Intensity-modulated radiation therapy with dynamic multileaf collimators

Intensity-Modulated Radiation Therapy With Dynamic Multileaf Collimators Arthur L. Boyer and Cedric X. Yu

Intensity-modulated radiotherapy (INIRT) has been considered as a means of providing dose distributions that conform to concave target volumes. For computer- controlled multileaf collimators (MLCs) to be used to modulate x-ray beams, some procedure must be used to determine the sequence of leaf positions used to produce the desired modulation. This article derives and compares four leaf-sequencing algorithms. MLC leaf sequencing can be accomplished by representing the areal intensity modulation of a beam with a series of beam profiles. A velocity-modulation equation for com- puting the modulation required for a one-dimensional

profile, described originally using more extensive alge- bra, is derived using a graphic approach. The velocity- modulation approach is compared with an equal incre- mental step-and-shoot approach derived by Bortfeld and Boyer. An areal step-and-shoot technique derived by Xia and Verhey is introduced and compared with the profile-by-profile methods. Finally, an approach is considered using multiple repeated arcs developed by Yu. This wide variety of methods can yield an approach to IMRT that conforms to the engineering constraints imposed by the design of a particular linear accelerator. Copyright �9 1999 by W.B. Saunders Company

C onformal radiotherapy has been proposed as a means to improve the efficacy of radiotherapy

by more closely collimating the radiation field to the three-dimensional projection of a tumor target volume. 1 Presumably, this collimation would allow the escalation of dose to the target volume, thereby increasing the likelihood of local control and survival? -4 Intensity-modulated radiation therapy (1MRT) was proposed as a further refinement. 5,6 It was shown that dose distributions could be significantly improved if not only the weight of individual beams, but also the areal intensity patterns within the margins of each field could be optimized. 7-1~ Multileaf collimators (MLCs) have been used as a means of rapidly shaping the relatively large number of fields used for conformal therapy, it MLCs have also been investigated as a means of realizing x-ray beam intensity modulation. 1215 One approach to IMRT is to modulate an arcing fan-beam with a short-stroke MLC.l~-18 Several hundred patients have already been treated using this technique, which employs a detachable MLC that modulates arcing fan beams 1 to 2 cm thick, each applied after successive longitudinal translations of the patient. 17 An extension of this technique is to treat with a continuously spiraling fan beam. 18 An alternative

From the Department of Radiation Oncology, Radiation Physics Divi- sion, Stanford Univeryity School of Medidne, Stanford, CA; and Department of Radiation Oneology, Universi(y of Maryland School of Medicine, Balti-' more, MD.

This work was supported in part by a grant CA43840 from the National Cancer Im'titute.

Address reprint requests to Arthur Boyer, PhD, Radiation Oncology Department--Room H0144, Stanford University School of Medicine, Stanford, CA 94305-5105.

Copyright �9 1999 by W.B. Saunders Company 1053-4296/99/0901-0004510.00/0

technique is to use an MLC to modulate a cone beam directed toward the patient from multiple fixed gantry angles.19-21 IMRT using modulated cone beams has also been used clinicallyfl 2

This article considers the principles by which sequences of leaf settings can be derived. For the analysis, we assume that one knows a beam fluence across the area of a treatment field that is required to deliver a dose distribution with some desirable char- acteristics. This areal fluence pattern would have. been computed by inverse planning or some optimization technique. The areal beam fluence may be divided into strips corresponding t ~ the projection of each leaf pair of the MLC. Each pair of MLC leaves is then required to modulate the fluence along its projection. This procedure reduces the two-dimensional problem to a one-dimensional problem. The development here focuses on the problem of producing the sequence of leaf settings needed to produce a required intensity profile. A detailed theoretical analysis of the many possible ways a profile can be generated by a leaf sequence has been carried out by Webb? 3

Velocity Algorithm The goal of the algorithms is to determine the leaf-setting sequence required to deliver a desired fluence. Let ~(x) be the fluence along the trajectory of the leaf pair. An example profile is given in Fig 1. The distance x can be taken to be the distance from a common origin measured at the plane at isocenter. Note that there are four regions marked along this particular fluence profile in which the gradient is either positive or negative. Each positive and nega-

