**5. Radiobiological evaluation of optimized HDR prostate brachytherapy implants**

High Dose Rate (HDR) Brachytherapy is becoming popular for treating localized prostate cancer tumors utilizing 3D ultrasound (U/S) and 192Ir based remote afterloaders. Compared to other 3D imaging modalities (CT, MR) U/S can provide real-time, accurate 3D information on the size and the position of the target volume, on the position of the organs-at-risk and the real time needle tracking and navigation. The use of inverse planning in HDR brachytherapy results in a fast planning process that produces reproducible high quality treatment plans that closely match the clinical protocol constraints (Baltas & Zamboglou 2006, Hsu et al. 2008, Martinez et al. 1989, Milickovic et al. 2002). During the last decade a number of inverse planning algorithms have been proposed (Alterovitz et al. 2006, Karabis et al. 2009, Lahanas et al. 1999, 2003) and many of them have been implemented in modern Treatment Planning Systems (TPS) (Oncentra Prostate™, Nucletron B.V., Veenendaal, The Netherlands, Oncentra Brachy™, Nucletron B.V., Veenendaal, The Netherlands, BrachyVision Treatent Planning™, Varian Medical Systems). It is a common characteristic for HDR implants optimized with such algorithms that there are a few very dominating dwell positions, where the largest part of the total dwell time is spent, which leads to a selective extension of high doses in volumes around such dwell positions. Presently, in HDR brachytherapy, new inverse optimization algorithms enable an adjustment of the source dwell time distribution within the implanted catheters according to user-defined objectives and penalties for the target volume(s) and organs at risk (OARs).

Use of Radiobiological Modeling in Treatment Plan

biologically effective uniform dose ( *D* ).

Evaluation and Optimization of Prostate Cancer Radiotherapy 251

(Mavroidis et al. 2008). For this evaluation the dose-response parameters of the prostate, urethra, bladder and rectum (Table 3) were used to calculate the corresponding response probabilities as well as the complication-free tumor control probability (*P*+) and the

Fig. 10. The differential DVHs of prostate, urethra, bladder and rectum derived from the

**Organs D50 (Gy) γ s α/β**

**PTV** 70.0 4.0 — 3.0 **Urethra** 120.0 3.0 0.03 3.0 **Bladder** 80.0 3.0 0.3 3.0 **Rectum** 80.0 2.2 0.7 3.0

Table 3. Summary of the model parameter values for the prostate cancer cases. *D*50 is the 50% response dose, γ is the maximum normalized value of the dose-response gradient and *s*

Finally, the conformal index COIN (Baltas et al. 1998), which is a measure of brachytherapy implant quality and dose specification, was applied in evaluation of the examined treatment plans. COIN considers also the conformity of the 3D dose distribution regarding the OARs based on three coefficients. The first coefficient is the fraction of the PTV that is enclosed by the prescription dose. The second coefficient is the fraction of the volume encompassed by the prescription dose that is covered by PTV and it is a measure of how much tissue outside the PTV is covered by the prescription dose. The third coefficient is the fraction of the

is the relative seriality, which characterizes the volume dependence of the organ.

volume of each OAR that receives doses that exceed their dose limit.

treatment plans. The prescription dose of the fraction is 11.5 Gy (100%).

In the present evaluation, the TPS Oncentra Prostate v.3.0 (Nucletron B.V., Veenendaal, The Netherlands) was used, where the Hybrid Inverse treatment Planning and Optimization (HIPO) algorithm has been implemented (Karabis et al. 2005, 2009). HIPO is an inverse planning algorithm that is based on 3D anatomy and it is capable of optimizing the dose distribution for a given needle configuration as well as finding an adequate needle configuration for each application. Furthermore, HIPO has the ability to apply a modulation restriction that limits the free modulation of dwell times eliminating the selective hot spots. It is based on dosimetric objectives, which penalize over/under dosage in target(s) while protecting OARs from overdosage (Karabis et al. 2009). Furthermore, in order to get restriction of the free modulation of dwell times allowing thus more smooth source movements and more smooth distributions of dwell time over dwell positions, HIPO offers the option of a modulation restriction (MR) parameter, which leads to a the dwell time gradient restriction.

The present analysis is based on the treatment plans of 12 prostate cancer patients, which were developed using their 3D ultrasound (U/S) image sets that were obtained intraoperatively right after the needle implantation. The twelve clinical implants for HDR brachytherapy of prostate cancer were selected as monotherapy for low-risk cases and they cover the whole range of prostate volumes with a full range of 26-101 cm3. In the present clinical protocol, the HDR Monotherapy is delivered in three implants separated by at least 2 weeks interval. In each implant a single fraction with a prescription dose of 11.5 Gy is delivered thus resulting in a total dose of 34.5 Gy. The prostate gland is considered as PTV and urethra, bladder and rectum are used as OARs in the treatment planning. The whole procedure including dose delivery is realized intra-operatively utilizing 3D and 2D Ultrasound imaging.

For the evaluation and report of the quality of the dose distributions, the following DVHbased parameters that have been proposed by GEC/ESTRO-EAU (19-22), have been considered (Baltas & Zamboglou 2006, Kovács et al. 2005, Nag et al. 1999).

*D***100**: The dose that covers 100% of the PTV volume, which is the Minimum Target Dose (MTD).

*D***90**: The dose that covers 90% of the PTV volume, which would be desirable to be equal or greater than the prescription dose.

