Finer leaf resolution and steeper beam edges using a virtual isocentre in concurrence to PTV-shaped collimators in standard distance – a planning study

General aspects

Normal linacs are not considered to be suitable for modern stereotactic irradiation (STX). The main reason is the isocentric leaf width of common multi-leaf collimators (MLC). Typical isocentric 0.5 cm MLCs are assumed too coarse for STX. Leaf widths of the order of 0.3 cm are recommended by Bortfeld et al. [1]. However, this value is subject to the typical 20–80% penumbra width of 0.25 cm to 0.3 cm. Since then, several authors more often consider MLC types and leaf widths [2–7], whereas other parameters which determine the dose gradient, such as the penumbra, are rarely examined or even varied. For example, the authors refer the reader to the method of penumbra control using intermediate energy photons [8] proposed by O’Malley et al. [8] or small-field flattening filters proposed by S.J. Thomas [9] in an older work,.

Virtual isocentre

The purpose of the present work is to investigate whether a reduced source to target distance combined with MLC (0.5 cm isocentric leaf width) can compete against reference source to isocentre distance (SID) 100 cm combined with an ideal round collimator (a limit of infinitely narrow leaves). The circular collimator is the ideal shape for spherical targets only. The reduced source to target distance can be realized using, e. g., a virtual isocentre approach (Bratengeier K, Holubyev K, Wegener S: Distance-dependent penumbra: Theoretical considerations and practical implications for stereotactic irradiation using a MLC, submitted): Table positions are a function of the gantry angle and the isocentric table angle in a way that a selected target point is always hit by the beam central axis in a certain fixed distance from the source. This point behaves like an isocentre and is therefore called “virtual isocentre”. Its distance from the source is called source to virtual isocentre distance (SVID) which is allowed to differ from SID 100 cm. The apparatus as a whole behaves like a linac with changed SID, but however, the radiation head remains unchanged. For the present study we consider the SVID reduced to 70 cm, which is a reasonable distance for head applications, and a SVID of 50 cm to demonstrate the trends at further reduced SVID. Our special interest is to examine the role of reduced MLC leaf width separately from penumbra effects regarding improved healthy tissue sparing at reduced SVID.

Planning system and target definition

The planning study was performed by means of the therapy planning system (TPS) Philips Pinnacle³™ version 9.10. A virtual sphere of diameter 20 cm and physical density 1.0 g/cm³ was created in TPS on a 0.1 cm sliced CT. The spherical planning target volume (PTV) was placed in the centre. PTV of diameters (∅) of 1.0 cm, 1.3 cm and 1.7 cm were created inflating a nearly point size central object using Pinnacle³™ expansion functions. Using three different target diameters was intended to investigate the effect of different curvatures. The diameters were chosen small to recognize the effects of MLC induced grating.

Evaluation parameters

Planning details

The MLC leaves were positioned using the “Expose-PTV” block margin function of the Pinnacle³ planning system in such a way that the MLC leaves touched the margin around the PTV in beam eye view projection. Also beams with PTV conformal, nearly circular blocks were created using the margin. The same margin was used for all beams of a given technique. To study the influence of prescription, the 70%-, 80%- and 90%-doses of the reference isocentre dose (=100%) were chosen as “PTV-surrounding”, respectively. They cover at least 99% of the PTV. A block thickness was chosen to produce the same transmission as the standard Elekta Agility^TM MLC with 0.5 cm leaf width at SID 100 cm. To carve out the impact of SVID and consequential effects of the penumbra changes, same conditions for block and MLC were simulated; the virtual block was placed in the MLC distance. Thus, the block behaved like a MLC with infinitely narrow leaves. To compare the techniques with each other, the same dose was prescribed to the isocentre; the PTV margin was iteratively adapted to achieve the same mean dose inside the PTV. Details of this method are described in Additional file 2. Changes of the penumbra were simulated exemplarily by a superposition of beams with different diameters. Beam charact eristics (profiles) were determined according to Additional file 3.

SID 100 vs. SVID 70/50

In more detail, the effect of reduced SVID on a radial dose distribution is shown Figs. 1 and 2 for circular collimator and MLC, respectively. The distributions were normalized to that one at SID 100 cm. For both, circular collimator and MLC, the decrease of the dose to the surrounding healthy tissue at the reduced SVID was almost independent from the prescription. However, the effect of healthy tissue sparing utilizing reduced SVID was more pronounced for the “MLC” situation (Fig. 2); most probably due to the additional effect of finer approximations of a circular beam formed by thinner MLC leaves. The next section is intended to quantify the MLC and penumbra contributions.

