The Potential and Limitations of IMRT: A Physicist’s Point of View

The Potential and Limitations of IMRT: A Physicist’s Point of View

R. Mohan, T. Bortfeld

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Contents

2.1 Introduction, Basic Concept, Short History . . . . 11

2.2 Potential of IMRT . . . . 12

2.2.1 Higher Conformality and Margin Reduction . 13 2.2.2 Target Dose Homogeneity . . . . 13

2.2.3 IMRT and Integral Dose . . . . 13

2.2.4 Potential for Efficiency . . . . 14

2.3 Limitations of IMRT . . . . 15

2.4 Potential Risks of IMRT . . . . 15

2.5 Outlook . . . . 16

References . . . . 17

2.1 Introduction, Basic Concept, Short History

The basic idea underlying intensity-modulated radio- therapy (IMRT) is that, in complex cases (and also in some not so complex cases, as we will discuss below), one needs radiation fields with optimized non-uniform

of incidence in order to achieve the desired dose distri- bution in the tumor target volume with adequate sparing of the near-by critical structures. IMRT may be consid- ered as a generalization of 3D conformal radiotherapy (3D CRT) in which multiple (sometimes non-coplanar) non-uniform radiation fields are used and shaped ac- cording to the projection of the tumor target volume, taking into consideration dose-volume constraints of the intervening and surrounding normal tissues. The two techniques are compared in Fig. 1.

That radiation fields with highly non-uniform in- tensities are sometimes needed to create the desired uniform dose to the target volume was first recognized and described by Brahme et al. in 1982 [1]. They con- sidered the irradiation of a ring-shaped target volume around a circular critical structure (organ at risk, OAR);

see Fig. 2. This could be a model of a tumor surrounding the spinal cord. The example could serve as a general motivation of IMRT. At first glance, an obvious treat- ment technique for such a tumor would be a rotation

technique with a central block as schematically shown in Fig. 2. However, this does not produce a uniform dose distribution in the ring-shaped target. In fact, the re- sulting dose profile through the center of the ring falls off gradually toward the OAR, where the dose is almost zero, as desired (solid line at the bottom of Fig. 1). The considerable target dose inhomogeneity resulting from blocking the central part of the beam can be under- stood with the geometrical argument presented in the previous chapter.

The idea of using IMRT in this example is that the dose distribution in the target can be made homoge-

distribution (beam profile) in the unblocked part of the beam as shown schematically by the dashed line in Fig. 2.

In this way the dose deficit in the target can be “filled up”. In reality the resulting dose distribution is of course not as perfect as depicted by the dashed line at the bot- tom of Fig. 2. There will be some scatter dose in the OAR, and the dose profile deviates somewhat from the rectangular shape due to the penumbra. Nevertheless, IMRT allows us to push the dose conformation poten- tial to the physical limits. This means in particular that

Fig. 1. Comparison of the principles of 3D conformal radiotherapy and IMRT. The use of conformal uniform fields generally yields a convex dose distribution. If the tumor “wraps around” a criti- cal structure, as shown in this example, the latter will get the full treatment dose. With IMRT one varies the intensity across each treatment field and can deliver more intensity to those rays that hit the target volume only, and reduce the intensities of the rays that pass through both the target and critical structures. Intensities within each beam are adjusted so that, when multiple beam are superimposed, the combination produces the desired dose cov- erage of the target volume and sufficient sparing of the critical structure(s)

Fig. 2. The original example of Brahme [1] representing an abstract case of a ring-shaped target volume around a critical structure (say, the spinal cord). The rotation with a centrally blocked beam produces an inhomogeneous dose distribution in the target. This is depicted by the solid line at the bottom, which is a dose profile through the isocenter. Only through the modulation of the intensity within the open part of the beam (dashed curve) can the missing dose be filled up (dashed curve at the bottom)

the dose gradient between the target and the OAR can be made as steep or even somewhat steeper than the dose gradient at the edge of a conventional uniform beam.

