Intensity-modulated radiotherapy by means of static tomotherapy: A ...

**Intensity**-**modulated** **radiotherapy** **by** **means** **of** **static** **tomotherapy**:

A planning and verification study

Mark Oldham and Steve Webb

Joint Department **of** Physics, Institute **of** Cancer Research and the Royal Marsden NHS Trust,

Downs Road, Sutton, Surrey, SM2 5PT, United Kingdom

Received 25 July 1996; accepted for publication 15 March 1997

There is currently much research interest in developing, evaluating, and verifying intensitymodulation

techniques. Of particular interest is how well the delivery **of** intensity-**modulated** pr**of**iles

can be simulated **by** planning algorithms, and how accurately these pr**of**iles can be delivered

given the specification constraints **of** linear accelerators. In this paper we present a planning and

verification study based on delivering radiation in ‘‘**static**-**tomotherapy**’’ mode via the NOMOS

MIMiC Multileaf intensity-modulation collimator, which sheds some light on these issues. An

inverse-planning algorithm was used to compute intensity-**modulated** pr**of**iles for a 9-coplanar-field

plan for a body phantom. The algorithm makes several approximations about the form **of** the

elementary fluence pr**of**ile through bixels during delivery. Specifically, it is independent **of** the state

**of** adjacent bixels i.e., open or closed and obeys the superposition principle. From the standpoint

**of** comparing the predicted versus the delivered dose, these assumptions were made irrelevant **by** a

final one-step forward dose calculation performed using the optimized intensity pr**of**iles. This forward

dose calculation took into account the penumbral characteristics **of** the delivery system **by**

decomposing the intensity pr**of**iles into the set **of** delivery components. Each component was assigned

the appropriate penumbral functions there**by** ensuring that the calculated dose distribution

closely predicted the delivered dose distribution. The nine intensity **modulated** fields were delivered

to a perspex phantom with the same geometry, containing a verification film. In general good

agreement was found between the predicted and the measured delivered dose distributions. All the

main features **of** the predicted dose distribution are seen in the delivered. The 90% isodoses were

consistently in spatial agreement to within 3 mm. At the 50% isodose level consistent spatial

agreement was again found to within 3 mm, the largest deviation being about 5 mm. The close

correspondence between the predicted and measured dose distribution demonstrates the potential **of**

the MIMiC delivery system. Our results indicate the level **of** dose conformation that is achievable

in practice and the accuracy **of** the dose computation algorithm. However, this study only concerned

delivery **of** radiation to a2cmthick slice, and the dose distribution was only verified in the central

plane **of** the phantom where the film was placed. We therefore cannot comment as yet on what

happens to the dose distribution away from the central film-plane. © 1997 American Association

**of** Physicists in Medicine. S0094-24059700506-3

Key words: intensity modulation, **radiotherapy**, conformal therapy, verification, **tomotherapy**, film

dosimetry

I. INTRODUCTION

New techniques to modulate the intensity **of** radiation in

external-beam **radiotherapy** enable much more precise tailoring

**of** the spatial distribution **of** the delivered high-dose region

to the shape **of** the tumor than can be obtained with

conventional therapy. Many physical methods have been

proposed that could achieve this modulation. The methods

differ in their complexity and in the hardware necessary to

deliver the radiation. All **of** these methods can be classified

into one **of** three groups, each group having as the common

denominator a type **of** hardware used to modulate the intensity

**of** radiation. These three hardware groups are a

multileaf-collimators, b **tomotherapy**-type slit collimators,

and c moving-bar collimators. In group a the intensity **of**

geometrically shaped radiation fields is **modulated** either **by**

dynamically moving the leaves **of** the MLC during irradiation,

or **by** multiple-**static** segmented irradiation. In group

b, a slit **of** radiation is rotated transaxially about the patient

with the long axis **of** the slit aligned transaxially. The radiation

along the slit is **modulated** **by** short vanes that move into

and out **of** the slit. This modulation can take place either with

continuous gantry rotation or with the gantry at a series **of**

fixed orientations. The latter we call **static**-**tomotherapy**. In

group c a small bar is moved across the field with varying

velocity during irradiation. All **of** these techniques aim to

improve on the use **of** compensators, the traditional way to

obtain intensity-**modulated** beams IMBs. 1

There is currently much interest in developing, evaluating,

and verifying all **of** the intensity-modulation techniques.

