real-time imaging for cardiac flow measurements€¦ · 3.3 results 46 3.3.1 image quality 46 3.3.2...

Real-time Imaging For Cardiac

Flow Measurements

MPhil to PhD Transfer Report

Jennifer Steeden

28th September 2009

Primary Supervisor David Atkinson

Secondary Supervisor Vivek Muthurangu

Publications

ISMRM ʼ09 Poster Edgar J Muthurangu V Taylor A Atkinson D Undersampled Spirals for Real-time Flow Measurements Proc Intl Soc Mag Reson Med 17 (2009) 20091855 ISMRM Flow workshop Sept rsquo09

Steeden J Atkinson D Taylor A Muthurangu V Real-time Flow Measurements for

the Assessment of Hemodynamic Response to Exercise

Under Review with JRMI

Steeden J Atkinson D Taylor A Muthurangu V Assessing Vascular Response To Exercise using a combination of Real-time Spiral Phase Contrast MR and Non-invasive Blood Pressure Measurements

i

CONTENTS

1 INTRODUCTION 1 11 Achieving Real‐time Imaging 2 111 Alternative trajectories 3 112 Parallel Imaging 5

12 Measuring Flow with MRI 7 121 Implementation of Phase Contrast Imaging 8 122 Accuracy of PC‐MRI 9 123 Concomitant Gradients in Flow Imaging 11 124 Additional Phase Offsets 13

13 Exercise Testing 14

2 LITERATURE REVIEW 16 21 Real‐time Flow Measurements 16 211 Efficient trajectories 16 212 Parallel Imaging 19

22 Performing MRI during exercise 22 221 Imaging During Suspension of Exercise 22 222 Imaging During Continuation of Exercise 23 223 Upright exercise 26 224 Measurement of Ventricle Volume During Exercise 27

23 Assessment of hemodynamic response using MRI 27

3 REALshyTIME FLOW MEASUREMENTS FOR THE ASSESSMENT OF HEMODYNAMIC

RESPONSE TO EXERCISE 32 31 Development of Real‐Time Flow Sequence 32 311 Maxwell Correction 35 312 Residual Phase Offsets 37

32 Methods 40 321 Study Population 40 322 Exercise Protocol 40 323 MR Protocol 41 3231 Standard flow assessment 42 3232 Real‐time flow assessment 42 3233 Real‐time volume assessment 43

324 Validation Experiments 43 3241 Flow Pump Validation 44 3242 In‐vivo Validation 44

ii

325 Analysis 44 3251 Image Analysis 44 3252 Statistical Analysis 45

33 Results 46 331 Image Quality 46 332 Phantom Validation 47 333 In‐vivo Validation 48 334 Vascular Hemodynamics During Exercise 50

34 Discussion 52 341 Limitations 53 342 RF Shielding 54 343 Conclusion 56

35 Hemodynamic Response To Mental Stress 56

4 FUTURE WORK 58 41 Discussion of Potential Projects 59 411 Improvement of Image Quality 59 4111 Discussion 62

412 Variable Density Spirals and kt‐SENSE 62 4121 Discussion 66

413 Fourier Velocity Encoding 66 4131 Discussion 67

414 Diffusion Weighted Imaging 67 4141 Discussion 68

415 Clinical validation 68 4151 Discussion 68

416 ldquoPre‐referencerdquo flow 69 4161 Discussion 73 4162 Initial results 73

417 Speeding up Reconstruction 77 4171 Discussion 79 4172 Further Use of GPUs 80

42 Time Scale 81

REFERENCES 83

1

1 INTRODUCTION

Real-time imaging is essential in areas of magnetic resonance imaging (MRI) where

conventional MRI techniques are too slow Real-time imaging is especially important

in applications where there is motion present for example in cardiac imaging

Conventional cardiac MRI techniques use cardiac gating to reduce artifacts from

motion of the heart however this greatly increases scan time and has limitations in

its use

Conventional cardiac MRI uses electrocardiogram (ECG) gating to synchronize the

acquisition of data with cardiac motion This limits image artifacts and allows different

phases of the cardiac cycle to be accurately captured Images from cardiac gated

sequences are formed over many cardiac cycles and reconstructed as an lsquoaveragersquo

cardiac cycle ECG gated images are therefore susceptible to artifacts from

additional motion eg respiratory motion There are some simple techniques to

reduce respiratory motion including breath-hold imaging However many patients

with cardiac disease have difficulty in holding their breath therefore multiple signal

averages may be performed or respiratory gating may be used ndash these techniques

greatly increase scan time Other forms of motion are more difficult to control

Successful cardiac gating requires a good quality periodic ECG waveform for

accurate detection of the R-wave Therefore conventional MRI techniques are

unsuccessful in subjects with arrhythmias or where there is an unreliable ECG

signal In these applications real-time imaging is highly desirable as it does not

require ECG gating Real-time MRI acquires data very rapidly (ie each frame takes

less than 100ms) making it less susceptible to motion This allows a great reduction

2

in scan time and may also allow observation of beat-to-beat variations (which are not

seen in conventional imaging) Real-time imaging does however come at the cost of

lower spatial resolution and also lower effective-temporal resolution

Real-time imaging is also essential in imaging subjects during exercise because

bull ECG gating is unreliable

bull Breath-holding is not feasible

bull High heart rates are observed

bull Excessive motion from breathing and exercise

MRI is a well validated method of measuring flow at rest however in this study we

would like to be able to measure flow during exercise with the use of real-time

imaging This will allow quantification of hemodynamic response to exercise and

assessment of vascular disease

11 Achieving Real-time Imaging

Real-time imaging requires data to be acquired very rapidly Common ways to

reduce acquisition times include

bull Reducing the matrix size

bull Rectangular field-of-view (where less lines are acquired at the top and

bottom of k-space)

bull Partial Fourier encoding (where less lines are acquired at the bottom of k-

space and the missing lines are calculated from the Hermitian symmetry of

k-space)

bull Sliding window reconstruction (where data is shared between frames)

In this study we are interested in reducing scan times further than these common

methods can achieve This study focuses on the use of alternative trajectories and

parallel imaging to achieve very high temporal resolution imaging

3

111 Alternative trajectories

Conventionally in MRI data is acquired one k-space line at a time This is a very

popular method of imaging as the gradient design is simple and the data lies on a

Cartesian grid Acquiring data in this way is very slow as only a small portion of k-

space is covered after each excitation and there are a large number of excitations

