Developing a New Method for MRI Triggering Using Doppler Ultrasound

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IN

DEGREE PROJECT MEDICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2019,

Developing a new method for MRI triggering using Doppler

Ultrasound

USAMA GAZAY

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH

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Abstract

Purpose: Magnetic Resonance Imaging (MRI) is a medical imaging technique used in radiology to produce high quality images of the anatomy and the physiological processes of the body. Cardiac gating is a triggering system used for the MRI scanner to synchronize the MRI scanner with the cardiac cycle of the patient while imaging. When applying cardiac gating, artifacts that results from small movement in the heart and blood flow are neglected. Re- cent MRI scanners uses Electrocardiogram (ECG) as a cardiac gating method, but with higher magnetic field strength the ECG signal get distorted. In this thesis DUS signal will be examined as a replacement cardiac gating method for the MRI scanner. In theory the DUS signal should not be affected by the high magnetic field strength.

Methods: Different sets of data were collected from three different subjects.

The data contain a synchronized ECG and DUS signal without the effect of the MRI magnetic field. A Filtering and peak detection algorithm were developed in MATLAB to process the DUS signal and the result was compared to the ECG signal as a reference method.

Results: The filtering algorithm showed good results in terms of being able to increase the signal to noise ration (SNR) of the signal to enable the processing phase. The peak detection algorithm was able to detect the peaks in the different data sets with low false positive (19 out of 24 data sets had lower FP errors then 10%) and false negative errors (17 out of 24 data sets had lower FN errors then 10%). Some data sets had low SNR even after the filtering phase, peak detection on those data sets were not functioning prop- erly. When comparing the DUS signal to the ECG signal, an average delay was detected to be around 0.26 seconds for the forward signal and around 0.5 seconds for the backward signal.

Conclusion: The DUS signal shows promising results to be able to be used as a cardiac gating method for the MRI scanner.

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Chapter 1 Introduction

Magnetic Resonance Imaging (MRI) is a medical imaging technique used in radiology to produce high quality images of the anatomy and the physiological processes of the body [1]. MRI uses a strong magnetic field and radio waves to generate images of the body. More in detail, MRI uses the fact that the body consists of roughly 70% water. Water molecules contain hydrogen atoms, and when the hydrogen atoms get exposed to high magnetic field the hydrogen atoms become aligned with the magnetic field of the MRI scanner (the protons magnetic field precess around the Z axis). To be able to detect the magnetic field of the hydrogen atoms, a radio wave is sent to flip the spins of the hydrogen atoms to precess around the X and Y axis. When the radio wave is turned off, the atoms gradually return to their normal spin.

The flip and return process produces an echo in a form of a radio signal that can be measured by receivers in the scanner and made into an image [2].

To construct the final image several echoes needs to be taken by the MRI scanner.

When using MRI the body movement needs to be limited as much as possible to increase the quality of the image. Since one image needs several echoes, all echoes that are needed to construct an image should be taken while the body is in the same position in each sequence. But there are some body movements that can not be eliminated such as the heart beat, breathing and blood flow. Therefore a triggering system needs to be used to synchronise the MRI imaging sequences with the cardiac cycle. This is to ensure that each echo of the MRI is taken with as little as possible body movement compared to the next echo [3].

Recent MRI scanners use Electrocardiogram (ECG) to synchronise the sampling sequence of the MRI scanner. However, ECG signals are distorted

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2 CHAPTER 1. INTRODUCTION

during MRI scans due to the Magnetohydrodynamic (MHD) effect, radio frequency pulses and fast-switching magnetic field gradients [4]. To avoid this problem several techniques have been tested that are in theory not affected by the MHD effect, such as Pulse Oximetry (POX), acoustic gating and Doppler Ultrasound (DUS) [5]. POX is the easiest and cheapest method to implement but in theory the acquired POX signal will have a delay compared to the ECG signal. This delay is caused by the nature of the POX signal which is taken normally from the finger of the patient. Since the pressure has to flow from the heart to the finger before a signal is generated, a delay in the POX signal will occur. This delay makes the POX method unreliable.

Acoustic gating is a method that uses phonocardiography to determine the cardiac cycle. This method is a promising method for cardiac gating but since we do not have access to any acoustic gating device in Lund’s research facilities any research on this field could not be done in this thesis.

DUS has been used in several MRI applications for motion and organ tracking and has shown promising results [6]. In a recent study, DUS has been used as cardiac gating method for MRI. The result of that research showed that the DUS setup needs further improvements in the algorithm of the signal filtering and peak detection [7]. Hence, the aim of this work was to examine the performance of DUS as a triggering method for the MRI scanner. To compare the results the performance of the DUS signal will be compared to the ECG signal as a reference method. This is because in the current MRI scanners, ECG is the method that is used for cardiac gating.

1.1 Research question

In this thesis I will examine the usage of DUS signals to replace the ECG signals as a trigger for the MRI scanner.

Specifically:

• Data gathering: A synchronized DUS- and ECG signals will be acquired from different subjects without the effect of the MRI magnetic field.

• Data processing The synchronized signal will be processed and ana- lyzed using MATLAB.

– A filtering algorithm will be developed to increase the SNR of the signal.

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CHAPTER 1. INTRODUCTION 3

– A peak detection algorithm will be developed to detect the peaks in the signal.

