Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project

Journal article

Background: Breast-conserving surgery is the most acceptable option for breast cancer removal from an invasive and psychological point of view. During the surgical procedure, the imaging acquisition using Magnetic Image Resonance is performed in the prone configuration, while the surgery is achieved in the supine stance. Thus, a considerable movement of the breast between the two poses drives the tumor to move, complicating the surgeon's task. Therefore, to keep track of the lesion, the surgeon employs ultrasound imaging to mark the tumor with a metallic harpoon or radioactive tags. This procedure, in addition to an invasive characteristic, is a supplemental source of uncertainty. Consequently, developing a numerical method to predict the tumor movement between the imaging and intra-operative configuration is of significant interest. Methods: In this work, a simulation pipeline allowing the prediction of patient-specific breast tumor movement was put forward, including personalized preoperative surgical drawings. Through image segmentation, a subject-specific finite element biomechanical model is obtained. By first computing an undeformed state of the breast (equivalent to a nullified gravity), the estimated intra-operative configuration is then evaluated using our developed registration methods. Finally, the model is calibrated using a surface acquisition in the intra-operative stance to minimize the prediction error. Findings: The capabilities of our breast biomechanical model to reproduce real breast deformations were evaluated. To this extent, the estimated geometry of the supine breast configuration was computed using a corotational elastic material model formulation. The subject-specific mechanical properties of the breast and skin were assessed, to get the best estimates of the prone configuration. The final results are a Mean Absolute Error of 4.00 mm for the mechanical parameters E_breast = 0.32 kPa and E_skin = 22.72 kPa. The optimized mechanical parameters are congruent with the recent state-of-the-art. The simulation (including finding the undeformed and prone configuration) takes less than 20 s. The Covariance Matrix Adaptation Evolution Strategy optimizer converges on average between 15 to 100 iterations depending on the initial parameters for a total time comprised between 5 to 30 min. To our knowledge, our model offers one of the best compromises between accuracy and speed. The model could be effortlessly enriched through our recent work to facilitate the use of complex material models by only describing the strain density energy function of the material. In a second study, we developed a second breast model aiming at mapping a generic model embedding breast-conserving surgical drawing to any patient. We demonstrated the clinical applications of such a model in a real-case scenario, offering a relevant education tool for an inexperienced surgeon

Authors: Mazier, A; Bilger, A; Forte, AE; Peterlik, I; Hale, JS

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Engineering with Computers
• Volume: 38
• Issue: 5
• Pages: 4099-4113
• Publication date: 2022-02-18
• DOI: 10.1007/s00366-021-01597-z
• EISSN: 1435-5663
• ISSN: 0177-0667
• Language: English
• Keywords: Structural engineering; Geometry; Jacobian matrix and determinant; Engineering; Mathematics; Deformation (meteorology); Finite element method; Computer science; Inverse problem; Inverse; Physics; Applied mathematics; Geology; Mathematical analysis; Hyperelastic material; Elasticity (physics); Mathematical optimization