Accelerating Interventional Real-Time MRI

Accelerating interventional real-time MRI

Pim Borman Accelerating interventional real-time MRI

Pim Borman Cover Batik pattern from Solo, Central Java, Indonesia Design: Pim Borman

Accelerating interventional real-time MRI PhD thesis, Utrecht University, The Netherlands

Manuscript Layout: P.T.S. Borman Typeset in: LATEX2ε Printed by: ProefschriftMaken BV ISBN: 978-90-393-7182-4

Financial support for publication of this thesis was kindly provided by Elekta B.V. and Modus Medical Devices Inc. Accelerating interventional real-time MRI

Versnelling van interventionele tijdsgetrouwe kernspintomograﬁe (met een samenvatting in het Nederlands)

Proefschrift

ter verkrijging van de graad van doctor aan de Universiteit Utrecht op gezag van de rector magniﬁcus, prof. dr. H.R.B.M. Kummeling, ingevolge het besluit van het college voor promoties in het openbaar te verdedigen op donderdag 7 november 2019 des middags te 2.30 uur

door Pim Timon Samuel Borman geboren op 04 november 1989 te Leiderdorp, Nederland Promotoren: Prof. dr. B.W. Raaymakers Prof. dr. C.T.W. Moonen Copromotoren: Dr. C. Bos Dr. H. N. Tijssen Contents

List of acronyms iii

1 Introduction 1

2 Towards real-time MR thermometry using SMS 11

3 Assessment of 3D motion modeling performance using SMS 31

4 Respiratory motion tracking using golden-angle SMS 47

5 Imaging latency of real-time MRI 59

6 ReconSocket: A low-latency raw data streaming interface 73

7 General discussion 87

8 Samenvatting 95

Bibliography 99

Publications 113

Acknowledgements 117

Curriculum vitae 119

List of acronyms

g-factor geometry factor k-t spectro-temporal adc analog-digital converter bart Berkeley advanced reconstruction toolbox caipirinha controlled aliasing results in higher acceleration cbct cone beam computed tomography cem cumulative equivalent minutes cg conjugate gradient ci confidence interval cnr contrast to noise ratio cs compressed sensing ct computed tomography ctv clinical target volume ebrt external beam radiotherapy epi echo planar imaging fft fast Fourier transform fifo first in first out fov field of view ga golden-angle gpu graphics processing unit gre gradient echo gui graphical user interface

iii List of acronyms hifu high intensity focused ultrasound litt laser-induced thermal therapy mae mean absolute error mb multiband mlc multileaf collimator mosse minimum output sum of squared error mpr multi-planar reconstruction mr magnetic resonance mri magnetic resonance (mr) imaging nufft non-uniform fast Fourier transform oar organ at risk pca principal component analysis pf partial Fourier pid proportional-integral-differential pins power independent number of slices pns peripheral nerve stimulation prfs proton resonance frequency shift ptv planning target volume recon external reconstructor recv ReconSocket receiver rf radio frequency roi region of interest sos stack-of-stars sar specific absorption rate sense sensitivity encoding sms simultaneous multi-slice snr signal to noise ratio sopi simultaneous orthogonal plane imaging spgr spoiled gradient echo iv List of acronyms spir spectral pre-saturation with inversion recovery sw sliding window tfe turbo field echo tv total variation us ultrasound xcat extended cardiac-torso

CHAPTER 1

Introduction

Every year the number of patients that are diagnosed with an invasive carcinoma increases, up to 116.000 cases in the Netherlands (IKNL 2018) and 18 million cases worldwide in the year 2018 (Bray et al. 2018). To date, chemotherapy, surgery, and radiotherapy (Delaney et al. 2005) are the most established types of cancer treatments available (Arruebo et al. 2011). Chemotherapy is a systemic therapy, targeting cancerous cells in the whole body. Surgery and radiotherapy, on the other hand, are local therapies used for solid tumor treatment. Often, the treatment consists of a combination of these modalities.

Surgery is generally a very invasive treatment with many side effects. For this reason there is an increasing need for less invasive treatments, which have less side effects and an improved survival rate. This thesis explores how innovative mr imaging (mri) techniques can be applied to radiotherapy and high intensity focused ultrasound (hifu) for better treatment control. A recent innovation in the field of radiotherapy is mr-guided external beam radiotherapy (ebrt) (figure 1.1) (Fallone 2014; Keall et al. 2014; Lagendijk et al. 2014; Mutic and Dempsey 2014), which improves the efficiency of dose delivery to the target while limiting dose deposition to healthy tissues (Pollard et al. 2017). Similarly, in the field of hifu, a recent innovation is the use of mr guidance for treating several types of cancer (figure 1.1) (Hynynen et al. 1993). In contrast to radiotherapy, which uses ionizing radiation, hifu uses acoustic radiation to ablate cancerous tissues. To date, only hifu treatments for bone metastasis are partially reimbursed in the ultrasound (us) (FUS 2019), but clinical trials have demonstrated its safety and feasibility for other tumor sites as well, such as prostate (Chaussy and Thüroff 2017) and breast (Hynynen et al. 2001).

1 Chapter 1 Introduction

(a) (b)

Figure 1.1: Schematic overview of mr-guided ebrt (a) and mr-guided hifu (b). The mr-guided ebrt system contains a rotating multileaf collimator (mlc), which can shape the radiation beam according to the target’s geometry. See also ﬁgure 1.2. The mr-guided hifu system contains a transducer immersed in a water bath to acoustically couple it to the target.

1.1 MR guidance of EBRT

The clinical introduction of hybrid mri-linac systems such as ViewRay’s MRIdian and Elekta’s Unity makes it possible to image the anatomy prior to treatment (pre-beam) and during treatment (beam-on) with an unrivalled soft-tissue contrast. Most commonly, other on-board imaging techniques such as digital X-ray or cone beam computed tomography (cbct) are being used to verify whether the treatment plan still matches the daily anatomy prior to each treatment fraction. Additional planning target volume (ptv) margins are generally needed to ensure that the clinical target volume (ctv) receives the intended dose, accounting for all uncertainties in the radiotherapy workﬂow, e.g. delineation, dose-calculation, patient positioning, and inter- and intra-fraction motion. Reducing these uncertainties leads to more conformal treatment plans which reduces toxicity and opens the door towards hypo-fractionation in which a higher dose per fraction is given (Kerkmeijer et al. 2016). The use of on-board mri has the advantage over the aforementioned imaging modalities that the tumor and organs at risk (oars) can be better distinguished (Chandarana et al. 2018). This allows for generating a new treatment plan prior to each fraction, which in turn allows for smaller ptv margins.

Mr imaging during beam-on has the advantage that intra-fraction anatomy changes due to e.g. respiratory motion can be visualized. This way, the position of the target and oars can be tracked over the course of a treatment fraction, which enables dose accumulation mapping (Stemkens et al. 2017), as described brieﬂy in section 1.1.2. Additionally, beam-on imaging allows for real-

2 Chapter 1 Introduction time adaptive treatment strategies such as gated delivery (Ohara et al. 1989) and mlc-tracking (Keall et al. 2001), as described below.

1.1.1 Motion management

Respiration-gated radiotherapy is particularly useful to treat targets that move with respiration. A gating window can be defined within which the tumor should reside during radiation delivery, which is generally the relatively stable expiration state, as illustrated in figure 1.2. Using mr imaging it can be automatically iden- tified when the tumor moves outside the gating window, such that the treatment beam can be turned off (Crijns et al. 2011). Its conceptual simplicity makes this method an interesting option for the reduction of ptv margins. However, a smaller gating window also leads to a longer total therapy time, such that an optimum must be found between treatment efficiency and treatment time (Heerkens et al. 2014). A promising development is to provide the patient with visual feedback of mr images, such that he can adjust his respiratory pattern to maximize the gating efficiency and hence minimize the total treatment time (van Sörnsen de Koste et al. 2018).

A more eﬃcient, but technically more demanding, way of adapting to the actual patient anatomy during treatment is by tracking the target with the mlc. Here, the mlc-segments are translated in real-time, adjusting the aperture to follow the moving target (Crijns et al. 2012; Glitzner et al. 2015c). Clinical feasibility studies have demonstrated a signiﬁcant tissue sparing capability of mlc-tracking (Fast et al. 2016). It does, however, impose more stringent requirements on the system, in particular on the mechanical reactance of the individual leafs. It has been shown that this can be controlled very accurately with mechanical latencies <20 ms (Glitzner et al. 2019). It is therefore to be expected that the success of mr-guided mlc-tracking will be mostly determined by the latency of the mr imaging, as is explored in this thesis.

Figure 1.2: Illustration of gated ebrt, where the treatment beam is turned oﬀ when the target is outside the gating window, and mlc-tracking where the individual mlc leafs move such that the treatment beam follows the moving target.

3 Chapter 1 Introduction

1.1.2 Dose accumulation Due to the dynamic nature of a patient’s anatomy, the planned dose is not necessarily equal to the delivered dose (Langen and Jones 2001). The actual dose distribution over the complete course of treatment is therefore, in general, poorly quantiﬁed (Jaﬀray et al. 2010). Three dimensional mr imaging of the target and surrounding healthy tissues during treatment enables real-time dose accumulation mapping, which can be used for inter-fraction or even intra-fraction treatment plan adaptations (Kontaxis et al. 2017). This would provide a way to track and adjust the treatment in real-time, albeit indirectly since the actual interaction between tissue and radiation cannot be visualized using mri.

1.2 MR guidance of HIFU

In contrast to mr-guided radiotherapy, the progress of a hifu treatment can be monitored directly by means of temperature mapping. For this, both us and mri have been suggested as image guidance modalities (Haar et al. 1989; Hynynen et al. 1993). Us has the advantages of having a high frame rate and being relatively cheap and portable. However, its major drawbacks are that reliable temperature measurements above 50 ◦C are currently not available (Lewis et al. 2015), and that spatial coverage can be limited due shadowing eﬀects of attenuating structures in the ultrasonic beam path. Although mri is more expensive and does not allow for high frame rate imaging, its superior soft tissue contrast and its capability to perform volumetric imaging as well as reliable temperature mapping, see section 1.2.2, make it the preferred image guidance modality of hifu (Siedek et al. 2019).

1.2.1 Motion management The combination of mr with phased-array hifu transducers makes it possible to monitor temperature and target location, and adjust the focus of the us-beam in near real-time by means of electronic beam steering (Ries et al. 2010). Analo- gously to mr-guided ebrt, motion compensation can be accomplished by gating the treatment beam, or by continuously tracking the moving target. The tracking capability is determined by the transducer’s electronic steering capabilities, which depend on design characteristics such as aperture, focal length, and spacing between individual elements (Ramaekers 2017).

1.2.2 MR Temperature mapping From the temperature and duration, the amount of damage to the tissue can be ◦ modeled using cumulative equivalent minutes (cem)at43 C(cem43) (Sapareto ◦ and Dewey 1984). 240 cem43 or reaching a temperature > 55 C is regarded as the lethal thermal dose limit at which the tissue can be considered necrotic (Wijlemans et al. 2012). The most commonly used mr thermometry sequence is based on the fact that the proton resonance frequency is temperature dependent and is therefore known as proton resonance frequency shift (prfs) thermometry. This method is only able to measure temperature diﬀerences, by observing the

4 Chapter 1 Introduction additionally accumulated phase in a voxel due to a temperature difference between two time points (Poorter 1995). This phase difference is related to the temperature difference ΔT according to

Δφ ΔT = , α · γB0 · TE where α =0.01 ppm/◦C is the temperature coefficient of the proton’s frequency 6 shift, γ =42.58 × 10 Hz/T the gyromagnetic ratio of a proton, B0 the magnetic field, and TE the echo time of the mr sequence. In practice, the reference phase image is acquired before treatment at a temperature Tref which can usually be ◦ assumed equal to 37 C, such that T = Tref +ΔT . Even though prfs thermometry is used in most mr-guided hifu treatments, it has some disadvantages. Most notably is its inability to measure temperature in adipose tissue and bone. A number of attempts have been made to characterize temperature in these tissues as well, using mri. A popular approach is to use the fact that the T1 and T2 relaxation times are temperature dependent, and hence can be used to estimate temperature changes or even absolute temperature (Rieke and Butts Pauly 2008). This approach is in principle suited for all tissues. Whenever possible, however, prfs thermometry is preferable because it is the only method that offers a linear relationship to temperature and has low susceptibility to the specific tissue type.

1.3 MR sequence design

The use of mri for guiding radiotherapy and hifu treatments poses very challenging constraints on the type of mri sequence that is used. The ideal image guidance sequence would have a high enough frame rate to follow anatomy changes and treatment progress, encompass the full 3D volume that is affected by the treatment, have a high resolution, and have a high signal to noise ratio (snr). Mri, however, is an inherently slow imaging modality compared to other modalities such as us and computed tomography (ct). The reason for this is that for an mr image every spatial frequency coefficient has to be measured sequentially, whereas us and ct have detection mechanisms that can measure multiple image components in parallel. After all frequency coefficients of the mr image have been measured, the image is transformed from frequency space, also known as k-space, to image space, typically by an inverse Fourier transform. For spatial encoding three sets of switching linear magnetic field gradients G are used. This way, a spatial frequency corresponds to k = γ G(t)dt. The different frequency components can then be obtained by varying G(t), and measure the response after radio frequency (rf) excitation (Bernstein et al. 2004).

The mr imaging speed is mostly limited by the maximum slew rate and amplitude of the gradient system. The first reason for this is that it is challenging to man- ufacture gradient coils that are perfectly linear over a large field of view (fov), especially with the current trend towards a wider bore size. The second, more fundamental, reason is that high slew rates generate high potential differences at the edges of the field of view, according to ∇ × E = dB/dt = dG/dt · x, where

5 Chapter 1 Introduction

E is the electric field, B the magnetic field, and x the distance to the iso-center. The potential difference can cause inductive currents to flow in e.g. nerve tissue, resulting in so-called peripheral peripheral nerve stimulation (pns). The mr imaging speed is therefore indirectly limited by the safety constraints imposed on the maximum amount of pns (Ham et al. 1997). For this reason, a higher imaging speed may not be achievable by hardware improvements alone, but should be complemented by improved acquisition and reconstruction methods as well.

Fortunately, quantities like spatial coverage, imaging time, and snr can be traded oﬀ with each other, such that depending on the application an optimal image guidance sequence can be constructed. In practice this usually means that instead of acquiring a 3D volume, the spatial coverage is restricted to a 2D slice, allowing for a frame rate of 4 Hz, which is considered suﬃcient for resolving respiratory motion. To reach this high frame rate, various image acceleration techniques can be employed, which mostly rely on reducing the number acquired data points, and account for the missing data in the image reconstruction algorithm.

1.3.1 Parallel imaging A popular acceleration technique is parallel imaging, which makes use of the spatial sensitivity variations of the receive coils. The most widely used method based on this idea is called sensitivity encoding (sense) and is oﬀered by all major mr vendors (Pruessmann et al. 1999). Using sense, the acquisition is accelerated with a factor n by only acquiring every nth phase encode, which essentially reduces the fov with a factor n. The resulting fold-over artifacts can be described voxel-wise, meaning that a voxel in the folded coil image is a linear combination of its original unfolded voxels, weighted by their local coil sensitivity: m = Sv. Here, m is the folded image, v the unfolded image and S the block diagonal sensitivity matrix. The unfolded image can thus be obtained by inverting S, whose block diagonality makes this computationally very eﬃcient. Sense does, however, lead to a loss of snr. First, because√ of the reduction of acquired data, which leads to an inherent loss of a factor n. Second, the ability of the sensitivity maps to unfold the folded image may be impaired, resulting in a spatially varying reduction factor called the (x) x x SNR√ geometric factor g( ). Therefore, SNRSENSE( )= ng(x) , limiting the maximum acceleration factor that can be achieved.

1.3.2 Simultaneous multi-slice Recently, the parallel imaging technique simultaneous multi-slice (sms), also known as multiband (mb) imaging, has been introduced, which allows for acquiring multiple parallel, non-contiguous slices simultaneously (Larkman et al. 2001). Sms works by exciting multiple frequency bands instead of a single frequency band and leaving the rest of the sequence unchanged. Since the readout pattern is still two dimensional, i.e. a single phase encode direction, the resulting image after the inverse Fourier transform shows all excited slices folded right on top of each other. This is very similar to the folding artifacts of sense, except that here it occurs in the slice direction instead of along the phase encoding direction.

6 Chapter 1 Introduction

The sense unfolding algorithm can therefore be used to reconstruct the two slices separately.

Often, however, there is limited coil sensitivity variation in the slice direction, leading to high geometry factors (g-factors) which reduce the snr and lead to a reduced slice unfolding result, as further explained in chapter 2. Therefore, sms is usually combined with a technique called controlled aliasing results in higher acceleration (caipirinha), which shifts the sms slices with respect to each other in the phase encoding direction (Breuer et al. 2005). This way, the voxels that are folded on top of each other are separated in both the slice and phase encoding directions, reducing the g-factor signiﬁcantly.

A diﬀerence with sense is that sms does not undersample the acquisition matrix, but rather samples multiple points simultaneously.√ The snr of sms is therefore only reduced by the g-factor and not by the n factor which is present for sense. Apart from the potentially higher snr, another advantage of sms is that the multiple slices have exactly the same timestamp such that no inter-slice motion is present as would be the case for an interleaved acquisition. Sms can therefore be considered as a true hybrid between 2D slice-based and 3D volumetric imaging. This can for instance be beneﬁcial when these slices are used to build a motion model, as described in chapter 3.

1.3.3 Acceleration by modelling motion The aim of motion models is to model the three-dimensional motion of the target and oars during treatment delivery with a high enough frame rate to resolve respiratory motion, resulting in a 3D+t mri series (McClelland et al. 2013; Stemkens et al. 2016b; Tryggestad et al. 2013). A motion model usually consists of prior knowledge, acquired at an earlier time point during or even pre-treatment, combined with current, high frame rate, sparse data. The prior knowledge restricts the parameter space such that the sparse data is suﬃcient for estimating the full 3D volume at that time point.

Currently, a popular approach is to use a pre-treatment 4D-mri as prior knowledge, where the fourth dimension corresponds to respiratory phase (Stemkens et al. 2018). The generation of 4D-mri scans is still an active ﬁeld of research. Many diﬀerent methods have been proposed, which can roughly be divided into 2D multislice and 3D volumetric acquisitions. During treatment, fast 2D cine sequences can be used as sparse data to drive the motion model and generate a synthetic 3D+time mri.Inmr-guided ebrt treatments, this series can then be used for retrospective or even real-time dose accumulation mapping.

1.3.4 Acceleration by using radial trajectories Instead of sampling k-space on a Cartesian grid, it is also possible to do this in a non-Cartesian way. This additional degree of freedom can be exploited to reach even higher frame rates, as explained below. Originally, mr acquisitions followed a

7 Chapter 1 Introduction radial sampling trajectory (figure 1.3b) instead of the Cartesian trajectories (figure 1.3a) that are currently most widely used in clinical scan protocols, because they are less susceptible to system imperfections. There has, however, been a continued research interest in non-Cartesian trajectories, some of which are now being introduced clinically, as hardware and reconstruction algorithm developments have progressed. Of particular interest are radial trajectories with angle increments of fractions of the golden-angle (ga) φ = 180/γ (figure 1.3c). Here, γ ≈ 1.618 and solves the equation γ2 = γ+1 (Winkelmann et al. 2007), making sure that at every point in time, the readout lines cover k-space as homogeneous as possible. The readout lines, in this context called spokes, never repeat themselves, but instead always fill the largest gap between two previous spokes.

(a) (b) (c)

Figure 1.3: Schematic overview of a Cartesian sampling pattern (a), radial sampling pattern (b) and golden-angle radial sampling pattern (c).

2D radial sampling trajectories have some distinct features which distinguishes them from Cartesian trajectories. First of all, because the center of k-space is heavily oversampled, radial trajectories are less sensitive to motion (Pipe 1999), which appears as blurring instead of as ghosting artifacts in the case of Cartesian trajectories. Furthermore, radial undersampling leads to incoherent streaks in the resulting image as opposed to the coherent fold-over artifacts in the Cartesian case. This resilience to undersampling is very fortunate, since in principle a factor π/2 more spokes are needed to obey Nyquist’s criterion. Because in radial imaging the data are not acquired on a Cartesian grid, the fast Fourier transform (fft) algorithm cannot be readily used. Instead, the non-Cartesian data is ﬁrst interpolated on a Cartesian grid, which is computationally intensive.

A feature of the golden-angle sampling pattern is that an arbitrary window of spokes can be used for image reconstruction. This means that either prospectively or retrospectively the number of spokes used for a single frame can be adjusted, which may be used to find a trade-off between imaging latency and image quality (chapter 5). At the same time, it is possible to share spokes of the previous frame with the current frame to artificially increase the frame rate, which is known as a sliding window (sw) reconstruction and demonstrated in figure 1.4.

8 Chapter 1 Introduction

(a) (b)

Figure 1.4: Schematic overview of a golden-angle acquisition without (a) and with (b) sliding window. Without sliding window, the total number of frames is Ns/ns where Ns is the total number of spokes and ns the number of spokes per frame. With sliding window this becomes fsw · Ns/ns, where fsw > 1 is the sliding window factor which determines the overlap between two frames.

1.3.5 Frame rate versus latency Although frame rate and latency are often related to each other, they are by definition very different concepts. Frame rate is fairly trivial and is defined as the number of reconstructed frames per second, and thus measured in Hertz. Imaging latency is defined as the time between physical change and the appearance of that change on the image. Because mr acquisitions are relatively slow, there is no well-defined moment of when the image is sampled. The detected latency therefore depends on how the acquisition is performed. The sampling trajectory in particular plays an import role here (chapter 5). The golden-angle sampling trajectory is especially noteworthy since the use of a sliding window reconstruction only increases the frame rate, and therefore decouples frame rate from latency.

9 Chapter 1 Introduction

1.4 Thesis overview

This thesis investigates novel mri techniques which are aimed at improving the use of mri for treatment guidance during hifu and ebrt treatments. In particular, this thesis focuses on the mr imaging during treatment delivery, where a large spatial coverage, along with a high imaging frame rate and low latency are key. The following chapters cover the use of sms for thermometry mapping (chapter 2), the use of sms for motion modelling (chapter 3), the combination of sms with a golden-angle radial trajectory (chapter 4), and a latency analysis of the diﬀerent sampling trajectories (chapter 5). The thesis concludes with a demonstration of a real-time low-latency reconstruction framework (chapter 6).