• Evaluate the results The result of the DUS signal will be compared to the ECG signal as a reference signal. The evaluation will be in terms of; delay, jitter, false positive- and false negative errors.

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Chapter 2 Methods

This section is divided into four parts; hardware setup, data collection, software setup and evaluation of results. The hardware setup section describes the hardware device that is used to collect the data for this study. The data collection section describes the different data that is included in this study.

The software setup section describes the software algorithm that is used to process the ECG and DUS signals. Finally, the evaluation of results describes how the results are being evaluated in terms of comparing the DUS signal to ECG signal as a reference.

2.1 Hardware setup

To acquire data for this thesis, a commercial DUS device with synchronized ECG was used provided from Northh Medical (Hamburg, Germany). The device have a built in ECG device that gives analog output ECG signal. The DUS signal is acquired by sending an ultrasound signal of 1 MHz towards the heart of the volunteer. The reflected signal will have a shift in the frequency being slightly larger or slightly lower then the transmitted frequency. The frequency shift corresponds to the motion of the measured tissue. The output DUS signal is a complex signal that have two parts the real partI (in-phase) and the imaginary partQ (quadrature).

2.2 Data collection

The data that were used in this thesis are taken from three different subjects and are acquired without the effect of the MRI magnetic field. DUS signal

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CHAPTER 2. METHODS 5

is acquired from two different locations in the chest area for each subject.

Two different DUS data collection were preformed from each location; 60 seconds free breathing, and 15 second breath hold. In each measurement two different DUS signals were measured, one to represent the heart wall motion caused by the contraction and relaxation phases of the heart and the second to represent the blood flow in the aorta caused by the blood pumping function of the heart. This results in 24 different data sets to study. All data are acquired by the same device.

2.3 Software setup

In order to get an interpretable signal, the noise must be extracted from the signal and the desired signal must be amplified. This was done to obtain a high signal-to-noise ratio (SNR) which thus facilitates the analysis of the signal. For this reason, a filtering algorithm was developed for the acquired DUS signals.

When the signal was interpreted, a peak detection algorithm was imple- mented on the filtered signal. The result of the peak detection algorithm was compared to the ECG peak detection method as a reference. Both the filtering algorithm and the peak detection algorithm were developed using MATLAB 2018b (The MathWorks Inc, Natick, United States).

2.3.1 Filtering of the Doppler Ultrasound signal

The method of the filtering algorithm of the DUS signal is described in the following steps:

1. A Low-pass filter at 4 kHz was applied: To be able to resample the signal it is important to implement a low-pass filter before the resampling step to eliminate aliasing in the signal.

2. Resampling the signal from 16 kHz to 4 kHz: The filtering algorithm started with a resampling step from 16 kHz to 4 kHz. This was done to minimize the size of data in the signal. Large unused data will slow the algorithm, and since the signal is used to acquire information about the cardiac cycle which can be at maximum 220 pulses in a minute 4 kHz sampling rate is enough. Therefore all data that have high frequency will not have any information about the heart rate of the patient.

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6 CHAPTER 2. METHODS

3. The Q and I signals are added together: After the resampling step the Q and I DUS signals were added together, where I was the real part and Q the imaginary part of the signal described in the formula,

Signal = I + iQ.

4. A complex band-pass filter was applied: The complex band-pass filter (as described in the appendix) was applied to generate the forward DUS signal and the backward DUS signal.

5. A final low-pass filter at 100 Hz was applied: Finally, a low-pass filter was applied for both signals to filter the unwanted high frequency in the forward and backward signals. The cutoff frequency of the final low-pass filter was 100 Hz. This was chosen since it is known that the data that acquire information about the heart rate does not have higher frequency then 4-5 Hz because of the limitation of the heart pumping rate.

2.3.2 Peak detection algorithm

The peak detection algorithm was developed in such a way to mimic a real time situation, because in a real situation the algorithm does not have access to all the data as it does now. In a real situation, the DUS data are being gathered in the same time as the MRI scanner is running. The algorithm is build so it in theory could work for a real situation purpose. This is done by having 5 seconds of data to treat at each time and adding new data in a for loop. The construction of the peak detection algorithm is described in the following steps:

1. Creating a buffer that holds 5 seconds of DUS data at a time.

2. Creating a for loop that adds 1 second of DUS data to the end of the buffer every time until it reaches the end of the DUS signal.

3. Data removal When new DUS data are added old DUS data are re- moved from the beginning of the buffer.

4. Peak detection implementation For each for loop a peak detection is applied on the buffer to find the peaks in the 5 second buffer signal.

5. Saving the peaks The peaks found in the buffer are added to a final matrix that holds all the peaks in the DUS signal.

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CHAPTER 2. METHODS 7

6. Presentation of all peaks When the peak detection algorithm has treated all the signal. The algorithm presents all the the peaks on the plotted DUS signal and the plotted ECG reference signal.

2.4 Evaluation of results

The results of the peak detection algorithm for the DUS signal was compared to the algorithm applied for the ECG signal. The algorithm was compared in terms of; delay, accuracy , jitter and false positive/false negative.