Methods of speeding up acquisition while maintaining data on a Cartesian grid

include the use of echo planar imaging (EPI) Single shot EPI is possible where the

entire of k-space is filled after one excitation or segmented EPI can be used where a

part of k-space is filled after each excitation

To convert k-space data into the image domain a Fourier transform must be applied

The fastest and most efficient method of performing a Fourier transform is with the

Fast Fourier Transform (FFT) In order to use the FFT data must lie on a uniform

Cartesian grid This means that k-space data acquired using non-uniform Cartesian

trajectories or non-Cartesian trajectories require the data to be resampled onto a

uniform rectangular grid before the FFT can be applied ndash this is called gridding (1)

Gridding of data in MRI requires convolution of the k-space data with a convolution

kernel Ideally a SINC kernel would be used however as this is an infinite function

the computation would be impractical The choice of kernel is a trade-off between

processing time and interpolation accuracy (2) A Kaiser-Besel kernel is commonly

used in MRI (3) as it has minimal residual aliasing and allows a relatively short

computation time It also has an analytic expression for its properties in the Fourier

domain

Non-Cartesian trajectories may offer more efficient methods of covering k-space or

non-uniform coverage of k-space The most common non-Cartesian trajectories used

in MRI include radials and spirals (see Figure 1) This study focuses on the use of

Spiral trajectories (4) as they provide a highly efficient method of traversing k-space

4

Spiral trajectories acquire a large proportion of the data to be acquired after each

excitation and they do not acquire the corners of k-space which are not necessary

for reconstruction As spiral trajectories start in the centre of k-space they have a

very short TE which means there is very little time for spins to dephase due to

motion This makes spiral trajectories optimal for measuring flow (5)

Figure 1 Common trajectories used in MRI a) Standard Cartesian with 12 lines b) Radial with 8 projections c) Single shot spiral

In order to acquire data on a spiral trajectory the gradient waveforms required are

sinusoidal in shape and are both frequency and amplitude modulated At the start of

the readout the gradients are limited by the slew rate however once the maximum

gradient amplitude has been reached this then limits the gradient waveforms Spiral

trajectories are designed using the following formulae (6)

euro

k( t) = λθ ( t)eiθ (t ) Equation 1

euro

λ =N int

D Equation 2

where

euro

k t( ) is the k-space position at time t

euro

θ t( ) is the azimuth angle (rad)

euro

N int is the

number of spiral interleaves required and

euro

D is the field of view (m) A spiral trajectory

that has multiple interleaves uses the same trajectory for each interleave however

each interleave is rotated by a multiple of

euro

2π N int radians

a) b) c)

5

112 Parallel Imaging

It is possible to further speed up image acquisition by missing out some of the data in

k-space (see Figure 2 For a Cartesian data set it is possible to increase the temporal

resolution by missing out entire lines of k-space (eg only acquiring every other line

gives a two-fold acceleration) In Spiral imaging the same principle can be used by

missing out entire spiral interleaves

Figure 2 Acceleration of data Fully sampled a) Cartesian data and c) spiral data with corresponding 2-fold undersampled data b) Cartesian and d) spiral

When reconstructing an accelerated Cartesian acquisition aliasing occurs where

replicas of the subject appear in the image along the phase-encode direction (see

Figure 3) spaced at FOVacceleration factor This is because an increase in the

spacing between lines in k-space causes an effective decrease in the FOV resulting

in wrap-around artifacts However in spiral imaging aliasing causes streaks and swirls

across the entire reconstructed image (see Figure 3) that are not related to the

anatomical region that generated the aliasing

Figure 3 Simulated effect of undersampling performed in MATLAB a) Fully sampled Shepp-Logan phantom Undersampled 4-fold with a b) Cartesian trajectory and c) spiral trajectory

a) b) c) d)

6

In order to reconstruct accelerated MRI data parallel-imaging is used where multiple

coils acquire data in parallel Although not the first parallel-imaging implementation

one simple method of parallel-imaging is SENSE (sensitivity encoding) which was

described by Pruessmann in 1999 (7) Other methods of parallel imaging not

investigated further in this work include kt-SENSE (8) SMASH (9) GRAPPA (10)

kt-GRAPPA (11) BLAST (12) and kt-BLAST (8)

In SENSE spatial dependence of multiple coils (the coil sensitivities) is used to imply

information about the origin of the signal in the image domain and remove aliasing

artifacts There are two methods of measuring the coil sensitivities (7) one method

requires a separate scan to be performed prior to the SENSE scan and the other

method uses the data from the scan to calculate the coil sensitivities The first

method requires a low resolution full FOV images to be acquired for each of the coils

along with a full FOV image from the body coil (which is assumed to be

homogeneous) The second method calculates an average full FOV image for each

coil by combining multiple measurements in k-space A lsquobody coil equivalentrsquo

magnitude image is formed from the sum-of-squares of all coils The coil sensitivities

are calculated by the division of each of the coil images by the body coil image

SENSE reconstruction of an accelerated Cartesian data set can be efficiently

performed by direct unfolding of the aliased images in the image domain (7)

However for undersampled spiral data the relationship between the pixels in the

aliased images and their contribution to the pixels in the full FOV image is not clear

(as seen in Figure 3) Pruessmann described a method of reconstructing

undersampled data from arbitrary trajectories in 2001 (3) This reconstruction uses

an iterative Conjugate Gradient (CG) algorithm to unwrap all pixels simultaneously A

generalized diagram of the CG algorithm is shown in Figure 4

7

Figure 4 Implementation of the iterative SENSE reconstruction for arbitrary trajectories (3)

12 Measuring Flow with MRI

MRI is a proven method of measuring flow at rest (1314) Measurements of flow are

very important in assessing cardiac performance and MRI allows visualization and

quantification of flow Clinical assessment of flow leads to detection management

and monitoring of heart disease

MRI is inherently motion sensitive as the applied magnetic gradients alter the

resonant frequency of spins according to the Larmor equation

euro

ω(x) = γ(B0 + x sdotGx ) Equation 3

where

euro

ω is the precessional frequency (rads)

euro

γ is the gyromagentic ratio (radsT)

Bo is the main magnetic field (T) and

euro

G is the strength of the gradient (T) at position

euro

x (m) This means that spins accumulate a phase over time depending on their

location according to the equation

euro

φ t( ) = γ G(u)x(u)du0

t

int

Equation 4

8

where G(u) is the amplitude vector (T) for an arbitrary gradient waveform at time u

