Soft tissue deformation tracking by means of an optimized fiducial marker layout with application to cancer tumors

  • Ye Han
  • Yoed Rabin
  • Levent Burak KaraEmail author
Original Article



Interventional radiology methods have been adopted for intraoperative control of the surgical region of interest (ROI) in a wide range of minimally invasive procedures. One major obstacle that hinders the success of procedures using interventional radiology methods is the preoperative and intraoperative deformation of the ROI. While fiducial markers (FM) tracing has been shown to be promising in tracking such deformations, determining the optimal placement of the FM in the ROI remains a significant challenge. The current study proposes a computational framework to address this problem by preoperatively optimizing the layout of FM, thereby enabling an accurate tracking of the ROI deformations.


The proposed approach includes three main components: (1) creation of virtual deformation benchmarks, (2) method of predicting intraoperative tissue deformation based on FM registration, and (3) FM layout optimization. To account for the large variety of potential ROI deformations, virtual benchmarks are created by applying a multitude of random force fields on the tumor surface in physically based simulations. The ROI deformation prediction is carried out by solving the inverse problem of finding the smoothest force field that leads to the observed FM displacements. Based on this formulation, a simulated annealing approach is employed to optimize the FM layout that produces the best prediction accuracy.


The proposed approach is capable of finding an FM layout that outperforms the rationally chosen layouts by 40% in terms of ROI prediction accuracy. For a maximum induced displacement of 20 mm on the tumor surface, the average maximum error between the benchmarks and our FM-optimized predictions is about 1.72 mm, which falls within the typical resolution of ultrasound imaging.


The proposed framework can optimize FM layout to effectively reduce the errors in the intraoperative deformation prediction process, thus bridging the gap between preoperative imaging and intraoperative tissue deformation.


Tumor deformation Shape reconstruction Fiducial markers Layout optimization Stochastic optimization Laplace–Beltrami operator 



Authors would like to thank Prof. Gal Shafirstein and Roswell Park Comprehensive Cancer Center for providing anatomical geometries from CT scanning.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© CARS 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA

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