An Optimal Control Problem for Elastic Registration and Force Estimation in Augmented Surgery

Mestdagh, Guillaume; Cotin, Stéphane

doi:10.1007/978-3-031-16449-1_8

Cited by 5 publications

(11 citation statements)

References 20 publications

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“…In this section, we present an organ registration result in the context of augmented surgery. This example, developed in our conference paper [29, Section 3.1], involves the Sparse Data Challenge 3 dataset. The dataset contains one tetrahedral mesh representing a silicone liver phantom in its initial configuration and 112 point clouds acquired from 112 deformed configurations of the same phantom [59,60].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Should this result extend to the linear elastic system, the existence of the solution would be guaranteed in any dimension for our problem. We refer to [52, ch. 4] for additional explanations.…”

Section: Analysis Of the Optimal Control Problemmentioning

confidence: 99%

“…The optimal control problem studied in this problem was already introduced in our conference paper [29], which includes numerical examples associated with the augmented surgery domain. Outside the augmented surgery domain, other approaches based on the physical causes of displacement involve an optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

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Organ registration from partial surface data in augmented surgery from an optimal control perspective

Cotin,

Mestdagh,

Privat

2024

Proc. R. Soc. A.

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We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal control, in an attempt to reconstruct a physically consistent surface load. The resulting optimization problem features an elastic model, a least-squares data attachment term based on orthogonal projections, and an admissible set of surface loads defined prior to reconstruction in the mechanical model. After a discussion about the existence of solutions, we analyse the necessary optimality conditions and use them to derive a suitable optimization algorithm. We implement an adjoint method and we test our approach on multiple examples, including the so-called Sparse Data Challenge . We obtain very promising results, that illustrate the feasibility of our approach with linear and nonlinear models.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Analysis Of the Optimal Control Problemmentioning

confidence: 99%

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Organ registration from partial surface data in augmented surgery from an optimal control perspective

Cotin,

Mestdagh,

Privat

2024

Proc. R. Soc. A.

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“…The seventh registration strategy is a biomechanical method using a linear elastic finite element model within an adjoint optimization scheme that solves for boundary forces on the posterior surface of the liver mesh [10]. This method iteratively minimizes the least squares objective function:…”

Section: Biomechanical Methods 2: Adjoint Boundary Reconstruction (Me...mentioning

confidence: 99%

“…(5) A deep learning method based on probabilistic shape occupancy maps (Jia 2021) [7]. (6) A biomechanical finite element method based on linearized iterative boundary condition reconstruction (Heiselman 2020) [8,9] (7) A biomechanical finite element method based on adjoint boundary condition reconstruction (Mestdagh 2022) [10].…”

Section: Registration Comparatorsmentioning

confidence: 99%

Comparison study of sparse data-driven soft tissue registration: preliminary results from the image-to-physical liver registration sparse data challenge

Heiselman

Collins

Ringel

et al. 2023

Medical Imaging 2023: Image-Guided Procedures, Robotic Interventions, and Modeling

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The ability to accurately account for intraoperative soft tissue deformations has been a longstanding barrier to efficacious translation of image-guided frameworks into abdominal interventions. In surgical applications, few data acquisition systems are amenable to stringent operative workflow constraints, and many are too costly for widespread adoption. Consequently, computational methods for surgical guidance based on sparse data obtained over the organ surface have become prevalent within approaches for image-to-patient alignment of soft tissue. However, the sparse data environment presents an especially challenging algorithmic landscape for accurately inferring deformable anatomical alignments between preoperative and intraoperative organ states from incomplete information sources. This work, presented as a preliminary conclusion to the image-to-physical liver registration sparse data challenge introduced at SPIE Medical Imaging 2019, seeks to characterize the potential for sparse data registration algorithms to achieve high fidelity predictions of intraoperative organ deformations from sparse descriptors of organ surface shape. A total of seven rigid and nonrigid biomechanical and deep learning registration techniques are compared, and the findings suggest that the family of biomechanically simulated boundary condition reconstruction techniques offers a promising opportunity for accurately estimating intraoperative organ deformation states from sparse intraoperative point clouds. Over a common dataset of 112 registration scenarios, this family of deformable registration techniques was found to outperform globally optimal rigid registrations, was robust to varying degrees of surface data coverage, and maintained good performance under added sources of measurement noise. Further analysis investigates error correlations among methods to illuminate sparse data performance within state-of-the-art image-to-physical registration algorithms.

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Real-Time Elastic Partial Shape Matching Using a Neural Network-Based Adjoint Method

Odot

Mestdagh

Privat

et al. 2023

Communications in Computer and Information Science

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An Optimal Control Problem for Elastic Registration and Force Estimation in Augmented Surgery

Cited by 5 publications

References 20 publications

Organ registration from partial surface data in augmented surgery from an optimal control perspective

Organ registration from partial surface data in augmented surgery from an optimal control perspective

Comparison study of sparse data-driven soft tissue registration: preliminary results from the image-to-physical liver registration sparse data challenge

Real-Time Elastic Partial Shape Matching Using a Neural Network-Based Adjoint Method

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