Int. J. Radiation Oncology Biol. Phys., Vol. 82, No. 3, pp. 1292–1298, 2012Copyright � 2012 Elsevier Inc.

Printed in the USA. All rights reserved0360-3016/$ - see front matter

jrobp.2010.06.020

doi:10.1016/j.i

PHYSICS CONTRIBUTION

BIOLOGICAL OPTIMIZATION IN VOLUMETRIC MODULATED ARCRADIOTHERAPY FOR PROSTATE CARCINOMA

IVAYLO B. MIHAYLOV, PH.D.,*y MIREK FATYGA, PH.D.,z KARL BZDUSEK, B.S.,x

KENNETH GARDNER, M.D.,y AND EDUARDO G. MOROS, PH.D.y

*Department of Radiation Oncology, Rhode Island Hospital/Brown Medical Center, Providence, RI; yDepartment of RadiationOncology, University of Arkansas for Medical Sciences, Little Rock, AK; zDepartment of Radiation Oncology, Virginia Commonwealth

University, Richmond, VA 23298; and xPhilips Radiation Oncology Systems, Fitchburg, WI

ReprinRadiationversity, RTel: (401Lifespan.

Purpose: To investigate the potential benefits achievable with biological optimization for modulated volumetric arc(VMAT) treatments of prostate carcinoma.Methods and Materials: Fifteen prostate patient plans were studied retrospectively. For each case, planning targetvolume, rectum, and bladder were considered. Three optimization schemes were used: dose–volume histogram(DVH) based, generalized equivalent uniform dose (gEUD) based, and mixed DVH/gEUD based. For each scheme,a single or dual 6-MV, 356� VMAT arc was used. The plans were optimized with Pinnacle3 (v. 9.0 beta) treatmentplanning system. For each patient, the optimized dose distributions were normalized to deliver the same prescrip-tion dose. The quality of the plans was evaluated by dose indices (DIs) and gEUDs for rectum and bladder. Thetallied DIs were D1%, D15%, D25%, and D40%, and the tallied gEUDs were for a values of 1 and 6. Statistical testswere used to quantify the magnitude and the significance of the observed differences. Monitor units and treatmenttimes for each optimization scheme were also assessed.Results: All optimization schemes generated clinically acceptable plans. The statistical tests indicated that biolog-ical optimization yielded increased organs-at-risk sparing, ranging from �1% to more than �27% depending onthe tallied DI, gEUD, and anatomical structure. The increased sparing was at the expense of longer treatment timesand increased number of monitor units.Conclusions: Biological optimization can significantly increase the organs-at-risk sparing in VMAT optimizationfor prostate carcinoma. In some particular cases, however, the DVH-based optimization resulted in superior treat-ment plans. � 2012 Elsevier Inc.

VMAT, Volumetric, Arc, Optimization, Dose, Prostate cancer.

INTRODUCTION

Intensity-modulated radiation therapy (IMRT) is rapidly be-

coming a standard of care. The primary reason is that it offers

great flexibility in delivering highly conformal dose distribu-

tions to complex targets while sparing the surrounding

healthy tissue and anatomical structures. IMRT treatments

can be delivered either with a fixed gantry angle technique

or with a recently commercially available volumetric

modulated arc (VMAT) technique. VMAT evolved from

intensity-modulated arc therapy (1), allowing for simulta-

neous variation of dose rate, gantry speed, and multileaf col-

limator (MLC) segments. The technique promises some

dosimetric benefits (2), together with reduced treatment times

(1, 3–6), which in turn can have significant radiobiological

impact (7–9).

t requests to: Ivaylo B. Mihaylov, Ph.D., Department ofOncology, Warren Alpert Medical School of Brown Uni-

hode Island Hospital, 593 Eddy St., Providence, RI 02903.) 444-8546; Fax: (401) 444-2149; E-mail: imihaylov@org

1292

IMRT inverse plan optimization is routinely performed by

dose–volume histogram (DVH) optimization objectives. In

DVH optimization, the planner specifies dose level(s) to dif-

ferent partial or total volumes of the anatomical organs and

targets of interest. The widespread use of DVH-based optimi-

zation stems from the wealth of clinical information, as well

as clinicians’ experience (10), relating organ volumes and

dose levels resulting in complications to the surrounding or-

gans at risk (OARs). DVH-based objective functions how-

ever do not adequately represent (11, 12) the nonlinear

response of tumors or OARs to dose—in particular, for

highly heterogeneous dose distributions, which are

common in IMRT. Therefore, the use of biological

information in the IMRT optimization holds tremendous

promise for improving local control or reduction of normal

tissue toxicity. The biological information can be supplied

This work was supported in part by Central Arkansas RadiationTherapy Institute (CARTI).

