Conformal radiosurgery and radiotherapy planning using intensity modulated photon beams


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Conformal radiosurgery and radiotherapy planning using intensity modulated photon beams
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Meeks, Sanford L., 1968
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Table of Contents
    Title Page
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    Table of Contents
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    Chapter 1. Introduction
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    Chapter 2. Review of the literature
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    Chapter 3. University of Florida treatment planning
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    Chapter 4. Inverse radiotherapy treatment planning
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    Chapter 5. Techniques for quantitative plan evaluation
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    Chapter 6. Clinical treatment planning studies
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    Chapter 7. Physical requirements of intensity modulation device
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    Chapter 8. Clinical efficacy of tomotherapy
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    Chapter 9. The effect of random positional errors on inverse radiotherapy plans
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    Chapter 10. Discussion
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    Appendix A. Calculation of normal tissue complication probability
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    Appendix B. Calculation of tumor control probability
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    Appendix C. Optimization of intensity modulation functions
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    Biographical sketch
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Full Text










I would like to express my sincere appreciation for the guidance provided by the

members of my supervisory committee. Special thanks are due to my committee

chairman, Dr. Frank Bova, who has taught me a great deal about medical physics, and

whom I will always respect and admire. I would also like to thank the Nomos

corporation for its support, and its technical staff for assisting me overcome numerous

obstacles caused by computer and/or operator error. I am also grateful to Dr. John

Buatti, Dr. Gerald Kutcher and Dr. Andrzej Niemerko for insightful discussions

regarding the dose-response modelling required for quantitative plan comparisons, and

Dr. John Buatti, Dr. Yvonne Mack, Dr. William Mendenhall and Dr. Robert Ziotecki

for assistance with delineation of target volumes. Finally, I would like to thank all of

my family, friends and co-workers who have supported me emotionally and helped make

this work enjoyable. In particular, I would like to thank my parents for their gentle

prodding throughout my educational experience, and my wife, Allyson, for her patience

and also for allowing me the greatest joy I've ever known by giving me a son, Alton.


ACKNOWLEDGEMENTS ...................................... ii

ABSTRACT .......................................... v


1 INTRODUCTION .................................. 1

Conventional External Beam Radiotherapy ..................... 1
Stereotactic Radiosurgery .................................. 2
Conformal Radiotherapy .................................. 3

2 REVIEW OF THE LITERATURE ........................... 9

Inverse Radiotherapy Planning Algorithms ..................... 9
Clinical Treatment Planning Studies ........................ 21


Conventional Treatment Planning .......................... 27
Three Dimensional Planning (Virtual Simulation) .............. 30
Stereotactic Radiosurgery Treatment Planning ................ 31


M IM IC .......................................... 37
Peacock PlanTM ............. 41
Peacock Plan TM .................................... 41
Verification of Dosimetry Algorithm ........................ 47


Dose Volume Histograms ................................. 52
Normal Tissue Complication Probability ...................... 56
Tumor Control Probability .............................. 60
Dosimetric Statistics .................................... 64
Biologically Normalized Dose Fractionation .................. 65

Score Functions ...............................
Delivery Efficiency .............................


Stereotactic Radiosurgery Patients ....................
Head and Neck Carcinomas .......................
Intact Breast .................................
Lung Cancer .................................
Carcinoma of the Prostate .........................
Discussion ....................................

DEVICE ..................................

Computer Simulation of Intensity Modulator .............
Derivation of Semiempirical Dose Model ...........
Description of Computer Algorithm ..............
Vane Width ...............................
Step Resolution ...........................
Clinical Resolution Requirements ....................

. 67
. 68

. 69

. . .. 73
. . .. 93
. . .. 94
. . .. 96
...... 98
. . .. 99

. . .. 130




10 DISCUSSION ...................................



. 199

PROBABILITY .................................. 209



REFERENCES ....................................... 263

BIOGRAPHICAL SKETCH ................................ 272

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Sanford L. Meeks

December 1994

Chairperson: Frank J. Bova, Ph.D.
Major Department: Nuclear Engineering Sciences

This paper investigates the efficacy of inverse radiosurgery and radiotherapy

planning in the clinical environment. Inverse radiotherapy plans were generated for

patients with lesions at various anatomical sites using the Peacock treatment planning

system, which determines the optimal conformal radiotherapy plan through

backprojection and simulated annealing. These treatment plans were then compared to

two- and/or three-dimensional conventional treatment plans generated for actual patient

treatment. Plan comparisons were accomplished through conventional qualitative review

of two-dimensional dose distributions in conjunction with quantitative techniques such as

dose volume histograms, dosimetric statistics, normal tissue complication probabilities,

tumor control probabilities, numerical scoring and treatment delivery efficiency. The

physical limitations of modulation devices based on multileaf collimators were studied

through computer simulation of these devices in addition to examination of their utility

in the clinical environment. Other treatment parameters which affect the clinical efficacy

of conformal radiotherapy plans that were also studied include the use of noncoplanar

beams versus single arc conformal therapy (tomotherapy) and uncertainty in patient



Conventional External Beam Radiotherapy

Radiation therapy is a clinical specialty devoted to the treatment of patients with

malignant or benign neoplasms through the use of ionizing radiation. The primary goal

of radiotherapy is to deliver a therapeutic dose to the targeted lesion with minimal dose

to surrounding normal tissue, resulting in uncomplicated eradication of the tumor.

Unfortunately, the dose required for tumor control often leads to a finite probability of

undesirable side effects in normal tissue. Nonetheless, radiation therapy is an appealing

alternative to surgery in many instances where surgical resection may produce

unacceptable anatomical, physiological or cosmetic results or for extensive lesions that

cannot be surgically rejected. Radiotherapy also serves as a powerful adjunct to other

treatment modalities such as surgery and chemotherapy. Radiotherapy is often used

preoperatively to shrink the tumor prior to resection, or alternatively, postoperatively in

order to eradicate microscopic disease left in the area of the gross tumor. Similarly,

chemotherapy is used in conjunction with radiation therapy in order to reduce the initial

number of clonogenic cells before irradiation, or to eradicate distant metastases which

may not be within the irradiated volume [Per92].

Radiation was first used for cancer treatment by Grubbe in 1896, shortly after

Roentgen's discovery of x rays in 1895 and the Curies' discovery of radium in 1896


[Wal88]. Technological advances in radiotherapy equipment have accrued steadily since

that initial experience with improved x-ray generators followed by cyclotrons,

synchocyclotrons, betatrons and linear accelerators [Per92]. Modem radiotherapy relies

primarily on high energy gamma rays from 'Co beams and high energy x rays and

electrons produced by linear accelerators, although other particulate and electromagnetic

irradiations are frequently utilized.

Stereotactic Radiosurgery

Stereotactic radiosurgery is a technique in which small focused beams of radiation

are utilized to treat intracranial targets. Radiosurgery is an attractive treatment modality

because it can be used to treat patients who have lesions which are not suitable for

conventional neurosurgical techniques, there is little risk of infection or hemorrhage, and

the procedure may be performed quickly on an outpatient basis [Win88]. At the

University of Florida, arteriovenous malformations are the most common lesions treated

with stereotactic radiosurgery, but a variety of solid lesions exist which are suitable for

treatment by radiosurgery. These include pituitary tumors, pinealomas, acoustic

neuromas, small malignant neoplasms and craniopharyngiomas [Fri89].

Stereotactic radiosurgery was first described by Lars Leksell of the Karolinska

Hospital in 1951. He first experimented with the use of finely collimated beams of 200

kVp x rays, but it was clear that higher energy radiation should be utilized [Lek51].

With the help of two physicists, Kurt Liden and Borje Larsson, Leksell experimented

with the use of proton beams and linear accelerators, but he decided these devices were

inadequate for radiosurgery. He and his coworkers then developed the Gamma KnifeTM,


which uses multiple 'Co sources focused at a central point [Lek83]. Using the Leksell

Gamma Unit, these and other researchers have reported impressive control rates for a

variety of small lesions [Lek87]. This high rate of success has been limited to small

targets, however, since the maximum Gamma Knife field size has an 18 mm diameter.

Since the average radiosurgery is approximately 24 mm, larger targets are treated with

many small shots from the Gamma Knife. The overlap of these small circular shots can

lead to an undesirable large dose inhomogeneity within the targeted region. In spite of

this success, the Gamma Knife is not practical for use in most radiotherapy clinics since

it is a costly dedicated unit with two hundred one 'Co sources which must be maintained

and periodically reloaded.

In order to construct an effective radiosurgical system that would be less expensive

yet flexible, researchers investigated the use of linear accelerators. These systems utilize

multiple noncoplanar arcs of radiation which intersect at the target to achieve a steep

dose gradient outside of the target. This allows one to achieve a high dose within the

targeted region while maintaining minimal dose to normal tissues outside of the target

[Fri92]. One such system has been developed at the University of Florida by Friedman

and Bova. This system has the highest proven treatment accuracy of the linac systems

currently used. It has a radiation beam accuracy of 0.2 + 0.1 mm [Fri89].

Conformal Radiotherapy

In order to reduce toxicity to normal tissues from radiotherapy, it is critical that the

high dose region be shaped to fit the intracranial target volume in all dimensions. The

contouring of the target region with the high dose region is known as conformation


therapy [Bra82]. Various methods have been utilized in an attempt to conform the dose

distribution to the shape of the target.

In conventional radiotherapy, combinations of weighted fields are used to help

shape the isodose distribution. Wedged fields are sometimes used in conjunction with

these weighted fields in order to produce dose gradients which help to further conform

the distribution. Combination of different radiation qualities and modalities (photons and

electrons) is a powerful tool often exploited in order to force dose deposition in a region

of interest and maximize dose falloff outside of this region.

Field shaping devices are employed to contour these radiation beams to the shape

of the targeted lesion. One common method of field shaping is the use of custom low

melting alloy blocks for each treatment field. These blocks may be designed using either

radiographic or computer generated Beam's Eye-View techniques (BEV). Radiographic

techniques have historically been more common, since the physician need simply outline

the shape of the block on radiographs taken through the target volume. CT scan data are

often used to aid the radiotherapist in delineation of target and critical structures on the

plane radiograph, but use of this data forces the physician to mentally integrate the two

dimensional CT slices into a three dimensional image [She87].

The BEV technique more fully exploits the information obtained from CT scans by

digitally reconstructing the data set in an arbitrary plane such that the observers eye may

be hypothetically placed at the radiation source. By viewing the patient along the central

axis of the radiation beam, the relative positions of anatomical structures may be easily

determined and the target may be accurately delineated [Goi83].


Obviously, these custom blocks can only be used for static radiotherapy treatments

which utilize a limited number of fields. Multileaf collimators may be utilized to

increase the number of static fields since the projections of the leaves into the field

approximate the smooth contour of custom shielding blocks. Dynamic multileaf

collimation has been proposed in order to combine the benefits of arc therapy with BEV

conformal techniques [Mos92]. Using the BEV, the leaves of these collimators may be

adjusted to conform to the projected area of the target as the gantry and/or treatment

couch are moving.

Similar conformation methods are employed in stereotactic radiosurgery. Various

sizes of circular collimators are available which adequately conform the radiation beam

to the shape of spherical lesions. Beam weighting and arc manipulations allow the

spherical distribution to be elongated and rotated to better conform the high dose region

to oblong target shapes. For highly irregularly shaped targets, more complicated

techniques such as the use of multiple isocenters may be required. The use of multiple

isocenters does often yield a conformal plan, but also leads to a large dose inhomogeneity

(e.g., hot spots where the spherical distributions overlap) within the target volume. This

appears to be undesirable since a retrospective study performed by Nedzi et al. indicates

that dose inhomogeneity is associated with an increased risk of complications for the

radiosurgery patient [Ned91]. McGinley et al. have designed an adjustable collimator

to tailor the shape of the high dose region to the shape of irregular target volumes. This

device consists of a circular collimator which was modified to allow the manual insertion

of lead blocks in order to alter the beam shape and cause an elongation of the dose

distributions [McG92]. The dose distribution can be elongated along the rotation axis or

perpendicular to this axis. Elongation along other axes is not possible, which limits the

clinical usefulness of this collimating device.

Dynamic field shaping is also under investigation for use in conformal

radiosurgery. A retrospective study by Bova and Leavitt of over forty patients treated

with radiosurgical techniques concluded that "over 2/3 of the patients would have

received a reduced radiation dose to the normal brain through use of conformational field

shaping techniques, had these capabilities been available" [Lea91,pg. 1249]. Conceptual

studies have been performed by Moss [Mos92] and Nedzi et al. [Ned92]. Moss

investigated the viability of dynamic multileaf collimation. Using computer simulations,

he compared the dose distributions that would result from the use of two and four jaw

multileaf collimating systems to shape the fields for treatment of a variety of target

shapes. He determined that either one of these systems would provide better conformal

therapy than a rotating collimation system [Lea91] or the circular collimating system

currently employed.

