MRI System

These algorithms are all based on the 𝑘-space locality principle [39], which as-sumes that points nearby in 𝑘-space are strongly correlated. Therefore, missing samples can be approximated as a linear combination of nearby 𝑘-space samples from all coils. After recovery of missing data from each channel, the coil image can be reconstructed by FFT and followed by employing coil combination methods such as the root of sum of squares (RSS) method. More information about𝑘-space based parallel imaging see [34].

There are several ways to combine data from different coils in order to obtain a single reconstructed image. The best unbiased estimation for the image is given by [24, 40]:

with an assumption that the signal noise is independently and identically dis-tributed (i.i.d) Gaussian white noise. Here 𝑐^*_𝑗 is the complex conjugate of the coil sensitivities and𝑠^_𝑗 is the image for each individual coil. Since the knowledge of coil sensitivities is required, a RSS operation is often used instead:

𝜌_rss =

√︃∑︁

𝑗

|^𝑠_𝑗|². (2.35)

The above equation (2.35) is an approximation of formula (2.34), where the sen-sitivity is approximated by 𝑐^*_𝑗 = ^𝑠^*_𝑗. Noteworthy, this assumption is only valid for locations with high signal. In the region of low signal intensity, a bias will be intro-duced [41, 42]. Alternatively, a usage of the more complicated phase-preserving method introduced in [40] will help to avoid this problem.

2.8 MRI System

All studies in this work were conducted on a Siemens Prisma whole body human scanner (Siemens AG, Erlangen, Germany) with the main magnetic field 𝐵0 = 2.89Tesla (T) and two build-in body coils for RF excitation and signal receiving.

The gradient system has a maximum gradient strength of 80 mT m⁻¹. The raster time for gradient switching is 10 𝜇s and the maximal slew rate is 200 mT m⁻¹ ms⁻¹. Several receiver coils are provided by the system for signal detection, i.e., a 64-channel head coil, a 18-element thorax coil and the 32-element spine coil.

Additionally, a commercial reference phantom (Diagnostic Sonar LTD, Scotland, UK) consisting of 6 compartments with defined 𝑇₁ values surrounded by water is used for quantitative validations in this study (Figure 2.12).

22 Chapter 2. Magnetic Resonance Imaging

Figure 2.12: (Top) MRI system, (bottom left) 64-channel head coil, (bottom mid-dle) 18-element thorax coil and (bottom right) a commercial𝑇1 phan-tom used in this thesis.

3 Real-time MRI

Real-time MR imaging refers to continuous monitoring of moving objects, such as the human cardiovascular system in real time. To achieve this, specific strategies for image acquisition and reconstruction have to be employed. Earlier applica-tions are based on so-called single-shot gradient-echo sequences, such as echo-planar imaging [43] and spiral imaging [44]. Since they usually require a long readout, images are prone to artifacts caused by off-resonance effects. Instead, a recent developed MRI technique which employs radial MRI and regularized nonlinear inversion does not have this problem and can achieve a much higher spatial-temporal resolution. The chapter introduces the general acquisition and reconstruction methods for this technique.

3.1 Undersampled Radial FLASH

The FLASH pulse sequence is a gradient-echo sequence with low flip angle RF pulses and short repetition time [9, 45]. Because low flip angle excitation is used instead of 90^∘ pulse in spin echo sequences, most of the longitudinal magnetiza-tion is remained and an immediate next excitamagnetiza-tion is then allowed. With a rapid repetition of this sequence, fast imaging is therefore possible. Depending on the response of the transverse magnetization in steady state, there are three types of sequences in the generic FLASH technique, i.e., spoiled, refocused FLASH and bal-anced steady state free precession (bSSFP). The radial FLASH sequence diagram is shown in Figure 3.1(a). Spoiled FLASH employs RF spoiling or gradient spoil-ing to destroy the transverse magnetization. For radial spoiled FLASH, besides RF spoiling with random phase increment, no additional spoiler gradient is necessary as the gradient spoiling is achieved through the applications of varying readout gradients from TR to TR. Spoiled FLASH produces images with 𝑇₁ contrast and has been used primarily for real-time MRI applications ranging from speaking, cardiovascular function to quantitative phase-contrast MRI. On the contrary, in re-focused FLASH a gradient of the same length but of opposite polarity is applied after readout to keep the residual transverse magnetization. The net phase per TR is constant. Refocused FLASH offers a 𝑇₂/𝑇₁ contrast and has been used for the study of temporomandibular joint (TMJ) dysfunctions. Further, to realize a

bal-23

24 Chapter 3. Real-time MRI

Figure 3.1: Undersampled radial FLASH sequences. (a) Sequence diagram of spoiled, refocused and balanced radial FLASH techniques. (b) An ex-ample of undersex-ampled radial spoke distribution in real-time MRI (i.e., 3 spokes per frame with 5 sequential turns).

anced condition which has zero net phase per TR, a dephasing gradient along the slice selection direction with the same strength and direction as the slice selection refocusing gradient is applied before each excitation. The bSSFP sequence offers excellent𝑇2/𝑇1 contrast between flowing blood and heart muscle (myocardium), therefore it is widely used in cardiovascular magnetic resonance imaging (CMR) studies. One main drawback of the bSSFP sequence is that it is prone to banding artifacts due to off-resonance effects.

Radial sampling was proposed in the beginning of MRI and regained a lot of interest in the last decade. Radial trajectories offer several advantages over the traditional Cartesian scheme. First, due to the absence of phase encoding and oversampling of 𝑘-space center, radial is less sensitive to motion which often in-duces ghosting artifacts in Cartesian sampling. Second, radial sampling is quite tolerant to undersampling. Most object information remains visible even for sig-nificant undersampling factors. This is due to the fact that the center of𝑘-space is always densely sampled and most of the energy is still kept in the case of under-sampling. Third, a readout oversampling which enlarges the circular-supported FOV and therefore helps to remove the aliasing effects can be easily employed without increasing acquisition time. Finally, each spoke carries an equal amount of low and high spatial frequencies, offering a more homogeneous image update in dynamic MRI. As a result of these properties, radial sampling is favorable for

3.2. Parallel Imaging as Nonlinear Inverse Problem 25