A quality factor to quantitatively compare the dosimetry of Gamma Knife radiosurgery and intensity-modulated radiation therapy as a function of target volume and shape*.*

Jonathan A. Borden, M.D. ^{1}, Anita Mahajan, M.D.^{2} and Jen-San Tsai, Ph.D.^{2}

Departments of Neurosurgery ^{1} and Radiation Oncology ^{2}, Tufts University School of Medicine and New England Medical Center, Boston Massachusetts

Address correspondence to:

Jonathan A. Borden, M.D. Department of Neurosurgery, Proger 7, New England Medical Center, 750 Washington Street, Boston Massachusetts, 02111

Telephone: 617-636-5859

Fax: 617-636-7587

E-mail: jonathan@openhealth.org

Running title: Radiosurgical Quality Factor

Keywords: radiosurgery, gamma knife, IMRT, dosimetry

Abstract

*Objective*: We have developed a quality factor to compare Gamma Knife radiosurgery, linear accelerator radiosurgery and intensity-modulated radiation therapy (IMRT) dosimetry. This quality factor (QF) relates the percent target covered (PTC) by the prescription radiation isodose, target volume (V_{T}) and enclosing tissue volume which receives greater than a particular dose (V_{X}).

QF_{X} = PTC*V_{T}/V_{X}.

We have investigated target shape independent of volume in predicting radiosurgical complication rates.

*Methods*: Plastic targets of a defined volume (0.2, 0.5, 1.5 and 10 cm^{3}) and four increasingly complex shapes (spherical, ellipsoid, star/AVM, and horseshoe) were created. Dosimetry was studied on Leksell GammaPlan, Adac/Pinnacle and Nomos Corvus workstations. We studied the dosimetry of a new 4mm x 10mm IMRT collimator array (the Nomos ‘Beak’) not yet validated for use in our clinical practice.

*Conclusion*s: At a prescription dose of 15 Gy to the target margin, the QF_{15} is a conformality index (CI). The 12 Gy volume (V_{12}) estimates the radiosurgical normal tissue complication rate for AVMs. When the target is well covered the QF_{12} is inversely proportional to the complication risk and is a measure of the plan quality.

Particularly for larger targets the Gamma Knife and IMRT ‘Beak’ plans show similar conformality (QF_{15}). Particularly for small and round targets the Gamma Knife plan quality is significantly higher (QF_{12}). As target volume and complexity increase, the IMRT ‘Beak’ QF_{12} approaches that of the Gamma Knife.

The QF_{12} of Gamma Knife dosimetry has an inverse correlation with target shape complexity independent of target volume.

Introduction

The goal of radiosurgery is to deliver a therapeutic does of radiation within a three dimensionally defined target volume while delivering as little as possible radiation to the normal structures outside the target volume. The dose volume histogram (DVH) is a calculated curve that yields the volume receiving a particular radiation dose within the region of interest.^{9} It is common practice to evaluate radiosurgical plans using measurements taken from the DVH of the target and surrounding structures. By outlining certain structures such as the brainstem or optic chiasm the DVH of such structures can be evaluated. The goal of a successful radiosurgical treatment is to provide a high target control probability (TCP) yet an acceptable normal tissue complication probability (NTCP). For many target tissue types, the TCP is related to the minimal marginal dose and hence the percent target covered (PTC) is used as an index of TCP. The ratio between the target and treatment volumes is termed the Conformality Index (CI) and is used to judge the conformality of the plan.^{1,7,15,17} The PTC is obtained from the DVH curve, and the DVH is used to estimate the NTCP within a defined volume.

Assuming a constant coverage (e.g. 95%), the CI measures the tightness of fit of the target volume and the marginal treatment volume. Although the CI may indicate a highly conformal plan, the dose falloff outside the target volume may be gradual and surrounding structures will receive an unacceptably high amount of radiation, i.e. high NTCP. A better measure of plan quality is the ratio TCP/NTCP ^{11}.

Our goal is to develop a target volume independent radiosurgical plan quality factor (QF) to study the relationship between target volume and target shape complexity/surface area and the ratio of TCP and CP.

Intensity Modulated Radiation Therapy (IMRT) is a relatively new computer controlled linear accelerator based system in which the radiation intensity is dynamically modulated through a linear array of collimators during the treatment arc ^{2,8,10,13,14}. We have compared the QF of plans created on Gamma Knife, conventional Linac and IMRT based radiosurgical systems. The QF is easily calculated from points along the DVH curve.