Nedzi et al. performed a computer modeling study which compared the use of five

different field shaping devices. They determined the dose distributions that would result

from utilizing these devices for the treatment of 43 tumors that had been previously

treated at the Joint Center for Radiation Therapy of Harvard Medical School. They

concluded that although an ideal multileaf collimator yields the best conformal plan, even

simple field shaping devices offer an advantage over the circular collimating devices that

are currently used. This improvement was most noticeable with irregularly shaped

targets that previously required multiple isocenters, where simple field shaping devices

can provide homogeneous dose distributions and adequate field shaping [Ned92].

One of these simple collimating devices is a rotating jaw collimator. A prototype

rotating jaw collimator has been designed and constructed by Leavitt et al. [Lea91]. This

device has two sets of rectangular collimators upstream from the existing circular

collimator. The rectangular collimators are mounted on rotating tables such that both

rotation and translation of the jaws are possible. Thus, this collimating system may

define a polygonal field shape having up to four straight and four curved edges.

Obviously, this device can not be used to effectively treat concave field shapes of lesions

that are extremely irregular. It is very simple mechanically, however, and has been

shown by Moss, Nedzi and Leavitt to be useful for many situations.

Although these techniques provide an attempt at conformal therapy, it is impossible

to design a collimation system which can exactly tailor the shape of the dose distribution

to the projected area of the target at every point on the target. These collimation

schemes also fail to conform to the shape of treatment volumes that contain concave

regions [Bor90]. A new conformation technique known as inverse radiotherapy planning

has been proposed which theoretically alleviates some of the problems associated with

current conventional techniques. Standard techniques in conformal therapy set up the

beams desired for treatment and then compute a dose distribution based on these beams.

If the distribution is not satisfactory, the beam set up is altered in an iterative fashion

until the distribution is satisfactory. In contrast, inverse radiotherapy techniques begin

with the desired dose distribution and calculate the fluences necessary to produce this

distribution [Bor90]. This treatment technique is analogous to the filtered backprojection

technique used for reconstruction of images in computed tomography (CT).

In CT, the two-dimensional density distribution of tissue within the patient is

projected onto one-dimensional lines. These projections may be filtered and then

backprojected resulting in a set of two-dimensional slice images. Analogously, inverse

radiotherapy planning starts with a set of prescribed two-dimensional dose distributions

which are projected onto lines. These projections may be mathematically filtered to

obtain an intensity modulation function (IMF), and irradiation of the patient

("backprojection" of the IMF) results in the desired dose distribution. As with CT

imaging, other methods have been attempted to solve this problem, and results of these

research efforts will be discussed further.

In radiotherapy and radiosurgery, once the high dose region has been defined by

the physician's outline of the target volume, the application of inverse planning has two

primary components: 1) determine the beam fluences necessary to produce the desired

dose distribution and 2) design a method of physically modulating the intensity of the

radiation beam in order to produce these intensities. Once adequate solutions are

obtained for these two components, inverse radiotherapy can theoretically produce a dose

distribution which is not only BEV conformal, but conformal to the target shape in all

dimensions. This research will investigate the efficacy of this conformal planning

technique for achieving the aforementioned goal of radiation therapy.


Inverse Radiotherapy Planning Algorithms

As mentioned previously, inverse radiotherapy planning offers a unique approach

to conformal therapy in which the beam fluences necessary to create the desired dose

distribution within a patient can be calculated from this very dose distribution. This

technique was first examined by Brahme et al. in 1982 [Bra82]. The aim of this

investigation was to determine the one-dimensional lateral dose profile required for an

incident beam to produce a desired radial dose distribution after one complete rotation

about the axis of symmetry of a cylindrical phantom. To further simplify the problem,

a plane parallel beam was assumed and depth dose was approximated by a simple

exponential characterized by a practical attenuation coefficient, Ax. Buildup near the

surface of the phantom was also disregarded. These simplifying assumptions allow the

desired dose distribution following one complete rotation to be computed as

D(r) = d(x)exp(- pz) -

where d(x) describes the lateral dose distribution (dose variation along the x-axis), z is

the distance from the center of the cylinder along the beam axis (perpendicular to the x-

axis) and r is the radial distance from the center of the cylinder to any point within the

cylinder. Through use of a transformation to polar coordinates, this integral may be

rewritten as


n 0 1
0 (r2-x2)2

which is the well known Abel integral equation. In order to obtain a solution for the

lateral dose distribution, d(x), of the incident beam the Abel equation can be transformed

into a convolution equation through another change of variables. The Laplace transform

was applied to this convolution equation, and after a return to the original variables the

explicit solution to the equation is

d(x) =- df cO--'-. D(r)rdr.
dx3 1
ro (x2-r2)2

Thus, if the dose distribution, D(r) is known to be a continuously differentiable function,

the lateral dose distribution of the incident beam may be calculated.

This simplified statement of the inverse problem allowed Brahme et al. to draw

several important conclusions. First, they realized that the solution to this problem is

nearly identical to the problem of filtered backprojection in CT scanning. Thus,

algorithms already in use may be adapted to fit the inverse problem. The use of these

algorithms can present problems, however, since they can lead to the need for physically

unrealistic negative fluences when used for the inverse problem. Negative beam fluences

are a recurring obstacle when one attempts to determine the beam fluences required to

produce an ideal dose distribution (eg., a high dose region surrounded by a zero dose

region). Obviously, it is physically impossible to have a high dose region surrounded

by a zero dose region because the radiation beam deposits some finite dose as it traverses

the region surrounding the target. Purely mathematical solutions to the inverse problem

thus yield negative beam fluences which essentially subtract dose from the regions

surrounding the target in order to produce the ideal dose distribution. Brahme et al.

suggest that this problem can be avoided in practice with the use of higher energy beams.

The lower attenuation coefficients associated with such beams lessens the need for

negative beam fluences.

Cormack [Cor87a] attempted to extend the work of Brahme for use with dose

distributions which are not circularly symmetric. Cormack utilized virtually the same

simplifying assumptions as were used in the previous work. Buildup near the surface

was ignored, as was scattering. These assumptions allow the dose to be directly

proportional to the beam intensity. Beam divergence was also ignored, which is a

reasonable approximation if the source is a large distance from the surface. This work

further simplified the problem into what was termed the zeroth approximation. This

approximation assumed that cosh(14x)= 1, where 4 is the attenuation coefficient and x is

the distance from the lesion to the surface. This assumption leads to a small error when

used with higher energy beams (> 10 MeV), but can cause a rather large error with

lower energies. Mathematically, the zeroth order attempt was formulated as follows.

The dose, D, delivered during a complete rotation at a point, P, with polar coordinates

(p,SO) is

D(p,p)=- f Apcos(Q-y),Q]d0,
'4' -nt/2

where f denotes the fluence delivered along a single line during the rotation, as depicted

in Figure 2-1.

Figure 2-1: Geometric representation of Cormack's formalism. An intensity distribution
f produces a constant dose along the line through P. The line OS makes an angle 7/2 -
0 with the x-axis. Reproduced with permission from Elsevier Science Ltd., UK
[Cor87a, pg. 625, Figure 2].

Thus, this problem takes the form of a Radon transform, which is simply the

problem of determining a function from its integrals along straight lines. Radon

transforms have a well established mathematical form which can be extended for use with

the inverse problem. The desired result can be obtained by expanding D in orthogonal

functions, and directly deriving the expansions of fl. The resulting equation is

(l+n)!P(li+n+2m+2) ,3,
frm (l +n+r)!f(l+n+m+3/2) s2

where s is the distance from the center of the patient to the intensity distribution, r is the

distance from the intensity distribution to the x-axis, G is a shifted Jacobi polynomial,

and 1, m, n, and X are integers.

Cormack also noted the requirement for negative beam intensities which is imposed

by the mathematical formalism. To deal with this problem, the beam intensity was set

equal to zero where negative intensity was required by the theory. Although this

approach fails to yield the ideal dose distribution, it is "perhaps no worse than the trial

and error method presently used in treatment planning" [Cor87a, pg. 630].

Cormack and Cormack [Cor87b] proceeded to a solution for what was termed the

first-order approximation. The first order approximation used the same formalism and

utilized many of the same assumptions (e.g., ignored scatter, buildup, and divergence)

as were used in the zeroth approximation. The first order approximation was extended

to include use with larger attenuation coefficients, and thus be useful with lower energy

beams. Thus the form of the equation required to solve for the integral dose after one

complete rotation is very similar to the one previously seen:

D(p,q)= f lpcos(O-q_),O]exp[-_.(R2-r2) 2]cosh[lpsin(O-9)]dO.

It was determined that the first order approximation was in the form of an

attenuated circular Radon transform. The problem was then solved for several specific

dose distributions with an axis of symmetry, but a general solution was not obtained due

to the mathematical difficulty encountered in solving this problem.

In 1988, Brahme attempted to apply the inverse approach in order to obtain optimal

dose distributions for dynamic therapy. The desired dose distribution was modeled as

a density of point irradiations, and the fluences required by at each gantry position were

obtained by backprojection of these densities on the position of the radiation source. The

optimal dose distribution was subdivided into basic optimal distribution densities for point

targets. The desired dose distribution could then be computed as the convolution of these

point dose densities with the point irradiation intensities,

D() =f ff (F)d( I F-,l \)d3r

where d is the point dose density, phi is the point irradiation intensity, r is the distance

from the center of the phantom to the point of dose calculation, and r0 is the center

coordinate for each point irradiation. This convolution was performed in Fourier space,

which eased the inversion of the equation since we now have a simple product of two

Fourier transforms

F{D(r} =F{ p(j I}Fd( Ir-F I)}

Inversion of this equation yields the irradiation intensities in Fourier space. Taking the

inverse Fourier transform yields the point intensities, but also results in zeros which

cause large oscillations in the intensity function. Analogous to CT filtered backprojection,

introduction of a low pass filter, Z(s,X) in Fourier space smooths the intensity function

resulting in the following form for solution of the point irradiation intensities:
(r3 =F-=F{Z(9,).) DOs-I
These point irradiation densities may then be decomposed into thin pencil beams and
These point irradiation densities may then be decomposed into thin pencil beams and

convolved back with the point dose distributions taking into account the true patient

geometry. This allowed the production of isodose lines, which were simply the reverse

of the procedure just completed multiplied by a correction for beam absorption during

backprojection. A comparison of the results from use of this technique with conventional

radiotherapy techniques can be seen in Figure 2-2. As seen in the figure, only complex

conventional treatments can provide adequate conformation in cases involving concave

targets. If the dose rate is varied along with the field size, however, Brahme theorized

that even simple treatments such as two or three field techniques are sufficient.


: i I

f *) --* ... --' : "b7T 'i f p- i

t I ..-". -, - / ,. ia / v ..-/
parallel oppsd beam therapy arc therapy four field box therapy conformation therapy

{r: ( . -----

', -
three field / minimal mean dose specified marximum dose minimal dos
technique outside target volume, to org at risk to organ at rtek
Figure 2-2: Schematic comparison of inverse radiotherapy planning with conventional
radiotherapy techniques. Modulation of beam fluence allows dose conformation (---) to
targets (shaded) as well as minimization of dose to critical organs. Reproduced with
permission from Elsevier Science Ltd., UK [Bra88, pg. 138, Figure 7].

Barth [Bar90] extended this work to the case of ideal dose distributions for convex

phantoms of arbitrary shape. The general approach was to represent arbitrary dose

distributions as numerous small radially symmetric dose distributions (see Figure 2-3).

The problem was then broken down into a summation of attenuated Radon transforms,

so the mathematical formalism was very similar to that used by Cormack and Cormack

[Cor87]. The inversion of these transforms lead to the required beam fluences. Scatter,

buildup and divergence were again ignored in order to simplify the problem. The

difficulty of negative beam fluences was again encountered, and these were simply set

to zero as usual.


Figure 2-3: A convex phantom of arbitrary shape with an arbitrarily shaped dose
distribution comprised of N small radially symmetric dose distributions. Reprinted with
permission from Elsevier Science Ltd., UK [Bar90, pg. 429, Figure 4].

Barth felt that these explicit methods of fluence calculation can not be used

to determine the final treatment plan due to the numerous simplifying assumptions which

must be employed in order to perform the calculations. Instead, he felt that this

technique would be useful as a starting point for traditional forward iterative methods of

plan optimization. Consequently, several methods have developed which exploit the use

of both analytical and iterative techniques. For example, Bortfeld et al. [Bor90] applied

image reconstruction techniques to the inverse problem. The required beam fluences,

or intensity modulation functions (IMF), were calculated utilizing two well established

CT algorithms: filtered backprojection and the iterative reconstruction technique (IRT).

Scattering, buildup, divergence and inhomogeneities were ignored. To perform

backprojection, the prescribed dose distributions were first projected onto lines, which

is basically a simple summation of dose densities along ray lines. A two-dimensional

Fourier transform of these lines was performed, and a high pass filter was applied.

Backprojection was then performed to obtain the IMF, and negative values of the IMF

were set to zero. It was determined that this procedure did not significantly effect the

isodose lines.

