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An Inverse Problem Approach to Recovery of In Vivo Nanoparticle Concentrations from Thermal Image Monitoring of MR-Guided Laser Induced Thermal Therapy

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Abstract

Quantification of local variations in the optical properties of tumor tissue introduced by the presence of gold–silica nanoparticles (NP) presents significant opportunities in monitoring and control of NP-mediated laser induced thermal therapy (LITT) procedures. Finite element methods of inverse parameter recovery constrained by a Pennes bioheat transfer model were applied to estimate the optical parameters. Magnetic resonance temperature imaging (MRTI) acquired during a NP-mediated LITT of a canine transmissible venereal tumor in brain was used in the presented statistical inverse problem formulation. The maximum likelihood (ML) value of the optical parameters illustrated a marked change in the periphery of the tumor corresponding with the expected location of NP and area of selective heating observed on MRTI. Parameter recovery information became increasingly difficult to infer in distal regions of tissue where photon fluence had been significantly attenuated. Finite element temperature predictions using the ML parameter values obtained from the solution of the inverse problem are able to reproduce the NP selective heating within 5 °C of measured MRTI estimations along selected temperature profiles. Results indicate the ML solution found is able to sufficiently reproduce the selectivity of the NP mediated laser induced heating and therefore the ML solution is likely to return useful optical parameters within the region of significant laser fluence.

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Notes

  1. Given two probabilities \({\mathbb{P}_1}\) and \({\mathbb{P}_2}\) over \(\Upomega,\) the conjunction of these probabilities, denoted \({\mathbb{P}_1 \land \mathbb{P}_2}\) is defined as

    $$ {\mathbb{P}}_1({\mathcal{A}}) = 0 \hbox { or } {\mathbb{P}}_2({\mathcal{A}}) = 0 \Rightarrow ({\mathbb{P}}_1 \land {\mathbb{P}}_2)({\mathcal{A}}) = 0 \quad \forall {\mathcal{A}} \subset \Upomega $$

  2. Specifically, the bounded Newton trust region (-tao_method tao_tron) solver available in TAO6 was used.

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Acknowledgments

The research in this paper was supported in part through NIH grants 5T32CA119930-03, 1R21EB010196-01, CA016672 and resources provided by the Apache Corporation Foundation. Canine data was supported by National Science Foundation grant OII- 0548741. The authors would like to thank Jon Schwartz from Nanospectra Biosciences, Inc. (AuroShells®) and Ashok Gowda and Roger McNichols from BioTex, Inc. (Visualase system). The authors would also like to thank the ITK,33 Paraview,30 PETSc,2 libMesh,37 and CUBIT8 communities for providing enabling software for scientific computation and visualization. Computations were performed using allocations at the Texas Advanced Computing Center.

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Authors and Affiliations

  1. Department of Imaging Physics, The University of Texas M.D. Anderson Cancer Center, Houston, TX, 77030, USA

    D. Fuentes, A. Elliott, J. D. Hazle & R. J. Stafford

  2. Department of Neurosurgery, The University of Texas M.D. Anderson Cancer Center, Houston, TX, 77030, USA

    J. S. Weinberg

  3. BioTex, Inc., Houston, TX, 77054, USA

    A. Shetty

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  1. D. Fuentes
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Correspondence to D. Fuentes.

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Associate Editor James Tunnell oversaw the review of this article.

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Fuentes, D., Elliott, A., Weinberg, J.S. et al. An Inverse Problem Approach to Recovery of In Vivo Nanoparticle Concentrations from Thermal Image Monitoring of MR-Guided Laser Induced Thermal Therapy. Ann Biomed Eng 41, 100–111 (2013). https://doi.org/10.1007/s10439-012-0638-9

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