Both inflow and the partial volume effect (PVE) are sources of error when measuring the arterial input function (AIF) in dynamic contrast-enhanced (DCE) MRI. This is relevant, as errors in the AIF can propagate into pharmacokinetic parameter estimations from the DCE data. A method was introduced for flow correction by estimating and compensating the number of the perceived pulse of spins during inflow. We hypothesized that the PVE has an impact on concentration–time curves similar to inflow. Therefore, we aimed to study the efficiency of this method to compensate for both effects simultaneously. We first simulated an AIF with different levels of inflow and PVE contamination. The peak, full width at half-maximum (FWHM), and area under curve (AUC) of the reconstructed AIFs were compared with the true (simulated) AIF. In clinical data, the PVE was included in AIFs artificially by averaging the signal in voxels surrounding a manually selected point in an artery. Subsequently, the artificial partial volume AIFs were corrected and compared with the AIF from the selected point. Additionally, corrected AIFs from the internal carotid artery (ICA), the middle cerebral artery (MCA), and the venous output function (VOF) estimated from the superior sagittal sinus (SSS) were compared. As such, we aimed to investigate the effectiveness of the correction method with different levels of inflow and PVE in clinical data. The simulation data demonstrated that the corrected AIFs had only marginal bias in peak value, FWHM, and AUC. Also, the algorithm yielded highly correlated reconstructed curves over increasingly larger neighbourhoods surrounding selected arterial points in clinical data. Furthermore, AIFs measured from the ICA and MCA produced similar peak height and FWHM, whereas a significantly larger peak and lower FWHM was found compared with the VOF. Our findings indicate that the proposed method has high potential to compensate for PVE and inflow simultaneously. The corrected AIFs could thereby provide a stable input source for DCE analysis.@en

Magnetic Resonance Imaging (MRI) is a flexible medical imaging technique that facilitates measurement of a wide range of contrasts particularly in soft tissue (e.g. brain and heart). Conventionally, qualitative images are acquired in which certain physical tissue properties are emphasized such as the transverse and longitudinal relaxation times. Such images are frequently referred to as "weighted", i.e. T₁-weighted. Quantitative MRI (qMRI) aims at measuring the underlying tissue parameters governing the contrast instead of yielding mere weighted images. These quantitative parameter estimations were proven to be more reproducible than conventional MR images and more sensitive to certain disease processes, enabling enhanced longitudinal comparisons within subjects as well as comparisons between subjects.

MR Fingerprinting (MRF) is an example of such a quantitative technique. MRF uses a combination of transient state acquisitions with varying flip angle patterns, severe undersampling and advanced signal models to allow for fast qMRI acquisitions and accurate estimation of a wide range of parameters.
While most qMRI methods assume a single tissue type per voxel, this is almost never a valid assumption. This assumption especially breaks down at tissue boundaries or when tissues consist of multiple, mixed compartments, such as water contained between myelin sheets in the brain, often called myelin water surrounded by extra-cellular water.

The goal of this thesis is to develop enhanced methodology for quantitative MRI by extending traditional signal and image post-processing methods. Specifically, the focus is on MR Fingerprinting in combination with multi-component estimations, in which different compartments are included in a mixed estimation model. This is done to obtain more information from the acquired data and to improve quantification, therefore possibly obtain new clinical insights. Important steps towards clinical use are to enhance estimation accuracy and precision compared to previous methods and reduce the scan time.


In this thesis the Sparsity Promoting Iterative Joint NNLS (SPIJN) algorithm is proposed for obtaining multi-component estimations from MRF data. This enabled sub-voxel, fractional estimation of signal components in a region of interest, without making a priori assumptions about tissues expected to be present. The main novelty of this method is to combine a non-negativity with a joint-sparsity constraint that limits the total number of tissues identified in a region of interest. As a result it became possible to obtain magnetization fraction maps of the white matter, gray matter, CSF and a component with shorter relaxation times related to myelin water.
The repeatability of the proposed method is studied in 5 subjects that were scanned 8 times with one week in between the scans each time. Comparison of the obtained white matter, gray matter and CSF maps with segmentations from conventional methods shows high repeatability of the estimated relaxation times and more fine structures in the CSF magnetization fraction maps.
Additionally, the proposed SPIJN algorithm was applied to data from a more conventional qMRI sequence, i.e. a multi-echo spin-echo sequence, to obtain estimations of the so-called myelin water fraction in the brain. The resulting images show significantly improved noise robustness compared to the standard multi-component analysis method, improving the usability.