This explicit approach does not force the isodose lines to exactly fit the target. To

further optimize the dose distribution, IRT was applied using the filtered backprojection

solution as its initial guess. The following criteria were deemed important for the

optimization process.

1) Target dose should be close to prescribed dose.

2) Target dose should be homogeneous.

3) Dose to sensitive organs should be below their tolerance level.

4) Dose to normal tissues surrounding the target should be low.

An objective function was formulated to mathematically incorporate the first two

criteria. The third requirement was stated as a constraint and the fourth is already

required by the conformal technique. The mathematical formulation of the objective

function was as follows:

FI =E (di-p)2=minimum

where d, is the calculated dose and p is the prescribed dose. The summation was taken

over all target points, and the function was minimized to obtain the best dose

conformation. Seven iterative steps with the objective function lead to adequate

conformation for complex targets, including convex shapes such as a horseshoe targets.

The authors felt that extremely complex targets, however, might require additional

iterative steps.

Holmes et al. have devised an iterative filtered backprojection algorithm based on

the analogy between SPECT image reconstruction and rotational radiotherapy [Hol94].

The initial beam profile is obtained through inversion of the ideal dose distribution. This

inversion is essentially a filtered fourier deconvolution of the dose distribution and a

monte carlo generated energy deposition kernel, which results in the incident energy

fluence. All negative fluence values are initialized to zero, and the forward dose is

calculated using a filtered Fourier convolution of this inversely obtained incident energy

fluence with the energy deposition kernel. The dose distribution thus obtained is then

compared against dose constraints for regions of interest, and if all points in the

distribution are within the constraints, the calculation is accepted. If the calculation is

deemed unacceptable, the residual dose in the regions of interest is utilized to determine

a new fluence profile. Dose is recalculated using this new energy fluence, and this

process continues iteratively until an acceptable solution is obtained.

Harmon also explored a compromise between analytic and iterative techniques by

combining deconvolution and optimization [Har94]. This approach offers more flexibility

than some others since it can calculate beam fluences for either rotational therapy or

multiple static beams. In order to determine a two-dimensional fluence profile for each

beam portal chosen by the user, deconvolution of a monte carlo generated single voxel

energy deposition kernel from the desired dose distribution is performed. This results

in a TERMA (total energy released to matter) profile for each beam, which can be used

to calculate the physical characteristics of the intensity modulator by ray tracing back

toward the radiation source. This ray trace includes inverse square, attenuation in

phantom and an effective attenuation through the modulation device. With this TERMA

profile in hand, forward dose calculation proceeds via convolution of the TERMA with

the aforementioned kernel. If multiple beam portals are designated, relative beam

weighting for each portal is determined by an optimization routine which varies all

weightings until the best fit to the desired dose distribution is obtained.

Purely iterative techniques have also been explored for solution of the inverse

radiotherapy planning problem, as exemplified by Webb's use of simulated annealing to

optimize the required beam configurations [Web89, Web91a, Web91b, Web92]. This

method "mimics the way a thermalized system . achieves its ground state as the

temperature slowly decreases" [Web89, pg. 1352]. Webb's initial approach begins with

a two-dimensional dose prescription and assuming that the treatment volume is axially

uniform, the dose in each small elemental beam is projected along one dimensional lines.

Scatter and buildup are ignored, and the dose is then calculated as the product of beam

weighting and exponential attenuation. The beam weighting is allowed to start at zero,

and weighting is slowly added iteratively until the desired weighting for each elemental

beam is determined. Later papers in the series extended Webb's initial work by

including scatter in the two-dimensional technique [Web91a] and determining optimal

elemental beam weightings for three-dimensional conformal treatment planning [Web91lb,

Web92]. Scatter is never included in Webb's three-dimensional technique. Interestingly,

this iterative technique represents a purely forward approach to solution of an inverse

radiation transport problem.

Inverse radiotherapy planning based on this technique has been commercialized by

the Nomos Corporation [Nom94]. Nomos models the elemental beams as lxl cm2

measured finite size pencil beams and calculates dose for each of these pencil beams

using a simple model based on tissue-maximum ratios and off-axis ratios. Optimal beam

weightings for these pencil beams are determined using a two-dimensional simulated

annealing algorithm. These two-dimensional optimized slices are then summed in order

to determine a three-dimensional dose calculation. Although two-dimensional

optimization does not guarantee an optimal three-dimensional treatment plan, time

required for execution of the three-dimensional optimization using computer hardware

currently available renders it impractical for this approach.

Clinical Treatment Planning Studies

Historically, treatment plans were designed utilizing a relatively limited number of

radiation field arrangements and the dose delivered from these fields was then

superimposed on only one or at most a select few transaxial images of the patient.

Comparison of rival treatment plans was thus relatively straightforward and based

primarily on the physician's experience and basic dosimetric endpoints such as target

dose uniformity and maximum critical organ dose as represented on this limited number

of axial slices [Kut92]. The advent of three dimensional and conformal treatment

planning systems and the complexity inherent in plans generated using such systems has

sparked interest in more sophisticated methods of plan evaluation. The principal

complicating factor in evaluation of such treatment plans rests in the large volume of data

generated by such systems. As opposed to the single slice evaluation required for

conventional treatment plans, three dimensional treatment planning systems often

superimpose the dose distribution on fifty or more contiguous axial CT slices. Although

displays are developing with tools which aid in the graphical comparison of rival

treatment plans, it remains extremely tedious and time consuming to correlate and

analyze the dose distributions on multiple axial slices of the patient [Mun91]. Conformal

treatment planning systems have further complicated plan evaluation by presenting the

clinician with dose distributions which deviate substantially from those typically utilized

for patient treatment.

Various numerical evaluation techniques have developed, but have historically

been associated primarily with computerized optimization routines [Nie93, Kal92,

Moh92, Web92]. These algorithms, some of which were discussed in the preceding

section, attempt to quantify the relative merit of plans through the use of dosimetric and

or biological parameters which are formulated into objective functions. The various

computerized algorithms then attempt to minimize or maximize the objective function,

which should result in the ideal plan. Niemierko et al., for example, optimized the beam

weightings for portals chosen by the user utilizing objective function based on normal

tissue complication probability (NTCP) and tumor control probability (TCP) [Nie93].

Reportedly, these researchers have studied over forty clinical treatment plans and found

that on average their optimization routine could quickly determine a better plan than one

constructed by an experienced treatment planner. Similarly, Mohan et al. designed an

algorithm based on simulated annealing that varies beam weightings in order optimize

an objective function based on NTCP and TCP [Moh92]. Demonstrating their algorithm

using a case of prostate cancer, the researchers found that their algorithm could design

a plan with higher TCP and lower NTCP than the plan used to treat the patient. Webb

[Web92] and Kallman [Kal92] both experimented with the use of dose response functions

in their respective optimizations and both presented clinical examples. Neither compared

these results to treatment plans designed by an experienced treatment planner and were

used simply to demonstrate the use of their respective algorithms.

The first wide-scale attempt at quantitative evaluation of clinical treatment plans

was undertaken by the Collaborative Working Group on the Evaluation of Treatment

Planning for External Beam Radiotherapy (CWG) and reported on in the International

Journal of Radiation Oncology Biology Physics. In their study of three dimensional

treatment planning systems, the CWG developed and or improved treatment plan

evaluation tools such as dose volume histograms (DVIHI) [Drz91], NTCP [Kut91a], TCP

and a subjective numerical scoring system [Mun91a]. In addition, the CWG reviewed

two-dimensional dose distributions superimposed on reconstructed axial, sagittal and

coronal planes within the patient. These tools were then used for the evaluation of three-

dimensional treatment plans generated for eight separate treatment sites: nasopharynx

[Kut91b], larynx [Coi91], intact breast [Sol91], Hodgkin's disease [Bro91], lung

[Ema91b], para-aortic node [Mun91b], prostate [Sim91] and postoperative rectum

[Sha91b]. Comparison of the three-dimensional plans with conventional plans used for

treatment of these lesions proved 3-D planning a useful tool which ensured proper

delineation of the target in all dimensions as opposed to one axial plane, and also allowed

clinicians to better avoid critical organs near the treatment volume.

Conformal radiotherapy planning has not enjoyed the benefit of thorough

investigation by a collaborative working group, although several researchers have studied

the efficacy of this approach. Due to the high incidence of acute and chronic toxicities

associated with conventional radiotherapy of the prostate, many researchers have studied

this disease site for conformal radiotherapy. In these studies, conformal is defined as

treatment in which fields are designed using a beam's eye view display (BEV). Several

use only a standard four field box technique with blocks designed using the BEV utility

[Vij93, Sha91a, Sof92], while others add oblique fields to this standard technique in

order to attain better distributions [San91]. These studies showed that dose to nearby

critical structures such as the bladder and rectum could be reduced by up to 31% and

25%, respectively, when compared to clinical controls [Sof92]. In addition, clinical

trials have proven that incidence of acute toxicity is reduced using BEV conformal

techniques for radiotherapy of prostate carcinoma. Based on these results, several

researches are initiating dose escalation studies in hopes of increasing local tumor control

without increasing normal tissue toxicity above acceptable levels.

Similarly, a group at Memorial Sloan Kettering Cancer Center has investigated the

use of three-dimensional conformal radiotherapy for prostate, nasopharynx and lung

lesions [Lei91, Arm93]. These studies also defined conformal therapy as treatment using

field shaping blocks designed with aid of the BEV utility. Rather than a clinical trial,

however, the investigators used the quantitative evaluation tools developed by the CWG

in order to compare their conformal and conventional therapy results. Similar to the

prostate clinical trials, these analyses suggest that three-dimensional conformal

radiotherapy may provide a clinical advantage over conventional techniques. For

example, a study of nine lung patients showed both an increase in the minimum target

dose and a significant decrease in the calculated NTCPs when conformal treatment

planning was used [Arm93].

Conformal stereotactic radiosurgery techniques have also been studied to determine

their efficacy for clinical treatments. Moss studied the use of multileaf collimators, both

real and hypothetical, for small intracranial lesions [Mos92]. Using dose distributions,

DVHs and the integrated logistic function, which is a dose-effect model based on NTCP

theory, he concluded that clinically useful conformal therapy for small targets could only

be achieved through the construction of multileaf collimators with 5 mm wide leaves

(size projected to isocenter) as opposed to the 1 cm wide leaves currently manufactured.

Nedzi et al. used forty-three patient data sets to study treatment plans designed using five

dynamic field shaping devices for stereotactic radiosurgery: fixed circular collimators,

two independent jaw collimator, four independent jaw collimator, four independent

rotatable jaw collimator and an ideal multileaf collimator [Ned92]. Comparison of rival

plans was accomplished via DVHs and a construct they termed the treatment volume

ratio, TVR. The TVR is defined as the target volume divided by the volume receiving

at least the minimum target dose. As expected, the ideal multileaf collimator provides

the best field shaping, but even simple BEV field shaping devices provide a clinical

advantage over fixed circular collimators.

Clearly, the literature indicates that the initial step towards acceptance of novel

treatment methods is to establish that they are clinically superior to the status quo.

Interestingly, however, this has not yet occurred with inverse radiotherapy planning.

Physicists have repeatedly demonstrated the utility of inverse radiotherapy planning for

fitting arbitrary desired dose distributions. Various conic sections [Woo93, Har94] and

concave targets [Hol94, Har94] are the most often matched by inverse planning

investigators. A few investigators have attempted clinical examples, but have not

compared these examples to conventional treatment plans [Har94]. The following

investigation will attempt to bridge the gap left between laboratory novelty and clinical


In so doing, it is also hoped that this work will contribute to the growing body of

knowledge that has been made possible by the advent of three-dimensional treatment

planning systems which adequately model dose deposition. Since accurate dose volume

data is only available through the use of such systems, radiotherapy treatment planning

has historically been based primarily on the training and experience of the physician.

Through this and other similar studies, more detailed dose-volume data can be obtained

for both the current state of the art in radiotherapy, and for potential future

improvements on the state of the art. Armed with these facts rather than dogma,

hopefully the art of radiotherapy treatment planning can some day be transformed into

a true science.


Traditionally, the term radiotherapy treatment planning has been used to describe

computation of the dose distribution for one or a few transaxial sections within the

patient. Recent advances have improved the way in which treatments are planned,

however. Improved imaging modalities such as computed tomography (CT) and

magnetic resonance imaging (MRI) coupled with improved computer assisted planning

techniques permit three-dimensional treatment planning based upon realistic

representation of the patient's anatomy [Goi88]. Recognizing the effect of these advances

on treatment planning, the term now generally includes target localization and delineation

in addition to field design and dose calculation. This chapter will briefly discuss

treatment planning for the three primary teletherapy planning methods used at the

University of Florida's Shands Cancer Center: conventional planning, three-dimensional

beam's eye view planning (virtual simulation) and radiosurgery treatment planning.