Based on this basic motivation we can give a defini- tion of IMRT as follows:

Definition of intensity modulated radiotherapy (IMRT):

IMRT is a radiation treatment technique with mul- tiple beams incident from different directions in which at least some of the beams are intensity- modulated so that each beam intentionally delivers a non-uniform dose to the target. The desired dose distribution in the target is achieved after super- imposing such beams. The additional degrees of freedom to adjust intensities of individual rays are utilized to achieve a better target dose conformality and/or better sparing of critical structures.

Of the various alternatives proposed for the deliv- ery of IMRT, two dominant but significantly different approaches have emerged. Based on the original ideas of Brahme et al., Mackie et al. [2] have proposed a rotational approach called “Tomotherapy” in which intensity-modulated photon therapy is delivered using a rotating slit beam. Intensity (or rather fluence) modu- lation is achieved through the use of a dedicated system that incorporates a temporally modulated slit multi-leaf collimator whose leaves move rapidly in or out of the slit. Like a CT scanner, the radiation source and the collimator revolve around the patient. Either the pa- tient is translated between successive rotations (serial tomotherapy) or continuously during rotation (helical tomotherapy). For the latter, the system looks like a con- ventional CT scanner and includes a megavoltage portal detector to provide for the reconstruction of megavolt-

age CT images. The first clinical helical tomotherapy machines have recently been implemented.

In the second approach, a set of intensity-modulated fields incident from fixed gantry angles and a standard multileaf collimator (MLC) are used to deliver the opti- mized intensity (or rather fluence) distribution in either dynamic mode, in which the leaves move while the radi- ation is on [3–5], or static or “step-and-shoot” mode, in which the sequential delivery of radiation sub-portals is combined to achieve the desired fluence distribu- tion [6]. Every major commercial treatment planning system manufacturer has implemented one or both of these modes. This approach is a relatively straightfor- ward extension of existing technology. It is facilitated by the fact that in most cases one does not need more than about nine intensity-modulated beams to achieve a dose distribution that is close to optimal [7]. In today’s prac- tice MLC-based IMRT often uses not more than seven beams [8].

The first clinical IMRT was delivered with a se- rial tomotherapy device in 1994 [9], shortly followed by MLC-based IMRT, which was first implemented into clinical use at Memorial Sloan-Kettering Cancer Center in 1995 [10] and rapidly gained wide accep- tance. Some other variants of IMRT delivery techniques have been described and brought into clinical practice.

They are described elsewhere in this volume (chapter 7).

For physical reasons it is clear that IMRT will not be able to achieve an ideal dose distribution that delivers dose to the tumor only and no dose to the surrounding healthy tissues. However, the greater flexibility of IMRT, which is due to the large number of degrees of freedom, will allow us to come closer to the ideal distribution than any other conventional photon radiotherapy method. It is also clear that, because of the great number of de- grees of freedom, IMRT requires computer-aided tools, not only for the computation of the dose distributions that result from a given set of treatment parameters (the “forward problem”), but also for the inverse prob- lem of determining treatment parameters based on the clinical objectives. Solution to the inverse problem may be achieved with specially designed optimization tech- niques (see chapter 4, this volume). This process is also often referred to as “inverse planning.”

2.2 Potential of IMRT

Most of the advantages of IMRT are based on its abil- ity to manipulate optimally intensities of individual rays (beamlets) within each beam. This ability per- mits greatly increased control over radiation fluence, enabling custom-design of optimum dose distributions.

Potential advantages of IMRT are described in the fol-

lowing paragraphs.

2.2.1 Higher Conformality and Margin Reduction The ability to control fluence can be used to produce sharper fall-off of dose at the PTV boundary and to produce dose distributions that are far more conformal than those possible with standard 3D CRT. (While the achievement of sharper boundaries is considered to be one of IMRT’s benefits, it should be noted that, if desired, a gradual fall off could also be accomplished.) Con- ceptually, the ability to achieve sharper boundaries has been addressed in the previous chapter and is further explained below.