(s) A Taylor expansion of Equation 4 shows that the phase accumulated by spins is

linearly proportional to the velocity of that spin

euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5

where Mn is the nth gradient moment and

euro

x0 and

euro

v0 are the initial displacement and

velocity of the spins along the direction of the gradient The sensitivity to velocity can

be seen in Equation 5 to be related to the first order gradient moment (M1)

The encoding of velocity in the phase of an MR signal is known as phase contrast

(PC) imaging (15) From PC-MRI images flow velocities and flow volumes can be

calculated The flow velocity is determined by the pixel intensity values in the phase

images and the flow volume is the flow velocity in a pixel multiplied by the pixel

volume Therefore the flow volume in a vessel can be calculated by summing the

flow volumes for all pixels within the vessel

121 Implementation of Phase Contrast Imaging

The motion sensitizing gradients

required to encode flow in MRI are

applied after the RF excitation and

before the readout gradient Flow

can be measured in any direction by

placing the motion sensitizing

gradients on the appropriate axis

however in this study we are only

interested in through-plane flow

where the gradients are played out

Figure 5 Effect of a balanced bipolar gradient on the phase of stationary and moving spins

9

on the slice-select (z) axis Flow encoding consists of a bipolar gradient with two

lobes of equal area but opposite polarity (see Figure 5) Because the net area of

these two gradients is zero (ie M0 is zero) stationary spins accumulate no net

phase Assuming there is no accelerative or higher order motion of spins Equation 5

can be seen to simplify to

euro

φ = γv sdot M1 Equation 6

The velocity encoding (VENC) determines the maximum velocity that can correctly

be encoded in PC-MRI before aliasing occurs a spin travelling at the plusmnVENC value

(ms) will cause a phase shift of plusmnπ radians Normally in PC imaging two acquisitions

are made one which is velocity compensated (ie has a VENC of zero) and one

which is velocity encoded The phases of the resultant images are subtracted in

order to remove phase offsets from additional sources eg B0 inhomogeneities or

eddy currents Therefore the phase difference is more commonly expressed as a

difference in the first order moments of the two images

euro

ΔM1

euro

Δφ = γv sdot ΔM1 Equation 7

Where the VENC can be calculated as

euro

VENC =π

γΔM1 Equation 8

122 Accuracy of PC-MRI

The accuracy of PC-MRI is very important Many studies have looked at the errors in

flow measurements Lotz et al (14) found a 3 difference between flow in the

ascending aorta and the pulmonary artery using a retrospective gated and breath-

hold sequence with an intra-observer variability of 2 and inter-observer variability

of 3 They also found a ~10 difference between cardiac output measured by

phase-contrast and by a modified thermodilution technique (14)

10

The accuracy of PC-MRI depends on

bull Adequate temporal resolution to accurately detect the peak flow velocities

bull Adequate spatial resolution to prevent partial-volume effects

bull A suitable match between the velocities in the vessel of interest and the

chosen VENC

o If the VENC is too small then wrap occurs where the phase shift is

greater than plusmnπc

o If the VENC is too large then noise may mask the true velocities ndash this

is known as the velocity-to-noise ratio (VNR)

bull The angle of the imaging plane to the main direction of flow ndash most precise

measurements are obtained if the plane is orthogonal to the flow for through-

plane flow

bull The presence of background phase offsets which may arise from concomitant

gradients or eddy currents (described in sections 123 and 124 respectively)

bull The accuracy of vessel segmentation

Tang et al (16) described the main factors that affect the accuracy of PC flow

measurements as being partial-volume effects and intravoxel phase dispersion

Partial-volume effects are observed when there is a mixture of stationary and flowing

spins within a voxel ndash this is important in voxels that are on vessel boundaries In

these edge pixels the volume flow rate is normally overestimated because the area of

the pixel is overestimated while the velocity is accurately measured The smaller the

vessel (or the larger the pixels) the larger the relative number of pixels influenced by

partial-volume effects compared to the number of pixels fully in the vessel thus the

greater partial-volume effects influence the flow measurement Intravoxel dephasing

occurs when there are spins with different velocities within a voxel which destroy

phase coherence ndash this may be caused by accelerative spins turbulent spins or

11

magnetic field inhomogeneity Both partial-volume effects and intravoxel dephasing

are reduced by increasing spatial resolution

Greil et al (17) performed a study on a

pulsatile flow phantom where the number

of pixels in the cross-section of the

phantom was varied (by changing the

matrix size and the FOV) from 145 to 16

They found that the percent error grew

linearly with increasing FOV (as seen in

Figure 6) for each 20-mm increment the

percent error increased by a mean of

07 When only 16 pixels were used in the cross section of the vessel the flow rate

was overestimated by a mean of 90 No statistical significance was found in

percentage error for varying slice thickness (from 4-8mm) slice inclination (up to

40o) RF flip angle (from 10-40o) variation in VENC (from 10-40ms) or with the

addition of background phase correction Greil concludes that providing the spatial

resolution is great enough PC-MRI is an accurate and robust method of measuring

flow (17)

123 Concomitant Gradients in Flow Imaging

Concomitant gradients (also known as Maxwell gradients) are unintentional gradients

with nonlinear spatial dependence which occur in addition to desired linear magnetic

field gradients These additional gradients are a consequence of Maxwellrsquos equations

for the divergence and curl of the magnetic field

Figure 6 Results from Greil et al (16) showing a linear relationship between the number of pixels in a vessel and the calculated error

12

Concomitant gradients cause undesired phase offsets in images and therefore

incorrect velocity measurements in PC-MRI The concomitant gradient field can be

calculated (18) from the equation

euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2

4minusGxGzxz minusGyGzyz

Equation 9

Therefore the phase accumulated from concomitant gradients is

euro

Δφc xyz( ) = γ Bc xyzt( )dtint Equation 10

From these equations the residual phase in PC-MRI caused by concomitant

gradients (after the phase difference calculation) can be found (18)

euro

Δφc xyz( ) = Az2 + B x 2 + y 2( ) + Cxz + Dyz

Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy

2(t)( ) fe1 minus Gx2(t) +Gy

2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0

Gx (t)Gz (t)[ ] fe1 minus Gx (t)Gz(t)[ ] fe2 dtint

D = minusγ2B0

Gy (t)Gz (t)[ ] fe1 minus Gy (t)Gz(t)[ ] fe2 dtint

Equation 12

The first flow image here is denoted fe1 and the second flow image is denoted fe2