Conventional Treatment Planning

Numerous imaging modalities, most notably CT and MRI, are utilized to determine

the extent of disease and its position relative to normal structures. Definitive treatment

field design is accomplished, however, via use of a treatment simulator, which

incorporates a diagnostic x-ray tube into an apparatus that duplicates the geometrical and

mechanical properties of the treatment unit. Although information obtained from CT and

MRI studies can be used as an aid for target delineation, conventional treatment planning

cannot fully exploit this three-dimensional data base due mainly to the fact that the

geometrical relationship between the patient's anatomy and the radiation beam cannot be

duplicated using a standard diagnostic x-ray unit [Kha84]. The simulator has

fluoroscopic capabilities which allow dynamic visualization of the patient's anatomy and

ensure proper positioning of the treatment fields. After the fields have been positioned,

plane radiographs are taken and the irregular fields which encompass the target are

designed on these films and digitized into the treatment planning computer system

(Theraplan, Version 5, produced by Theratronics International Limited). Dose

calculation requires not only information regarding the irregular field shapes, but also the

patient's external contour. This information is obtained via placement of solder wire

around the patient and passing through the central axes of the treatment fields. Since the

wire is quite malleable it easily conforms to the contour of the patient. This contour

information may then be digitized into the treatment planning computer to generate a

central axis slice of the patient (generally transaxial).

After input of these treatment data, Theraplan calculates dose from photon fields

using a two-dimensional semiempirical model which separates dose deposition into its

primary and scattered components. The primary dose may simply be modeled as [The90]

D,, = f(d,x,y) -DA (d) -TAR(d,O)

where f(d,x,y) = a function which describes the beam intensity profile in air at depth d,
DA = the dose in free space at depth d and
TAR(d,0) = the zero area tissue air ratio, which describes attenuation of the primary
beam by a thickness, d, of tissue.

The scatter dose contribution, which is deposited by photons which undergo at least

one interaction before depositing dose, is calculated using a Clarkson integration

technique [Joh83]. Since this scatter component is dependent both on field size and

shape, the field is divided into n equal sectors with an angle, 0, between each. The

scatter components from all n sectors are then summed as follows

6 n
.= E .SAR(dr)
27t i

where SAR(d,r)= scatter air ratio for circular field size r at depth d = TAR(d,r) -

TAR(d,0). After performing these two calculations, the scatter and primary contributions

are reassembled in order to determine the total dose calculation.

Electron dose calculation is performed in Theraplan by first dividing each electron

beam into square pencil beams measuring 0.5 cm on each side. Using a modification of

a semiempirical method derived from the age diffusion equation [Kaw75], the dose

contribution, D, from each pencil at a point (x,y,z) is calculated as [The90]

y. = [ ,.(z)-x Xo(z)+ .1 Y(e, -Y (z)-y)
D(xyz,.) = A e rf( )+ erf(--- + )j rf )+ erf(- )
2 rK-r 2xr 2L 2v/icr 2^ Jiv
SZ2 Z 2 1exp( )2( SSD )2
*cos(GI- + G2- + G)-exp( VX-0

where X0(z) = half the pencil width at depth z
Y0(z) = half the pencil length at depth z
x = distance from pencil center to calculation point in direction of field width
y = distance from pencil center to calculation point in direction of field length
z = depth in tissue
Rp = practical range for electrons = intersection of depth dose curve with
bremsstrahlung background
KT = (C/RP + 0.051")
SSD = distance form source to surface of patient

GI, G2, G3, C, N, and A = parameters which Theraplan varies in order to obtain the
best fit to measured data. After calculation of the dose contribution from each pencil

beam, each pencil is weighted depending on its position relative to the field edge. The

weighted doses from all the pencil beams are then summed to determine the total dose

given to the point (x,y,z).

Three-dimensional Treatment Planning (Virtual Simulation)

Although CT scanners provide detailed information about the anatomy of a patient,

it is not in a practical form for radiotherapy treatment planning. When utilizing these

scans as an aid to treatment planning, the radiotherapist must "mentally integrate a set

of 2D shapes into a 3D structure, visualize the intersection of his prescribed treatment

beams with that structure, visualize the resulting film, correlate that imagined film with

the actual simulation film, and determine what if any adjustments need to be made."

[She87, pg 433]. Virtual simulation more adequately integrates the CT scanner into the

treatment planning process and thus allows the radiation oncologist to better exploit the

3D data set by reconstructing a virtual patient from the CT data transferred to Theraplan.

In order to ensure accurate coordinate transfer between the CT scanner, treatment

planning computer and treatment machine, CT scans must be performed with the patient

immobilized in the treatment position. Position information is registered in an

imagesinfo file that is stored along with the image data. These CT simulation scans are

transferred to the treatment planning computer, where delineation of target and critical

structures can be performed. Although Theraplan allows the user to now digitize the

fields into the system from simulation films, the strength of virtual simulation is that it

allows the user to design radiation portals utilizing a beam's eye view display.


Theraplan's BEV utility places the user's eye at the radiation source, and permits

interactive portal design while the user looks along the central axis of the beam. From

this vantage point, the radiotherapist can view the full 3D anatomy at once and examine

the relative positions of anatomical structures as seen by the primary beam [Goi88].

This option provides a superior display from which to vary field size and also to design

field shaping blocks to match the patient's anatomy. Unfortunately, the time investment

required for collaboration of physician and dosimetrist to perform virtual simulation

prohibits its use except for cases in which portal design is especially difficult.

Dose calculation in Theraplan is performed the same for virtual simulations as it

is for conventional treatment planning situations. Although the system performs all

calculations in 2D, it can perform a pseudo 3D calculation. This option calculates the

2D dose distribution on all of the transaxial slices within the data set and presents a 3D

dose distribution. Using this tool, the radiotherapist may calculate the 3D dose

distribution from portals he has designed, and then interactively alter these portals if this

distribution is deemed unacceptable.

Stereotactic Radiosurgery Treatment Planning

Stereotactic radiosurgery was the first clinical application of virtual simulation since

treatment plans are designed exclusively using a virtual patient recreated from imaging

studies of the actual patient. In order to accurately localize the lesion, a frame of

reference known as the Brown-Roberts-WellsTM (BRW) ring must be attached to the

patient's head. This device is a metal ring which attaches to the patient's head via four

aluminum pins [Fri89]. Once this frame is attached, it becomes the reference point for

all localization and enables accurate coordinate transfer between imaging devices,

treatment planning system and linear accelerator.

To obtain CT images, the BRW ring is affixed to the CT couch and a localizer is

then attached to the BRW ring via three tooling balls. The CT localizer consists of nine

rods; three pairs which are aligned with the patient and angled rods between each pair

[Saw87]. After a scout image has been obtained, transverse slices are obtained in the

region of the lesion. The localizer rods also appear in each image slice. Since the

spacing of the rods is known, the position of any object within the CT localizer can be

determined [Saw87].

Certain types of lesions require other diagnostic localization techniques. For

example, arteriovenous malformations often require the use of contrast angiography in

addition to CT. A special angiographic localizer cage is required for radiographic

localization. This localizer has four lucite plates which each contain fiducial marks.

These fiducial marks act as the reference points for localization [Sid87]. After the BRW

ring is attached to an immobilization mount and the localizer, a standard angiogram is

performed. After numerous biplane images are obtained, the anteroposterior (AP) and

lateral images where the nidus is best defined are selected.

Another special localization technique is the use of magnetic resonance imaging

(MRI). This technique is most often utilized for the localization of acoustic neuromas

or tumors which are near a bone that could cause an artifact in CT localization. Since

high magnetic fields are used in MRI, a special BRW head ring made of aluminum is

attached to the patient's head with nonmagnetic pins. Once again, a special localizer

cage is required. Geometrically, this cage is exactly the same as the CT localizer cage.

Due to the magnetic fields, however, the cage is composed of plastic. The localizer rods

on the MRI localizer are filled with a contrast material, propandiol, so that they may be

seen on the scan. To improve the signal-to-noise ratio of the scan, a special head coil

was designed for use in stereotactic localization. Once the BRW ring is attached to the

localizer cage and a special bracket on the head coil, the MRI scan proceeds as a normal

head scan.

A three-dimensional treatment planning system is utilized which runs on a SUN

SPARCstation. CT images are transferred to the SUN system via a network connection.

The nine localization rods must be identified in the first slice, and each pixel is mapped

into stereotactic space. The computer program automatically locates the position of the

rods in subsequent slices. The neurosurgeon then uses a mouse to outline the target in

the axial, coronal and sagittal planes. A treatment plan is designed which will focus

noncoplanar arcs of radiation such that they intersect at the center of the target, which

is known as the treatment isocenter. Figure 3-1 illustrates the location of arcs relative

to the patient's external contour. The intersection of these arcs at the isocenter

concentrates the dose in the targeted region while spreading low dose throughout the

normal tissue, thus creating a very steep dose gradient outside of the target.

Typically the first step in treatment design is selection of a standard treatment plan

which contains default values for the number of arcs, table angle, gantry start and stop

angles and weighting for each arc. These treatment variables are then altered such that

the dose distribution best conforms to the projected area of the target in three

dimensions. For example, the collimator size is chosen such that it will produce a

circular beam which best fits the size of the target. Arcs and/or table angles may be

altered or deleted which changes the shape of the distribution. For nonspherical lesions

multiple isocenters are sometimes employed, although as stated earlier, the dose

inhomogeneity introduced by this technique may be undesirable. This iterative technique

is repeated until the dose distribution fits the shape of the lesion with minimal dose to

normal tissues. The 80% isodose line is generally chosen as the portion of the dose

distribution which should best conform to the shape of the lesion. The fit may be

examined by starting at the first CT slice and having the computer step through the

subsequent slices in 1 mm increments. The system computes and displays the isodose

lines for each slice as it steps through the images.

290 70

310 500

3500\ / .1 100

Figure 3-1: Location of nine standard table angles relative to patient's head. Typically,
arcs are 100 degrees in length at each table angle. Figure redrawn from [Spi92].

The dose algorithm uses tissue-phantom ratios (TPR), off axis ratios (OAR), and

the inverse square law to compute the dose anywhere along the beam [Bov90]. TPR

gives the relationship of the dose along the central axis of the beam, OAR is used to

determine the relative intensity along the cross section of the beam, and the inverse

square law gives the variation of the intensity of the beam with distance from the source.

Thus, the dose at any point, p, in a circular field may be computed from [Suh90]:

D,(c,STD,d,r) = D,,f.ROF(c) -TMR(wd) -OAR(c,STDdw) (-SAD)2

where c = field size at SAD
STD = source-to-target distance
d = depth of point p
r = off axis distance
w = field size at point p
D, = reference dose
and ROF = relative output factor.

Similar treatment planning techniques are employed with MRI and angiographic

localization. MRI images are transferred via the network system and treatment planning

proceeds as it does with the CT localization. Since the images obtained through use of

MRI can have spatial inaccuracies, planning is also performed using the stereotactic CT

images, and the end plans are correlated to ensure accuracy.

The procedure is slightly different when angiographic localization is used. Since

the angiographic images are not stored digitally, the AP and lateral plane films chosen

during localization are utilized for treatment planning. The films are placed on a

digitizer and the positions of the fiducial marks are entered. The digitizer is then used

to outline the nidus in both projections. Using this data, the computer can calculate the

geometric center and the center of mass of the target. Angiography presents several

problems that make it inadequate for localization by itself. These problems include

errors in determining target size and shape [Bov91]. For example, there is a risk of

underestimating the true maximum target diameter by as much as 41% [Bov91]. Thus,

when angiographic localization is utilized, it must be used in conjunction with CT

localization in order to avoid significant errors which can lead the unnecessary treatment

of a large amount of normal tissue [Bov92].

Since the stereotactic CT scans are always utilized, the planning system allows the

user to plan and evaluate the plan in three dimensions using interpolated reformatted CT

scans. Through the use of this technique, the full set of anatomic data is available to the

user. The system allows the user to contour lesions and anatomical structures, but these

tools are not commonly utilized since they are very time consuming and unnecessary for

evaluation of a given treatment plan. Without these contours, however, it is impossible

to obtain dose volume histograms for the structures of interest. For purposes of

comparison within this project, these data were obtained for several stereotactic

radiosurgery patients.


Inverse radiotherapy treatment planning may be performed using the Peacock

Plan' system developed by the Nomos corporation. This treatment planning system is

part of an integrated 3D conformal planning/multivane intensity modulating system.

Treatment plans produced using Peacock Plan generate a set of beam weights which

allow the multivane intensity modulating compensator (MIMIC) to deliver a conformal

treatment [Nom93].


The operation of the treatment planning system is best understood if one first has

some understanding of the device which is simulated by Peacock Plan. The MIMIC

consists of twenty independent vanes which each project a lx1 cm block at the machine

isocenter. It attaches directly to a linear accelerator and modulates the intensity of a slit

collimated radiation beam. Intensity modulated slit irradiation, in conjunction with the

rotation of the gantry about the patient, allows for a slice of the patient to be treated with

a radiation dose that conforms to the shape of the target volume within the slice. After

this slice has been treated, the table is indexed and the next slice is treated. This

procedure may then be repeated until all slices within the target volume have been

treated. Obviously, this treatment modality is analogous to the method in which CT

scanners image in a slice by slice fashion. In order to shorten the required treatment

time, the MIMIC is capable of modulating two one centimeter thick slices per gantry


Figure 4-1: Beam's Eye View (BEV) of MIMIC, which contains two sets of twenty 1
cm wide independent tungsten vanes.

