressure (R=0.87). In these patients, no method had significant correlation with anatomical percent stenosis measurements.

87 80 Figure 4.6 Pressure differences measured with Doppler ultrasound and different PC VIPR methods in pulmonary artery stenosis patients 4.9 DISCUSSION This feasibility study demonstrates the utility of 4D phase contrast MRI, specifically PC VIPR, for quantifying vessel anatomy and 4D pressure gradients in both the aorta and pulmonary arteries in humans. The complete spatial and temporal coverage may help evaluate the impact of local pathologies such as stenoses and coarctations on regional and global pressure gradients over the cardiac cycle. Furthermore, one can combine pressure gradient data with additional information from the 4D PC MRI, including flow visualization, flow quantification and other derived hemodynamic parameters such as local pulse wave velocity, shear stress, turbulent energy, and more. It was shown that time-averaged aortic and pulmonary vessel geometry can be derived from 4D flow MRI data and can successfully be used with the acquired velocity field to calculate time-resolved pressure gradients and 4D pressure difference maps. Excellent correlation was found between CE-MRI and PC VIPR vessel measurements. In PAS patients, larger differences in vessel anatomy measured with PC VIPR and CE MRA were seen. These

88 81 differences are not entirely understood but could be due to the small vessel sizes imaged and reduced vessel contrast in this very young patient cohort. Moderate agreement was found between maximum velocities and Bernoulli pressure differences measured with ultrasound and PC VIPR. PC VIPR maximum velocities tended to be lower than those measured with ultrasound, except in the case of the cylinder measurement method, possibly because that method is most sensitive to noise. PC VIPR underestimation of maximum velocity compared with ultrasound could possibly be related to the lower spatial and temporal resolution in MRI resulting in partial volume effects and temporal filtering. Large variations were seen between PC VIPR pressure difference measurements calculated with the different methods. Some of the methods (cylinder, max of planes along spline) are more sensitive to pressure variations and would be expected to yield larger pressure differences but are also more sensitive to noise. Based on the results presented here, further investigations are needed to identify the most robust algorithm for making these pressure difference measurements. In this study, PC VIPR and Doppler ultrasound pressure differences were compared. However, the Bernoulli approximation used in these measurements is a simplification and contains user-dependent and intrinsic errors. It has been shown that US pressures correlate well with catheter measurements (R > 0.76) with a systematic overestimation of pressure on the part of echocardiography (120, 121), especially when proximal velocities exceed 1 m/s or when pressure drops across the stenosis are low (120). In a mild stenosis, ultrasound overestimates the pressure drop because the velocity proximal to the stenosis is relatively higher compared with the distal velocity (122). Therefore, ultrasound is an

89 82 imperfect standard for comparison and some disagreement in this study could be due to inaccuracy of Doppler measurements. Additionally, the shape of the stenosis and velocity jet has an impact on the measured velocity. With 4D PC MRI, it is possible to measure pressure development over long distances without being influenced by vessel shape and jet stream location in the stenosis. Furthermore, 4D PC MRI can be used to measure pressure in regions that cannot be examined with ultrasound. Although this study lacked catheter pressure measurements, previous studies have shown good agreement between PC VIPR noninvasive pressure and invasive pressure measurements in the carotid, iliac, and renal arteries with small underestimation of pressures measured by PC VIPR (40, 46). In this work, the agreement between echocardiography and PC VIPR pressure measurements was lower than in previous studies, and without a gold standard, it is difficult to isolate the reason for these differences. In order to fully evaluate the potential new analysis strategies presented in this work for the aorta and pulmonary arteries, further tests are needed. In the subsequent chapter (Chapter 3), a study is described in which pressure was evaluated in a stenosis model and PC VIPR results were compared with computational fluid dynamics and a pressure probe.

90 83 Chapter 4 IN VITRO VALIDATION OF PC VIPR PRESSURE MEASUREMENTS IN A STENOTIC FLOW PHANTOM Portions of this work were submitted to the Proceedings of the 21 th Annual Meeting of the International Society for Magnetic Resonance in Medicine in Salt Lake City, Utah ABSTRACT The purpose of this study was to compare 4D phase contrast (4D PC) MRI and computational fluid dynamics (CFD) pressure measurements in a simple stenosis phantom with pressure wire measurements. A stenosis phantom was designed and manufactured with high precision. The phantom was connected to a programmable flow pump and pressure measurements were obtained with 4D PC MRI and a pressure wire at three constant flow rates. CFD pressure maps were calculated with the same three flow rates. It was found that pressure gradients calculated from 4D PC MRI were comparable to those obtained from pressure probes and computational fluid dynamics.