48 Seminars in Radiation Oncology, Vol 9, No 1 (January), 1999:pp 48-59

IMR T With Dynamic Multileaf CoUimators 49

A250

200 1 ~50 ~'(x)l o ~

0

B

"C'(x)

0 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40

Position, X ( cm) Pos i t i on , X ( cm)

C

"~"(x)

D

~'(x)

0 5 10 IS 20 25 30 35 40

Position, X ( cm)

0 5 10 15 20 25 30 35 40

Position, X (cm)

Figure 1. (A) An arbitrary fluence profile q)(x). The positive and negative gradient regions are separated by vertical lines on the continuous profile. (B) Time reversals removed with the reflection operation on negative gradient regions. A'rR 1 is the average value of the portion of the profile having a negative gradient within the R1 gradient region, and A'rR2 is the average value of the portion of the profile having a negative gradient within the R2 gradient region. (C) Time reversals removed with the reflection operation on negative gradient regions with a translation operation. (D) Infinite velocities removed with shear operation on the continuous profile.

tive region pair is centered around a maxima. Two methods can be used to modulate the beam: by closing the leaves down on each maxima in turn or by sweeping a window of varying width across the field. We analyze the latter. We derive the sequence with the leaves moving from left to right and designate the leading leaf as the B leaf and the trailing leaf as the A leaf. To deliver the fluence ~(x), one must determine the arrival times at x, tA(x ) for l ea fA and re(x) for ieaf B, such that

o~(~) = +(~) IrA (~)-- t~ ( x ) ] (1)

where ~(x) is the incident fluence across the field. The units of the arrival times can be seconds, or they can be expressed as monitor units (MU). One can indicate the irradiation time interval at x between the opening of the ray by leaf B and the shielding of the ray by leafA as

T(x) = tA (~) - t~ (x) >_ o (2)

The opening time is calculated from the desired fluence and the incident off-axis flux as

a , ( ~ ) ~(~) - .

r ( 3 )

Using Equation (3), the fluence axis in Fig 1 can be scaled to be the opening time. Figure 1 can then be considered to be a time-position graph for the two leaves. The upper border of the shaded area could be interpreted to be the leaf A trajectory and the lower border, or x-axis, to be the leaf B trajectory. The problem with this interpretation is that it requires leaf B to travel with infinite velocity and leaf A to travel backwards in time. The di lemma can be resolved by applying a sequence of operations that transform the two trajectories such that they become deliver- able while still delivering the desired intensity pattern.

To remove the time reversal from the continuous

50 Boyer and Yu

fluence profile, we introduce a reflection operator defined by

(a)

where ATR1 is the average value of the portion of the profile having a negative gradient within the R1 gradient region, and A"rR2 is the average value of the portion of the profile having a negative gradient within the R2 gradient region. The reflection operator is applied to the curves in the negative gradient regions to yield curves that do not require the leaves to travel backwards in time. The results are in Fig lB. The operations have introduced a discontinuity in the leaf-sequence curves that can be removed by applying a translation operator defined in region R2by

�9 (,) = ~'(,) + a ~ (5)

where the increments A-r(x) are selected to remove the discontinuity between region R1 and R2 as illustrated in Fig 1C. For the sake of generality, in region R1, the translation constant is 0. Now, however, there are still horizontal portions of the curves that represent infinite velocity of the leaves. There is always a horizontal segment occurring in either the leaf A or leaf B trajectories_ across the entire sequence. To remove the infinite velocity, we introduce some additional slope to each leaf trajectory. This can be achieved by applying a shear operator to the entire lengths of both leaf trajectories. The shear operator is defined by

r " ( . ) = r"(~) + x/8 (6)

This operator tilts the upper and lower horizontal bounds of each segment of the sequence by an amount determined by the maximal leaf velocity resulting in a sequence that can be practically delivered. The slope of the shear is the inverse of the maximal velocity that the leaves can move, 8. The resulting leaf-setting sequence is given in Fig 1D. The leaves start the sequence dosed at the left side of the field and end the sequence dosed together at the right side of the field. In a region in which the original fluence gradient is positive, the leading leaf, leaf B, moves with a constant slope determined by the maximal velocity, and the trailing leafA moves along the trajectory given in Equation (6). In those regions in which the fluence gradient is negative, the trailing leaf, leaf A, moves with the maximal velocity, while the leading leaf moves along the trajectory given in Equation (6).

