Computer-assisted needle trajectory planning and mathematical modeling for liver tumor thermal ablation: A review

Rui Zhang; Shuicai Wu; Weiwei Wu; Hongjian Gao; Zhuhuang Zhou; Rui Zhang; Shuicai Wu; Weiwei Wu; Hongjian Gao; Zhuhuang Zhou

doi:10.3934/mbe.2019244

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4846-4872. doi: 10.3934/mbe.2019244

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Computer-assisted needle trajectory planning and mathematical modeling for liver tumor thermal ablation: A review

1.
College of Life Science and Bioengineering, Beijing University of Technology, Beijing 100124, China
2.
College of Biomedical Engineering, Capital Medical University, Beijing 100069, China

Received: 12 April 2019 Accepted: 15 May 2019 Published: 29 May 2019

Radiofrequency ablation (RFA) and microwave ablation (MWA) have become an important means for treating liver tumors. RFA and MWA are a minimally invasive therapy which involves an ablation applicator or needle (i.e., radiofrequency electrode or microwave antenna) inserted percutaneously into a tumor under the guidance of medical imaging, so as to destroy the tumor in situ by heating-induced coagulation necrosis. Treatment planning, particularly needle trajectory planning, is crucial to RFA and MWA. In clinical procedures, however, needle trajectory planning still relies on the personal experience of clinicians. Manual needle trajectory planning is tedious and may cause inter-operator difference. Therefore, computer-assisted needle trajectory planning techniques are of clinical value and have been extensively explored. However, a literature review that focuses on computer-assisted needle trajectory planning for liver tumor RFA and MWA has not been reported. In this paper, we conducted an extensive review on computer-assisted needle trajectory planning for RFA and MWA of liver tumors. Fundamentals of needle trajectory planning are summarized. Algorithms for single-needle and multi-needle trajectory planning are analyzed. Shortcomings of current computer-assisted needle trajectory planning algorithms are discussed and future developments are suggested.
- liver tumor,
- radiofrequency ablation,
- microwave ablation,
- needle trajectory planning,
- optimization problem
Citation: Rui Zhang, Shuicai Wu, Weiwei Wu, Hongjian Gao, Zhuhuang Zhou. Computer-assisted needle trajectory planning and mathematical modeling for liver tumor thermal ablation: A review[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4846-4872. doi: 10.3934/mbe.2019244

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Abstract

Radiofrequency ablation (RFA) and microwave ablation (MWA) have become an important means for treating liver tumors. RFA and MWA are a minimally invasive therapy which involves an ablation applicator or needle (i.e., radiofrequency electrode or microwave antenna) inserted percutaneously into a tumor under the guidance of medical imaging, so as to destroy the tumor in situ by heating-induced coagulation necrosis. Treatment planning, particularly needle trajectory planning, is crucial to RFA and MWA. In clinical procedures, however, needle trajectory planning still relies on the personal experience of clinicians. Manual needle trajectory planning is tedious and may cause inter-operator difference. Therefore, computer-assisted needle trajectory planning techniques are of clinical value and have been extensively explored. However, a literature review that focuses on computer-assisted needle trajectory planning for liver tumor RFA and MWA has not been reported. In this paper, we conducted an extensive review on computer-assisted needle trajectory planning for RFA and MWA of liver tumors. Fundamentals of needle trajectory planning are summarized. Algorithms for single-needle and multi-needle trajectory planning are analyzed. Shortcomings of current computer-assisted needle trajectory planning algorithms are discussed and future developments are suggested.