MRF scans can be acquired in a relatively short acquisition time of less than 30 seconds per slice, but this will still result in 15 minutes of total scan-time when full brain coverage is needed. A further reduction in acquisition time is desirable for clinical usage, in which every minute counts. Therefore, improved reconstruction methods for MRF data are proposed, especially tailored to multi-component estimations. In in vivo scans we showed the improved image quality enabled by the proposed methods.

In another study, We applied the SPIJN algorithm to MRF brain scans from MS patients. In the results that we obtained we observe that white matter changes are reflected in a component with prolonged transverse relaxation times which is less pronounced in data of healthy controls. We hypothesize that the observed component reflects an increase in extra-cellular water and allows for early characterization of white matter damage.

In a related project, an adaptation on the SPIJN algorithm was introduced that is more sensitive to small local changes. The adjusted algorithm is applied to imaging data of MS patients and it is shown that it can help to identify small cerebral lesions.

MRF sequences can be chosen rather freely, to further reduce the scan time and reduce the estimation error these sequences can be optimized. A method is proposed in which parameter maps of the brain are used as reference upon which the MRF flip-angle series is optimized, taking into account the used undersampling trajectories. As a result undersampling errors, a major source of estimation errors, are effectively minimized.

Finally, we investigated an adjusted simulation method of MRF sequences that is able to accurately model the effects of through-plane motion, which is a major source of errors in MRF scans. Such a model may support the development of new retrospective correction methods for this type of motion as it enables proper simulation of its effects.

In summary, this thesis proposes new methods for multi-component reconstruction and analysis, sequence optimization and studying the effects of motion in MRF and further investigates the possibilities of multi-component MRF.@en

T₂-hyperintense lesions are the key imaging marker of multiple sclerosis (MS). Previous studies have shown that the white matter surrounding such lesions is often also affected by MS. Our aim was to develop a new method to visualize and quantify the extent of white matter tissue changes in MS based on relaxometry properties. We applied a fast, multi-parametric quantitative MRI approach and used a multi-component MR Fingerprinting (MC-MRF) analysis. We assessed the differences in the MRF component representing prolongedrelaxation time between patients with MS and controls and studied the relation between this component's volume and structural white matter damage identified on FLAIR MRI scans in patients with MS. A total of 48 MS patients at two different sites and 12 healthy controls were scanned with FLAIR and MRF-EPI MRI scans. MRF scans were analyzed with a joint-sparsity multi-component analysis to obtain magnetization fraction maps of different components, representing tissues such as myelin water, white matter, gray matter and cerebrospinal fluid. In the MS patients, an additional component was identified with increased transverse relaxation times compared to the white matter, likely representing changes in free water content. Patients with MS had a higher volume of the long- component in the white matter of the brain compared to healthy controls (B (95%-CI) = 0.004 (0.0006–0.008), p = 0.02). Furthermore, this MRF component had a moderate correlation (correlation coefficient R 0.47) with visible structural white matter changes on the FLAIR scans. Also, the component was found to be more extensive compared to structural white matter changes in 73% of MS patients. In conclusion, our MRF acquisition and analysis captured white matter tissue changes in MS patients compared to controls. In patients these tissue changes were more extensive compared to visually detectable white matter changes on FLAIR scans. Our method provides a novel way to quantify the extent of white matter changes in MS patients, which is underestimated using only conventional clinical MRI scans.

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Purpose: To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues. Methods: The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference. Results: The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0% (Formula presented.) 5.8% with the conventional, two-step approach to 9.6% (Formula presented.) 3.9% and 9.6% (Formula presented.) 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN). Conclusion: The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method.