The algorithm used to calculate the velocity modulation of the slower leaf can be derived by differentiat- ing Equation (6) with respect to distance:

dr" 1 dr" 1 + (7)

& v(.) a~

The derivative with respect to x of the opening time r" can be obtained from Equation (5) and is simply the derivative of "r' in all subdivisions of the trajectory. The derivative of "r' can be obtained from Equation (4) and depends on the sign of the fluence gradient:

V(I) < ~ dx dx

d.~' d.~(,) V a p > 0 ~ - = + &

(8)

The derivative of'r can be seen in Equation (3) to be

d~(.) d~(x)/ax - - - - - (9 )

d~ +(~)

assuming the variation in the incident fluence is. negligible with respect to x. Using these results in Equation (7), the velocity modulation equation becomes

1 dOP/dx 1 = _+ - - + ( 1 0 )

v(~) ~ 8

where the positive sign applles to positive fluence gradient regions, and the negative sign applies to negative fluence gradient regions. Rearranging to obtain the modulated velocity, one arrives at

v(,) - dCb/d, (I1) 1 + _ ~ . ~ +

This is the result obtained by various authorsJ 3-15 It can be used to generate the velocity modulation required to deliver the fluence profile (I)(x) starting with the leaves closed together at Xmin and. ending with the leaves closed together ag-ain at Xm~. The leaf-setting sequence computed by the velocity equation for the original fluence in Fig 1 is given in Fig 2A. The delivered fluence is plotted as squares in Fig 1. The results are exact. Spirou and Chni 13 have shown formally this to be the most time-efficient way to modulate the velocity of the leaves. This formal

IM_R T With Dynamic Multileaf Collimators 51

A 80

70

60

50

40 E

I - -

30

20

10

B 250

0 5 10 15 20

Position (cm)

25 30 35

200

150

100

50

Figure 2. (A) Leaf-setting sequence computed by the velocity-modulation method. (B) Ef- fect of random velocity errors on the delivered beam profile.

-50

result agrees with intuition because at any given position one or the other leaf is moving at maximal velocity across the entire profile.

An important consideration is the effect of errors in the velocity of the leaves during a velocity- modulated sequence. If random errors are introduced into the velocities of the leaves, the delivered profile becomes distorted. An example is given in Fig 2B in which the velocities have been randomly varied around the ideal velocities up to the maximal veloc-

Position (cm)

ity. The profile is shifted to the left because of the asymmetric distribution of velocity errors imposed by the constraint that there is a maximal velocity.

Step-and-Shoot Fluence Bin Sequence

A somewhat different method for developing the leaf-setting sequence is described by Bortfeld et al. 19 It starts by binning the fluence into equal intensity or fluence intervals. This technique is described using a

52 Boyer and Yu

5.0

4.0

3.0

intensity Level

2s

1.(

O. �84

x-Position +1 +2

simple fluence pattern graphed in Fig 3. This figure represents a 6 X 4 cm field modulated at five discrete levels. The intensity pattern is further discretized in one spatial direction by the requirement that it be modulated by MLC leaves 1 cm wide. The fluence pattern inFig 3 is also arbitrarily discretized in the x-direction in 1-cm increments. The area of the intensity pattern can be analyzed as four blocky beam profiles corresponding to the four MLC leaf traces. The beam profile for leaf-pair number 12 is shown in Fig 4A. The fluenee profile is the contour that starts at the position axis at - 3 , rises to a maximal value of 5, and ends at the position axis at a value of +3. The intersections of the fluence profile with the centers of the discrete intensity levels are easily determined by interpolation over the line segments that constitute the profile definition. These intersections are indicated by numbered circles in Fig 4A. The intersections are segregated into points that occur on the positive gradient (open circles in Fig 4A) and points that occur on the negative gradient (filled circles in Fig 4A). An equal number of such intersection points is found for positive gradient and negative gradient occurrences.