For mr-guided thermal therapies such as hifu, it is important to monitor the temperature as accurate and precise as possible, with a reasonable snr. Apart from the target, it is important to also monitor the temperature of the near- field and far-field, where acoustic impedance differences may lead to unintended heating. Chapter 2 describes how sms can be used to monitor the temperature in multiple parallel slices simultaneously, and how it can complement acceleration by using sense. To increase the temporal resolution and spatial coverage, sms and sense can be used alone or together, where sms has a potential snr advantage over sense, as discussed earlier.

The increase in spatial coverage by sms can also be used to improve a 3D+t motion model. Chapter 3 focuses on the use of sms for validating a motion model that is constructed by combining a pre-treatment 4D-mri with a cine 2D sms sequence. The additional sms slices can be used to construct multiple independent motion models which can be compared to each other, or combined into a more robust motion model.

Chapter 4 combines sms with a golden-angle radial sampling trajectory, allowing for an increased spatial coverage with an increased frame rate using a sliding window reconstruction. Its feasibility is demonstrated by a real-time implementation on the vendor’s reconstruction platform.

For therapy guidance purposes also the imaging latency plays an important role. Chapter 5 investigates the influence of different sampling schemes on the imaging latency. By comparing the measurements with simulations, the contributions of the data acquisition itself and of the reconstruction process are quantified separately.

Chapter 6 presents a framework that streams acquired k-space profiles in real- time to a third-party receiver. This way, dedicated real-time reconstruction pipelines can be deployed and prototyped easily on custom hardware without the overhead of vendor specific sub-routines that are not written specifically for real- time interaction with the machine. This is demonstrated by latency measurements of a 2D golden-angle sequence and a 3D golden-angle stack-of-stars (sos) sequence. Both are reconstructed using a sliding window on a custom, gpu-equipped, server to achieve a low reconstruction time and a high frame rate.

10 CHAPTER 2

Towards real-time MR thermometry using SMS

The following chapter is based on: Borman, P. T. S., Bos, C, Boorder, T de, Raaymakers, B. W., Moonen, C. T. W., and Crijns, S. P. M. (2016a). “Towards real-time thermometry using simultaneous multislice MRI”. in: Physics in Medicine and Biology 61.17, N461–N477

11 Chapter 2 Towards real-time MR thermometry using SMS

Abstract

mr-guided thermal therapies, such as mr-guided hifu and mr-guided laser- induced thermal therapy (litt) are increasingly being applied in oncology and neurology. mri is used for guidance since it can measure temperature non-invasively based on the proton’s resonance frequency. For therapy guidance using prfs thermometry, high temporal resolution and large spatial coverage are desirable. We propose to use the parallel imaging technique sms in combination with caipirinha to accelerate the acquisition. We compare this with the sense acceleration technique. Two experiments were performed to validate that sms can be used to increase the spatial coverage or the temporal resolution. The first was performed in agar gel using litt heating and a gradient echo (gre) sequence with echo planar imaging (epi), and the second was performed in bovine muscle using hifu heating and a gre sequence without epi. In both experiments temperature curves from an unaccelerated scan and from sms, sense, and sense+sms accelerated scans were compared. The precision was quantified by a standard deviation analysis of scans without heating. Both experiments showed a good agreement between the temperature curves obtained from the unaccelerated, and sms accelerated scans, confirming that accuracy was maintained during sms acceleration. The standard deviations of the temperature measurements obtained with sms were significantly smaller than when sense was used, implying that sms allows for higher acceleration. In the litt and hifu experiments sms factors up to 4 and 3 were reached, respectively, with a loss of precision of less than a factor of 3. Based on these results we conclude that sms acceleration of prfs thermometry is a valuable addition to sense, because it allows for a higher temporal resolution or bigger spatial coverage, with a higher precision.

2.1 Introduction

Thermal therapies such as hifu and litt are increasingly being considered as alternatives to conventional surgery for treating e.g. uterine ﬁbroids (Quinn and Gedroyc 2015), breast cancer (Peek et al. 2015), prostate cancer (Cordeiro et al. 2012), and brain cancer (Staﬀord et al. 2010). This is mainly because of their minimally invasive nature. To guide the treatment in real-time, i.e. monitor how much energy is delivered where and when, mri is a good imaging modality (Hynynen et al. 1993). It can be used to monitor the temperature non-invasively, based on the thermal sensitivity of the proton’s resonance frequency (Rieke and Butts Pauly 2008; Quesson et al. 2000).

The temporal resolution that is needed depends on the application. For typical hifu treatments an acquisition time of 3.5-7.2 s is considered acceptable (Lam et al. 2015; Ramsay et al. 2013). Depending on the time scale of the temperature

12 Chapter 2 Towards real-time MR thermometry using SMS changes a higher temporal resolution is needed. Another case where a higher temporal resolution may be needed is in the abdomen because of the presence of motion (Senneville et al. 2010), for which sampling at a higher frame rate can reduce intra-scan motion artifacts.

At the same time the spatial resolution must be high enough to accurately measure the temperature in the focus, meaning the voxel size must be < 2 mm (Ramsay et al. 2013; Weidensteiner et al. 2003). Furthermore, spatial coverage is important. During hifu treatments, near and far ﬁeld regions need to be monitored to ensure that not too much energy is deposited there.

A limitation of current prfs thermometry sequences that are used during therapy guidance, is that the acquisition time is rather long, even though epi is already used in most situations (Stafford et al. 2004; Weidensteiner et al. 2003). For this reason much effort has been spent on speeding up the acquisition by for example spiral readouts (Stafford et al. 2000) or fitting a constrained baseline image to undersampled data (Gaur and Grissom 2015). Spiral acquisitions are however still very sensitive to hardware errors, and the fitting to undersampled data currently takes about 10 s for a 192 × 192 matrix. Even if these techniques have potential, alternative methods are still needed that achieve sufficient spatial coverage and temporal resolution with a reconstruction that is fast enough for use during therapy guidance.

This paper focuses on such a method, namely the parallel imaging method sms (Larkman et al. 2001) in combination with caipirinha (Breuer et al. 2005), to accelerate prfs thermometry. This method is compared with sense (Pruessmann et al. 1999), and the possibility of acceleration by combining sms and sense is investigated.

Because sms has a potential snr advantage compared to sense, we hypothesize that this translates in a higher precision of the temperature measurements. In that case the acceleration could be used to increase the temporal resolution or the spatial coverage by increasing the number of slices. To test this we use sms, sense, and combined sense/sms accelerated sequences during hifu and litt heating and analyze the accuracy and precision of the temperature measurements, in phantom experiments.

2.2 Theory

Prfs thermometry relies on the principle that the resonance frequency of the water protons linearly depends on the temperature as

φ(t) − φ0 ΔT (t)= , (2.1) α · γB0 · TE where ΔT (t) is the temperature diﬀerence in Kelvin at time t with respect to time t0, φ(t) is the phase at time t, φ0 the phase at time t0, TE the echo time and α = −0.01 ppm/K a phenomenological constant representing the linear dependence

13 Chapter 2 Towards real-time MR thermometry using SMS of the electron screening on the temperature (Hindman 1966). From eq. (2.1) it can be derived (Conturo and Smith 1990) that the standard deviation of the temperature diﬀerence is inversely proportional to the snr of the magnitude image,

σΔT ∼ Δφ/snrmag. (2.2)

This shows the importance of high magnitude snr for precise temperature measurements. The reconstruction of sms images is similar to a sense reconstruction where aliased images are unfolded into unaliased images using coil sensitivities. The acquisition is however quite diﬀerent since sense acquires less phase encoding lines per slice whereas sms acquires data containing signal from multiple slices simultaneously. Because sms does not undersample, it has a potentially higher snr compared to sense as explained by

snrold snrold snrsense = √ , snrsms = . (2.3) gsense R gsms

Here snrold is the snr of the unaccelerated scan, R is the acceleration factor and g is the spatially varying geometry√ factor. When we combine this with equation 2.2 we see that σΔT is a factor R lower for sms than for sense. The g-factor quantiﬁes the noise ampliﬁcation due to imperfect unfolding and depends on the aliasing pattern and coil geometry. It is calculated from the coil sensitivity matrix S and the noise correlation matrix Ψ, given by (Pruessmann et al. 1999) H −1 H gρ = (S ΨS)ρ,ρ(S ΨS)ρ,ρ. (2.4)

Because the aliasing patterns of sense and sms are different, their g-factors will in general not be equal. As shown in eq. (2.3), the snr of sense is limited by both the acceleration factor R and the g-factor. The snr of sms on the other hand is only limited by the g-factor, that is minimized by controlled aliasing which shifts the simultaneous acquired slices with respect to each other (Breuer et al. 2005). This shifting is induced by a slice dependent phase ramp in k-space. For regular gradient echo sequences this phase ramp can be applied by cycling different mb rf pulses, while for epi sequences this is effectively done by using gradient blips in the slice selection direction (Setsompop et al. 2012).

2.3 Materials and methods

To test our hypothesis we performed two experiments. In the ﬁrst we used litt heating and sms to increase the spatial coverage. In the second we used hifu heating and sms to also increase the temporal resolution.

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2.3.1 LITT experiment: increased spatial coverage The use of sms for increased spatial coverage was validated in a phantom experiment using litt heating. The experiments were performed on a 1.5 T Philips Ingenia scanner (Philips Healthcare, NL) with a maximum gradient strength of 45 mT/m and a maximum slew rate of 200 T/m/s. The phantom was a cylindrical 2% agar gel with a main axis of 12 cm, aligned with the magnetic ﬁeld, and a diameter of 18 cm. It was doped with 0.20 g/L CuSO4 to enhance absorption of laser power.

A MICRODOM litt fiber (KLS Martin, DE) with a core diameter of 400 μm and an active area of 25 mm was inserted into the phantom and connected to a Nd:YAG laser (TT Yag-80; Trumpf Medizine Systeme, DE). A fiber optic Luxtron probe (LumaSense Technologies, US) was inserted 14 mm from the litt fiber to validate the accuracy of the mr temperature measurements. Because the laser interferes with the Luxtron probe, its measurements during heating were not reliable and were therefore omitted (Reid et al. 2001). A 15-channel coil array was used for signal reception. The setup is illustrated in figure 2.1a.

Heating was applied with the laser operating at 36 W for 60 s. The total scan time was about 4 minutes, consisting of 30 s prior to heating, 60 s continuous heating and 150 s cooldown. In between scans a cooldown time of 15 minutes allowed the heated region to return to thermal equilibrium, which was veriﬁed by the Luxtron probe.

The imaging sequence was a gradient echo multi-shot epi sequence (epi factor = 2 7, fov = 210 × 210 mm , matrix size = 140 × 140, TR/TE = 30/15 ms, ﬂip angle = 12 ◦, slice thickness = 5 mm, slice gap = 0 mm). The caipirinha controlled aliasing pattern of sms was induced by gradient blips. The unaccelerated scan contained 4 slices and had a dynamic scan time of 2.8 s. The accelerated scans had the same dynamic scan time and imaging parameters, with the exception of scans with acceleration factor 6, which had also a shorter dynamic scan time. In that way, the stack did not extend beyond the phantom and the number of locations to be unaliased was equal to the acceleration factor. The spatial coverage and dynamic scan time are shown in table 2.1.

The slices were placed in transverse orientation such that the center 4 slices were at the same position for each experiment. To measure the standard deviation of the temperature maps, all scans were repeated without heating, acquiring 100 dynamics (Goerner and Clarke 2011).

2.3.2 HIFU experiment: increased temporal resolution The use of sms for increased temporal resolution was validated in an ex-vivo bovine tissue experiment using hifu heating. The experiments were performed on a 1.5 T Philips Achieva scanner (Philips Healthcare, NL) with maximum gradient strength of 33 mT/m and maximum slew rate of 80 T/m/s. The sample consisted of a piece of bovine tissue and a 2% agar, 2% silica gel placed beside it to obtain a

15 Chapter 2 Towards real-time MR thermometry using SMS No Accel. SENSE 2 SMS 2 SENSE 3 SENSE 1.5 +SMS2 SMS 3 SENSE 4 SENSE 2 + SMS 2 SMS 4 SENSE 5 SMS 5 SENSE 2 + SMS 3 SMS 6 Acceleration factor 1223 3 34 4 455 6 6 Number of slices 4 8 812121216161620201818 Scan time per dynamic (s) 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.1 2.1

Table 2.1: Spatial coverage expressed in number of slices, and temporal resolution expressed in scan time per dynamic for the unaccelerated (No Accel.) and accelerated scans of the litt experiment.

(a) (b)

Figure 2.1: Illustrations of the setups of the litt experiment (a) and hifu experiment (b). realistically sized object of 12 × 20 cm with the largest dimension in the right-left direction. A 2-channel coil array integrated in the tabletop and a 16-channel coil array on top of the phantom were used for signal reception. The coil elements of the 2-channel coil array are positioned next each other in the right-left direction, hence we chose the phase-encoding in this direction. The setup is illustrated in ﬁgure 2.1b.

Heating was applied by using a clinical hifu system (Sonalleve, Philips Healthcare, FI), using a transducer with a focal length of 140 mm. In the bovine tissue, regions of 4 mm in diameter and 8 mm in length were sonicated for 60 s at 40 W. Between sonications the sample was allowed to cool down for 15 minutes. As before, the scan time was 4 minutes, consisting of 30 s prior to heating, 60 s heating and 150 s cooldown.

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The imaging sequence was a fat-suppressed turbo field echo (spectral pre- saturation with inversion recovery (spir)-turbo field echo (tfe)) sequence (tfe 2 factor = 13, fov = 234 × 234 mm , matrix size = 156 × 156, TR/TE = 13/9.2 ms, flip angle = 10◦, slice thickness = 5 mm, slice gap = 20 mm). The caipirinha controlled aliasing pattern of sms was induced by phase cycling different mb rf excitation pulses. They were calculated in matlab (The Mathworks, US), tak- ing as inputs the intended excitation profile, flip angle, and phase shifts for the controlled aliasing (Sbrizzi et al. 2011).

The unaccelerated scan contained 2 slices and had a dynamic scan time of 6.5 s. The accelerated scans were similar to the litt experiment, although the maximal acceleration factor studied was lower because of the diﬀerent coil conﬁguration. The acceleration was used to increase the temporal resolution as well as the spatial coverage which is arguably the most useful for hifu. The spatial coverage and dynamic scan time are shown in table 2.2. No Accel. SENSE 2 SMS 2 SENSE 3 SENSE 1.5 + SMS 2 SMS 3 SENSE 4 SMS 4 Acceleration factor 1223 3 344 Number of slices 2223 2 344 Scan time per dynamic (s) 6.5 3.3 3.0 3.3 2.2 3.0 3.3 3.0

Table 2.2: Spatial coverage expressed in number of slices, and temporal resolution expressed in scan time per dynamic for the unaccelerated (No Accel.) and accelerated scans of the hifu experiment.

The dynamic scan time of the sms sequences is slightly lower than the sense sequence with equal imaging parameters.

Again, the sequences were repeated without heating, acquiring 100 dynamics to measure the standard deviation. All images were reconstructed oﬀ-line in matlab using ReconFrame (GyroTools, CH) and a custom sense implementation. The g- factor maps were calculated from eq. (2.4).

2.3.3 Image analysis A high-snr baseline image was formed by averaging the first 5 pre-heating dynamics, after spatial phase-unwrapping (Maier et al. 2014). Subsequently, the temperature maps were calculated frame by frame from the phase difference with this baseline image, according to eq. (2.1). Any residual phase-wraps after sub- traction were removed by a modulus operation such that the final phase difference was between −π and π. Subsequently the temperature maps were corrected for

17 Chapter 2 Towards real-time MR thermometry using SMS

ﬁeld drift by subtracting the average of a large region of interest (roi) outside the heated region. The precision was quantiﬁed by calculating the temporal standard deviation in each voxel from the repeated scans without heating.

2.4 Results

Selected temperature maps of the unaccelerated and accelerated scans using litt and hifu heating are shown in ﬁgures 2.2 and 2.3 respectively. Two slices are depicted: the slice through the focus and a parallel slice at 10 mm distance. The geometry of the heated regions of the unaccelerated and accelerated scans are in agreement with each other. The temperature maps also show that sms has a higher temperature-to-noise ratio than sense, especially during hifu. During litt this diﬀerence is less obvious due to the lower noise level.

2.4.1 LITT experiment: increased spatial resolution In the litt experiment the accelerations were mainly used to increase the spatial coverage while keeping the dynamic scan time fixed. The temperature curves obtained from the Luxtron probe and from the mr thermometry sequences are shown in figure 2.4. The temperature curves from the unaccelerated scan were in good agreement with the temperature curves from the accelerated scans, confirming consistency between the unaccelerated, sms accelerated, sense accelerated, and sense/sms accelerated scans. The pre-heating (0-30 s), heating (30-90 s), and cool-down (90-240 s) regions can be clearly distinguished with the peak temperature difference in the focus reaching 21 ◦C. The temperature curves from mr thermometry also show good agreement with the temperature curves from the Luxtron probe during the cooldown period, confirming that accuracy during cooldown is unaffected by the acceleration techniques. During heating the optical sensors of the Luxtron probe interfered with litt, which is why this data is not shown.

The temperature proﬁles also suggest that the precision of the measurements was improved by using sms instead of sense, especially for acceleration factors 3-5. Acceleration factor 6 shows that sense 2+sms 3 has less noise than sms 6, illustrating the usefulness combining both parallel imaging techniques.

The improvements in precision were further quantiﬁed by the standard deviation calculations obtained from the scans without heating. At the focus and for accel- ◦ ◦ eration factor ≤ 2 in particular, these were σunacc. =0.28 C, σsms2 =0.29 C, and ◦ √σsense2 =0.40 C. The ratios σunacc./σsms2 =1.01 and σunacc./σsense2 =1.38 ≈ 2 quantify the degradation in precision of the temperature measurements from the accelerated scans with respect to the unaccelerated√ scan. These results are in accordance with equation 2.3, which predicts a factor 2 improvement of sms 2 over sense 2, for similar g-factors.

To appreciate how the diﬀerent acceleration techniques perform we require a more global approach, that takes the spatial variation of the g-factor, and hence of the

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Figure 2.2: Selected temperature maps of the unaccelerated (A), sense 2 accelerated (B) and sms 2 accelerated (C) scans during litt. Two slices are depicted: the ﬁrst contained the center of the focus and the Luxtron probe( white marker), the second was at 10 mm distance. The distance between the focus and the Luxtron probe was 14 mm. Note the piecewise linear temperature scale to highlight the noise level as well as the heating.

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Figure 2.3: Selected temperature dynamics of the unaccelerated (A), sense 2 accelerated (B) and sms 2 accelerated (C) scans scans during hifu. Two slices are depicted with a slice gap of 20 mm. The ﬁrst one contains the center of the focus.

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Figure 2.4: Temperature curves using litt heating measured by mr thermometry at the focus (solid blue) and at the Luxtron location (solid red), and measured by the Luxtron probe at the Luxtron location (dashed green). The epi sequences were unaccelerated, sense accelerated, sms accelerated, and sense/sms accelerated as indicated in the ﬁgure. The rois were 2 × 2 mm2.

21 Chapter 2 Towards real-time MR thermometry using SMS precision into account. This is done by calculating the aforementioned ratio for every voxel and every slice. In figure 2.5, maps of σacc./σunacc. are shown for the slice through the focus, illustrating the spatial variation of the degradation in precision. The corresponding g-factor maps are also shown. For acceleration factors up to 3 the g-factors are still smaller than 2 for all scans at all locations. We see however that with sms the precision degrades less than with sense and that the combination of sense 1.5 and sms 2 performs better than√ sense 3, but worse than sms 3. These differences can be attributed to the R penalty that sense with acceleration factor R suffers from, since the g-factors are very similar between the three scans in most regions. For acceleration factors 4 and 5 we see the g-factor rising rapidly for both sense and sms√ , with the latter still performing better since the snr does not suffer from the R penalty. Acceleration factor 5 is clearly the limit of sms, showing regions where precision is strongly degraded.

In figure 2.6 boxplots of two different rois in the precision degradation maps of figure 2.5 are shown, with one roi at the focus and one roi at the center of the image. These boxplots quantify the local precision degradation variation. We can clearly see that the difference√ between sense 2 and sms 2 is close to the potential theoretical value of 2 from eq. (2.3). The same holds for sense 3 and sms 3, and sense 4 and sms 4, at least at the focus where g-factors are relatively low. The g-factors are higher at the center of the image, and also show√ more variation there between sense and sms. We therefore not always see this R improvement factor in this region. In both regions sms 5 is still better than sense 5, but sms 6 is worse than sense 2+sms 3. This is another indication that sms starts to break down at acceleration factor 6.

2.4.2 HIFU experiment: increased temporal resolution In the hifu experiment the acceleration methods were used to increase the temporal resolution and/or increasing the spatial coverage, as indicated in table 2.2. The resulting temperature curves are shown in ﬁgure 2.7.

The temperature measurements of the accelerated scans agree with those of the unaccelerated scan. The figure also shows that sms acceleration resulted in temperature measurements that were more precise than when sense acceleration was used. This last observation was confirmed by the standard deviations obtained from the scans without heating. At the focus and for acceleration factor ≤ 2 in ◦ ◦ ◦ particular, these were√ σunacc. =1.0 C, σsms2 =1.1 C, and σsense2 =1.6 C, resulting in a factor 2 improvement in precision of sms 2oversense 2. In figure 2.8 maps of the ratio σacc./σunacc. are shown for the slice containing the focus. We see that in all regions sms 2 performs better than sense 2. When we go to acceleration factor 3 we see that sense 3 breaks down in most regions, but that sms 3 and sense 1.5 + sms 2 give more noisy but still accurate results. At acceleration factor 4 we see that sms also breaks down, leading to high degradation factors.

In figure 2.9 boxplots of two different rois in the precision degradation maps of figure 2.8 are shown, with one roi at the focus and one roi at the center of the

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Figure 2.5: For the litt experiment, maps of the standard deviations of the accelerated scans divided by the standard deviation of the unaccelerated scan are shown in the colored figures, and the corresponding g-factor maps are shown in gray scale. The figure shows acceleration factors 2 - 6, (A) - (E), containing different combinations of sense and sms as indicated in the figure. The fov was 210×210 mm2.

23 Chapter 2 Towards real-time MR thermometry using SMS

" σacc. σunacc.

Figure 2.6: Boxplots of the spatial variation of σacc./σunacc., of which maps are shown in ﬁgure 2.5. The roi was 10×10 mm2, centered at the location of the laser ﬁber.