When a photon beam traverses the body, it is scat- tered, depositing dose not only along the path of each ray of the beam but also at points away from it. The electrons knocked out by the incident photons travel laterally to points in the neighborhood of each ray, depositing dose along the way. Near the middle of a uniform beam, incoming electrons offset outgoing electrons and equilibrium exists. However, at and just inside the boundaries of the beam, there are no incom- ing electrons to balance electrons flowing out of the beam. Therefore, a “lateral disequilibrium” exists and leads to a dose deficit inside the boundaries of beams.

For lower energy beams and at large depths, scattered photons also contribute significantly to this effect. The conventional approach to overcome this deficiency is to add a margin for the beam penumbra to the PTV so that the tumor dose is maintained at the required level.

For IMRT plans there is another method to counterbal- ance the dose deficit. The intensity of rays just inside the beam boundary may be increased. Since some of the increased energy must also flow out, a very large increase would be required if the margin for the penum- bra were set to zero or to a very small value. Therefore, an increase in boundary fluence alone is not enough.

A combination of an increased fluence and the addi- tion of a margin, albeit a much smaller one, is a better solution [11, 12].

The sharpening of beams and higher conformality means smaller margins. A reduction of the margins attributable to the penumbra by as much as 8 mm has been found to be feasible for prostate treatments [12].

High conformality means that the volume of normal tissues exposed to high doses may be reduced signif- icantly, which, in turn, may allow escalation of tumor dose or reduction of normal tissue dose or both, lead- ing presumably to improved outcome. A lower rate of complications may also mean lower cost of patient care following the treatment.

2.2.2 Target Dose Homogeneity

Dose distributions within the PTV, in theory, can be made more homogeneous with IMRT. The PTV dose

homogeneity is traditionally considered to be a highly desirable feature of dose distributions.

Experience with current IMRT systems has led to an impression among many that IMRT inherently pro- duces inhomogeneous dose distribution within the target volume. If all things were equal, the IMRT plan should always produce more homogeneous dose distribution than a plan made with uniform beams. The inhomogeneity commonly observed is due to the overriding need to partially or wholly protect one or more critical organs, as well as due to the limitations of some inverse planning systems.

The degree of dose heterogeneity depends upon the severity of constraints on normal structures and their proximity to the PTV. If the dose-volume tolerances of the normal structure in the immediate vicinity of the PTV are much lower than the prescription dose, and if unobstructed paths for sufficient number of beams can- not be found, the PTV dose distributions are likely to be inhomogeneous. Furthermore, dose inhomogeneity may become more significant when dose is escalated.

Dose homogeneity also depends upon the complexity of anatomy. For a simple case, for instance, if all normal tis- sues outside the target volume were to be avoided equally and all had identical constraints, then PTV dose can be made nearly perfectly homogeneous. Another factor that affects target dose inhomogeneity is the number of beams. The larger the number of beams, the larger the number of rays passing through each volume ele- ment and, thus, the greater the ability to compensate for PTV dose deficits caused when some of the rays must be blocked due to normal tissue constraints.

2.2.3 IMRT and Integral Dose

It is commonly believed that IMRT has a tendency to spread low, but still potentially damaging, doses to large volumes of normal tissues and that integral doses for IMRT are higher than for 3D conformal radiotherapy.

In fact, this has been one of the concerns inhibiting the application of IMRT to lung and esophagus treatments.

Preclinical treatment design studies indicate that such

concerns may be unwarranted. Two recent studies, one

for lung and the other for esophagus, showed that vol-

umes receiving higher than 10 Gy as well as the integral

dose are reduced with IMRT [13–16]. Figure 3 shows data

for lung patients. The volumes receiving doses above 20

and 30 Gy were reduced with IMRT as compared to 3D-

CRT. Volumes at 10 Gy were about the same and, in many

cases, volumes receiving higher than 5 Gy increased. Fig-

ure 4 shows integral dose for 3D-CRT and IMRT plans

for the same group of lung patients. In all cases the IMRT

integral dose is less than or equal to the 3D-CRT inte-

gral dose. It should be mentioned that all IMRT plans

Fig. 3. Comparison of healthy non-target volumes treated at small dose levels with 3D CRT and IMRT for a group of lung patients.