Pairing the rank ordered intersection positions creates the leaf sequence as demonstrated in Fig 4A. In this algorithm, leafB starts inserted into the field at the location of the first maximum. An increment of dose is delivered as indicated by the shaded area of unit height in Fig 4A. The sequence continues with both leaves moving then an increment of dose being delivered. At the end of the sequence, the desired beam fluence is accumulated as shown in Fig 4B. The

+3

12

,eaf Pair

Figure 3. A 6 • 4 cm square field whose intensity is defined at five levels. Each 1-em- wide row of the beam is to be modulated by the leaves numbered 12, 13, 14, and 15.

leaf sequences for the four leaf pairs are plotted in Fig 5. The trajectories for the first three profiles require only 8, 6, and 9 instances, whereas the trajectory for leaf-pair 15 requires 10 instances. One may handle this condition in a number of ways. Here the leaves that finish sooner are closed together at the far side of the field. If the MLC is a tertiary device beneath secondary x-ray collimators, they can be parked beneath the x-ray collimators to reduce leakage between the leaf ends. All four individual leaf trajectories are put back together to create a sweeping window or shutter to modulate the field. The 10 sets of leaf settings for this example are shown in Fig 6. As the modulating window moves from left to right, the coordinates of the leaf ends are increased from one instance to the next. For this particular intensity pattern, the window, in fact, breaks up into several isolated openings that create the relatively isolated peaks around the periphery of the intensity pattern observed in Fig 3.

When delivered with a digital dynamic control system that is driven by MU delivered rather than by time of delivery, there is never a request that the leaves move faster than the maximal velocity. The leaves are moving at their maximal velocity during the steps, and dose is delivered at the maximal dose rate during the shoots.

Each Of these algorithms increases the total number of MU that must be expended to generate the intensity-modulated profiles over the number of MU required to deliver the global maximum of each profile. This factor has been termed the modulation scale factor. 2~ The modulation factor is always greater

IMR T With Dynamic Mullileaf Collimators 53

5

4

3 ca

2

O

Figure 4. (A) The algorithm for discrete step leaf sequencing applied to the profile for 5 leaf-pair 12 in Fig 3. The open circles are at the centers of the intensity level bins along 4 the positive gradient of the profile, and the closed circles ~ 3 are on the negative gradient. ~a The leaf sequence is the rank- ordered pairs of bin-center co- ~ 2 ordinates. The A-leaf and B- leaf are shown in the position for the first irradiation, and 1 the dose delivered by the first step is shaded. (B) How the 0 profile is reconstituted by the leaf sequence as the multiIeaf collimator leaf pair is swept across the field.

-3 -2

0

-3 -2 -1 +2 +3

-1 0 +1

Position

0 +1

Position

+2 +3

than unity. The closer the factor is to unity, the more efficient the leaf-sequencing algorithm. An algo- ri thm can be efficient without accurately producing the desired profile, however.

A dynamic leaf-setting algorithm was compared

with a step-and-shoot, leaf-setting algorithm using a digital dynamic MLC system (Dynamic MLC, Varian Oncology Systems, Palo Alto, CA). The leaf sequences were computed using the logic described previously encoded using C. Table 1 compares se-

54 Boyer and Yu

Leaf Pair 12

-2 -1 0

Position

Leaf pair 13

-2 -1 0

position

Leaf Pair 14

-3 -2 -1 0

position

Leaf pair 15

-3 -2 -1 0 position

s gerlerated by the four Figure 5. The leaf sequence attern in Fig 3. The profiles constituting the intensit).'~ories, and the lower upper curves are the A-leaf trajC~ curves are the B-leaf trajectories'

a step end-shoot algorithm quences computed using ~ the dynamic atgo-

" ed usin~ . with sequences comput ~.,sted for a SlX-fietd rithm. The sequences were c~ e maxillaI'/sinus.

lan desi ned to treat a tumor m" , ~ __~n,s P g ~1 ottrooer oi segmc ~ , For each algorithm, the tot~*

the number of MU, and the d e l i v e r y time in minutes are given along with their t o t a l s fo r the six fields that were used at the indicated g a n t r y angles. The total number of segments MU, a n d t i m e was slightly but not significantly greater for t h e dynamic algorithm.

