Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure

Robust frequency-dependent diffusion kurtosis computation using an efficient direction scheme, axisymmetric modelling, and spatial regularization

Frequency-dependent diffusion MRI (dMRI) using oscillating gradient encoding and diffusion kurtosis imaging (DKI) techniques have been shown to provide additional insight into tissue microstructure compared to conventional dMRI. However, a technical challenge when combining these techniques is that the generation of the large b-values required for DKI is difficult when using oscillating gradient diffusion encoding. While efficient encoding schemes can enable larger b-values by maximizing multiple gradient channels simultaneously, they do not have sufficient directions to enable fitting of the full kurtosis tensor. Accordingly, we investigate a DKI fitting algorithm that combines axisymmetric DKI fitting, a prior that enforces the same axis of symmetry for all oscillating gradient frequencies, and spatial regularization, which together enable robust DKI fitting for a 10-direction scheme that offers double the b-value compared to traditional direction schemes. Using data from mice (oscillating frequencies of 0, 60, and 120 Hz) and humans (0 Hz only), we first show that axisymmetric modelling is advantageous over full kurtosis tensor fitting in terms of preserving contrast and reducing noise in DKI maps, and improved DKI map quality when using an efficient encoding scheme with averaging as compared to a traditional scheme with more encoding directions. We also demonstrate how spatial regularization during fitting preserves spatial features better than using Gaussian filtering prior to fitting, which is an oft-reported preprocessing step for DKI, and that enforcing consistent axes of symmetries across frequencies improves fitting quality. Thus, the use of an efficient 10-direction scheme combined with the proposed DKI fitting algorithm provides robust maps of frequency-dependent directional kurtosis parameters that can be used to explore novel biomarkers for various pathologies.Comment: 41 pages, 9 figures, 2 supplementary figure

DTI denoising for data with low signal to noise ratios

Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1×1×1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable

From Diffusion to Tracts

Diffusion of water molecules within the brain tissue can be used to modulate the nuclear magnetic resonance signal that is used to form magnetic resonance images (MRI). As the signal itself can be noisy and its meaning challenging to interpret, mathematical models are generally fitted to these measurements to obtain the more accurate characterization of the brain microstructure. This, of course, requires that the mathematical model itself is sound in respect to the measurement setup. This dissertation focuses on the extensively used tensor models as they have been shown to unravel details of the physical diffusion phenomena along with various applications in the basic neuroscience, the clinical research, and even in the neurosurgery. One of the greatest challenges in the diffusion weighted MRI measurements is subject motion during the image acquisition as that can cause a complete loss of the measurement which is especially highlighted in ill or uncooperative patients studies. Due to the used acquisition technique, this loss extends to multiple measurements simultaneously resulting in an enormous gap in the sampling. Such gaps can be problematic for any model fitting, even for the currently available robust means developed to exclude outlier measurements from affecting the estimate. Hence in this dissertation, a tool coined as SOLID was developed to detect these outliers and to robustly process them during the tensor based model estimation. SOLID was implemented as a part of the widely used ExploreDTI toolbox to allow the rapid international distribution of the tool. Unfortunately, any reduction in the measurement sampling will lead to increasing error propagation during the model estimation. Mathematically this is detailed in terms of a condition number for the matrix inversion in the linear least squares fitting. Previously, the condition number has been used to optimize the diffusion weighted MRI acquisition gradient scheme but in this dissertation it was renovated into a novel quality control tool. The condition number of the matrix inversion that provides the model estimate can be calculated after the outliers are excluded to assess spatially and directionally varying error propagation to obviate any bias in subject or population studies. To motivate the importance of the robust methods and diffusion weighted MRI at large, neurocognitive studies with neonates’ visual abilities and bilinguals’ acquisition age of the second language were conducted as a part of this thesis. The findings in these studies indicated that premature birth affects the white matter structures across the brain whereas the age of acquisition of the second language affects only the speech related brain structures.Aivojen rakenteessa tapahtuvien muutosten mittaaminen on avainasemassa tutkittaessa esimerkiksi keskosena syntyneen lapsen kehitystä tai uusien taitojen, kuten kielten, oppimista. Ihmisaivojen tutkiminen on aiemmin rajoittunut aivojen toiminnan arviointiin aivosähkökäyrän ja neurokognitiivisten testien avulla. Viime vuosikymmenten kehitys magneettikuvaustekniikassa on tuonut mahdollisuuden tutkia kajoamattomasti myös aivojen rakennetta ja jopa seurata sen muutosta lapsen kasvaessa tai ihmisen oppiessa uusia taitoja. Yksi lupaavimmista aivojen tutkimusmenetelmistä on diffuusiopainotettu magneettikuvaus, jolle on löytynyt lukuisia käyttökohteita niin neurotieteessä, lääketieteellisissä tutkimuksissa kuin neurokirurgiassakin. Menetelmä perustuu vesimolekyylien lämpöliikkeen mittaamiseen aivoissa. Molekyylien liike on vapaata muun muassa valkean aineen rakenteiden myötäisesti, mutta lähes mahdotonta kohtisuoraan niiden lävitse. Jäljittämällä nämä reitit voidaan muodostaa tarkka malli aivojen rakenteesta. Mallin pohjalta on mahdollista laskea kuvaavia arvoja, jotka auttavat esimerkiksi määrittämään aivovaurion astetta. Diffuusiopainotetun magneettikuvauksen suurin haaste on menetelmän monimutkaisuus sekä mittauksen että analyysin osalta. Vain hyvin yksinkertaisissa tapauksissa asiantuntija voi arvioida suoraan diffuusiopainotetusta magneettikuvasta poikkeamia aivoissa. Yleensä käytetään matemaattisia menetelmiä kuvan tarkempaan analysointiin. Tällöin keskeistä on inversio-ongelman ratkaisu, missä potilaasta tehdyt mittaukset sovitetaan aivoja kuvaavaan matemaattiseen malliin. Sopivan mallin valinnalla on siis suuri vaikutus lopputuloksen hyödyllisyyteen. Diffuusiopainotettu magneettikuvaus on myös häiriöherkkä ja mittaukset sisältävät luonnostaan paljon kohinaa, jonka vaikutusta vähennetään tekemällä toistomittauksia. Toistomittaukset pidentävät kuvausaikaa, joka puolestaan voi olla haasteellinen potilaalle, koska potilaan pitää olla liikkumatta koko kuvauksen ajan. Potilaan pään pienikin liike voi johtaa huomattaviin mittavirheisiin, koska menetelmällä mitataan vesimolekyylien liikettä, jonka suuruus on vain kymmenien mikrometrien luokkaa. Tässä fysiikan väitöskirjassa keskityttiin diffuusiopainotetun magneettikuvauksen mallintamismenetelmien kehitystyöhön ja niiden käyttöönottoon Helsingin yliopistollisessa sairaalassa. Kehitimme kansainvälistä huomiota herättäneen SOLID-työkalun, jolla voidaan havaita sekä korjata potilaan liikkeestä aiheutuvia virheitä mittaustuloksissa. Tämän lisäksi esitimme laadunvalvonta menetelmän, jolla voidaan arvioida esimerkiksi potilaiden välisten mallinnustulosten vertailukelpoisuutta. Kehitettyjä menetelmiä testattiin ja sovellettiin kahdessa tutkimuksessa: Osoitimme, että vastasyntyneen lapsen kyky seurata katseellaan liikkuvaa kohdetta liittyy laaja-alaisiin muutoksiin aivojen valkean aineen rakenteessa. Lisäksi näytimme, että toisen kielen oppimisajankohta vaikuttaa aivojen puheentuottoon liittyvien aivorakenteiden muodostumiseen

Recommendations and guidelines from the ISMRM Diffusion Study Group for preclinical diffusion MRI: Part 1 -- In vivo small-animal imaging

