A simple dose gradient measurement tool to complement the conformity index

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✓A dose gradient index (GI) is proposed that can be used to compare treatment plans of equal conformity. The steep dose gradient outside the radiosurgical target is one of the factors that makes radiosurgery possible. It therefore makes sense to measure this variable and to use it to compare rival plans, explore optimal prescription isodoses, or compare treatment modalities.

The GI is defined as the ratio of the volume of half the prescription isodose to the volume of the prescription isodose. For a plan normalized to the 50% isodose line, it is the ratio of the 25% isodose volume to that of the 50% isodose volume.

The GI will differentiate between plans of similar conformity, but with different dose gradients, for example, where isocenters have been inappropriately centered on the edge of the target volume.

In a retrospective series of 50 dose plans for the treatment of vestibular schwannoma, the optimal prescription isodose was assessed. A mean value of 40% (median 38%, range 30–61%) was calculated, not 50% as might be anticipated. The GI can show which of these prescription isodoses will give the steepest dose falloff outside the target.

When planning a multiisocenter treatment, there may be a temptation to place some isocenters on the edge of the target. This has the apparent advantage of producing a plan of good conformity and a predictable prescription isodose; however, it risks creating a plan that has a low dose gradient outside the target. The quality of this dose gradient is quantified by the GI.

Abbreviations used in this paper: GI = gradient index; GKS = Gamma Knife surgery; PIV = prescription isodose volume.

Article Information

Address reprint requests to: Ian Paddick, M.Sc., Gamma Knife Centre, Cromwell Hospital, Cromwell Road, London, SW5 OTU, United Kingdom. email: ian@physicsconsulting.co.uk.

© AANS, except where prohibited by US copyright law.



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    Neuroimage of a treatment plan for a cavernous sinus meningioma, revealing the 75%, 50%, 25%, 15%, and 10% isodose lines. There is excellent conformity of the 50% isodose line and the periphery of the target; however, the 25% isodose volume covers a significant volume of brainstem and temporal lobe.

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    Neuroimages of three plans for treatment for the same vestibular schwannoma. All three plans have equal conformity indices as described by Paddick17 (PCI), but the volumes enclosing half the prescription dose are markedly at variance. a: Plan 1 consists of 5 × 14–mm isocenters prescribed to the 46% isodose, PCI = 0.87, PIV46%= 3.7 cm3, PIV23%=12.2 cm3, GI = 12.2/3.7 = 3.30. b: Plan 2 consists of 16 × 8–mm isocenters prescribed to the 50% isodose, PCI = 0.87, PIV50%= 3.6 cm3, PIV25%= 10.6 cm3, GI = 10.6/3.6 = 2.94. c: Plan 3 consists of 2 × 14–mm collimators, 2 × 8–mm collimators, and a single 4-m collimator, PCI = 0.87, PIV42%= 3.7 cm3, GI = 9.8/3.7 = 2.65. The prescription isodose of 42% has the greatest deviation from the gold standard of 50%, but nevertheless has the sharpest dose falloff outside the target. This contradicts the generally held belief that many small isocenters and a 50% isodose line produce a sharper dose falloff.

  • View in gallery

    Neuroimage of dose planning for a vestibular schwannoma. The 45% and 95% isodose lines are shown. The addition of the final 8-mm isocenter (large circle) causes contraction of the isodoses, because of its proximity to the hot spot. The dose planner has three choices: 1) Move the 8-mm isocenter further out into the brainstem. 2) Accept a renormalized plan and use a lower prescription isodose. 3) Replace the 8-mm isocenter with 4-mm isocenters to move the isodose line closer to the border (no need to renormalize the plan).

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    Graph showing the variation of the proposed GI against the prescription isodose line for individual collimators.

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    Graph showing the variation of the GI with prescription isodose diameter in the x and y planes for the four single collimators.

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    Graph showing the variation of mean GI with prescription isodose for 50 vestibular schwannoma treatment plans. The flat bottom of the curve shows 1.5% variation in the GI between the 33% and 43% isodose lines.

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    Graph showing the optimal GI plotted against the number of isocenters for a series of 50 vestibular schwannoma treatment plans.

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    A simplified dose profile along a line through a multiisocenter dose plan. When planning using multiple isocenters, the maximum dose gradient is still at approximately the 70% isodose line of each individual isocenter. As multiple isocenter configurations produce maxima that are much higher than the individual isocenter maxima, the renormalization of the plan means that the area of steepest dose gradient is found at much lower isodose volumes. In this example it is found at 40% of the peak dose of the plan.


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