2.4.1 Delay and jitter

The delay in the DUS signal was measured by comparing the position of the peaks in the DUS signal compared to their position in the reference ECG signal. The jitter effect in the DUS signal was measured by taking standard deviation of the time for each cardiac cycle (time from peak to peak) in the DUS signal. The jitter effect in the DUS signal will be compared to the jitter effect in the ECG signal. To have a better understanding of this have a look at Figure 2.1.

Figure 2.1: The ECG signal and the DUS signal with marked peaks, where the blue signal is the ECG signal and the red signal is the DUS signal. Delay is taken by comparing the position of each peak in the DUS signal compared to its location at the ECG signal. Jitter is measured by taking the standard deviation of the peak to peak time in the DUS signal

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8 CHAPTER 2. METHODS

2.4.2 False positive and false negative

False positive (FP) errors were measured by counting the number of times the peak algorithm shows a peak in the DUS signal when there were no peak in that location of the ECGsignal. False negative (FN) errors were measured by counting the number of times the peak algorithm does not show a peak in the DUS signal when there were a peak present in the ECG signal.

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Chapter 3 Results

3.1 Results from the filtering algorithm

The signal is presented after each step in the filtering algorithm. Figure 3.1 shows the raw Q and I signals. Figure 3.2 shows the signal after it being resampled and added as a complex signal. Finally Figure 3.3 and Figure 3.4 shows the signals after the last step, the complex band pass filter. The filtering algorithm divides the signal into two different signals, one to represent the forward DUS signal in Figure 3.3 and the second to represent the backward DUS signal in Figure 3.4. All of these figures are taken from the first data set of the 24 studied.

Figure 3.1: The raw Q and I DUS signals. The blue signal in the Figure represent the Q DUS signal and the red signal in the Figure represent the I DUS signal

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10 CHAPTER 3. RESULTS

Figure 3.2: The absolute value of the added complex DUS signal

Figure 3.3: The forward DUS signal after the filtering algorithm

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CHAPTER 3. RESULTS 11

Figure 3.4: The backward DUS signal after the filtering algorithm

3.2 Results from the peak detection algorithm

The result of the peak detection algorithm is presented in Figure 3.5 and Fig- ure 3.6. Figure 3.5 represent the forward DUS signal and Figure 3.6 represent the backward DUS signal. Some data sets suffered from low SNR even after the filtering algorithm. Theses data enable FP and FN errors when applying the peak detection algorithm on them. Figure 3.7 and 3.8 shows DUS signals that suffers from low SNR resulting in high FN errors in Figure 3.7 and high FP errors in Figure 3.8.

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Figure 3.5: The forward DUS signal after the filtering and peak detection algorithm

Figure 3.6: The backward DUS signal after the filtering and peak detection algorithm

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Figure 3.7: The forward DUS signal with low SNR which enable high FN errors after the peak detection algorithm

Figure 3.8: The backward DUS signal with low SNR which enable high FP errors after the peak detection algorithm

3.3 Evaluation of the Doppler Ultrasound sig- nal compared to the reference ECG sig- nal

The evaluation of all 24 data sets of the DUS signal is compared with the ECG signal as a reference signal. The comparison in terms of; delay, jitter,

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false positive and false negative is presented in Table 3.1 for the forward DUS signal and Table 3.2 for the backward DUS signal.

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Table 3.1: The evaluation of the forward DUS signal in terms of; delay compared to the ECG signal, jitter effect in the DUS signal and FP and FN errors in the DUS signal

Evaluation of the forward DUS signal

Data sets Delay

(s)

Jitter (s)

Jitter ECG

FP (%) FN (%) SNR

S1 P1 15s Wall 0.318 0.064 0.017 0% 0% 7.1

Blood 0.309 0.053 0.017 0% 0 % 3.3

60s Wall 0.333 0.062 0.031 2% 0% 2.5

Blood 0.356 0.235 0.031 1% 1% 2.1

P2 15s Wall 0.287 0.064 0.017 0% 0% 3.5

Blood - - 0.017 0% 100% 1.3

60s Wall 0.321 0.090 0.044 0% 19% 2.1

Blood - - 0.044 0% 96% 1.5

S2 P1 15s Wall 0.233 0.006 0.007 0% 0% 3.7

Blood - - 0.007 70% 0% 1.6

60s Wall 0.230 0.027 0.023 1% 0% 2.6

Blood 0.300 0.423 0.023 15% 6% 2.1

P2 15s Wall 0.249 0.084 0.011 0% 0% 3.4

Blood 0.267 0.244 0.011 0% 11% 2.3

60s Wall - - - -

Blood 0.320 0.159 0.018 0% 31% 1.9

S3 P1 15s Wall 0.217 0.167 0.015 0% 0% 4.1

Blood - - 0.015 0% 53% 1.7

60s Wall 0.240 0.350 0.039 25% 0% 1.9

Blood 0.230 0.286 0.039 3% 0% 2.9

P2 15s Wall 0.121 0.044 0.013 0% 0% 3.6

Blood 0.235 0.121 0.013 0% 0% 4.1

60s Wall 0.268 0.078 0.078 0% 0% 3.5

Blood 0.210 0.293 0.078 25% 0% 1.9

STD Wall 0.060 0.094 0.020 7.16% 5.48% 1.40

Flow 0.051 0.115 0.020 20.6% 37.8% 0.821

STD (Wall + Flow) 0.045 0.207 0.020 15.8% 29.5% 1.28

Mean Wall 0.256 0.094 0.026 2.33% 1.58% 3.45

Flow 0.278 0.227 0.026 9.5% 24.8% 2.23

Mean (Wall + Flow) 0.266 0.15 0.026 6.45% 13.8% 2.81

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Table 3.2: The evaluation of the backward DUS signal in terms of; delay compared to the ECG signal, jitter effect in the DUS signal and FP and FN errors in the DUS signal