Similar amounts of volume are treated at or above 10 Gy with both modalities. At higher dose levels IMRT provides better sparing, while 3D CRT is better at the lowest dose level of 5 Gy. (From Liu et al. [13])

Fig. 4. Comparison of the overall integral dose delivered with 3D CRT and IMRT for the same group of lung patients as in Fig. 3.

IMRT delivers similar or somewhat lower integral doses than 3D CRT. (From Liu et al. [13])

of Figs. 3 and 4 used nine beams. Liu et al. also found that the use of a smaller number of beams (five or seven) reduced the 10 Gy volumes to below the 3DCRT levels without perceptibly compromising the target dose. Fur- thermore, the differences of 5 Gy volumes between the IMRT and 3D-CRT plans was found to be statistically insignificant.

2.2.4 Potential for Efficiency

IMRT has the potential to be more efficient with regard to treatment planning and delivery than standard 3DCRT, although this potential has not yet been widely recognized or realized due to the evolving nature of the field.

The treatment design process is relatively insensitive to the choice of planning parameters, such as beam di- rections. There are no secondary field shaping devices other than the computer-controlled multi-leaf collima- tor (MLC). Furthermore, large fields and boosts can be integrated into a single treatment plan and, in many cases, electrons can be dispensed with, permitting the use of the same integrated boost plan for the entire course of treatment. An integrated boost treatment may offer an additional radiobiological advantage in terms of lower dose per fraction to normal tissues while de- livering higher dose per fraction to the target volume.

Higher dose per fraction also reduces the number of fractions and hence lowers the cost of a treatment course.

In general, the automation of various aspects of plan- ning, quality assurance and delivery of IMRT should lead to considerable improvement in efficiency.

Clinical Sites Where IMRT may be Most Advantageous:

In principle, IMRT could be used to treat just about any treatment site. However, the extra effort and time re- quired, at least in the current way IMRT is practiced, may not justify its use unless significant potential for clinical benefit exists. IMRT is considered to be of value primarily for concave target volumes. The most promi- nent example is that of the prostate planning target volume when the PTV overlaps the rectum and espe- cially when seminal vesicles are involved. As illustrated in Fig. 5, blocking the rectum (dotted magenta line) from receiving unacceptable doses without blocking the tar- get volume (dotted cyan line), especially when escalating prescription doses, is one of the initial successes of IMRT.

In addition, IMRT has been shown to be effective when arbitrarily shaped targets (including convex ones) may be surrounded by or be in the vicinity of complex normal tissue anatomy (Fig. 6). In this respect, the ad- vantage of IMRT is being exploited for head and neck cancers. Another key advantage of IMRT is its capac- ity to deliver the same or different doses per fraction to different targets simultaneously. An example of the former is the simultaneous stereotactic radiotherapy of multiple brain nodules [17, 18]. Figure 7 illustrates

Fig. 5. IMRT dose distribution for a prostate treatment with good sparing of the rectum

Fig. 6. IMRT provides a potential advantage not only for the treat- ment of concave target volumes, but also for simple convex target volumes if critical structures are nearby. This illustration shows that 3D CRT leads to some dose load in the critical structure (shown in green) unless only the lateral beam is used (which would lead to unacceptably high entrance and exit doses). IMRT allows one to spare the critical structure completely while maintaining good target coverage through intensity modulation

Fig. 7. Simultaneous treatment of different target areas with dif- ferent doses for a head and neck case. (From Wu et al. [19])

simultaneous treatment of gross target volume, micro- scopic extensions and nodes to 2.33, 2 and 1.8 Gy per fraction respectively for 30 fractions.