Several questions are **of** particular significance. These include:

1 How much **of** an improvement can intensity modulation

make to **radiotherapy** dose distributions? 2 What

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828 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 828

FIG. 2. The planning problem studied in this paper dimensions given in the

text. The PTV is the ‘‘bean-shaped’’ invaginated region resulting from the

removal **of** parts **of** two circles the OARs from an ellipse. The problem

represents a prostate PTV with bladder and rectum OARs. The ‘‘I values’’

are the importance-factors used in the inverse planning.

FIG. 1. A schematic illustration **of** the slit beam **of** the MIMiC and its bixels

in relation to the patient. Open bixels are shown as white spaces and closed

bixels as black spaces. The vanes **of** the MIMiC are not shown, but five **of**

the actuating mechanisms which can open or close the vanes are shown

schematically.

level **of** intensity modulation is optimal? 3 Where does the

trade-**of**f start to become unfavorable between increasingly

complex and expensive treatments and improved dose distributions?

And 4 which tumor types and disease sites will

the new techniques be most useful for? Two **of** the most

central questions are how well can the intensity-**modulated**

dose delivery be simulated with current planning algorithms,

and how accurately can an intensity-**modulated** plan be delivered

in practice given the specification constraints **of** linear

accelerators? In this paper we present a planning and

verification study, in the **static**-**tomotherapy** framework,

which sheds some light on the latter two issues. Investigating

the dosimetry **of** the MIMiC in **static** **tomotherapy** mode is

easier than for rotational **tomotherapy** due to the lack **of**

smearing **of** the dose distribution and issues **of** the stability

**of** MU delivery per degree. This study is therefore a necessary

first step in investigating the dosimetry **of** the MIMiC.

II. METHOD

In this paper we present a planning and verification study

based on delivering radiation in ‘‘**static**-**tomotherapy**’’ mode

via the NOMOS 2591 Wexford Bayne Road, Suite 315,

Sewickley, PA, 15143 MIMiC 2–7 Multileaf **Intensity**-

Modulation Collimator Fig. 1. The MIMiC device attaches

to the blocking tray **of** the linear accelerator and positional

adjustment screws and bolts enable the collimation slit to be

accurately aligned with the cross wires. The center **of** the

cross wires coincides with the center **of** the slit, the edges **of**

which are made parallel with the respective cross wire. The

intensity along the slit beam **of** the MIMiC can be **modulated**

**by** small absorbing vanes illustrated in Fig. 1 that move in

and out **of** the slit under computer control. The vanes are

arranged in two parallel banks, one superiorly and one inferiorly

to the slit. The MIMiC can be used in either rotational

mode, where the vanes move as the gantry rotates, or **static**

mode, where the vanes move but the gantry is fixed at some

orientation. The former is conventionally termed **tomotherapy**

and the latter we refer to as **static** **tomotherapy**.

The planning problem addressed is an idealized model **of**

the treatment **of** an invaginated prostate patient illustrated in

Fig. 2. The patient contor was assumed elliptical with major

and minor axes **of** lengths 29 and 25 cm, respectively. The

planning-target-volume PTV was part **of** an ellipse, major

and minor axes **of** 9 and 7 cm, the center **of** which was

**of**fset vertically below the center **of** the contour **by** 2 cm.

Two circular organs-at-risk OAR were located above and

below the PTV with radii 4 and 1.5 cm, respectively. The

centers **of** the OARs were positioned 5 cm above and 4 cm

below the center **of** the PTV, the latter being defined as the

isocenter. The PTV was the invaginated region created **by**

the subtraction **of** parts **of** the circular OARs from the ellipse.

A circular radius 7.25 cm region **of** sensitive tissue was

defined enclosing the PTV and both OARs as shown. The

axial thickness **of** the phantom was specified as extending for

12 transaxial slices each **of** thickness 1 mm, with no change

in the contours **of** any **of** the structures.

Fitting the high-dose region to such an invaginated PTV,

with directly abutting OARs constitutes a very difficult planning

problem, and one that would not be achievable with

conventional **radiotherapy** techniques. 8

A. Inverse planning and forward dose calculation **by**

components

A relative dose prescription **of** 1.0 in the PTV, 0.1 in the

two small OARs and 0.3 in the circumscribing sensitive tissue,

was specified in the planning problem **of** Fig. 2 see

Appendix B for a discussion **of** these units. Then a plan

consisting **of** nine equi-spaced co-planar fixed slit fields was

designed, with gantry angles **of** 0°, 40°, 80°, 120°, 160°,

200°, 240°, 280°, and 320°. A set **of** intensity-**modulated**

beams was computed **by** solving the inverse problem **by**

least-squares iteration. 9 The planning s**of**tware was written

in-house to exactly simulate the geometry **of** the MIMiC, and

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829 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 829