References

[1]	R. L. Siegel, K. D. Miller and A. Jemal, Cancer statistics, 2019, CA Cancer J. Clin., 69 (2019), 7–34.
[2]	L. S. Poulou, E. Botsa and I. Thanou, et al., Percutaneous microwave ablation vs radiofrequency ablation in the treatment of hepatocellular carcinoma, World J. Hepatol., 7 (2015), 1054–1063.
[3]	K. A. Cronin, A. J. Lake and S. Scott, et al., Annual report to the nation on the status of cancer, part I: National cancer statistics, Cancer, 124 (2018), 2785–2800.
[4]	J. Tejeda-Maldonado, I. García-Juárez and J. Aguirre-Valadez, et al., Diagnosis and treatment of hepatocellular carcinoma: An update, World J. Hepatol., 7 (2015), 362–376.
[5]	N. Bhardwaj, A. D. Strickland and F. Ahmad, et al., A comparative histological evaluation of the ablations produced by microwave, cryotherapy and radiofrequency in the liver, Pathology, 41 (2009), 168–172.
[6]	C. Schumann, Visualization and heuristic modeling for planning of minimally-and non-invasive tissue ablation, Ph.D.Dissertation, Jacobs University Bremen, Bremen, Germany, (2017).
[7]	M. W. Lee, S. S. Raman and N. H. Asvadi, et al., Radiofrequency ablation of hepatocellular carcinoma as bridge therapy to liver transplantation: A 10-year intention-to-treat analysis, Hepatology, 65 (2017), 1979–1990.
[8]	M. Ahmed, L. Solbiati and C. L. Brace, et al., Image-guided tumor ablation: standardization of terminology and reporting criteria-a 10-year update, Radiology, 273 (2014), 241–260.
[9]	W. Wu, Z. Zhou and S. Wu, et al., Automatic liver segmentation on volumetric CT images using supervoxel-based graph cuts, Comput. Math. Methods Med., 2016 (2016), 9093721.
[10]	W. Wu, S. Wu and Z Zhou, et al., 3D liver tumor segmentation in CT images using improved fuzzy C-means and graph cuts, BioMed. Res. Int., 2017 (2017), 5207685.
[11]	R. Zhang, Z. Zhou and W. Wu, et al., An improved fuzzy connectedness method for automatic three-dimensional liver vessel segmentation in CT images, J. Healthc. Eng., 2018 (2018), 2376317.
[12]	K. F. Chu and D. E. Dupuy, Thermal ablation of tumours: biological mechanisms and advances in therapy, Nat. Rev. Cancer, 14 (2014), 199–208.
[13]	M. Mendiratta-Lala, O. R. Brook and B. D. Midkiff, et al., Quality initiatives: strategies for anticipating and reducing complications and treatment failures in hepatic radiofrequency ablation, Radiographics, 30 (2010), 1107–1122.
[14]	A. Z. Fonseca, S. Santin and L. G. L. Gomes, et al., Complications of radiofrequency ablation of hepatic tumors: Frequency and risk factors, World J. Hepatol., 6 (2014), 107–113.
[15]	S. N. Goldberg, C. J. Grassi and J. F. Cardella, et al., Image-guided tumor ablation: standardization of terminology and reporting criteria, Radiology, 235 (2005), 728–739.
[16]	Schumann C, Rieder C and Preusser T, et al., State of the art in computer-assisted planning, intervention, and assessment of liver-tumor ablation, Crit. Rev. Biomed. Eng., 38 (2010), 31–52.
[17]	C. Schumann, J. Bieberstein and C. Trumm, et al., Fast automatic path proposal computation for hepatic needle placement, Medical Imaging 2010: Visualization, Image-Guided Procedures, and Modeling, (2010), 76251J.
[18]	C. Baegert, C. Villard and P. Schreck, et al., Multi-criteria trajectory planning for hepatic radiofrequency ablation, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2007), 676–684.
[19]	C. Baegert, C. Villard and P. Schreck, et al., Precise determination of regions of interest for hepatic RFA planning, Medical Imaging 2007: Visualization and Image-Guided Procedures, (2007), 650923.
[20]	A. Seitel, M. Engel and C. M. Sommer, et al., Computer-assisted trajectory planning for percutaneous needle insertions, Med. Phys., 38 (2011), 3246–3259.
[21]	J. Nocedal, and S. Wright, Numerical optimization, 2nd edition, New York: Springer, (2006), 29–32.
[22]	E. Triantaphyllou, B. Shu and S. N. Sanchez, et al., Multi-criteria decision making: an operations research approach, Encyclopedia of Electrical and Electronics Engineering, 15 (1998), 175–186.