Areal Step-and-Shoot

The areal step-and-shoot a p p r o a c h is based on the notion that the most efficient w a y to decompose a number is by powers of 2. W o r k i n g through the example of Fig 3 can d e m o n s t r a t e the principle using Fig 7. In Fig 7, the light g r a y areas represent the positions of the A leaves, a n d the da rk gray areas represent the positions of the B leaves. The highest level in the pattern is 5, so t he highest power of 2 contained in the levels is 4. E a c h row in Fig 7 is a step in the first column and a shoot in the second column. The first instance of the sequence moves the leaves so that they irradiate all a r ea containing values of 4 or more. Then a dose of 4 is delivered. The residual left to be delivered is shown in first row in the second column. In the second row, the re are still some areas of 4 or more to be treated, so a second positioning of the leaves is required. In the second row, a second dose of 4 is delivered, leaving the residual shown in the second column of the second row of Fig 7. In the third row, the next lower power of 2, namely 2, is delivered. A value of 2 mus t be delivered again in the fourth row. The residual, however, is then unity or 0 at all locations. It takes three more rows to irradiate all the areas containing values of 1. This sequence was, in fact, shorter than the one-dimensional profile step-and-shoot results for this particular intensity pattern. The one-dimensional algorithm required 20 instances, whereas the areal algorithm required 14. This is the order of magnitude increase in efficiency that is expected by Xia and Verheyd 4

Intensity-Modulated Arc Therapy

Intensity-modulated arc therapy (IMAT) is a technique for delivering tomotherapy treatment plans. A tomotherapy treatment plan requires a two-dimensional intensity distribution at every degree-.(or every few degrees) of gantry angle within a range of gantry angles. In tomotherapy, these two-dimensional intensities are considered as concatenated one-dimensional intensity profiles and delivered slice-by-slice by rotat ing an intensity-modulated fan beam around the patient. With IMAT, each of these two-dimensional intensity distributions is considered as a super-

IMRT With Dynamic Mu#ileaf Collimators 55

Figure 6. The sweeping win- dows created by the coordi- nated leaf trajectories in Fig- ure 5. Each of the 10 fields represents one step followed by one shoot. Altogether the sequence is composed of 20 instances.

position of multiple uniform fields of different sizes and shapes. Instead of using a slit (or fan) beam to treat a single slice of the patient at a time, as in tomotherapy or other slice-based treatments , 95-97 1MAT uses MLC-shaped fields, which change shape during gantry rotation, to deliver the dose to the t rea tment target. An arbitrary intensity distribution

is delivered at each angle by employing multiple arcs. Because it combines spatial and temporal intensity modulation, the dose conformity is equivalent to that achievable with tomotherapy and other slice-based t rea tment techniques. Patient setup time is the same as conventional t reatments. An optimal t rea tment for most clinical sites requires fewer than five arc

56 Boyer and Yu

Table 1. Sequences Computed Using Step-and-Shoot Algorithm Versus Sequences Computed Using Dynamic Algorithm

Static Dynamic

FieM Time Time Angb~) Segmen~ MU (mi~ S~men~ MU (mi~

55 14 98 0.50 23 118 0.65 90 20 75 0.21 31 89 0.49

125 24 91 0.54 36 118 0.64 235 14 74 0.39 22 90 0.55 270 22 70 0.43 39 96 0.57 305 24 83 0.50 38 110 0.57

Totals 118 491 2.57 189 621 3.47

Abbreviat ion: MU, moto r units.

rotations, making EVIAT efficient as compared with conventional treatment techniques. The steps in- volved with IMAT include planning, intensity to arc conversion, MLC prescription, and delivery.