Materials and Methods:

We define the QF_{X} as:

__Equation 1.__ QF_{X} := PTC*V_{T}/(V_{X})

Where PTC = percent target covered, V_{T} = target volume and V_{X} = X Gy volume.

Alternatively:

__Equation 2.__ QF’_{X} := PTC* V_{T}/(V_{X} - V_{T})

might be expected to correlate with TCP/NTCP however the former equation (QF_{12}) best fits the results from the Cooperative AVM Radiosurgery Study ^{4}.

We created plastic targets (Aquaplast) of increasing complexity: roughly spherical, epllipsoid, spoked (i.e. AVM) and horseshoe shaped. By creating the targets of plastic, we had control of the volume independent of shape. We created targets of 0.5, 1.5 and 10 cm^{3} volumes and additionally created a small spherical (0.2 cm^{3}) volume. The targets were placed into a humanoid phantom (Rando) and scanned by Computed Tomography (CT) using after application of a Leksell stereotactic frame for the Gamma Knife/GammaPlan 5.20, and the Radionics BRW frame for the ADAC/Pinnacle circular collimator Linac system and for the Nomos Corvus 3.0 IMRT system. In each case the data sets were transferred over the hospital Ethernet to each of the treatment workstations using the DICOM protocol. The most experienced member of our team for each modality developed the treatment plans.

In comparing plans we have required a target coverage (PTC) of at least 95%. The marginal target dose is tissue dependent. We have selected 15 Gy for the purposes of this experiment, this being the dose we typically prescribe to the margin of meningiomas.

The Leksell Gamma Knife plans were intended to represent real-world treatment plans. They were developed in a similar amount of time as we use to develop patient treatment plans and using similar criteria except that the tissue surrounding the target was treated as homogeneous in eloquence.

The Nomos Corvus IMRT plans were created assuming 0 mm of gantry sag, 0 mm of patient motion and 0 mm of target location error. It is our common practice to add a border surrounding the target for patient treatments to correspond to the gantry sag and positioning errors we have measured in our institution ^{12,13,14}. The 10 mm collimator array has been extensively verified ^{14} and is in active clinical use for intracranial and body targets. The 4 mm collimator, the "Beak" has not yet been clinically validated and is not currently in use. Hence the results presented here are more consistent what is theoretically achievable with this IMRT system, rather than what is achievable in a clinical situation.

Similarly the ADAC/Pinnacle plans assume 0 mm of gantry sag. The created treatment plans are significantly more complex than what we have clinically performed. In particular the large horseshoe target was treated with 14 isocenters, which is far more complex than what we have used.

Dose volume histograms of each target and a surrounding matrix were created. The PTC, target and treatment volumes were measured for QF_{12} and QF_{15}. The data was analyzed and graphed in Microsoft Excel.

Results

For small round targets the Gamma Knife quality factor is superior for both QF_{12} and QF_{15 }(Figures 1 and 2). QF_{15 }is essentially a conformality index and for larger and more complex targets the Gamma Knife and IMRT have similar conformality. The Beak demonstrates a higher QF than current IMRT even in larger volumes. The QF_{12} demonstrates a more significant improvement with Gamma Knife versus IMRT particularly for smaller targets. This is presumably due to the sharper dose falloff.

Particularly with Gamma Knife dosimetry, a significant inverse relationship exists between target complexity and QF_{12} as demonstrated in Figure 3. This relationship is not so clear-cut with IMRT or Linac until complex targets are treated (figures 4,5,6).

Discussion

Our quality factor, QF, differs from the commonly used conformality index, CI, by factoring the target coverage, PTC and the 12 Gy volume rather than the treatment volume. The result that Gamma Knife is better than IMRT in sparing normal tissue outside the target volume are consistent with prior dosimetric comparisons ^{10,18} . Similarly the dosimetry of IMRT and conventional Linac radiosurgical systems has been compared.^{8 } The quality factor incorporates previously used quantities into a single number.

Our quantitative results measuring QF_{12} as a function of target shape complexity and volume confirm our impression that as target complexity and volume increase, IMRT techniques become more appropriate. Recent improvements in IMRT multileaf collimator technology will likely improve the dosimetry quality achievable via IMRT.

The radiosurgical NTCP has been predicted by the integrated logistic formula ^{3-6}. One might predict that the NTCP would be related to the volume of normal tissue receiving greater than a minimal toxicity dose (e.g. 12 Gy). A recent cooperative study of complication rates after AVM radiosurgery suggests that the complication probability (CP) better correlates with the 12 Gy volume including both target and normal surrounding tissue.^{4} This empirical correlation between 12 Gy volume and complication rate has been determined from AVM data and may not hold true for other target pathologies.