Conflict of interest: Karl Bzdusek is an employee of Philips Ra-diation Oncology Systems.

Received Oct 9, 2009, and in revised form June 3, 2010. Acceptedfor publication June 9, 2010.

Biological optimization in VMAT therapy for prostate carcinoma d I. B. MIHAYLOV et al. 1293

in terms of normal tissue complication probability models

(13, 14) or generalized equivalent uniform doses (gEUDs)

(15, 16).

Generally, in DVH optimization several (2–4) DVH

objectives must be specified for any target or OAR. In

contrast, in gEUD or combination of DVH and gEUD

(hybrid) optimizations fewer (no more than 2) objectives

per anatomical structures are enough for adequate IMRT

optimization. It has been shown that biological

optimization is superior to DVH-based optimization in

OAR sparing (with satisfactory target coverage) for multiple

fixed gantry angle IMRT (11, 17–23).

The purpose of this study is to compare the results and

evaluate the achievable dosimetric benefits, as well as the

possible pitfalls, of DVH- (ArcDVH), gEUD- (ArcgEUD),

and hybrid-based (ArcHybrid) optimization for VMAT tech-

nique in prostate carcinoma

METHODS AND MATERIALS

PatientsThe data set for this work consisted of 15 prostate IMRT treat-

ment plans, derived from patients treated at the Department of Radi-

ation Oncology at University of Arkansas for Medical Sciences. For

each patient, clinical target volume (CTV) and planning target vol-

ume (PTV) were contoured by the attending physician. The PTV

was obtained from the CTV by a uniform expansion of approxi-

mately 1 cm. In addition, rectum and bladder were outlined as

OARs and used in the IMRT optimization as critical anatomical

structures limiting the PTV dose escalation.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1564006600680070007200740076007800640066006800700072007400760078008000

ArcDVHArcHybrid

PTV

D95

%[c

Gy]

Patient Number

ArcDVH ArcgEUD

PTV

D95

%[c

Gy]

Fig. 1. Comparison among planning target volume (PTV) D95%

dose indices achieved with the three different optimization schemes.In addition, dose standard deviations (two s) across the PTV are pre-sented as error bars. ArcDVH = dose–volume histogram–based arctherapy; ArcgEUD = generalized equivalent uniform doses–basedarc therapy; ArcHybrid = combination of ArcDVH and ArcgEUD.

Treatment planningThe treatment planning was performed with Pinnacle3 (beta v.

9.0, Philips Radiation Oncology Systems, Fitchburg, WI) treatment

planning system. The patient plans were optimized for a VMAT

treatment (3) on a Varian 21EX (Varian Medical Systems, Palo

Alto, CA) linear accelerator equipped with a 120-leaf Millennium

MLC. Each plan used either a single or a dual volumetric modulated

arc covering 356�, from 2� to 358� (Varian convention). All plans

were optimized for a single photon energy of 6 MV. Control points

were set 4� apart across the arcs for the machine parameter optimi-

zation. The dose calculations were performed with Pinnace3 col-

lapsed cone convolution superposition (24, 25) dose calculation

algorithm.

The ArcDVH optimization was performed with the Pinnacle3

IMRT optimization algorithm, whereas the ArcgEUD and ArcHy-

brid optimizations used the Pinnacle3 gEUD-based biological opti-

mization algorithm. The details of the VMAT arc generation and

optimization have been described elsewhere (3).

The ArcDVH optimization was performed first. The prescription

doses to 95% of the PTV ranged from 6,600 to 7,800 cGy, depend-

ing on the patient anatomy. The prescription doses were varied on

a case-by-case bases, subject to the following OAR constraints.

