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

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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 profiles

can be simulated by planning algorithms, and how accurately these profiles 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 profiles for a 9-coplanar-field

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

elementary fluence profile 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 profiles. This forward

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

decomposing the intensity profiles into the set of delivery components. Each component was assigned

the appropriate penumbral functions thereby 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-off 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

offset 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 software 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 profile

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 profile variation,

inhomogeneity, and gantry sag. In this study the elemental

fluence profile 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

profile, which we call the ‘‘stretched-fit’’ profile, has the

property that when the fluence profiles of adjacent open bixels

are combined corresponding to two bixels being open at

the same time the resulting fluence profile 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 profile since superposition of the measured

profiles 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

dimensionsof300 300 12.

Once the intensity-modulated profiles 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 profile used for each bixel assumes

that the neighboring bixels are closed. This is necessary

as a priori information of the intensity-modulated

profile 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 intensitymodulated

profiles 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 profile 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 software, 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 profiles were

assigned to each component. Between adjacent open bixels

the stretched-fit profile was assigned ensuring a flat profile.

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 profile was assumed. By accurately modeling

how the MIMiC delivers an intensity-modulated profile 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

profile 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 profile 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

profile 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 profile and gradually shutting them as required, this is

the actual decomposition pattern delivered by the MIMiC.

The intensity profiles found by inverse planning for all nine

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

was performed with the IMB profiles 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 profiles 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-off experimental demonstration of principle. The manual

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

profiles 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

software 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 profile to be delivered has been produced

by the PEACOCK planning software. 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 intensitymodulated

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-proof 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 software

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 software simulation of an

intensity-modulated radiotherapy treatment. An inverse optimization

algorithm was used to compute intensity-modulated

profiles for the nine fields of the plan. This algorithm makes

several unrealistic assumptions about the form of the elementary

fluence profile 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 profiles.

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 profiles into the delivery components. Each

component was assigned the appropriate penumbral functions

thereby 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 profiles 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 intensitymodulated

profiles found by the inverse-planning algorithm

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

set of intensity profiles that produce a dose distribution that

most closely matches the prescription. This assumption is

not entirely valid because the stretched-fit elementary fluence

profile assumed at the planning stage is a fit of the measured

profile to a function obeying the superposition principle. This

means that although the fluence profile 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 software 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-

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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, Professor W. Swindell, Dr. Alan

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

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

discussions and proofreading.

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 profile 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, whereby, 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, whereby 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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