the inverse algorithm assumed an elemental fluence pr**of**ile

for each bixel which incorporated the penumbral effects **of**

the surrounding closed vanes. Bixel is the term used to refer

to the cross-sectional area **of** a vane **of** the MIMiC through

which radiation can pass if the vane is open. The planning

algorithm is essentially similar to that used in the PEACOCK

planning system. It was written to provide the potential to

independently study effects such as bixel pr**of**ile variation,

inhomogeneity, and gantry sag. In this study the elemental

fluence pr**of**ile was found **by** fitting the measured dose data,

delivered **by** a single open vane at 10 cm depth in water, to a

mathematical function which obeys the superposition principle.

This function is a convolution **of** a double exponential

with a rect function equal to the bixel size. 10,11 The resulting

pr**of**ile, which we call the ‘‘stretched-fit’’ pr**of**ile, has the

property that when the fluence pr**of**iles **of** adjacent open bixels

are combined corresponding to two bixels being open at

the same time the resulting fluence pr**of**ile is flat across the

two bixels as it must be in reality. The terminology stretched

fit signifies that the fitting procedure actually widens the elementary

fluence pr**of**ile since superposition **of** the measured

pr**of**iles leads to regions **of** low fluence between bixels. This

fitting procedure is discussed in detail in an earlier report. 11

The dose computation grid was set at 1 mm resolution, with

dimensions**of**300 300 12.

Once the intensity-**modulated** pr**of**iles were determined

for the nine **static** ports, a forward dose calculation was performed

to predict the delivered dose taking into account the

characteristics **of** the delivery method. This is a crucial point

we wish to elaborate on. The key point is that during planning

the elemental fluence pr**of**ile used for each bixel assumes

that the neighboring bixels are closed. This is necessary

as a priori information **of** the intensity-**modulated**

pr**of**ile is not available. When it comes to the delivery **of** the

fluence through a bixel however, the neighboring bixels may

well be either open, closed, or open for part **of** the irradiation.

In essence, the penumbral effects assumed at the planning

stage do not reflect what happens during the delivery.

To circumvent this discrepancy, the first step **of** the forward

dose calculation is the decomposition **of** the intensity**modulated**

pr**of**iles into their respective components. 11 Each

component is a combination **of** open and closed vanes

through which an amount **of** radiation is delivered. The delivery

**of** any intensity-**modulated** pr**of**ile must, in practice,

adopt this decomposition concept. The alternative is to deliver

each bixel independently, with all other bixels closed,

which would be far too time consuming and give too high a

leakage dose. As with the planning s**of**tware, this forward

dose calculation was written in-house to allow independent

study **of** effects such as the penumbral characteristics during

delivery. The NOMOS planning system PEACOCK does not

use our component delivery method to model the penumbral

effects during delivery.

The forward dose calculation used in this study first computed

the component bixel patterns for each gantry angle

Appendix A. Then the appropriate fluence pr**of**iles were

assigned to each component. Between adjacent open bixels

the stretched-fit pr**of**ile was assigned ensuring a flat pr**of**ile.

FIG. 3. The variation in relative-output-factor ROF between different bixels

along the MIMiC for the PHILIPS SL 75/5. ROF’s are given in percentages,

defined with respect to a 10 10 cm 2 open field measured at the dose

maximum.

Between an open and closed bixel, the appropriate measured

penumbral pr**of**ile was assumed. By accurately modeling

how the MIMiC delivers an intensity-**modulated** pr**of**ile via

components, this forward dose calculation takes account **of**

the penumbral characteristics **of** the delivery system. Furthermore,

the variation in relative-output-factor ROF for

bixels at different positions in the slit was incorporated **by**

assigning each bixel a unique ROF obtained from fitting all

bixels to the measured data for the open slit field Fig. 3. It

is noted that only the centrally positioned bixels numbers

6–15 have a significant amount **of** radiation passing through

them in this study. An example **of** an intensity-**modulated**

pr**of**ile and its corresponding delivery components are given

in Fig. 4 and Table I. Note that this is only one **of** many

possible decomposition patterns. 12 However, as the MIMiC

was operated **by** initially opening as many leaves as possible

FIG. 4. The intensity-**modulated** pr**of**ile found **by** inverse-planning for the

field at gantry angle 0°.

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830 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 830

TABLE I. This table illustrates the decomposed components, and the number

**of** monitor units delivered to each component, **of** the intensity-**modulated**

pr**of**ile **of** Fig. 4.

