The IMRT information process—mastering the degrees of freedom in external beam therapy

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INSTITUTE OF PHYSICS PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 51 (2006) R381–R402 doi:10.1088/0031-9155/51/13/R22

REVIEW

The IMRT information process—mastering thedegrees of freedom in external beam therapy

Anders Ahnesjo1,2, Bjorn Hårdemark3, Ulf Isacsson1

and Anders Montelius1

1 Department of Oncology, Radiology and Clinical Immunology, Uppsala University,Akademiska Sjukhuset, SE-751 85 Uppsala, Sweden2 Nucletron Scandinavia AB, Box 1704, SE-751 47 Uppsala, Sweden3 RaySearch Laboratories AB, Sveavagen 25, 111 34 Stockholm, Sweden

E-mail: anders.ahnesjo@onkologi.uu.se

Received 6 February 2006, in final form 27 March 2006Published 20 June 2006Online at stacks.iop.org/PMB/51/R381

AbstractThe techniques and procedures for intensity-modulated radiation therapy(IMRT) are reviewed in the context of the information process central totreatment planning and delivery of IMRT. A presentation is given of theevolution of the information based radiotherapy workflow and dose deliverytechniques, as well as the volume and planning concepts for relating the doseinformation to image based patient representations. The formulation of thedose shaping process as an optimization problem is described. The differentsteps in the calculation flow for determination of machine parameters for dosedelivery are described starting from the formulation of optimization objectivesover dose calculation to optimization procedures. Finally, the main elements ofthe quality assurance procedure necessary for implementing IMRT clinicallyare reviewed.

Contents

1. Introduction 3822. Evolution of the information driven radiotherapy workflow 382

2.1. From simulators to treatment planning computers 3822.2. Algorithm development 383

3. Treatment delivery techniques 3843.1. Tomotherapy 3843.2. Cone beam IMRT 3853.3. Other IMRT techniques 3853.4. Positioning and compensation for organ motion 386

0031-9155/06/130381+22$30.00 © 2006 IOP Publishing Ltd Printed in the UK R381

R382 Review

4. Handling dose distributions in anatomical space 3864.1. Anatomical volumes for treatment planning 3874.2. Treatment plan quality measures 389

5. From dose sculpturing to machine settings 3905.1. Optimization variables 3905.2. Fluence modelling and dose calculations 3915.3. Optimization goals 3935.4. Optimization algorithms 3945.5. Leaf sequencing for MLC dose delivery 395

6. Quality assurance of the IMRT process 3956.1. Commissioning and testing of the treatment planning and delivery systems 3966.2. Routine QA of the delivery system 3966.3. Patient-specific QA 396

7. Conclusions and outlook 397References 397Biography 402

1. Introduction

A long-standing key issue for development of radiotherapy technology has been to providemeans to concentrate the radiation dose to the tumour while sparing dose burdens to normaltissues. IMRT, or intensity-modulated radiation therapy, is the result of a long evolutionwhere several technological achievements combine to take this final step in providing dosedistributions, now about to approach the physical limits for photon beam dose delivery. Theevolutionary aspect is illustrated by the fact that no one is actually credited with coining theterm ‘IMRT’. The acronym is now well established, although it has come to carry the incorrectphysical term ‘intensity’ instead of ‘fluence’.

The IMRT planning and delivery technique offers many degrees of freedom to shape dosedistributions for photon beam irradiation. These possibilities now give incentives to improvethe control over other parts of the radiotherapy process, from tumour characterization overimage based localization to more detailed treatment reporting and patient follow-up. At allstages, relevant computer based representations of the patient make information technology acentral aspect for inventions and improvements of the radiotherapy process.

IMRT has had its historical forerunners, and has been reviewed several times from differentaspects. The present review sets its perspective from a treatment planning point of view, with anemphasis on the concepts used to formulate and process the information driven radiotherapyworkflow governing IMRT. With respect to IMRT in general, there is now a large set ofpublications that have followed the pioneering works in the 1980s and early 1990s. There areseveral in depth reviews; see, e.g., Webb (2003, 2004) for a physics background, Galvin et al(2004) for a clinical process guideline, or Guerrero Urbano and Nutting (2004a, 2004b) for asummary of published data of clinical results. A historical review has been included in Purdyet al (2001).

2. Evolution of the information driven radiotherapy workflow

2.1. From simulators to treatment planning computers

The clinical introduction of ‘high energy’ photon radiation from isotope (i.e. 60Co) machinesand bremsstrahlung from betatrons and linear accelerators in the 1950s led to radiotherapy

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workflows where most of the parameters for treatment delivery were determined by means ofa radiotherapy simulator. With these one could take x-ray projective images of the patient tocheck beam angles, their (rectangular) field size and blocking to spare critical organs by meansof bone landmarks. The homogeneity of the dose distribution was tuned by use of treatmentplanning systems providing dose calculations in a two-dimensional (2D) cross section of thepatient. In these systems the patient individual shape was typically represented by manuallydrawn contours, supported by direct measurements with flexible lead rulers, or similar devices.The clinical availability of CT images in the early 1980s provided a high-tech replacementof the rulers and greatly improved the anatomy information. The vision of what later was tobe known as three-dimensional (3D) conformal radiotherapy (3D-CRT) was now clear, whereeach selected beam aperture would be designed to match the projected outline of the target.

It took another decade before computers were powerful enough to allow fullimplementation of the 3D-CRT vision. Two papers, Goitein et al (1983), and Goitein andAbrams (1983) were particularly influential in spreading interactive visualization conceptssuch as the beams-eye-view for 3D planning of beam directions. Also, the concept of dose–volume histograms was pivotal for evaluating dose distributions calculated by treatmentplanning systems (Shipley et al 1979). When 3D-CRT eventually went clinical, theproper definitions of irradiation target volumes became critical. The ICRU report (ICRU501993) introduced a series of standard volume concepts that have been widely adopted; seesection 4.1.1. Together with margin recipes for considering uncertainties in volumedetermination and location, see review by van Herk (2004), this now forms the foundation forhow to set up the geometrical basis for IMRT treatment planning.