The model used in the current experiment assumes a constant complication risk within the normal tissue surrounding the target volume. In clinical situations, radiosurgical planning takes surrounding tissue eloquence as well as radiobiological tissue sensitivities into account. A more accurate quality factor might integrate a weighted tissue sensitivity across the volume surrounding the target. Nor does our model factor dose inhomogeneity within the target volume. Typical Gamma Knife dose planning does not attempt to improve intratarget dose homogeneity, aiming for a prescription at the 50 % isodose surface. In contrast, IMRT planning prefers dose homogeneity, aiming for a higher treatment prescription isodose.^{1,8,10,14,17,18} We have not studied the effect of treatment isodose on 12 Gy volume.

The inverse relationship between dosimetric quality and target shape complexity with Gamma Knife dosimetry is demonstrated in Figure 3. Assuming a perfectly conformal plan, the 12 Gy volume is equal to the target volume (or 15 Gy volume) + the integral of the isodose surface area between 15 and 12 Gy. When isodose falloff is rapid, this volume is proportional to the target surface area. Our results indicate that target shape complexity, or surface area, predicts the 12 Gy volume, and hence complication rate, independently of target volume.

Conclusions

The quality factor of the 12 Gy volume, QF_{12}, is readily computed from the dose volume histogram curve. As measured by QF_{12, }Gamma Knife radiosurgery is predicted to have a lower complication rate particularly for small round targets. As the target volume and shape complexity increase newer IMRT technologies are predicted to approach Gamma Knife plan quality. The theoretical delivery capability of such IMRT techniques remains to be validated for clinical suitability.

Particularly for Gamma Knife dosimetry, the 12 Gy volume and normal tissue complication probability is predicted to be dependent on target shape complexity and surface area independent of target volume.

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Figure Legend

Figure 1: Quality Factor of the 15 Gy volume (QF_{15}) *y-axis* as a function of target volume and complexity and modality. Target volumes *x-axis* of 0.2 cm3, 0.5 cm^{3}, 1.5 cm^{3} and 10 cm^{3} were employed. Gamma Knife, ‘Beak’ Intensity Modulated Radiation Theraphy (IMRT) (4 x 10 mm collimator array), conventional IMRT (10 x 10 mm collimator array) and Linac radiosurgery systems were compared. (a) QF15 versus target volume for the spherical target (b) QF15 versus target volume for the ellipsoid target (c) QF15 versus target volume for the AVM/star target (d) QF15 versus target volume for the horseshoe target. For each graph the QF is plotted as a function of target volume

Figure 2: Quality Factor of the 12 Gy volume (QF_{12}) *y-axis* as a function of target volume and complexity and modality. Target volumes *x-axis* of 0.2 cm3, 0.5 cm^{3}, 1.5 cm^{3} and 10 cm^{3} were employed. Gamma Knife, Beak IMRT, conventional IMRT and Linac radiosurgery systems were compared. (a) QF12 versus target volume for the spherical target (b) QF12 versus target volume for the ellipsoid target (c) QF12 versus target volume for the AVM/star target (d) QF12 versus target volume for the horseshoe target. For each graph the QF is plotted as a function of target volume.

Figure 3: Gamma Knife QF_{12 }as a function of target complexity. The target volume sets (0.5,1.5 and 10 cm^{3}) are plotted individually.

Figure 4: Beak IMRT QF_{12 }as a function of target complexity. The target volume sets (0.5,1.5 and 10 cm^{3}) are plotted individually.

Figure 5: IMRT QF_{12 }as a function of target complexity. The target volume sets (0.5,1.5 and 10 cm^{3}) are plotted individually.

Figure 6: Linac QF_{12 }as a function of target complexity. The 10 cm^{3} target volume set was employed.

Table 1: Abbreviations

AVM – arteriovenous malformation

CI – conformality index

DVH – dose volume histogram

IMRT – intensity modulated radiation therapy

Linac – linear accelerator

NTCP – normal tissue complication probability

QF – quality factor

QF12 – quality factor assuming 12 Gy volume

QF15 – quality factor assuming 15 Gy volume

PTC – percent target covered

TCP – tumor/target control probability

V_{T} – target volume

V_{X} – volume enclosed by X Gy surface/ volume receiving at least X Gy