Evaluation of the backward DUS signal

Data sets Delay

(s)

Jitter (s)

Jitter ECG

FP (%) FN (%) SNR

S1 P1 15s Wall 0.532 0.028 0.017 0% 0 % 7.1

Blood 0.554 0.037 0.017 0% 0% 5.3

60s Wall 0.468 0.179 0.031 8% 0% 3.7

Blood 0.452 0.040 0.031 0% 0% 3.5

P2 15s Wall 0.513 0.032 0.017 0% 0% 4.2

Blood 0.509 0.033 0.017 0% 0% 4.6

60s Wall 0.475 0.096 0.044 0% 0% 3.5

Blood 0.512 0.212 0.044 0% 0% 3.7

S2 P1 15s Wall - - 0.007 88% 5% 1.9

Blood 0.502 0.167 0.007 5% 0% 3.2

60s Wall 0.560 0.366 0.023 0% 20% 2.2

Blood - - 0.023 85% 1% 1.4

P2 15s Wall 0.568 0.191 0.011 0% 11% 2.3

Blood 0.579 0.380 0.011 5% 23% 2.1

60s Wall 0.271 0.214 0.018 1% 0% 4.0

Blood - - 0.018 0% 73% 1.5

S3 P1 15s Wall 0.170 - 0.015 0% 45% 1.3

Blood - - 0.015 0% 100% 1.2

60s Wall 0.130 0.577 0.039 0% 14% 2.9

Blood 0.135 0.255 0.039 18% 27% 2.6

P2 15s Wall 0.551 0.278 0.013 20% 0% 2.3

Blood 0.586 0.281 0.013 20% 0% 2.3

60s Wall - - 0.078 77% 1% 1.9

Blood - - 0.078 66% 0% 1.7

STD Wall 0.168 0.174 0.020 31.6% 13.48% 1.56

Flow 0.146 0.133 0.020 28.7% 33.6% 1.32

STD (Wall + Flow) 0.156 0.152 0.020 20.0% 25.5% 1.43

Mean Wall 0.424 0.218 0.026 16.2% 8.00% 3.11

Flow 0.479 0.217 0.026 16.6% 18.7% 2.76

Mean (Wall + Flow) 0.448 0.204 0.026 16.4% 13.3% 2.93

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Chapter 4 Discussion

4.1 Data acquisition

In this thesis 24 data sets have been studied, where all of them differs in appearance. This is due to the fact that those data sets differs from each other in; the position they are taken from (two different positions in the chest area are used), the measured entity (two different functions are measured: heart wall motion and blood flow), and the measurement procedure (two different procedures are measured: 15 sec hold breath and 60 seconds free breathing).

The data acquisition could be improved in the sense of being more consistent in appearance. The acquisition of a good consistent DUS signal requires training when it comes to the positioning of the ultrasound transducer. When comparing the acquired data sets in this thesis, the amplitude of the signal differs from each data sets. This differentiation makes it harder for the peak detection algorithm to process all of those different data sets with different amplitudes. The algorithm needs to be adjusted slightly for each data set to be able to achieve the desired results. To overcome this problem, an automatic amplitude adjustment function needs be added to the algorithm. In this case the algorithm would be able to process different data with different amplitudes.

4.2 The filtering algorithm

The filtering algorithm is functioning as desired when it comes to filtering the noise data from the signal and amplify the needed data in the signal. The- oretically, all the sources of noise are treated and filtered and the algorithm fulfills the function of improving the SNR of the measured DUS signal.

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18 CHAPTER 4. DISCUSSION

Since there are different data sets that have been studied and they differs in appearance from each other, the developed algorithm was developed carefully to be user friendly, so that the parameters of the filtering algorithm could be adjusted easily to suit different types of DUS signals.

4.3 The peak detection algorithm

The peak detection algorithm has shown good results. When the signal is consistent the algorithm has been able to detect all the peaks in the DUS signal compared to the ECG signal as a reference. The biggest challenge for the peak detection algorithm to work was to feed it with a consistent DUS signal that has around the same SNR.

One of the errors observed while gathering the results was that in some signals, some parts have a low SNR which in return make the it impossible for the peak detection algorithm to detect a peak there. It is thought that this error depends on small movements on the ultrasound transducer while ac- quiring the data. Some adjustments in the filtering algorithm may be needed to overcome such errors.

When observing the results in Figure 3.1 and Figure 3.2, it shows that for the majority of the data sets the FP and the FN is 0%. That means that the peak detection algorithm worked perfectly on those data sets. The data sets that have FP and/or FN errors suffers from low SNR on some parts of the signal which enable FP and FN errors. To achieve a 0% FP and/or FN errors the minimum SNR required is more then 3 (see Table 3.1 and Table 3.2).