91 INTRODUCTION Localized blood vessel anatomy and hemodynamics play an important role for diagnosis and treatment planning in patients with congenital heart disease. Particularly, blood pressure differences along a vessel are a key factor for assessing the severity of arterial stenosis. The gold standard for determining transstenotic pressure gradients in clinical practice is an invasive measurement using a pressure catheter. Pressure gradients can also be estimated noninvasively from Doppler ultrasound (US) or 2D phase contrast (PC) MRI using a simplified Bernoulli equation. However, pressure gradients estimated from 2D PC are highly subject to plane location and errors arising from fluid acceleration and turbulence (118). The kinetic energy of blood accelerated though a stenosis is partially recovered downstream and diminishes the net loss of pressure across the valve, compared with the Bernoulli equation result. 4D PC MRI with dynamic, three-directional velocity encoding has potential to derive the spatial and temporal distribution of pressure differences and additionally, account for viscosity effects. This approach has been used successfully in vivo and corroborated with other pressure measures (40, 46, 119). However, many factors impact the accuracy of pressure measures including pressure recovery, imaging parameters, and algorithm used to derive pressure. Subsequently, a thorough understanding of the accuracy and limitations of this technique is required. The purpose of this study was to compare 4D phase contrast (4D PC) MRI pressure measurements in a stenosis phantom with pressure wire measurements as well as with computation fluid dynamics (CFD).

92 THEORY Pressure gradients were calculated using the Navier-Stokes equation from cine velocity vector fields measured using 4D PC MRI: 5.1 Where p is the pressure, μ is the fluid viscosity, v is the measured three-directional velocity, ρ is the fluid density, and g is the gravitational force. This method was originally proposed by Yang et al. using 2D PC velocity data (123) and extended to 3D by Tyszka et al. (103). This equation is derived from conservation of momentum and describes the time varying laminar flow of a viscous, incompressible fluid. The term on the left-hand side of the equation is three-dimensional pressure gradient. The terms on the right hand side of the equation from left to right are the transient inertia, the convective inertia, gravitational force, and the viscous resistance. The gravitational term was excluded in calculations because subjects were lying horizontally in the scanner. The Navier-Stokes relationship is also used in computational fluid dynamics (CFD) to solve for pressure fields. 3D velocity fields acquired with 4D PC MRI can be used directly in Equation 5.1 using difference equation in place of derivative operators to produce a pixel by pixel pressure gradient. The nearest spatial and temporal neighbors were used for calculation of a central difference as an approximation of temporal (dv/dt) and first and second order spatial derivatives (, ). To computer scalar pressure from the pressure gradient, the pressure gradient equation was solved:

93 Where A is a matrix representing the discrete derivative operation evaluated at each point. In this study, the relative pressure at each point was evaluated with a matrix inversion MATERIALS AND METHODS Stenosis Model: A stenosis phantom was designed in SolidWorks (Dassault Systèmes S.A., Waltham, MA) to approximate a pediatric aortic coarctation with a 75% stenosis by diameter. Figure 4.1 shows a schematic diagram with the dimensions of the stenosis phantom. The stenosis was machined from a solid polycarbonate rod and polished to be smooth. The stenosis was connected to rigid, one foot polycarbonate tubes to ensure fully developed laminar flow inlet conditions. The stenosis was submerged in deionized water for calibration and to reduce susceptibility artifacts. The stenosis model was connected to a programmable flow pump (CompuFlow 1000 MR, Shelley Medical Imaging Technologies, London, ON, CA) and filled with blood mimicking fluid (ρ=1.02 g/cm 3, µ=4.1 cp) for pressure probe and MRI experiments.

94 87 Figure 4.1 Stenosis phantom machined from polycarbonate and acrylic. The stenosis is a 75% by diameter narrowing and is submerged in a water back to reduce susceptibility artifacts. One foot long rigid tubes were connected to the stenosis to ensure a developed Laminar flow inlet and an undisturbed outlet velocity jet. Pump Flow Rate Calibration: We validated programmed pump flow rates with an inline flow probe (ME6PXN Inline Flowsensor, Transonic Systems Inc., Ithaca, NY). Measurements were made using a multichannel flow meter console (T403, Transonic Systems, London, ON, CA). The flow probe was calibrated for a specific flow range and temperature and specifications state the accuracy of measured flow should be within ±2%. Pump programmed constant flow rates between 5 ml/s and 26 ml/s were compared to those measured with the flow probe. Computational Fluid Dynamics: A stationary 2D axisymmetric model of the stenosis was developed in COMSOL (Comsol, Inc. Burlington, MA) using a laminar inflow boundary conditions of 7.5 ml/s, 15 ml/s, and 22.5 ml/s. The model assumes a fictitious inlet channel, defined to be 30 cm long, to ensure fully developed flow at the entry of the stenosis. The