2.2. Algorithm development

In dose calculations, accurate algorithms that are fast enough for practical planning have formany years been an issue. Empirical, factor based algorithms have dominated until recently.Although the basic interactions of photons and electrons have been known for long, a fullyreductional transport calculation scheme, as in event-by-event Monte Carlo, has always takentoo much CPU time to be practical, motivating the search for more efficient methods. At the1984 ICCR meeting three speakers independently presented proposals for a new family of dosecalculation methods based on scatter kernels pre-calculated with Monte Carlo methods (thefirst author of this paper had the luck to be re-scheduled as the first speaker). One-and-a-halfdecade later, kernel based methods had matured into a standard option for treatment planning;see the review by Ahnesjo and Aspradakis (1999). However, for accurate dose calculations,correct modelling of the radiation output of the machine is equally important as modellingthe scattering processes in the patient. This was initially much less recognized, but is today athoroughly investigated area, much due to the dedicated accelerator head simulation softwareBEAM developed by Rogers et al (1995). Monte Carlo dose calculations have generallybeen anticipated to replace kernel based methods but with the increased dose calculation loadcaused by the iterative approach in optimization of IMRT, the current praxis has rather tendedtowards simplified pencil kernel methods for speed efficiency.

The clinical introduction of 3D-CRT radically changed the radiotherapy workflow froma simulator oriented ‘beam adjustment’ philosophy to an information driven, computerbased process where the machine settings for treatment delivery were determined by useof a treatment planning system (TPS) by which realistic calculations could be done. Theinformation process was a main focus of the Nordic collaborative study CART (Westerlund1988), as well as in commercial TPS development; see, e.g., Jung et al (1997). The number ofparameters to set, i.e. the degree of freedom in treatment delivery, was however still limited to

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beam energy, directions and field shapes for typically 2 to 4 fields. This amount of informationwas still possible to manually transfer from the TPS to the treatment machine. Connectingthe nodes of information in a clinic into a network holding information management systems,and establishing standards for data structuring, e.g. DICOM (NEMA, 1998), finally paved theway for the treatment planning application to meet the IMRT challenge. Only one piece wasmissing—algorithms for automated optimization of the beam fluence modulation.

The beam directions, beam weights, field shapes etc, constituting the free variables in3D-CRT could be manually optimized. However, by conceptually dividing each beam portalinto approximately 102–103 ‘beamlets’ for which the ‘modulation’ (i.e. fluence) could beset independently of all other beamlets led to the formulation of a large-scale optimizationproblem, intractable by manual procedures. Initially, the optimization was viewed as an inverseproblem, partly due to a successful analytical solution of a special problem in rotationaltherapy (Brahme et al 1982), and partly inspired by the similarities with the inverse basisof image reconstruction in computed tomography (Cormack 1987, Cormack and Cormack1987). However, the physical lack of negative dose prohibited purely inverse solutions and theproblem formulation gradually shifted towards optimization, as illustrated by representativepapers from leading research groups during the 1990s, for example Karolinska in Stockholm(Lind 1990, Gustafsson et al 1994, Lof et al 1998, Brahme, 2000), Heidelberg (Bortfeldet al 1990, Bortfeld 1999) and Madison (Holmes and Mackie 1994, Shepard et al 2000). Thework of Webb has consistently used the optimization formulation (Webb 1989, 2003). Theterm ‘inverse planning’, however, is still used. It now refers to the planning workflow wheredose distribution goals are input to, and used by, the computer before the dose calculationsthat determines the treatment delivery parameters are done. This work sequence of dose goalhandling is considered reversed as compared to the non-IMRT procedure where explicit doselevels are not processed by the TPS except for documentation and reporting (Brahme 1988).

The hallmark of IMRT is its ability, through extensive calculations in a TPS, to delivercontrolled, heterogeneous dose distributions of high resolution. So far this ability has beenalmost exclusively applied to construct homogeneous target dose distributions by superposingheterogeneous dose from multiple fields of different directions. The degree of freedom tocustomize the dose from voxel to voxel is now in our hand but remains to be clinicallyexplored. To gain from this freedom we need to adapt, and expand, our knowledge of cancerand radiation biology, cf Brahme (2001), Bentzen (2005a, 2005b) or Yang and Xing (2005),ensuring that radiation oncology will still have be a vital discipline in the future.

3. Treatment delivery techniques

Most of the early scientific work addressed IMRT applied to standard, cone beam C-armlinear accelerators equipped with multileaf collimators (MLC), i.e. the main stream IMRTequipment of today. However, the first IMRT delivery method commercially available forclinical use was an add-on equipment enabling standard linear accelerators to deliver serial,fan beam tomotherapy. Tomotherapy is now also available by dedicated machines based onhelical (spiral) delivery of fan beams. A third class of delivery systems comprises specialrobotic and hybrid techniques that do not readily fit into the other two groups.

3.1. Tomotherapy

Tomotherapy, or rotational fan beam IMRT, can be delivered in two ways, serial and spiral(helical) tomotherapy (Webb 2004). Historically, the serial fan beam IMRT system by MIMiCand CORVUS TPS (Nomos Corporation) was the first commercially available IMRT system

Review R385

with many installations in hospitals throughout the world. It uses a binary modulated miniMLC, attached to the treatment head of a standard linear accelerator. It irradiates two narrowslices of the patient by rotating a slit collimator through a series of gantry angles. Aftercompleting a gantry rotation, the patient is moved to the position of the next two slices andthe procedure is repeated until the entire treatment volume has been irradiated.

Later, a dedicated machine and planning software system for helical tomotherapybecame commercially available through Tomotherapy Inc. in collaboration with University ofWisconsin; see, e.g., Mackie et al (1993), Welsh et al (2002) or Beavis (2004). Photon radiationis produced by a linear accelerator mounted in a standard, large aperture CT chassis. Theaccelerator rotates in the gantry around the patient while the couch moves the patient slowlythrough it thus creating a spiral (helical) pattern of beam delivery. A computer-controlledMLC with two sets of interlaced leaves continuously modulates the radiation beam during therotation. A special feature of the tomotherapy unit is the capability to acquire megavoltageCT-scans with low doses from the therapy beam, and integrating this image information intothe delivery workflow. All moving parts of the machine are encapsulated enabling the highrotation speed needed for high-quality volumetric imaging.

