What Do We Mean When We Talk about the Linac Isocenter?


Purpose: The isocenter of a medical linac system is a frequently used concept in clinical practice. However, so far not all the isocenters are rigorously defined. This work is intended as an attempt of deriving consistent and operable isocenter definitions. Methods: The isocenter definition is based on a fundamental concept, the axis of rotation of a rigid body. The axis of rotation is determined using the trajectory of any point on a plane that intersects the rigid body. A point on the axis of rotation is found through the minimal bounding sphere of the trajectory when the rigid body makes a full rotation. The essential mathematical tool of the isocenter definition system is three-dimensional coordinate transformation. Results: The axes of rotation of the linac collimator, gantry, and couch are established first. The linac mechanical isocenter (linac isocenter) is defined as the center of a circle that best fits the trajectory of a select linac X-ray source position. The axis of rotation and the minimal bounding sphere are cornerstones for the rotation isocenters of the collimator, gantry and couch. The definition of radiation isocenter incorporates a surrogate of the useful beam axis. Conclusions: A framework of isocenter definitions for medical linacs is presented in this manuscript. Consistent meanings of the mechanical and radiation isocenters can be achieved using this approach.

Share and Cite:

Zhang, M. , Zhou, S. and Qu, T. (2015) What Do We Mean When We Talk about the Linac Isocenter?. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 4, 233-242. doi: 10.4236/ijmpcero.2015.43028.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Nath, R., Biggs, P.J., Bova, F.J., Ling, C.C., Purdy, J.A., van de Geijn, J. and Weinhous, M.S. (1994) AAPM Code of Practice for Radiotherapy Accelerators: Report of AAPM Radiation Therapy Task Group No. 45. Medical Physics, 21, 1093-1121.
[2] Klein, E.E., Hanley, J., Bayouth, J., Yin, F.F., Simon, W., Dresser, S., Serago, C., Aguirre, F., Ma, L., Arjomandy, B., Liu, C., Sandin, C. and Holmes, T., Task Group 142, American Association of Physicists in Medicine (2009) Task Group 142 Report: Quality Assurance of Medical Accelerators. Medical Physics, 36, 4197-4212.
[3] Huang, Y., Zhao, B., Chetty, I.J., Brown, S., Gordon, J. and Wen, N. (2015) Targeting Accuracy of Image-Guided Radiosurgery for Intracranial Lesions: A Comparison across Multiple Linear Accelerator Platforms. Technology in Cancer Research & Treatment.
[4] Lutz, W., Winston, K.R. and Maleki, N. (1988) A System for Stereotactic Radiosurgery with a Linear Accelerator. International Journal of Radiation Oncology* Biology* Physics, 14, 373-381.
[5] Kutcher, G.J., Coia, L., Gillin, M., Hanson, W.F., Leibel, S., Morton, R.J., Palta, J.R., Purdy, J.A., Reinstein, L.E., Svensson, G.K., et al. (1994) Comprehensive QA for Radiation Oncology: Report of AAPM Radiation Therapy Committee Task Group 40. Medical Physics, 21, 581-618.
[6] Rowshanfarzad, P., Sabet, M., O’Connor, D.J. and Greer, P.B. (2011) Isocenter Verification for Linac-Based Stereotactic Radiation Therapy: Review of Principles and Techniques. Journal of Applied Clinical Medical Physics, 12, 185-195.
[7] Khan, F.M. (1994) The Physics of Radiation Therapy. 2nd Edition, Lippincott, Williams & Wilkins, Philadelphia, 518.
[8] Khan, F.M. (2009) The Physics of Radiation Therapy. 4th Edition, Lippincott, Williams & Wilkins, Philadelphia, 145.
[9] Du, W., Gao, S., Wang, X. and Kudchadker, R.J. (2012) Quantifying the Gantry Sag on Linear Accelerators and Introducing an MLC-Based Compensation Strategy. Medical Physics, 39, 2156-2162.
[10] Rowshanfarzad, P., McGarry, C.K., Barnes, M.P., Sabet, M. and Ebert, M.A. (2014) An EPID-Based Method for Comprehensive Verification of Gantry, EPID and the MLC Carriage Positional Accuracy in Varian Linacs during Arc Treatments. Radiation Oncology, 9, 249.
[11] Schiefer, H., Ingulfsen, N., Kluckert, J., Peters, S. and Plasswilm, L. (2015) Measurements of Isocenter Path Characteristics of the Gantry Rotation Axis with a Smartphone Application. Medical Physics, 42, 1184-1192.
[12] González, A., Castro, I. and Martínez, J.A. (2004) A Procedure to Determine the Radiation Isocenter Size in a Linear Accelerator. Medical Physics, 31, 1489-1493.
[13] Rosca, F., Lorenz, F., Hacker, F.L., Chin, L.M., Ramakrishna, N. and Zygmanski, P. (2006) An MLC-Based Linac QA Procedure for the Characterization of Radiation Isocenter and Room Lasers’ Position. Medical Physics, 33, 1780-1787.
[14] Du, W. and Gao, S. (2011) Measuring the Wobble of Radiation Field Centers during Gantry Rotation and Collimator Movement on a Linear Accelerator. Medical Physics, 38, 4575-4578.
[15] Moyers, M.F. and Lesyna, W. (2004) Isocenter Characteristics of an External Ring Proton Gantry. International Journal of Radiation Oncology*Biology*Physics, 60, 1622-1630.
[16] Welzl, E. (1991) Smallest Enclosing Disks (Balls and Ellipsoids). In: Maurer, H., Ed., New Results and New Trends in Computer Science, Lecture Notes in Computer Science, Vol. 555, Springer, New York, 359-370.
[17] Larsson, T. (2008) Fast and Tight Fitting Bounding Spheres. Proceedings of the Annual SIGRAD Conference, Vol. 34, Stockholm, 27-30.
[18] Zhang, M., Zaider, M., Worman, M. and Cohen, G. (2004) On the Question of 3D Seed Reconstruction in Prostate Brachytherapy: The Determination of X-Ray Source and Film Locations. Physics in Medicine and Biology, 49, N335-N345.
[19] Siddon, R.L. (1981) Solution to Treatment Planning Problems Using Coordinate Transformations. Medical Physics, 8, 766-774.
[20] Tatcher, M. and Bjärngard, B. (1992) Head-Scatter Factors and Effective X-Ray Source Positions in a 25-MV Linear Accelerator. Medical Physics, 19, 685-686.
[21] Jaffray, D.A., Battista, J.J., Fenster, A. and Munro, P. (1993) X-Ray Sources of Medical Linear Accelerators: Focal and Extra-Focal Radiation. Medical Physics, 20, 1417-1427.
[22] Sharpe, M.B., Moseley, D.J., Purdie, T.G., Islam, M., Siewerdsen, J.H. and Jaffray, D.A. (2006) The Stability of Mechanical Calibration for a kV Cone Beam Computed Tomography System Integrated with Linear Accelerator. Medical Physics, 33, 136-144.
[23] Tideman Arp, D. and Carl J. (2012) EXACTRAC X-Ray and Beam Isocenters—What’s the Difference? Medical Physics, 39, 1418-1423.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.