√ image. For acceleration factor 2, an improvement factor of 2 of sms√ over sense is observed. Acceleration factor 3 shows an improvement factor of 3 of sms over sense at the location of the hifu focus, where the g-factors of sense and sms are similar.

Experiments using smaller slice gaps showed that the temperature measurements were hardly influenced by the slice gap when using sms with rf pulse alternation, see figure 2.10. Scans with a slice gap of 5 mm were in agreement with those with a slice gap of 15 mm. Only when the simultaneous excited slices were immediately adjacent, the temperature curve deviated. This means that even stacks with relatively few slices placed close together can benefit from acceleration by sms. This can be the case for hifu, where some clinical protocols have slice distances of less than 1 cm (Merckel et al. 2016).

2.5 Discussion

This study showed that prfs thermometry can be accelerated with sms.The litt experiments in the phantom showed that sms can accurately accelerate epi sequences which can be used to increase the spatial coverage. The snr advantage √of sms over sense led to an improvement in precision of approximately a factor R, with R =2, 3, 4 the acceleration factor, as expected from eq. (2.3), for the same spatial coverage and acquisition time. From acceleration factor 5 and over the precision degraded rapidly. The hifu experiment showed that sms can also be used to increase the temporal resolution and increase the spatial coverage, where

24 Chapter 2 Towards real-time MR thermometry using SMS

Figure 2.7: Temperature curves from hifu heating in ex-vivo bovine tissue of the heated focus (blue) and far ﬁeld (green) measured by prfs thermometry. The sequences were unaccelerated, sense accelerated, sms accelerated and sense/sms accelerated as indicated in the ﬁgure. The rois were 2 x 2 mm2.

25 Chapter 2 Towards real-time MR thermometry using SMS

Figure 2.8: For the hifu experiment, maps of the standard deviations of the accelerated scans divided by the standard deviation of the unaccelerated scan are shown in in color and the corresponding g-factor maps are shown in grayscale. The figure shows acceleration factors 2-4, (A)-(C), containing different combinations of sense and sms as indicated in the figure. The fov was 234 × 234 mm2.

the same improvement in precision over sense was observed. Here the method broke down at acceleration factor 4. The accuracy was maintained down to a slice gap as small as 5 mm. A deviation of the temperature curve was seen when the simultaneous excited slices touched each other, which was likely caused by unfolding and excitation errors.

The g-factor is a potentially limiting factor of sms and depends on the coil geometry and the controlled aliasing pattern used. Current clinical mr-guided hifu (Deckers et al. 2015) and mr-guided litt (Carpentier et al. 2011) systems often have coils that do not allow for parallel imaging. This study showed that even coils with a limited number of elements allow for a signiﬁcant increase in acceleration when using (combinations of) sense and sms. We therefore believe that mr systems for imaging guidance, where imaging speed is often a key factor, will beneﬁt greatly from having multichannel coil systems.

26 Chapter 2 Towards real-time MR thermometry using SMS

Figure 2.9: Boxplots of the spatial variation of σacc./σunacc., of which maps are shown in ﬁgure 2.8. The roi was 10×10 mm2, centered at the location of the hifu focus.

20 gap 15 mm gap 5 mm 15 gap 0 mm

10 T (°C) Δ 5

0 0 60 120 180 240 time (s)

Figure 2.10: Heating curves using sms during hifu with decreasing slice gaps. Only when the slices are immediately adjacent (green curve) the temperature deviates.

27 Chapter 2 Towards real-time MR thermometry using SMS

In other applications of sms such as functional mri and diﬀusion tensor imaging, mb factors up to 12 are achieved with coils with 32 channels (Feinberg and Set- sompop 2013), and over. Such coils are not practical for current mr-guided hifu and mr-guided litt systems, and even with these coils there remains a need to restrain the g-factor. Sms is therefore almost always used in combination with controlled aliasing techniques such as caipirinha.

The peak B1 of mb rf pulses can be very high in some applications, because it increases linearly with the mb factor when no optimization is performed. In prfs thermometry, however, the ﬂip angles are relatively low because the short repetition time results in a low Ernst angle. It is therefore unlikely that the peak B1 will be too high. E.g., in our experiments B1 < 6 μT.

Successful acceleration has also been achieved by using epi alone (Holbrook et al. 2010), reaching 3.43 fps. This can however lead to geometric distortions. The combination of epi with sms in the litt experiment allowed us to use a relatively low epi factor of 7, reducing these distortions. Reduced geometric distortions lead to a better adaptive feedback loop during mr-guided litt and mr-guided hifu, because the temperature map and the actual focus are better aligned.

In this study we did not have the possibility to use sms with epi during hifu heating because of system incompatibilities. Furthermore, in the hifu experiment we used the prepulse-based fat suppression technique spir whereas a spectral-spatial mb rf pulse might be preferable, since it would potentially shorten the acquisition time. Recently, a power independent number of slices (pins) based spectral-spatial mb pulse was proposed, however, the extent of the excited slice locations would limit its application for real-time interventional guidance (Anderson et al. 2014).

There are several scenarios in which sms can be of value. Typically, a hifu protocol consists of a coronal stack perpendicular to the beam containing slices through the focus, near ﬁeld, and far ﬁeld, and of a saggital stack to capture the heating along the beam path (Voogt et al. 2012). Especially when non-circular or multiple transducers are used to create the lesion (Deckers et al. 2015), it could be desirable to have multiple slices in the focus because its shape may not be symmetric any- more. In that case sms could be used to increase the coverage while maintaining temporal resolution and precision.

During stereotactic litt treatments, real-time mr thermometry can be used to switch off the laser when the temperature reaches a certain threshold (Curry et al. 2012). Increasing the spatial coverage of the focus by using sms could help to make this procedure more robust, especially when there is some uncertainty in the location of the laser tip. During litt treatments with a diffusing laser tip, the energy is distributed over a larger volume. An increase in spatial coverage could help to better characterize the lesion during real-time mr thermometry. Likewise, litt could benefit from an increased temporal resolution to accommodate for fast temperature changes.

Increased spatial coverage has also been succesfully achieved with 3D mr ther-

28 Chapter 2 Towards real-time MR thermometry using SMS mometry, which has the advantage of high snr (Todd et al. 2012). The authors accelerated this sequence by using undersampling in combination with temporally constrained reconstruction. Without this undersampling the acquisition time of the 3D sequence was comparable to the 2D sms sequence, about 2.8 s for 8 slices with similar fov and epi factors. It would be interesting to see how sensitive to motion the 2D sms sequence is, and compare that to the 3D sequence, but that was outside the scope of this note.

Sms is a very versatile technique in the sense that it can be combined with many other acceleration methods. In this work we combined it with sense and multi- shot epi, but it is also possible to use it with for example spiral sequences (Zah- neisen et al. 2014). It has been shown that prfs thermometry with a spiral readout can reach a temporal resolution of 0.58 s/image (Staﬀord et al. 2000). This may be further improved by combining it with sms, although gradient imperfections may hamper its current clinical applicability. Additional improvement may also be obtained by Kalman ﬁltering, which relies on a model that describes the heat transfer in biological tissues. This has been shown to be able to increase accuracy and precision of prfs sequences with low snr (Roujol et al. 2012).

Sms accelerated imaging might also be useful for mr-guided radiotherapy with the mri-linac system, aiming at real-time and on-line mr guidance of external beam radiotherapy. Fast imaging is crucial for the adaptive feedback loop of such a system.

2.6 Conclusion

Sms is a viable method to accelerate prfs thermometry while maintaining accuracy and precision. The speedup that can be achieved depends mainly on the coil geometry. In our experiments sms consistently outperformed sense, reaching higher precisions with similar acceleration factors.

Acknowledgements

The authors thank the ITEA (project 12026, SoRTS) for funding.

CHAPTER 3

Assessment of 3D motion modeling performance using SMS

The following chapter is based on: Borman, P. T. S., Bos, C, Stemkens, B, Moonen, C. T. W., Raaymakers, B. W., and Tijssen, R. H. N. (2019a). “Assessment of 3D motion modeling performance for dose accumulation mapping on the MR-linac by simultaneous multislice MRI”. in: Physics in Medicine & Biology 64.9, p. 095004

31 Chapter 3 Assessment of 3D motion modeling performance using SMS

Abstract

Hybrid mri-linac systems enable intra-fraction motion monitoring during radiation therapy. Since time-resolved 3D mri is still challenging, various motion models have been developed that rely on time-resolved 2D imaging. Continuous validation of these models is important for accurate dose accumulation mapping. In this study we used 2D sms imaging to improve the principal component analysis (pca)-based motion modeling method developed previously (Stemkens et al. 2016b). From the additional simultaneously acquired slices, several independent motion models could be generated, which allowed for an assessment of the sensitivity of the motion model to the location of the time-resolved 2D slices. Additionally, the best model could be chosen at every time-point, increasing the method’s robustness. Imaging experiments were performed in six healthy volunteers using three simultaneous slices, which generated three independent models per volunteer. For each model the motion traces of the liver tip and both kidneys were estimated. We found that the location of the 2D slices influenced the model’s error in five volunteers significantly with a p-value < 0.05, and that selecting the best model at every time-point can improve the method. This allows for more accurate and robust motion characterization in mr-guided radiotherapy.

3.1 Introduction

Current commercial mri-linac systems (Lagendijk et al. 2008; Mutic and Dempsey 2014) oﬀer on-line tumor motion monitoring. However, the required sub-second imaging frame rate restricts this type of imaging to single-slice (2D) acquisitions. While 2D imaging is suﬃcient for tracking the tumor, one would ideally obtain volumetric (3D) information during treatment in order to calculate the accumulation of radiation dose to the tumor as well as to the organs at risk oars for each fraction (Glitzner et al. 2015c; Stemkens et al. 2017). Accurate dose accumulation mapping allows inter-fraction, or even intra-fraction, treatment adaptation if the tumor coverage or oar constraints are violated (Kontaxis et al. 2015).

To generate volumetric images with a suﬃciently high frame rate, several groups have developed motion models (McClelland et al. 2013; Stemkens et al. 2018) that rely on surrogate signals (McClelland et al. 2017) or prior respiratory-correlated 4D-mri data (Siebenthal et al. 2007; Harris et al. 2016; Stemkens et al. 2016b). One of the latter approaches is to parametrize the motion from the 4D-mri scan by a pca. This model is then used in combination with incoming 2D data at the time of treatment to warp a 3D reference image to the current anatomy. Although this method of generating 3D+t images has been demonstrated before as a proof- of-principle (Stemkens et al. 2016b), the performance and robustness needs to be characterised and monitored in order to be clinically applicable.

32 Chapter 3 Assessment of 3D motion modeling performance using SMS

Sms imaging (Barth et al. 2015) is a recently introduced parallel imaging method in which multiple parallel slices are acquired simultaneously using mb rf pulses. The collapsed slices are unfolded during image reconstruction using parallel imaging techniques (Pruessmann et al. 1999). Sms thus increases the spatial coverage without decreasing the imaging frame rate. Unlike standard (in-plane) parallel imaging, sms acceleration introduces only a marginal snr penalty (Barth et al. 2015). Apart from the obvious advantages for real-time motion tracking (i.e., tracking of multiple anatomical sites such as tumor and oars), the additional slices can be used as an independent validation-by-consistency check to assess the quality of the generated 3D+t data, since all slices are acquired synchronously. Sms therefore provides the means to assess the accuracy of the motion model at locations outside the input slice.

In this work we assess the performance of the pca-based motion model developed previously by (Stemkens et al. 2016b). We investigate the model’s sensitivity to the location of the input slices. By using multiple distinct subsets of sms input slices, different 3D cine data sets are generated and assessed. We show that the location of the input slices affects the performance of the motion model. By combining the different models into a best selection model, we were able to make the technique more robust against outliers.

3.2 Materials and methods

All imaging experiments were performed on a 3 T Ingenia system (Philips Health- care, NL) in six healthy volunteers who were scanned under a technical development protocol approved by the institutional review board. The acquisition consisted of a respiratory-correlated 4D-mri sequence followed by a cine sms sequence.

3.2.1 Acquisition The 4D-mri acquisition consisted of a spoiled gradient echo (spgr) sequence with a spir fat suppression pre-pulse, using a golden-angle stack-of-stars readout tra- ◦ jectory, with the following scan parameters: ﬂip angle = 10 , TR/TE = 2.8/1.2 ms, time between inversion pulses / inversion delay = 146/29 ms, resolution 2.1×2.1×4 mm3, fov 350×350×170 mm3. The acquisition took 5 minutes during which 2000 projections were collected. The reconstruction was performed oﬀ-line in matlab (The Mathworks, US). First, the respiratory navigator signal was calculated per projection from the signal at the center of k-space (k =0) (Zhang et al. 2016). Based on this navigator signal, the projections were subsequently sorted into 10 respiratory phase bins, creating a 4D k-space. After this, the data was transformed to image space using an xD-GRASP reconstruction (Feng et al. 2016).

The sms acquisition was implemented on the scanner to allow for multiple interleaved stacks of slices using an spgr sequence with spir fat suppression. The phase cycling that is required for sms was implemented by small gradient blips before each readout (Setsompop et al. 2012). This sms acquisition was used to ac-

33 Chapter 3 Assessment of 3D motion modeling performance using SMS quire three simultaneous coronal slices interleaved with three simultaneous sagittal slices during free breathing for 90 s. The acquisition time was 400 ms per frame per stack orientation. The imaging parameters were: ﬂip angle = 15◦, TR/TE = 2.7/1.1 ms, time between inversion pulses / inversion delay = 136/23 ms, resolution 2.34 × 2.34 mm2, fov 350 × 350 mm2, slice thickness = 8 mm, inter-slice distance = 23 mm. The slices were positioned in the abdomen such that at least one pair intersected the right kidney and the others contained parts of the liver. The images were reconstructed oﬀ-line in matlab using ReconFrame (Gyrotools, CH) and a custom implementation of the sense unfolding algorithm (Pruessmann et al. 1999).

Figure 3.1: Schematic overview of the motion model generation (left) and analysis (right). Three independent motion models are calculated using three disjunct sets of input slices, sets 1, 2, and 3, for the cost function minimization. This cost function minimization calculates the weights of the principle components, resulting in a 3D deformation ﬁeld that warps the reference volume to the current state of the anatomy.

3.2.2 model generation Following (Stemkens et al. 2016b) the motion model was created by registering the different respiratory phase volumes to each other using non-rigid image registration based on optical flow (Zachiu et al. 2015), after which a principal component decomposition of the corresponding motion fields was performed, see figure 3.1. Using the motion fields, a mid-position state was estimated, which served as the 3D reference volume (Vref ). To prevent overfitting of the model and to limit computation time, only the first and second principal components (P1,2) were selected, since this is the minimum number required to describe hysteresis. Any linear combination of these two principal components describes a 3D motion field that can be used to transform the reference volume to a different motion state.

The registration was based on the image gradient ∇I instead of the intensity I, to allow for contrast diﬀerences between the sms and 4D-MR images (Ying Sun

34 Chapter 3 Assessment of 3D motion modeling performance using SMS et al. 2004). The two coeﬃcients c1,2 of this linear combination were estimated for every frame of the sms sequence by maximizing the gradient similarity between the sms slices (Isms) and the corresponding slices of the transformed reference volume. The cost function that was minimized was

L(c1,c2)=− |Gi,trans||Gi,sms| cos(2(θi,trans − θi,sms)), with (3.1) i∈voxels

Gtrans = ∇(S · (c1P1 + c2P2)Vref ), and Gsms = ∇Isms.

Here, Gtrans and Gsms are the transformed and sms gradient images with gradient directions θtrans and θsms. The cosine term causes the algorithm to favour parallel and anti-parallel gradients, which allows for contrast differences. The first two principal components, P1,2, act as operators that transform the reference volume. The operator S performs a multi-planar reconstruction (mpr) on the transformed volume to select those slices corresponding to the location of sms images Isms. For this non-linear optimization problem a pattern search algorithm (Audet and Dennis 2002) was used, which was initialized with the optimized parameters from the previous time point. To eliminate the influence of motion between the interleaved coronal and sagittal slices, they were treated as independent frames, i.e. the model was fit to the coronal and sagittal slices separately, effectively doubling the frame rate compared to the earlier method by (Stemkens et al. 2016b). There the model was fit to the sagittal slice, and independently validated by the subsequent coronal slice. The models 1,2, and 3 therefore each consist of two independent interleaved sagittal/coronal models.

To assess the influence of the position of the model input slices three independent motion models were calculated based on three different disjunct sets of 2D sms input slices (figure 3.1: outlined in red, blue, and green). For the first model the anterior coronal and right sagittal slices were used, containing the liver and intestines (red outlines). For the second model the middle coronal and middle sagittal slices were used, containing the liver and a small part of the kidney (blue outlines). Finally, for the third model the posterior coronal and left sagittal slices were used, containing the liver and a large part of the kidney (green outlines). Since the 2D sms slices in each orientation (i.e. each stack) were acquired simultaneously, the only differences between the model inputs were the slice positions.

3.2.3 Analysis Model comparison The differences between the three models were quantified by tracking five landmarks on both the 2D sms slices (termed reference) and the 3D time-series generated by the three models (termed model estimate). For this a matlab implementation of the minimum output sum of squared error (mosse) tracking algorithm was used (Bolme et al. 2010; Heerkens et al. 2014), which was visually validated to ensure all landmarks were tracked accurately. The precision was quantified

35 Chapter 3 Assessment of 3D motion modeling performance using SMS by tracking several points in the spine, which could be assumed stationary, resulting in a standard deviation of 0.65 mm. The landmarks were located in the coronal slices (tip of the liver, left kidney, right kidney) and in the sagittal slices (liver, right kidney), resulting in ﬁve displacement curves over time. These displacements were calculated with respect to the temporal mean position of the reference, which is representative of the mid-position. For simplicity, the analysis was limited to the cranial-caudal direction of motion only. Error curves were generated by subtracting the reference displacements from the model estimates. The error curves were summarized in boxplots, showing the error distribution, and the number of outliers (> 5 mm error) were counted. The variability of the error between the three models was compared by using the Brown-Forsythe test which calculates the probability that two or more data sets have equal variances (Brown and Forsythe 1974). Additionally, a linear regression was performed on the displacements estimated from the models as a function of the displacements estimated from the reference. Here, the intercept is a measure for the accuracy of the model’s temporal mean position and the slope quantiﬁes a possible bias towards either underestimating (slope < 1) or overestimating (slope > 1) the amount of motion.

Best selection estimate Apart from comparing the three independent models as a means for validation based on consistency, it is also possible to combine them and create a so-called best selection. This was done by selecting at every time point the model with the least absolute error, averaged over the landmarks. By construction, this best selection has the smallest mean error, and is less sensitive to incidental outliers of an individual motion model.

3.3 Results

Selected frames of the 2D sms sequence and 3D+t model are shown in ﬁgure 3.2. The three saturation bands that are visible in the sms images are a result of the interleaved acquisition of the sagittal and coronal slices. Although both the 2D sms images and the 4D-mri were acquired with a T1-weighted sequence, there is an apparent contrast diﬀerence between the sms slices and the motion model, especially with regard to the vessel structure in the liver as indicated by the white arrows.

The red circles in figure 3.2 denote the landmarks that were tracked using the mosse algorithm. An example of such a motion trace is shown in figure 3.3a, where the top graph shows the displacements estimated by the three independent models and by the minimum error model. The errors with respect to the 2D sms images, figure 3.3c, show that in this volunteer motion models 1 and 2 are accurate within 5 mm for most time points, while motion model 3 is inaccurate across the entire time series. At two instances in time models 1 and 2 diverge: at 41 s model 1 underestimates the motion by 12 mm and at 44 seconds model 2 underestimates

36 Chapter 3 Assessment of 3D motion modeling performance using SMS the motion by 10 mm. The best selection model, however, is accurate within 5 mm at both time points.

Figure 3.2: Selected coronal frames (top) and sagittal frames (bottom) of the 2D sms sequence and the 3D+t model. The model was generated using the posterior coronal slice and left sagittal slice (set 1 in ﬁgure 3.1). The red open dots denote landmarks in the liver, right kidney, and left kidney that were tracked using the mosse algorithm. The white arrows signify the vessel structure in the liver that is more apparent on the model than on the 2D sms images.

A scatter plot of the estimated displacements from the models versus the estimated displacements from the sms images is shown in figure 3.3b. The intercepts of the linear regressions for the three models are 0.1 ± 0.2 mm, 0.1 ± 0.2 mm, and 0.2 ± 0.3 mm respectively, which indicates that the temporal mean position of the models has no systematic offset with respect to the temporal mean position of the reference. The slopes however do show a significant deviation from the diagonal: 0.8±0.1, 0.8±0.1, and 0.6±0.3, indicating a underestimation of the motion by the models (see Table 3.1 for regression results in all subjects). Figure 3.3c confirms

37 Chapter 3 Assessment of 3D motion modeling performance using SMS

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Figure 3.3: Estimated displacements (a) and displacement errors (c) of the right kidney in volunteer 4 for the three independent models (red, blue, and green) and for the best selection (black). The displacement errors in (c) are relative to the displacements obtained from the coronal 2D sms images (gray waveform, panel a), and therefore only calculated at the time points where the coronal slices were acquired. (b): scatter plot of the displacements from models 1,2,3 versus the displacements from the sms images. The slope of the linear ﬁt shows that all models have a bias towards underestimating the motion. that the largest errors occur at the peaks and troughs of the respiratory waveform.