Component Open bixels Monitor units

1 6–8, 12–15 1

2 6–8, 13–15 6

3 6–7, 14–15 6

4 6–7, 14 1

for a pr**of**ile and gradually shutting them as required, this is

the actual decomposition pattern delivered **by** the MIMiC.

The intensity pr**of**iles found **by** inverse planning for all nine

gantry angles are shown in Fig. 5. The forward dose calculation

was performed with the IMB pr**of**iles discretized to the

nearest integer MU since fractions **of** a MU cannot be delivered

in practice. The absolute values were chosen to give

0.82 Gy to the maximum dose point Appendix B.

B. Delivery and film measurement

The intensity pr**of**iles **of** the nine fields Fig. 5 were delivered

to a perspex phantom with the geometry given in Fig.

2. The perspex phantom was constructed in two parts, each

part having the dimensions **of** Fig. 2 with a thickness **of** 2

cm. These two parts were then placed back-to-back on the

treatment couch sandwiching a piece **of** Kodak X-OMAT V

standard verification film between them. For each component

**of** each field, the vane configuration was set manually via

interaction with the touch-screen computer that is attached to

the MIMiC. The same IMB was fed into each bank at any

one orientation, and the MIMiC was attached to a PHILIPS

SL 75/5 accelerator. The appropriate number **of** monitor

units **of** dose was then delivered through that component’s

vane configuration. This procedure necessitated that an operator

entered the treatment room to set the MIMiC for each

configuration. In all there were 62 component-vane configurations

set making the total treatment time completely unfeasible

for clinical routine about 2 h but acceptable for a

one-**of**f experimental demonstration **of** principle. The manual

FIG. 5. The intensity pr**of**iles found **by** inverse-planning for the MIMiC fields at gantry angles 0°, 40°, 80°, 120°, 160°, 200°, 240°, 280°, and 320°. The

pr**of**iles were discretized to the nearest MU.

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831 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 831

setting **of** vane configurations was necessary as the control

s**of**tware to automatically deliver components in this way is

not yet available. The functionality to automatically deliver

a sequence **of** component vane configurations, without the

need for an operator to enter the treatment room, does exist if

the intensity-**modulated** pr**of**ile to be delivered has been produced

**by** the PEACOCK planning s**of**tware. 6,13

At delivery the perspex phantom was positioned vertically

on the couch so that the flat plane **of** the phantom was in the

plane **of** gantry rotation. The couch was then adjusted so that

the plane **of** the verification film sandwiched between the

two halves **of** the phantom coincided with the AB cross wire.

The film was thus positioned in the same plane as the source,

and in the middle **of** the slit **of** radiation defined **by** the two

banks **of** the MIMiC. During delivery, both banks **of** bixels

were treated identically, so that, in effect, the nine intensity**modulated**

fields were delivered to a2cmtransaxial slice **of**

the phantom. The verification film was located centrally in

this 2 cm slice.

The complex nature **of** the above nine field irradiation

made an accurate comparison **of** the absolute predicted and

measured dosimetry difficult. A second irradiation experiment

was therefore performed to verify the absolute dosimetry

**of** the forward dose calculation for the case **of** a single

intensity **modulated** field: That at gantry angle zero Fig. 4

and Table I. In this simpler problem the confusing effects **of**

dose smearing from multiple-fields, gantry sag, flatness, and

output variation with gantry angle etc., are reduced. The

number **of** monitor units in Table I were increased **by** a factor

**of** 3 for this irradiation to give an appropriate dose to the

film in the absence **of** the other eight beams. A new high

performance verification film was used which is reported 14 to

be highly linear between 0–0.5 Gy, to have negligible energy

response, and to have a 2% inter and intrafilm consistency.

A further advantage **of** this film is that it is available in

vacuum-sealed water-pro**of** packaging removing problems

associated with air spaces trapped in the film packaging and

enabling depth-dose measurements in water. Our measurements

confirm the superior performance **of** this film calibration

curve is shown in Fig. 6a, and a comparison **of** the

depth-dose curve in water measured **by** film and ion chamber

in Fig. 6b, however we observed saturation at the much

lower dose value **of** about 0.6 Gy compared to the reported

0.9 Gy. 14 Both the CEA and Kodak film sensitivity were

greater when the film was oriented perpendicular to the incoming

radiation Fig. 6a. In both experiments the film

was actually oriented parallel to the incoming radiation and

so the parallel orientation calibration curves were used to

convert from optical density to dose. It is clear from Fig. 6b

that the sensitivity **of** both types **of** film remains independent

**of** any spectral hardening with depth. It was not feasible to

use the CEA film for the nine field irradiation experiment

because its low-dose saturation property would necessitate

delivering less MU for each field and much **of** the fine detail

would have been lost.