The MIMIC shapes the intensity of the beam through temporal modulation. Each

of the singly focused vanes may be independently addressed and translated into the path

of the radiation beam via use of pneumatic pistons. Since the eight cm tall tungsten

vanes allow minimal transmission of the primary beam (approximately 2% for 10 MV

x rays), the intensity of the beam underneath a vane will be proportional to the amount

of time that the vane is open during irradiation. The Peacock PlanT allows for eleven

different dwell times, which leads to effective transmittance values ranging from 0

(actually 2) to 100 percent in ten percent increments. For computer simulation purposes

this number of transmittances may be varied, and if found to significantly effect the

treatment plans it could easily be modified for the MIMIC.

This all or nothing approach to dynamic beam compensation has two primary

advantages. First, beam transmission is determined by the dwell time of full height

tungsten vanes, so beam hardening effects need not be considered as they must be with

conventional compensation techniques and collimators which spatially modulate the beam.

Secondly, unlike spatial modulating collimators, accurate distance encoding is not

necessary for the vanes since the vanes have only two positions (in or out) [Mac94].

As with any one-dimensional multivane dynamic modulator, the MIMIC has several

limitations. These problems are due primarily to the inefficiency of dose delivery

through these devices. Modulation of the beam intensity requires blockage of a majority

of the beam for the patient treatment. Thus, to deliver the same dose, the beam on time

is much more than with conventional treatments. Since there is a small transmission

through the vanes, a small background dose will be present within the patient. Further,

since the beam on time is lengthened, there will be an increase leakage dose from the

linear accelerator which may necessitate increased shielding thickness of the secondary

barriers in the treatment vault or increase in linac head shielding. These are engineering

details which can be examined if intensity modulated treatments prove beneficial. In fact,

with clever design, some of the current disadvantages of intensity modulation could

possibly become advantages. For example, utilizing a two-dimensional modulator can

potentially increase the efficiency of treatment under certain situations such as with

stereotactically treated brain lesions which require multiple isocenters [Har94].

I \
Xray Beam



Open Closed

Figure 4-2: Illustration of MIMIC operation. Reproduced with author's permission
[Mac94, pg. 1711, Figure 3].


Peacock Plan'

The general concept of inverse radiotherapy planning allows the user to specify the

desired result, and then the treatment planning system automatically computes a plan that

satisfactorily produces this distribution. In order to specify this desired result, Peacock

Plan' has various tools which allow the user to delineate the contour of the target tissue

and any critical structures that appear on CT data which have been transferred to the

system. It is imperative that this image overlay data contain all structures pertinent to

the planning process, since the inverse planning process relies on information about the

sensitivity of critical structures near the treatment volume and their importance

(weighting) relative to the target. Peacock also requires input of dose prescribed to

target (cGy), desired treatment complexity and safety margins which take into account

setup inaccuracies and the possibility of microscopic disease surrounding the target.

Once these data are input, the planning process is performed automatically by the

computer. The isocenter is determined as the geometric center of the defining rectangle

of the target. Peacock Plan' then simulates the MIMIC by subdividing each beam

portal into 20 one by one centimeter pencil beams. An initial guess for the weight of

each of these pencil beams is obtained through a backprojection technique

Beam Weight = Volume-- get (4-1)

where Volume,, is the volume of the target that is intercepted along the ray line of the

pencil beam and d,., is the depth at which the target is first intercepted along the ray

line of the pencil beam. Although this backprojection technique yields only a crude

approximation to the required beam weightings, accuracy is not that important at this

juncture since these weightings will serve as input to an optimization routine that will

determine the best plan.

Optimization is performed using simulated annealing, a method which

mathematically models the annealing process of metals in which the many final

crystalline configurations are possible depending on the rate of cooling [Boh86].

According to the general principles of statistical mechanics, any system that is cooled

sufficiently slowly will seek its state of minimum energy. Assuming that the cooling rate

is chosen correctly, simulated annealing will avoid local traps and minimize the objective

function for a given situation.

The annealing process is mathematically modelled as a biased random walk that

samples the objective function. The first sampling is performed using the objective

function calculated using the beam weights obtained from the initial backprojection. A

random pencil beam is then chosen, and a step of ten percent transmission (a beam

"grain") is taken in a random direction. The objective function is then recalculated.

This new step is always accepted if the new objective function is smaller than the first.

If the new objective function is not smaller, however, there is still a finite probability of

acceptance given by

p = -(- (4-2)

where po is the objective function and 3 is inversely proportional to the temperature of

the system. This probability of accepting a detrimental step follows directly from the

statistical mechanics of annealing, in which the probability that the system will transit

from a state of lower energy to one of higher energy is

---- (4-3)
p = e

where k is Boltzmann's constant (8.62 x 10- ev/K) and T is the absolute temperature of

the system.

Conditional acceptance is unique to simulated annealing, and is the feature which

makes it so powerful. Unlike purely downhill optimization methods which greedily

accept local minima, the probability of accepting a bad move allows the system to step

back out of a local minimum. As the temperature is decreased, the probability of

accepting an uphill step is also decreased and the steps should become confined to the

global minimum of the function. This is extremely important in radiotherapy

optimization, since the solution space can be extremely complex and many local minima

may exist near the global optimum solution. An example of this complexity can be seen

in the fact that a single arc optimized by Peacock may have as many as 200 dimensions

to randomly vary while it attempts to minimize the following average square deviation

objective function

V (D. -Dj?2 2
qp = <- w-weighttrge. +
D;.,( (4-4)
E (2 'weightar- e



n. = number of targets or critical structures,

weight = user defined weight for each target or structure (0.0 < weight < 2.0) and

D. = maximum target dose or dose goal for target i or structure j

The brackets (< >) denote an average over all i target voxels or j structure voxels.

Obviously this function, in its attempt to achieve high consistent target dose and low

critical structure dose, can contain a large number of local minima.

Figure 4-3: Downhill methods (dotted arrows) seek nearest well and are easily trapped
in local minima. Conditional acceptance of bad steps allows simulated annealing (solid
arrows) to escape these traps and find the best global solution.

Peacock Plan's optimization has some limitations, however. Although simulated

annealing is widely accepted as a reliable optimization method, there are situations in

which it can get trapped in local minima. The problem generally lies in the definition

of an annealing schedule that cools the system sufficiently slowly. Success is often

determined by the choice of annealing schedule, and the choice is quite often problem

dependent [Pre91]. Given an infinite amount of time and iterations, simulated annealing

can find the global optimum for any problem. For example, logarithmic cooling

schedules have been proven to always approach the absolute minimum, but these

schedules are far too slow for routine clinical use [Pre91]. In an effort to speed the

optimization, Peacock Plan' uses a simple inverse cooling schedule which results in an

algorithm known as the Fast Simulated Annealing optimization method. At each

iteration, the temperature is determined by


T = kTo0'- (4-5)
where kT0 is set to 0.1 and ni...g is the number of iterations completed before this

iteration. Using fast simulated annealing the plan may be computed in a reasonable

amount of time, but there is also a possibility that the final result will actually be a local

minimum rather than the global optimum solution.

Another limitation within the system is that Peacock Plan' develops its 3D plan

as a series of two-dimensional slices that overlap the target volume. Since optimization

is such a slow process and computational time increases rapidly with the number of

dimensions in an optimization, the optimization is performed on a slice by slice basis.

After the beam weighting has been optimized for each slice, the dose is computed using

a three-dimensional dose model. The inherent assumption is that the sum of optimized

slice plans yields an optimized plan. This assumption, however, has not been proven.

The forward dose calculation algorithm uses measured finite size pencil beam data

(MFSPB) and is based loosely on a model developed by Luxton for stereotactic

radiosurgery [Lux91]. The actual calculation is

D(d,rdL) = TMR(d)-OAR(r) -[ j (4-6)

This model assumes that the MIMIC is composed of separate lxW cm pencil beams, each

having the same off axis ratios (OAR) across the pencil. Tissue-maximum ratios (TMR),

however, are assumed to vary for each pencil due to spectral changes across the beam

axis, and separate TMRs must be measured for each pencil beam. SAD is the distance

from source to isocenter distance, STD is the distance along the beam central axis and

r' is the off axis distance of the calculation point from the central ray at depth d.,

(assuming that OARs are measured at dcLand is equal to

r/ = r (SAD +d) (4-7)
where r is the actual off axis distance of the calculation point. Noticeably absent from

the calculation is an output factor to account for field size dependence as multiple vanes

are open during irradiation. This factor is implicitly included in the calculation since the

off-axis ratio data are acquired in the penumbral region outside of the one centimeter

width of the pencil beam in order to account for side scatter from each pencil beam. The

doses from pencil beams are then summed and the penumbral overlap found in this

summation accounts for the output factor (see Fig 4-4).

Figure 4-4: Overlap of measured finite size pencil beams yields effective output factor
(field size dependence) when their profiles are summed.

Dose is calculated separately for each pencil beam using equation 4-6, and these

doses are all summed. As with conventional treatment planning systems, the dose is then

normalized to the maximum value within the calculation grid and two dimensional dose

distributions may be superimposed on the reconstructed CT images in the axial, coronal

and sagittal planes.

Verification of Dosimetry Algorithm

Peacock Plan' currently models beam data for the MIMIC attached to a 10 MV

linear accelerator at Methodist Hospital in Houston, Texas. Experimental verification

of the system was performed at Methodist Hospital [Gra94], and required production and

execution of several different treatment planning scenarios. A cubic film phantom

containing Kodak XV-2 film was placed in the beam during execution of the treatment

plan, and film dosimetry was performed utilizing a Helium-Neon laser scanning

densitometer. Two example plan verifications are illustrated in Figures 4-5 and 4-6: a

small spherical treatment and a U shaped distribution, respectively. Isodose distributions

on three planes are represented for each test to allow qualitative evaluation. The first

shown is the central axis slice, while the other two plots represent planes that are + 6

mm off of the central axis.

Recent quality assurance documents have recommended acceptable criteria for the

uncertainty of treatment planning algorithms dependent upon the dose in the region of

interest and the dose gradient within this region [Van93]. The primary criteria of

concern are that the uncertainty not exceed + 4% in a low dose gradient, high dose

region and that positional uncertainty of isodose contours within a high dose gradient

remain less than 4 mm [Van93]. VanDyk et al. define high dose as > 7% of the

normalization (prescribed) dose, while a high dose gradient is defined as > 30%/cm.

Data from the two cases presented are tabulated in Table 4-1. As seen in the table, data

on the central axis slice is very good, while off axis the uncertainty increases. Also, it

is suspected that the one very bad data point may be the result of positional errors during

film readout.

P I ( iml '. j )

pxel 1 (2 mm/pixel)

Pixel $ (2 m=/pixel)
Figure 4-5: Isodose plots for a planned circluar distribution on (a) the central axis, (b)
+6 mm off axis, and (c) -6 mm off axis. Dashed lines represent the planned
distribution, while the solid lines were measured from XV-2 film.

P 1e (2 a) /pixel)

7- -

Pixel / (2 w//pixel)

Figure 4-6: Isodose plots for planned U-shaped distribution on (a) the central axis, (b)
+6 mm off axis, and (c) -6 mm off axis. Dashed lines represent the planned
distribution, while the solid lines were measured from XV-2 film.

Table 4-1: Average uncertainties in Peacock Plan dosimetry for circle and U on the
central axis (CA), 6 mm off the central axis and -6 mm off of the central axis for the
treatment plan [Gra94]. ______

Circle Circle Circle U U U
CA 6 mm -6 mm CA 6 mm -6 mm
High dose, 1.86% 0.85% 12% 2.5% 4.5% 4.3%
low gradient ____ ____
High gradient 3.8mm 2.7mm 3.0mm 2.8mm 4.4mm 3.8mm
Total Volume 1.9% 0.8% 12.2% 2.2% 4.2% 3.6%


As conformal therapy techniques have developed, their ability to produce arbitrary

dose distributions has been thoroughly investigated [Har94, Car93, Mos92, Hol94]. The

true test of the utility of inverse radiotherapy planning will be in its ability to produce

clinical treatment plans which are superior to those produced through conventional

treatment planning. The comparison of such plans is quite difficult, however, due to the

large amount of data which must be reviewed for a full three-dimensional evaluation

[Kut91a]. Historically, treatment plan evaluation has been achieved through the graphical

display of the two-dimensional dose distributions superimposed on the patient contour.

In addition to these dose distributions, tools for quantitative plan evaluation have been

developed. Some of these tools will be discussed in the following sections.