3.2. Cone beam IMRT

The present mainstream IMRT delivery is based on standard C-arm machines for cone beamdelivery with MLCs. These collimators were initially designed for block replacement tofacilitate the 3D-CRT workflow, but the potential for beam modulation by moving collimatorswas also early recognized (Kijewski et al 1978, Brahme 1987, 1988). Several papers soonproposed algorithms for realization of arbitrary fluence distributions by means of multileaffield ‘segmentation’ where one by superimposing differently shaped beams (segments) couldfreely shape the delivered fluence pattern (Convery and Rosenbloom 1992, Bortfeld et al 1994,Svensson et al 1994). Most equipment used for IMRT today is still essentially designed forblock replacement with MLC, rather than being dedicated for IMRT. Delivery of multiple fieldsegments (‘subfields’) where the leaves do not move during irradiation, has often been referredto as step-and-shoot IMRT, while modulation by moving the MLC leaves during irradiation isreferred to as dynamic MLC (dMLC) technique. The dMLC delivery is generally consideredto be faster than the step-and-shoot technique, but calculations are more complicated sincethe discretization of the beams into well-defined beamlets is not as straightforward as forthe step-and-shoot technique. To minimize interleaf leakage MLC leaves are often shapedwith thin parts (‘tongues’ and ‘grooves’) overlapping the sides to adjacent leaves. This canyield an unwanted underdosage as the penumbras shaped over the overlapping parts do notadd to yield a homogeneous fluence. Much of this tongue-and-groove effect can be removedby synchronized segment patterns, but at the cost of increased treatment time and hence anincreased leakage outside the treated area (van Santvoort and Heijmen 1996, Webb et al 1997).

Attenuating metal filters with varying thickness, ‘compensators’, is an alternative to MLCfor realization of a modulated cone beam. This technique has long been used to providehomogeneous dose at depth by ‘compensating’ the difference in attenuation through tissuebetween adjacent rays. It is straightforward and requires neither MLC nor advanced computercontrol during beam delivery. The filter fabrication and handling, however, is labour intensiveand therefore becoming less used.

3.3. Other IMRT techniques

It has been argued that robotic IMRT, where a linear accelerator mounted on a robotic armcan deliver multiple beams to a target from any angle, might become the ultimate IMRT

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delivery technique combining the two treatment approaches radiosurgery and radiotherapy(Webb 1999, 2000). The CyberKnife R© (Accuray Inc.) system provides an integrated patientimaging system and motion tracking of external skin markers to ensure accurate positioning(Schweikard et al 2000, Schweikard and Adler 2000).

3.4. Positioning and compensation for organ motion

In recent years increased availability of imaging in the treatment room has boosted interestin the implementation of protocols to increase delivery precision based on image guidedradiotherapy, IGRT, and adaptive radiotherapy, ART. In clinical practice, portal imaging withprojective images is the present workhorse for checking and correcting patient positioning;see review by Herman (2005). With increased image acquisition and processing capabilitiesvolumetric CT imaging can be done at the treatment couch, which has great potential (Mackieet al 2003, Jaffray 2005, Yan et al 2005). Implementation of protocols fully using the potentialfrom volumetric imaging requires extensive integration of treatment planning data using bothrigid and deformable image registration techniques to consider changes in both position andshape (Mackie et al 2003).

The implementation of ART can in principle follow two tracks, either an indirect methodwhere the planning is performed onto the PTV and with online imaging used to reduce theapplied margins with no feedback data for explicit re-planning, or a more direct feedbackapproach where new and updated plans are formed based on the feedback information fromprevious fractions (including providing compensatory dose for misses in earlier fractions).The first, indirect approach has been used for years, while the more direct approach has beenlimited to modelling and simulation studies, see e.g. Lof et al (1998), Birkner et al (2003) orRehbinder et al (2004).

All methods for patient immobilization are aiming to minimize patient movements. Somemovements cannot be suppressed completely, e.g. heartbeat and breathing. Breathing is amajor problem in the thorax region where important targets are located such as breast andlung cancers. The movements are large and since the speed of the MLC movements are of thesame order of magnitude as breathing, movement interference can cause significant deviationsbetween planned and delivered dose. Therefore, IMRT for moving targets require techniquesfor respiratory control or gating, or must be restricted to 3D-CRT with margins large enoughto allow for breathing motions. Several solutions have been proposed for treatments in therespiratory affected regions; see reviews by Keall (2004) and Mageras and Yorke (2004).

4. Handling dose distributions in anatomical space

A single IMRT dose fraction of 2 Gy to a deep seated target induces in the order of 1017–1018

ionization events into the target, and 10 to 20 as many ionizations in surrounding healthytissues. The cell sterilization action is mediated by breaking DNA strands, most effectively ifboth strands are broken close to each other (double strand break, DSB). Single strand breaksare repaired more effectively through the structural support by the unbroken strand. The vastmajority of the ionizations from x-rays do not induce any irreparable DSB, partly because thecell nucleus fills only a fraction of the cell volume, and partly because most ionizations yieldrepairable (single) strand breaks. For a dose of 1 Gy, approximately 105 ionizations per celloccur, but the yield of DSB is only about 40 per cell. Several of the DNA bound breakingsresponsible for DSB might be due to reactions with OH-radicals from hydrolysis of water,and by low energy, non-ionizing events induced at the track-ends of the secondary electronsreleased in ionizing events (Boudaiffa et al 2000).

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Although one in principle can follow individual radiant particles in detail through track-structure simulations, see e.g. Nikjoo et al (2001), the excessive amount of information andcomputer simulation time requires a different approach to practical treatment planning. Insteadof keeping track of individual cells, regions of interest are delineated from anatomical patientimages composed of macroscopic physical quantities such as x-ray attenuation (CT) or nuclearspin magnetic resonance imaging (MRI). Instead of keeping track of ionizations, macroscopicdistributions of energy deposition, i.e. dose, are calculated. To make the problem tractable, thecandidate dose distribution is intersected with relevant regions of interest, and the informationis further reduced to a small set of numbers for assessing the plan quality. Logically, finalplan judgment should be in terms of likelihood for providing cure without severe side effects(Agren et al 1990, Soderstrom and Brahme 1993, Brahme 1999). However, direct calculationand maximization of such a quantity for the individual patient involves uncertainties and iscurrently used on research basis only (Turesson et al 2003). Instead, the current clinicalparadigm is to use protocols specifying physical dose levels to targets and tolerance levels forregions at risk.

4.1. Anatomical volumes for treatment planning

Tomographic imaging has evolved from providing pictures of the patient to become digitalrepresentations of the patient in the computer. The target determination process has developedinto a qualified, computer aided sculpturing process in 3D. However, while CT is an anatomicalimaging that solely maps x-ray absorption variations in tissue, emerging imaging technologycan map properties related to specific functions of the cells. This ‘functional imaging’ canprovide for detailed tumour spatial mapping and biological characterization for predictionof radiation therapy response. As reviewed by Apisarnthanarax and Chao (2005), positronemission tomography (PET) and MRI provide potential to map both hypoxia, proliferation,apoptosis and hormone receptor status. Hence, the dose could be increased to selected confinedvolumes containing, e.g., hypoxic cells. However, validation of the imaging-pathologicalrelations, and the cost and time of clinical outcome studies will indeed delay the introductionof these promising possibilities into clinical routine.

