| 1. |
- Boito, Deneb, et al.
(author)
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Applying positivity constraints to q-space traj ectory imaging : The QTI plus implementation
- 2022
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In: SoftwareX. - : Elsevier. - 2352-7110. ; 18
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Journal article (peer-reviewed)abstract
- Diffusion MRI is a powerful technique sensitive to the microstructure of heterogeneous media. By relating the dMRI signal obtained via general gradient waveforms to the moments of an underlying diffusion tensor distribution, q-space trajectory imaging (QTI) provides several quantities indicative of the structural composition of the medium. Substantial improvements in the reliability of the produced estimates has been achieved via incorporating necessary positivity constraints in the estimation by employing Semidefinite Programming. Here we present the Matlab code implementing said constraints, provide a simple example showing the main functionalities of the package, and point to resources within the package that can be used to reproduce results recently published with this software. The block-based structure of our implementation allows the selection of steps to be performed, and facilitates the incorporation of new constraints in future releases.
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| 2. |
- Boito, Deneb, 1993-, et al.
(author)
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Diffusivity-limited q-space trajectory imaging
- 2023
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In: Magnetic Resonance Letters. - : KeAi Publishing Communications. - 2772-5162. ; 3:2, s. 187-196
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Journal article (peer-reviewed)abstract
- Q-space trajectory imaging (QTI) allows non-invasive estimation of microstructural features of heterogeneous porous media via diffusion magnetic resonance imaging performed with generalised gradient waveforms. A recently proposed constrained estimation framework, called QTI+, improved QTI’s resilience to noise and data sparsity, thus increasing the reliability of the method by enforcing relevant positivity constraints. In this work we consider expanding the set of constraints to be applied during the fitting of the QTI model. We show that the additional conditions, which introduce an upper bound on the diffusivity values, further improve the retrieved parameters on a publicly available human brain dataset as well as on data acquired from healthy volunteers using a scanner-ready protocol.
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| 3. |
- Dela Haije, Tom, et al.
(author)
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Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming
- 2020
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In: NeuroImage. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 1053-8119 .- 1095-9572. ; 209
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Journal article (peer-reviewed)abstract
- In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.
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| 4. |
- Herberthson, Magnus, et al.
(author)
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Q-space trajectory imaging with positivity constraints (QTI plus )
- 2021
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In: NeuroImage. - : Elsevier. - 1053-8119 .- 1095-9572. ; 238
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Journal article (peer-reviewed)abstract
- Q-space trajectory imaging (QTI) enables the estimation of useful scalar measures indicative of the local tissue structure. This is accomplished by employing generalized gradient waveforms for diffusion sensitization alongside a diffusion tensor distribution (DTD) model. The first two moments of the underlying DTD are made available by acquisitions at low diffusion sensitivity (b-values). Here, we show that three independent conditions have to be fulfilled by the mean and covariance tensors associated with distributions of symmetric positive semidefinite tensors. We introduce an estimation framework utilizing semi-definite programming (SDP) to guarantee that these conditions are met. Applying the framework on simulated signal profiles for diffusion tensors distributed according to non-central Wishart distributions demonstrates the improved noise resilience of QTI+ over the commonly employed estimation methods. Our findings on a human brain data set also reveal pronounced improvements, especially so for acquisition protocols featuring few number of volumes. Our methods robustness to noise is expected to not only improve the accuracy of the estimates, but also enable a meaningful interpretation of contrast in the derived scalar maps. The techniques performance on shorter acquisitions could make it feasible in routine clinical practice.
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| 5. |
- Özarslan, Evren, et al.
(author)
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Diffusion within pores fully revealed by magnetic resonance
- 2023
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In: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 158:16
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Journal article (peer-reviewed)abstract
- The diffusion propagator fully characterizes the diffusion process, which is highly sensitive to the confining boundaries and the structure within enclosed pores. While magnetic resonance has extensively been used to observe various features of the diffusion process, its full characterization has been elusive. Here, we address this challenge by employing a special sequence of magnetic field gradient pulses for measuring the diffusion propagator, which allows for "listening to the drum," mapping structural dispersity, and determining not only the pores shape but also diffusive dynamics within it.
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