FIG. 6. a Calibration curves for the CEA dotted lines and Kodak

X-OMAT V solid lines film. The two calibration curves for each film

correspond to whether the film is perpendicular or parallel to incoming

radiation. Radiation sensitivity is higher for perpendicularly oriented film in

both cases. b Comparison **of** depth-dose measurements in water taken with

CEA film triangles, Kodak X-OMAT V film stars and an ion chamber

squares. The data were normalized at 5 cm depth. The close agreement

indicates the negligible energy response **of** both the CEA and Kodak film.

III. RESULTS

The measured and predicted absolute isodose lines for the

single field irradiation are shown in Fig. 7. Predicted isodoses

were found **by** interpolation from dose points on a 2

mm grid spacing. Note—As the distribution was only computed

for the region inside the circular outer OAR **of** Fig. 2,

the predicted isodoses do not extend to the full extent **of** the

measured. Excellent agreement is observed between the film

and the forward dose calculation prediction, although the effect

**of** the increased spatial resolution **of** the film is visible in

the regions **of** high dose gradient at the edges. The close

agreement between measurement and prediction indicates

that the component delivery CD forward dose calculation

model is accurate to within a few percent. Use **of** the new

high performance CEA film enabled a more accurate measurement

than would have been possible with conventional

verification film.

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832 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 832

FIG. 7. Comparison **of** predicted dotted lines with measured solid lines

absolute isodose lines cGy for the single intensity **modulated** field irradiation.

The predicted dose distribution corresponding to the nine

intensity-**modulated** fields as found **by** the forward dose calculation

step outlined in Sec. II A is shown in Fig. 8a.

Isodoses, interpolated from dose points on a2mmgrid spacing,

are shown after the distribution has been normalized to

the maximum dose in the plane. As the distribution was only

computed for the region inside the circular outer OAR **of**

Fig. 2, the very low isodoses follow this OAR at the edges.

In reality the isodoses will not assume this circularity at the

edge. At delivery, Fig. 5 shows that a total **of** almost 200

monitor units were delivered to the perspex phantom via the

62 component vane configurations. This arrangement led to a

maximum dose in the PTV as predicted **by** the planning s**of**tware

**of** 0.82 Gy Appendix B. On completion **of** the delivery,

the film was developed and the delivered dose distribution

was scanned Fig. 8b via an optical densitometer

Wellhöffer WP102. The scan performed was a 2D net scan

with each line **of** the scan containing 16 values per mm along

its length, and with line spacing **of** 0.5 cm. The 2D netscan

lines were performed in both the x and y directions. Conversion

from optical density values to dose values was achieved

using a calibration curve obtained from irradiations **of** other

verification films in the same pack.

The predicted and measured dose distributions Figs. 8a

and 8b were compared **by** photocopying the predicted distribution

onto an OHP transparency so that it could be overlaid

on top **of** the measured distribution. The general agreement

between the two dose distributions is very good. The

90% isodose line **of** the delivered distribution clearly shows

two concavities where the OARs are adjacent to the PTV.

FIG. 8. Isodoses **of** the computer-calculated and film-measured dose distributions.

Isodose lines on both plots are starting from outter lines and moving

inwards 30%, 40%, 50%, 60%, 70%, 75%, 80%, 85%, 90%, 95%,

100% **of** the maximum dose. A scale-drawing **of** the PTV and OAR’s has

been superimposed onto the isodose lines. a The predicted dose distribution

as found **by** the forward dose calculation which takes into account the

penumbral characteristics **of** the delivery technique. b The delivered dose

distribution as measured **by** verification film.