4.4 Evaluation of the method

When comparing the DUS signal with the ECG signal, a delay in the DUS signal is present as expected. The physiological explanation of this error is that the ECG signals acquire the electrical signals in the heart cells to generate a signal, while DUS acquire the displacement of the blood to generate a signal (see Appendix A.4.1). For the purpose of this thesis, a delay in peaks in the DUS signal compared to the ECG signal is not unacceptable as long as the delay is consistent. In clinical use, the MRI scanner uses a delay after the detection of peaks in the ECG signal, if the DUS signal has a delay compared to the ECG and it is consistent the MRI scanner could be programmed to take account for that consistent delay. However, if the delay is inconsistent it would be unpractical to use a DUS signal that have inconsistent delays

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CHAPTER 4. DISCUSSION 19

since it would affect the MRI scanner timings resulting in artifacts in the MRI images.

The jitter effect in the DUS signal is slightly higher compared to the ECG signal as observed in Table 3.1 and Table 3.2. However, it is believed that it will not have any effect on the MRI scanner. FP and FN errors were not present for the major part of the data sets. although, some data sets suffers from one of those errors. The FN errors were at it maximum in the 18th data set (Subject 3, Pos 1, 60 sec, Blood flow) see Figure 3.7. The FP errors were at it maximum in the 9th data set (Subject 2, Pos 1, 15 sec, Wall motion) see Figure 3.8. The reason behind those errors are discussed in the previous chapter.

4.5 Future work

The result of this research is that the usage of the DUS signal as a cardiac gating method for the MRI scanner shows promising results. Before a conclusion can be made about the DUS as a cardiac gating method for the MRI scanner more practical research should be done. Such as implementing this method on a hardware and acquire DUS signals under the effect of the magnetic field of the MRI scanner.

For future work, the filtering and peak detection algorithm needs to be adjusted to be able to handle different data sets that have different appearance. Also a microcontroller that would be able to receive DUS signals and regulate the MRI scanner should be programmed with the developed filtering algorithm and peak detection algorithm and observe the results of those methods when they are applied in a practical usage. It is thought that some adjustments will be needed on the developed algorithms since programming in a MATLAB environment differs from programming in a microcontroller environment.

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Chapter 5 Conclusions

After completion of this thesis work, it can be concluded that,

• The filtered DUS signal shows clear peaks in the signal that represent the cardiac cycle.

• The developed peak detection algorithm was able to detect the peaks in the DUS signals as long as the DUS signals were consistent.

• The DUS signal shows promising results to be able to be used as a cardiac gating method for the MRI scanner.

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24 BIBLIOGRAPHY

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Appendix A

Theoretical background

MRI scanners that have higher magnetic field strength gives higher resolution MRI images. That is why researchers always try to develop new MRI scanners with higher magnetic strength. But higher magnetic strength have some drawbacks. One of the major drawbacks it causes a distortion in the ECG signal that is taken simultaneously with the MRI to monitor the patient inside the MRI machine and gate the MRI scanner when cardiac gating is necessary. This signal distortion is caused by an effect that arises when a conducting fluid is flowing under the influence of an external magnetic field.

This effect is called the magnetohydrodynamic effect. To solve this problem researchers have studied different methods then ECG that are not effected by the magnetohydrodynamic effect such as POX, acoustic gating and DUS.

The method that is used in this thesis is the DUS method and the results of this method will be compared to the ECG siganl as a reference.

To be able to apply this method basic knowledge about MRI machine and DUS needs to be known. Also knowledge about signal processing and programming is needed.

A.1 Magnetic Resonance Imaging

MRI exquisite soft tissue contrast of high spatial resolution, with a 3D to- mographic presentation and the capability of demonstrating dynamic physiologic changes. It is possible to generate images that report an enormous array of physical/physiologic phenomena based on the physics of Nuclear Magnetic Resonance (NMR). Images can be created with contrast reflecting proton density, T1 and T2 relaxation times [8], tissue susceptibility varia- tions [9], diffusion [10], fields of motion [11], biomechanical properties [12],

1

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2 APPENDIX A. THEORETICAL BACKGROUND

tissue perfusion [13], and spectra of key biochemical molecules [14]. MRI does this in a non-invasive manner, which permits safe repeated scans with no known harm [15]. These advantages have made MRI to become a central pillar to much of modern medical practice.

A.1.1 Magnetic Resonance Imaging principles

NMR is enabled due to the existence of a property of many subatomic par- ticles known as spin. The spin feature is restricted to those with an odd number of neutrons or protons [16]. In the case of MRI, the majority of imaging that is performed today is based on the nucleus of hydrogen. This is because hydrogen is the most abundant isotope in the human body and it has the highest gyromagnetic ratio. Those two factors are important to generate large NMR signals. But other elements can also be used, some of them are listed in Table A.1. The spin is expressed in fractional values of Planck’s constant. This is a measure of the angular momentum of the nucleus, which is a feature of rotating objects to continue in their rotation unless disturbed.

Table A.1: MRI elements

To have a better understanding of the spin feature consider Figure A.1, where a proton is described as a spinning sphere with charge. The spin of the proton, seen as a rotation of the nucleus about some axis, gives the proton a magnetic property. If this magnetic structure was placed in an external magnetic fieldB0, it would tend to align with that magnetic field, as shown in Figure A.1. Further more, the spin gives the proton angular momentum.