An optimized treatment plan, which uses many

-3 -2 -1 I 2 3

t5 4 5

12 * ' 5

-3 -2 -1 t 2 3

-3 -2 -1 1 2 3

12 ~ h l 3 s 2

-3 -2 -I 1 2 3

15 14 13 12

-3 -2 -t 1 2 3

t2 1 1 1

-3 -2 -1 1 2 3

15 14 13 12

-3 -2 -t 1 2 3

15 14 13 12

-3 -2 -1 1 2 3

15 14 13 t2

-3 -2 -1 1 2 3

t4 o

12 :?r :%~U~'~ 1

-3 -2 -1 I 2 3

t4 t3 s t2 N ~ ) 1 1 0

-3 -2 -1 1 2 3

15 t4 t3 t2

-3 -2 -1 1 2 3

t5 t4 13 t2

-3 -2 -1 1 2 3

15 14 t3 t2

-3 -2 -1 1 2 3

t5 14 13 t2

Figure 7. The delivery of the intensity pattern in Fig 3 by the areal step-and-shoot technique.

intensity-modulated beams at equally spaced beam angles, is first required. The two-dimensional intensit-/distributions at all the beam angles required by the treatment plan are considered as superpositions of multiple radiation fields of different sizes and shapes each with a uniform intensity. In the planning process, the number of intensity levels is specified as one of the optimization constraints (ie, for a five-level intensity distribution, the required intensities are given as multiples of 20%). Therefore, there is no quantization error when converting such intensity distributions into superimposed unmodulated fields. These uniform intensity beams that form the required two-dimensional intensity distribution at each beam angle are referred to as subfields for the given gantry angle. An arc is a sequence of field shapes formed by taking one subfield from each beam angle. One arc delivers one level of the intensities for all the beam angles. Multiple arcs are required to finish all the subfields at all the beam angles. As a result, the number of superimposing arcs required for a treatment depends on the maximal number of subfields required at a beam angle, which, in turn, depend on the number of discrete intensity levels and complexity of the required intensity distributions.

In converting the required beam intensities at all" beam angles to superpositions of subfields, one notes that the field shapes and the sequence of the shapes may have a large number of selections. Because of physical limitations of the MLC, the field shapes between two successive gantry angles must not be dramatically different. To ensure the smooth transition between two ad jacen tbeam orientations, a method used for decomposing the intensity distributions into multiple uniform intensity subfields is described as follows.

The two-dimensional intensity distributions at different gantry angles are first segmented into multiple one-dimensional intensity profiles each aligned with a pair of opposing MLC leaves. The leaf positions for each leaf pair in all the subfields that delivers a given beam intensity are then deduced from the one-dimensional intensity profile aligned with this leaf pair. It can be shown that, for an N-level intensity profile of only one peak, there-are (N!) 2 decomposition patterns. For the simple one-dimensional intensity distribution having three levels, there exist (3!) 2 = 36 different decomposition patterns. One can designate different decomposition patterns with a computer algorithm using the fact that each pair of left and right edges determines a leaf aperture. For efficient and complete decomposition, each

IMR T With Dynamic Mulgileaf Collimat~rs 57

edge must be used for leaf positioning once. By assigning indices to the edges of different intensity levels and permuting the indices exhaustively, all the (N!) 9 decomposition patterns can be generated.

The large number of possible decomposition patterns is important for the feasibility of IMAT. As the gantry is rotating around the patient and the radiation beam is on, it is important that the subfields of adjacent beam angles not require the MLC leaves to travel long distances. For arcs with similar field shapes at all angles, high dose rate and high speed of gantry rotation can be applied, resulting in less overall beam time. In the actual decomposition process, not all the decomposition patterns need to be compared. The translation routine compares the decomposition patterns of a given beam angle to the finalized decomposition pattern of the previous beam angle. Once a decomposition pattern is "found t o register with that of the previous angle with a spatial discrepancy less than a preset maximum, the translation routine accepts it and proceeds to the next beam angle. The decomposition process described here is based on a one-dimensional intensity profile, which is delivered with one pair of opposing leaves. As the profiles aligned with all the leaf pairs are decomposed, the decomposition patterns combined together form a stack of two-dimensional field shapes, or subfields.