4.1.1. The ICRU volumes. The currently used target concept for radiotherapy planning,as defined by ICRU (ICRU50 1993, ICRU62 1999), is the PTV (planning target volume)constructed by adding a margin accounting for organ movement and set-up errors to the CTV(clinical target volume), which in turn is defined by the GTV (gross tumour volume) withmargin regions to cover assumed spread of invading tumour growth. The PTV concept hasbeen criticized for being dependent on treatment technique arguing that set-up margins wouldbe more logical to define in the machine system than anatomically (Aaltonen et al 1997).Although adding a set-up margin is simple for 3D-CRT, it is less practical for fields modulatedby MLC segmentation techniques. The ICRU concepts now dominate for handling bothset-up margins and internal movements. This standardization has had a profound influence inestablishing a common framework for the radiotherapy community.

4.1.2. Margins for positional uncertainties. As depicted in figure 1, the planning CT studyis viewed as a snapshot in time of the patient, and the deviation between the snapshot and (thenot available) time averaged CTV position introduces a systematic error present all through thedelivery sequence, which requires attention (Stroom and Heijmen 2002). The ICRU reportsdo not state any particular algorithm for calculation of the margin but several authors haveaddressed the problem. Stroom et al (1999) chose the margins such that the 95% isodose

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Unknown, mean position of CTV

PTV formed from snapshot CTV using a translational margin ellipsoid to cover most possible positions of CTV

, ,2.5 0.7i i i i x y z== ⋅ + ⋅m Σ σmm

m

CT planning study snapshot of CTV

(a) (b)

Figure 1. (a) The margin concept for generating a PTV from a CTV. The planning study snapshotof the CTV introduces a systematic deviation. The outer envelope formed by a margin ellipsoidconvolved with the CTV surface constitutes the PTV. The ellipsoid axes are composed by thestandard deviations �i of the systematic error, and the standard deviations σi of the randompositional error from each fraction, and scaled so that at least 90% of the treated patients getat least 95% of the prescribed dose to the entire CTV. Adapted from McKenzie et al (2000).(b) Instead of using margins, an alternative concept is to distribute possible instances of the CTV,with correlated OAR positions, and optimize with an objective designed to consider all volumeinstances over many, representative multi-fractional treatment series. The approach is computationintensive, but provides possibilities to better shape dose at targets close to critical organs.

should enclose, on average, at least 99% of the CTV. van Herk et al (2000) chose a differentapproach where 90% of treatment plans should result in a CTV dose that everywhere isgreater than 95% of the prescribed dose. The size of the needed margins, applied by a 3Dregion growing algorithm as proposed by Stroom and Storchi (1997), were similar for bothapproaches despite the differences in assumptions; cf van Herk (2004).

It is important to realize that any margin algorithm applied to a 3D object must beintrinsically 3D in its implementation. Sequential use of a 2D margin growing algorithm forthe slices of a contoured 3D object is not recommended since it can lead to severe marginerrors, particularly in the direction perpendicular to the image plane as clearly shown byStroom et al (1998).

The ICRU reports did also propose an expansion of organs at risk volumes, OAR, intoplanning organ at risk volumes, PRV. Much less attention has been given to the problem ofdevising algorithms and protocols for designing a PRV from an OAR. McKenzie et al (2002)have worked out class solution recommendations for organs of ‘parallel’ architecture, and‘serial’ architecture, respectively. Lung is an example of a parallel organ where small hotspots resulting in local loss of function are much less severe than in a serial organ such asthe spinal cord where even small volumes of affected tissue may result in severe side effects.Muren et al (2005) have studied the application of the PRV concept applied to the rectum,which in prostate treatment is a critical organ with rather large positional uncertainties.

4.1.3. Direct modelling of positional uncertainties. The correlation in movement betweenCTV and OAR is not explicitly considered through the margins inherent in PTV and PRV

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outlines. Hence, optimization objectives formulated for the CTV and OAR with positionalerror modelling integrated in the optimization procedure itself is an interesting approach. Bysimulating populations of replica instances of the same patient, where the CTV and OARpositions are sampled according to an organ displacement model, the yielded dose–populationhistograms can be used to more precisely tailor dose compromises between CTV and OAR(Yang et al 2005, Trofimov et al 2005). The potential benefit of such optimizations is thatsharper gradients of delivered dose can be achieved by giving more dose at the edges of theCTV, assuming that the positional spread will smear the dose heterogeneity over the fractionsto yield homogeneous dose in the end.

Convolving the dose with patient geometry variations is a simple way to get the expectationdose values, but the usual number of delivery fractions (approximately 30) is not large enoughto reduce the variance of the total dose in gradient regions. Hence, reducing the variancemust be part of the optimization objectives. Unkelbach and Oelfke (2004, 2005a, 2005b)have presented a more detailed analysis using estimated probability distributions of possiblepatient geometries and investigated the influence of uncertainties in those distributions. Baumet al (2006) used CTV and OAR coverage probabilities as weights to maximize the CTVequivalent uniform dose (EUD) and to keep the EUD of the OAR below a certain thresholdin order to shape a robust dose distribution. Extending the optimization procedure in routineplanning to cover also patient geometry uncertainties requires more CPU time and/or moreapproximations in calculations.

Improved positioning methods may in the future reduce the margins such that thedifference between a CTV and its PTV will be of less practical importance. If not, methodsfor CTV based planning to improve the consideration of OAR are at hand. Although the PTVin this type of optimization is no longer needed for dose shaping, the resulting dose envelopeto the patient will still be larger than the CTV. Hence, the dose reporting specifications thatnow are based on the PTV need to be revisited before implementing CTV based planningprotocols clinically.

4.2. Treatment plan quality measures

Ranking the quality of competing plans is a prerequisite for both manual plan comparison, andin automated optimization with iterative improvements. The most obvious score to directlyreflect a curative intent is the probability of uncomplicated control

P+ = TCP(1 − NTCP) (1)

where TCP is the tumour control probability and NTCP is the normal tissue complicationprobability (assumed uncorrelated in equation (1)). Procedures for maximization of P+ havebeen extensively discussed in research papers from the Stockholm group; see, e.g., Brahmeet al (2001), Brahme (2001).