The integrals are evaluated over a time period from the end of the RF excitation

pulse to the beginning of the ADC readout

Maxwell gradients also affect all imaging gradients and may play an important roll in

spiral imaging (19) In spiral imaging the effect of concomitant gradients is much

harder to correct as each point in the readout has to be corrected by a different

phase offset from the concomitancy of the gradients

13

124 Additional Phase Offsets

Additional phase offsets in PC imaging have been widely observed (2021) These

phase offsets may arise from inhomogeneities in the magnetic field and eddy current

effects They are affected by many parameters including the imaging position VENC

maximum gradient amplitude and maximum gradient slew rate Like concomitant

gradients these offsets cause incorrect velocity measurements in PC-MRI

Commonly manual post processing techniques are used to remove additional phase

offsets One such method involves estimation of the phase offset from a region of

stationary tissue near to the vessel of interest (141720) ndash this method does not work

well in the great vessels as there is very little surrounding stationary tissue

Alternatively a separate scan may be performed on a stationary phantom with

identical imaging parameters to calculate the phase offsets in the same region as

the vessel (22) This is time consuming and inconvenient in clinical practice as it

must be carried out for every individual PC image acquired

One semi-automated method was first described by Walker et al in 1993 (23) This

method assumes the phase offsets vary linearly in space This surface is estimated

by fitting a plane through stationary pixels in the phase image and subtracting this

plane from the velocity images This technique is widely used (1720212425) as it

can be completely automated and therefore does not require any additional

processing by the user However this technique will not work for very noisy data or

data where there is very little stationary tissue

14

13 Exercise Testing

Exercise is a powerful stimulator of the cardiovascular system Exercise testing is a

common medical exam carried out to assess for cardiac disease In common stress

testing the patient is placed on a treadmill and the level of exercise is progressively

increased Normally only the ECG heart rate and blood pressure of the subject are

recorded - these are not sensitive markers of early vascular disease Therefore the

sensitivity of exercise testing could be improved through additional measurements of

cardiac output systemic vascular resistance (SVR) and vascular compliance (C)

SVR is the amount of resistance to flow that must be overcome to push blood

through the peripheral circulatory system SVR is calculated as the mean arterial

blood pressure divided by the cardiac output

Compliance is a measure of the ability of the wall of a blood vessel to distend and

increase volume with increasing transmural pressure A simple approximation of

compliance is the ratio of stroke volume to pulse pressure However this is thought to

overestimate true arterial compliance (26) The pulse pressure method is thought to

give a more accurate estimation of true compliance by parameter optimization of the

two-element Windkessel model (27) as discussed further in section 23

The calculation of both SVR and C require measurements of flow as well as blood

pressure measurements Normally in SVR and C measurements catheters are used

to measure pressure and the Fick principle is used to quantify flow Previous studies

measuring SVR and C using MRI are discussed in section 23

Instead of using exercise to increase the load on the heart a pharmacological stress

test can be used ndash one such pharmacological agent is called dobutamine

Pharmacological stress tests are important in subjects with physical limitations eg

severe arthritis prior injury reduced exercise tolerance however exercise testing is

15

advantageous over pharmacological stress tests due to the physiologic effects that

exercise also has on blood pressure and heart rate During exercise adverse

symptoms may also be observed by the physician (including exercise-induced

irregular heart beats) and the subjects tolerance to exercise can also be assessed

There are also no potential side-effects to the agents used

16

2 Literature Review

In this section literature on the following areas will be discussed

bull Real-time flow measurements

bull Performing MRI during exercise

bull Assessment of hemodynamic response using MRI

21 Real-time Flow Measurements

Real-time flow measurements have been achieved through the use of efficient

trajectories (eg EPI and spirals) and more recently through the use of parallel

imaging

211 Efficient trajectories

The use of spiral trajectories to measure flow volumes in real-time was first

investigated by Gatehouse et al in 1994 (5) In this study a single shot spiral with 32

cycles was used giving a readout time of 40ms (and TETR of 6ms50ms per

encoding) Sixteen PC frames were acquired over two cardiac cycles in the first

cycle 16 phase-compensated data sets were acquired and in the second cycle 16

phase encoded data sets were acquired This allowed an effective temporal

resolution of 20 framessec Gatehouse performed an in-vitro experiment on a steady

flow phantom to measure through-plane and in-plane flow The results from the

spiral sequence were compared to those obtained using a conventional sequence

and also against the ldquobucket and stopwatchrdquo technique A good correlation was seen

between the techniques used (see Figure 7)

17

Figure 7 Results from Gatehouse (5) showing correlation between ldquobucket and stopwatchrdquo method and MR techniques (both a conventional gated sequence and their RT-spiral sequence) for both a) through-plane and b) in-plane flow

Gatehouse also performed an in-vivo

experiment measuring the flow in

the descending aorta in normal

volunteers where the spiral

sequence was found to detect a

lower velocity than the conventional

sequence (see Figure 8) This is

thought to be due to the lower spatial resolution of the spiral scan causing greater

partial volume effects (see section 122)

In 2000 Nayak et al (28) extended the work by Gatehouse to use rapid interleaved

spiral trajectories with a water-selective spectral-spatial excitation pulse (duration

7ms) to avoid blurring from off-resonant fat signals Nayak interleaved the PC

readouts to maintain temporal coherence so that each interleave was acquired once

with flow compensated gradients and once with flow encoding gradients before the

next interleave was acquired This meant that ECG-gating was not required In this

study 3 spiral interleaves (each with 16ms duration) were used with the following

parameters TR 30 ms flip angle 30deg VENC 242 cmsec FOV 20cm Nayak

further increased the effective temporal resolution of his sequence by the use of a

a) b)

Figure 8 In-vivo result comparing conventional MR sequence to Gatehouses (5) RT-spiral sequence

18

sliding window reconstruction This allowed an effective temporal resolution of ~6

imagessec with a spatial resolution of 24x24 mm

Nayak showed a good correlation (within 5)

between a reference PC sequence and the

spiral flow sequence in a constant flow

phantom with through-plane and in-plane

measurements (see Figure 9) Experiments

in a pulsatile flow pump showed that the

spiral sequence was able to accurately

capture the shape and peak of the velocity

waveform compared to results obtained from

continuous-wave Doppler ultrasound Nayak

also showed the use of this sequence in-vivo (with no validation) to observe aortic

and mitral regurgitation in-plane flow through the carotid bifurcation in-plane flow

through the iliac aorta bifurcation through-plane flow in the popliteal artery during

systole and through-plane flow in the coronaries during diastole Nayak discusses the

need for greater temporal resolution and better visualization of fast flow which could

be improved through shorter excitations and shorter readout gradients

Other non-spiral trajectories have been used for real-time flow imaging Klein et al