With the decomposition algorithm described previously, the number of subfields required for delivering a one-dimensional intensity profile depends on the number of intensity levels and the complexity of the intensity profile. Specifically the number of subfields needed is the number of rising or declining edges in an intensity profile. For intensity profiles with only one peak, each intensity level has one rising edge, and the number of subfields needed is the same as the number of intensity levels. For beam profiles with multiple intensity peaks, or with Spatially dis- jointed beam intensities, more subfields are required.

Arcs are formed by picking one subfield from the stack of subfields at each beam angle in a top-down order. Once the decomposition patterns for all the beam angles are determined with consideration of all the physical constraints, the sequences of MLC leaf positions for all the arcs are then written in the dynamic NfLC prescription format required by the MLC controller for dynamic treatments. A percent- age of the total number of MUs is also assigned to each subfield. The entire MLC prescription is then

transferred to the MLC controller through a network link in the same way as for conventional static beams.

If the MLC controller and the linear accelerator are not integrated on one processing unit, the actions of both components must be synchronized properly for any dynamic treatments. To deliver IMAT treatments, the linear accelerator should be programmed to deliver conventional arc treatments and the MLC programmed to step from one subfield to the next automatically. Both the delivered MUs and the leaf stepping must be slaved to the gantHr rotation. For smooth gantry rotation, the dose rate must be main- tained at a constant based on the maximal leaf transition between angles used in the intensity decomposition process. When the delivered MUs are increasing, the gantry is rotating continuously, and mean- while the MLC is driving the leaves from one subfield shape to the next. If the delivered MUs and MLC leaf stepping are independently slaved to the gantry rotation, the MU information is not needed by the MLC controller. The gantry angle information, however, can be fed to the MLC controller as a redundant check.

In general, the speed of leaf motion is propor- tional to the length of leaf transition between the current position and next position subject to the lower and higher limits. No precise speed control, however, is applied to the leaves. Therefore although the field shapes must be exactly the same as prescribed at each beam angle, spaced every 5 ~ in this study, the shapes between two adjacent beam angles are not evenly interpolated. The adverse effect of this uneven interpolation of field shapes between two adjacent beam angles, if any, can be reduced by either introducing precise speed control to the leaves or spacing the beams with smaller angular intervals. The latter would have no significant impact on the beam delivery but would lengthen the time required by the treatment planning system to optimize the beam intensities.

The beam delivery mechanism has been tested by delivering various examples to phantoms. Computed tomography images of both the phantoms and actual patients were used by the Peacock (NOMOS Corpo- ration, Sewickley, PA) treatment planning system for inverse treatment planning. The phantoms were set up according to the treatment plan. Inside the phantom, films (XV2 Verification Film, Kodak, Roch- ester, NY) were sandwiched vertically in the plane of gantry rotation. Dynamic MLC prescriptions were loaded in the same manner as for static treatments. The linear accelerator was set as for conventional arc

58 Boyer and Yu

treatment. Once the radiation was started, the gantry started to rotate at a constant speed, and the MLC leaves were stepping through the prescribed field shapes.

One of the examples tested was a C-shaped target that partially wraps around a circular critical structure. A total of 55 10-MV x-ray beams spread between -135 ~ (225 ~ ) and 135 ~ gantry angles at 5 ~ intervals were used. Beam intensities were expressed as multiples of 20% (ie, the number of intensity levels was limited to 5). Calculated isodose contours normal- ized to the maximal dose were superimposed on the transverse slice of the treatment geometry. The inner and outer isodose contours on the C-shaped target were 90% and 80%. The inner and outer isodose contours on the circular critical structure are 10% and 20%.