2.3 Limitations of IMRT

We should, however, recognize that IMRT has lim- itations. There are certain dose distributions (or dose-volume combinations) that are simply not phys- ically achievable. The optimization of IMRT plans involves tradeoffs that balance specified normal tissue objectives against each other and against tumor objec- tives. Generally, improvement in the benefit to any one of the anatomic structures cannot be achieved without increasing the cost to another [20,21]. Furthermore, our

knowledge about what is clinically optimal and achiev- able and how best to define clinical and dosimetric objectives of IMRT is limited. Moreover, the best so- lution may elude us because of the limitations of the mathematical formalism and methods used to find it or due to the practical limits of computer speed and the time required. For instance, the optimization process may get trapped in a local minimum in the space of so- lutions that may be far from acceptable or, if acceptable, may be far from optimum. Furthermore, the direction of incident beams (in MLC-based IMRT from a predefined set of beams) are generally chosen to be equispaced or based on intuition or convention. These directions may be good enough but not necessarily optimum.

Uncertainties of various types, e.g., those related to daily (inter-fraction) positioning, displacement and distortions of internal anatomy, intra-fraction motion and changes in physical and biological char- acteristics of tumors and normal tissues during the course of treatment, may limit the applicability and efficacy of IMRT.

Figure 8 shows that when a prostate IMRT plan de- signed based on the planning CT (left panel) is applied to one of the CT images obtained during the course of ra- diotherapy, there is a significant loss of target coverage.

Blue, red, yellow and green regions represent prostate, seminal vesicles, bladder and rectum respectively.

Dosimetric characteristics of a delivery device, such as radiation scattering and transmission through the MLC leaves, introduce some limitations in the accuracy and deliverability of IMRT. For instance, leakage through the MLC and the large number of monitor units typi- cally required for IMRT may make it difficult to achieve very low doses. In addition, the limited accuracy of the current IMRT dosimetric verification systems (based principally on radiographic film) diminishes the confi- dence in the delivered dose. Furthermore, most current dose calculation models are limited in their accuracy, especially for the small, complex shapes required for IMRT. It is quite conceivable that inaccuracies in dose calculations may yield a solution different from the one if dose calculations were accurate [22]. Perhaps the most important factor that may limit the immediate success of IMRT is the inadequacy of imaging to define the true extent of the tumor, its extensions and the radiobiolog- ical characteristics and geometric, dose-response and functional characteristics of normal tissues.

2.4 Potential Risks of IMRT

We should also be aware of the potential risks of IMRT.

The effect of the large fraction sizes used in integral

boost IMRT on tissues embedded within the GTV is un-

Fig. 8. For this illustration a prostate IMRT plan was designed using the planning CT (left panel) and was then applied to one of the CT images obtained during the course of radiotherapy. The variation of the anatomy from day to day can lead to a significant

loss of target coverage. Blue, red, yellow and green regions represent prostate, seminal vesicles, bladder and rectum respectively. (Dong, unpublished)

certain and may present an increased risk of injury [23].

There may also be an increased risk that the high de- gree of conformation with IMRT may lead to geographic misses of the disease and recurrences especially for dis- ease sites where positioning and motion uncertainties play a large role or where there are significant changes in anatomy and biology during the course of radiother- apy. Similarly, high doses in close proximity of normal critical structures may pose a greater risk of normal tissue injury. In addition, IMRT dose distributions are unusual and highly complex and existing experience is too limited to interpret them properly and evaluate their efficacy and may lead to unforeseen sequelae. Figure 9a compares a 3D-CRT lung plan with an IMRT plan and Fig. 9b shows the corresponding DVHs. While it is clear that the IMRT plan produces a more homogeneous dose distribution in the target volume and spares more lung above 10 Gy, it is not clear what the consequences of larger volumes receiving less than 5 Gy might be.