Dose Volume Histograms

Dose volume histograms effectively condense the dose distribution data by

graphically displaying the volume of tissue irradiated through execution of a given

treatment plan. There are two common forms for dose volume histograms which may

be found in the literature: differential and cumulative. Differential dose volume

histograms are plotted as histograms according to the mathematical definition, with dose

binned along the abscissa and the height of each bin proportional to the volume of the

organ which receives a dose within that range (see Figure 5-1). Alternatively,

cumulative dose volume histograms are frequency distributions which represent the

fractional volume of an organ receiving a dose greater than or equal to a specified dose

as a function of dose (see Figure 5-2).

Since differential dose volume histograms represent the volume in each dose bin

directly, they can facilitate comparison of dose intervals between rival plans. Also, the

finer structure provided by true histograms offers more detail for quantitative analysis

than that given by cumulative frequency distributions. The appearance of differential

histograms can become confusing, however, when one attempts to use them for

comparison of rival plans [Drz91]. Cumulative dose volume histograms can alleviate this

problem when presented as smooth line graphs. Thus, cumulative dose volume

histograms will be used as the graphic display for visual comparison of rival plans, while

quantitative analysis of plans will require the finer structure provided by differential dose

volume histograms. In order to remain consistent with the literature, the term dose

volume histogram (DVH) will be applied to the cumulative frequency distribution


DVHs are generally computed for the target volume and each organ within the

irradiated volume. Ideal DVHs for target and critical structure are shown in Figures 5-

3a and 5-3b. Thus, DVHs for rival plans may be compared simply by plotting them on

the same graph and noting how closely each approximates the ideal graph. This

comparison can become muddled, however, if the DVHs cross each other as in Figure

5-4 so that it is not clear which histogram is better [Kut92]. The presence of multiple

critical organs within the irradiated volume also increases the complexity of treatment




'" 0.1




0.0 0-1 0.2 0.3

0.4 0.5 0.6 0.7 0.8 0.9 1.0
Normafized Dose

Figure 5-1: Example differential dose volume histogram for target volume.





5 0.6


0.1 0.2 0.5 0.4 0.5 0.6
Normrized Dose

0.7 0.8 0.9 1.0

Figure 5-2: Cumulative DVH corresponding to Fig 5-1.

0 0-1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Dose

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized Dose

Figure 5-3: Ideal DVH for (a) target volume and (b) normal tissue volume.


plan comparison via DVHs. A further limitation of DVHs exists in their inability to

provide spatial information regarding the location of hot and cold spots within the

irradiated volume [Drz91]. Thus, if hot or cold spots are detected using a DVH, their

position must be obtained through the use of spatial dose distributions. Nevertheless,

dose volume histograms are a powerful tool for evaluation of many treatment planning

situations due to their ability to condense a vast amount of information into a limited

number of distributions.


0.0 0-1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Normalized Dose

Figure 5-4: Crossing dose volume histograms for normal tissue volume.

Normal Tissue Complication Probability

Although DVHs provide very accurate information about the dosimetric properties

of treatment plans, it may be difficult to infer the clinical significance from differences

in rival DVHs [Kut92]. Therefore, a means of quantifying the clinical importance of

rival plans is desirable. One method of quantifying the biological implications of a

given treatment plan is to estimate the radiation toxicity to normal tissues through the

calculation of normal tissue complication probabilities (NTCPs). Ideally, this calculation

could then be balanced with the tumor control probability to provide an absolute

numerical value which represents the validity of a given treatment plan [Moh92].

Unfortunately, these calculations are still under development and may provide

probabilities which are highly uncertain. However, these calculations represent an

attempt to model the clinical relevance of a given treatment plan and have proven

worthwhile in the comparison of rival treatment plans [Kut92].

New models under development start from basic biological principles and should

prove more accurate than current models [Jac93]. The most promising new model

assumes that organs are comprised of functional subunits (FSUs), for example the kidney

is comprised of nephrons, and the radiosensitivity of the organ depends on the

radiosensitivity of the FSUs as well as their organization. FSU organization may be

classified broadly as serial or parallel. Organs with a serial architecture have a chance

of complication when a very small volume is irradiated since their function is disrupted

if a single FSU is destroyed. Parallel organs have a threshold volume which must be

irradiated before a complication arises since a certain number of FSUs must be destroyed

before organ function is disrupted. Since many organs fall somewhere in between, their

behavior is described using a parameter related to their relative seriality.

Since this model is still under development and many of the requisite parameters

are unknown for specific tissues, NTCP may be calculated utilizing a four parameter


model suggested by Lyman [Lym85] and used by the collaborative working group in

their study [Kut91a]. This model estimates the complication probability arising from

uniform irradiation of a partial organ by fitting a general sigmoidal function to the

available clinical data for dose volume relationships. Although this model does not

explicitly contain the radiological parameters of other models, all relevant radiobiological

aspects are implicitly taken into account within the NTCP calculation [Lym85].

Two general sigmoidal functions have been investigated for analytic representation

of the response of an organ to irradiation: a logistic function and the integrated standard

normal distribution. It has been shown that these two functions differ by less than 0.9%

over their entire range, however, so the choice is essentially irrelevant [Sch85].

Following the model originally proposed by Lyman, the integrated standard normal

distribution may be used to determine the NTCP for an organ of volume Vrf, with partial

volume V irradiated to a homogeneous dose D as


NTCP- 1 fe 5t 1'2dt (5-1)
v'2T- --

where t, the normal deviate, represents the number of standard deviations D is away

from the tolerance dose and may be determined from

[D TD5o(v)] (5-2)
t = (5-2)

TD()where -
v (5-3)

and TD5o is the tolerance dose at which 50% of patients can expect a radiation related

complication within five years after treatment. The partial and whole volume tolerance

doses are related by a power law relationship [Sch83]

TD(v) = TD(V) v - (5-4)

Two fitting parameters, n and m, which govern the volume and dose dependence of

NTCP, respectively, may be found in a report by Burman et al. [Bur91]. Tolerance

doses for a variety of organs were compiled by Emami et al. based on data available in

the literature [Ema91]. The fourth parameter required by the model, Vref can be obtained

from the CT data if the entire organ is included in the scan, or alternatively, a standard

value may be utilized. Data used for these calculations are shown in table 5-1.

In order to utilize this model for clinically realistic situations in which the organ

is inhomogeneously irradiated, it is necessary to convert the nonuniform dose distribution

into a uniform distribution. The effective volume histogram reduction method proposed

by Kutcher et al. transforms a nonuniform differential DVH into a one step histogram

with an effective volume V, and dose equal to the maximum dose of the histogram, DM

[Kut91]. Assuming that each volume element, Vi with dose Di, of the differential DVH

independently obeys the same dose volume relationship as the whole organ, each interval

may be transformed into an effective volume with dose DM through the power law


V = Vi(DJDM (5-5)

This procedure is repeated for each interval of the dose volume histogram, and the total

effective volume may be found from the sum of equation 5-5

Y= V (D DM)- =Ev
i e i


The effective volume, Vff, found using this method may then be substituted for V in

equations (5-2) through (5-4) in order to calculate the NTCP for inhomogeneous partial

organ irradiation.

Table 5-1: Normal tissue endpoints and tolerance parameters [Bur91].

Organ V"f n m TD50 End Point
Bladder Whole organ 0.5 0.11 80 Symptomatic contracture
Brain Whole organ 0.25 0.15 60 Necrosis
Brain Whole 0.16 0.14 65 Necrosis
Stem organ
Femur Whole organ 0.25 0.12 65 Necrosis
Heart Whole organ 0.35 0.10 48 Pericarditis
Lens Whole organ 0.30 0.27 18 Cataract
Lung Whole organ 0.87 0.18 24.5 Pneumonitis
Optic Nerve Whole organ 0.25 0.14 65 Blindness
Rectum Whole organ 0.12 0.15 80 Proctitis/necrosis
Retina Whole organ 0.20 0.19 65 1Blindness
Skin 100 cm2 0.10 0.12 70 Necrosis/ulceration
Spinal Cord 20 cm 0.05 0.17 66.5 Myelitis/necrosis

Tumor Control Probability

While minimizing normal tissue toxicity is an important goal of conformal therapy,

it is also important to determine the probability of tumor sterilization using rival

treatment plans. As with NTCP, currently there is no model which can provide an

accurate assessment of the absolute tumor control probability (TCP). Models do exist,

however, which should be useful in comparison of rival treatment plans that are similar

in nature. The model used is based on that developed by Goitein [Goi94,Goi83] and

Niemierko [Nie94] which assumes that the tumor consists of non-interacting clonogens

which all must be killed in order to control the tumor. The probability of killing a

clonogen after a single treatment fraction is estimated by determining the surviving

fraction using the following variation of the linear quadratic formula

d rg/p4 +d]
dF rf+dI (5-7)
SFd- SF2[~~2

where d is the dose per fraction to the clonogen, SF2 is the probability that the clonogen

will survive a dose of 2 Gy and ca/ is the ratio of linear quadratic parameters which

determine the curvature of the dose survival curve for a cell population. The clonogen's

survival probability after undergoing n fractions may then be expressed as

i 4 r" ta (5-8)
SF = SF 't2 a -

The model further assumes that clonogens within an individual's tumor may differ in

their radiation sensitivities, and this variation may be expressed as a gaussian distribution

of SF2,md around the tumor mean with a standard deviation ad
F2.W 3F-, j
F_ 1 fe 2.o SF-d(SF ) (5-9)

Assuming that a tumor is composed of NC clonogens, an individual's tumor control

probability may then be calculated as

-NC i,-SF, (5-10)
TCPi = e i

where the sum is taken over the NB bins of the differential dose volume histogram, each

with a fractional volume vi. In addition to the intratumoral variation in cell sensitivities,

Goitein's model also assumes there exists an interpatient heterogeneity which may be

expressed as a gaussian distribution. Inclusion of this function yields the following final

version of the TCP calculation

(SF,.b.,d F-2,,
TCP 1- fe 2"' -TCP,,d(SF2, (5-11)

In order to perform the preceding calculation, certain biological parameters must

be input. The first is the slope of the dose response curve, gamma-50, as defined by

Brahme [Bra84]

Y = TCD5 d(TCP) ID=TCD5 (5-12)

where TCD50 represents the dose required to achieve TCP of fifty percent. TCD50 is not

a well known parameter, while gamma-50 has been tabulated for many tumors [Mun91a,

Tha92]. Thus, it is often easier to reverse the calculation. For example, physicians can

generally estimate the TCP for a treatment assuming that the entire tumor is

homogeneously irradiated to the prescription dose. This dose is the TCDTcp, or the dose

required to eradicate TCP percentage of such tumors. Assuming that the values are on

the linear portion of the dose response curve, the TCD50 can then be approximated from

TCD5 = TCD, *-yY50(5-13)
Y -+0.01 -(TCP-50O)

In addition to the dose response, the model requires a parameter, X, which characterizes

the variation of TCD50 with volume. The model also requires input of the linear

quadratic parameters a and 3, which have been tabulated for many tumors.

Using these input radiobiological parameters, all other parameters within the model

can be easily calculated. Internal parameters calculated from these input values include

the number of clonogens NC,

TCD" (5-14)
NC = /n2-10 "

and the surviving fraction at 2 Gy, SF2

SF2 10-2/ (5-15)

After utilization of such a model to determine the TCP for a malignancy,

Munzendrider et al. have observed that in regions of microscopic or suspected disease

TCP is underestimated [Mun91a]. This is because there is a finite probability that no

tumor exists in such regions, and thus there is non-zero probability of tumor control even

with zero dose delivered to the region. To compensate for this possibility, the calculated

probability is modified using

TCP = P. U, + (1 -P, uo TCP0 (5-16)

where Pno tumor is the probability that no tumor exists in the targeted region.

Dosimetric Statistics

As previously mentioned, the ideal radiotherapy treatment would result in

homogenous irradiation of the targeted region to the prescribed dose. In general,

however, it is physically impossible to homogenously irradiate the tumor while

homogeneously sparing normal tissue. Thus, treatment of the entire lesion to the

prescription dose produces hot spots within the volume. These hot spots can help destroy

the lesion, but they can also damage or necrose the underlying tissue stroma and increase

the risk of complications. For example, Nedzi et al. have correlated stereotactic

radiosurgery tumor dose inhomogeneity and the corresponding increase in maximum

tumor dose with increased complication rates [Ned91]. Unfortunately, this effect is not

well understood and varies widely according to the type and location of tumor. For

example, primary tumors located in the breast [Lim89] and larynx [Par94] have exhibited

susceptibility to radiation damage from hot spots within the irradiated volume, while

locations such as the nasopharynx [Par94] and prostate [Lei94, Per94] do not seem

particularly sensitive to radiation dose escalation. Further, it is difficult to determine

whether increased risk is due to necrosis of the target stroma or due to increased dose

to surrounding normal tissue. Due to the vagueness of this problem, radiation

oncologists typically avoid the situation by limiting the allowable target dose

inhomogeneity and no method has been proposed for determining the probability of

damaging the connective tissue and fine vasculature that may be associated with the target

volume. Since the algorithm within Peacock Plan places no constraint on the dose

inhomogeneity, large hot spots can result which complicate the comparison with rival

conventional plans.