(29) have used a fast EPI-PC sequence to achieve a temporal resolution of ~83

framessec with a spatial resolution of ~47x24mm (depending on the subject) Klein

compared vessel diameter and velocity measurements between the fast EPI-PC

sequence and a standard PC sequence in large and medium sized vessels (with

diameters ~20-55mm and ~6-13mm respectively) as shown in Table 1

Figure 9 Correlation between a reference sequence and the RT spiral sequence used by Nayak (25) in a steady flow phantom

19

Table 1 Flow volume and velocity results from Klein (29) showing comparison of a standard sequence to their RT-EPI sequence in different size vessels

A good agreement was found in the measured size of the vessel diameter from the

fast EPI-PC sequence and the standard PC sequence for both large and medium

size vessels However a good agreement the peak velocity and flow volumes

measured from the two techniques was only found in the large vessels (see Table 1)

This demonstrates well the need for acceptable spatial resolution to prevent partial

volume effects (see section 122)


Further increases in temporal resolution have been achieved through the use of

parallel-imaging including SENSE (see section112) One such study (which does

not acquire data in real-time however uses retrospective gating to achieve higher

temporal resolution) was carried out in 2003 by Beerbaum et al (30) Beerbaum

studied rapid left-to-right shunt quantification in 25 children by combining a standard

gated Cartesian PC-sequence with SENSE SENSE acceleration factors of 2 and 3

were investigated allowing scan-time to be reduced to 28 and 19 of the standard

PC-MRI protocol respectively These reductions are not as expected as the standard

PC-MRI has a 70 rectangular FOV with 2 signal averages whereas the SENSE

PC-MRI sequences have a 100 rectangular FOV with only 1 signal average The

spatial resolution achieved in this study was111309423x31mm2 with an effective temporal

resolution of ~20-25 framescycle

20

Beerbaum demonstrated a good correlation in a pulsatile flow pump between the

ldquobucket and stopwatchrdquo method and both the SENSEx2 (r=0999) and SENSEx3 (r=

0999) In-vivo a negligible difference (of plusmn3) was found between the standard PC

sequence and the undersampled sequences for the QpQs ratio in the pulmonary

artery This can be seen in Figure 10 where the results are shown from SENSEx2

Figure 10 Comparison of flow volumes in the aorta and Bland Altman analysis as measured by a standard PC sequence and an accelerated SENSEx2 sequence as found by Beerbaum (30)

Beerbaum extended this study in 2005 to measure flow in 13 healthy adult

volunteers using this technique (31) Beerbaum discusses the drawbacks of this

technique which include the need for a 1-minute scan at the beginning of the

examination to calculate the coil sensitivities (see section 112) Also a large FOV

was necessary to enable the SENSE reconstruction to perform correctly which

meant a reduction in the spatial resolution

In 2004 Nezafat et al (32) describe a real-time (non-gated) autocalibrated SENSE

method which removed the need for an additional scan to calculate coil sensitivities

Nezafat used an undersampled spiral sequence where adaptive coil sensitivities

(which can track changes from respiratory motion) were calculated from a full

unaliased images (see section 112) Nezafat used this method to measure flow in

the ascending aorta of healthy volunteers using the following parameters

21

TETR=23152 ms VENC =150 cms flip angle =30o FOV=340mm BW= 125kHz

interleaves = 8 with SENSE acceleration=4 This allowed a spatial resolution of

27x27mm2 and a temporal resolution of 608ms (~165 framessec) to be achieved

The paper does not show any validation of the sequence in-vivo but states that ldquoThe

blood velocity measured with the real-time was compared with the [standard] gated

sequence and showed excellent agreement [with the spiral-SENSE sequence] with a

slight underestimation of the peak blood flow due to averaging of blood flow through

the cardiac phaserdquo (32)

Koperich et al (33) developed a real-time single-shot EPI sequence accelerated with

SENSE to provide high spatial and temporal resolution PC-MRI In this study a matrix

size of 112x128 with a FOV of 300x340mm allowed a spatial resolution of

27x27mm2 A SENSE factor of 4 combined with half-fourier technique allowed a

reduced the number of k-space lines per TR to 19 This allowed a temporal resolution

of 39ms to be achieved (~25 imagessec) for a VENC of 200cms In this study a

separate 1min scan was performed to calculate the coil sensitivities Koperich

validated the real-time EPI-PC sequence using a pulsatile flow phantom by

comparison of flow volumes with the ldquobucket and stopwatchrdquo method A good

correlation was found (r=0999) with a moderate overestimation (y=126x+003) and

relative differences of 128-281 (Plt0006) In-vivo experiments were carried out in

14 patients with cardiac left-to-right shunt The mean QpQs ratios determined by

conventional PC-MRI was 191plusmn064 (range 117-333) and by and real-time PC-MRI

was 194plusmn068 (range 105-317) Bland-Altman analysis showed a bias of 103 (with

limits of agreement from 089 to118) in the PA and a bias of 102 (with limits of

agreement from 087-119) in the aorta

22

22 Performing MRI during exercise

Most studies investing the response to exercise with MRI use supine ergometers as

it is not possible for subjects to be upright within normal scanners The first studies to

measure response to exercise using MRI required ECG gating in order to achieve

suitable temporal resolution In these studies the subjects were often required to

suspend exercise in order to perform MRI measurements This is non-physiological

as cardiac dynamics change rapidly after exercise (34) Suspension of exercise also

makes ramped exercise protocols difficult to perform

221 Imaging During Suspension of Exercise

The first study of exercise using MRI was described in 1995 by Mohiaddin et al (35)

This study uses the single-shot spiral PC-technique developed by Gatehouse (5)

described in section 211 with the addition of a section-selective excitation Imaging

was performed at rest and immediately after exercise in 10 healthy volunteers in the

descending thoracic aorta at the mid-ventricular level Low spatial resolution was

achieved (~5x5mm2) as a 30cm FOV with matrix of 64x64 was used However an

effective temporal resolution of ~50ms was achieved (by acquiring the flow

compensated and flow encoded data in separate heart cycles) Mohiaddin observed

the expected hemodynamic changes an increase in the mean and peak aortic flow

and a decrease in the time to peak aortic flow as seen in Table 2

Table 2 Hemodynamic response to exercise observed by Mohiaddin (35)