The 55 two-dimensional intensity distributions were first decomposed into 13 subfields of unit intensity. Optimization was made to minimize leaf motion among adjacent fields at adjacent beam angles. The results were then written as 13 MLC field sequences corresponding to 13 arcs in the format required by the MLC controller. The length of the arcs varied between 25 ~ gantry rotation and 275 ~ gantry rotation. All arcs were delivered with 0.1 MUs per degree of gantry rotation. A total of 250 MUs were delivered with a beam time of approxi- mately 14.5 minutes.

The comparison of:{lie planned and delivered dose distributions demonstrated the feasibility of the new delivery method. As with sliced delivery schemes, the IMAT can deliver beams with both spatial and temporal intensity modulations. In comparison with the NOMOS (Sewickley, PA) Peacock delivery, IMAT has many advantages. It may be implemented on existing linear accelerators equipped with an MLC. Therefore it maintains the flexibility of a linear accelerator. Nontransaxial arc treatments can be achieved to a certain extent, and partial arc rotations are easily achievable. Because it does not collimate the beam into a slit, more of the target is in the beam during the delivery, maintaining a high efficiency in using the photons generated in the x-ray target. No additional patient transport mechanisms are required to move the patient from slice to slice. Eliminating the slicing also eliminates the problem of beam abutment between slices, and the potential cold and hot spots associated with the abutments. Theoretically, such abutment problems among slices would be much more severe if patient motion between treatment slices were considered. Finally,

because the intensity modulation for the NOMOS Peacock relies on a set of leaves to open or close the slit beam, the resolution of the beam intensities is the slit width by the leaf width. The resolution of the NOMOS Peacock is 1 • 1 cm. For IMAT treatments, the resolution is the width of the leaf in the leaf width direction (typically 1 cm) and continuous in the length direction of the leaves. The field aperture in the leaf width direction is ,.cgllimated by the backup jaws and is therefore continuous. If the inverse treatment plans are optimized for IMAT treatments, the beam intensities can be of higher resolution than that optimized for the NOMOS Peacock.

What makes IMAT more attractive is the fact that the number of arcs required for achieving the best dose conformity is relatively small. For a prostate case, reducing the number of intensity levels from 10 to 2 showed little degradation in dose conformity. Because some of the 72 two-dimensional intensity distributions have more than one peak, the plan requires three arcs (one full 360 ~ arc and two partial arcs) to deliver. For more complex cases, such as cancer of the nasopharynx, three intensity levels or five arcs are sufficient. The main reasons for not requiring a large number of intensity levels is the large number of beam orientations in an arc and the. quantization effects are largely eliminated in the optimization process when the number of intensity levels is set as one of the optimization constraints. The dose volume histograms or subsequently derived biological scores generally depend on the total number of strata, which is the product of the number of beams and the intensity levels within each beam. As the number of beams increases, the number of intensity levels required to obtain optimal dose distribution is reduced. Therefore a typical treatment can be delivered in 5 to 10 minutes, which can be reduced with modification of the linear accelerators and with improved algorithms for converting the intensity distributions into the arc sequences.

Conclusion

This article has covered the underlying principles of leaf-setting sequences but has not considered many of the practical implementation tSi~0blems, such as dealing with finite acceleration, the accuracy of digital and analogue controls, interleaf leakage, and the tongue-and-groove effect. 28 These problems are associated with the specifics of the implementation of the procedures for a given apparatus. Intensity modulation by MLCs is fairly well understood. Techniques

IMR T With Dynamic Multileaf Collimators 5 9

t h a t l end t h e m s e l v e s to a va r i e ty o f t echn ica l specifi-

ca t ions of var ious med ica l l i nea r acce le ra to r s sys tems

have b e e n developed. T h e clinical efficacy of t he

p r o c e d u r e s t h a t I M R T prov ides shou ld b e c o m e

c l ea r e r as the o u t c o m e s of cl inical i m p l e m e n t a t i o n s

a re ana lyzed in the fu ture .

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Intensity-modulated radiation therapy with dynamic multileaf collimators