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MR fingerprinting (MRF) is a promising method for quantitative characterization of tissues. Often, voxel-wise measurements are made, assuming a single tissue-type per voxel. Alternatively, the Sparsity Promoting Iterative Joint Non-negative least squares Multi-Component MRF method (SPIJN-MRF) facilitates tissue parameter estimation for identified components as well as partial volume segmentations. The aim of this paper was to evaluate the accuracy and repeatability of the SPIJN-MRF parameter estimations and partial volume segmentations. This was done (1) through numerical simulations based on the BrainWeb phantoms and (2) using in vivo acquired MRF data from 5 subjects that were scanned on the same week-day for 8 consecutive weeks. The partial volume segmentations of the SPIJN-MRF method were compared to those obtained by two conventional methods: SPM12 and FSL. SPIJN-MRF showed higher accuracy in simulations in comparison to FSL- and SPM12-based segmentations: Fuzzy Tanimoto Coefficients (FTC) comparing these segmentations and Brainweb references were higher than 0.95 for SPIJN-MRF in all the tissues and between 0.6 and 0.7 for SPM12 and FSL in white and gray matter and between 0.5 and 0.6 in CSF. For the in vivo MRF data, the estimated relaxation times were in line with literature and minimal variation was observed. Furthermore, the coefficient of variation (CoV) for estimated tissue volumes with SPIJN-MRF were 10.5% for the myelin water, 6.0% for the white matter, 5.6% for the gray matter, 4.6% for the CSF and 1.1% for the total brain volume. CoVs for CSF and total brain volume measured on the scanned data for SPIJN-MRF were in line with those obtained with SPM12 and FSL. The CoVs for white and gray matter volumes were distinctively higher for SPIJN-MRF than those measured with SPM12 and FSL. In conclusion, the use of SPIJN-MRF provides accurate and precise tissue relaxation parameter estimations taking into account intrinsic partial volume effects. It facilitates obtaining tissue fraction maps of prevalent tissues including myelin water which can be relevant for evaluating diseases affecting the white matter.

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Purpose: To develop a method for MR Fingerprinting (MRF) sequence optimization that takes both the applied undersampling pattern and a realistic reference map into account. Methods: A predictive model for the undersampling error leveraging on perturbation theory was exploited to optimize the MRF flip angle sequence for improved robustness against undersampling artifacts. In this framework parameter maps from a previously acquired MRF scan were used as reference. Sequences were optimized for different sequence lengths, smoothness constraints and undersampling factors. Numerical simulations and in vivo measurements in eight healthy subjects were performed to assess the effect of the performed optimization. The optimized MRF sequences were compared to a conventionally shaped flip angle pattern and an optimized pattern based on the Cramér–Rao lower bound (CRB). Results: Numerical simulations and in vivo results demonstrate that the undersampling errors can be suppressed by flip angle optimization. Analysis of the in vivo results show that a sequence optimized for improved robustness against undersampling with a flip angle train of length 400 yielded significantly lower median absolute errors in (Formula presented.) : (Formula presented.) and (Formula presented.) : (Formula presented.) compared to the conventional ((Formula presented.) : (Formula presented.), (Formula presented.) : (Formula presented.)) and CRB-based ((Formula presented.) : (Formula presented.), (Formula presented.) : (Formula presented.)) sequences. Conclusion: The proposed method is able to optimize the MRF flip angle pattern such that significant mitigation of the artifacts from strong k-space undersampling in MRF is achieved.

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Purpose: To develop an accelerated postprocessing pipeline for reproducible and efficient assessment of white matter lesions using quantitative magnetic resonance fingerprinting (MRF) and deep learning. Methods: MRF using echo-planar imaging (EPI) scans with varying repetition and echo times were acquired for whole brain quantification of (Formula presented.) and (Formula presented.) in 50 subjects with multiple sclerosis (MS) and 10 healthy volunteers along 2 centers. MRF (Formula presented.) and (Formula presented.) parametric maps were distortion corrected and denoised. A CNN was trained to reconstruct the (Formula presented.) and (Formula presented.) parametric maps, and the WM and GM probability maps. Results: Deep learning-based postprocessing reduced reconstruction and image processing times from hours to a few seconds while maintaining high accuracy, reliability, and precision. Mean absolute error performed the best for (Formula presented.) (deviations 5.6%) and the logarithmic hyperbolic cosinus loss the best for (Formula presented.) (deviations 6.0%). Conclusions: MRF is a fast and robust tool for quantitative (Formula presented.) and (Formula presented.) mapping. Its long reconstruction and several postprocessing steps can be facilitated and accelerated using deep learning.