Although many institutions probably use TCP and NTCP for ranking competing nearlyequivalent plans, and for evaluating candidate treatment protocols, the scepticism regardingthe predicting power of the biological models, together with a perceived higher risk forcomplications, has hampered their direct application in clinical IMRT. Contributing isprobably also the lack of routine methods to quantitatively monitor and score treatmentresponses. Translating the biological response into terms of equivalent dose has insteadgained considerable interest. The EUD concept (Niemierko 1997) is defined as the uniformdose causing equal surviving fraction

SF(EUD) = SF(D(r)) (2)

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where D(r) is the dose distribution for the volume of interest. The general characteristic ofthe non-linear dose response has been incorporated into a computation friendly application ofthe EUD concept based on a power law average proposed by Niemierko (Wu et al 2002) thathas been frequently employed. Mavroidis et al (2001) proposed a quantity ¯D, the biologicallyeffective uniform dose linked directly to the response probability through

P( ¯D) = P(D(r)) (3)

where P can be either TCP or NTCP. Whatever biological index considered, the biologicalmacroscopic response to radiation is non-linear, and the more heterogeneous D(r) is, the moresensitive to the underlying biological model, and its parameter values, will the result be!

Most plan optimization is done on physical dose–volume criteria aiming for homogeneousdose coverage of the target, and minimal dose outside. Various conformity indices have beenconstructed to directly score the planning success in terms of dose coverage, as reviewed byFeuvret et al (2006). A conformity index can be very useful for characterization of a treatmentplan, but unlike a biological index as EUD, a conformity index is not aimed for automatedoptimization engines since direct derivates versus the optimization variables are lacking, orhard to describe quantitatively.

5. From dose sculpturing to machine settings

Besides an appropriate representation of the patient, automated optimization of IMRT requiresformulation of the problem into a set of optimization variables that controls the incidentradiation, models for converting the irradiation pattern to dose, and a dose distribution qualitymeasure (objective function). Iterative search procedures are used to find the best combinationof irradiation control parameters, and it is obvious that the more direct and well behavinginfluence the optimization variables have on the objective function, the more effective searchalgorithms can be designed.

5.1. Optimization variables

The DICOM standard for radiotherapy data specifies the data structures that are needed forbeam delivery (NEMA 1998). The data have to be structured into control points specifyingbeam angles, MLC settings and monitor units. However, variation in leaf edge position farfrom a dose point has a very weak influence on the dose, while the direct photon energy fluencehas an almost linear influence. Hence, the most common approach to IMRT optimization isto use a discretization of the beam apertures as optimization variables, although other sets ofvariables are also possible.

5.1.1. Discrete fluence apertures—bixels. Discretizing a beam aperture into elements,commonly rectangles sized by the width of the leaf times an arbitrary set discrete step length,provides a way to represent the energy fluence distribution of the beam as a set of numbersthat can be used as optimization variables. The irradiation through a bixel yields a dosedistribution forming a discrete kernel that can be pre-computed to save computation time.The dose to the voxels directly irradiated through a bixel is practically linear to the bixels’energy fluence (we will in the following use ‘fluence’ for short, instead of the for photon dosecalculations more relevant ‘energy fluence’), but scattering processes add dose contributionthrough contributions from kernels from other bixels of the beam. Normalizing the kernelsper incident fluence yields directly the derivative of the dose distribution with respect to thebixel fluence optimization variable.

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The number of bixels is in the order of 102–103 per beam making the optimization alarge-scale problem. The use of bixels as optimization variables may cause some drawbacks.There is a tendency that the resulting optimized fluence distribution becomes highly irregular,as a consequence of requesting sharp dose gradients (Alber et al 2002b). The magnitude ofthe fluence irregularities depends on both the size of the discrete bixels, size of dose voxels aswell as on the optimization technique.

As there is no hardware (except attenuating filters) that can deliver modulated fluenceprofiles directly, the optimal fluence profiles must be converted into machine parameterssuch as MLC control points. This conversion may deviate from the desired fluence dueto approximations in calculations and limitations in MLC settings. Hence, the resulting,deliverable, fluence profile will no longer be optimal. To ensure modelling and deliveryconsistency, the dose should always be (re)calculated with an appropriate model consideringactual beam settings. The corresponding degradation of the plan quality will be morepronounced for large irregularities of the fluence, and its realization will also require moremonitor units (MU). Several methods have been proposed that produce smoother, more regularfluence distributions, which are easier to deliver, either by explicitly imposing variousregularity constraints on the fluence pattern directly (Chvetsov et al 2005, Coselmon et al2005), by indirect methods such as modifying the requirements on the dose (Price et al 2003),or by using optimization methods with inherent smoothing properties (Xiao et al 2004).

5.1.2. Machine parameters. One method to avoid the problems associated with fluenceoptimization is to take the machine settings into account during the optimization. This can beachieved by incorporating the MLC sequencing into the optimization (Alber and Nusslin 2001)or by optimizing the machine parameters directly (Lof 2000, Tung et al 2005) as depictedin the upper part of figure 2. Gradient based, direct optimization is local and dependent onan initial set of leaf settings. One way to obtain this is to first perform a coarse fluenceoptimization with a leaf sequencing step. Alternatively, control points can be generated basedon geometrical attributes, such as the projection of the target and the OAR.

5.1.3. Beam orientation. Other parameters that can be optimized include the numberof beams, and the beam orientation (gantry, couch and collimator angles) and isocentrepositions. This increases the complexity of the optimization problem considerably since allbixel variables are dependent on beam orientations. Suggested methods to combat this includespeedups for solving the (repeated) fluence optimization, for example by using a clustereddose grid (Scherrer et al 2005) and heuristic choice of candidate beams (Ehrgott et al 2005).Furthermore, the beam orientation can be optimized locally, starting from an initial point givenby the planner (Lof 2000). A local optimization cannot guarantee that a global optimum isfound, but may still improve the plan significantly.

In conjunction with MLC sequencing, or direct optimization, the collimator angle is animportant parameter, and a correct utilization of this degree of freedom can provide increasedtreatment quality (Chapek et al 2005). In helical tomotherapy optimization, all beam directionswithin the treatment region are considered, yielding up to about 105 bixels for optimization(Shepard et al 2000), which puts even higher computational demands on the planning system.

