An Inverse Problems Approach to MR-EPT Image Reconstruction

Borsic, Andrea; Perreard, Irina; Mahara, Aditya; Halter, Ryan J.

doi:10.1109/tmi.2015.2466082

Cited by 32 publications

(42 citation statements)

References 19 publications

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“…These derivative‐based methods can be classified as “direct methods,” because they aim to reconstruct tissue EPs directly from the measured

{normalB}_{1}^{+}

field. To circumvent derivative operations on noisy measured

{normalB}_{1}^{+}

data, different approaches have been recently proposed . In these approaches, based on an integral formulation, the reconstruction problem has been reformulated into an inverse fashion (i.e., they fit a model of the EPs distribution to the measured

{normalB}_{1}^{+}

field using iterative minimization methods) therefore avoiding derivative operations.…”

Section: Discussionmentioning

confidence: 99%

Error analysis of helmholtz‐based MR‐electrical properties tomography

Mandija

Sbrizzi

Katscher

et al. 2017

Magnetic Resonance in Med

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“…These derivative‐based methods can be classified as “direct methods,” because they aim to reconstruct tissue EPs directly from the measured

{normalB}_{1}^{+}

field. To circumvent derivative operations on noisy measured

{normalB}_{1}^{+}

{normalB}_{1}^{+}

field using iterative minimization methods) therefore avoiding derivative operations.…”

Section: Discussionmentioning

confidence: 99%

Error analysis of helmholtz‐based MR‐electrical properties tomography

Mandija

Sbrizzi

Katscher

et al. 2017

Magnetic Resonance in Med

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“…In this manuscript we present a novel MR-EPT reconstruction algorithm resulting from further development and enhancement of initial work developed by the authors [14], [15]. The algorithm is based on an inverse approach applied to (2).…”

Section: Agnetic Resonance-electrical Prop-erties Tomography (Mr-ept)mentioning

confidence: 99%

“…Elements of corresponding to the domain boundary are defined using mirroring boundary conditions. Specifically, if the term in (13a) falls outside the domain, is assumed equal to and the second derivative for that image location is expressed as: (15) Similar conditions are used for derivatives in and .…”

Section: A Quadratic Regularizationmentioning

confidence: 99%

Magnetic Resonance-Based Electrical Property Tomography (MR-EPT) for Prostate Cancer Grade Imaging

College¹

2016

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for Public Release; Distribution Unlimited SUPPLEMENTARY NOTES ABSTRACTDetermining whether a man recently diagnosed with prostate cancer has aggressive disease requiring immediately radical therapy or indolent disease requiring a more passive watchful waiting or active surveillance approach is a current clinical challenge. This technology development study is focused on developing Magnetic Resonance -Electrical Property Tomography (MR-EPT) specifically for prostate imaging. MR-EPT is an imaging modality that may enable clinicians to image the electrical properties of prostate at near MR resolution. These electrical properties are hypothesized to provide sufficient contrast for distinguishing between aggressive and indolent prostate cancer. Much of the third year of this program has focused on additional MR-EPT image reconstruction algorithm development and optimization, experimental imaging of both simplistic and anatomically accurate phantoms, continued recruitment for ex vivo and in vivo prostate imaging, and statistical analysis of ex vivo prostate data. During this year we have demonstrated additional imaging capabilities of MR-EPT through phantom studies, have recruited and imaged the majority of our proposed ex vivo cohort of prostates, and continued recruitment for the in vivo imaging phase of this program. The no-cost-extension 6 months of the program will primarily focus on completing our in vivo data acquisition, statistical analysis of our data, and preparation of publications and proposals for follow-on more clinically focused studies. INTRODUCTIONThis program builds off of our extensive experience in using electrical properties of prostate to distinguish malignant from benign tissues [1][2][3][4][5] and specifically stems from exciting new data published in The Prostate [6] in which we demonstrated significant electrical property differences...

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“…The first approach is to solve the PDE using an iterative optimization calculation [18]- [21]. In these iterative methods, it is important to give the optimal initial value, without which a local minimum solution can be obtained.…”

Section: Introductionmentioning

confidence: 99%

A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

Fushimi

Nara

2017

SICE Journal of Control, Measurement, and System Integration

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: The electrical properties (EPs) of biological tissue, consisting of conductivity and permittivity, provide useful information for the diagnosis of malignant tissues and the evaluation of heat absorption rates. Recently, magnetic resonance electrical properties tomography (MREPT), by which EPs are reconstructed from internal magnetic field data measured by using magnetic resonance imaging (MRI), has been actively studied. We previously proposed an explicit pointwise reconstruction method for MREPT based on a complex partial differential equation (PDE), known as the D-bar equation, of the electric field and its explicit solution given by an integral formula. In this method, as in some other conventional methods, EP values on the boundary of the region of interest must be given as a Dirichlet boundary condition of the PDE. However, it is difficult to know these values precisely in practical situations. Therefore, in this paper, we propose a novel method for reconstructing EPs in a circular region without any knowledge of boundary EP values. Starting from the integral solution to solve the D-bar equation in a circular region with the Neumann boundary condition, we show that the contour integral term of the integral formula is eliminated by using Faraday's law and solve the PDE based only on magnetic field data measured by using MRI. Numerical simulations show that the proposed method yields a good reconstruction results without any knowledge of boundary EP values.

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An Inverse Problems Approach to MR-EPT Image Reconstruction

Cited by 32 publications

References 19 publications

Error analysis of helmholtz‐based MR‐electrical properties tomography

Error analysis of helmholtz‐based MR‐electrical properties tomography

Magnetic Resonance-Based Electrical Property Tomography (MR-EPT) for Prostate Cancer Grade Imaging

A Boundary-Value-Free Reconstruction Method for Magnetic Resonance Electrical Properties Tomography Based on the Neumann-Type Integral Formula over a Circular Region

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