The superficially averaged dose gradient at the target volume's boundary: A two-dimensional formulation and solution...

Dose conformity and steepness of dose fall-off at a target volume's boundary are important quality criteria in treatment planning to predict complication rates in normal tissue and critical structures. Several dose gradient measures are in use; ICRU Report 91 recommends one of two gradient metrics for reporting. All of the common gradient indices are one-dimensional, although dose gradient problems are at least two-dimensional and anisotropic. Four of ten investigated gradient indices show false characteristics on the mean value of the physical dose gradients. Anisotropic dose gradient measures can be the basis of clinical therapeutic decisions if tumours are surrounded by organs at risk with various tolerance dose values. To close this information gap, the author presents a mathematical description and solution of anisotropic dose gradient problems.

The new two-dimensional dose gradient measure is called the superficially averaged dose gradient (SADG). The particular informative content of the ten common dose gradient indices was assessed by classification and analysing their properties. The correlations between all of the dose gradient measures were investigated for linac-based stereotactic radiosurgery of 13 brain metastases.

From all of the one-dimensional dose gradient indices, the approximated SADG* showed the best correlation on the SADG. Here, Pearson's correlation coefficient was 1.000 and the relative errors were in a range of -0.2 to 2.9%. Distributions of anisotropic dose gradients were graphically represented by dose gradient-solid angle histograms.

Two-dimensional dose gradient measures such as the SADG are urgently required for lesions that are located in non-homogeneous normal tissue. The quality of each present and future dose gradient measure concerning the description of anisotropic dose gradient problems is now verifiable by use of the SADG. Through the SADG, the influences of collimation types on the dose fall-off at the target volume's boundary can be investigated. The algorithm for determining the SADG should be implemented in treatment planning systems to utilise the formalism for all users. The dose gradient indices recommended in ICRU Report 91 overestimate and underestimate physical dose gradients, respectively.