Geometric interpretation of the gamma dose distribution comparison technique: interpolation-free calculation.

The gamma dose comparison tool has been used by numerous investigators to quantitatively compare multidimensional dose distributions. The gamma tool requires the specification of dose and distance-to-agreement (DTA) criteria for acceptable variations between the dose distributions. The tool then provides a comparison that simultaneously evaluates the dose difference and distance to agreement of the two dose distributions. One of the weaknesses of the tool is that the comparison requires one of the dose distributions to have a relatively high spatial resolution, with points spaced significantly closer than the DTA criterion. The determination of gamma involves an exhaustive search process, so the computation time is significant if an accurate gamma is desired. The reason for the need for high spatial resolution lies with the fact that the gamma tool measures the closest point in one of the dose distributions (the evaluated distribution) with individual points of the other distribution (the reference distribution) when the two distributions are normalized by the dose difference and DTA criteria for the dose and spatial coordinates, respectively. The closest point in the evaluated distribution to a selected reference distribution point is the value of gamma at that reference point. If individual evaluated dose distribution points are compared, the closest point may not accurately reflect the closest value of the evaluated distribution as if it were interpolated on an infinite resolution grid. Therefore, a reinterpretation of the gamma distribution as the closest geometric distance between the two distributions is proposed. This is conducted by subdividing the evaluated distribution into simplexes; line segments, triangles, and tetrahedra for one, two, and three-dimensional (3D) dose distributions. The closest distance between any point and these simplexes can be straightforwardly computed using matrix multiplication and inversion without the need of interpolating the original evaluated distribution. While an exhaustive search is still required, not having to interpolate the evaluated distribution avoids the drastic growth of calculation time incurred by interpolation and makes the gamma tool more practical and more accurate. In our experiment, the geometric method accurately computes gamma distributions between 3D dose distributions on a 200 x 200 x 50 grid within two minutes.

[1]  J. Cygler,et al.  Commissioning and quality assurance of treatment planning computers. , 1993, International journal of radiation oncology, biology, physics.

[2]  J A Purdy,et al.  Systematic verification of a three-dimensional electron beam dose calculation algorithm. , 1996, Medical physics.

[3]  D. Low,et al.  A technique for the quantitative evaluation of dose distributions. , 1998, Medical physics.

[4]  D A Low,et al.  A software tool for the quantitative evaluation of 3D dose calculation algorithms. , 1998, Medical physics.

[5]  James A. Purdy,et al.  Intensity-modulated radiotherapy: current status and issues of interest. , 2001, International journal of radiation oncology, biology, physics.

[6]  D. Huyskens,et al.  A quantitative evaluation of IMRT dose distributions: refinement and clinical assessment of the gamma evaluation. , 2002, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[7]  Lars E Olsson,et al.  MAGIC-type polymer gel for three-dimensional dosimetry: intensity-modulated radiation therapy verification. , 2003, Medical physics.

[8]  J. Dempsey,et al.  Evaluation of the gamma dose distribution comparison method. , 2003, Medical physics.

[9]  Joseph O Deasy,et al.  CERR: a computational environment for radiotherapy research. , 2003, Medical physics.

[10]  M. Alber,et al.  A revision of the gamma-evaluation concept for the comparison of dose distributions. , 2003, Physics in medicine and biology.

[11]  D Baltas,et al.  3D dose verification in 192Ir HDR prostate monotherapy using polymer gels and MRI. , 2003, Medical physics.

[12]  M. Alber,et al.  A revision of the γ-evaluation concept for the comparison of dose distributions , 2003 .

[13]  M. Stock,et al.  Interpretation and evaluation of the γ index and the γ index angle for the verification of IMRT hybrid plans , 2005 .

[14]  M. Stock,et al.  Interpretation and evaluation of the gamma index and the gamma index angle for the verification of IMRT hybrid plans. , 2005, Physics in medicine and biology.

[15]  Brenda G. Clark,et al.  A comparison of two commercial treatment‐planning systems for IMRT , 2005, Journal of applied clinical medical physics.

[16]  P Keall,et al.  Dosimetric impact of geometric errors due to respiratory motion prediction on dynamic multileaf collimator-based four-dimensional radiation delivery. , 2005, Medical physics.

[17]  R. Fenstermaker,et al.  Dosimetric accuracy of a staged radiosurgery treatment , 2005, Physics in medicine and biology.

[18]  Comparison of measured and computed portal dose for IMRT treatment , 2006, Journal of applied clinical medical physics.

[19]  M. V. van Herk,et al.  Accurate two-dimensional IMRT verification using a back-projection EPID dosimetry method. , 2006, Medical physics.

[20]  Jie Yang,et al.  Monte Carlo based IMRT dose verification using MLC log files and R/V outputs. , 2006, Medical physics.

[21]  T. Solberg,et al.  Dosimetric characteristics of a new linear accelerator under gated operation , 2006, Journal of applied clinical medical physics.

[22]  A. Monti,et al.  Dosimetric verification of 6 and 18 MV intensity modulated photon beams using a dedicated fluoroscopic electronic portal imaging device (EPID). , 2006, Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology.

[23]  I. Troprès,et al.  Polymer gel dosimetry for synchrotron stereotactic radiotherapy and iodine dose-enhancement measurements , 2007, Physics in medicine and biology.

[24]  Stefano Gianolini,et al.  Introducing gel dosimetry in a clinical environment: customization of polymer gel composition and magnetic resonance imaging parameters used for 3D dose verifications in radiosurgery and intensity modulated radiotherapy. , 2007, Medical physics.

[25]  W. Renner 3D dose reconstruction to insure correct external beam treatment of patients. , 2007, Medical dosimetry : official journal of the American Association of Medical Dosimetrists.

[26]  Jan-Jakob Sonke,et al.  A fast algorithm for gamma evaluation in 3D. , 2007, Medical physics.

[27]  Interpretation and evaluation of pulmonary function tests. , 2009, Nursing standard (Royal College of Nursing (Great Britain) : 1987).