Lower isodose lines also clearly show that the dose in the

OARs has been kept relatively very low compared to the

dose in the PTV. All the main features **of** the predicted dose

distribution are seen in the delivered except for the artificial

circularity **of** low-dose isodoses at the edges. The 90% isodoses

are consistently in spatial agreement to within 3 mm

except for in the lower right hand region where the predicted

isodose makes a small kink into the body **of** the PTV. At the

50% isodose level consistent spatial agreement is again

found to within 3 mm, the largest deviation being about 5

mm. Although the general shape **of** the distributions agree

well, the delivered distribution is asymmetrically hotter on

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833 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 833

FIG. 9. Plot **of** the relative dose-per-MU arbitrary units against the number

**of** MU delivered for Gantry settings **of** 0° and 90°.

the left hand side. The reason for this asymmetry is probably

due to any combination **of** a small air spaces in the film, b

misalignment **of** the film in the narrow 2 cm treatment plane,

c gantry sag, d the asymmetric interference **of** a metal

tubular bar on the underside **of** the couch that will have

slightly attenuated the two most posterior fields, and e nonlinearity

**of** dose per MU for small MU see below.

Due to the limitations **of** using film to measure absolute

dosimetry, this study was primarily concerned with investigating

the relative dosimetric agreement between the planned

and delivered distributions. Errors in excess **of** 10% in the

absolute measurement may be introduced **by** any **of** (a – e)

above together with uncertainty in the film calibration.

Against this background **of** uncertainty we measured a maximum

dose on the film **of** (0.97 0.08) Gy compared to the

predicted (0.85 0.04) Gy the uncertainty quoted here is

that **of** the measurement **of** the ROF for a single bixel—see

Eq. A9. One reason for this underestimate in the predicted

dose can be traced to the nonlinearity **of** dose per MU for

small MU deliveries Fig. 9. Figure 9 shows that in the MU

region **of** the majority **of** the component deliveries in the

plan out **of** 62 components, 49 were 6 MU and 38 were

3MUthe dose per MU was 4%–7% higher than that used

in the dose calculation algorithm.

IV. DISCUSSION AND CONCLUSIONS

The first part **of** this study was a s**of**tware simulation **of** an

intensity-**modulated** **radiotherapy** treatment. An inverse optimization

algorithm was used to compute intensity-**modulated**

pr**of**iles for the nine fields **of** the plan. This algorithm makes

several unrealistic assumptions about the form **of** the elementary

fluence pr**of**ile through bixels during delivery.

From the standpoint **of** comparing the predicted versus the

delivered dose, however, these assumptions were made irrelevant

**by** the final one-step forward dose calculation performed

using the optimized intensity-**modulated** pr**of**iles.

This forward dose calculation step took into account the penumbral

characteristics **of** the MIMiC delivery system, attached

to a PHILIPS SL75/5 accelerator, **by** decomposing

the intensity pr**of**iles into the delivery components. Each

component was assigned the appropriate penumbral functions

there**by** ensuring that the calculated dose distribution

should predict as closely as possible the delivered distribution.

The second part **of** the study concerned the delivery **of**

the intensity-**modulated** plan, its measurement, and the comparison

**of** the delivered dose with the predicted. Both the

inverse planning and the forward dose calculation delivery

model includes ‘‘out-**of**-line-**of**-sight’’ scatter and therefore

our study does not suffer from the problems highlighted **by**

Mohan et al. 15

The major uncertainties in the simulation are: a How

well the inverse-planning optimization algorithm performed

i.e., how optimal are the intensity-**modulated** pr**of**iles predicted

for the nine fields, and b how well the forward dose

calculation has modeled the actual delivered dose. In this

paper we are not concerned so much with a as we take as

our starting assumption that the optimized intensity**modulated**

pr**of**iles found **by** the inverse-planning algorithm

are near optimal. Note we use ‘‘optimal’’ here to mean that

set **of** intensity pr**of**iles that produce a dose distribution that

most closely matches the prescription. This assumption is

not entirely valid because the stretched-fit elementary fluence

pr**of**ile assumed at the planning stage is a fit **of** the measured

pr**of**ile to a function obeying the superposition principle. This

**means** that although the fluence pr**of**ile across adjacent open

bixels **of** the same intensity is accurately modeled, for adjacent

bixels with nonidentical intensities the penumbral effects

are only approximated. Intuitively one would expect

this effect to be small, a conclusion which is supported **by**

the fact that the planned dose distribution Fig. 8a appears

so good in terms **of** homogeneity **of** dose to the PTV while

sparing the OARs.

Uncertainties and omissions in the forward dose calculation

compared with the real delivery situation are i mechanical

factors such as gantry and collimator sag, ii the

uncertainty on the ROF parameter for a single 1 cm 2 bixel

Eq. A9, iii the nonlinearity **of** dose per monitor unit for

small monitor unit doses, and iv errors in positional setup

**of** the phantom. At this stage we are not able to comment

further on the implications or magnitudes **of** these effects. In

future work we intend to expand the planning s**of**tware so

that it can investigate and predict their magnitude.