95 88 geometry included an outlet channel of cm with a zero-pressure outlet boundary condition. At the walls, assumed to be rigid, a non-slip (zero velocity) boundary condition was specified. Fluid properties represented those of blood: 1060 kg/m 3 for density and 3.5 cp as the viscosity. Triangular elements were used for discretization of the geometry, resulting in 31,182 elements. Resulting velocity and pressure fields were graphed as contour plots and compared with experimental measurements. The pressure was plotted with respect to the distance from the inlet, representing the pressure along the lumen and allowing pressure difference calculations. Peak velocities were used in the simplified Bernoulli equation to calculate these pressure differences. Pressure Probe: A fiber optic pressure probe (opsens, Quebec, Quebec, CA) with the Fabry- Perot interferometer configuration (124) was used to make measurements at 17 points along the long axis of the phantom: one measurement 10 cm proximal to the stenosis, 15 measurements 1 cm apart through the stenosis and distal to the stenosis and then one measurement distal to the stenosis at the connector the flow pump. The probe senses pressure via a microeletromechanical system (MEMS) which houses a diaphragm that deflects in proportion to the amount of strain imparted on it. Pressures measured at constant flow with a sampling rate of 1000 Hz were averaged over 10s. MRI: The phantom imaging was performed on a clinical 3T system (Discovery MR 750, GE Healthcare, Waukesha, WI) with a maximum gradient strength of 50 mt/m and a maximum slew rate of 200 mt/m/ms. The stenosis phantom described above was placed in the center of an 8-channel flexible knee coil for optimized signal. Five-point encoded PC VIPR (107) data sets were acquired with the following parameters: 0.5mm 3 isotropic

96 89 spatial resolution, TE150=3.2ms/TE300=3.1ms, BW=83.33 khz, TR 6.2ms, 10,000 projections, scan time ~ 8 min). Constant flow scans were acquired with prospective gating to avoid imaging during the pump turn around. Table 4.1 shows a list of 5-point PC VIPR scans acquired with constant flow. At each flow rate, two 5-point encoded PC VIPR scans were acquired: one with a Venc = 300 cm/s and one with Venc = 150 cm/s. Table 4.1 PC VIPR scans acquired with constant flow Constant Pump Flow (ml/s) Approximate Max Velocity (cm/s) High V enc (cm/s) Low V enc (cm/s) Number of Projections Before flow pressure calculations, MRI data was cropped and the vessel was segmented using Mimics (Materialise, Leuven, Belgium). For pressure difference calculations, a mask was created along the centerline to avoid including voxels in stationary region of the phantom. Flow and pressure drop across the stenosis were calculated at each Venc and programmed pump flow rate RESULTS Pump Flow Rate Calibration: Excellent agreement was found between the programmed pump flow rate and flow rate measured by the flow probe (R 2 = 0.99) as shown in Figure 4.2. Measured flow rates were, on average 6% higher than the prescribed flow rates with ±0.07 standard deviation.

97 Flow Probe Measured Flow Rate [ml/s] y = 1.06x R² = Programmed Pump Flow Rate [ml/s] Figure 4.2 Validation of flow pump rate against flow probe measured flow rates. Identity is displayed with the dashed line. Standard deviations are not shown on the graph because they are smaller than the data markers. Pressure Gradient Comparison: Peak pressure drops from CFD, probe and 4D PC were relatively similar (Table 4.2); however 4D PC shows pressure recovery post-stenosis which is not seen in CFD or probe data. The largest difference between PC VIPR and CFD pressure drops was 21%. The largest difference between pressure probe and MR data was 22%. Bernoulli pressure differences calculated from 4D PC MRI and CFD data varied from Navier-Stokes pressure calculations by as much as 18%. Bernoulli pressure difference estimates tended to be lower than pressure differences measured with a pressure probe and those calculated using the Navier-Stokes equations.

98 91 Table 4.2 Pressure differences (in mmhg) measured with the different techniques in the stenosis phantom. Maximum velocities calculated with CFD and measured with MRI were used with the simplified Bernoulli equation to calculate pressure differences for comparison. Flow (ml/s) Pressure Probe CFD PC VIPR Venc150 Venc300 Venc150 Venc300 Navier- Stokes Bernoulli Navier-Stokes Bernoulli ± ± ± Figure 4.3 shows velocity and pressure maps from CFD calculations and 4D PC MRI. Peak velocities are similar in each case; however, the velocity jet is more persistent in CFD as expected, due to the fact that there is zero pressure at the outlet and the PC VIPR data is offset spatially from the CFD data. Figure 4.4 shows pressure profiles calculated along the centerline of the stenosis obtained from different methods with a flow rate of 15 ml/s. The inlet pressures 10 cm from the inlet were set to the same value for all methods for comparison.

99 Figure 4.3 Results from CFD and PC VIPR at Venc = 150 cm/s and Venc = 30 cm/s at a flow rates = 15 and 22.5 ml/s: (a) velocity fields and (b) calculated pressure maps. A single central slice of volumetric 4D PC MRI and CFD data is displayed. 92