Doses to 15%, 25%, and 40% of the rectum were limited to

7,500, 7,000, and 6,000 cGy, respectively. Similar constraints

were used for bladder, although in some cases, slightly higher doses

were accepted as clinically viable because the bladder has somewhat

higher tolerances (26) than the rectum. In addition, the prescription

dose to 95% of the PTV was subject (affected) to the requirement

that the standard deviation of the dose over the PTV was within

3% (27). The IMRT objectives for the ArcDVH optimization used

minimum, maximum, and uniform dose for PTV, as well as the

above-mentioned three constraints of 6,000, 7,000, and 7,500 cGy

for rectum and bladder. The relative weights of the PTV were set be-

tween 10 and 20, and the relative weights fro the OARs were slightly

lower, ranging between 5 and 20. The doses to 15%, 25%, and 40%

of rectum and bladder volumes were reduced as much as possible

given that therapeutic prescription dose with small standard devia-

tion was achieved. Usually four to six manual interventions in the

optimization process were adequate for a clinically acceptable

plan. The same parameters, such as arc length, number of optimiza-

tion iterations, and convergence criteria, were used for the ArcgEUD

optimization. The PTV objectives for minimum and maximum

gEUDs with ‘‘a values’’ of –10 and +10 (11) were used in the Arc-

gEUD optimization. Similarly, two maximum EUD parameters

were used for either rectum and bladder, with a values of 6 (11)

and 1 (average dose), respectively. In the gEUD formalism, ‘‘a’’

is an organ-specific parameter describing dose–volume effects. If

a = N, the gEUD represents the maximum dose, whereas if a =

–N, the gEUD represents the minimum dose. For a = 1, the

gEUD is the mean dose. The a value can be determined empirically

by fitting published dose response data (26). This parameter usually

has large negative value for tumors, large positive values for serial

structures such as the spinal cord, and small (�1) positive value

for structures that exhibit large volume effect, such as lungs or pa-

rotid glands. The gEUD-based optimization in the Pinnacle3 treat-

ment planning system is realized by incorporating gEUDs (20),

rather than a sum of doses on a voxel-by-voxel basis, in a quadratic

objective function, which is subsequently minimized by the IMRT

optimization algorithm. In the ArcgEUD optimization, PTV relative

weights were set in the range of 80 to 100, and the OAR relative

weights were similar to the weights used in the ArcDVH optimiza-

tion. The maximum gEUDs for rectum and bladder for a value of 6

were set between 5,000 and 6,500 cGy, whereas for a value of 1,

they were set between 3,000 and 5,500 cGy on a case-by-case basis.

Through several trial-and-error steps, the objectives were lowered as

much as possible without compromising the prescription dose and

1294 I. J. Radiation Oncology d Biology d Physics Volume 82, Number 3, 2012

PTV dose uniformity. The number of required manual interventions

was similar to that used in ArcDVH optimization.

The ArcHybrid optimization utilized the same objectives for the

PTV as the ArcDVH optimization, i.e., minimum, maximum, and

uniform dose, while using the gEUD constraints for the OARs in

the ArcgEUD-based optimization with the same a values. The clin-

ical viability of the ArcgEUD and ArcHybrid plans was based on the

same criteria used for ArcDVH results. In the ArcHybrid optimiza-

tion, PTV relative weights were set in the range of 20 to 100,

whereas the OAR relative weights were similar to the weights

used in the ArcgEUD optimization. The maximum gEUDs for rec-

tum and bladder, as well as the manual intervention frequency in the

optimization process, were the same as in ArcgEUD optimization.

AnalysesThe dose distributions computed with ArcDVH optimization

were used as a reference to which the dose distributions computed

with the ArcgEUD and ArcHybrid optimizations were compared.

The metric used in the comparison was based on dose indices

(DI) and generalized equivalent uniform doses. The evaluated

dose indices were PTV D95% (dose covering 95% of the PTV vol-

ume), and rectum and bladder D1%, D15%, D25%, and D40%. They

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.40.50.60.70.80.91.00.5

0.6

0.7

0.8

0.9

1.0

1.10.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

D40%ArcgEUD D40% ArcHybrid

Patient Number

D25% ArcgEUD D25% ArcHybrid

Nor

mal

ized

dos

e in

dice

s D

com

pare

d/Dre

fere

ncefo

r rec

tum

D15% ArcgEUD D15% ArcHybrid

Fig. 2. Comparison of normalized dose indices for rectum. The nor-malization was performed with respect to the dose indices derivedfrom ArcDVH optimization scheme. Open symbols denote the re-sults for ArcgEUD optimization, and the filled symbols denote theresults for ArcHybrid optimization. The top, middle, and bottompanels denote the comparisons for rectum D15%, D25%, and D40%,respectively. The ‘‘one’’ level is denoted in each panel by a dashedline. It indicates where the compared dose indices equal each other.ArcDVH = dose–volume histogram–based arc therapy; ArcgEUD =generalized equivalent uniform doses–based arc therapy; ArcHybrid= combination of ArcDVH and ArcgEUD.

were the same as the DIs used in establishing the IMRT DVH-

based optimization objectives (except D1%) in ArcDVH optimiza-

tion. The evaluated gEUDs were for PTV, rectum, and bladder.