This paper is more concerned with b above i.e., establishing

how well the forward dose calculation has modeled

the actual delivered dose. We are also interested in investigating

the feasibility **of** the delivery method, and establishing

the level **of** dose conformation achievable with the MIMiC in

**static** **tomotherapy**. The close agreement between the predicted

and measured absolute isodose lines in the single field

experiment **of** Fig. 7 indicate the high accuracy **of** our CD

mode forward dose calculation. 11 The close correspondence

between the predicted and measured dose distribution,

shown in Figs. 8a and 8b, demonstrate the potential **of** the

MIMiC delivery system. These figures indicate the level **of**

dose conformation that is achievable in practice and the ac-

Medical Physics, Vol. 24, No. 6, June 1997

834 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 834

curacy **of** the dose-computation algorithm. It is pointed out

however, that this study only concerned delivery **of** radiation

toa2cmthick slice, and the dose distribution was only

verified in the central plane where the film was placed. We

therefore cannot comment as yet on what happens to the

dose distribution away from the mid plane. A further important

question-mark hangs over the significance **of** the

matchline problem. The latter concerns the situation where it

is necessary to index the couch in order to treat a PTV that

extends outside **of** the 2 cm delivery slice. To investigate

these areas a full 3D map **of** the delivered dose is required

such as could be obtained **by** gel dosimetry.

ACKNOWLEDGMENTS

We are very grateful to the NOMOS corporation for the

loan **of** a MIMiC and for the help given during installation

and commissioning. In particular to Dr. Mark Carol, Dr.

Alan Bleier, and Dr. Alexis Kania. Dr. James Bedford ICR

gave timely help with the delivery. Thanks also to Dr. Philip

Evans, Dr. Dave Convery, Pr**of**essor W. Swindell, Dr. Alan

Nahum, Mr. Jim Warrington, Mr. Glyn Shentall, Mr. Carl

Rowbottom, and Ms. Vibeke Hansen, **of** ICR/RMNHST for

discussions and pro**of**reading.

APPENDIX A: FORWARD DOSE CALCULATION BY

COMPONENT DELIVERY

The purpose **of** this Appendix is to explain in more detail

the principle **of** dose computation **by** component delivery

CD as introduced **by** Webb and Oldham 1996.

At the inverse-planning stage **of** determining the set **of**

IMBs, the delivery **of** radiation through any one bixel is considered

independent **of** the state **of** opening or closing **of**

adjoining bixels so-called ‘‘independent-vane IV model’’

since there is no other option. Each ith bixel delivers an

elemental dose distribution j f p

i to the jth dose point D j

weighted **by** its weight w i and the resulting dose distribution

is simply the superposition **of** all independent contributions.

The superscript P distinguishes from the corresponding

quantity at the delivery stage. That is,

N

D j C

i1

jf i P •w i ,

A1

FIG. 10. A beam’s-eye-view illustration **of** the principle **of** component delivery

CD with two banks **of** bixels. Consider the delivery **of** the radiation

through the superior bixel whose intensity is B. This bixel is flanked inferiorly

**by** a bixel whose intensity is B I and flanked in the same bank **by** a

right bixel with intensity B R and a left bixel with intensity B L . When the

four intensities are ranked as shown, the delivery requires the three separate

components shown, each with different components **of** intensity arrowed

and different wall conditions. Note ‘‘right’’ and ‘‘left’’ refer to the beam’seye-view

where converts from dimensionless bixel weight to bixel

MU, and C converts from MU to dose in Gy see Appendix

B.

However, at the treatment delivery stage, while the radiation

through a particular bixel is being delivered, the state **of**

opening and closing **of** adjacent bixels will change, since it is

this change which characterizes the intensity modulation.

Consequently the bixel will experience changes in the state

**of** its collimation. For example, if all surrounding bixels are

closed, the bixel has four lead ‘‘walls’’ surrounding it and a

corresponding penumbra. However if one or more adjacent

bixels opens, one or more walls disappears, changing the

state **of** collimation.

To accommodate this a forward dose calculation, subsequent

to inverse planning, was performed in ‘‘componentdelivery

CD mode’’. The delivery through any one bixel i

was broken down into Q i components such that the component

intensities w i,q sum to the total bixel intensity w i , but

the collimation, fixed for each component, changes between

components. Thus the delivered dose distribution becomes

N

D j C

i1

Q i

q1

jf D i,q •w i,q ,

A2

where the quantity j f D

i,q is the dimensionless fractional contribution

from the qth component **of** the ith bixel to the jth

dose point and the superscript D distinguishes this from the

corresponding quantity j f p i at the planning stage. The component

‘‘wall conditions’’ or penumbrae are embodied in

jf D i,q . This principle is illustrated in Fig. 10.