These limitations and risks point to the need for con- tinued investigations to improve the methodology and to minimize the uncertainties. Such investigations are

Fig. 9. Comparison of 3D CRT and IMRT lung plans. While IMRT provides better sparing at or above the 10 Gy dose level, it treats

bigger volumes at doses around 5 Gy. The biological consequences of this have yet to be determined

essential to exploit the full power of IMRT. Even in its current form, however, IMRT has a significant potential to improve outcome.

2.5 Outlook

In spite of the fact that IMRT is already in clinical use in several institutions in Europe and many in the USA, much needs to be done to integrate it more efficiently and seamlessly into the clinical workflow environment.

This is essential to make full use of its potential without

getting trapped in the shortcomings of the implementa-

tion. The first hurdle is the initial implementation and

the commissioning of the IMRT system. Turnkey IMRT

solutions have been advertised but the reality is differ-

ent. Often, the interfacing of the different components

of the imaging, IMRT planning, leaf sequence genera-

tion and delivery chain together turns out to be a major

problem. Current developments aim at more stream-

lined and integrated solutions. Some recent approaches

try to optimize the sequence of MLC shapes directly, without using the intermediate stage of the intensity maps [24, 25].

Another practical IMRT issue is that it has become common practice to require resource-intensive patient- specific verification of IMRT. One of the arguments for this is that IMRT is more complex than 3D-CRT, and therefore it is more error-prone. Whether this assertion is true or not, there is no doubt that more efficient tools are needed to make the process of IMRT verification less labor-intensive and less time-consuming. Later chapters in this book will deal with these issues in detail (see chapters 10 and 11, this volume).

Other research and development activities aim at im- proving the planning of IMRT. In most systems, IMRT planning is considered as an optimization problem. The goal is to find the parameters (intensity maps, some- times also beam orientations, energy, etc.) that yield the best possible treatment plan taking into account vari- ous clinical, technical, and physical prescriptions and constraints. Even though the IMRT planning systems claim to yield the optimal treatment plan, treatment planners often find the result of the first optimization run unacceptable. Significant tweaking of optimization parameters and re-runs of optimization are then nec- essary. In difficult cases it may be necessary to cycle through this “human iteration loop” more than ten times, which is unsatisfactory and involves trial and error as in conventional planning.

The fundamental limitation of current optimization approaches is that a clinician often finds it difficult to formulate a complete set of optimization crite- ria in the quantitative mathematical terms required by the optimization systems, even though he/she is capable of ranking individually the prepared plans.

Clinicians, optimization experts, and physicists have re- cently started to work together to find ways out of this dilemma [26].

Current IMRT planning systems optimize the inten- sity maps for a number of beams with given orientations.

In fully rotational approaches such as in tomotherapy, individual beams do not exist and therefore it is not nec- essary or even possible to select beam angles. However, in MLC-based IMRT with multiple beams, the orienta- tions have to be manually pre-selected. There has been an on-going debate as to whether or not there is merit in automatically optimizing beam angles in addition to beam intensities, and what the optimum number of beams is [27]. From a mathematical point of view, op- timization of beam angles is a very difficult problem, much more difficult than the optimization of intensity maps. In the current practice the most common ap- proach is to use “class solutions.” Based on experience or published work, one first determines appropriate beam angles for different classes of cases (i.e., disease sites), and these beam angles and numbers are then used for future treatments of cases of this class. The question still

remains as to what to do in new cases, especially since it is known that the most suitable beam angles in IMRT can be drastically different from the best 3D-CRT beam angles [28]. Therefore, beam angle optimization could play an important role in IMRT.

The degree of dose conformality that is achievable with IMRT is beginning to challenge the accuracy and precision with which the target volume and critical structures can be localized, especially in extra-cranial treatments. Day to day setup errors, internal organ motion, and outlining errors can compromise the achievable dose localization by a larger degree than the finite dose gradient due to the remaining physical and technical limitations in IMRT. Several chapters in this book address issues of image guided targeting, control of internal organ motion, and time-adaptive radiotherapy strategies.