The a value for the PTV was –10, whereas for rectum and bladder,

it was 6. In addition, the average doses for the OARs were also eval-

uated. The evaluated gEUDs were essentially the same as the

gEUDs used in the ArcgEUD and ArcHybrid optimizations as opti-

mization objectives. In the comparison between the DIs and gEUDs

derived from the various optimization schemes, the difference of 3%

was used as a threshold for clinical significance (28–30).

Statistical significance tests were used to determine the magnitude

of the differences between the tallied DIs and gEUDs derived from

the various optimization schemes. The details and the implementa-

tion of the tests have been presented elsewhere (31, 32). Briefly, the

statistical tests comprised two one-tailed paired t tests (33), where

statistical significance was determined by p value (34) <5% (0.05).

RESULTS

The plans optimized with the various optimization

schemes for each patient were normalized such that 95% of

the PTV received the same dose. In addition, the standard de-

viation of the dose across the PTV was within 3% (27) for

each plan. The target coverage and the dose uniformity result-

ing from the different optimization schemes were essentially

the same, as can be observed in Fig. 1.

Dose index comparisonsThe results for the rectum DIs, D15%, D25%, D40%, are

presented in the top, middle, and bottom panels of Fig. 2 re-

spectively. ArcgEUD and ArcHybrid evaluation metrics

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.30.40.50.60.70.80.91.01.10.5

0.6

0.7

0.8

0.9

1.0

1.10.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

D40%ArcgEUD D40% ArcHybrid

Patient Number

D25% ArcgEUD D25% ArcHybrid

Nor

mal

ized

dos

e in

dice

s D

com

pare

d/Dre

fere

ncefo

r bla

dder

D15% ArcgEUD D15% ArcHybrid

Fig. 3. The same comparisons as in Fig. 2 but for bladder.

0.85

0.90

0.95

1.00

0.90

0.92

0.94

0.96

0.98

1.00

1.02

a = 6 ArcgEUDa = 6 ArcHybrid

gEU

Ds

gEU

Dco

mpa

red/g

EUD

refe

renc

efo

r bla

dder

Biological optimization in VMAT therapy for prostate carcinoma d I. B. MIHAYLOV et al. 1295

were expressed as fractions of the corresponding ArcDVH

metrics. Consequently, the dose indices derived from Arc-

gEUD and ArcHybrid optimization were normalized to the

dose indices derived from ArcDVH optimization. This nor-

malization eases the comparison, especially when different

patients have different prescription doses (32) and different

OAR objectives. In majority of the cases, the normalized

DIs are less than unity, indicating increased rectum sparing

for ArcgEUD and ArcHybrid optimization schemes. Similar

results are evident on Fig. 3, where bladder normalized DIs

are presented. For some patient plans, the normalized DIs

are slightly greater than unity, indicating that no improve-

ment is achievable with the gEUD or the hybrid optimization.

However, in the majority of the cases, the normalized DIs are

less than unity, demonstrating the potential of biological op-

timization methods for increased OAR sparing.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.65

0.70

0.75

0.80

Patient Number

a = 1 ArcgEUDa = 1 ArcHybrid

Nor

mal

ized

gEUD comparisonsThe results from the gEUD comparisons for rectum and

bladder are presented in Figs. 4 and 5, respectively. The

ArcgEUD and ArcHybrid gEUDs (a value of 6) and

average doses (a value of 1) have been normalized with

respect to the gEUDs and the average doses derived from

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

Patient Number

a = 1 ArcgEUDa = 1 ArcHybrid

a = 6 ArcgEUDa = 6 ArcHybrid

Nor

mal

ized

gEU

Ds

gEU

Dco

mpa

red/g

EUD

refe

renc

efo

r rec

tum

Fig. 4. Comparison of normalized gEUDs for rectum. The top andbottom panels represent the average doses (a value of 1) and thegEUDs for a value of 6, respectively. The open symbols are forthe ArcgEUD comparison, and the filled symbols are for the ArcH-ybrid comparison. The ‘‘one’’ level is denoted in each panel bya dashed line. It indicates where the compared gEUDs equal eachother. ArcgEUD = generalized equivalent uniform doses–basedarc therapy; ArcHybrid = combination of dose–volume histo-gram–based arc therapy and ArcgEUD.