Circular collimator vs. MLC

The gradient index in Table 2 clearly showed lower GI values for circular collimators with respect to MLC. Accordingly, Fig. 3 compares the dose distributions for a MLC and a circular collimator at the same SVID. Clearly, the MLC always led to an additional dose in the surrounding healthy tissue. This additional contribution decreased at reduced SVID. This decrease was not always most effective for SVID 50, assumedly due to”digitization” effects of the circular shape by slots of finite width. Obviously, the influence of MLC-beam-shaping was less than the distance effects shown in Fig. 1.

MLC at SVID 70/50 or optimal shape at SID 100?

Can a reduced SVID compensate for the “roughness” of MLC beam shaping? In four of the five cases listed in Table 2, the GI for the MLC at SVID 70 cm was lower than ideal beam shaping by a circular collimator at SID 100 cm (and in the one remaining case, the values differed only marginally). Clearly, the steeper penumbra at reduced SVID overcompensated the deteriorating effect of MLC beam shaping even for the 0.5 cm MLC. In more detail, the cumulative effect of combining reduced SVID with MLC can be deduced from Fig. 4, which shows the MLC dose distributions normalized to that of circular collimator at standard SID 100 cm. In any case for the high dose region (hence, up to double PTV radius), using a MLC at SVID 70 cm was preferable to a perfect beam shaper (using appropriate circular collimators of optimized diameter) at SID 100 cm.

Clinical relevance?

Effects of superposition and penumbra increase

To evaluate the increase in the healthy tissue dose resulting from an enlarged penumbra for combined beam arrangements, we artificially raised the penumbra at constant SID using a superposition of beams with differing diameters.

As a reference, we considered a PTV ∅ of 1.0 cm and used circular collimator with a margin around PTV to meet the demands of a D80% prescription (Fig. 5). We considered superposition of pairwise wider and narrower beams, identical for the whole arrangement. Two cases were generated with PTV margins of additional +0.10 cm and −0.10 cm (case α), and +0.15 cm and −0.05 cm (case β). The same prescription was used for both cases. The relative beam weights were adjusted to achieve the same mean dose to the PTV (71.5 and 28.5%, respectively, for α, 35.4 and 64.6% for β). We found that for 0.20 cm difference between PTV margins the penumbra increased from 0.35 cm (reference) to 0.37 cm (α) or 0.38 cm (β). The associated increase of the healthy tissue dose reached its maximum of about 7% at a distance of 0.5 cm from the PTV, for both α and β, see Fig. 5. The penumbra increase depended on the difference between margins only. Assuming this dependence to be linear, we estimated the systematic increase of the healthy tissue dose at SID 100 cm for a margin step 0.02 cm not to exceed 0.7%. At SVID 70 cm for margin step 0.04 cm it did not exceed 1.4%, and at SVID 50 cm for margin step 0.10 cm 3.5%. Thus, combining beams to achieve the prescribed radial mean PTV dose (see Additional file 1 and methods section) did not influence the results for the healthy tissue at SID 100 cm and SVID 70 cm. For SVID 50 cm, used for demonstration purposes, the systematic dose increase from beam superposition did not exceed 3.5%.

MLC beam shaping

Not surprisingly, the use of a MLC instead of optimal circular collimators leads to more dose to the healthy tissue around the PTV, see Fig. 3. However, the effect of MLC is less pronounced than intuitively expected. At SID 100 cm the MLC provides coarser approximation of the circular collimator as at SVID 70 cm or even 50 cm. In the worst case of 1.0 cm diameter spherical PTV, a 1.0 cm × 1.0 cm square MLC approximation leaves 27% of the area around the PTV unblocked, if the two MLC leaves, at both sides each, touch the PTV in the beam projection. For SVID 50 cm the unblocked area would numerically be 19% for four leaves at both sided of a circle. Interestingly, the planning study shows that the effect of MLC vs circular collimator (Fig. 3) increases the dose to the healthy tissue only by half of that, 10–13%. This is due to the fact that, depending on prescription, the MLC apertures have to be generated from negative PTV margins [16] and thus not always fully contribute to the primary dose in healthy tissue. In contrast, the penumbra in any case contributes to the primary dose in the healthy tissue, so its effect seems to be always larger. The deterioration of the dose falloff from MLC apertures can be overcompensated by a reduced SVID, as demonstrated in Fig. 4. In the high dose area adjacent to the PTV, the SVID ≤ 70 cm combined with MLC performs better than the perfectly adapted circular collimator at standard SID 100 cm. The effect must be traced back to the steeper penumbra as depicted in Fig. 6 and quantified in Fig. 5. An increase of 20–80% penumbra width by 0.02 or 0.03 cm leads to 7% larger healthy tissue dose. For the MLC as modelled in the planning system SID 100 cm compared to SVID 70 cm leads to penumbra increase of 0.03 cm in J direction, 0.08 cm in L direction. This is semiquantitatively in good agreement with the increase of the healthy tissue dose of about 12–14% seen in Fig. 2 (D80%, ∅ 1.3 cm).