In order to provide some idea of dose inhomogeneity for plans presented in this

work, dose statistics such as minimum dose, mean dose and maximum dose will be

included. To further quantify the tumor dose inhomogeneity, researchers have often

simply reported dose endpoints such as the D95, which is the dose received by at least

95% of the region of interest and D5, which is the dose received by at least 5% of this

volume [Kut92]. Presentation of such data provides a clear indication of tumor coverage

and the magnitude of hot or cold spots within the tumor volume and critical structures,

and should help clarify the information found in DVHs and previously described

biologically based statistics. While these statistics do not provide an absolute score to

ease plan comparison, they do provide enough information that a physician can easily

discern whether or not he is comfortable with the use of a given treatment plan.

Biologically Normalized Dose Fractionation

Dosimetric information for NTCP and TCP calculations is entered through

differential dose volume histograms as described previously. Normal tissue tolerance has

only been tabulated for conventional fractionation schedules of 180-200 cGy [Ema91].

In addition, the NTCP and TCP calculations are valid only if the dose per fraction is

equal at each calculational point [Nie94]. In order to account for differences in

fractionation schedules and the radiosensitivity of various tissues, a biologically

normalized dose volume histogram (BNDVH) may be calculated from the differential

dose volume histogram, and then input into the TCP calculation [Nie92]. This

transformation follows directly from a manipulation of the linear quadratic formula which

yields the following rule of thumb for the dose response of tissue to variable fractionation

schedules [Wit83]:

D d +a/P3 (5-17)
D d'+ a/P

where D is the total dose given in fractions of size d. The BNDVH normalizes the

differential DVH to 2 Gy per fraction by using a variant of this calculation [Nie91]:

BND, = D (di + al) (5-18)

where Di is the dose for bin i of the differential DVH, di is the corresponding

fractionated dose and BND1 is the total dose for bin i normalized to 2 Gy per fraction.

NTCP calculations for variable fractionation schedules require a modification of

the TD)50 in order to normalize these tolerance data to 2 Gy/fraction. For this work, the

biologically normalized tolerance dose, BNTD50, will be defined as:

BNTD = TD a f/ + 2 Gy (5-19)

using the same manipulation of the linear quadratic equation as before. The TCDs0 used

for the TCP calculation in this work need not be similarly normalized, since this

parameter is determined uniquely for each case subsequent to user input of pertinent data.

Although normalization of these data facilitates NTCP and TCP calculations for

treatment schedules other than 2 Gy/fraction, it should be noted that such normalization

contributes additional error to the probability calculations. This matters little for

comparison of the rival plans in this study, since the fractionation schedules will remain

constant for each comparison. Thus, normalization of these dosimetric parameters should

enhance the realism of calculations for variable fractionation schedules, but discretion

should be exercised when comparing calculated probabilities with those expected.

Score Functions

Although the tools discussed previously are very effective in condensing the amount

of information required for treatment plan evaluation, a method of numerically scoring

each plan such that a single number may quantify the merit of a given plan is desired to

further reduce the amount of information. The simplest objective score function is the

probability of uncomplicated tumor control [Sch85]. This function, although objective,

is based on NTCP and TCP calculations, and is therefore limited in its ability to achieve

an absolute probability. It is, however, a simple calculation that yields a single number

with which to quantify the merit of a particular treatment plan. This score function, S,

may be expressed as a product of the fractional probability of effect for each organ

within the irradiated volume [Kut92]:

S = I (l-P) (5-20)


PO = 1 -TCP P,>o = NTCP


Delivery Efficiency

In addition to dose conformity, any system clinically utilized must have the ability

to deliver treatments quickly and efficiently. All methods of intensity modulation of the

radiation beam will result in an increase in monitor units required for a treatment, and

it is important to appreciate the effect this can have in clinical situations. The delivery

efficiency of a conformal treatment system can be quantified via modification of an

expression suggested by Galvin et al [Gal93]:

Efficiency = MUcowd'f"aI7tWP (5-22)
This efficiency factor reveals several features of the conformal treatment plan in relation

to its conventional counterpart. First, beam on time increases linearly with an increase

in monitor units, which possibly leads to a prolonged treatment session. Conformal

treatment systems may, however, reduce time required for patient set up and compensate

for this increased beam on time. Decreasing the delivery efficiency may have even more

severe consequences on shielding requirements. A system which requires a large number

of monitor units may effect linear accelerator design in terms of transmitted radiation

through the primary and secondary collimators, as well as increase the leakage

contribution to the room shielding requirements.


After consulting staff physicians at University of Florida, it was determined that

several treatment sites could best demonstrate the potential benefit from conformal

therapy and should be included in the clinical study; these sites and respective patient

designations appear in Table 6-1. CT scans were obtained of the diseased region, and

staff physicians delineated the regions of gross tumor and suspected disease. This

volume has been designated the biological target volume (BTV) by the photon treatment

planning collaborative working group [Smi91]. The physicians also designated any

margin necessitated by set up uncertainties and organ motion. Including this margin

around the BTV yields the mobile target volume (MTV).

Table 6-1: Treatment sites chosen for study and the respective patient designations.

Site Patient Designations
Intracranial lesions SRS-1, SRS-2, SRS-3,
treated stereotactically SRS-4, SRS-5, SRS-6
Head and Neck HN-1, HN-2
Intact Breast B-1, B-2
Lung L-l
Prostate P- 1, P-2

Three separate treatment plans were generated for each patient with the first being

the conventional treatment plan as described in Chapter 3. These conventional plans

were used for actual patient treatment, and thus represent the optimum plan as designed

by the attending physician and dosimetrist or physicist. A 3D plan was then generated

with traditional field arrangements but using the full volumetric CT information to design

the fields instead of just a central axis slice. The conventional and 3D plans are the same

for stereotactic radiosurgery and other virtual simulation applications, so only two plans

were designed for these cases. The third and final plan is the conformal plan generated

utilizing the Peacock Plan' system.

Table 6-2: Default five table angle plan parameters for Peacock. Table angles are given
using the 360 degree convention described in Figure 3-1.

Site Table Angles (degrees) Arc Length (degrees)
Head 0 290
30 & 330 245
60 & 300 215
Head and Neck 0 290
15 & 345 245
30 & 330 215
Abdomen/Thorax 0 290
15 & 345 245
30 & 330 215

All conformal plans generated using Peacock were designed using five table angles.

When the user selects five table angles, Peacock starts with the default sets shown in

Table 6-2, and determines the actual arcs used through its optimization process.

Intuitively, the optimal dose gradient is obtained when the beam entrance points are

evenly distributed over the entire surface of the patient. To approximate this, the

treatment planning system starts with long arcs which can be altered by the system.

Given a perfect optimization algorithm or alternatively a large amount of computer time,

this is the best approach since beams which deleteriously effect the dose distribution will

be discarded. However, experience with stereotactic radiosurgery has shown that when

the irradiation geometry is reduced from 4-r it must be reduced to less than 2-w in order

to avoid parallel opposed beams which decrease the steepness of the dose falloff [Pik90].

Since Peacock currently allows these opposing fields, suboptimal plans with a poor dose

gradient can result. Since this effect was most obvious for the intracranial plans, these

plans were all run utilizing the three different arc sets shown in Table 6-3: the Peacock

default arc set, the Peacock set with shortened arcs and a default five arc set used in the

University of Florida stereotactic radiosurgery program. These three plans were

compared and the best was chosen. For one patient (SRS-3) the shortened arc sets never

resulted in a plan which adequately conformed to the target and the default arc set was

used. Comparing the dose gradient achieved with this plan (see Figure 6-6) with the

dose gradient in other plans, the effect of the opposing fields becomes obvious. For all

other plans, one of the shortened arc set plans was utilized.

Table 6-3: Arc sets used for planning intracranial cases in Peacock system.

Name Table Angles Arc Lengths
Peacock Default 0 290
30 & 330 245
60 & 300 215
Shortened Peacock 0 160
Default 30, 60, 300 & 330 110
UF SRS Default 20, 55, 270, 305 & 340 100

Upon completion of the treatment planning process, Peacock specifies the minimum

dose to the target. Although this could be chosen as the prescription isodose for the

plan, the manufacturer suggests that the user slightly increase the prescription line which

allows the prescription dose to slightly clip the target volume. This seems reasonable

since the underdosed regions are generally comprised of individual voxels protruding

from the delineated target and modem tumor dose response models have found a stronger

correlation between mean tumor dose and TCP than between minimum target dose and

TCP [Bra87, Kut92, Nie93]. Thus, by slightly increasing the prescription line, one can

decrease the normal tissue dose and magnitude of hot spots within the tumor without

profoundly effecting the probability of tumor control. In order to maintain consistency,

all plans were prescribed to an isodose line which underdosed no more than 1.5% of the

tumor volume.

As previously mentioned, three-dimensional planning generates a large amount of

data which can complicate plan comparison. In order to condense this information, the

quantitative tools discussed in Chapter 5 will be used along with displays of two

dimensional slices through the lesion for selected representative patients. All treatment

plans were designed to match the MTV, while target DVH and TCP calculations were

performed for the BTV only. When viewing these plans it is important to remember that

the conventional and conformal treatment planning systems contain inherent inaccuracies,

and the dose calculations are not exact. This study is not designed to examine these

inadequacies, but rather the clinical efficacy of inverse radiotherapy planning. If this

method is deemed beneficial, then it will be appropriate to allocate the necessary

resources to develop more sophisticated methods of dosimetry calculation. Following are

the parallel planning studies for the chosen treatment sites.

Stereotactic Radiosurgery Patients

SRS-1 is a 40-year-old male with a centrally located posterior third ventricle area

arteriovenous malformation (AVM). Conventional treatment was executed through a

single isocenter plan using 9 arcs delivered through a 20 mm collimator to a total dose

of 1500 cGy prescribed to the 80% isodose line. The conformal treatment plan achieved

high target dose homogeneity with the prescription dose delivered to the 94% isodose

line. The inferior dose gradient provided by the intensity modulation device, however

resulted in a spread in the low isodose lines and a higher average critical structure dose.

Although TCP calculations were not necessarily designed for AVMs, TCP was still

calculated in order to provide relative scores for the rival treatment plans. For this and

the other AVM examples, it is especially important to recall that TCP does not represent

a true probability, but rather a quantitative evaluation of a proposed treatment plan.

Table 6-4: Conventional treatment plan designed for SRS-1.

Arc Isocenter Collimator Angle Arc Start Arc Stop Weight
1 1 20 10 30 130 1
2 1 20 30 30 130 1
3 1 20 50 30 130 1
4 1 20 70 30 130 1
5 1 20 350 230 330 1
6 1 20 330 230 330 1
7 1 20 310 230 330 1
8 1 20 290 230 330 1
9 1 20 270 230 330 1


SRS-2 is a 59-year-old female with metastatic adenocarcinoma of the lung to the

right frontal lobe of her brain. A dose of 1750 cGy was delivered to the 80% isodose

line through a nine arc single isocenter plan which used both the 20 and 24 mm

collimators. Since the lesion is fairly spherical, it may be easily treated through

conventional stereotactic radiosurgery using spherical collimators. The plan designed by

Peacock is also quite conformal and treats the lesion with a more homogeneous dose

distribution, although the average brain dose experiences a significant increase. This

increase is partially offset by a decrease in the maximum brain dose, but still represents

an undesirable increase.

Table 6-5: Conventional treatment plan for SRS-2.

Arc Isocenter Collimator Table Arc Start Arc Stop Weight
1 1 20 10 30 130 1
2 1 20 30 30 130 1
3 1 24 50 30 130 1
4 1 24 70 30 130 1
5 1 20 350 230 330 1
6 1 20 330 230 330 1
7 1 24 310 230 330 1
8 1 24 290 230 330 1
9 1 24 270 230 330 1

SRS-3 is a 62-year-old male with a left trigone AVM. Due to the highly irregular

shape of the AVM nidus, the treatment plan generated utilizing the SRS software

required two isocenters. The first isocenter consisted of nine arcs treated with a 24 mm

collimator, while the second isocenter required 4 arcs using the 12 mm collimator. The

resultant distribution from the combination of the two isocenters delivered 1500 cGy

normalized to the 70% isodose line. Peacock again generated a homogenous distribution,

but the overlapping and opposed fields also resulted in an inferior dose gradient.