IMRT is probably the ultimate radiotherapy tech- nique using photon beams. Nevertheless, as mentioned above, it still has limitations that are based on the physi- cal properties of the interaction of photons with matter.

Among those limitations are the relatively high integral dose and the inability to spare simultaneously multiple critical structures surrounding the target volume. Com- plex critical treatments such as pediatric treatments therefore leave something to be desired in terms of both target coverage and critical structure sparing. The more fundamental physical limitations can only be avoided by going to a different treatment modality such as proton therapy. It has recently been shown that intensity mod- ulation can play an important role in proton therapy as well [14, 29].

References

1. Brahme A, Roos JE, Lax I (1982) Solution of an integral equation in rotation therapy. Phys Med Biol 27:1221–1229 2. Mackie TR, Holmes TW, Swerdloff S, Reckwerdt PJ, Deasy JO,

Yang J, Paliwal BR, Kinsella TJ (1993) Tomotherapy: a new concept for the delivery of conformal radiotherapy. Med Phys 20:1709–1719

3. Convery DJ, Rosenbloom ME (1992) The generation of intensity-modulated fields for conformal radiotherapy by dy- namic collimation. Phys Med Biol 37(6):1359–1374

4. Stein J, Bortfeld T, Doerschel B, Schlegel W (1994) Dynamic X-ray compensation for conformal radiotherapy by means of multi-leaf collimation. Radiother Oncol 32:163–173 5. Svensson R, Kallman P, Brahme A (1994) An analytical solution

for the dynamic control of multileaf collimators. Phys Med Biol 39:37–61

6. Bortfeld T, Kahler DL, Waldron TJ, Boyer AL (1994) X-ray field compensation with multileaf collimators. Int J Radiat Oncol Biol Phys 28:723–730

7. Bortfeld T, Burkelbach J, Boesecke R, Schlegel W (1990) Methods of image reconstruction from projections applied to conformation radiotherapy. Phys Med Biol 35:1423–1434 8. Palta JR, Mackie TR (eds) (2003) Intensity-modulated radia-

tion therapy – the state of the art. Medical Physics Publishing

9. Woo SY, Sanders M, Grant W, Butler EB (1994) Does the “pea- cock” have anything to do with radiotherapy? Int J Radiat Oncol Biol Phys 29(1):213–214

10. Ling CC, Burman C, Chui CS, Kutcher GJ, Leibel SA, LoSasso T, Mohan R, Bortfeld TR, Reinstein L, Spiro S, Wang X-H, Wu Q, Zelefsky M, Fuks Z (1996) Conformal radiation treatment of prostate cancer using inversely-planned intensity-modulated photon beams produced with dynamic multileaf collimation.

Int J Radiat Oncol Biol Phys 35(4):721–730

11. Chen Z, Wang X, Bortfeld T, Mohan R, Reinstein LE (1995) The influence of scatter on the design of the optimized intensity modulators. Med Phys 22(11):1727–1733

12. Mohan R, Wu Q, Wang X-H, Stein J (1996) Intensity modula- tion optimization, lateral transport of radiation and margins.

Med Phys 23(12):2011–2022

13. Liu HH, Wang X, Dong L, Wu Q, Liao Z, Stevens CW, Guer- rero TM, Komaki R, Cox JD, Mohan R (2004) Feasibility of sparing the lung and other thoracic structures with intensity- modulated radiation therapy (IMRT) for non-small cell lung cancer (NSCLC). Int J Radiat Oncol Biol Phys 58(4):1268–1279 14. Oelfke U, Bortfeld T (2003) Optimization of physical dose dis- tributions with hadron beams: comparing photon IMRT with IMPT. Technol Cancer Res Treat 2(5):401–412