[23]	A. L. Jaimes, S. Z. Martınez and C. A. C. Coello, An introduction to multiobjective optimization techniques, Optim. Polymer Processing, (2009), 29–57.
[24]	R. T. Marler and J. S. Arora, Survey of multi-objective optimization methods for engineering, Struct. Multidiscipl. Optim., 26 (2004), 369–395.
[25]	M. J. D. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Comput. J., 7 (1964), 155–162.
[26]	J. A. Nelder and R. Mead, A simplex method for function minimization, Comput. J., 7 (1965), 308–313.
[27]	A. Khachaturyan, S. Semenovsovskaya and B. Vainshtein, The thermodynamic approach to the structure analysis of crystals, Acta Crystallogr. A, 37 (1981), 742–754.
[28]	C. Villard, L. Soler and N. Papier, et al., RF-Sim: a treatment planning tool for radiofrequency ablation of hepatic tumors, Seventh International Conference on Information Visualization, (2003), 561–566.
[29]	C. Villard, C. Baegert and P. Schreck, et al., Optimal trajectories computation within regions of interest for hepatic RFA planning, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2005), 49–56.
[30]	C. Baegert, C. Villard and P. Schreck, et al., Trajectory optimization for the planning of percutaneous radiofrequency ablation of hepatic tumors, Comput. Aided Surg., 12 (2007), 82–90.
[31]	D. Craft, Multi-criteria optimization methods in radiation therapy planning: a review of technologies and directions, arXiv preprint arXiv:1305.1546, (2013).
[32]	N. Hamzé, J. Voirin and P. Collet, et al., Pareto front vs. weighted sum for automatic trajectory planning of deep brain stimulation, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2016), 534–541.
[33]	W. Stadler, A survey of multicriteria optimization or the vector maximum problem, part I: 1776–1960, J. Optim. Theory Appl., 29 (1979), 1–52.
[34]	O. Castillo, L. Trujillo and P. Melin, Multiple objective genetic algorithms for path-planning optimization in autonomous mobile robots, Soft Comput., 11 (2007), 269–279.
[35]	K. Teichert, A hyperboxing Pareto approximation method applied to radiofrequency ablation treatment planning, Fraunhofer-Verlag, (2014).
[36]	C. Schumann, J. Bieberstein and C. Trumm, et al., Fast automatic path proposal computation for hepatic needle placement, Medical Imaging 2010: Visualization, Image-Guided Procedures, and Modeling, (2010), 76251J.
[37]	J. P. Snyder, Album of Map Projections, United States Geological Survey Professional Paper, United States Government Printing Office, (1989), 1453.
[38]	J. P. Snyder, Map projections--A working manual, US Government Printing Office, (1987).
[39]	C. Schumann, J. Bieberstein and S. Braunewell, et al., Visualization support for the planning of hepatic needle placement, Int. J. Comput. Assist. Radiol. Surg., 7 (2012), 191–197.
[40]	N. Greene, Environment mapping and other applications of world projections, IEEE Comput. Graph. Appl., 6 (1986), 21–29.
[41]	R. Khlebnikov, B. Kainz and J. Muehl, et al., Crepuscular rays for tumor accessibility planning, IEEE Trans. Vis. Comput. Gr., 17 (2011), 2163–2172.
[42]	C. Schumann, C. Rieder and S. Haase, et al., Interactive access path exploration for planning of needle-based interventions, Roboter-Assistenten Werden Sensitiv., (2013), 103–106.
[43]	B. Laugwitz, T. Held and M. Schrepp, Construction and evaluation of a user experience questionnaire, Symposium of the Austrian HCI and Usability Engineering Group, (2008), 63–76.
[44]	C. Schumann, C. Rieder and S. Haase, et al., Interactive multi-criteria planning for radiofrequency ablation, Int. J. Comput. Assist. Radiol. Surg., 10 (2015), 879–889.
[45]	A. Helck, C. Schumann and J. Aumann, et al., Automatic path proposal computation for CT-guided percutaneous liver biopsy, Int. J. Comput. Assist. Radiol. Surg., 11 (2016), 2199–2205.
[46]	S. Liu, J. Liu and J. Xu, et al., Preoperative surgical planning for robot-assisted liver tumour ablation therapy based on collision-free reachable workspaces, Int. J. Robot. Autom., 32 (2017).
[47]	L. Mundeleer, D. Wikler and T. Leloup, et al., Computer-assisted needle positioning for liver tumour radiofrequency ablation (RFA), Int. J. Med. Robot., 5 (2009), 458–464.