Table 6-6: Conventional treatment plan for SRS-3

Arc Isocenter Collimator Table Arc Start Arc Stop Weight
1 1 24 10 80 230 1
2 1 24 30 80 130 1
3 1 24 50 80 130 1
4 1 24 70 100 130 2
5 1 24 350 230 280 1
6 1 24 330 230 280 1
7 1 24 310 230 280 1
8 1 24 290 230 260 1
9 1 24 270 230 260 2
10 2 12 10 30 130 1.5
11 2 12 30 30 130 1.5
12 2 12 350 230 330 1.5
13 2 12 330 230 330 1.5

SRS-4 is a 50-year-old female with 2 metastatic brain lesions. This patient provides

an interesting test of the conformal radiotherapy system, since it has the ability to treat

both lesions through a single isocenter. The conventional treatment plan required two

isocenters consisting of 7 arcs each. Both isocenters utilized the 10 mm collimator, since

the lesions were compact, and a dose of 1500 cGy was prescribed to the 80% isodose

line. Peacock designed a plan which delivered the 1500 cGy to the 79% line. As can

be seen from the statistics, the dose to critical structures (brain) is again increased in the

Peacock plan relative to conventional SRS planning. This two target plan illustrates one

distinct advantage of inverse radiotherapy planning, however; the ability to treat multiple

lesions using a single isocenter. Unfortunately, the MIMIC treats in a slice by slice

manner and cannot take full advantage of this ability. Two dimensional modulation

devices which treat the entire volume in one arc, however, could easily treat both lesions

in one arc and increase delivery efficiency [Har94].

Table 6-7: Conventional treatment plan for SRS-4

Arc Isocenter Collimator Table Arc Start Arc Stop Weight
1 1 10 30 30 130 1
2 1 10 50 30 130 1
3 1 10 70 30 130 1
4 1 10 330 230 330 1
5 1 10 310 230 330 1
6 1 10 290 230 330 1
7 1 10 270 230 330 1
8 2 10 30 30 130 1
9 2 10 50 30 130 1
10 2 10 70 30 130 1
11 2 10 330 230 330 1
12 2 10 310 230 330 1
13 2 10 290 230 330 1
14 2 10 270 230 330 1

SRS-5 is a 73-year-old female with a right petroclival meningioma which presented

a significant treatment planning challenge. The lesion was treated using a 3 isocenter

plan with 15 total arcs and 4 separate collimators: 22, 26 and 12 mm, respectively. As

is characteristic of multiple isocenter plans, there was significant dose inhomogeneity

within the target volume and the dose was prescribed to the 70% isodose line. Due to

the target's proximity to the brain stem, a relatively low target dose of 10 Gy was

prescribed. The plan designed by Peacock provided better and more homogeneous target

coverage than did the conventional plan, resulting in dose prescription at the 83 % isodose

level. It did, however result in a higher dose delivered to critical normal structures.

Table 6-8: Conventional treatment plan for SRS-5.

Arc Isocenter Collimator Table Arc Start Arc Stop Weight
1 1 22 10 50 80 1
2 1 22 350 230 260 1
3 1 22 330 230 260 1
4 1 22 310 240 300 1
5 1 26 290 260 310 1
6 1 26 270 260 310 1
7 1 26 70 50 80 1
8 2 12 10 60 90 .75
9 2 12 30 60 90 .75
10 2 12 350 240 290 .75
11 2 12 330 240 290 .75
12 3 12 10 60 90 .75
13 3 12 30 60 90 .75
14 3 12 350 240 290 .75
15 3 12 330 240 290 .75

SRS-6 is a 65-year-old male with an AVM located in the right anterior portion of

the corpus callosum. Since the nidus was fairly compact and regular, treatment was

delivered in a single isocenter with the 16 mm collimator through nine arcs. A dose of

1500 cGy was prescribed to the 80% line. Peacock designed a five arc plan which

would deliver the 1500 cGy to the 89 % line, thus lowering the tumor dose inhomogeneity

and maximum brain dose.

Table 6-9: Conventional treatment plan for SRS-6.

Arc Isocenter Collimator Table Arc Start Arc Stop Weight
1 1 16 10 30 130 1
2 1 16 30 30 130 1
3 1 16 50 30 130 1
4 1 16 70 30 130 1
5 1 16 350 230 330 1
6 1 16 330 230 330 1
7 1 16 310 230 330 1
8 1 16 290 230 330 1
9 1 16 270 230 330 1

Since NTCP calculations for brain irradiation were formulated based on data from

large field irradiation using conventional fractionation schedules, the NTCP parameters

may not be suitable for stereotactic radiosurgery. Data from Kjellberg et al. are

commonly used as standards for choosing treatment doses in linear accelerator

radiosurgery [Kje83]. It has been shown that their 1% isoeffect line for brain necrosis

from treatment with x rays and protons closely matches the 3% isoeffect line for brain

necrosis from linear accelerator radiosurgery [Fli90]. Further, all patients with

permanent radiation induced complications in the University of Florida series received

doses above this line [Fri92]. As shown in Figure 6-1, NTCP calculations using the

model parameters found in the literature underestimate the actual complication

probability. In an attempt to force the NTCP calculations to better fit the radiosurgery

data in the literature, the NTCP model parameters were modified using a simulated

annealing optimization algorithm. This computer program varied the parameters

governing dose (m) and volume (n) dependence to provide the best fit to Kjellberg's 1%

necrosis line over the range of doses and collimators of interest. As shown in Figure 1,

calculations using the modified parameters provide a much better fit to the Kjellberg's

curve although the slope of the predicted isoeffect line is still less than expected.Thus,

NTCP calculations for stereotactic brain irradiation were performed using these modified

parameters. Results of these planning studies are shown in Figures 6-2 through 6-14.


30 "N


-- -. KjIllberg's Curve
-- Calulated NTOP (Orgingh Parameters)
e-O Caloulated NTCP (Modified Parameters)

10 20 30 40
Average Diameter (mm)

Figure 6-1: Kjellberg's isoeffect curve for 1% brain necrosis compared to 3% isoeffect
curves obtained from NTCP calculations using parameters (n and m) found in the
literature and modified parameters.

[ .5t. '
'::'.) 'm...' -" ? -,;. B^iiiv"'^^ir
I -r I-
**'' sS'lBy^ i f^.
*-t'^si a i^ *?-' f

7,,7fXIWl I

I Is

Figure 6-2: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and
coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS- 1.






> 40-





I Min D_95 Mean I D_5


AVM 780.4 1387.5 1739.9 1856.3 1875.0 81.5
Brain 0.0 3.2 51.6 161.2 1866.1 1.1
Score 80.5








> 40-




0 200 400 600 800 1000 1200 1400 1600 1800 2000
Dose (cGy)

Min D_95 Mean D_5 Max NTCP/TCP
AVM 1362.9 1524.5 1566.6 1604.4 1612.9 80.8

I Bra!n I 0.0

I Ri I 15fl7 I Afl~ 7 I 1~Q~ R I

1 Q

I rin00 2 1 1 0 4 57 -I I a I

I Score 1 79.3 I

Figure 6-3: DVH and statistics for (a) conventional and (b) conformal plans for SRS-1.

200 400 600 800 1000 1200 1400 1600 1800 2000
Dose (cGy)


I I I is

Figure 6-4: 17.5, 8.75, 3.5 and 1.75 Gy isodose lines are superimposed on orthogonal
slices through isocenter from (a) conventional and (b) conformal plans for SRS-2.





" 60


> 40





Dose (cGy)

Min D_9 5 Mean I


Target 1708.9 1950.0 2090.7 2175.0 2187.5 78.8
Brain 0.0 2.4 55.2 225.9 2121.4 2.5

Score 76.8







> 40



0 500 1000 1500 2000 2500
Dose (cGy)

Min D_95 Mean D-5 Max NTCP/TCP
Target 1673.1 1779.3 1843.5 1903.2 1923.1 77.1
Brain 0.0 8.0 126.2 442.3 1884.6 3.3

I Score I


Figure 6-5: DVH and statistics for (a) conventional and (b) conformal plans for SRS-2.

A' ~ mIll

I I ',

Figure 6-6: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and
coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS-3.

Brain stem


Dose (cOy)

I Min I D_95 Mean I D_5


AVM 1362.9 1493.8 1601.8 1908.7 2130.8 81.0
Brain 0.0 3.0 77.5 320.0 2074.5 1.8
Brain Stem 19.4 29.1 193.6 514.6 853.1 0.0
Score 79.6


90 AVM

j- 60-
> 40
201 Brain stem
0 300 600 900 1200 1500 1800 2100
Dose (cGy)

Min D_95 Mean D_5 Max NTCP/TCP
AVM 1292.2 1593.8 1724.5 1795.8 1807.2 81.5
Brain 0.0 21.6 179.8 564.8 1798.2 3.2
Brain Stem 36.1 46.2 120.1 217.4 533.1 0.0
Score 78.8
Figure 6-7: DVH and statistics for (a) conventional and (b) conformal plans for SRS-3.



-, l1, 1 1 ,1 .,I 1 .4 .ki "

Figure 6-8: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on orthogonal slices
through isocenter one for (a) conventional and (b) conformal plans for SRS-4.



.~hI I I I I .1 4



Figure 6-9: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on orthogonal slices
through isocenter two from (a) conventional and (b) conformal plans for SRS-4.







> 40





Min D_95 Mean


Target 1 1222.1 1395.0 1684.8 1824.8 1824.8 81.3
Target 2 1741.1 1753.1 1808.9 1858.3 1858.3 82.8
Brain 0.0 0.0 24.9 24.9 1832.1 0.9
Score 66.7


100- -

rTorget 1 -

Torgel 2

> 40-

2 Brain

0 200 400 600 800 1000 1200 1400 1600 1800 2000
Dose (cGy)

Min D_95 Mean D-5 Max NTCP/TCP
Target 1 1598.3 1652.8 1726.9 1780.2 1785.7 81.9
Target 2 1410.8 1437.1 1563.9 1654.2 1660.7 79.9
Brain 0.0 5.6 71.3 254.5 1750.1 1.4
Score 64.5


Figure 6-10: DVH and statistics for (a) conventional and (b) conformal plans for SRS-4.

-A r i7 1 1 *:! rI i 1 1:1

Figure 6-11: 10, 5, 2 and 1 Gy isodose lines are superimposed on axial, sagittal and
coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS-5.



Dose (cGy)

Min D_95 Mean D_5 Max NTCP/TCP
Tumor 776.8 857.1 1088.3 1285.7 1372.8 92.1
Brain 0.0 7.7 50.9 174.1 1044.6 0.6
Brain Stem 46.9 43.0 304.2 565.0 957.6 0.9
Score 90.7




70 Target

S 60- Ba in Stemrn

> 40-

30 Brain


0 200 400 600 800 1000 1200 1400 1600
Dose (cGy)

Min D_95 Mean D_5 Max NTCP/TCP
Tumor 925.0 1072.1 1171.0 1236.7 1250.0 94.4
Brain 0.0 9.5 88.8 256.3 1237.5 0.9
Brain Stem 93.8 110.0 292.3 746.4 1075.0 3.7
Score 90.2
Figure 6-12: DVH and statistics for (a) Conventional and (b) conformal plans for SRS-5.


i Ik

Figure 6-13: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and
coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS-6.

, l I,-\l/ l/- l. 'J. J - I






> 40




Dose (cGy)

Min D-95 Mean D-5 Max NTCP/TCP
AVM 1037.9 1200.9 1661.1 1858.3 1875.0 81.2
Brain 17.0 19.6 56.2 152.7 1815.2 1.2
Score 80.3






> 40-



Min D_95 Mean D_5 Max NTCP/TCP
AVM 1441.0 1555.9 1628.8 1676.6 1685.4 81.1
Brain 0.0 6.9 100.9 273.1 1677.0 1.5
Score 79.9
Figure 6-14: DVH and statistics for (a) Conventional and (b) conformal plans for SRS-6.

Head and Neck Carcinoma

The first patient studied (HN-1) is a 66-year-old female diagnosed with a T4 left

maxillary sinus adenoid custic carcinoma. Due to the extensive nature of her disease, she

was not a viable candidate for surgery, and thus underwent a course of radiotherapy.

She was treated to a dose of 7480 cGy in 68 fractions employing a twice daily

fractionation schedule with 6 MV photons. A three field technique (AP and laterals) with

wedges was used and the portals were reduced at 5060 cGy in order to reduce normal

tissue toxicity. Through BEV planning the radiation portals can be designed to better

match the target volume thus better sparing normal tissue and avoiding tumor

underdosage. The Peacock plan further spares normal tissue, but results in a fairly

significant tumor dose inhomogeneity with the dose prescribed to the 74 percent isodose

line. Results of conventional, BEV and conformal plans are shown in Figures 6-15

through 6-20.

HN-2 is a 17 year-old female who suffered from T4N3B carcinoma of the

nasopharynx. Using modem radiotherapy techniques, local control rates for nasopharynx

carcinomas range from 80-90% for T1 or T2 primaries to about 50% for more advanced

tumors [Kut91b]. Although this control rate is already very good using conventional

techniques, the proximity of the nasopharynx to critical structures such as brain, brain

stem, spinal cord and eyes leads to a high risk of complication from radiotherapy. Thus,

it is attractive to use inverse radiotherapy planning in order to conformally avoid these

critical structures. The conventional treatment plan required 7200 cGy in 60 fractions

to the primary disease site delivered using mixed photon (Co) and electron (10 MeV)