Di-chromatic interpolation of magnetic resonance metabolic images

Abstract

Objective

Magnetic resonance imaging with hyperpolarized contrast agents can provide unprecedented in vivo measurements of metabolism, but yields images that are lower resolution than that achieved with proton anatomical imaging. In order to spatially localize the metabolic activity, the metabolic image must be interpolated to the size of the proton image. The most common methods for choosing the unknown values rely exclusively on values of the original uninterpolated image.

Methods

In this work, we present an alternative method that uses the higher-resolution proton image to provide additional spatial structure. The interpolated image is the result of a convex optimization algorithm which is solved with the fast iterative shrinkage threshold algorithm (FISTA).

Results

Results are shown with images of hyperpolarized pyruvate, lactate, and bicarbonate using data of the heart and brain from healthy human volunteers, a healthy porcine heart, and a human with prostate cancer.

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Acknowledgements

The authors would like to thank Roselle Abraham, Rahul Aggarwal, Robert Bok, Hsin-Yu Chen, John Kurhanewicz, James Slater, and Daniel Vigneron for their assistance in the imaging of human subjects. The authors would like to thank Gennifer T. Smith for her helpful suggestions regarding the editing of this document. ND would like to thank the Quantitative Biosciences Institute at UCSF and the American Heart Association as funding sources for this work.

Funding

ND has received post-doctoral training funding from the American Heart Association (Grant number 20POST35200152). ND has received funding from the Quantitative Biosciences Institute at UCSF (no grant number). JG has received funding from the National Institute of Health/National Institute of Biomedical Imaging and Bioengineering (Grant number U01EB026412). PL has received funding from the National Institute of Health (Grant number NIH R01 HL136965).

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Correspondence to Nicholas Dwork.

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Human and animal participants

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. MR data of humans were gathered with institutional review board (IRB) approval and Health Insurance Portability and Accountability Act (HIPAA) compliance. Informed consent was obtained from all individual participants included in the study. All applicable international, national, and/or institutional guidelines for the care and use of animals were followed. Animal experiments were done in accordance with relevant laws and ethics under permission from The Animal Experiments Inspectorate of Denmark.

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ND would like to thank the Quantitative Biosciences Institute at UCSF and the American Heart Association as funding sources for this work.

Appendix: Fast iterative shrinkage threshold algorithm

Appendix: Fast iterative shrinkage threshold algorithm

The fast iterative shrinkage threshold algorithm (FISTA) solves problems of the form:

$$\begin{aligned} \underset{x\in {\mathbb {R}}^N}{\text {minimize}} \quad F(x) + G(x), \end{aligned}$$

where F is differentiable and G has a simple proximal operator [2, 38]. The FISTA algorithm with line search is described in Algorithm 2. Note that \(\langle \cdot ,\cdot \rangle\) represents an inner product. To initialize the algorithm, set \(v^{(0)} = x^{(0)}\), where \(x^{(0)}\) is the initial guess and can be any value. Select a \(t_0>0\), and select a maximum number of iterations K. Select a backtracking line search parameter \(r\in (0,1)\) (a common choice of r is 0.9) and select a step size scaling parameter \(s>1\) (a common choice of s is 1.25).

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Dwork, N., Gordon, J.W., Tang, S. et al. Di-chromatic interpolation of magnetic resonance metabolic images. Magn Reson Mater Phy 34, 57–72 (2021). https://doi.org/10.1007/s10334-020-00903-y

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Keywords

  • Interpolation
  • Image processing
  • MRI
  • Spectroscopy