23

In 1999 Pederson et al (36) used a segmented EPI technique to perform ECG-

gated PC-imaging in a single breath-hold immediately after stopping exercise Nine

healthy volunteers were imaged at rest and at four exercise levels (33W 65W 98W

and 131W) where imaging lasted 12 cardiac cycles Even after suspension of

exercise at 131W two measurements failed and two other measurements skipped 1-

2 heart beats due to triggering problems They claim that the heart rate in the

subjects decreased less than 4 during the first six heart beats and less than 13

after the first 12 heart beats making scanning directly post-exercise representative of

controlled exercise levels They observed that retrograde flow patterns in the

abdominal aorta are reduced with increasing levels of exercise as seen in Table 3

Table 3 Hemodynamic response to exercise as observed by Pederson (36)

Pederson et al (37) have also used this technique to measure the flow in the

Superior Vena Cava (SVC) and in the left and right pulmonary arteries of 11 patients

with total cavopulmonary connection (TCPC)

222 Imaging During Continuation of Exercise

More accurate hemodynamic responses are obtained when MRI imaging can be

performed during the continuation of exercise ndash this also allows ramped protocols As

previously discussed ECG gating is generally unreliable during exercise due to

excessive motion however some studies have used ECG gated sequences to

measure flow during the continuation of exercise

24

In 1996 Niezen et al (38) performed PC-GRE imaging during exercise in 16 healthy

volunteers using retrospective gating from a peripheral pulse unit attached to one of

the fingers Acquisition time for flow measurement in the aorta and pulmonary aorta

were about 2-3 minutes (depending on the heart rate) They claim that ldquowith the

peripheral gating device used in the present study heart rate measurements were

adequate in all subjects Tests performed in a small number of volunteers using

standard ECG gating during exercise yielded an ECG signal too distorted to

guarantee reliable flow measurementsrdquo Gating data during continuation of exercise

would be expected to give many image artifacts due to excessive motion however

Niezen states that ldquoalthough motion artifacts increased with higher workloads image

quality was sufficient to obtain reliable flow measurements during exerciserdquo

In 2003 Hjortdal et al (39) investigated the influence of breathing on real-time flow

in the caval veins and in the aorta at rest and during the continuation of exercise (at

workloads of 05 and 10 Wkg) in 11 patients with TCPC A real-time (non-gated)

segmented-EPI sequence with 08 half-scan factor used 13 readouts to achieve a

temporal resolution between 48-56 ms with spatial resolution of 34x21 mm2 At

each exercise level 120 consecutive PC images were acquired in the Aorta IVC and

SVC and the blood flow and stroke volume were measured over two respiratory

cycles as seen in Table 4

25

This study confirmed that resting Inferior Vena Cava (IVC) flow has marked

respiratory variability in the TCPC circulation It also indicates that the venous return

in the TCPC circulation is influenced by the cardiac output respiration and a

peripheral pump (that acts through muscles surrounding venous capacitance vessels

in the body) The relative contribution of these three mechanisms is thought to

change from rest to exercise states

Table 4 Mean blood flow (Lmin per m2) in total respiratory cycle during inspiration and during expiration as observed by Hjordal (36)

26

223 Upright exercise

Some studies have been

carried out by Cheng et al

(40-42) measuring flow using a

low-field (05T) open-bore MRI

system which allowed upright

exercise

This system was developed in

2003 (40) when it was tested

on one volunteer using an

ECG-gated sequence with

respiratory compensation

during the continuation of

exercise

A study in 10 healthy children was carried out in 2004 using the same ECG-gated

sequence with respiratory compensation which took 2ndash3 min at rest and 1ndash2 min

during exercise Exercise intensity corresponding to a 50 increase in heart rate

caused mean blood flow to increase in the RPA LPA and MPA by 93 97 and

91 respectively with a mean blood flow increase in the SVC of only 36 and in

the IVC of 238

In 2005 an upright exercise study on 17 healthy children and adults (42) was

compared with supine results from Niezen et al (38) (described in section 222)

Cheng observes that with comparable exercise workloads and increases in heart

rate an upright posture produces greater ranges in mean blood flow rate and stroke

volume than a supine posture In the study by Cheng (42) 8 of 51 flow

Figure 11 Photograph of subject within open bore MRI with upright exercise machine used by Cheng (37-39)

27

measurements could not be used due to excessive body and respiratory motion

which caused inadequate image quality

224 Measurement of Ventricle Volume During Exercise

Previous studies by Roest et al (4344) have measured left ventricular volumes after

suspension of exercise using a prospectively gated breath-hold EPI sequence

A study by Lurz et al carried out at the Institute of Child Health (ICH) (45) measured

left ventricular volume in 12 healthy volunteers during continuation of exercise using

a real-time (non-gated) radial sequence which was accelerated (by a factor of 8)

using kt-SENSE In each frame 16 radial projections were acquired The sampling

pattern was rotated in subsequent frames so that 8 consecutive frames comprised a

fully sampled k-space This allowed temporal resolution of 35ms to be achieved with

a spatial resolution of 30x30mm2 Eleven to 13 contiguous slices were acquired

consecutively in the short axis to cover the entire ventricle This sequence has

previously been validated at rest (46)

In this study Lurz observed that stroke volume increased with exercise due to a

significant decrease in biventricular end systolic volume (ESV) and no change in end

diastolic volumes (EDV) in the left or right ventricles

23 Assessment of hemodynamic response using MRI

In the pulmonary vasculature MR flow measurements have been combined with

invasive pressure measurements to calculate vascular resistance (47) and

compliance (48)

Muthurangu et al (47) measured pulmonary vascular resistance (PVR) in 24

subjects by combining MRI flow measurements with simultaneous invasive pressure

measurements The PVR measurements derived from MR were compared to those

28

derived from the Fick method at baseline at 30 oxygen + 20ppm NO and at 100

oxygen + 20ppm NO A summary of their results is shown in Table 5

Table 5 Comparison of SVR measurements from the Fick method and PC-MRI as found by Muthurangu et al (47)

Muthurangu et al showed reasonable agreement between Fick and MRIndashderived

PVR at baseline (see Table 5 and Figure 12) however in the presence of NO there

was less agreement between the methods and with 100 oxygen there was a large

bias It was believed that these errors were from inaccuracies in the Fick method

rather than the MR as Fick is known to be inaccurate in the presence of high blood

flow and high concentrations of oxygen (47)

Figure 12 Comparison of PVR measured by Fick method and by MRI at baseline conditions as observed by Muthurangu (47)

Bland Altman Analysis () PVR Fick (WUm2)

PVR PC-MRI (WUm2)

Correlation coefficient Bias Lower

limit Upper limit

Baseline 47plusmn46 46plusmn35 091 (Plt005)