The value of in vivo preclinical diffusion MRI (dMRI) is substantial. Small-animal dMRI has been used for methodological development and validation, characterizing the biological basis of diffusion phenomena, and comparative anatomy. Many of the influential works in this field were first performed in small animals or ex vivo samples. The steps from animal setup and monitoring, to acquisition, analysis, and interpretation are complex, with many decisions that may ultimately affect what questions can be answered using the data. This work aims to serve as a reference, presenting selected recommendations and guidelines from the diffusion community, on best practices for preclinical dMRI of in vivo animals. In each section, we also highlight areas for which no guidelines exist (and why), and where future work should focus. We first describe the value that small animal imaging adds to the field of dMRI, followed by general considerations and foundational knowledge that must be considered when designing experiments. We briefly describe differences in animal species and disease models and discuss how they are appropriate for different studies. We then give guidelines for in vivo acquisition protocols, including decisions on hardware, animal preparation, imaging sequences and data processing, including pre-processing, model-fitting, and tractography. Finally, we provide an online resource which lists publicly available preclinical dMRI datasets and software packages, to promote responsible and reproducible research. An overarching goal herein is to enhance the rigor and reproducibility of small animal dMRI acquisitions and analyses, and thereby advance biomedical knowledge.Comment: 69 pages, 6 figures, 1 tabl

Fast diffusion MRI based on sparse acquisition and reconstruction for long-term population imaging