38 Chapter 3 Assessment of 3D motion modeling performance using SMS 10 06 12 09 11 07 ...... 0 0 0 0 0 0 ) of the motion. 1 ± ± ± ± ± ± > 81 79 81 04 08 03 ...... 001 001 001 0.06 . . . -value means at least one 0 0 0 p 11 0 estimates, averaged over the . < < < 0413 0 0 0706 0 0 0 . . . . 13 0 0 0 0 0 . ± 0 sms ± ± ± ± 05 01 19 28 07 ± . . . . . 0.07 0.58 0 0 92 98 1 05 01 0 . . . . . − < < 1013 0 0 12 1 12 0 141 0 05 0 17 0 ...... 0 0 0 0 0 1 0 0001 0001 0001 ) or overestimation (slope . . . ± ± ± ± ± ± 1 0 0 0 < < 84 83 29 18 19 95 < < < ...... 01 01 01 05 24 0 . . . . . 0810 0 0 13 0 1421 0 0 0 0 0 0 . . . . . 20 0 0 . 0 0 0 < < < < 0 ± ± ± ± ± ± 76 95 0 29 07 02 ...... 01 05 0 . . 0.15 0.34 0.17 0 0 < < 14 0 2123 0 0 . . . 0916 0 15 0 1 0 0 0 . . . 81 0 0 0 . ± ± ± 0 0001 0001 0001 0001 ± ± ± . . . . 11 11 26 0 0 0 0 . . . 90 92 73 0 0 0 . . . < < < < − − − 1113 0 15 0 0 10 15 14 ...... 0 0 0 0 0 0 ± ± ± ± ± ± 84 66 56 13 26 32 ...... 0 0 0 0 0 0

Right kidney Right kidney Left kidney Liver tip Liver

cor. sag. Volunteer # 1 2 3 4 5 6 model 1 model 1 model 2 model 3 model 2 model 3

-values from the Brown-Forsythe Analysis-of-variances test for all volunteers and landmarks. These values offset slope p Results of the linear regression of the model estimates versus the reference 2D Volunteer # 1 2 3 4 5 6 five landmarks. The offsetmean (mm) position describes and the the deviation slope of describes the a model’s model’s temporal underestimation mean (slope position from reference’s temporal represent the probabilities thatmodel the has a errors variance of that all is three significantly models different from have the the other same models. variance. A low Table 3.1: Table 3.2:

39 Chapter 3 Assessment of 3D motion modeling performance using SMS

The errors in the estimated displacements of the liver, left kidney, and right kidney are shown for all volunteers as boxplots in figure 3.4. The variation (random component) and mean error (systematic component) are indicative for the eventual dosimetric error when these data are used for dose accumulation. This figure shows that for all models the median error is close to 0, but the variability of the error varies between models and subjects. The best selection, created from the three models, has a variance that is consistently equal or lower compared to the three models separately. Also the number of outliers (panel d) of the best selection is lower. The significance of this variation is quantified by the Brown-Forsythe analysis, whose p-value results are outlined in table 3.2. For most, but not all, subjects the variability differs significantly depending on which slice is used as input to the motion model.

3.4 Discussion

Motion modeling is a powerful approach that facilitates intra-fraction dose accumulation by constructing synthetic 3D data sets at the frame rate of the fast 2D image acquisitions currently used for tumor tracking. The clinical applicability, however, is dependent on the accuracy and robustness of the method of use. Methods to check the validity of the motion model outside the 2D input slice are currently lacking.

Sms is a recent image acceleration technique in which multiple slices are acquired synchronously, thereby providing additional image information to assess the performance of the motion model. Moreover, sms oﬀers added ﬂexibility in how the motion model is generated as any of the simultaneously acquired slices may serve as a motion input. In cases where the primary tracking slice provides a suboptimal motion model, a more favorable adjacent slice can serve as input. In practice, one can choose the input that produces the smallest error when comparing the input (2D) data to the volumetric 3D+t cine data produced by the model. This may improve the robustness of the method, but comes with a computational expense since multiple models need to be calculated.

The motion model that was assessed is generated using a series of complex steps, each of which may contribute to the error in the ﬁnal result. Potential sources of error include residual motion information in the discarded principal components, misregistration by the optical ﬂow algorithm (Zachiu et al. 2015), or failure to converge to the global minimum (Audet and Dennis 2002).

Overall, the errors that we found were in line with the previous findings of (Stemkens et al. 2016b), but somewhat higher than the errors reported by (Harris et al. 2016) who developed a different motion model. In contrast to these previous works, the extended spatial coverage provided by sms allowed for error estimations of landmarks outside the primary tracking slice. The results showed no systematic error bias of landmarks in the primary tracking slice with respect to landmarks in other slices (e.g. in figure 3.4a model 3 was generated using the landmark’s slice, but models 1 and 2 perform generally better). Naturally, the analysis was still

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Figure 3.4: Error distribution results of the three independent models (model 1,2,3) and the best selection at the landmarks on the coronal sms slices (a-c) and on the sagittal sms slices (e-f). The number of outliers (> 5 mm error) is shown per model and per landmark in (d).

41 Chapter 3 Assessment of 3D motion modeling performance using SMS limited to the locations at which slices were acquired.

The major finding of this study is that the errors depend significantly on the slice location and vary between subjects. This difference may be attributed to the presence of non-respiratory motion (e.g. inflow, drift, or intestinal motion), which is not resolved by the 4D-mri generation (e.g., intestines have a blurry appearance). The amount of structures with irregular motion varies per slice location. As a consequence, the image gradients, on which the registration is performed varies between the 2D input slice and 3D reference volume (see Fig. 3.5). Although the cost function (Eq. 3.1) is set up in such a way that the contribution to the total cost L is small if a gradient feature only appears in one of the images, large structures like the bowel bag may still influence the optimization, while smaller structures like the liver vessels in the 4D-mri and the saturation bands in the sms images have little influence.

Our results show that the errors in the estimated displacements vary considerably between volunteers. Inspection of the data showed that this is partly explained by differences in slice positioning (e.g., the primary slice of model 3, volunteer 4 contained a lot of bowel), or respiratory amplitude. The linear regression analysis in table 3.1 shows that the motion model underestimates the respiratory motion proportional to the respiration amplitude. The offsets, on the other hand, are negligible which means that the temporal mean position of the models does not deviate from the temporal mean position of the reference. A dose accumulation analysis based on the motion model will therefore map the dose to the correct position, but the amount of respiration induced dose blurring will be underesti- mated. Based on the error distributions shown in shown in figure 3.4, we expect that the best selection model, which demonstrates the smallest variance and is most consistent between subjects, may be applicable for accumulated dose estimation in future patient studies. A thorough dosimetric analysis, however, is still needed.

Instead of using the sms slices to generate multiple independent models for validation, it is also possible to use the slices collectively as input for a single motion model. The availability of more input data could potentially lead to a better determined motion model. We have seen, however, that in most volunteers this was not the case. Instead, the combined model showed a higher average error (see Fig. 3.6). We believe this is caused by the deteriorating eﬀect of slices that contain little respiratory motion. In volunteers 1 and 4, for example, the slices used for model 3 would only deteriorate the result if they were added to the input of models 1 or 2. It might be possible to combine the sms slices in a better way, for example by masking out regions containing irregular motion, but that was outside the scope of this work.

The data in this work were acquired in an interleaved sagittal/coronal fashion in analogy to many previous studies (Paganelli et al. 2018b). The disadvantage of this, in combination with sms, is the appearance of more than one saturation bands (Fig. 3.2), which could potentially interfere with tracking algorithms. Recently

42 Chapter 3 Assessment of 3D motion modeling performance using SMS a new technique was proposed where orthogonal planes are acquired simultaneously, simultaneous orthogonal plane imaging (sopi) (Mickevicius and Paulson 2017). This has recently been applied to multi-slice based 4D-mri (Mickevicius et al. 2018), but could also be valuable as an input for the motion model used in this work. Both sms and sopi have the beneﬁt of acquiring diﬀerent slices simultaneously.

From the saturation bands it can be observed that the 2D sms slices are slightly curved. This effect is known as slice chipping and is caused by gradient non- linearities (Janke et al. 2004). In this work the slice chipping has not been taken into account in the model optimization, since the 4D-mri was centered close to iso-center and its extent in the cranial-caudal direction was limited such that it’s influence is small (Borman et al. 2018b). In slices that are positioned far from iso- center, slice chipping may become significant and should be taken into account.

In our implementation the reconstructions of the 4D-mri and interleaved sms sequences were not performed in real-time on the scanner due to computational and technical constraints. When sms is used for tumor tracking or gating, it will be important to have a low-latency real-time image reconstruction and tracking algorithm available (Borman et al. 2018a). The test group of our study consisted of healthy volunteers, which in future work we want to expand to include patients with abdominal tumors. It would be interesting to investigate how different tumor locations influence the models generated from different slice positions, and whether these would lead to significant changes in accumulated dose.

3.5 Conclusion

We have explored the use of sms to assess the performance of a pca based motion model (Stemkens et al. 2016b). Using sms we have observed that the model output depends on the location of the 2D slices that are used in the ﬁtting process. The model performance was furthermore variable across subjects, which suggests that model validation is needed when the method is to be used for dose accumulation mapping in patient studies. By generating multiple motion models, based on diﬀerent input slices of the sms acquisition, a best selection model was constructed, which has an error variability that is consistently equal or lower compared to any individual model separately.

Acknowledgements

The authors would like to acknowledge the ﬁnancial support by ITEA2 (SoRTS project, ref ITEA131001)

43 Chapter 3 Assessment of 3D motion modeling performance using SMS

Supplementary material

Gradient image differences Figure 3.5 shows selected gradient images of the anterior and posterior coronal sms and 4D-mri slices that were used as input data for the fitting of these models, i.e. ∇Isms, ∇Itrans in equation (3.1). Visual inspection of these slices shows that especially the anterior slice contains a lot of bowel, which undergoes intestinal motion (i.e. peristalsis) that is not encoded by the principal components of the motion model. The posterior slice, on the other hand, mostly contains structures that are either static, such as the spine, or whose motion is respiratory-correlated, such as the liver and kidneys. This variation in image content is a possible ex- planation for the differences between the generated motion models. See also the supplementary video, showing the coronal sms images for subject 4.

Figure 3.5: Gradient images of the anterior (left), and posterior (right) coronal sms slices (top) and 4D-mri slices after mpr (bottom) which were used as inputs for the motion models.

Combined SMS slices Instead of using the three sms slices separately to generate three independent motion models, they could also be used jointly in the optimization step of equation (3.1). Figure 3.6 shows selected results where an additional combined model was generated using all three coronal sms slices jointly. The errors were estimated in the same way as for the other models at the respective landmarks. These results show that by combining the slices, the error variability is not minimized, but is between model 1 and model 3.

44 Chapter 3 Assessment of 3D motion modeling performance using SMS

15 model 1 combined 10 model 2 best selection model 3 5 0 -5 error (mm) -10 -15 Liver tip Left kidney right kidney

Figure 3.6: Error distribution results of the three independent models (model 1,2,3), the combined model, and the best selection model for the coronal landmarks of volunteer 1. The combined model was generated using all three coronal sms slices.

CHAPTER 4

Respiratory motion tracking using golden-angle SMS

The following chapter is based on: P.T.S. Borman, R.H.N. Tijssen, B.W. Raaymakers, C.T.W. Moonen, C. Bos. Work in progress

47 Chapter 4 Respiratory motion tracking using golden-angle SMS

Abstract

Hybrid mri-linac systems enable intra-fraction motion monitoring during radiotherapy treatments. Since time-resolved volumetric mri is still challenging, most real-time motion monitoring methods rely on 2D acquisitions. These can use various sampling schemes, of which a golden-angle radial trajectory is particularly interesting due to its ability to reconstruct the data for multiple undersampling factors and at multiple temporal resolutions. In this work we combined such a sampling trajectory with sms, increasing the spatial coverage to contain multiple slices, and implemented the method on-line in the vendor’s reconstruction framework. Simulation and imaging experiments were performed to investigate the influence of the undersampling factor and of the sms factor on the image quality, and on the motion traces of the liver dome. These were obtained using an optical flow based image registration algorithm. We found that up to sms factor 4, good image quality could be achieved at a frame rate of 5 Hz, using a sliding window reconstruction. This method allows for flexible reconstructions at multiple temporal resolutions, which could be beneficial when the data is used as input for multiple applications, such as simultaneous mlc tracking and dose accumulation mapping.

4.1 Introduction

The recent introduction of hybrid mri-linac systems (Fallone 2014; Keall et al. 2014; Lagendijk et al. 2014; Mutic and Dempsey 2014) oﬀers the possibility to monitor the anatomy throughout the treatment using fast cine-mri sequences (Hu et al. 2015; Menten et al. 2017). This way, the inﬂuence of e.g. respiratory motion on the tumor position and oars can be monitored and if needed acted upon by gating the radiation beam (Crijns et al. 2011) or by controlling the mlc to track the moving target (Fast et al. 2016; Glitzner et al. 2015a). Additionally, cine-mri during treatment allows for real-time dose accumulation mapping, which enables inter- and intra-fraction treatment re-planning (Kontaxis et al. 2017).

Mri is a relatively slow imaging modality, which essentially limits real-time motion monitoring sequences to 1D and 2D acquisitions. These have been used as inputs to motion models, which additionally rely on prior knowledge such as respiratory correlated 4D-mri, acquired pre-treatment (Harris et al. 2016; Siebenthal et al. 2007; Stemkens et al. 2018). This way, it has been shown to be feasible to generate a sequence of volumes at a reasonable frame rate, albeit with an increased latency due to the additional time it takes to apply the model. Real-time respiratory motion tracking is therefore currently limited to slice-wise acquisitions.

To increase the spatial coverage of a 2D tracking sequence, sms can be applied, without substantially increasing the acquisition time (Larkman et al. 2001). Using

48 Chapter 4 Respiratory motion tracking using golden-angle SMS sms, multiple non-contiguous slices are acquired simultaneously, such that there is no time delay between them as would be the case with interleaved acquisition. Sms was originally proposed for Cartesian acquisitions (Larkman et al. 2001; Breuer et al. 2005), but has recently been adopted for radial proﬁle orderings as well (Yutzy et al. 2011). It was demonstrated that by using an iterative reconstruction, radial sms could outperform Cartesian sms at moderate to high acceleration factors. For this, a linear radial proﬁle ordering was used. In principle, however, sms is also compatible with a ga sampling trajectory.

Sampling a ga radial trajectory has several important advantages over a linear radial trajectory. First, it ensures an optimal sampling of k-space, that is az- imuthally of nearly homogeneous density for all possible undersampling factors (Winkelmann et al. 2007), potentially allowing for high accelerations even with a limited number of receive coils. Secondly, it naturally allows for sliding window reconstructions, where proﬁles are shared between multiple frames, increasing the frame rate and decoupling frame rate from imaging latency. A high frame rate is beneﬁcial for mlc-tracking since it reduces the sample-and-hold pattern, allowing for a smoother control signal for the mlc (Glitzner et al. 2019). To reduce the latency, the data may be reconstructed using radial undersampling, by reducing the sliding window width i.e., reducing the number of spokes per reconstructed frame.

The purpose of this work is to demonstrate that the combination of sms with a ga proﬁle ordering is feasible using an on-line implementation of the reconstruction algorithm. We show in simulations and experiments that sms can be used to increase the spatial coverage, while the ga proﬁle ordering allows for sliding window and undersampled reconstructions, enabling respiratory motion tracking.

4.2 Materials and methods

Radial sms was implemented following the method described by Yutzy et al. in (Yutzy et al. 2011). Analogous to Cartesian sms,amb rf pulse is used to excite multiple slices. Before the readout, a short gradient was added in the slice direction to induce a phase diﬀerence across the slices. This phase diﬀerence Δφ varied from spoke to spoke according to

2π Δφ(s, p)=s · p · (mod 2π), nsms where s is the slice index, p the spoke index and nsms the sms factor. In Cartesian sms this method is known as blipped-caipirinha (Setsompop et al. 2012) and leads to a shift between the slices in image space such that a sense reconstruction can be used to unfold them. In radial sms, however, the phase cycling leads to destructive interference of all slices with s =0 , which appear as incoherent artifacts on top of slice s =0. To reconstruct the slices, a phase-conjugate operator is applied before the Fourier transform. This operator simply multiplies the spokes

49 Chapter 4 Respiratory motion tracking using golden-angle SMS by their conjugate phase, i.e. exp(−iΔφ(s, p)), such that the signal from slice s constructively adds and all other slices interfere destructively. This operation is repeated for all slices and is computationally very eﬃcient (Yutzy et al. 2011).

4.2.1 Simulations Simulations were performed to investigate the influence of the window width and the sms factor on the motion estimation from the radial sms images. These were performed in matlab (The Mathworks, US) using the digital 4D extended cardiac- torso (xcat) phantom (Segars et al. 2010), which was adapted to provide mri contrast. The phantom was set to simulate a periodic breathing pattern, during which a ga sms acquisition was simulated by generating k-space data using an open-source non-uniform fast Fourier transform (nufft) (Fessler and Sutton 2003), applying the phase-cycling pattern described above, and summing the slices together. The image reconstruction was performed by applying the appropriate phase-conjugate operator for every slice and applying the inverse nufft. From the reconstructed images, motion curves of the liver dome were estimated by registering the images on a common reference frame using optical flow (Zachiu et al. 2015) and averaging the corresponding deformation motion fields over a roi of 3 × 3 voxels on the liver-lung interface. These simulations were performed for window widths of 32, 64, 128, and 180 spokes, where 283 spokes corresponds to a fully sampled acquisition, and for sms factors 1, 2, 3, and 4.

4.2.2 Image acquisition All imaging experiments were performed on a 1.5 T Ingenia mri system (Philips Healthcare, NL) in a single healthy volunteer who signed informed consent, under a technical development protocol approved by the institutional review board. A 2D spoiled gradient-echo sequence was used with a ga radial sampling trajectory and sequence parameters TR/TE = 3.0/1.12 ms, BW = 733 Hz/voxel, and acquisition matrix 180 × 180. The scans were limited to one minute of data acquisition. Various slice orientations (coronal and sagittal) and sms factors (1, 2, 3, 4) were acquired.

4.2.3 Reconstruction To test the real-time capability of radial sms, the conjugate-phase reconstruction and sliding window reconstruction were implemented in the vendor’s reconstruction framework Recon 2.0 (Philips Healthcare, NL), using the vendor’s nufft module. Each frame was reconstructed using a window width of 180 spokes, corresponding to an undersampling factor of π/2 with respect to Nyquist’s criterion which would require 283 spokes. 180 spokes were chosen to match the temporal footprint of a fully sampled Cartesian acquisition. We applied a sliding window factor of 3, meaning that 66% of a frame is shared with the subsequent frame, resulting in a reconstruction frame rate to 5 Hz.

50 Chapter 4 Respiratory motion tracking using golden-angle SMS

To investigate the influence of the window width, the data were reconstructed retrospectively with 32, 64, and 128 spokes, and compared to the on-line reconstruction with 180 spokes. Motion curves were generated by registering the images using optical flow and selecting an roi, analogously to the simulations. To investigate the influence of the sliding window on the sample-and-hold behavior of the motion trace, the data were retrospectively reconstructed without a sliding window and compared to the on-line reconstruction with a sliding window.

4.3 Results

The simulations showed that the image quality decreases with increasing undersampling factor, as expected, resulting in prominent streaking artifacts for a window width of 32 spokes, as shown in figure 4.1a. The motion traces of the liver dome (figure 4.1b) show that a window width of 180 spokes (blue) results in a phase shift with respect to the phantom’s reference trace (black). This phase shift is caused by the acquisition latency, which is proportional to the window width for a radial sequence (Borman et al. 2018a). The phase shift decreases for smaller window widths, which in turn results in an increased amount of randomly distributed errors, as can be seen from the trace with 32 spokes (gray). These random errors are most likely related to registration artifacts due to a reduced image quality. The errors of the four traces are visualized as deviations from the diagonal in figure 4.1c, showing a systematic error for a window width of 180 spokes, corresponding to a phase shift and hence a latency, which turns into a more randomly distributed error for a window width of 32 spokes. The mean absolute errors (maes) were 1.6 mm, 1.2 mm, 1.1 mm, and 1.3 mm for the four window widths of 180 spokes, 128 spokes, 64 spokes and 32 spokes, respectively.

The simulations using a variable sms factor show a slight increase in streaking artifacts with increasing sms factor, figure 4.2a, although not as severe as in the undersampling case. This is reflected in the resulting motion traces shown in figure 4.2b, which are comparable and do not show large deviations from each other. Even so, the sms 3 trace seems to exhibit more irregular behavior than the sms 4 trace, which is somewhat counter intuitive. The traces show a similar phase shift with respect to the reference, indicating a similar latency, which was expected since the window width is constant.

Selected images from the in-vivo experiments using the on-line reconstruction are shown in ﬁgure 4.3 for sms factors 2, 3, and 4. The reconstructed sms slices show no visible coherent inter-slice separation artifacts, which could potentially emerge when the destructive interference of the out-of-phase slices is not complete. The overall image quality of the sms 2, 3, and 4 series is qualitatively very similar, showing no large deterioration with increasing sms factor. The streaking artifacts get only slightly more pronounced, similarly to the simulation results in ﬁgure 4.2a.

The eﬀect of a variable window width was examined by retrospectively reconstructing the acquired k-space data from the coronal sms 2 series using window

51 Chapter 4 Respiratory motion tracking using golden-angle SMS

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Figure 4.1: Eﬀect of undersampling on the estimated motion. (a): Sim- ulated reconstructions of the digital xcat phantom for sms factor 2 and varying window width. (b): Corresponding motion traces of the liver dome in combindation with the reference trace (black). (c): Errors with respect to the reference trace, visualized as deviations from the diagonal and quan- tiﬁed by the mae.

52 Chapter 4 Respiratory motion tracking using golden-angle SMS

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position (vox) -15

024681012141618 time (TR) (b)

Figure 4.2: Eﬀect of sms on the estimated motion. (a): Simulated reconstructions of the digital xcat phantom for a ﬁxed window width of 180 spokes and for sms factors 1, 2, 3, and 4, respectively. (b): corresponding motion traces of the liver dome in combination with the reference trace (black).

widths of 32 spokes, 64 spokes, and 128 spokes per frame. The resulting motion traces of the liver dome, including the motion trace from the on-line reconstruction with a window width of 180 spokes, are displayed in figure 4.4a. These show no clear latency difference between the 128 and 180 spoke traces, whereas the latency of the 64 spoke trace is evidently smaller. The 32 spoke trace is, similarly to the simulations in figure 4.1b, very inaccurate, which is likely caused by increased streaking artifacts, leading to inaccuracies in the image registration.

A comparison between a reconstruction with and without sliding window is shown in ﬁgure 4.4b. A reconstruction with sliding window provides a much smoother motion trace with a reduced the sample-and-hold behavior compared to the reconstruction without sliding window. This is potentially beneﬁcial when such signals are used as input for mlc-tracking or gating.

53 Chapter 4 Respiratory motion tracking using golden-angle SMS

Figure 4.3: Selected frames from the real-time reconstructed images with sms factors 2, 3, and 4, for both sagittal and coronal orientations, using a window width of 180 spokes.