5.2. Fluence modelling and dose calculations

For any iterative optimization technique, fast dose calculations are necessary since the dosedistribution needs to be calculated repeatedly. The required number of iterations may varyfrom 101–105 depending on type of algorithm. The most common way to meet both thesedemands is to store pre-computed dose distributions from each bixel representing the fluence

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leaf positions ( )ξ

segment weights ( )w

energy fluence ( )w,ξΨΨ =

dose ( )( )wDD ,ξΨ=

objective ( )( )( )wDff ,ξΨ=

grad. w.r.t. energy fluence

ΨΨ d

d

d

d

d

d D

D

ff =

grad. w.r.t dose, D

f

d

d

grad. w.r.t. leaf pos.

ξΨ

Ψξ ∂∂=

∂∂

d

d

d

d D

D

ff

evaluation

Figure 2. The figure illustrates the calculation workflow in treatment planning. Calculationsfor 3D-CRT start by defining leaf settings (upper left), and end with the calculated dose, thatcan be improved by manually testing new beam set-ups and repeating the procedure. The IMRToptimization process starts by defining an objective (lower left) for the dose distribution. Guided bythis objective, the planning process is automated through an optimization feedback loop (upwarddirected arrows), where gradients of the objective with respect to dose are used to find newproposals of the fluence pattern directly (middle left directed arrows), or, for direct machineparameter optimization, the gradients are expressed with respect to leaf positions and segmentweights (upper loop of hatched arrows). The IMRT optimization can be repeated with new set-upsof the objective to evaluate different clinical compromises in a trial and error process.

discretization. To limit memory needs and computational operations, the kernels are oftencut off neglecting distant scatter. The accuracy lost by neglecting scatter can be compensatedfor by more accurate calculations at intermediate iterations by, e.g., a point kernel method(Ahnesjo 1989). Conceptually, the impact from heterogeneities can be fully regarded duringthe pre-calculation of pencil kernels (Gustafsson et al 1994), but in practice dose is oftenapproximated by use of correction methods as in 3D-CRT pencil kernel dose calculations, seee.g. Ahnesjo et al (1992) or Bortfeld et al (1993), to shorten the kernel pre-calculation time.Critical for calculation accuracy is the ability to handle the influence imposed by the beam andtreatment head geometry, such as scatter from the flattening filter, impact of rounded shapeof leaf ends, etc. Of particular interest to IMRT is the modelling and delivery accuracy ofsmall field segments. The small field ‘regime’ prevails when the combined effects of sourcesize blurring (i.e. direct fluence penumbra), and lateral electron transport (including rangeshift introduced by heterogeneities) are of the same characteristic length as the segment widthitself. When this happens, the lateral charge particle equilibrium is lost which makes the dosevery sensitive to small changes and errors of leaf positions as demonstrated by LoSasso et al(1998).

Since optimization may enforce ‘more-than-wanted’ approximations of the calculateddose, it is pertinent that the treatment plan evaluation and dose reporting is based on the bestpossible dose calculations performed with the actual machine settings used for dose delivery,and that due consideration is taken to crucial effects invoked by the segment characteristics(small fields, head scatter output, etc). The difference between the optimized dose distributionand the delivered dose should be as small as possible, requiring that TPS vendors must integrateas much as possible of the beam characteristics into the optimization loops (Reynaert et al2005).

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5.3. Optimization goals

The treatment planning process aims to produce a feasible treatment plan considering specificgoals. To drive the optimization the goals must be cast in mathematical form that quantifiesthe deviation from the goals, and eventual restrictions on the solution. Hence, an optimizationproblem consists of a set of constraints that must be fulfilled and an objective function to beminimized (or maximized) with respect to a set of independent variables.

5.3.1. Constraints. A constraint is a non-negotiable, a priori requirement on an optimizationproblem, and the objective will be minimized (or maximized) only to the extent allowed by theconstraints. Constraints do not have weights, and are not part of the objective function, withhigh weights or otherwise. Confusingly, the term ‘DVH constraint’ is often used to denoteDVH based objectives. The most straightforward application of a constraint is to give absoluteprecedence to a part of the objective function, for example to guarantee that the dose do notexceed a critical maximum dose level, but they can also be used to define more elaborateoptimization problems in order to improve the user interaction; cf section 5.3.3.

The non-negativity requirements of fluence or dose are physical constraints, as well asthe interdigitation of MLC settings. The former represents a simple bound, while the lattercan be formulated as a linear constraint. Simple bounds and linear constraints are easier toimplement into an optimization algorithm, and feasibility can be guaranteed and maintained(Luenberger 1984). With non-linear constraints, such as a TCP constraint, the search pathmay frequently violate the constraints and feasibility is usually obtained only at the optimum.

5.3.2. Objective functions. The objective function may be composed of any number offunctions, combined to produce a single number, usually through a weighted sum. It isdifficult to convey the knowledge and experience of a clinician to an optimizer through oneor more simple functions. An optimizer will follow the instructions given in the objectivefunction literally: only what is explicitly asked for will be obtained, and anything not explicitlyforbidden may appear. The most commonly used objective function, a weighted sum of penaltyfunctions based on satisfying a set of DVH points, may not be ideal for this purpose. A smallset of DVH points is often insufficient to avoid undesired properties, and a large set maybe overly strict, and force the solution into inefficient compromises. Biological treatmentmeasures like EUD, TCP or NTCP are technically well suited since they all consider the dosedistribution for a full volume and not only the parts violating a certain condition.

When using gradient based optimization algorithms, differentiability and convexity aredesired properties; see section 5.1.1. The more degrees of freedom an optimizer has to itsdisposal, the more detailed objectives need to be defined. A beam set-up for prostate avoidingthe femoral heads does not need objectives for those, but if the optimizer is free to change thebeam configuration, it must be given a more specific objective that penalizes high doses to thefemoral heads.

The formulation of efficient and intelligible objective functions is of paramountimportance for the planning process requiring effective tools for user interactivity.