Diffusion weighted magnetic resonance imaging (dMRI) is a unique MRI modality to probe the diffusive molecular transport in biological tissue. Due to its noninvasiveness and its ability to investigate the living human brain at submillimeter scale, dMRI is frequently performed in clinical and biomedical research to study the brain’s complex microstructural architecture. Over the last decades large prospective cohort studies have been set up with the aim to gain new insights into the development and progression of brain diseases across the life span and to discover biomarkers for disease prediction and potentially prevention. To allow for diverse brain imaging using different MRI modalities, stringent scan time limits are typically imposed in population imaging. Nevertheless, population studies aim to apply advanced and thereby time consuming dMRI protocols that deliver high quality data with great potential for future analysis. To allow for time-efficient but also versatile diffusion imaging, this thesis contributes to the investigation of accelerating diffusion spectrum imaging (DSI), an advanced dMRI technique that acquires imaging data with high intra-voxel resolution of tissue microstructure. Combining state-of-the-art parallel imaging and the theory of compressed sensing (CS) enables the acceleration of spatial encoding and diffusion encoding in dMRI. In this way, the otherwise long acquisition times in DSI can be reduced significantly. In this thesis, first, suitable q-space sampling strategies and basis functions are explored that fulfill the requirements of CS theory for accurate sparse DSI reconstruction. Novel 3D q-space sample distributions are investigated for CS-DSI. Moreover, conventional CS-DSI based on the discrete Fourier transform is compared for the first time to CS-DSI based on the continuous SHORE (simple harmonic oscillator based reconstruction and estimation) basis functions. Based on these findings, a CS-DSI protocol is proposed for application in a prospective cohort study, the Rhineland Study. A pilot study was designed and conducted to evaluate the CS-DSI protocol in comparison with state-of-the-art 3-shell dMRI and dedicated protocols for diffusion tensor imaging (DTI) and for the combined hindered and restricted model of diffusion (CHARMED). Population imaging requires processing techniques preferably with low computational cost to process and analyze the acquired big data within a reasonable time frame. Therefore, a pipeline for automated processing of CS-DSI acquisitions was implemented including both in-house developed and existing state-of-the-art processing tools. The last contribution of this thesis is a novel method for automatic detection and imputation of signal dropout due to fast bulk motion during the diffusion encoding in dMRI. Subject motion is a common source of artifacts, especially when conducting clinical or population studies with children, the elderly or patients. Related artifacts degrade image quality and adversely affect data analysis. It is, thus, highly desired to detect and then exclude or potentially impute defective measurements prior to dMRI analysis. Our proposed method applies dMRI signal modeling in the SHORE basis and determines outliers based on the weighted model residuals. Signal imputation reconstructs corrupted and therefore discarded measurements from the sparse set of inliers. This approach allows for fast and robust correction of imaging artifacts in dMRI which is essential to estimate accurate and precise model parameters that reflect the diffusive transport of water molecules and the underlying microstructural environment in brain tissue.Die diffusionsgewichtete Magnetresonanztomographie (dMRT) ist ein einzigartiges MRTBildgebungsverfahren, um die Diffusionsbewegung von Wassermolekülen in biologischem Gewebe zu messen. Aufgrund der Möglichkeit Schichtbilder nicht invasiv aufzunehmen und das lebende menschliche Gehirn im Submillimeter-Bereich zu untersuchen, ist die dMRT ein häufig verwendetes Bildgebungsverfahren in klinischen und biomedizinischen Studien zur Erforschung der komplexen mikrostrukturellen Architektur des Gehirns. In den letzten Jahrzehnten wurden große prospektive Kohortenstudien angelegt, um neue Einblicke in die Entwicklung und den Verlauf von Gehirnkrankheiten über die Lebenspanne zu erhalten und um Biomarker zur Krankheitserkennung und -vorbeugung zu bestimmen. Um durch die Verwendung unterschiedlicher MRT-Verfahren verschiedenartige Schichtbildaufnahmen des Gehirns zu ermöglich, müssen Scanzeiten typischerweise stark begrenzt werden. Dennoch streben Populationsstudien die Anwendung von fortschrittlichen und daher zeitintensiven dMRT-Protokollen an, um Bilddaten in hoher Qualität und mit großem Potential für zukünftige Analysen zu akquirieren. Um eine zeiteffizente und gleichzeitig vielseitige Diffusionsbildgebung zu ermöglichen, leistet diese Dissertation Beiträge zur Untersuchung von Beschleunigungsverfahren für die Bildgebung mittels diffusion spectrum imaging (DSI). DSI ist ein fortschrittliches dMRT-Verfahren, das Bilddaten mit hoher intra-voxel Auflösung der Gewebestruktur erhebt. Werden modernste Verfahren zur parallelen MRT-Bildgebung mit der compressed sensing (CS) Theorie kombiniert, ermöglicht dies eine Beschleunigung der räumliche Kodierung und der Diffusionskodierung in der dMRT. Dadurch können die ansonsten langen Aufnahmezeiten für DSI erheblich reduziert werden. In dieser Arbeit werden zuerst geeigenete Strategien zur Abtastung des q-space sowie Basisfunktionen untersucht, welche die Anforderungen der CS-Theorie für eine korrekte Signalrekonstruktion der dünnbesetzten DSI-Daten erfüllen. Neue 3D-Verteilungen von Messpunkten im q-space werden für die Verwendung in CS-DSI untersucht. Außerdem wird konventionell auf der diskreten Fourier-Transformation basierendes CS-DSI zum ersten Mal mit einem CS-DSI Verfahren verglichen, welches kontinuierliche SHORE (simple harmonic oscillator based reconstruction and estimation) Basisfunktionen verwendet. Aufbauend auf diesen Ergebnissen wird ein CS-DSI-Protokoll zur Anwendung in einer prospektiven Kohortenstudie, der Rheinland Studie, vorgestellt. Eine Pilotstudie wurde entworfen und durchgeführt, um das CS-DSI-Protokoll im Vergleich mit modernster 3-shell-dMRT und mit dedizierten Protokollen für diffusion tensor imaging (DTI) und für das combined hindered and restricted model of diffusion (CHARMED) zu evaluieren. Populationsbildgebung erfordert Prozessierungsverfahren mit möglichst geringem Rechenaufwand, um große akquirierte Datenmengen in einem angemessenen Zeitrahmen zu verarbeiten und zu analysieren. Dafür wurde eine Pipeline zur automatisierten Verarbeitung von CS-DSI-Daten implementiert, welche sowohl eigenentwickelte als auch bereits existierende moderene Verarbeitungsprogramme enthält. Der letzte Beitrag dieser Arbeit ist eine neue Methode zur automatischen Detektion und Imputation von Signalabfall, welcher durch schnelle Bewegungen während der Diffusionskodierung in der dMRT entsteht. Bewegungen der Probanden während der dMRT-Aufnahme sind eine häufige Ursache für Bildfehler, vor allem in klinischen oder Populationsstudien mit Kindern, alten Menschen oder Patienten. Diese Artefakte vermindern die Datenqualität und haben einen negativen Einfluss auf die Datenanalyse. Daher ist es das Ziel, fehlerhafte Messungen vor der dMRI-Analyse zu erkennen und dann auszuschließen oder wenn möglich zu ersetzen. Die vorgestellte Methode verwendet die SHORE-Basis zur dMRT-Signalmodellierung und bestimmt Ausreißer mit Hilfe von gewichteten Modellresidualen. Die Datenimputation rekonstruiert die unbrauchbaren und daher verworfenen Messungen mit Hilfe der verbleibenden, dünnbesetzten Menge an Messungen. Dieser Ansatz ermöglicht eine schnelle und robuste Korrektur von Bildartefakten in der dMRT, welche erforderlich ist, um korrekte und präzise Modellparameter zu schätzen, die die Diffusionsbewegung von Wassermolekülen und die zugrundeliegende Mikrostruktur des Gehirngewebes reflektieren