If the proton is left uninterrupted, it would naturally align vertically parallel to the direction of the magnetic fieldB₀.

However, if the spin was tipped from its natural alignment with the applied magnetic field, it would precess about the direction of the applied magnet fieldB₀, as shown in Figure A.1. Its precessional frequency known as the Larmor frequency (ω), is dictated by the strength of the applied magnetic

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APPENDIX A. THEORETICAL BACKGROUND 3

Figure A.1: Spin FeatureReprinted with permission from [17]

fieldB₀ through a constantγ known as the gyromagnetic ratio. For exam- ple, at a field strength of 1 Tesla, the proton Larmor frequency is42.57 MHz.

The Larmor frequency is the product of the field strengthB₀ and the gyromagnetic ratioγ.

A.1.2 Excitation

In the absence of a magnetic field, spins are expected to point randomly in all directions. When a magnetic field is applied, the spins will still point randomly in all directions, but they will have a minor tendency to point along the direction of the magnetic field [18]. The number of protons that will point along the direction of the field are approximately 3 per million within a 0.5T field, in a 1.0T system there are 6 per million. The amount of affected protons is proportional with the magnetic field B₀ [19]. This is

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also the reason why higher magnetic field systems generate better images than systems with lower field strengths. In order to generate an NMR signal, the magnetization must be tipped away from this equilibrium alignment so that a component of the magnetization lies in the transverse plane where it is free to precess. In order to accomplish this, the spins are exposed to an alternating magnetic fieldB1that must have a frequency equal to the Larmor frequency of the nucleus. This process is called excitation.

A.1.3 Relaxation

The excitation part lifts the protons into a higher energy state. This happens because the protons absorb energy from the RF pulse. Protons prefer to align with the main magnetic field (be in a low energy state) [20]. The action of the protons going from higher energy state to the lower energy state that is aligned with the magnetic field is called relaxation and can be divided into two parts: T1 and T2 relaxation. T1 is defined as the time it takes for the longitudinal magnetization(Mz) to reach 63% of the original magnetization [20] and T2 is defined as the time it takes for the spins to de-phase to 37% of the original value [21]. Different tissue have different T1 and T2 values and that is what gives MRI the good contrast resolution property.

A.1.4 MRI synchronization

The fundamental challenges of Cardiac Magnetic Resonance Imaging (CMR) is the movement and the function of the heart throughout the cardiac cycle.

When the heart is in the systole phase (working phase of the heart) it pumps the blood to the body and this blood flow creates a movement in the body which in return produce motion artifacts in the image. Cardiac gating can be used to solve this problem. It allows MRI scanner to acquire data only during a specified part of the cardiac cycle, typically during diastole when the heart is not moving [22]. There are several different methods that have been used for cardiac gating.

Electrocardiogram

One of the most used methods for cardiac gating is using ECG. ECG is a method of imaging the heart’s activity. With electrodes on the chest, electrical activity is captured from the heart muscle and represents this as a function of time in a chart [23]. This electrical activity arises from the heart cells

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when they depolarize and repolarize during each heartbeat. The pattern of this electrical activity includes three waves, which have been named P, QRS (a wave complex), and T wave, where R wave represents depolarization of the main mass of the ventricles hence it is the largest wave [24]. The MRI data acquisition uses the R wave of the ECG signal as a reference when using ECG for cardiac gating. When an R wave is detected MRI uses a given delay before sampling the data. This insures that data acquisition takes place with as little as possible heart movement. Final images are created from data sampling over a portion of cardiac cycles.

Even though ECG is a great method for cardiac gating, it suffers from a major drawback. When using ECG as a cardiac gating in an MRI system that uses a high magnetic field, the ECG signal gets distorted because of the MHD effect [4]. When the ECG signal gets distorted, it becomes hard for the MRI system to detect the R wave in the ECG signal this results in artifacts in the final MRI images [25].

Acoustic gating

Unlike ECG-triggering the acoustic approach employs the phonocardiogram’s first heart tone for triggering instead of electrophysiological signals [26].

When using acoustic gating, recordings of a phonocardiogram inside of the magnet bore are paralleled by acoustic noise due to gradient coil switching consisting of several sharp harmonic segments, which are related to the echo time and the repetition time. For this reason, acoustic measurements needs to be controlled to evaluate the acoustic signal-to-noise ratio between the sound pressure level generated by the cardiac activity and the sound pressure level induced by the gradient noise [27].

Pulse oximetry

Pulse oximetry is very common in medical care that it is often regarded as a fifth vital sign [28]. Pulse oximetry is based on the principle that oxyhemoglobin absorbs more near-IR light than deoxyhemoglobin, and deoxyhemoglobin absorbs more red light than oxyhemoglobin [29]. It uses two light- emitting diodes in the transducer that each emit light of specific wavelength through the skin, such as that of the digits or the ear lobe. A photo diode detector at the far side detect the intensity of transmitted light at each transmitted wavelengths, from which oxygen saturation can be derived [30]. The detected signal displays as a sharp waveform with a clear notch indicates the

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cardiac cycle [31]. It has been reported that pulse wave triggering seems to be robust and might be advantageous to ECG triggering [32].