Fig. 5. The same comparisons as in Fig. 4 but for bladder.

the ArcDVH optimization in the same fashion as the DIs.

The results are qualitatively similar to the results for the

DIs. In majority of the cases, the ArcgEUD and ArcHybrid

optimization schemes resulted in an increased sparing of

the OARs.

Statistical analysisTable 1 contains the average values of the tallied DIs for

rectum, the statistically different dose interval, and the per-

cent change in the dose index necessary to establish statistical

equivalence for the results derived from ArcDVH, Arc-

gEUD, and ArcHybrid optimization schemes. It is evident

from the table that as the tallied DI corresponds to a bigger

and bigger OAR volume, the statistically significant differ-

ence increases from �1% to almost 28%. This indicates

that there is an increased OAR sparing with volumes above

decreasing dose limits. The gEUD statistical analyses among

the three optimization schemes are presented in Table 2.

Those results also indicate a statistically significant increase

in the sparing of rectum and bladder with increasing OAR

volume because higher values of a correspond to increased

importance of higher doses (10), which in turn are the doses

to smaller volumes of the OARs.

DISCUSSION

The plans generated by ArcgEUD optimization yielded

slightly higher dose heterogeneity within the PTV22. The

ArcHybrid scheme generated slightly better dose homogene-

ity than ArcgEUD scheme. However, this optimization re-

sulted in somewhat smaller OAR sparing. Statistical

Table 1. Average values for rectum DIs derived from ArcDVH, ArcgEUD, and ArcHybrid optimization results, together with thestatistically significant dose differences and p values.

Dose IndexAverage ValueArcDVH [cGy]

Average ValueArcgEUD [cGy]

Average ValueArcHybrid [cGy]

Difference ArcDVHvs. ArcgEUD [cGy]/[%]

Difference ArcDVHvs. ArcHybrid [cGy]/[%] p value

Rectum D1% 7783 7803 7742 72/0.9 91/1.2 <0.05Rectum D15% 7150 6750 6738 640/8.9 714/8.6 <0.05Rectum D25% 6470 5652 5702 1199/18.5 1121/17.3 <0.05Rectum D40% 5444 4267 4372 1519/27.9 1433/26.3 <0.05Bladder D1% 7813 7720 7781 154/2.0 104/1.3 <0.05Bladder D15% 7353 6919 6973 707/9.6 380/5.4 <0.05Bladder D25% 6523 5959 5896 1032/15.8 1057/16.2 <0.05Bladder D40% 5053 4348 4276 1128/22.3 1143/22.6 <0.05

Abbreviations: ArcDVH = dose–volume histogram–based arc therapy; ArcgEUD = generalized equivalent uniform doses–based arc therapy;ArcHybrid = combination of ArcDVH and ArcgEUD; DI, dose index.

1296 I. J. Radiation Oncology d Biology d Physics Volume 82, Number 3, 2012

analyses (not presented explicitly) comparing DIs from

ArcHybrid and ArcgEUD optimization schemes indicated in-

creased bladder sparing ranging from �2% (D15%) to �6%

(D40%) and rectum sparing ranging from �2% (D15%) to

�8% (D40%) with ArcgEUD. The overall magnitude of

the OAR sparing with gEUD optimization ranged from

�1% to >27%, depending on the tallied index and the ana-

tomical structure. These findings are qualitatively and quan-

titatively similar to published data for fixed gantry angle

IMRT (20, 22), where OAR sparing of �4% to �23% was

estimated.

Some studies (11, 22) have suggested increased maximum

doses resulting from gEUD based IMRT optimization.

Although an increase of the maximum dose in the PTV will

not be very relevant, such an effect may be important in

OARs. The maximum dose increase effect was investigated

by tallying D1% for rectum and bladder. Statistical analysis

results, comparing the three optimization schemes, are

presented in Table 1. As can be inferred from the data, the sta-

tistically significant differences for both indices in either com-

parison are within 2%, indicating a minimal change of the

maximum dose from one optimization scheme to another.

Because the VMAT technique is potentially less time-

consuming than the multiple fixed gantry angle IMRT tech-

nique (1, 3–6), treatment times and monitor units (MUs)

for each optimization schemes were tallied and assessed.