[48]	C. Villard, L. Soler and A. Gangi, Radiofrequency ablation of hepatic tumors: simulation, planning, and contribution of virtual reality and haptics, Comput. Methods Biomech. Biomed. Eng., 8 (2005), 215–227.
[49]	T. Livraghi, S. N. Goldberg and S. Lazzaroni, et al., Hepatocellular carcinoma: radio-frequency ablation of medium and large lesions, Radiology, 214 (2000), 761–768.
[50]	L. Crocetti, T. De Baere and R. Lencioni, Quality improvement guidelines for radiofrequency ablation of liver tumours, Cardiovasc. Intervent. Radiol., 33 (2010), 11–17.
[51]	S. K. Y. Chang, W. W. Hlaing and L. Yang, et al., Current technology in navigation and robotics for liver tumours ablation, Ann. Acad. Med. Singapore, 40 (2011), 231–236.
[52]	H. Ren, K. Wu and X. Kang, Surgical navigation and planning with minimum radiation in orthopaedic interventions, Orthop. Proc., 95 (2013), 53.
[53]	N. Toshikuni, Y. Takuma and T. Goto, et al., Prognostic factors in hepatitis C patients with a single small hepatocellular carcinoma after radiofrequency ablation, Hepatogastroenterology, 59 (2012), 2361–2366.
[54]	T. Butz, S. K. Warfield and K. Tuncali, et al., Pre-and intra-operative planning and simulation of percutaneous tumor ablation, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2000), 317–326.
[55]	G. D. Dodd III, M. S. Frank and M. Aribandi, et al., Radiofrequency thermal ablation: computer analysis of the size of the thermal injury created by overlapping ablations, AJR Am. J. Roentgenol., 177 (2001), 777–782.
[56]	Y. S. Khajanchee, D. Streeter and L. L. Swanstrom, et al., A mathematical model for preoperative planning of radiofrequency ablation of hepatic tumors, Surg. Endosc., 18 (2004), 696–701.
[57]	M. H. Chen, W. Yang and K. Yan, et al., Large liver tumors: protocol for radiofrequency ablation and its clinical application in 110 patients-mathematic model, overlapping mode, and electrode placement process, Radiology, 232 (2004), 260–271.
[58]	A. Meijster, J. B. T. M. Roerdink and W. H. Hesselink, A general algorithm for computing distance transforms in linear time, In: Goutsias J., Vincent L., Bloomberg D.S. (eds), Mathematical Morphology and Its Applications to Image and Signal Processing, Boston: Springer, (2002), 331–340.
[59]	K. Trovato, S. Dalal and J. Krücker, et al., Automated RFA planning for complete coverage of large tumors, Medical Imaging 2009: Visualization, Image-Guided Procedures, and Modeling, (2009), 72610D.
[60]	L. Yang, R. Wen and J. Qin, et al., A robotic system for overlapping radiofrequency ablation in large tumor treatment, IEEE/ASME Trans. Mech., 15 (2010), 887–897.
[61]	B. Duan, R. Wen and C. B. Chng, et al., Image-guided robotic system for radiofrequency ablation of large liver tumor with single incision, 2015 12th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), (2015), 284–289.
[62]	P. Liu, J. Qin and B. Duan, et al., Overlapping radiofrequency ablation planning and robot-assisted needle insertion for large liver tumors, Int. J. Med. Robot., 15 (2019), e1952.
[63]	P. G. Bolhuis, D. Frenkel and S. C. Mau, et al., Entropy difference between crystal phases, Nature, 388 (1997), 235–236.
[64]	S. X. Liu, S. Dalal and J. Kruecker, Automated microwave ablation therapy planning with single and multiple entry points, Medical Imaging 2012: Image-Guided Procedures, Robotic Interventions, and Modeling, (2012), 831635.
[65]	R. H. Byrd, P. Lu and J. Nocedal, et al., A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput., 16 (1995), 1190–1208.
[66]	C. Zhu, R. H. Byrd and P. Lu, et al., Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM T. Math. Software, 23 (1997), 550–560.
[67]	K. F. Wang, W. Pan and F. Wang, et al., Geometric optimization of a mathematical model of radiofrequency ablation in hepatic carcinoma, Asian Pac. J. Cancer Prev., 14 (2013), 6151–6158.
[68]	H. Ren, E. Campos-Nanez and Z, Yaniv, et al., Treatment planning and image guidance for radiofrequency ablation of large tumors, IEEE J. Biomed. Health Inform., 18 (2014), 920–928.