Doppler Ultrasound

Another method that is theoretically not affected by MHD effect is ultrasound [33]. Doppler ultrasound (DUS) reflects the physiologic activity of the heart in terms of blood flow and cardiac wall motion and hence directly reflects the motion that should be fixed in time. Moreover, depending on the location of the transducer, the DUS signal corresponds to distinct times in the cardiac cycle, potentially providing more precise information for cardiac triggering than conventional ECG [34].

A.1.5 The magnetohydrodynamic effect

The MHD effect is a physical phenomenon describing the motion of a conducting fluid flowing under the influence of an external magnetic field [35].

The MHD effect, due to blood flowing through the static magnetic fieldB₀, may induce electrical fields superimposed on the ECG signal. This elevates the T-wave portion of the ECG signal, which can compromise the determi- nation of R-R segments of the cardiac cycles [36]. The magnitude of the voltages produced by the MHD effect is determined by the flow velocity of the blood, the diameter of the vessel, and the strength of the magnetic field [37].

A.1.6 The 7 Tesla facility in Lund

As mentioned earlier, research’s have showed a correlation between the strength of the magnetic field of an MRI scanner and a the resolution of the images taken by that MRI scanner. Higher magnetic field tend to give higher resolution on the MRI images. With higher resolution images, researcher’s in Lund have carried out imaging the brain activity in the human body. One of the vital parameters to image in the brain is the blood flow. To be able to image the blood flow with high resolution cardiac gating needs to be used for the MRI scanner. One problem that arises is the distortion of the ECG signal that is used for cardiac gating. Due to the MHD effect the ECG signal gets distorted and cardiac gating becomes impossible to do. This is the primary reason behind this thesis to examine and develop a new method for cardiac gating for the 7 Tesla MRI scanner that is not affected by the MHD effect.

The method of cardiac gating using DUS signals is enabled to examine due

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to a collaboration with Northh Medical. Northh Medical have have provided researchers at 7T facility in Lund with a device that gives a synchronized ECG and DUS signals as output. This will enable us to acquire synchronized ECG and DUS data to analyze and compare using different filtering and peak detection algorithm in MATLAB.

A.2 Doppler Ultrasound

Doppler ultrasonography is a technique that can give a relatively inexpen- sive, noninvasive real-time measurement of the blood flow. According to the principle of DUS, ultrasound waves emitted from the Doppler transducer are transmitted through the human body and reflected by the moving red blood cells within the blood vessels or the heart. The difference in the frequency between the emitted and reflected waves, referred to as the “Doppler shift frequency” is directly proportional to the speed of the moving red blood cells (blood flow velocity) [38]. In this thesis we will acquire two different types of DUS signals. The first DUS signal is measuring the heart wall motion while the heart is pumping. The second DUS signal is measuring the blood flow of the aorta. Those two different signals can be acquired by aiming the DUS transducer at different locations on the chest area of the volunteers.

A.3 Digital signal processing

Digital signal processing is the use of digital processing (computers or more specialized digital signal processors) to achieve a wide variety of signal processing operations. The signals processed are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency.

To digitally analyze and process an analog signal, it must be digitized with an analog-to-digital converter (ADC) [39]. Sampling is usually done in two stages, discretization and quantization. Discretization means that the signal is divided into equal sequences of time, and each interval is repre- sented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set. The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal [40].

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A.3.1 Digital filters

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to decrease or increase certain aspects of that signal.

A low-pass filter is a filter that pass through signals with a frequency lower than a determined cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. An ideal low-pass filter completely eliminates all frequencies higher then the cutoff frequency while passing those below unchanged.

A high-pass filter is a filter that pass through signals with a frequency higher than a determined cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design.

High-pass and low-pass filters are also used in digital image processing to perform image modifications, enhancement, noise reduction, etc., using designs done in either the spatial domain or the frequency domain [41].

A.3.2 Anti-aliasing filter

An anti-aliasing filter (AAF) is a filter used before a signal sampler to re- strict the bandwidth of a signal to approximately or completely satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is zero. A realizable anti-aliasing filter will typically have a trade off to either permit some aliasing to occur or else attenuate some in-band frequencies close to the Nyquist limit. For this reason, many practical systems sample higher than would be theoretically required by a perfect AAF in order to ensure that all frequencies of interest can be reconstructed, this practice is called oversampling.

A.3.3 Quadrature signals

A complex signal, also called quadrature signals, is a two-dimensional signal whose value at some instant in time can be specified by a single complex number having two parts the real part (in-phase) and the imaginary part (quadrature). [42]. A pair of periodic signals are said to be in “quadrature”

when they differ in phase by 90 degrees. The “in-phase” or reference signal

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is referred to as “I,” and the signal that is shifted by 90 degrees (the signal in quadrature) is called “Q.”

A.3.4 Complex band-pass filter

Complex band-pass filters are used in many applications. They are designed by starting with a simple low-pass prototype and apply a complex shift frequency transformation. More in detail, a low-pass or high pass filters are filters that filter either the high or the low frequencies in the signal. When having both negative and positive frequencies in one complex signal, both positive and negative frequencies needs to be treated. To have a better understanding of this have a look at Figure A.2.