54 Chapter 4 Respiratory motion tracking using golden-angle SMS

20 180 spokes 64 spokes 15 128 spokes 32 spokes

5 position (mm)

0 0 5 10 15 time (s) (a) 15 no sliding window sliding window 10

5 position (mm)

0 0 5 10 15 time (s) (b)

Figure 4.4: Motion traces of a landmark in the liver dome for varying window widths (a) and for varying sliding window factors (b). The traces in (b) are plotted as staircases to emphasize the inﬂuence of a sliding window on the input signal to the mlc.

4.4 Discussion

The combination of sms with a ga sampling trajectory is a powerful approach to increase the spatial coverage from a single slice to multiple slices, while simultaneously increasing the frame rate by undersampling the acquisition matrix or by applying a sliding window during reconstruction. The increased spatial and temporal coverage that can be achieved with this method is potentially beneﬁcial for intra-fraction motion monitoring during mr-guided radiotherapy, enabling position monitoring of landmarks in multiple slices. The position signal can then be used to adapt the treatment in real-time either by gating the treatment beam or by performing mlc-tracking.

The slice separation algorithm of radial sms consists only of a phase-conjugate operator, and is therefore less computationally complex than Cartesian sms, where a sense reconstruction is generally performed. Radial sms relies on destructive

55 Chapter 4 Respiratory motion tracking using golden-angle SMS interference of all but one slice. If this destructive interference is incomplete, residual artifacts may appear. The results show, however, that the image quality of the sms 4 series is only slightly degraded with respect to the sms 2 series, such that an even higher sms factor may be feasible. The simulations in ﬁgure 4.2b show that the estimated position for various sms factors is similar at most time points, but that the sms 3 trace deviates most. This may be related to the optical ﬂow registration algorithm, and needs further investigation.

The imaging latency is determined by the window width i.e., the number of spokes per reconstructed frame. For mlc-tracking it is important to minimize the latency since it may compromise dosimetric coverage of the tumor. The results of this work show that by reducing the window width and hence undersampling the acquisition matrix, the latency can be reduced at the cost of increased streaking artifacts. These streaking artifacts can lead to inaccurate image registration results and therefore to errors in the motion trace, as shown in the results for a window width of 32 spokes. Therefore, in practice, a trade-oﬀ needs to be made between increased latency and image quality.

An advantage of the ga sampling trajectory is that this trade-off can be made during reconstruction by selecting a different window width, making it possible to reconstruct the same data with multiple window widths. This may be beneficial when the data is used as input for multiple applications in parallel, such as for real- time motion monitoring (Stam et al. 2013) and simultaneous dose accumulation mapping (Stemkens et al. 2017). Such applications could be implemented using the raw-data streaming solution presented in chapter 6. Although this flexibility in reconstruction could potentially interfere with the sms phase-cycling pattern, resulting in decreased destructive interference, it has been shown in simulations that this effect is negligible (Borman et al. 2017a).

The ability to perform sliding window reconstructions is one of the key advantages of a ga trajectory over a Cartesian trajectory. The results show that sliding window provides a higher frame rate, essentially decoupling frame rate from imaging latency, and reducing the sample-and-hold behavior of the position signal. A higher frame rate may be beneficial for mlc-tracking, since the mlc controller consists of proportional-integral-differential (pid) control in combination with feed- forward control (Glitzner et al. 2019). These control mechanisms can benefit from a higher sampling rate.

The combination of higher sms factors with increased radial undersampling has not been investigated in this work, but is topic of ongoing research. It can be expected, however, that radial undersampling will reduce the destructive interference, necessary to separate the sms slices from each other, leading to additional streaking artifacts. This may be alleviated by performing iterative reconstructions such as conjugate gradient (cg)-sense (Yutzy et al. 2011) or compressed sensing (cs) using temporal total variation (tv) as a sparsifying transform (Feng et al. 2014). Another way of reducing streaking and improving image quality is to reconstruct the data at a lower resolution, which has been shown to provide accurate

56 Chapter 4 Respiratory motion tracking using golden-angle SMS registration results (Glitzner et al. 2015a).

4.5 Conclusion

Achieving a suﬃcient spatial coverage and temporal resolution is one of the main challenges in motion monitoring for mr-guided radiotherapy. In this work we have shown that by combining sms with a ga sampling trajectory, it is possible to acquire multiple slices simultaneously, which can be reconstructed using a sliding window at various temporal resolutions. This has been demonstrated using an on- line implementation of the reconstruction algorithm. The sliding window increases the frame rate, reducing the sample-and-hold behavior of the resulting motion trace. By applying radial undersampling we could reduce the imaging latency, at the cost of image quality.

CHAPTER 5

Imaging latency of real-time MRI

The following chapter is based on: Borman, P. T. S., Tijssen, R. H. N., Bos, C, Moonen, C. T. W., Raaymakers, B. W., and Glitzner, M (2018a). “Characterization of imaging latency for real-time MRI-guided radiotherapy”. In: Physics in Medicine & Biology 63.15, p. 155023

59 Chapter 5 Imaging latency of real-time MRI

Abstract

Hybrid mri-linac systems can use fast dynamic mr sequences for tumor tracking and adapt the radiation treatment in real-time. For this the imaging latency must be as short as possible. This work describes how different acquisition parameters influence this latency. First, the latency was measured for Cartesian readouts with phase encode orderings linear, reverse-linear, and high-low. Second, the latency was measured for radial readouts with linear and golden-angle profile orderings. To reduce the latency, a spectro-temporal (k-t) filter that suppresses the k-space center of earlier acquired spokes was implemented for the golden- angle sequence. For Cartesian readouts a high-low ordering achieved a three times lower latency compared to a linear ordering with our sampling parameters. For radial readouts the filter was able to reduce the acquisition latency from half the acquisition time to a quarter of the acquisition time. The filter did not compromise the signal-to-noise ratio and the artifact power.

5.1 Introduction

Hybrid mri-linac systems are able to monitor the anatomy and adapt the radiation treatment in real-time, by directly tracking tumor positions on continuously acquired mr images. To account for tumor displacements during treatment, motion compensation strategies such as gating or tracking can be used. These strategies rely on a continuous feedback chain between mr acquisition and mlc control. Any substantial latency in this chain can induce a systematic oﬀset between the measured and real tumor position. This can lead to signiﬁcant errors in dose deposition as the irradiated area does not agree with the intended target area (Bedford et al. 2015; Glitzner et al. 2015c). It is therefore very important to characterize and minimize the components contributing to the total loop latency.

The loop latency can be divided into machine control (Glitzner et al. 2017), image processing (Roujol et al. 2010), and imaging latencies. We deﬁne imaging latency as the delay between the moment of physical change and its emergence in the reconstructed image. This latency can be further subdivided into contributions related to the acquisition and to non-zero data transfer and reconstruction times. Here we will mainly focus on the contribution related to the acquisition. mr acquisitions consist of line-by-line readouts in frequency (k-)space, resulting in typical scan times in the order of several hundred milliseconds for a 2D image. Since physiological motion is also of that time scale, moving structures may appear blurred. Apart from these blurring artifacts, the apparent object position derived from the mr image will lag behind the actual object position at the time the acquisition is ﬁnished, even without reconstruction and processing times. We

60 Chapter 5 Imaging latency of real-time MRI call this contribution the acquisition latency, which together with the non-zero reconstruction latency forms the imaging latency.

In this work we investigate the nature of the acquisition latency and characterize it for various fast mr readouts typically used in real-time mri for therapy monitoring.

Latency Motion platform motion platform MR image position time (a) Latency schematic (b) Motion platform

Figure 5.1: (a): Schematic view of the imaging latency where the apparent trajectory of an object on the mr image (red) has a latency Δt with respect to the physical trajectory (blue). (b): Picture of the motion platform (ModusQA, CA).

Previously, Riederer et al. (Riederer et al. 1988) demonstrated that for Cartesian readout patterns, the moment of sampling the central k-space proﬁle (i.e. k = 0) determines the position of the object in the image and hence the imaging latency. Since then, this principle has been used extensively to determine the timestamp of the image (Ries et al. 2010). Based on this qualitative principle, we aim to systematically quantify the acquisition latency on an mri-linac system and a conventional mri system, for diﬀerent Cartesian and radial readout patterns.

Radial tracking sequences have been proposed in the past (Rasche et al. 1997), and have recently become widely available clinically, motivated by their attractive properties for monitoring dynamic processes (Zhang et al. 2010). Radial sequences have incoherent undersampling artifacts and allow sliding window reconstructions of nearly arbitrary frame rate. These beneﬁts ﬁt neatly to the needs of mr-guided tracking, which is why we incorporated them in the latency analysis of this work.

For Cartesian sequences we measure the impact of partial Fourier (pf) reconstruction and the phase encode ordering on the acquisition latency. Pf is a common acceleration technique in which a certain percentage of the data is not acquired, but accounted for in the reconstruction. For linearly sampled radial sequences we measure the latency dependence on the sampling fraction.

Finally, we measure the latency and image quality of ga radial sequences and the design and implementation of a so-called spectro-temporal (k-t) filter (Song and Dougherty 2004). We evaluate if such a filter can significantly reduce the acquisition latency while retaining image quality in terms of signal-to-noise ratio

61 Chapter 5 Imaging latency of real-time MRI and artifact power.

5.2 Materials and methods

5.2.1 Experimental setup and simulations Experiments were performed on two diﬀerent systems: the clinical prototype of the 1.5T mri-linac (Elekta, SE) and a diagnostic 3 T Ingenia (Philips Healthcare, NL). The contrast giving object used for imaging was a plastic cylinder with a 2% agar solution, moved by a mr compatible 4D motion platform (ModusQA, CA) that performed a 1D sinusoidal motion trajectory in the cranial-caudal direction, see ﬁgure 5.1b. The motion period was set to 6 s and the amplitude to 15 mm. A custom TCP interface was developed to allow for real-time logging of position coordinates on a separate workstation. The logged positions served as the zero-delay gold standard. The object position calculated from the continuously acquired mr images was determined by the center-of-mass of the high-contrast object. In order to get an estimate of the latency, a sinusoidal model

x(t)=A0 sin(2πf[t + t0]) (5.1) was fit to both the reference and mr position traces. The latency TL can then be REF MR defined through the phase difference as TL := t0 − t0 , see figure 5.1a for a schematic illustration.

On the mri-linac the Cartesian and linear radial acquisitions were reconstructed on the scanner, after which the images were streamed to a separate workstation and timestamped immediately upon reception. The latency estimated from equation (5.1) therefore includes acquisition, reconstruction, and data transfer times, but not image processing (i.e. object tracking). The combined data transfer and reconstruction time had a standard deviation of 5.7 ms. The calculated latency was not expected to be influenced by this jitter, since the sinusoidal model was fit to many frames, averaging out its influence. The position coordinates from the motion platform were streamed to the same workstation such that both had the same time base. See figure 5.2 for an overview of this workflow.

The Cartesian and linear radial experiments were repeated on the 3 T mr. This system also allowed for acquisitions with a radial ga profile order, that were reconstructed offline using matlab (The Mathorks, US) with ReconFrame (GyroTools, CH). To separate acquisition latency from reconstruction and data transfer latencies, the acquisition time of every profile was logged on the spectrometer, instead of the arrival of the entire image. This enabled a direct comparison with simulations. For each frame, the acquisition time of its last profile was used as the acquisition timestamp of that frame. In order to synchronize the spectrometer with the motion platform, the time bases were matched by correcting for the 0th (offset) and a 1st (linear frequency drift) order errors between the internal clocks.

Simulations were performed with imaging parameters matching the mri-linac and 3Tmr to validate the experimental results. The simulated latency was determined

62 Chapter 5 Imaging latency of real-time MRI

Figure 5.2: Workﬂow diagrams for the mri-linac (left) and 3 T mr (right) experiments. On the mri-linac images and positions were streamed during imaging, resulting in a combined acquisition+reconstruction latency. On the3Tmr, data was timestamped upon acquisition, send to the database and synchronized with the motion platform during data processing. This resulted in only acquisition latency. from an analytical square that was moved during k-space ﬁlling (Guerquin-Kern et al. 2012). Both the analytical phantom and the experimental phantom had a single contrast (signal or no signal) and straight edges parallel and perpendicular to the direction of motion.

The edges of the analytical phantom were comparable to the experimental phantom, minimizing a potential latency difference due to different object geometries. Using an analytical phantom allowed us to calculate the k-space data with arbitrary precision. Relaxation effects were neglected such that the reconstructed images depended only on the k-space trajectory. Similar to the 3 T mr experiments, the timestamp of every frame was set to the simulation time of its last profile. The measured positions were obtained from the center-of-mass of the object. The reference positions were the actual locations of the object’s center-of-mass at the simulation time of each frame’s last profile. The latency was calculated by fitting a sinusoidal model as described by equation (5.1).

5.2.2 Cartesian In the Cartesian experiments and simulations the latency was measured for a series of pf factors1 0.625, 0.75, 0.825, and 1 (no pf) for the different phase encode ordering schemes linear, reverse-linear, and high-low. Figure 5.3 shows an illustration of these profile orderings with and without pf. Regarding the time axis, it is apparent that the moment of k =0acquisition is latest for high-low, variable for reverse-linear, and earliest for linear, which suggests different latency responses as explained in section 5.1.

Images were acquired using a spoiled gradient echo (SPGR) sequence with ﬂip angle α =10◦ and matrix size = 256 × 256. The sequence timing parameters were

1Sampled fraction relative to the fully sampled matrix

63 Chapter 5 Imaging latency of real-time MRI set to TR/TE = 2.9/1.4 ms for the mri-linac, and to TR/TE = 2.3/1.1 ms for the 3 T mr.

Simulations were performed using the same sequence parameters. A homodyne ﬁlter (Noll et al. 1991) was implemented to reconstruct the pf acquisitions, which is similar to the implementation in the reconstruction software on the used Philips mr scanners (Philips 2018).

Figure 5.3: Cartesian phase encode ordering schemes without (left) and with (right) pf. The time from sampling k =0until the end of the acquisition is hypothesized to determine the acquisition latency. This time scales linearly with the PF factor for reverse-linear, is constant for linear, and zero for high-low.

5.2.3 Radial Experiments and simulations with a linear radial readout were performed on both the mri-linac and 3 T mr system, whereas experiments with a ga radial readout were only run on the 3 T mr system. To retain similar image contrast, similar acquisition parameters as for the Cartesian experiments were used. The linear radial readouts were acquired with sampling fractions 125%, 100%, 75%, 50%, and 25%2, reducing the sampling density uniformly. The sequence timing parameters were TR/TE = 3.4/1.5 ms for the mri-linac, and TR/TE = 2.8/1.2 ms for the 3Tmr. These experiments were reconstructed on the scanner and compared to simulations that were reconstructed using a NUFFT matlab toolbox (Fessler and Sutton 2003). See ﬁgure 5.4 for schematics of the linear and ga radial proﬁle orderings.

The ga radial experiments were reconstructed offline with this NUFFT toolbox for varying window sizes containing 10 to 200 spokes. The uniform k-space coverage of the ga profile ordering allows for a spectro-temporal (k-t) filter that weighs individual spokes based on their relative acquisition time, without creating coherent

2100% equals the fully sampled matrix, i.e. 256 spokes.

64 Chapter 5 Imaging latency of real-time MRI

Figure 5.4: Schematics of the linear radial (left) and ga radial (right) sampling trajectories. The ga trajectory covers k-space uniformly at all times during the acquisition and independent of the number of spokes. For the linear profile ordering, k-space is only covered uniformly once the entire acquisition has completed. image artifacts (Song and Dougherty 2004; Winkelmann et al. 2007). To reduce the latency, a filter was designed to scale down the low frequency samples of earlier acquired spokes, while retaining the high frequency samples. By retaining the high-frequency samples, Nyquist’s criterion is not violated by the filter, which is expected to prevent enhancement of streaking artifacts. The low-frequency samples on the other hand are by definition oversampled, which allows for scaling down earlier acquired ones to lower the latency. The applied filter

1 f(k, s)=[1− S(s)]k2 + S(s), where S(s)= (5.2) x 1+e−α(s−ns/2)

is shown in ﬁgure 5.5 as a function of readout sample kx and spoke number s.

The first term indicates a quadratic high-pass weighting (Cheng et al. 2015) while the second term indicates a uniform weighting. The transition between these two regimes is modulated by the sigmoid function S(s) which depends on the filter parameter α and window size ns. This parameter was set to α =50by comparing latency and snr for different values of α, see figure 5.6. For this value the latency had converged to a stable minimum, without notably reducing the snr, while keeping the transition as smooth as possible.

In the reconstruction an additional density compensation step was added after gridding to account for the altered signal density due to the k-t ﬁlter (Pipe and Menon 1999; Magnusson et al. 2009). This was done by applying the k-t ﬁlter on the sampling pattern, gridding it from radial k-space onto a Cartesian grid, and

65 Chapter 5 Imaging latency of real-time MRI

1 1 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0 0 -128 0 128 0 50 100 150 200 (a) k-t weighting ﬁlter (b) Weighting over read- (c) Weighting over spokes, out, solid line in (a) dashed line in (a)

Figure 5.5: k-t ﬁlter consisting of a quadratic weighting along the spokes and a sigmoid function to modulate the strength of this weighting per spoke, depending on the acquisition time.

0.3 15

0.25

0.2 10

0.15

0.1 5

0.05

0 0 0 50 100 150 200

Figure 5.6: Latency and snr dependence on the ﬁlter parameter α. The number of spokes per frame was ﬁxed at 200. For α =50the latency has converged to a minimum value.

66 Chapter 5 Imaging latency of real-time MRI divide the gridded sampling data by this.

The image quality was quantiﬁed using the artifact power metric

||I − I ||2 AP = ref , (5.3) ||Iref ||2 described by Xiao et al. (Xiao et al. 2008). This was done in simulations only since in the experimental images the undersampling artifacts appeared under the noise level. Equation (5.3) was used on an analytical Shepp-Logan phantom, outside of which a high contrast object was moved to generate image artifacts caused by motion of a distant object. Instead of the analytical square used in the latency simulations, the Shepp-Logan phantom with a moving object could generate more realistic and time-varying undersampling artifacts.

5.3 Results

5.3.1 Cartesian The Cartesian results are shown in figure 5.7 for the mri-linac (left) and 3 T mr experiments (right). The offset between these two is caused by a different TR. Note that apart from the repetition time, the results are also sensitive to the acquired matrix size.

The experimental mri-linac results (solid lines) show that a linear phase encode ordering leads to a constant latency of 550 ms, independent of the pf factor. A reverse-linear ordering leads to a latency that increases linearly with increasing pf factor, matching the increasing scan time (dotted light blue line). A high-low ordering leads to a constant latency of 155 ms, independent of the pf factor. These results show that the time difference between sampling k =0and sampling the last profile, as illustrated in figure 5.3, is the dominant factor that determines the latency. The mri-linac simulations (dashed) show a latency offset of 80 ms with respect to the experiments. This offset is caused by the fact that the simulated latency only includes acquisition latency, while the experimental latency also includes reconstruction and data transfer latencies.

The experimental 3 T mr results show the same pattern. Contrary to the mri-linac results, here the experimental latency results do overlap with the simulated latency since they both include only the acquisition latency. Note that for pf factor =1 (i.e. fully sampled) the linear and reverse-linear phase encode orderings give a latency equal to half the scan time. This can be intuitively explained by the fact that for both orderings the k =0proﬁle is acquired halfway through the acquisition, see ﬁgure 5.3.

5.3.2 Radial The results from a linear radial readout are shown in ﬁgure 5.8. The mri-linac results show a diﬀerence of 122 ms between the measured and simulated latency,

67 Chapter 5 Imaging latency of real-time MRI

1 1 1 1 linear Acq. time linear Acq. time reverse linear reverse linear high-low high-low 0.8 0.8 0.8 0.8 measured measured simulated simulated 0.6 0.6 0.6 0.6 tency (s) tency (s) 0.4 0.4 0.4 0.4 a a L L Acquisition time (s) 0.2 0.2 Acquisition time (s) 0.2 0.2

0 0 0 0 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 Partial Fourier factor Partial Fourier factor (a) mri-linac latency (b) 3Tmr latency

Figure 5.7: Cartesian latency results for the mri-linac (a) and 3 T mr (b) experiments. The acquisition time per frame is plotted on the right axes (gray line). The solid lines show the measured values whereas the dashed lines show the simulated values. which is an indication of the image reconstruction and data transfer time on that particular system. The 3 T mr results again show an overlap between the measured and simulated latency, since reconstruction latency is not included. Here it is apparent that the latency is consistently equal to half the acquisition time, which conﬁrms previously reported ﬁndings that every spoke contributes equally to the object position on the image (Stemkens et al. 2016a).

1.5 1.5 1 1 Radial simulated Radial simulated Radial measured 1.25 1.25 Radial measured 0.8 0.8 Acq. time Acq. time 1 1 0.6 0.6 0.75 0.75

tency (s) tency (s) 0.4 0.4 a a

L 0.5 0.5 L

Acquisition time (s) 0.2 0.2 Acquisition time (s) 0.25 0.25

0 0 0 0 0 25 50 75 100 125 0 25 50 75 100 125 Sampling fraction (%) Sampling fraction (%) (a) mri-linac latency (b) 3Tmr latency

Figure 5.8: Linear radial latency results for the mri-linac (a) and 3 T mr (b) experiments as a function of the sampling fraction. The gray line denotes the acquisition time per frame.

The ga results are plotted in ﬁgure 5.9. Here, the interdependence between window size (positive x-axis), latency (positive y-axis), snr (negative x-axis), and artifact power (negative y-axis) is shown in four connected quadrants. The red lines represent the results with k-t ﬁlter and the blue lines the results without k-t

68 Chapter 5 Imaging latency of real-time MRI

filter. Quadrant I of this figure shows that the latency with filter is approximately half the latency without filter for a given window size. The snr and artifact power are not influenced by the filter demonstrated by the fact that the blue and red lines overlap in quadrants II and III. Quadrant IV shows that for a given latency we can obtain a higher snr when applying the filter. Conversely, if the required snr is known (e.g. 10), we can follow the red and blue rectangles to find the corresponding latency, window size and artifact power. Selected images reconstructed with and without k-t filter are shown in figure 5.10. These images show that there is no apparent qualitative difference in image quality with and without k-t filter.

Figure 5.9: Four quadrants figure of the ga results with (red) and without (blue) k-t filter containing the interdependence of window size and latency (quadrant I), window size and artifact power (quadrant II), SNR and artifact power (quadrant III), and SNR and latency (quadrant IV). By fixing one quantity (e.g. snr) the other three quantities are easily found by moving on a rectangle from axis to axis.