23 455 502

30 oxygen + 20ppm NO

33plusmn32 37plusmn21 078 (Plt005)

280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29

Kuehne et al (49) and Sanz et al (50) have also measured PVR in patients with

pulmonary hypertension using the same technique as Muthurangu These studies

also show good correlation between PC flow volumes and alternative volume

measurements for the measurement of PVR however in these studies they are

unable to perform simultaneous invasive blood pressure measurements (instead the

blood pressure was measured directly before the subject was moved into the MR)

Muthurangu et al (48) have measured vascular compliance in 17 subjects using the

two-element Windkessel model (discussed in section13) by combining PC-MRI

measurements with simultaneous invasive blood pressure data The equation

defining the windkessel model is

euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13

where P is pressure R is vascular resistance C is compliance and Q is measured

flow curve over time (t) In this study a series of modeled pressure curves (P) were

generated using values of C between 0001 and 70 mlmmHg Compliance was

taken to be the value that produced the best match with the actual pulse pressure

See (48) for further details

Compliance measured with the pulse pressure method (Cppm) was correlated with

that calculated from the stroke volume (Csv) at 30 O2 and at 30 O2 + 20ppm NO

A summary of the results can be seen in Table 6 and Figure 13

30

Table 6 Comparison of compliance measurements from the stroke volume method and the pulse pressure method using PC-MRI as found by Muthurangu et al (48)

In all cases there was a significant difference between mean Cppm and Csv (P lt

005)

Figure 13 Comparison of Csv and Cpp as measured by Muthurnagu (48)

Lankhaar et al (51) has extended the technique used by Muthuragu et al by using

the three-element windkessel model to measure resistance compliance and

characteristic impedance by combining invasive blood pressure measurements with

MRI flow measurements

Bland Altman Analysis () Csv Cppm Relationship Correlation coefficient

Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85

Overall - - Csv = 185Cppm+ 004

098 (Plt0001)

61 38 84

31

From the literature review it can be seen that

bull Spiral trajectories have previously been combined with phase contrast

techniques used to successfully measure flow in MRI

bull Data undersampling and SENSE reconstructions have been successfully used

to measure flow in real-time

bull A few previous studies have been able to measure flow-volume response

during exercise using MRI however many of these studies do not acquire data

in real-time

bull A few previous studies have combined MRI flow measurements with invasive

blood pressure measurement in order to quantify pulmonary vascular

resistance and compliance

In this study a real-time flow sequence will be developed using an undersampled

spiral trajectory which is reconstructed using a SENSE algorithm This will be used

to measure flow-volume response to exercise and these results combined with non-

invasive blood pressure measurements to quantify pulmonary vascular resistance

and compliance in the Aorta

32

3 REAL-TIME FLOW MEASUREMENTS FOR THE

ASSESSMENT OF HEMODYNAMIC RESPONSE TO

EXERCISE

The aims of this study were to

bull Develop an in-house real-time flow sequence and online reconstruction

bull Validate this sequence in a flow phantom

bull Validate this sequence in-vivo at rest and during exercise

bull Demonstrate the feasibility of using this sequence to measure the

hemodynamic response to exercise

31 Development of Real-Time Flow Sequence

As described in section 11 real-time imaging in this study was achieved by the use

of efficient spiral trajectories and undersampling of data The spiral trajectories were

designed using adapted code developed by Brain Hargreaves (52) This takes into

account the FOV number of interleaves maximum slew rate maximum gradient

amplitude sampling period and k-space radius required

The sequence developed uses a standard PC technique (12) to measure through-

plane flow The PC readouts were interleaved to maintain temporal coherence so

that each spiral interleave was acquired once with flow compensated gradients and

once with flow encoding gradients before the next spiral interleave was acquired

The resulting flow data was formed by subtraction of the phase information from the

33

two images A sequence diagram can be seen in Figure 14 for one pair of spiral

readouts

Figure 14 A sequence diagram for one pair of spiral interleaves for the PC-spiral sequence developed

In spiral imaging it is necessary to keep the readout times relatively short to ensure

signal throughout the entire readout and to reduce cumulative trajectory errors

(which may lead to image rotation or blurring) The length of the readout train

regardless of matrix size can be altered by the number of spiral interleaves used

However the overall scan time is increased when using multiple interleaves as

multiple excitations (and flow gradients) are also required Therefore there is a trade

off between the overall scan time and the resultant image quality

In parallel imaging there is also a trade-off between the undersampling factor used

and the resultant image quality The greater the undersampling the lower the

resultant SNR

Flow compensated gradients

Flow encoded gradients

Flow compensated readout

Flow encoded readout

34

euro

SNRSENSE =SNRNORMAL

g R Equation 14

where g is the lsquogeometry factorrsquo which determines how independent the coils used

are and R is the acceleration factor When undersampling a spiral data set the un-

accelerated number of interleaves must be exactly divisible by the acceleration factor

used In this study a trade-off was reached to achieve the desired temporal resolution

while maintaining acceptable image quality A good compromise was achieved with

the use of eight spiral interleaves undersampled by a factor of four ndash this means that

only two spiral interleaves were acquired per frame The sampling pattern was

rotated for each frame so that four consecutive PC frames comprised a fully sampled

k-space with eight interleaves as seen in Figure 15

Frame 1

Interleave 1 Interleave 5

Frame 2


Figure 15 SENSE reconstruction with 8 spiral interleaves accelerated by a factor of 4 Each interleaf is acquired twice (once with flow compensation and one with flow encoding) Two interleaves are used with SENSE to make one reconstructedframe The sampling pattern is then rotated so that four consecutive frames constitute one fully sampled data set

35

This undersampled data was reconstructed online using an iterative SENSE

algorithm (see section 112) All coil sensitivity and regularization information

required for the reconstruction process was calculated from the sum-of-squares of all

coil data over all time frames (as described in section112)

311 Maxwell Correction

The effect of the concomitant field (see section 123) is small (52 ppm at 15 T with a

gradient amplitude of 10mTm and a 20-cm distance from isocenter) and is thus

largely neglected in most imaging situations (18) However in this study we are using

a low-field system (15T) with a high amplitude gradient system (40mTm) and for this

application are generally interested in performing imaging off-centre Therefore

concomitant magnetic fields were observed to be important in the resultant phase

contrast images from the developed sequence (see Table 7) Maxwell correction was

performed to remove the effects of concomitant gradients originating from the flow

encoding gradients (18) (see section 123) as seen in Table 7

36

Without Maxwell Correction

Maxwell Correction With Maxwell Correction

Scale

Transverse (isocentre)