Validity of the planning study results

Note that the conclusions above probably are quite general and independent from the beam shaping device, although a special (spherical) PTV shape was chosen. The present study was performed for small spherical targets of different diameters. These targets stand for objects with various curvatures. The simple circular shape allows the definition of an optimal circular aperture, which is regarded as the limit of an infinitely small leaf width. All results were qualitatively independent from the PTV diameter. They were also independent from different prescription schemes, be that D70%, D80% or D90%.

The role of penumbra steepness

For circular collimator (Fig. 1) combined with reduced SVID, the improved healthy tissue sparing comes from the penumbra decrease. For MLC, the improvement in healthy tissue sparing at reduced SVID (Fig. 2) is dominated by the penumbra decrease, which can be inferred by comparing Fig. 2 vs. Fig. 1 and can be concluded from Fig. 4. As long as penumbra is decreased by 0.02 cm or more at reduced SVID, the MLC performs better than an ideal collimator at standard SID 100 cm. Although this was shown for the Agility^TM head, this result can be assumed relevant also for other MLCs, as the effect can be traced back to the geometrical penumbra. Independent from the present planning study, the importance of the penumbra can be deduced from more theoretical considerations (Bratengeier K, Holubyev K, Wegener S: Distance-dependent penumbra: Theoretical considerations and practical implications for stereotactic irradiation using a MLC, submitted).

In this study, the healthy tissue sparing effect of reduced SVID decreases for a larger PTV radius independently of beam shaping device, see Figs. 1 and 2. The sparing effect is dominated by penumbra decrease, which becomes less important for larger PTV: the volume of a thin layer around PTV, where penumbra dose dominates, becomes smaller relative to the PTV volume itself.

Advantages of reduced SVID

The effect of using MLC instead of ideal circular collimator (Fig. 3) is found (almost independent of SVID and prescription) at the level of 10% dose increase to the healthy tissue. The effect of reduced SVID is proven for SVID 70 cm, practical for head irradiations, at the level of 10% dose decrease due to decreased penumbra. Thus, at SVID 70 cm combined with MLC the two effects compensate and the plan quality is at least as good as at SID 100 cm combined with circular collimator (Fig. 4). In fact, the additional improved beam shaping due to narrower effective leaf widths ensures even further healthy tissue sparing.

Relation to neurosurgical literature data

The increase of quality by using SVID 70 cm or less is clearly significant and relevant: Dose to the surrounding decreases, as can be seen from GI and V _66.7% .

The GI for higher dose maxima and for more extended targets decreases below the intended GI <3.0 as demanded by the radiosurgery consortium [14], even for the 0.5 cm MLC at SVID 70 and below. For targets of 1.0 cm diameter, D50% should be used instead of D70%, because Paddick and Lippitz demonstrated a strong decrease of GI with increasing maximum dose [12] for typical beam profiles.

The presented results even assume infinitely variable collimator diameters, which will not be available for fixed sets of applicators of different diameters. In contrast, MLC and jaw can be steered in sub-millimeter range, as in the presented study. This fact additionally favours the MLC-SVID-approach. This is all the more the case for the shaping of non-spherical targets. Certainly, shaping by a MLC will be even more advantageous compared to circular applicators, if non-spherical targets are to be treated: the application time may be reduced. The treatment time is further decreased as a result of the inverse-quadratic law.

Recently, several authors pushed dynamic techniques using table movement [17] or complex leaf steering (see i.e., [18]) that require fail-safe and precise table and leaf movements, much more than needed for the present study. Therefore we excluded safety and precision aspects for the present study.