5.4 Discussion

Compared to other components in a tracking feedback chain (Glitzner et al. 2015c), imaging latency is a substantial contributor to the total loop latency. This work shows that the acquisition part of the imaging latency is highly dependent on the sequence and timing parameters. When not treated carefully, this can lead to suboptimal results. We have quantiﬁed the acquisition latency for Cartesian, linear radial and ga radial readouts with various sequence parameters. As expected, we

69 Chapter 5 Imaging latency of real-time MRI

(a) No ﬁlter (b) With ﬁlter

Figure 5.10: Experimental phantom images for window sizes of 150, 100, and 50 spokes, without k-t filter (a) and with k-t filter (b). The images with filter are comparable to the images without filter.

could conﬁrm the qualitative notion that the moment of sampling k =0determines most of the object’s position (Riederer et al. 1988).

Currently, most tracking sequences use 2D Cartesian readout trajectories because of their robustness. The Cartesian results in section 5.3.1 show that a linear phase encode ordering, which is the default setting on the tested mri scanners, leads to an acquisition latency of 0.5∗Tacq for pf factor 1 and does not decrease for lower pf factors. A simple modification of the phase encode ordering, a high-low ordering, leads to a latency of 0.16 ∗ Tacq, a threefold reduction. These ratios are specific to our sampling scheme and might be sensitive to other sampling parameters such as resolution, field-of-view, and acceleration scheme. In addition, they also depend on the distribution of the object’s energy in k-space. For natural images, however, this distribution is very similar and decreases exponentially with the distance from the center of k-space (Tolhurst et al. 1992).

This shows that it is worthwhile to choose a high-low or similar ordering when imaging latency is an important factor, as expected. The fact that the high-low ordering did not result in a zero latency, shows that proﬁles other than k =0do inﬂuence the position information obtained from the image.

Radial tracking sequences allow for sliding window reconstructions of nearly arbitrary frame rate. The acquisition latency, however, is independent of the frame rate since it only depends on the number of spokes in the reconstruction window. The results from linear radial readout in section 5.3.2 show that every spoke in the window contributes equally to the acquisition latency, resulting in 0.5 · Tacq, similar to the linear Cartesian ordering. The beneﬁt of ga sampling with respect to linear sampling is that neighboring spokes are not acquired close in time. This

70 Chapter 5 Imaging latency of real-time MRI allows for a filter that suppresses the lower frequency components of earlier acquired spokes, without introducing a global density variation. Our analysis showed that this filter reduced the latency by half without compromising snr and artifact power. However, the optimal shape of the filter has not been investigated. The quadratic weighting over the spokes may be improved to better approximate the real k-space energy distribution.

The artifact power was measured in simulations only because the increase in undersampling artifacts (i.e. streaking) appeared under the noise level. They may be visible when a sequence with higher snr is used, such as a balanced gradient echo, but this was outside the scope of this work. The spoiled gradient echo sequence that was used here, was selected because it is more robust to ﬁeld inhomogeneities and susceptibility diﬀerences. The results of this work are expected to be valid for balanced gradient echo sequences as well, which are frequently used because of their high snr. However, more severe eddy current artifacts can be expected with a high-low ordering because of their rapid gradient switching. Compensation strategies have been devised to minimize this behavior (Bieri et al. 2005). Apart from snr, the contrast to noise ratio (cnr) has been discussed to be very relevant for tumor tracking as well (Wachowicz et al. 2016). In addition to latency and frame rate, the mr sequence parameters should therefore also be optimized to yield the best cnr between tumor and background.

The ga experiments were not performed on the mri-linac, but only on the 3 T mr, with a delayed reconstruction. The implementation of this sequence with the ﬁlter on the mri-linac will be part of future work, so that we can not only measure the acquisition latency but also the online reconstruction time.

A rigorous analysis of reconstruction times was outside the scope of this work, but is very relevant. The oﬀset diﬀerences between measured and simulated latencies in the mri-linac experiments are a measure of the reconstruction latency, but do not show how it scales with e.g. matrix size. Also (iterative) parallel imaging algorithms can have a large impact on the reconstruction time (Majumdar et al. 2012). In contrast to the reconstruction latency, the acquisition latency is independent of the computer hardware and only depends on the sequence parameters. For this reason it is useful to investigate and optimize them separately.

Apart from the imaging itself, the image processing that is needed to extract the motion information (Fast et al. 2017; Bourque et al. 2018; Zachiu et al. 2015) also has a finite latency that contributes to the overall system latency. From x-ray based tumor tracking it is known that including system latencies into motion prediction algorithms can improve the tracking accuracy (Ren et al. 2007). Examples of such prediction algorithms are Kalman filtering, linear adaptive filtering, kernel density estimation (Toftegaard et al. 2018), and neural networks (Murphy and Dieterich 2006). Sharp et al. concluded that using x-ray imaging with prediction improves gated treatment accuracy for systems that have latencies of 200 ms or greater, and imaging rates of 10 Hz or slower (Sharp et al. 2004). Similar conclu- sions may hold for mr based tumor tracking since the latencies and imaging rates

71 Chapter 5 Imaging latency of real-time MRI are in the same range.

5.5 Conclusion

Acquisition latency is a considerable component of the total feedback loop latency. In this work we have shown that the readout strategy of the mri sequence plays an important role in its reduction. For Cartesian readouts we have shown that a simple modification from a linear to a high-low phase encode ordering significantly reduces the acquisition latency. For radial readouts the acquisition latency was found to be 0.5 ∗ Tacq. We have shown that this could be significantly reduced, without loss of image quality, by using a ga profile ordering in combination with a k-t filter.

Acknowledgements

The authors would like to acknowledge the ﬁnancial support by ITEA2 (SoRTS project, ref ITEA131001)

72 CHAPTER 6

ReconSocket: A low-latency raw data streaming interface

The following chapter is based on: Borman, P. T. S., Raaymakers, B. W., and Glitzner, M. (2019d). “ReconSocket: a low-latency raw data streaming interface for real-time MRI-guided radiotherapy”. In: Physics in Medicine and Biology In press.

73 Chapter 6 ReconSocket: A low-latency raw data streaming interface

Abstract

With the recent advent of hybrid mri-guided radiotherapy systems, continuous intra-fraction mr imaging for motion monitoring has become feasible. The ability to perform real-time custom image reconstructions is however often lacking. In this work we present a low-latency streaming solution, Re- conSocket, which provides a real-time stream of k-space data from the mri to custom reconstruction servers. We determined the performance of the data streaming by measuring the streaming latency (i.e., non-zero time delay due to data transfer and processing) and jitter (i.e., deviations from periodicity) using an ultra-fast 1D mri acquisition of a moving phantom. Simultaneously, its position was recorded with near-zero time delay. The feasibility of low-latency custom reconstructions was tested by measuring the imaging latency (i.e., time delay between physical change and appearance of that change on the image) for several non-Cartesian 2D and 3D acquisitions using an in-house implemented reconstruction server. The measured streaming latency of the ReconSocket interface was 3.18±1.67 ms. 98% of the incoming data packets arrived within a jitter range of 367 μs. This shows that the ReconSocket interface can provide reliable real-time access to mri data, acquired during the course of a mri-guided radiotherapy fraction. The total imaging latency was measured to be 221 ms (2D) and 3889 ms (3D) for exemplary acquisitions, using the custom image reconstruction server. These imaging latencies are approximately equal to half of the temporal footprint (Tacq/2) of the respective 2D and 3D golden-angle radial sequences. For radial sequences, it was previously showed that Tacq/2 is the expected contribution of only the data acquisition to the total imaging latency. Indeed, the contribution of the non-Cartesian reconstruction to the total imaging latency was minor (<10%): 21 ms for 2D, 300 ms for 3D, indicating that the acquisition, i.e. the physical encoding of the image itself is the major contributor to the total imaging latency.

6.1 Introduction

Recently, hybrid on-line mri-guided radiotherapy systems have been developed and deployed (Lagendijk et al. 2014; Mutic and Dempsey 2014; Raaymakers et al. 2017). These systems allow for continuous intra-fraction imaging in order to spatially resolve the target anatomy in real-time, resolving (i) target uncertainties, (ii) positioning uncertainties (Herk et al. 2000) and (iii) physiologic motion (e.g. respiration (Moerland et al. 1994), spontaneous motion (Kleijnen et al. 2016) and drifts (Zachiu et al. 2015)).

In the acquired image stream, target structures can be detected and tracked using on-board mlcs (Menten et al. 2016; Yun et al. 2013; Crijns et al. 2012). Pre-

74 Chapter 6 ReconSocket: A low-latency raw data streaming interface viously, it was shown, that the tracking quality is primarily determined by the latency of the entire tracking system (i.e., system latency) (Fast et al. 2014) which is composed of image acquisition, image reconstruction, image processing and mlc response (Bedford et al. 2015). The acquisition and reconstruction latencies together form the total imaging latency. Moreover, for mri-guidance, it was shown, that the imaging latency is the main contributor to system latency (Borman et al. 2018a), especially when compared to the individual latencies of the mlcs(∼40 ms) (Fast et al. 2014; Glitzner et al. 2015c; Poulsen et al. 2010), and image processing (Roujol et al. 2010; Bourque et al. 2018).

In addition to target tracking, the on-line mri can be employed to perform dose reconstruction based on 3D updates of the anatomy (Glitzner et al. 2015b; Stemkens et al. 2016a), which enables on-line intra-fraction re-planning (Kontaxis et al. 2017). Unfortunately, conventional volumetric 3D mri is inherently slow (Glitzner et al. 2015a; Sawant et al. 2014), as Cartesian image sampling scales quadratically with linear increments of the fov size. To overcome this penalty in acquisition speed, motion models that infer 3D data from sparser (and faster) acquisitions have been developed (Paganelli et al. 2018a; Stemkens et al. 2018). In contrast to Cartesian sampling, non-Cartesian sampling (Winkelmann et al. 2007) shows benign artifact formation for heavily undersampled, i.e., accelerated, image acquisitions, depending on the undersampling pattern. However, only a small number of these image sampling types are available on current mri machines. Furthermore, low-latency reconstructions of these non-Cartesian acquisitions are generally not fully supported on current vendor-provided reconstruction platforms.

In this work, we introduce ReconSocket, a real-time raw data interface for rapid data streaming from on-line mri into the treatment workﬂow. A similar streaming solution for custom on-line reconstructions is Gadgetron (Hansen and Sørensen 2013), which consists of a comprehensive set of reconstruction methods and is available as open-source1. To our knowledge, however, Gadgetron currently does not oﬀer streaming support for Philips mri platforms. The ReconSocket interface is built and deployable on current Unity (Elekta, Stockholm, Sweden) mri-linac and other clinical Philips Recon2.0-based platforms, e.g. Achieva and Ingenia (Philips, Best, The Netherlands). ReconSocket is designed as a real-time pathway to

1. provide a raw data stream for virtually arbitrary sequence types with excep- tionally low streaming latency, and

2. push raw data to experimental reconstruction platforms for the development of experimental workﬂows for mri-guided radiotherapy (Raaymakers et al. 2017).

For (1), we determine the isolated streaming latency of the ReconSocket interface, using an ultra-fast, navigator-style sequence. To show the feasibility of an in-

1http://gadgetron.github.io/

75 Chapter 6 ReconSocket: A low-latency raw data streaming interface house real-time reconstruction platform (2), we provide performance ﬁgures of a proof-of-concept graphics processing unit (gpu)-based reconstruction platform, enabling low-latency and high frame-rate reconstructions of radial ga 2D and 3D acquisitions.

Motion platform

(a) Latency (b) Motion platform

Figure 6.1: Schematic view of the imaging latency (a) where the apparent trajectory of an object on the MR image (solid) has a latency Δt with respect to the physical trajectory (dashed). (b): Picture of the motion platform (ModusQA, CA). Figure adapted from (Borman et al. 2018a).

6.2 Methods

To determine the ReconSocket performance we measure the latencies between physical motion and the arrival of the mri raw data representing that motion, as indicated in ﬁgure 6.1. For image reconstructions from the real-time image reconstruction framework, image quality metrics and additional temporal metrics relevant for on-line image reconstructions are added.

6.2.1 Motion stage A QUASAR MRI4D motion stage (Modus Medical Devices Inc., London, Canada) was used to generate 1D motion along the head-feet direction. A cylindrical plastic container ﬁlled with CuSO4-doped agar gel (3% solution) was translated accord- ingly. For all experiments the motion stage was programmed to follow a sinusoidal trajectory

t − t0 P (t)=A sin 2π , (6.1) target T with an amplitude (A) of 15 mm and a period (T ) of 3 s or 6 s. The motion stage additionally served as a quasi-ideal motion sensor by exposing an interface through which the current position can be requested by the ReconSocket software. The time diﬀerence between sending a request and receiving a response was <1 ms, showing that the feedback latency of the motion stage is negligible.

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6.2.2 mr imaging platform For all experiments, an Elekta Unity mri-linac was used. On the mri-side, the Unity features a 1.5 T main magnet with imaging gradient and acquisition hardware characteristics similar to Ingenia system (Philips, Best, The Netherlands). A dedicated radiolucent 8-channel coil-array was used for signal reception. By default, the built-in reconstruction framework allows for experimental alterations in the form of modules, i.e. reconstruction modules, tapping the data ﬂow through the vendor reconstruction framework.

Phantom Navigator

H H 6- A 6- t (a) (b)

Figure 6.2: Sagittal (H=head, A=anterior) T1 image of the phantom (a) and 1D spoke navigator (b), consisting of a projection onto the head-feet motion axis which is sampled every TR (t=time). The solid curve indicates the center-of-mass position trace, whereas the dashed curve indicates the true position trace of the phantom. (Note: the phase shift between the curves is exaggerated for visualization purposes.)

6.2.3 ReconSocket The ReconSocket library was developed in-house as an additional module for the vendors’ reconstruction framework. Figure 6.3 shows an illustration of the data flow through steps (a-f). The measured frequency profiles of all receiver channels together are sent from the acquisition hardware (6.3a) to the vendor’s reconstruction platform where they first pass through several pre-processing modules (6.3b) before being processed by the ReconSocket module (6.3c). These pre-processing modules perform a dc-offset correction, random phase correction, profile-dependent-amplification correction, and a measurement phase correction. The ReconSocket module saves the profiles in memory and has a separate thread listening for incoming data requests.

A ReconSocket receiver (recv) (6.3d), i.e. a 3rd party computer of virtually any kind, can connect to the ReconSocket (6.3c) and request the collection of pro- ﬁles measured up to this point, which is then sent as a reply. In our case, this request-reply pattern was repeated as fast as possible by a (C++-written) recv

77 Chapter 6 ReconSocket: A low-latency raw data streaming interface module that was built and deployed on a computer equipped with an 8 thread Xeon E3-1240 (Intel Corporation, Santa Clara, USA), 16 GB of memory and running Debian 9. The recv was connected to the vendor’s reconstruction network via 1 GBit Ethernet. Upon reception, each proﬁle was immediately timestamped and asynchronously written as binary raw data to the local solid state disk. The interaction between the vendors’ reconstruction framework and the ReconSocket receiver was designed completely asynchronous in order to avoid blocking condi- tions on the vendor side. This asynchrony necessarily introduces timing variations (i.e. jitter) between the precisely clocked mri acquisition, which acquires data at exact TR time intervals, and the ReconSocket receiver, which is running at an arbitrary clock rate (i.e., as fast as possible).

It is therefore important to quantify both the streaming latency (cumulative delay of 6.3a-d) and the jitter of the ReconSocket interface. For this a 1D projection image was acquired every repetition time using a 1D navigator sequence (figure 6.2). The navigator profiles were timestamped and saved, and retrospectively reconstructed by performing an inverse 1D Fourier transform and combining the receiver channels using a sum-of-squares. By fitting sinusoidal models to both the measured center-of-mass positions and the reference positions from the feedback of the motion phantom, the latency of only the raw data streaming could be determined from the difference in phase offset. In the ideal case, where all data processing happens instantaneously, the measured streaming latency is expected to be in the order of readout time of the analog-digital converter (adc), i.e. ≈ 1 ms. To minimize the effect of the readout time, all sequences were run with maximum readout bandwidth (1200 Hz per pixel on the Elekta Unity mri-linac), which amounts to an acquisition time of 0.83 ms. To estimate the jitter behaviour, we observed the time differences between incoming profiles, Δti = ti − ti−1, which should ideally be equal to TR. The jitter is therefore characterized by the statistics of the distribution of

ji =Δti − TR. (6.2)

6.2.4 Image acquisition and reconstruction Image data was acquired using a 2D ga gre sequence with imaging parameters 2 TR/TE =4.1 ms / 1.78 ms, flip angle = 20, fov = 300 × 300 mm , resolution = 2 × 2 mm2, and motion stage parameters (A, T )=(15mm, 3 s). Secondly, a 3D stack-of-stars gre sequence (Block et al. 2014) was used with imaging parameters 3 TR/TE =4.1 ms / 2.1 ms, flip angle = 18, fov = 400×400×300 mm , resolution = 3×3×3 mm3 and 136 ms shot length per blade. The motion stage speed was slowed down to account for the long temporal footprint, i.e. (A, T )=(15mm, 60 s).In the 2D case, data packets consisting of single profiles (i.e. spokes) were forwarded continuously by the recv (6.3d) to the recon (6.3e) with a frequency of 1/TR Hz. Here, the recv acted as a gateway between the mri-linac and the recon, which was located in a different network segment. In the 3D case the data packets consisted of single blades, which were forwarded with a frequency of np/TR Hz, where np is the number of partitions.

78 Chapter 6 ReconSocket: A low-latency raw data streaming interface

Figure 6.3: Schematic overview of the data ﬂow. Raw k-space data is sent from the mri-linac (a) to the vendor reconstructor (b) where pre-processing is performed. The corrected k-space proﬁles are then sent through the ReconSocket interface (c) to the ReconSocket receiver (d) and forwarded to the external reconstructor (recon) (e), where they are transformed into images and sent to the ReconSocket graphical user interface (gui)(f).

The recon software was developed in C++ and built and deployed on a Debian 9 computer equipped with a 4 thread Intel Xeon W-2102, 32 GB of memory and a Titan V (NVIDIA, Santa Clara, US) gpu with 12GB of memory. Spokes (2D) or blades (3D) were buffered by the recon in a first in first out (fifo) data structure, whose size n determines the number of spokes or blades that are used for the reconstruction of a single frame. This number could be changed dynamically by the user during data acquisition. The image reconstruction was performed continuously and asynchronously with the data buffering in the fifo. This means that after a certain frame has finished reconstructing, the next frame starts reconstructing immediately using the most current state of the fifo. If the reconstruction time Trecon is smaller than the temporal footprint, i.e. Trecon < n ∗ TR (2D) or Trecon

The actual image reconstruction relied on the open-source gpuNUFFT library (Knoll et al. 2014), which contains a CUDA implementation of a nufft algorithm. After transforming the k-space data to image data, the receiver channels of the 8-channel coil-array were combined using a sum-of-squares and the resulting 2D or 3D image was sent asynchronously to the gui (6.3f), where they were timestamped and saved. The gui was running on the same computer as the recv such that their clocks were inherently synchronized. This way the total imaging latency, i.e. the time diﬀerence between the moment of change and the moment that change appears in the image, could be measured. The number of spokes or blades per

79 Chapter 6 ReconSocket: A low-latency raw data streaming interface reconstructed frame could be set through the gui during data acquisition, changing the temporal footprint of the reconstructed frames and hence the total imaging latency and image quality, (for screen casts of the gui during operation see the supplementary data/supporting information).

6.2.5 Imaging latency Using the 2D sequence and the aforementioned workflow, the total imaging latency and snr were assessed for 10-500 spokes, corresponding to a temporal footprint of 41-2050 ms per reconstructed frame. The contribution of the reconstruction to the total imaging latency was determined separately by measuring the time difference between the moment when frame n was received by the gui (6.3f) and the moment the last profile used to reconstruct frame n was received by the recv (6.3d). The gui was running on the same computer as the recv such that their clocks were inherently synchronized. Using the 3D sequence, the total imaging latency was determined for 50 blades per reconstructed frame, corresponding to a temporal footprint of 8 s. The contribution of the reconstruction time was measured in a similar way as for the 2D sequence.

For both the 2D and 3D sequences, the latencies were calculated by ﬁtting a sinusoidal model to the motion trace of the center-of-mass of the high-contrast object on the reconstructed images and comparing the resulting phase to the phase of the reference curve.

6.3 Results

6.3.1 ReconSocket performance The performance of the ReconSocket was quantified by the streaming latency of the 1D-profile navigator, and the timing jitter of incoming profiles. The streaming latency was estimated to 3.18 ms (±1.67 ms confidence interval (ci) of the fit), which includes the raw data pre-processing and the data transmission from the receive coil-array to the recv. The measured jitter, as defined in equation(6.2), is shown in figure 6.4. The time trace (figure 6.4a) shows that the jitter is very small, apart from regular outliers appear with a 4 s interval. These outliers are however so sparse that they are hardly visible in the histogram (figure 6.4b). The jitter distribution (figure 6.4c) approximates a normal distribution centered around the origin, with the 1st,50th (median) and 99th percentiles amounting to p1 = −189 μs, p50 =1μs, and p99 = 178 μs, respectively.

6.3.2 Imaging latency The imaging latency and snr results for the 2D ga sequence are shown in ﬁgure 6.5. The total imaging latency shows a linear correlation with the number of spokes per reconstructed frame, of which the reconstruction time (recon) forms only a minor component: For an exemplary acquisition of 100 spokes (SNR≈7.5), the total imaging latency was estimated at 221 ms, of which only 21 ms amounted

80 Chapter 6 ReconSocket: A low-latency raw data streaming interface

6 4 2 (ms)

R 0 -T

i -2 t

Δ -4 -6 10 15 20 25 30 35 40 45 0 200 400 600 time (s) count (a) (b) 600 1 Histogram Cumulative histogram 0.75 p =178 μs 400 99 0.5 p =-189 μs count 1

200 fraction 0.25 p =1 μs 50 0 0 -500 -400 -300 -200 -100 0 100 200 300 400 500 Δt -T ( μs) i R (c)

Figure 6.4: Jitter behaviour of the ReconSocket as a function of time (a) and summarized in a histogram (b). The peak of the histogram is depicted in more detail in (c), overlaid with the normalized cumulative histogram for which the p1, p50, and p99 values are indicated. Note that the oﬀset with respect to the the TR has been removed. to reconstruction time. More than 90% of the latency are therefore rooted in the mri signal acquisition. For the 3D stack-of-stars acquisition with 50 blades (6800 ms temporal footprint), the reconstruction time was 300 ms whereas the total imaging latency was 3889 ms.