[69]	Z. Yaniv, P. Cheng and E. Wilson, et al., Needle-based interventions with the image-guided surgery toolkit (IGSTK): From phantoms to clinical trials, IEEE Trans. Biomed. Eng., 57 (2010), 922–933.
[70]	H. Zhang, F. Banovac and S. Munuo, et al., Treatment planning and image guidance for radiofrequency ablation of liver tumors, Medical Imaging 2007: Visualization and Image-Guided Procedures, (2007), 650922.
[71]	H. Ren, W. Guo and S. S. Ge, et al., Coverage planning in computer-assisted ablation based on genetic algorithm, Comput. Biol. Med., 49 (2014), 36–45.
[72]	R. Chen, F. Lu and K. Wang, et al., Semiautomatic radiofrequency ablation planning based on constrained clustering process for hepatic tumors, IEEE Trans. Biomed. Eng., 65 (2018), 645–657.
[73]	H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., 1 (1948), 93–122.
[74]	C. Cattaneo, Surune forme de l'equation de la chaleur eliminant la paradoxe d'une propagation instantantee, Compt. Rendu., 247 (1958), 431–433.
[75]	P. Vernotte, Les paradoxes de la theorie continue de l'equation de la chaleur, Compt. Rendu, 246 (1958), 3154–3155.
[76]	J. A. L. Molina, M. J. Rivera and M. Trujillo, et al., Effect of the thermal wave in radiofrequency ablation modeling: an analytical study, Phys. Med. Biol., 53 (2008), 1447.
[77]	P. Liang, B. Dong and X. Yu, et al., Computer-assisted dynamic simulation of microwave-induced thermal distribution in coagulation of liver cancer, IEEE Trans. Biomed. Eng., 48 (2001), 821–829.
[78]	W. Zhai, J, Xu and Y, Zhao, et al., Preoperative surgery planning for percutaneous hepatic microwave ablation, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2008), 569–577.
[79]	Q. Nan, X. M. Guo and F. Zhai, The contrast of two kinds of microwave antenna SAR simulation, Appl. Mech. Mat., 553 (2014), 379–383.
[80]	F. Hübner, R. Schreiner and C. Reimann, et al., Ex vivo validation of microwave thermal ablation simulation using different flow coefficients in the porcine liver, Med. Eng. Phys., 66 (2019), 56–64.
[81]	J. Chiang, K. Hynes and C. L. Brace, Flow-dependent vascular heat transfer during microwave thermal ablation. 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (2012), 5582–5585.
[82]	U. Zurbuchen, C. Holmer and K. S. Lehmann, et al., Determination of the temperature-dependent electric conductivity of liver tissue ex vivo and in vivo: Importance for therapy planning for the radiofrequency ablation of liver tumours, Int. J. Hyperthermia, 26 (2010), 26–33.
[83]	J. A. López-Molina, M. J. Rivera and M. Trujillo, et al., Assessment of hyperbolic heat transfer equation in theoretical modeling for radiofrequency heating techniques, Open Biomed. Eng. J., 2 (2008), 22–27.
[84]	M. Zhang, Z. Zhou and S. Wu, et al., Simulation of temperature field for temperature-controlled radio frequency ablation using a hyperbolic bioheat equation and temperature-varied voltage calibration: a liver-mimicking phantom study, Phys. Med. Biol., 60 (2015), 9455–9471.
[85]	R. Chen, F. Lu and F. Wu, et al., An analytical solution for temperature distributions in hepatic radiofrequency ablation incorporating the heat-sink effect of large vessels, Phys. Med. Biol., 63 (2018), 235026.
[86]	E. H. Ooi, K. W. Lee and S. Yap, et al., The effects of electrical and thermal boundary condition on the simulation of radiofrequency ablation of liver cancer for tumours located near to the liver boundary, Comput. Biol. Med., 106 (2019), 12–23.
[87]	C. Rieder, T. Kroeger and C. Schumann, et al., GPU-based real-time approximation of the ablation zone for radiofrequency ablation, IEEE Trans. Vis. Comput. Gr., 17 (2011), 1812–1821.
[88]	C. Schumann, C. Rieder and J. Bieberstein, et al., State of the art in computer-assisted planning, intervention, and assessment of liver-tumor ablation, Crit. Rev. Biomed. Eng., 38 (2010), 31–52.
[89]	P. Mariappan, P. Weir and R. Flanagan, et al., GPU-based RFA simulation for minimally invasive cancer treatment of liver tumours, Int. J. Comput. Assist. Radiol. Surg., 12 (2017), 59–68.