Sagital (isocentre)

Coronal (isocentre)

Double oblique

Table 7 Effects of concomitant gradients observed on a stationary phantom on phase images from the undersampled PC-spiral sequence The scale is shown in values of radians where plusmnπ gives a phase shift of plusmnVENC

No additional Maxwell correction was carried out for the spiral readout gradients (19)

37

312 Residual Phase Offsets

When investigating the effects of concomitant gradient correction on double oblique

orientations it was seen that Maxwell correction did not entirely remove the

background phase offsets (see Table 7) However it was observed that if the TE time

(ie the time between the end of the flow encoding gradients and the beginning of the

readout) was increased (see Table 8a) or the slew rate of the flow encoding

gradients was decreased (and the TE was minimized see Table 8b) the phase

offsets were reduced These observations imply that the phase offsets are a result of

residual eddy currents from the flow compensationflow encoding gradients This has

been commonly noted previously (see section 124)

To reduce these background offsets a similar principle to Walker (23) was used (see

section 124) where stationary tissue was identified by the intensity of the pixels in

an average magnitude image (over all time frames) and also by the standard

deviation of the pixels in the phase image The residual phase was observed to be

predominantly linear (with some higher order terms ndash see Figure 16) and did not

change significantly over an in-vivo time series A quadratic surface

(Ax2+By2+Cxy+Dx+Ey+F) (2124) was then fitted through the stationary pixels (in a

time averaged phase image) using a Cholesky decomposition algorithm This

surface was then subtracted from each of the phase images to correct for residual

background phase errors (see Table 9)

Figure 16 3D plot of stationary pixels found in phantom showing residual phase to be predominantly linear with some higher order terms

38

Table 8 Effect on the residual background phase observed in a stationary phantom of altering the minimum TE and b) altering the slew rate For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)

39

Table 9 Calculation of quadratic surface to estimate residual background phase offsets For the scale shown plusmn2046 represents a phase shift of plusmnVENC (which was set to 150cms)

i

CONTENTS

1 INTRODUCTION 1 11 Achieving Real‐time Imaging 2 111 Alternative trajectories 3 112 Parallel Imaging 5

12 Measuring Flow with MRI 7 121 Implementation of Phase Contrast Imaging 8 122 Accuracy of PC‐MRI 9 123 Concomitant Gradients in Flow Imaging 11 124 Additional Phase Offsets 13

13 Exercise Testing 14

2 LITERATURE REVIEW 16 21 Real‐time Flow Measurements 16 211 Efficient trajectories 16 212 Parallel Imaging 19

22 Performing MRI during exercise 22 221 Imaging During Suspension of Exercise 22 222 Imaging During Continuation of Exercise 23 223 Upright exercise 26 224 Measurement of Ventricle Volume During Exercise 27

23 Assessment of hemodynamic response using MRI 27

3 REALshyTIME FLOW MEASUREMENTS FOR THE ASSESSMENT OF HEMODYNAMIC

RESPONSE TO EXERCISE 32 31 Development of Real‐Time Flow Sequence 32 311 Maxwell Correction 35 312 Residual Phase Offsets 37

32 Methods 40 321 Study Population 40 322 Exercise Protocol 40 323 MR Protocol 41 3231 Standard flow assessment 42 3232 Real‐time flow assessment 42 3233 Real‐time volume assessment 43

324 Validation Experiments 43 3241 Flow Pump Validation 44 3242 In‐vivo Validation 44

ii












42 Time Scale 81

REFERENCES 83

1

1 INTRODUCTION






its use

















2


















bottom of k-space)



k-space)





3






















domain





4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


ii












42 Time Scale 81

REFERENCES 83

1

1 INTRODUCTION






its use

















2


















bottom of k-space)



k-space)





3






















domain





4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


1

1 INTRODUCTION






its use

















2


















bottom of k-space)



k-space)





3






















domain





4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


2


















bottom of k-space)



k-space)





3






















domain





4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


3






















domain





4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


4












euro


euro

λ =N int

D Equation 2

where

euro


euro


euro

N int is the


euro




euro

2π N int radians

a) b) c)

5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


5
















a) b) c) d)

6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


6


























7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


7









euro


where

euro


euro



euro


euro



euro


t

int

Equation 4

8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


8




euro

φ(t) = γ M0x0 + M1v0 + + 1nMn

dnxdt 2

t= 0

+

Equation 5


euro

x0 and

euro






















9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


9






euro










euro

ΔM1

euro



euro

VENC =π

γΔM1 Equation 8








10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


10





chosen VENC







plane flow















11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


11


















flow (17)







12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


12




euro

Bc xyzt( ) =12B0

Gx2z2 +Gy

2z2 +Gz2 x 2 + y 2


Equation 9


euro




euro


Equation 11

where

euro

A =γ2B0

Gx2(t) +Gy


2(t)( ) fe2 dtint

B =γ8B0

Gz2(t) fe1 minusGz

2(t) fe2 dtint

C = minusγ2B0


D = minusγ2B0


Equation 12








13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


13






















14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


14

13 Exercise Testing

























15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


15






16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


16

2 Literature Review








imaging













17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


17




















a) b)


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


18


























19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


19





















20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


20



















21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


21

























22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


22





















23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


23





















24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


24




















25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


25








26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


26







exercise







exercise






the IVC of 238







27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


27





















compliance (48)




28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


28












PVR PC-MRI (WUm2)


limit Upper limit


23 455 502



280 953 1513


24plusmn23 30plusmn19 059 (P=002)

542 660 1744

29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


29











euro

˙ Q (t) =P(t)

R+ C dP(t)

dt Equation 13









30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


30



005)







Bias Lower limit

Upper limit

30 O2

187 (128)

099 (068)

Csv = 186Cppm+ 002

099 (Plt0001)

61 38 84

30 O2 + 20ppm NO

201 (099)

106 (058)

Csv = 183Cppm+ 007

097 (Plt0001)

61 37 85


098 (Plt0001)

61 38 84

31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


31








in real-time









32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


32



EXERCISE


















33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


33


readouts











resultant SNR





34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


34

euro

SNRSENSE =SNRNORMAL

g R Equation 14










Frame 1


Frame 2



35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


35















36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


36



Scale


Sagital (isocentre)

Coronal (isocentre)

Double oblique



37






















38


39


37






















38


39


38


39


39


real-time imaging for cardiac flow measurements€¦ · 3.3 results 46 3.3.1 image quality 46 3.3.2...

Documents