6.4 Discussion

In this work we presented ReconSocket, a real-time raw data streaming interface for currently marketed mri-linac hardware and Philips mri equipment. To show the feasibility and performance of on-line real-time reconstructions using ReconSocket, we implemented and tested an external reconstruction server which was designed to connect to a raw data stream.

The performance of ReconSocket was evaluated using a rapid 1D spoke navigator sequence, reducing the contribution of the mri acquisition process to a minimum. The streaming latency and jitter of ReconSocket was estimated to be in the range of

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1000 total linear fit recon 500 latency (ms)

0 0 50 100 150 200 250 300 350 400 450 500 number of spokes (a) 200 15 total 150 linear fit recon 10 100 SNR 5 50 latency (ms)

0 0 0 20406080 0 100 200 300 400 500 number of spokes number of spokes (b) (c)

Figure 6.5: Latency (a with close-up in b) and snr (c) dependency on the number of spokes per reconstructed frame for the 2D ga sequence. The total imaging latency (total) shows a linear dependence on the number of spokes. The reconstruction latency (recon) is approximately constant and contributes only marginally to the total.

commonly used repetition times of fast gre sequences. This renders the impact of raw data streaming virtually negligible, making ReconSocket suitable for a variety of applications in which a reliable low-latency raw data stream is important. The measured streaming latency of 3.8 ms encompasses steps (6.3a-d) and includes the vendor’s proprietary raw data pre-processing modules. This number is expected to scale with the number of receive coils and matrix size, as the computation costs on the vendor side of the pipeline increase.

The maximum tolerable imaging latency differs depending on the application: in the golden-angle 2D and 3D imaging examples presented in this work, the influence of streaming jitter is relatively benign since a single 2D or 3D image uses multiple spokes or blades, respectively. For a 2D ga sampling scheme we have observed that the total imaging latency (i.e., the cumulative latency due to acquisition, data streaming, and reconstruction) scales linearly with the number of spokes per reconstructed frame. Consequently, the influence of the jitter imposed on single spokes becomes negligible with respect to the total imaging latency of the image stream, which is two orders of magnitude larger.

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In the case of a navigator, where single profiles are used independently (e.g. for acceptance gating), jitter may be more important, especially if there are large incidental outliers, as we have observed (see figure figure 6.5a). These outliers occurred continuously and repeatedly with a 4 s interval. This is likely caused by the fact that the vendor’s reconstruction framework, including the ReconSocket module, is hosted by an operating system, whose task scheduling does not provide means to meet hard real-time requirements(Baskiyar and Meghanathan 2005). We hypothesize that a high-priority system process, such as the firewall, causes interrupts which are responsible for these regular peaks in jitter. Since they are relatively small (< 6 ms) and sparse (∼ 1 ppm), they are not expected to be of significance for most applications.

Every data packet in the ReconSocket has an approximate size of 23 kB and comes in bursts of TR (2D) or nz × TR (3D). For the investigated 3D acquisition, the maximum packed size was therefore 20 × 23 kB = 460 kB, which, on a 1 GBit full-duplex Ethernet link, takes about 3.95 ms to transfer. Similarly, for the 2D sequence the transfer time was about 17 μs. Compared to the total imaging latencies of both the 2D and 3D sequences, the networking speed can therefore be considered insigniﬁcant (<1%).

The performance of the image reconstruction pipeline was tested using ga acquisitions with variable temporal footprint. As shown earlier for retrospective reconstructions (Borman et al. 2018a), the acquisition latency scales linearly with the acquisition’s temporal footprint. As a rule of thumb, the acquisition latency of radial sequences is equal to half the acquisition time. With our reconstruction pipeline, the total reconstruction time, including data transfer and processing, amounted to under 25 ms for the 2D ga sequence. For an exemplary setting of 100 spokes (snr of about 7), the reconstruction time takes up only 10% of the total imaging latency. For the 3D stack-of-stars sequence, consisting of 50 blades per frame, the reconstruction time (300 ms) contributed only 8% to the total imaging latency. This shows that the reconstruction contributes only marginally to the total imaging latency, and that the major contributor is the acquisition process itself.

The reconstruction only consisted of the vendor’s proprietary raw data corrections and a subsequent nufft followed by a sum-of-squares over the receiver channels. Although the nufft library (Knoll et al. 2014) supports the use of coil-sensitivity maps, we did not include them due to technical complexity in transmitting them during acquisition. Additionally, we did not correct the images for system imperfections such as gradient non-linearities (Janke et al. 2004). This is important when the image content needs to be geometrically accurate, e.g. for mlc tracking. This correction involves warping the image according to the known gradient distortion map (Janke et al. 2004) and takes in the order of milliseconds for 2D or hundreds of milliseconds for 3D, depending on the matrix size.

Furthermore, in this work we only investigated sinusoidal motion patterns. Al- though these are very convenient for quantifying imaging latencies, more realistic

83 Chapter 6 ReconSocket: A low-latency raw data streaming interface motion patterns should be used when investigating the dosimetric impact.

One of the main benefits of ReconSocket is that it helps lowering the threshold of bringing custom, retrospective reconstructions on-line on Philips mri systems that are equipped with Recon2.0. In this sense, ReconSocket is comparable to Gadgetron (Hansen and Sørensen 2013), which offers similar streaming capabilities for Siemens mri systems. Gadgetron offers a wide range of reconstruction methods, making it an ideal end-point for ReconSocket. In future work we aim to extend ReconSocket to stream raw data in the ismrmrd format (Inati et al. 2017) to make it more vendor-agnostic and make it compatible with Gadgetron and other (future) reconstruction platforms.

The availability of raw data in a streaming fashion, rather than retrospectively, allows for flexible types of image reconstructions during data acquisition, such as the sliding window technique used in this work. This would not have been possible using the soft- and hardware provided by the vendor alone. Other possible applications include the mr-riddle (Bruijnen et al. 2019a) sequence where intermediate reconstructions with increasing resolution are made, on-line 4D motion models (Stemkens et al. 2018), and deep-learning based reconstructions (Wang et al. 2016) that require a gpu. Apart from mri-guided radiotherapy, also cardiac imaging and speech imaging could benefit from ReconSocket, since real-time reconstructions are also there often desirable (Lingala et al. 2016; Saybasili et al. 2014). All of these applications are currently still in a research setting and could benefit from solutions like ReconSocket to incorporate them in a clinical workflow, potentially reducing implementation time and vendor dependencies. A real-time implementation of such techniques will make on-line inter- and intra-fraction dose reconstruction (Stemkens et al. 2017) and therefore replanning (Kontaxis et al. 2017) feasible.

6.5 Conclusion

The ReconSocket is able to transmit k-space proﬁles in real-time from the mr data acquisition system to an external receiver, which forwards it to a custom reconstruction server, allowing for on-line low-latency image reconstructions. The streaming latency and jitter of the raw data stream were found to be insigniﬁcant for most imaging situations. Using this on-line reconstruction pipeline, the reconstruction and data processing latencies of non-Cartesian 2D and 3D sequences were negligible with respect to the total imaging latency, which is dominated by the acquisition itself. Therefore, future research has to go into minimizing the effective temporal footprint, e.g. using undersampling patterns, while maintaining the ability to reconstruct on-line and in real-time.

6.6 Acknowledgements

This research was supported by Elekta AB (Stockholm, Sweden) and Philips (Best, The Netherlands) and was partially funded by the ITEA project 16016 STARLIT.

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The Titan V used for this research was donated by the NVIDIA Corporation.

CHAPTER 7

General discussion

The recent clinical introduction of mri-linac systems and the ongoing innovation in mr-guided hifu have boosted the role mri plays in radiotherapy and hifu treatments. mri has become an important part of many ebrt and hifu work- flows, and can be expected to only increase in the coming years, expanding from diagnostic imaging towards real-time treatment guidance. Currently, however, the commercially available mri-linac systems predominantly rely on diagnostic sequences, which are generally not optimized for real-time therapy guidance. This is also the case for currently available mr-guided hifu systems, although these systems do have dedicated prfs thermometry sequences for temperature monitoring. Generally, mri offers better contrast than ct and us but its acquisition times are significantly longer. Luckily, however, acquisition speed can be traded off against snr, spatial coverage and spatial resolution. Every optimized mr sequence is therefore an application dependent compromise.

For motion monitoring during treatment, the spatial coverage and temporal resolution are the two most important factors. The success of treatment progress monitoring, on the other hand, is also determined by quality of the mr thermometry sequence in the case of mr-guided hifu and the ability to perform accurate dose accumulation mapping in the case of mr-guided ebrt. The ﬁrst part of this thesis has explored the possibility of using the parallel imaging technique sms for increasing the spatial coverage without increasing the acquisition time. The second part focused on the imaging latency, which was shown to be highly dependent on the sampling trajectory and not directly related to the frame rate.

7.1 SMS applicability

The beneﬁt of sms over other parallel imaging techniques such as sense is that it does not undersample the original acquisition matrix, but rather samples multiple

87 Chapter 7 General discussion points simultaneously. This leads to a higher snr, as demonstrated in chapter 2. The actual snr advantage depends on the spatially varying g-factor which in turn is determined by the geometry of the coil array. In general, the maximum acceleration factor of sense scales with the number of coils in the phase encoding direction whereas the maximum acceleration factor of sms scales with the number of coils in both the phase and slice encoding directions. For this reason, 64 or even 128 channel coil arrays are no longer an exception. Usually, however, these are dedicated head coils used for high resolution brain mri. The coil arrays used in mr-guided hifu and mri-linac systems contain much fewer coils, severely limiting the acceleration potential of sense and sms.

In the case of mr-guided hifu, the table-top coil array needs to be placed in the beam’s pathway while maintaining good acoustic coupling between the transducer and the target. Such coil arrays are currently only available with a limited amount of channels, e.g. 2 channels on the system used in chapter 2 and only a single channel on a dedicated breast mr-guided hifu system, based on the Sonalleve system (Merckel et al. 2013).

The receive coil arrays of mri-linac systems are also placed in the beam’s pathway, and therefore need to be radiolucent. This means that all electronic components must be on the cranial-caudal edges of the array such that they are minimally exposed to radiation at every gantry angle. This design limitation is the reason that the current clinical coil array of Elekta’s Unity mri-linac system consists of a single row of four parallel loops for the anterior coil array, and similarly for the posterior coil array. This single row conﬁguration provides limited acceleration capability in the cranial-caudal direction. Currently, a prototype of a 32-channel radiolucent coil array is under development, for which preliminary experiments have shown that higher sense acceleration factor can be achieved. A similar improvement of sms can therefore be expected such that more slices can be acquired simultaneously.

As noted in chapter 5, sms for radial readout trajectories does not rely on the Cartesian sense reconstruction algorithm and may therefore be less limited by a low number of coil elements. In principle, radial sms could be expected to work even with a single coil, although this has not been investigated in this thesis. It can be expected that single coil radial sms will suﬀer from some incoherent streaking artifacts, but not from the coherent fold-over artifacts that make single coil Cartesian sms infeasible. Especially for interventional mri systems with limited number of coils, radial sms may provide a viable solution for imaging multiple slices simultaneously. Examples of such systems are the aforementioned breast mr-guided hifu system and the ExAblate 4000 (Insightec) brain mr-guided hifu system (Iacopino et al. 2018).

As discussed above, sms is a very versatile parallel imaging technique but it does have some limitations. The mb rf pulse that is needed to excite the slices may be longer than the single band rf pulse and may therefore increase the repetition time. The reason for this is that the pulse may need to be stretched to not

88 Chapter 7 General discussion exceed the maximum B1 value of the rf amplifier. Additionally, the higher energy deposition may lengthen the repetition time to not exceed physiological specific absorption rate (sar) constraints, although this is less of a problem on low field (≤ 1.5T) systems. The most straightforward way of implementing a mb pulse is simply adding the corresponding single band pulses together. For sms factors larger than two, this becomes very inefficient, leading to very long pulses. For this reason several techniques such as phase-optimizing (Wong 2012), time-shifting (Auerbach et al. 2013), and root-flipping (Sharma et al. 2016), have been developed that reduce pulse length while maintaining a good slice profile.

Because sms acquires several slices simultaneously, all slices have the same timestamp, making sms a true intermediate between slice-based 2D and volumetric 3D imaging. These slices can, however, not be positioned arbitrarily. They need to be parallel to each other. This is one of the most important practical limitations of using sms for mr guidance, since it is often desirable to monitor the target’s motion in two or three orthogonal planes. Sms is therefore mostly applicable to monitoring the motion of multiple different targets. In mr-guided hifu, sms can be used to monitor the temperature of the target, near-field, and far field whereas in mr-guided hifu, sms may be used to monitor the position of the target and oars, such as nearby lymph nodes, or serve as extra input to a motion model, as demonstrated in chapter 3. Recently, a new technique has been proposed, which allows simultaneous orthogonal plane imaging (sopi) (Mickevicius and Paulson 2017). Instead of using a mb rf pulse, sopi excites the slices sequentially within a single repetition time and uses simultaneous image refocusing to acquire the signal of both slices under separate portions of a shared frequency encoding gradient. This technique is very successful in eliminating inter-slice motion of interleaved acquisitions, but does require significantly longer repetition times, 5-6 ms versus 2.5-3 ms of single slice excitations. Although its acceleration potential is therefore somewhat limited, the increased spatial coverage may be valuable for motion models, especially when combined with sms.

7.2 Further acceleration methods

The maximum acceleration of real-time mr sequences is generally limited by snr constraints. Snr efficiency is therefore one of the most important factors that should be taken into account when designing such sequences. For this reason, acceleration using sms may be preferable over sense when multiple slices need to be monitored. Another way to increase the snr and simultaneously decrease the acquisition time is to increase the voxel size and hence decrease the resolution. Even though image resolution is an important parameter for human observers, it is of relatively low importance for automated deformable image registration algorithms due to their ability to accurately measure sub-voxel displacements. For the optical flow registration algorithm it has for example been shown that similar deformation fields were obtained from 2.5 mm and 5 mm isotropic volumes (Glitzner et al. 2015c). Boosted by advances in computing performance, iterative reconstructions have become increasingly popular over the past decade, reformu-

89 Chapter 7 General discussion lating the reconstruction problem as an optimization problem which can include prior knowledge in the form of regularization terms

2 argmin ||Eu − f|| + λiΨi(u). u i

Here, E is the sampling operator, u is the image, f is the acquired data, λi the regularization parameters, and Ψi(u) the regularization terms. The goal of these regularization terms is to provide a separation between the target image u and the aliasing artifacts due to undersampling. A special case which has been proven to be very effective in denoising heavily undersampled images is compressed sensing (cs). The fundamental idea behind cs is that mr images can actually be considered sparse in some domain, meaning that most coefficients are zero. The specific sparsifying domain depends on the type of image. For static anatomic images this is usually the wavelet domain (Lustig et al. 2007), whereas cine series can also be considered sparse in the temporal frequency domain (Gamper et al. 2008). Another useful regularization method is tv. This method exploits the fact that mr images are generally smooth, and is therefore useful for reducing streaking artifacts resulting from undersampled radial and spiral acquisitions. These iterative type of reconstructions are however computationally very expensive. Even with modern hardware they may require minutes or even hours to converge. Although this makes them less suitable for real-time mri, they do have value for retrospective reconstructions for e.g. dose accumulation mapping. Another complication in the case of cine mr is that the imaging latency will depend on the type and amount of regularization that is used. A large amount of tv, for instance, can be expected to behave as an effective low-pass filter and subsequently increasing the imaging latency.

A promising way of mitigating the long reconstruction times of iterative algorithms, is by using machine learning, in particular deep learning, to learn a mapping between the undersampled k-space and the artifact-free target image (Knoll et al. 2019). This is a very interesting ﬁeld, which was not covered in this thesis, but could have large implications for low-latency real-time mri. In contrast to iterative cs reconstructions, a deep learning reconstruction may take only hundreds of milliseconds instead of seconds since it usually consists only of a series of con- volutions with learned kernels. Using such methods it may even become possible in the future to develop robust volumetric target tracking sequences, which is the holy grail of real-time mri.

7.3 Motion modelling

Even though signiﬁcant accelerations can be achieved with undersampling strategies, for now there remains a need for motion models to temporally resolve respiratory motion in a 3D volume. The rationale behind motion models is that anatomic motion is not random but highly correlated. This means that sampling a full 3D frame at every time point would produce a lot of redundant information

90 Chapter 7 General discussion and should therefore not be necessary. As shown in chapter 3, the generation of a motion model is however not a trivial task and consists of several complex steps. That motion model was constructed from a pre-treatment 4D-mri and a 2D cine mri, which were registered to each other. Errors may appear in any of these steps. Furthermore, the model may break down when motion occurs that has not previously been encoded by the 4D-mri. This shows that it is not a-priori obvious when a motion model can be expected to perform well and when to break down. Validation is therefore critical when these type of models will be used clinically. The problem with motion model validation is that usually no independent ground truth data is available, especially not in real-time.

Chapter 3 showed a possible way of generating independent data which could be used for an independent consistency validation. For this, an sms sequence was used as a motion sensor based on which the coeﬃcients of the principal components of motion were estimated. The principal components itself were estimated from a pre-treatment 4D-mri. By using multiple sms slices, the variation of the model based on the slice position could be estimated, and minimized by averaging over the sms slices. It was found that the slice position had a signiﬁcant impact on the generated model. Apart from the model discussed in this thesis, similar models have been suggested in the literature (Harris et al. 2016; Stemkens 2017; King et al. 2012). They all rely on a principal component analysis of a prior dynamic 3D-mri dataset, combined with real-time 2D imaging. Sms may therefore have value for these models as well.

When validated properly, these motion models can be used for dose accumulation mapping which can be forwarded into the adaptive planning process to adjust the remaining part of the treatment (Kontaxis et al. 2017). This can be done retrospectively, after each fraction, but ideally this would be done in real-time to fully compensate the treatment for intra-fraction motion.

7.4 Geometric ﬁdelity

An important aspect of mri for treatment guidance, which has not been investigated explicitly in this thesis, is its geometric fidelity (Moerland et al. 1995). As explained in the introduction, the spatial encoding of mri relies on linear magnetic field gradients, which cause spatially varying variations of the magnetic field. Because these variations are relatively small, deviations of only parts per million from the intended magnetic field may lead to distortions of the image. These distortions can cause targeting inaccuracies when used as a basis for treatment. Important causes of these magnetic field deviations are the susceptibility of the patient himself and the presence of non-linear components in the gradient fields, as discussed below.

For time-resolved imaging, strong imaging gradients are generally used for speed reasons. For field strengths up to 1.5 T, strong gradients can usually sufficiently reduce a sequence’s sensitivity to patient-specific susceptibilities (Wachowicz et al. 2010). Alternatively, these susceptibility induced image distortions can be

91 Chapter 7 General discussion corrected for in post-processing, based on a previously acquired ΔB0 map (Crijns et al. 2011).

Distortions caused by non-linear components in the gradient fields can be accurately described by a spherical harmonics model. This model can be used to warp the distorted image back to the undistorted image based on gradient-specific non- linearity coefficients. For 3D volumes, this method works well, but for 2D slices the correction can only be performed in the two in-plane directions, since inherently no out-of-plane data is available. Therefore, the content of a 2D or sms image is not sampled from a straight, but from a curved plane, an effect known as potato chipping. The amount of distortion depends on how far from iso-center the slice is positioned. Figure 7.1 shows an example of slice distortion on a Unity mri-linac system (Elekta, SE), where the same slice is acquired twice with the object moved parallel to the slice. Overlaid is the slice distortion expected from the spherical harmonics model. It shows that the actual distortion follows the model and that there is an interior region around the iso-center of 20×20 cm2 where the distortion is <2 mm.

(a) (b)

Figure 7.1: 2D mri images overlaid with the predicted out-of-plane distortion map, units are in meters. The same coronal slice is acquired with the diﬀerence being that in (a) the object was placed horizontally in the iso- center and in (b) it was shifted 10 cm to the right. The phantom consisted of a rectangular legotm grid immersed in agar gel.

When tracking a moving structure using 2D or sms imaging, the slice curvature may need to be taken into account, depending on the amount of distortion. Since the distortions can be modeled accurately, it might be beneﬁcial to include this information in the treatment workﬂow, such as by displaying it during planning of the stacks on the anatomy of interest and, if applicable, by incorporating it into any motion model used for dose accumulation.

7.5 Latencies and system control

The use of mri guidance for real-time hifu and ebrt treatment adaptation through gating or target tracking introduces additional complexities to the work-

92 Chapter 7 General discussion

ﬂows. Especially for target tracking, there is a continuous feedback loop running between the imaging and the transducer / mlc control. The latency of this feedback loop consists of several components, of which only the mri part was discussed in this thesis. Other important latency components are the beam steering and mlc reactance for mr-guided hifu and mr-guided ebrt, respectively. These are discussed below.

Real-time target tracking for mr-guided hifu has been investigated (Kokuryo et al. 2012; Ries et al. 2010), using fast epi sequences of up to 15 Hz. Even so, the total loop latency was found to be in the order of 150-250 ms, resulting in tracking errors of more than 5 mm. This was reduced by using a Kalman-ﬁlter for motion prediction. mlc-tracking also makes use of prediction methods by adding feed- forward control terms to the conventional pid control of the motors driving the leafs, reducing the latency. On the Elekta Unity mri-linac system it was shown that by adding these feed-forward terms, the latency of the mlc alone could be reduced from 140 ms to 20 ms (Glitzner et al. 2019). The mlc latency is therefore small compared to the imaging latencies discussed in chapters 5 and 6. These were found to be in the order of 100 ms and varying depending on the type of sampling trajectory that is used. In light of these results, future optimization eﬀorts should focus on the reducing the imaging latency, both at the acquisition side and the reconstruction side.

All latency experiments described in this thesis were conducted with a rigid phantom experiencing 1D sinusoidal motion. The advantage of such a smooth and periodic pattern is that it helps the regression analysis, resulting in accurate and precise latency numbers. For quality assurance and system characterization purposes these numbers are important since they result from easily reproducible experiments and are straightforward to interpret. It is however also necessary to investigate the latencies of more representative respiratory breathing patterns and their impact on dose conformity (Bedford et al. 2015).