5.3.3. User interaction. The iterative process of setting up the optimization problem canbe very time consuming, and several attempts can be used to facilitate the process. Earlyfeedback of intermediate results enables the user to estimate how the compromises work out,without waiting for a full optimization with MLC sequencing and final dose calculation tobe completed. This is facilitated if MLC sequencing is integrated into the loop. Prioritizedtreatment goals can be more intuitive to use instead of an objective function consisting of a

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weighted sum of conflicting goals. This method is sometimes referred to as lexicographicoptimization, and is based on separating the objectives into categories of importance. First,only the most important category is included in an optimization. Then, the result is transformedinto constraints, and the next category is introduced as objectives, and so on. Guided problemmodification aims at reducing the number of iterations by providing tools to analyse andmodify the problem. Sensitivity analysis has been proposed by Alber et al (2002a) togive the user information on how much a change in one objective or constraint will affectothers. For example, it may provide an estimate on how much the maximum dose inan organ at risk can be reduced by allowing a higher target dose heterogeneity. Othertools include voxel based weighting, in which voxels that received undesired doses canbe individually reweighted (Yang and Xing 2004). Evaluation of precomputed plans canhelp in setting planning compromises by producing a large number of plans with differentcompromises (possibly overnight) and then choosing one or combining several plans to obtaina usable plan (Kufer et al 2003). When producing such plans, it is only relevant to considerPareto efficient plans, i.e. plans where no objective can be improved without worseninganother.

5.4. Optimization algorithms

The IMRT optimization problem is a large-scale problem requiring sophisticated algorithmsto efficiently navigate the solution space. The most common algorithms for IMRT usedeterministic methods to determine search patterns, often by using information about thegradient of the objective function. Gradient based algorithms work iteratively by first selectinga direction, and then search along this direction to find a good point from which to start thenext iteration; see, e.g., Luenberger (1984). The simplest algorithms use the gradient directlyas a search direction, but performance increases drastically if information about the secondderivatives (the Hessian) is used (Zhang et al 2004). Such information improves the localapproximation of the objective function and thus improves the search direction. Gradientbased algorithms are local, and are guaranteed to find the global optimum only for convexfunctions. Luckily, many of the most commonly used objectives are convex functions of thedose, and hence also the fluence; see, e.g., Romeijn et al (2004).

As mentioned in section 5.1.1, the optimal fluences may become very irregular. For mostgradient algorithms, these irregularities do not appear instantly, but increase gradually withthe number of iterations used. However, due to the degeneracy of the IMRT optimizationproblem (Alber et al 2002b), the modifications made in later iterations have little or no clinicalrelevance, especially when considering the influence from the subsequent leaf sequencing.Therefore, limiting the number of iterations can provide a way to obtain high-quality dosedistributions, while retaining smooth fluence profiles (Carlsson and Forsgren 2006).

Linear programming has also been applied as search method for a number of dose basedobjectives (Romeijn et al 2003). This method requires that all objectives and constraints arelinear functions of the optimization variables.

If the objectives or constraints are non-convex, non-differentiable or otherwise infeasiblefor gradient based methods, common alternatives include simulated annealing and geneticalgorithms; cf Michalewicz and Fogel (2004). These algorithms are stochastic, using randommodifications to the optimized variables. In theory, these algorithms can find the globalminimum, but the performance is highly dependent on good heuristics. Examples of non-convex problems where stochastic algorithms have been used include optimization of machineparameters (Shepard et al 2002) and beam configurations (Djajaputra et al 2003, Li et al2004).

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5.5. Leaf sequencing for MLC dose delivery

The fluence optimization results in a fluence distribution that has to be translated into asequence of control points for the MLC. The process by which these are computed is referredto as leaf sequencing, and can be performed for step-and-shoot or dynamic delivery.

5.5.1. Step-and-shoot delivery. Most leaf sequencing algorithms require a discrete number offluence values into which the bixel fluence values have to be approximated. Some sequencerslet the integers represent equidistant fluence levels, and some use clustering techniques tochoose levels such that the error introduced by the approximation is minimized.

Assuming somewhat idealized conditions, leaf sequencing algorithms aim to exactlyreproduce the integer matrix created by the discretization. This problem has been well studied,and elegant solutions exist that guarantee that the number of MUs is minimized (Kamath et al2003). It has been shown that it is practically impossible to guarantee optimality with respectto the number of segments (Kalinowski 2005), but there are many heuristic algorithms thatseem to obtain good results; see Siochi (1999), Wu et al (2001) or Bar et al (2001).

Current leaf sequencers are able to incorporate many of the MLC constraints, such asminimum and maximum tip differences and interdigitation, and some are also able to explicitlyavoid the tongue-and-groove effect. One powerful method to incorporate these constraints isto regard the segment generation as a transportation problem through a network of connectednodes representing different leaf configurations (Ahuja and Hamacher 2004). Constraints of amore global nature, such as maintaining a minimum segment area, have not yet been efficientlyincorporated to the knowledge of the authors of this paper.

There are numerous approximations in leaf sequencing algorithms. Will small fieldeffects with partial source blocking and leaf tip shape and positioning accuracy be critical?Are there small modifications that can be made in the matrix that would allow reducing thenumber of segments or MUs without causing clinically relevant changes in the dose? Howwill scattering, transmission and lateral variations in the beam quality affect the differencebetween the original and the resulting fluence? How can the jaws be utilized to fine-tune thesegment edges? Many of these questions can be resolved by optimizing the segments directly,but the optimization algorithms must be very innovative in order to exploit the possibility toadd, delete or combine segments and to incorporate beam model and delivery uncertainties.

5.5.2. Dynamic delivery. In dMLC delivery the leaves move continuously while the beamis on. For each leaf pair, trajectories can be computed to generate a stepwise constant fluenceprofile (Ma et al 1998), much like for step-and-shoot, or to generate a smooth continuousfluence profile (Svensson et al 1994). A common method is sliding window in which theleaves move in one direction with variable leaf separation to modulate the fluence. There arealso bi-directional approaches as the close-in technique where the leaves move towards eachother, but such techniques may not be more efficient (Kamath et al 2004).

An issue to consider for dynamic mode delivery is the increased MLC leakage. Thebackup jaws typically do not move during the sequence, and large parts of the field may beblocked by the MLC only for many MUs. The leakage needs to be considered in calculations,and also the beam hardening effect of the MLC (Kim et al 2001).

6. Quality assurance of the IMRT process

IMRT is a complex task all through from imaging over treatment planning to its delivery, and areliable QA of the dose distribution within the patient is of extraordinary importance (Bogneret al 2004). Besides commissioning and testing of the TPS and the treatment delivery systems,

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routine testing QA of the delivery system, and (routine) patient-specific QA are required(LoSasso et al 2001, Galvin et al 2004). The routine parts may be done less frequently withtime when confidence and experience of the full procedure is gained. Extensive data gatheringfor QA also raises particular issues regarding evaluation of test data and setting relevant actionlevels.