The average planned MUs for ArcDVH, ArcgEUD, and

ArcHybrid schemes were 443.8 (330–625), 768.2 (492–

999), and 590.3 (447–738), respectively. The estimated

Table 2. Same as Table 1 but comparing generalized EUDs (a = 6) andoptimization s

Dose IndexAverage ValueArcDVH [cGy]

Average ValueArcgEUD [cGy]

Average ValueArcHybrid [cGy

Rectum (a = 6) 6096 5781 5775Rectum (a = 1) 4838 3936 3966Bladder (a = 6) 6152 5976 5987Bladder (a = 1) 4592 3869 3897

Abbreviations: ArcDVH = dose–volume histogram–based arc therapy; AArcHybrid = combination of ArcDVH and ArcgEUD.

average delivery times (3) for the optimization schemes

were 67.7, 101.7, and 74.3 s. These results indicate that

gEUD-based optimization generates VMAT plans with the

best OAR sparing at the expense of longer treatment times

and an increased number of monitor units compared with

mixed DVH and gEUD-based or DVH-based optimizations.

The major concern with more MUs in IMRT plans is the in-

creased MLC leakage. The Varian Millennium MLC leakage

for 6-MV photon energy is �2%. Therefore, the average dif-

ference of 325 MU between ArcDVH and ArcgEUD plans

will correspond to dose increase of �6.5 cGy per fraction

at the location of maximum dose (dmax, approximately at

1.5 cm depth in tissue). However, in a VMAT delivery,

this excessive dose will be spread over the entire arc. The

arc length used in this study is 356�, and if uniform gantry

speed is presumed, then the dose spread will be less than

0.02 cGy per degree per fraction, or <0.7 cGy per degree

over the entire course of treatment.

In either case, when gEUD-based VMAT optimization

was employed, statistically significant differences for rectal

and bladder gEUDs (cf. Table 2) were observed with respect

to the gEUDs derived from ArcDVH-based optimization.

The magnitude of the achievable rectum sparing ranged

from �7% to >20%, depending on the a value used in the

gEUD estimation and, to a somewhat smaller extent, for

the bladder. These results demonstrate the advantages of

the biological VMAT optimization because rectal complica-

tions have been correlated with EUD-like models (35). There

have been suggestions in the literature (22), however, that in

average dose (a = 1) among ArcDVH, ArcgEUD, and ArcHybridchemes

]Difference ArcDVH

vs. ArcgEUD [cGy]/[%]Difference ArcDVH

vs. ArcHybrid [cGy]/[%] p value

432/7.1 412/6.8 <0.051031/21.3 992/20.5 <0.05

274/4.5 240/3.9 <0.05908/19.8 705/17.3 <0.05

rcgEUD = generalized equivalent uniform doses–based arc therapy;

Biological optimization in VMAT therapy for prostate carcinoma d I. B. MIHAYLOV et al. 1297

principle, it is possible to achieve similar plan quality with

DVH- and gEUD-based optimization schemes. The major

difference between the two types of optimization implied in

that study is the overall time required to achieve the optimal

solution. It requires more planning experience as well as

more trial-and-error steps with DVH-based compared with

gEUD-based optimization for comparable plans. To asses

each optimization scheme fairly, the same approach should

be applied in all cases. An initial educated guess, derived

from the planner experience, should be followed by consec-

utive manual interventions aimed at delivering a uniform tar-

get dose while sparing OARs as much as possible.

DVH-based objectives are simplified surrogates of biolog-

ical outcomes from a radiotherapy treatment. Arguably (11),

there is a multitude of DVHs that can lead to a similar dose

response for a particular anatomical structure. The high de-

generacy of the DVHs makes a large space of biologically

equivalent dose distributions for each organ equally accept-

able. Therefore, biologically based optimization achieves

better OAR sparing, at the expense of a minimal increase

in maximum target doses, for a preset number of human in-

terventions in the treatment planning process.

CONCLUSIONS

The findings presented here indicate that biological opti-

mization has a significant potential to improve the treatment

plans for VMAT delivery. The results demonstrate that

a combination of DVH and gEUD objectives delivers accept-

able dose uniformity across the targets, increased sparing of

the surrounding critical structures, and a reasonable compro-

mise for treatment time and delivered monitor units com-

pared with the routinely used DVH optimization. Readers

should be cautioned that our conclusions are based on statis-

tical inferences, and, in some cases, DVH-based optimization

may yield better VMAT plans.

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