Figure A.2: Complex band-pass filter, where the orange signal represent a normal low-pass filter. The blue signal is the shifted low-pass frequency that result in a complex band-pass filter that attenuate the positive frequency spectrum (that is quadrant 1 and quadrant 4 in the complex signal). The resulting signal from this filter is a signal that contains only of quadrant 2 and quadrant 3 data of the complex signal which consists of negative frequencies.

this signal will represent the backward DUS signal. This filter is shifted by 3.18 Hz in the positive spectrum

The filter equation looks like following:

Y (n) =

∞

X

n=−∞

X(n) ∗ Ae^jW

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WhereX(n) is the signal before the filter, and Y (n) is the signal after the filter. Ae^−jW is the filter coefficient. To shift the filter, a shifted factor must be multiplied with the filter coefficient resulting in the following formula:

Y_{shif t}(n) =

∞

X

n=−∞

X(n) ∗ Ae^jW ∗ e^jW^{shif t}

Wheree^jW^{shif t} is the shifted factor. The formula can then be simplified to:

Yshif t(n) =

∞

X

n=−∞

X(n) ∗ Ae^{j(W +W}^{shif t}⁾

By shifting the filter in the opposite direction a filter that attenuate the negative frequency spectrum (that is quadrant 2 and quadrant 3 in the complex signal) is achieved. This will give the forward DUS signal.

A.4 Evaluation of results

To evaluate the result of this thesis, the algorithm for filtering and peak detection of the DUS signal will be compared to the reference ECG signal. The algorithm was compared in terms of; delay, accuracy , jitter and false positive/false negative. In this section each one of those terms will be described.

A.4.1 Delay

In theory, a DUS signal that is acquired from a patient will have a delay compared to an ECG signal that is taken from the same patient. This delay is caused by the nature of the DUS signal. DUS signal acquire information about the cardiac function by sending ultrasound signals to the heart and detect the reflected ultrasound signals from the heart. Those signals represent the heart contraction and relaxation phase. While ECG signal is acquired by the electrical activities in the cells of the heart.

From a physiological point of view, it is known that the contraction of the heart is a response to the electrical depolarization in the cells of the heart.

With that said, it means that the contraction of the heart will happen shortly after an electrical depolarization in the cells of the heart. This results in a delay between a signal that represent the electrical depolarization and a signal that represent the heart contraction.

Since cardiac gating requires precise detection of the heart function and the goal of this thesis is to study the usage of DUS signal as a cardiac gating method for the MRI scanner, delay becomes an important factor to consider when studying different cardiac gating methods.

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A.4.2 Jitter

Jitter effect is the effect that occurs when a process that is to be repeated at regular intervals does not occur at a stable rate. In this case, if the DUS signal have irregular delay between each peaks or if the delay is irregular between the DUS signal and the ECG signal then a jitter effect is present in the signal.

Since the DUS signal is used to gate the MRI scanner, jitter effect in the signal will give irregular pulses to the MRI scanner resulting in artifacts in the MRI images.

A.4.3 False positive and false negative

In peak detection, false positive error means that the peak algorithm shows a peak in the signal when there were no peak in that location of the signal.

a false negative error means that the peak algorithm does not show a peak in the signal when a peak is present.

False positive errors will result in artifacts in the MRI images because the scanner is scanning without concern to the cardiac cycle. Many false positive errors in the algorithm will result as if the MRI scanner is functioning without cardiac gating. False negative errors will affect the running time for the MRI scanner. Since a cardiac gated MRI scanner will not scan the patient if there is no detected heart beats, many false negative errors will result into making the session time for the MRI procedure longer.

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TRITA CBH-GRU-2019:087

www.kth.se

Developing a New Method for MRI Triggering Using Doppler Ultrasound

Developing a new method for MRI triggering using Doppler

Ultrasound

USAMA GAZAY

Abstract

Contents

Chapter 1 Introduction

1.1 Research question

Chapter 2 Methods

2.1 Hardware setup

2.2 Data collection

2.3 Software setup

2.3.1 Filtering of the Doppler Ultrasound signal

2.3.2 Peak detection algorithm

2.4 Evaluation of results

2.4.1 Delay and jitter

2.4.2 False positive and false negative

Chapter 3 Results

3.1 Results from the filtering algorithm

3.2 Results from the peak detection algorithm

3.3 Evaluation of the Doppler Ultrasound sig- nal compared to the reference ECG sig- nal

Chapter 4 Discussion

4.1 Data acquisition

4.2 The filtering algorithm

4.3 The peak detection algorithm

4.4 Evaluation of the method

4.5 Future work

Chapter 5

Conclusions

Bibliography

Appendix A

Theoretical background

A.1 Magnetic Resonance Imaging

A.1.1 Magnetic Resonance Imaging principles

A.1.2 Excitation

A.1.3 Relaxation

A.1.4 MRI synchronization

A.1.5 The magnetohydrodynamic effect

A.1.6 The 7 Tesla facility in Lund

A.2 Doppler Ultrasound

A.3 Digital signal processing

A.3.1 Digital filters

A.3.2 Anti-aliasing filter

A.3.3 Quadrature signals

A.3.4 Complex band-pass filter

A.4 Evaluation of results

A.4.1 Delay

A.4.2 Jitter

A.4.3 False positive and false negative