It should be noted that for any particular IMB, quantised

into L discrete intensity levels, there are L! 2 entirely equivalent

possible decompositions **of** the pr**of**ile Yu et al. 1995.

The one illustrated in Table I is just one convenient decomposition.

It is not the same decomposition pattern as the forward

dose calculation in CD mode described above, which

was carried out bixel-**by**-bixel. Provided the accelerator output

is linear with increasing MU, the two are equivalent.

However nonlinearities in accelerator output remove this

Medical Physics, Vol. 24, No. 6, June 1997

835 M. Oldham and S. Webb: **Intensity**-**modulated** **radiotherapy** 835

equivalence and are a possible source **of** comparative error.

The code to make CD calculations is not set up to model this

problem.

APPENDIX B: CALIBRATION AND

DISCRETIZATION OF IMB SETS

Inverse planning creates the bixel intensities or weights

in dimensionless units but with meaningful relative values

such that, when the radiation through the bixels is delivered,

the dimensionless dose distribution created matches the dimensionless

prescription as closely as possible.

The purpose **of** this Appendix is to explain how the bixel

intensities in the IMB sets were determined in units **of** MU.

Let there be N bixels, labeled **by** i with w i the weight **of**

the ith bixel determined at the inverse-planning stage and

M i the corresponding value in MU. Let the corresponding

component weights be w i,q and M i,q see Appendix A

where, with the ith bixel delivered in Q i components

w i

q1

M i

q1

Q i

w i,q , B1

Q i

M i,q . B2

Let the dose in Gy at the jth dosepoint be D j and the maximum

dose in the plan be (D j ) max . Let j f D

i,q be the dimensionless

fractional contribution from the qth component **of** the

ith bixel to the jth dosepoint. The superscript D distinguishes

this from the corresponding quantity j f P i at the planning

stage—see Appendix A. Let convert from dimensionless

bixel weight to bixel MU. Let C convert from MU

in beam space to dose in Gy in dose space C was determined

**by** definition and experiment—see later.

Then for the ith bixel, the dose to the jth dose point is

Q i

D j C jf D i,q •M i,q .

B3

q1

The total dose to the jth dose point from all N bixels is

N

D j C

i1

By definition

Q i

q1

M i,q w i,q .

jf D i,q •M i,q .

So, combining Eqs. B4 and B5

N

D j C

i1

Q i

q1

jf D i,q •w i,q .

The maximum dose in the plan is

D j max C

N

i1

Q i

q1

B4

B5

B6

jf D i,q •w i,q . B7

max

Inverting Eq. B7 gives the conversion factor

N

Q i

D j max /C

i1

q1 jf D i,q •w i,q . B8

max

Radiotherapy machines which deliver simple open fields are

calibrated and setup so that, **by** definition, 100 MUs gives a

dose **of** 1 Gy to the maximum **of** the depth-dose curve for a

field **of** size (10 10) cm 2 where, C 0.01 Gy MU 1 . For

the MIMiC, however, we measured the relative output factor

ROF, determining that, for a single open bixel, 100 MU

delivered a dose **of** 0.822 Gy, where**by**, from Eq. B3 with

Q i 1 and j f D

i,q 1, C 8.22 10 3 Gy MU 1 . In inverse

planning the dose distribution was normalized so

N

i1

Q i

q1

jf D i,q •w i,q 1.0.

max

It was decided that, in order to arrange that the dose distribution

fell on the linear part **of** the film response curve

(D j ) max was set to 0.822 Gy in the central plane **of** one leaf

bank, where**by** from Eq. B8, 100.

Thus the weights w i and their components w i,q determined

**by** inverse planning were multiplied **by** 100 Eq. B5

to arrive at the bixel intensities M i and their components

M i,q in MU. The IMB sets were then discretized so each

bixel intensity was at the nearest integer number **of** MUs

since the accelerator can only deliver integer numbers **of**

MUs. In passing we may note that, from Eqs. B6 and B7

isodoses in the plan are defined such that the pth isodose,

expressed as a fraction, is

D j

p

D j max

N

i1

Q i

q1

N

jf D i,q •w i,q

i1

Q i

q1

jf D i,q •w i,q , B9

max

and an alternative, but equivalent, definition **of** normalizing

to the dose (D j ) max at the isocenter, is

N

D j iso /C

i1

Q i

q1

jf D i,q •w i,q . B10

iso

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