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Purpose

To develop an efficient algorithm for multi‐component analysis of magnetic resonance fingerprinting (MRF) data without making a priori assumptions about the exact number of tissues or their relaxation properties.
Methods

Different tissues or components within a voxel are potentially separable in MRF because of their distinct signal evolutions. The observed signal evolution in each voxel can be described as a linear combination of the signals for each component with a non‐negative weight. An assumption that only a small number of components are present in the measured field of view is usually imposed in the interpretation of multi‐component data. In this work, a joint sparsity constraint is introduced to utilize this additional prior knowledge in the multi‐component analysis of MRF data. A new algorithm combining joint sparsity and non‐negativity constraints is proposed and compared to state‐of‐the‐art multi‐component MRF approaches in simulations and brain MRF scans of 11 healthy volunteers.
Results

Simulations and in vivo measurements show reduced noise in the estimated tissue fraction maps compared to previously proposed methods. Applying the proposed algorithm to the brain data resulted in 4 or 5 components, which could be attributed to different brain structures, consistent with previous multi‐component MRF publications.
Conclusions

The proposed algorithm is faster than previously proposed methods for multi‐component MRF and the simulations suggest improved accuracy and precision of the estimated weights. The results are easier to interpret compared to voxel‐wise methods, which combined with the improved speed is an important step toward clinical evaluation of multi‐component MRF.
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Demyelination is the key pathological process in multiple sclerosis (MS). The extent of demyelination can be quantified with magnetic resonance imaging by assessing the myelin water fraction (MWF). However, long computation times and high noise sensitivity hinder the translation of MWF imaging to clinical practice. In this work, we introduce a more efficient and noise robust method to determine the MWF using a joint sparsity constraint and a pre-computed B₁⁺-T₂ dictionary. A single component analysis with this dictionary is used in an initial step to obtain a B₁⁺ map. The T₂ distribution is then determined from a reduced dictionary corresponding to the estimated B₁⁺ map using a combination of a non-negativity and a joint sparsity constraint. The non-negativity constraint ensures that a feasible solution with non-negative contribution of each T₂ component is obtained. The joint sparsity constraint restricts the T₂ distribution to a small set of T₂ relaxation times shared between all voxels and reduces the noise sensitivity. The applied Sparsity Promoting Iterative Joint NNLS (SPIJN) algorithm can be implemented efficiently, reducing the computation time by a factor of 50 compared to the commonly used regularized non-negative least squares algorithm. The proposed method was validated in simulations and in 8 healthy subjects with a 3D multi-echo gradient- and spin echo scan at 3 ​T. In simulations, the absolute error in the MWF decreased from 0.031 to 0.013 compared to the regularized NNLS algorithm for SNR ​= ​250. The in vivo results were consistent with values reported in literature and improved MWF-quantification was obtained especially in the frontal white matter. The maximum standard deviation in mean MWF in different regions of interest between subjects was smaller for the proposed method (0.0193) compared to the regularized NNLS algorithm (0.0266). In conclusion, the proposed method for MWF estimation is less computationally expensive and less susceptible to noise compared to state of the art methods. These improvements might be an important step towards clinical translation of MWF measurements.

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We propose a novel multi-component analysis for MR fingerprinting that enables detection of small lesions, while taking partial volume effects into account. The algorithm uses a joint sparsity constraint limiting the number of components in local regions. It is evaluated in simulations and on MRF-EPI data from a patient with multiple sclerosis (MS). MS-lesions are separated from other tissues based on having increased T2* relaxation times. The improved sensitivity to multiple components makes it possible to detect components with long relaxation times within the lesion, possibly increasing our insight into these small pathologies.@en

We propose a quantum-mechanical device consisting of transmon qubits connected to single-photon transmission lines that can be used to perform a boolean quantum private query on a database. Using numerical simulations verified by analytical calculations we analyse the dynamics of the query process in the proposed system by calculating the reflection and transmission probabilities of the photons encoding the questions. We show that the proposed device, which consists of experimentally available components, is capable of performing a quantum private query with high reliability and may form the basic building block of a lager-scale private search engine.

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