15. Murshed H, Liu HH, Liao Z, Barker JL, Wang X, Tucker SL, Chandra A, Guerrero T, Stevens C, Chang JY, Jeter M, Cox JD, Komaki R, Mohan R (2004) Dose and volume reduction for normal lung using intensity-modulated radiation therapy for advanced-stage non-small cell lung cancer. Int J Radiat Oncol Biol Phys 59(4):1258–1267

16. Chandra A, Liu H, Tucker SL, Liao Z, Stevens C, Chang J, Jeter M, O’Reilly M, Mohan R, Cox JD, Komaki R, Guerrero T (2003) IMRT reduces lung irradiation in distal esophageal cancer over 3D CRT. Int J Radiat Oncol Biol Phys 57(2 Suppl):S384–S385

17. Benedict SH, Cardinale RM, Wu Q, Zwicker RD, Broaddus WC, Mohan R (2001) Intensity-modulated stereotactic ra- diosurgery using dynamic micro-multileaf collimation. Int J Radiat Oncol Biol Phys 50(3):751–758

18. Mohan R, Cardinale RC, Wu Q, Benedict S (2000) Intensity- modulated stereotactic radiosurgery. In: Molls M (ed) Three-dimensional radiation treatment, technological inno- vations and clinical results. S Karger AG, Basel, Switzerland,

Munich, Germany, pp 40–48

19. Wu Q, Mohan R, Morris M, Lauve A, Schmidt-Ullrich R (2003) Simultaneous integrated boost intensity-modulated ra- diotherapy for locally advanced head-and-neck squamous cell carcinomas. I: Dosimetric results. Int J Radiat Oncol Biol Phys 56(2):573–585

20. Yu Y (1997) Multiobjective decision theory for computational optimization in radiation therapy. Med Phys 24(9):1445–1454 21. Küfer K-H, Scherrer A, Monz M, Alonso F, Trinkaus H, Bort- feld T, Thieke C (2003) Intensity modulated radiotherapy – a large scale multi-criteria programming problem. OR Spec- trum 25:223–249

22. Siebers JV, Mohan R (2003) Monte Carlo and IMRT. In: Mackie TR (ed) Intensity-modulated radiotherapy – the state of the art. Medical Physics Publishing, Madison, WI, pp 531–560 23. Mohan R, Wu Q, Manning M, Schmidt-Ullrich R (2000) Ra-

diobiological considerations in the design of fractionation strategies for intensity-modulated radiation therapy of head and neck cancers. Int J Radiat Oncol Biol Phys 46(3):619–630 24. De Meerleer G, Vakaet L, De Gersem W, Villeirs G, De Neve W

(2004) Direct segment aperture and weight optimization for intensity-modulated radiotherapy of prostate cancer. Strahlen- ther Onkol 180(3):136–143

25. Shepard DM, Earl MA, Li XA, Naqvi S, Yu C (2002) Direct aperture optimization: a turnkey solution for step-and-shoot IMRT. Med Phys 29(6):1007–1018

26. Langer M, Lee EK, Deasy JO, Rardin RL, Deye JA (2003) Opera- tions research applied to radiotherapy, an NCI-NSF-sponsored workshop February 7–9, 2002. Int J Radiat Oncol Biol Phys 57(3):762–768

27. Soderstrom S, Brahme A (1996) Small is beautiful – and often enough (Letter to the Editor). Int J Radiat Oncol Biol Phys 34(3):757–758

28. Stein J, Mohan R, Wang X-H, Bortfeld TR, Wu Q, Preiser K, Clifton Ling C, Schlegel W (1997) Number and orientations of beams in intensity-modulated radiation treatments. Med Phys 24(2):149–160

29. Lomax AJ, Boehringer T, Coray A, Egger E, Goitein G, Gross- mann M, Juelke P, Lin S, Pedroni E, Rohrer B, Roser W, Rossi B, Siegenthaler B, Stadelmann O, Stauble H, Vetter C, Wisser L (2001) Intensity modulated proton therapy: a clinical exam- ple. Med Phys 28(3):317–324