6.1. Commissioning and testing of the treatment planning and delivery systems

In many ways, the issues that must be addressed during commissioning and testing of thetreatment planning and delivery systems for IMRT are analogous to those necessary for3D-CRT (Purdy et al 2001). Compared to 3D-CRT, more of the delivered dose in IMRT willbe composed of leaf leakage and penumbras, and small fields. Hence, the commissioning dataset must be more carefully examined with respect to data influencing dose in such regions.

6.2. Routine QA of the delivery system

The relationship between monitor unit (MU) setting and radiation dose for IMRT fields ismuch more complex than for non-modulated fields as the beam portals are composed of manysegments. The machine control data are too large for simple manual verification. For smallfields and large dose gradients, small errors in the MLC positioning yield significant doseerrors (Budgell et al 2000, LoSasso et al 2001, Bogner et al 2004). For dMLC, the gap widthis the critical parameter for accurate dose delivery and MLC position calibration and leaf motorfatigue are recognized as primary sources of gap inaccuracy (LoSasso et al 2001). Hence,TPS data and modelling consistency with machine performance characteristics is pertinent.

MLC leaf position variations can be tested to a precision of about 0.2 mm by usingmatch-line uniformity for periodic QA (Galvin et al 2004). Another useful test to semi-quantitatively check the MLC leaf positional accuracy is to expose a film to a sequencethat creates 1 mm strips at regular intervals. A fast visual inspection can detect improperpositioning to a precision of about 0.5 mm (Galvin et al 2004).

6.3. Patient-specific QA

Implementing a patient-specific QA process complements the delivery system QA, and ensuresthat the planned MLC data for individual patients are properly documented and correctlytransferred and executed by the MLC control system (LoSasso et al 2001). The most appliedprocedure is to replace the patient by a standard phantom. By exposing the phantom toirradiation using the same MLC segments, leaf trajectories and MU for each field as for thefinal patient calculation, and do a similar calculation in the TPS, test data can be createdand compared to data from dosimeters placed in the phantom (Galvin et al 2004). Althoughionization chambers are preferred for point dose checks in IMRT phantoms, they cannot bepractically used for scanning 2D or 3D dose distributions since the entire treatment plan mustbe delivered for each measured point (Purdy et al 2001). Film is therefore a convenientpossibility that can provide 2D distributions, either for fluence verification of single beams,or for dose verification in a phantom for the complete treatment. There is only one suitableradiographic film for 2D dose distribution verification (Bogner et al 2004). However, thistype of film needs processing, which often deteriorates the reproducibility. More recently, aradiochromic, self-processing film has shown good dose linearity and reproducibility (Devicet al 2005). Electronic portal imaging devices, 2D ionization chamber and diode arrays havealso been used for single beam fluence verification (Letourneau et al 2004, Spezi et al 2005,Winkler et al 2005) or for the reconstruction of the delivered dose to the patient (McNutt et al1996, Steciw et al 2005, Dahlgren et al 2002).

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Some errors in calculated data will not be caught by using phantom plans, since the dosedistribution in a standard phantom will not be the same as in the patient due to anatomicalinhomogeneities not present in the phantom. Alternatives being explored for more completeerror mappings are Monte Carlo simulations and gel dosimetry as reviewed by Pawlicki andMa (2001) and MacDougall et al (2002), respectively. Independent monitor unit calculations,i.e. software that imports field specifications from the TPS and then calculate dose usingmethods and dosimetry data independent of the TPS, provide a viable alternative to intercepterrors and mistakes (Kung et al 2000).

All verification data, measurements or calculations, require comparison with data fromthe TPS calculations. Evaluations involving distributions can be complex motivating use ofdata visualization and data reduction methods. The γ -index method combines dose deviationsand spatial differences into one dimensionless quantity that can be scaled for different absolutetolerance levels, often chosen so that 3% dose difference and 3 mm distance to agreementconstitutes the acceptance levels (Low et al 1998, Low and Dempsey, 2003). Further datareduction is possible by using index–volume, or index–area, histograms to set appropriatetolerance limits considering their relative importance (Dahlgren et al 2002, Stock et al 2005).Further plan analysis can also be made using modelling accuracy linked modulation complexityindex like the leaf step index proposed by Stock et al (2005).

7. Conclusions and outlook

In this journal, almost 40 years ago, Barber (1967) reported from a conference on the use ofcomputing machinery for radiotherapy. The conclusion was that ‘with the increasing capabilityand accuracy of treatment planning techniques, it was apparent that these had already outgrownthe accuracy of tumour localization and diagnosis. These deficiencies are likely to limit theoverall efficiency of treatment as the planning stage becomes more effectively automated,unless steps are taken to develop these techniques. There was evident appreciation that thecomputer was not merely a fast calculating machine but rather a piece of complex decisionmaking equipment to be integrated into an overall system of treating patients . . . . The efficientutilization of computing technology throughout the whole range of hospital activities is oneof the exciting challenges of the present day’.

About 5 years after Barber’s report was published, CT was invented and had soonchallenged the TPS of that time with an overflow of information on patient anatomy. Sincethen, the development of 3D-CRT and IMRT has shown that localization of photon dosedelivery by means of computers can be efficiently implemented close to its physical limitations.Today, with IMRT leaving its infancy, we are back to the situation 40 years ago where thebottleneck for development of more efficient radiotherapy is to acquire, process and handlemore information about the malignancies to treat. Current development in radiobiologyand imaging gives better insight into the basic pathways of radiation response and hencepossibilities for increasing therapeutic gain by, e.g., using drugs. Maybe this developmentwill make another quantum leap and force us to re-conceptualize the delivery and planning ofRT? Meanwhile, full exploration of the IGRT and ART concepts and biological optimizationwill need the engagement of physicists in medicine and biology. Will reviewing old issues ofPMB in 2056 tell the story?

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Biography

Anders Ahnesjo obtained a PhD in radiation physics from the University of Stockholm in 1991.He has worked at Scanditronix AB, Uppsala, on development of stereotactic treatment planning forLeksell Gamma Units (1981–82); at UDAC, Uppsala University Comp. Center, on development oftreatment planning systems (1983–87); at Allan Blair Memorial Cancer Clinic, Regina, Canada,on a visiting research fellowship for 4 months (1986–87); at Helax AB, Uppsala, on developmentof treatment planning systems (1987–90); and at Helax AB/MDS Nordion/Nucletron, Uppsala,as manager of the research department (1990). He was an Adjunct Professor at Umeå University(2003–2006), and since 2005 an Adjunct Professor at Uppsala University and a research scientist

at Nucletron.