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application

Diffusion Kurtosis Magnetic Resonance Imaging and Its Application to Traumatic Brain Injury

Diffusion tensor imaging (DTI) is a popular magnetic resonance imaging technique that provides in vivo information about tissue microstructure, based on the local water diffusion environment. DTI models the diffusion displacement of water molecules in tissue as a Gaussian distribution. In this dissertation, to mimic the complex nature of water diffusion in brain tissues, a diffusion kurtosis model is used, to incorporate important non-Gaussian diffusion properties. This diffusion kurtosis imaging (DKI) is applied in an experimental traumatic brain injury in a rat model, to study whether it provides more information on microstructural changes than standard DTI. Our results indicate changes in ordinary DTI parameters, in various brain regions following injury, normalize to the baseline by the sub-acute stage. However, DKI parameters continue to show abnormalities at this sub-acute stage, as confirmed by immunohistochemical examination. Specifically, increased mean kurtosis (MK) was found to associate with increased reactive astrogliosis, a hallmark for inflammation, even in regions far removed from the injury foci. Findings suggest that monitoring changes in MK enhances the investigation of molecular and morphological changes in vivo. Extending DKI to clinical usage, however, poses several challenges: (a) long image acquisition time (~20 min) due to the augmented measurements required to fit the more complex model, (b) slow image reconstruction (~90 min) due to required nonlinear fitting and, (c) errors associated with fitting the inherently low signal-to-noise ratio (SNR) images from higher diffusion weighting. The second portion of this dissertation is devoted to developing imaging schemes and image reconstruction methods that facilitate clinical DKI applications. A fast and efficient DKI reconstruction method is developed with a reconstruction time of 2-3 seconds, with improved accuracy and reduced variability in DKI estimation over conventional methods. Further analysis of diffusion weighted imaging schemes and their affect on DKI estimation leads to the identification of two clinically practical optimal imaging schemes (needing 7-10 min) that perform comparably to traditional schemes. The effect of SNR and reconstruction methods on DKI estimation is also studied, to provide a foundation for interpreting DKI results and optimizing DKI protocols

"MASSIVE" Brain Dataset: Multiple Acquisitions for Standardization of Structural Imaging Validation and Evaluation

PURPOSE: In this work, we present the MASSIVE (Multiple Acquisitions for Standardization of Structural Imaging Validation and Evaluation) brain dataset of a single healthy subject, which is intended to facilitate diffusion MRI (dMRI) modeling and methodology development. METHODS: MRI data of one healthy subject (female, 25 years) were acquired on a clinical 3 Tesla system (Philips Achieva) with an eight-channel head coil. In total, the subject was scanned on 18 different occasions with a total acquisition time of 22.5 h. The dMRI data were acquired with an isotropic resolution of 2.5 mm(3) and distributed over five shells with b-values up to 4000 s/mm(2) and two Cartesian grids with b-values up to 9000 s/mm(2) . RESULTS: The final dataset consists of 8000 dMRI volumes, corresponding B0 field maps and noise maps for subsets of the dMRI scans, and ten three-dimensional FLAIR, T1 -, and T2 -weighted scans. The average signal-to-noise-ratio of the non-diffusion-weighted images was roughly 35. CONCLUSION: This unique set of in vivo MRI data will provide a robust framework to evaluate novel diffusion processing techniques and to reliably compare different approaches for diffusion modeling. The MASSIVE dataset is made publically available (both unprocessed and processed) on www.massive-data.org. Magn Reson Med, 2016