The ReconSocket framework, introduced in chapter 6, was used for low-latency reconstructions of golden-angle sequences with a sliding window on dedicated hardware. Apart from this specific application, the framework may be useful for pro- totyping other real-time reconstruction methods for the Elekta Unity mri-linac system. Especially for methods that cannot be integrated into the vendor’s reconstruction platform in a straightforward manner, ReconSocket may offer a solution. Additionally it offers a way to interface with existing, vendor-agnostic, reconstruction libraries such as the Berkeley advanced reconstruction toolbox (bart) (Uecker and Tamir 2018), Gadgetron (Hansen and Sørensen 2013), and gpunufft (Knoll et al. 2014). The ability to use such libraries in an on-line setting, offers great potential for the development of novel mri methods for mr-guided ebrt.

7.6 Conclusion

Over the past decades, the use of mri has expanded from only diagnostic imaging to therapy guidance. This is revolutionizing cancer treatments, resulting in,

93 Chapter 7 General discussion amongst others, mr-guided radiotherapy and mr-guided hifu. Interventional mri has become a very active research area, where new developments are continuously ongoing of which this thesis forms only a minute part. This thesis has shown that sms can be used to increase the spatial coverage during mr thermometry, allowing real-time temperature monitoring in multiple slices during mr-guided hifu. Fur- thermore, this thesis showed that sms could help to increase the robustness and validity of a motion model. The extension of sms to radial sampling trajectories allowed for high frame rates by using ﬂexible sliding window reconstructions which decouple frame rate from latency. The imaging latency was shown to be highly dependent on the sampling trajectory and should therefore be reckoned with during protocol optimization.

94 HOOFDSTUK 8

Samenvatting

Met de komst van kernspintomograﬁe (hierna: mri) geleide radiotherapie en mr- geleide hoge intensiteit gefocuseerd ultrageluid (hierna: hifu) systemen is het mogelijk geworden om de tumor accurater en preciezer te bestralen door vlak voor en tijdens de behandeling mri scans te maken. Het voordeel van mri ten opzichte van andere beeldmodaliteiten zoals us en ct is dat het een beter contrast kan geven tussen verschillende soorten weefsels, waardoor bijvoorbeeld een tumor beter afgebeeld kan worden. Bovendien kan met mri ook temperatuur gemeten worden, waardoor de voortgang van een hifu behandeling tijdsgetrouw (hierna: real-time) gevolgd kan worden.

In dit proefschrift wordt onderzocht hoe nieuwe mri technieken kunnen bijdragen aan het beter in beeld brengen van bewegende anatomie tijdens radiotherapie en hifu behandelingen. Hierbij is het belangrijk om een zo groot mogelijk volume met een zo hoog mogelijke temporele resolutie af te beelden, waarbij de latentie zo laag mogelijk dient te zijn. Om door de ademhaling geïnduceerde bewegingen te kunnen volgen, wordt als vuistregel vaak een minimum temporele resolutie van 4 Hz gehanteerd. Een volumetrische 3D mri scan kan echter al snel enkele minuten duren waardoor deze ongeschikt zijn voor het continu volgen van bewegingen. Om die reden wordt meestal gebruik gemaakt van 2D mri, waarbij één of meerdere doorsnedes (hierna: slices) wordt geacquireerd. Op die manier is het toch mogelijk om, weliswaar ten koste van het spatiële bereik, tóch een hoge temporele resolutie te bewerkstelligen. Vanwege de relatief hoge temporele resolutie wordt deze mri methode ook wel cinemri genoemd.

Op basis van dit soort snelle mri scans tijdens de bestraling is het mogelijk de behandeling in real-time aan te passen door middel van gating, waarbij de bestraling onderbroken wordt wanneer de het doel buiten gegeven limieten beweegt, of door middel van tracking, waarbij het focus wordt meebewogen met het doel. Tracking

95 Hoofdstuk 8 Samenvatting is het meest eﬃcient, maar technisch ook het meest ingewikkeld. Bij hifu kan dit voor elkaar gekregen worden door elektronische sturing van een fasegestuurde transducer, terwijl bij radiotherapie de lamellen van de collimator (mlc) het doel kunnen volgen. In dit proefschrift wordt onderzocht hoe mri het best gebruikt kan worden als inputsignaal voor zulke adaptieve behandelingsstrategieën.

Een relatief nieuwe methode om meerdere slices tegelijk te acquireren zonder de scantijd te verlengen, is sms.Inhoofdstuk 2 wordt onderzocht hoe sms kan helpen het spatiële bereik van mr thermometrie te vergroten en wordt het gecom- bineerd en vergeleken met de versnellingsmethode sense. Het verschil tussen de twee is dat met sms het mr signaal van verschillende slices tegelijk wordt gemeten terwijl met sense een gedeelte van de fasecodering van een enkele slice wordt overgeslagen. De reconstructie van de twee is vergelijkbaar: voor beiden worden de spoelgevoeligheden gebruikt om de slices to ontvouwen. Een verschil is dat sms een potentieel hogere signaal-ruis verhouding (snr) heeft omdat het meer data acquireert dan sense.Inhoofdstuk 2 is in fantoom en ex-vivo experimenten aangetoond dat met sms de te temperatuur in meerdere slices tegelijk precies en accuraat kan worden gemeten. Vergeleken met sense was de precisie signiﬁcant hoger voor eenzelfde versnellingsfactor. Dit is aangetoond voor gre sequenties met en zonder epi tijdens verwarming door middel van zowel litt als hifu.

In hoofdstuk 3 wordt beschreven hoe sms gebruikt kan worden als onafhankelijke controle van een bestaand 4D-bewegingsmodel. Het model bestaat uit een 4D- mri scan die gemaakt wordt voor de behandeling en waaruit met een pca de hoofdcomponenten van de beweging worden bepaald. Tijdens de behandeling wordt door middel van snelle 2D cinemri de schaling van de componenten bepaald voor elk beeld of frame. Op die manier kan een 3D cinemri worden verkregen. Tijdens de behandeling kan echter bepaalde beweging voorkomen die niet bevat is in de hoofdcomponenten, daarnaast is het mogelijk dat er fouten optreden bij de beeldregistraties die nodig zijn om de juiste schalingsfactoren te berekenen. Door gebruik te maken van sms cinemri is aangetoond dat het mogelijk is meerdere onafhankelijke bewegingsmodellen te genereren op basis van de verschillende SMS slices. Er is laten zien dat de positie van de slices een signiﬁcante invloed kan hebben op het uiteindelijke model en dat wanneer de sms slices tegelijk worden gebruikt als input, het model robuster kan worden voor inconsistenties tussen de slices.

Hoofdstuk 4 behandelt de combinatie van sms met een radiëel bemonsterings- (hierna: sampling) patroon waarbij de hoek tussen twee opeenvolgende profielen de gulden hoek (ga)van111, 25 ◦C is. Een illustratie van verschillende samplingpatronen is weergegeven in figuur 1.3. Dit specifieke patroon is interessant omdat de frequentieruimte azimuthaal optimaal gesampled wordt en de data daardoor op verschillende tijdsresoluties kan worden gereconstrueerd. Dit kan door een zo- genaamd sliding window (sw) toe te passen, waarbij data tussen opeenvolgende frames gedeeld wordt (zie ook figuur 1.4), en door ondersampling van de acqui- sitiematrix. Ondersampling heeft tot gevolg dat de temporele voetafdruk wordt verkleind wat weer invloed heeft op de latentie en de beeldwaliteit. Hoofdstuk 4

96 Hoofdstuk 8 Samenvatting laat zien dat het mogelijk is sms te combineren met een ga samplingpatroon, wat leidt tot een groter spatieel bereik en, door het toepassen van ondersampling en sw, tot een hogere temporele resolutie. Hoewel sw de temporele resolutie slechts artiﬁcieel verhoogt, kan dit toch nuttig zijn voor bijvoorbeeld mlc-tracking omdat het een meer continu input signaal geeft.

In Hoofdstuk 5 wordt vervolgens ingegaan op latentie verschillen tussen verschillende mri sequenties. Hierbij is hoofdzakelijk gekeken naar de invloed van het samplingpatroon op de acquisitie latentie. Voor Cartesische patronen bleek dat een fasecoderingsvolgorde van hoog naar laag de laagste latentie gaf. Dit is niet verbazingwekkend aangzien de lage spatiële frequenties de meeste informatie bevatten. Voor lineair en ga radiële samplingpatronen bleek dat de latentie lineair schaalt met het aantal profielen per frame. Een manier om de latentie te verlagen is door simpelweg minder profielen per frame te samplen. Dit heeft echter een verlies in snr en een verhoging van streepartefacten tot gevolg. Echter, door een filter toe te passen op de profielen waardoor lage frequenties minder worden mee- gewogen dan hogere frequenties, is het mogelijk gebleken de latentie te halveren zonder in te leveren op snr en beeldkwaliteit.

Hoewel radiële samplingpatronen veel gunstige eigenschappen hebben, is een na- deel dat de gemeten frequenties niet op een Cartesisch rooster liggen, waardoor het nodig is een niet-uniforme Fourier transformatie (nufft) toe te passen in de beeldreconstructie. Zulke transformaties zijn computationeel erg complex, wat onacceptabele latenties tot gevolg kan hebben. Omdat het lastig kan zijn hard- en software aanpassingen te maken in de reconstructie-infrastructuur van de fabrikant, is in hoofdstuk 6 een alternatief framework ontwikkeld dat het mogelijk maakt om in real-time en met een lage latentie zelf ontwikkelde reconstructies uit te voeren. Hiervoor is in de software van de fabrikant een module toegevoegd die tijdens de mri scan de (ruwe) data proﬁelen streamt naar externe ontvanger. De latentie en jitter van deze datastream zijn verwaarloosbaar klein, respectievelijk 3,18 ms en 367 μs. Vanuit de externe ontvanger wordt de data vervolgens gestreamed naar een externe reconstructieserver, waar met behulp van gpus een snelle nufft wordt toegepast. De beelden worden vervolgens terug gestreamed naar de externe ontvanger en opgeslagen. Op deze manier is de reconstructietijd van een slice met 100 proﬁelen beperkt to 21 ms, wat slechts 10% van de totale latentie. De reconstrctietijd van een 3D ga stack-of-stars (sos) scan was slechts 300 ms, waardoor het mogelijk is om met een sw reconstructie een 3D temporele resolutie van 3 Hz te halen.

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111

Publications

Journal articles

Borman, P. T. S., Bos, C, Boorder, T de, Raaymakers, B. W., Moonen, C. T. W., and Crijns, S. P. M. (2016a). “Towards real-time thermometry using simultaneous multislice MRI”. in: Physics in Medicine and Biology 61.17, N461– N477

Borman, P. T. S., Tijssen, R. H. N., Bos, C, Moonen, C. T. W., Raaymakers, B. W., and Glitzner, M (2018a). “Characterization of imaging latency for real-time MRI-guided radiotherapy”. In: Physics in Medicine & Biology 63.15, p. 155023

Bourque, A. E., Bedwani, S., Carrier, J.-F., Ménard, C., Borman, P. T. S., Bos, C., Raaymakers, B. W., Mickevicius, N., Paulson, E., and Tijssen, R. H. (2018). “Particle Filter-Based Target Tracking Algorithm for Magnetic Resonance- Guided Respiratory Compensation: Robustness and Accuracy Assessment”. In: International Journal of Radiation Oncology Biology Physics 100.2, pp. 325–334

Borman, P. T. S., Bos, C, Stemkens, B, Moonen, C. T. W., Raaymakers, B. W., and Tijssen, R. H. N. (2019a). “Assessment of 3D motion modeling performance for dose accumulation mapping on the MR-linac by simultaneous multislice MRI”. in: Physics in Medicine & Biology 64.9, p. 095004

Borman, P. T. S., Raaymakers, B. W., and Glitzner, M. (2019d). “ReconSocket: a low-latency raw data streaming interface for real-time MRI-guided radiotherapy”. In: Physics in Medicine and Biology In press.

Ferrer, C. J., Bos, C., Senneville, B. D. de, Borman, P. T. S., Stemkens, B., Tijssen, R. H. N., Moonen, C. T. W., and Bartels, L. W. (2019). “A planning strategy for combined motion-assisted/gated MR guided focused ultrasound treatment of the pancreas”. In: International Journal of Hyperthermia 36.1, pp. 702–711

Glitzner, M., Woodhead, P. L., Borman, P. T. S., Lagendijk, J. J. W., and Raaymakers, B. W. (2019). “MLC-tracking performance on the Elekta unity MRI- linac”. In: Physics in Medicine and Biology

113 Publications

Conference proceedings

Borman, P. T. S., Crijns, S. P., Bos, C., Moonen, C. T., and Raaymakers, B. W. (2015). “Towards real-time PRFS thermometry using Simultaneous MultiSlice acquisitions”. In: Proceedings of the 57th Annual Meeting of AAPM

Borman, P. T. S., Crijns, S. P., Bos, C., Moonen, C. T., and Raaymakers, B. W. (2016b). “Towards Real-Time PRFS Thermometry Using Simultaneous MultiSlice Acquisitions”. In: Proceedings of 11th interventional MRI symposium

Borman, P. T. S., Bos, C., Moonen, C. T., Raaymakers, B. W., and Crijns, S. P. (2016c). “Using Simultaneous Multi-Slice Imaging for PRFS Thermometry”. In: Proceedings of the 24th Annual Meeting of ISMRM

Borman, P. T. S., Tijssen, R. H. N., Raaymakers, B. W., Moonen, C. T. W., and Bos, C. (2017a). “On the proﬁle ordering of Golden Angle radial Simultaneous Multi-Slice imaging”. In: Proceedings of the 25th Annual Meeting of ISMRM

Borman, P. T. S., Bos, C., Crijns, S. P., Moonen, C. T., Raaymakers, B. W., and Tijssen, R. H. (2017b). “Using Multi-Stack Simultaneous Multi-Slice BSSFP for Improved Motion Characterization During MR-Guided Radiotherapy”. In: Proceedings of the 25th Annual Meeting of ISMRM

Shcherbakova, Y., Berg, C. A. T. van den, Borman, P. T. S., Moonen, C. T., and Bartels, L. W. (2017). “2D Acquisition Mode for T1 and T2 Estimation Using an Ellipse-Fitting Approach on Phase Cycled BSSFP Data”. In: Proceedings of the 25th Annual Meeting of ISMRM

Bourque, A. E., Bedwani, S., Carrier, J.-F., Ménard, C., Borman, P. T. S., Bos, C., Paulson, N., and Tijssen, R. H. (2017). “Abdominal Organ Tracking on a Hybrid MR-Linac System Using a Particle Filter Based Algorithm”. In: Proceedings of the 25th Annual Meeting of ISMRM

Borman, P. T. S., Tijssen, R., Bos, C, Moonen, C., Raaymakers, B. W., and Glitzner, M (2018b). “Error estimation of slice chipping eﬀects due to gradient non-linearity on the MR-Linac”. In: MRinRT 2018 conference proceedings

Borman, P. T. S., Tijssen, R. H., Bos, C., Moonen, C. T., Raaymakers, B. W., and Glitzner, M. (2018d). “Imaging latencies for Cartesian and Golden Angle 2D MRI in real-time MR-guided radiotherapy”. In: Proceedings of the 26th Annual Meeting of ISMRM

Borman, P. T. S., Tijssen, R. H., Bos, C., Moonen, C. T., Raaymakers, B. W., and Glitzner, M. (2018c). “How the sampling strategy of 2D MRI aﬀects imaging latencies in real-time MR-guided radiotherapy”. In: Proceedings of the 37th Annual Meeting of ESTRO

114 Publications

Ferrer, C. J., Bos, C., Borman, P. T. S., Tijssen, R. H., Stemkens, B., Moo- nen, C. T., and Bartels, L. W. (2018). “A planning strategy for combined self- scanned/gated MR-HIFU treatment in the pancreas”. In: Proceedings of the 6th international symposium on Focused Ultrasound

Borman, P. T. S., Kerkmeijer, L. G. W., Raaymakers, B. W., and Glitzner, M. (2019e). “Whole-frame 2D cineMR prediction using deep neural networks”. In: Proceedings of the 38th Annual Meeting of ESTRO

Borman, P. T. S., Raaymakers, B. W., and Glitzner, M. (2019c). “ReconSocket: a low-latency data streaming solution for real-time MRI-guided radiotherapy”. In: MRinRT 2019 conference proceedings

Borman, P. T. S., Raaymakers, B. W., and Glitzner, M. (2019b). “Imaging latency of Golden Angle 2D MRI using real-time GPU-accelerated image reconstruction for MR guided radiotherapy”. In: Proceedings of the 27th Annual Meeting of ISMRM

Bruijnen, T., Borman, P. T. S., Lagendijk, J. J., Raaymakers, B. W., Berg, C. A. T. van den, Glitzner, M., and Tijssen, R. H. (2019b). “Real-time sliding window reconstruction of golden angle stack-of-stars acquisition for continuous 3D tumor trailing”. In: MRinRT 2019 conference proceedings

115

Acknowledgements

Hoewel slechts mijn naam op de voorkant prijkt, is dit proefschrift met name het resultaat van een intense en goede samenwerking tussen mij en mijn co-promotoren Clemens, Rob en Sjoerd. Van jullie heb ik ontzettend veel geleerd en jullie enthousiasme werkte aanstekelijk op momenten dat dat nodig was.

Clemens, jij bent de afgelopen jaren de meest constante factor geweest in mijn doordeweekse leven. Ik kijk met heel veel plezier terug op onze wekelijkse besprekingen en vele scan-sessies. Van jou heb ik geleerd hoe belangrijk het is een verhaal goed op te schrijven, zodat ik nu bij elke zin denk “hoe zou Clemens dit verwoorden?” Sjoerd, jij hebt me in het begin wegwijs gemaakt in de pro- grammeeromgeving van de MRI systemen, wat de basis heeft gevormd voor elk hoofdstuk in dit proefschrift. Ik heb ontzettend veel bewondering voor je scherpe blik en hands-on mentaliteit (“dit is experimentele natuurkunde Pim, druk ge- woon op start scan”). Ik vond het dan ook ontzettend jammer dat je na twee jaar besloot bij Philips te gaan werken, hopelijk kruisen onze paden elkaar nog eens. Rob, ik was erg blij dat jij het stokje van Sjoerd wilde overnemen. Jouw ervaring als klinisch fysicus heeft mij enorm geholpen bij het inzien van de toepasbaarheid en klinische relevantie van mijn onderzoek. Daarnaast vond ik onze besprekingen altijd erg ﬁjn en waardevol, vooral wanneer ik weer eens afgedwaald was van waar ik eigenlijk mee bezig moest. Ik hoop in de toekomst nog veel met je te kunnen samerwerken.

Dat brengt mij bij mijn promotoren, Chrit en Bas. Van jullie kreeg ik altijd goed en nuttig commentaar op concept-artikelen en op de verschillende hoofdstukken van dit proefschrift. Bas, jij hebt er samen met Markus voor gezorgd dat toen mijn contract aﬂiep en mijn proefschrift nog verre van af was, ik tijdelijk als junior onderzoeker verder kon. Bedankt hiervoor! Je positivisme en relativerend vermogen werkt aanstekelijk en was op gezette tijden broodnodig. Komende tijd zullen we ongetwijfeld nog veel samenwerken, ik zie er erg naar uit!

Markus, your name has already been mentioned, but since you are my paranimf you get your very own paragraph. For years we shared oﬃces, and now I’m literally sitting in your chair. The last few years we worked together on multiple projects, the result of which is an important part of this thesis. I learned a lot from you such as C++, the concept of a four-quadrant plot, and lots of general knowledge, mostly revolving around panini’s and cats. I’m very happy to have you as a friend

117 Acknowledgements and hope that every now and then you ﬁnd time to visit Utrecht.

Furthermore, I would like to thank my fellow OIO’s, postdocs, and colleagues: Cornel, Yulia, Yuana, Roel, Suzanne, Isabell, Beatrice, Anna, Maxence, Maureen, Matteo, Bjorn, Tom, Tim, Tristan, Stefano, Jean-Paul, Robin, Maarten, Stefan, Soraya, Federico, Mark, Dennis, Fieke, Frank, Daan, Mick, Joris, Alexis, Gijs, Hans, Martin, Thijs, Merlijn, and others that I’m forgetting for the interesting discussions, many coffee breaks, lunches, dinners and conference trips. In particular, I want to thank Arjan, for some great evenings hacking the scanner, Charis for being an awesome current office mate, Cyril for being my ex office mate and faithful coffee partner, and Filipa for sharing the stress of finishing our theses on time.

Graag wil ik ook mijn lieve vrienden bedanken die mij gedurende mijn promotie met raad en daad terzijde hebben gestaan: Pascal, Chris, Joost, Guusje, Stepha- nie, Matthijs, Faranaaz en Sjaak. Guido, als paranimf wil ik jou speciaal bedanken. Ik bewonder je ontembare enthousiasme voor natuurkunde en nuchtere kijk op het leven, ondanks de waanwetenschappers waar je mee te maken kreeg.

Lieve familie: Paula, Tim, Daan en Sam, bedankt voor jullie mentale steun tijdens mijn promotie. Jullie maken dat een bezoek aan de Oranjelaan nog steeds voelt als thuiskomen.

Puji, saya merasa sangat senang kamu telah muncul dalam hidup saya. Yang terbaik tentang pekerjaan S3 adalah saya bisa meluangkan banyak waktu untuk mengunjungi kamu di Indonesia, kadang-kadang selama beberapa hari saja untuk merayakan ulang tahun atau wisuda kamu. Pernikahan kita adalah momen terpen- ting di tahun-tahun yang lalu. Saya berterimakasih kamu mau pindah ke Utrecht untuk mulai hidup baru bersama.

118 Curriculum vitae

I was born on the 4th of November 1989 in Leiderdorp. After graduating from high school at the Johan van Oldenbarnevelt gymnasium in Amersfoort, I enrolled in the bachelor programs physics & astronomy and mathematics at Utrecht University in 2008. In 2011, I graduated from both programs cum laude and enrolled in the master program theoretical physics at the same university. During three years I followed various condensed matter and high energy physics courses and graduated with a thesis written under supervision of prof. Stoof on the duality between black holes and strongly interacting condensed matter systems. At the same time I followed a semester of law courses, mainly focusing on Dutch constitutional law.

In the fall of 2014 I started my PhD on the topic of interventional real-time mri under supervision of prof. Raaymakers and prof. Moonen at the UMC Utrecht, the result of which you are currently holding. At the time of writing, I am working at the radiotherapy department of the UMC Utrecht as part of the clinical computer science team, translating research software to a clinical setting and continuing research on real-time mri for radiotherapy guidance.

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