[90]	D. R. Di, Z. Z. He and Z. Q. Sun, et al., A new nano-cryosurgical modality for tumor treatment using biodegradable MgO nanoparticles, Nanomedicine., 8 (2012), 1233–1241.
[91]	Q. Wang, Z. S. Deng and J, Liu, Theoretical evaluations of magnetic nanoparticle-enhanced heating on tumor embedded with large blood vessels during hyperthermia, J. Nanopart. Res., 14 (2012), 974–984.
[92]	Z. Q. Sun, Y. Yang and J. Liu, In vivo experiments and numerical investigations on nanocryosurgical freezing of target tissues with large blood vessels, J. Biomed. Nanotechnol., 8 (2012), 10–18.
[93]	N. Hamzé, I. Peterlík and S. Cotin, et al., Preoperative trajectory planning for percutaneous procedures in deformable environments, Comput. Med. Imaging Graph., 47 (2016), 16–28.
[94]	X. Tan, P. Yu and K. B. Lim, et al., Robust needle trajectory planning for flexible needle insertion using Markov decision processes, Int. J. Comput. Assist. Radiol. Surg., 13 (2018), 1439–1451.
[95]	P. Li, Z. Yang and S. Jiang, Needle-tissue interactive mechanism and steering control in image-guided robot-assisted minimally invasive surgery: a review, Med. Biol. Eng. Comput., 56 (2018), 931–949.
[96]	H. M. Luu, W. Niessen and T. V. Walsum, et al., An automatic registration method for pre-and post-interventional CT images for assessing treatment success in liver RFA treatment, Med. Phys., 42 (2015), 5559–5567.
[97]	W. H. Greene, S. Chelikani and K. Purushothaman, et al., Constrained non-rigid registration for use in image-guided adaptive radiotherapy, Med. Image Anal., 13 (2009), 809–817.
[98]	J. Zhang, M. Ding and F. Meng, et al., Respiratory motion correction in free-breathing ultrasound image sequence for quantification of hepatic perfusion, Med. Phys., 38 (2011), 4737–4748.
[99]	T. P. O'shea, J. C. Bamber and E. J. Harris, Temporal regularization of ultrasound-based liver motion estimation for image-guided radiation therapy, Med Phys, 43 (2016), 455–464.
[100]	Y. H. Noorda, L. W. Bartels and M. A. Viergever, et al., Subject-specific four-dimensional liver motion modeling based on registration of dynamic MRI, J. Med. Imaging, 3 (2016), 015002.
[101]	A. Mastmeyer, M. Wilms and H. Handels, Population-based respiratory 4D motion atlas construction and its application for VR simulations of liver punctures, Medical Imaging 2018: Image Processing, (2018), 1057417.
[102]	N. Mohammed, S. Currie and M. Glegg, et al., Analysis of heart substructures motion and changes using 4DCT dataset and heart atlas in lung cancer patients, Int. J. Radiat. Oncol. Biol. Phys., 102 (2018), e557.
[103]	M. Abayazid, T. Kato and S. G. Silverman, et al., Using needle orientation sensing as surrogate signal for respiratory motion estimation in percutaneous interventions, Int. J. Comput. Assist. Radiol. Surg., 13 (2018), 125–133.
[104]	J. Borgert, S. Krüger and H. Timinger, et al., Respiratory motion compensation with tracked internal and external sensors during CT-guided procedures, Comput. Aided Surg., 11 (2006), 119–125.
[105]	P. Lei, F. Moeslein and B. J. Wood, et al., Real-time tracking of liver motion and deformation using a flexible needle, Int. J. Comput. Assist. Radiol. Surg., 6 (2011), 435–446.
[106]	C. S. Park, S. K. Hall and C. Liu, et al., A model of tissue contraction during thermal ablation. Physiol. Meas., 37 (2016), 1474–1484.
[107]	D. Liu and C. L Brace, Numerical simulation of microwave ablation incorporating tissue contraction based on thermal dose, Phys. Med. Biol., 62 (2017), 2070–2086.
[108]	V. Lopresto, L. Strigari and L. Farina, et al., CT-based investigation of the contraction of ex vivo tissue undergoing microwave thermal ablation, Phys. Med. Biol., 63 (2018), 055019.
[109]	C. S. Park, C. Liu and S. K. Hall, et al., A thermoelastic deformation model of tissue contraction during thermal ablation, Int. J. Hyperthermia, 34 (2018), 221–228.
[110]	L. Farina, Y. Nissenbaum and M. Cavagnaro, et al., Tissue shrinkage in microwave thermal ablation: comparison of three commercial devices, Int. J. Hyperthermia, 34 (2018), 382–391.

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