*V***100**: The percentage of prostate volume (PTV) that has received at least the prescription dose (100% = prescribed dose).

*V***150**: The volume that has received 50% more than the prescribed dose (150% of the prescription dose).

Regarding the OARs, the following dosimetric descriptors for the maximum doses have been considered:

*D***2cm³**: the dose for the most exposed 2 cm3 of rectum or bladder,

*D***0.1cm³**: the dose for the most exposed 0.1cm3 of the urethra as an estimate of the maximum dose

*D***10**: the highest dose covering 10% of the OAR volume (rectum, bladder, urethra)

All the clinical implants have been inversely planned using HIPO with modulation restriction (MR), which was selected based on the maximum values resulting in plans that completely fulfilled the constraints of the dosimetric protocol. In the treatment plan evaluation, the individual tissue DVHs were calculated for each plan (Fig. 10).

The different treatment plans were further evaluated in conjunction with radiobiological dose non-uniformity evaluation measures in order to estimate their expected clinical impact

In the present evaluation, the TPS Oncentra Prostate v.3.0 (Nucletron B.V., Veenendaal, The Netherlands) was used, where the Hybrid Inverse treatment Planning and Optimization (HIPO) algorithm has been implemented (Karabis et al. 2005, 2009). HIPO is an inverse planning algorithm that is based on 3D anatomy and it is capable of optimizing the dose distribution for a given needle configuration as well as finding an adequate needle configuration for each application. Furthermore, HIPO has the ability to apply a modulation restriction that limits the free modulation of dwell times eliminating the selective hot spots. It is based on dosimetric objectives, which penalize over/under dosage in target(s) while protecting OARs from overdosage (Karabis et al. 2009). Furthermore, in order to get restriction of the free modulation of dwell times allowing thus more smooth source movements and more smooth distributions of dwell time over dwell positions, HIPO offers the option of a modulation restriction (MR) parameter,

The present analysis is based on the treatment plans of 12 prostate cancer patients, which were developed using their 3D ultrasound (U/S) image sets that were obtained intraoperatively right after the needle implantation. The twelve clinical implants for HDR brachytherapy of prostate cancer were selected as monotherapy for low-risk cases and they cover the whole range of prostate volumes with a full range of 26-101 cm3. In the present clinical protocol, the HDR Monotherapy is delivered in three implants separated by at least 2 weeks interval. In each implant a single fraction with a prescription dose of 11.5 Gy is delivered thus resulting in a total dose of 34.5 Gy. The prostate gland is considered as PTV and urethra, bladder and rectum are used as OARs in the treatment planning. The whole procedure including dose delivery is realized intra-operatively

For the evaluation and report of the quality of the dose distributions, the following DVHbased parameters that have been proposed by GEC/ESTRO-EAU (19-22), have been

*D***100**: The dose that covers 100% of the PTV volume, which is the Minimum Target Dose

*D***90**: The dose that covers 90% of the PTV volume, which would be desirable to be equal or

*V***100**: The percentage of prostate volume (PTV) that has received at least the prescription

*V***150**: The volume that has received 50% more than the prescribed dose (150% of the

Regarding the OARs, the following dosimetric descriptors for the maximum doses have

*D***0.1cm³**: the dose for the most exposed 0.1cm3 of the urethra as an estimate of the maximum

All the clinical implants have been inversely planned using HIPO with modulation restriction (MR), which was selected based on the maximum values resulting in plans that completely fulfilled the constraints of the dosimetric protocol. In the treatment plan

The different treatment plans were further evaluated in conjunction with radiobiological dose non-uniformity evaluation measures in order to estimate their expected clinical impact

*D***10**: the highest dose covering 10% of the OAR volume (rectum, bladder, urethra)

evaluation, the individual tissue DVHs were calculated for each plan (Fig. 10).

considered (Baltas & Zamboglou 2006, Kovács et al. 2005, Nag et al. 1999).

*D***2cm³**: the dose for the most exposed 2 cm3 of rectum or bladder,

which leads to a the dwell time gradient restriction.

utilizing 3D and 2D Ultrasound imaging.

greater than the prescription dose.

dose (100% = prescribed dose).

prescription dose).

been considered:

(MTD).

dose

(Mavroidis et al. 2008). For this evaluation the dose-response parameters of the prostate, urethra, bladder and rectum (Table 3) were used to calculate the corresponding response probabilities as well as the complication-free tumor control probability (*P*+) and the biologically effective uniform dose ( *D* ).

Fig. 10. The differential DVHs of prostate, urethra, bladder and rectum derived from the treatment plans. The prescription dose of the fraction is 11.5 Gy (100%).


Table 3. Summary of the model parameter values for the prostate cancer cases. *D*50 is the 50% response dose, γ is the maximum normalized value of the dose-response gradient and *s* is the relative seriality, which characterizes the volume dependence of the organ.

Finally, the conformal index COIN (Baltas et al. 1998), which is a measure of brachytherapy implant quality and dose specification, was applied in evaluation of the examined treatment plans. COIN considers also the conformity of the 3D dose distribution regarding the OARs based on three coefficients. The first coefficient is the fraction of the PTV that is enclosed by the prescription dose. The second coefficient is the fraction of the volume encompassed by the prescription dose that is covered by PTV and it is a measure of how much tissue outside the PTV is covered by the prescription dose. The third coefficient is the fraction of the volume of each OAR that receives doses that exceed their dose limit.

Use of Radiobiological Modeling in Treatment Plan

having *P*B = 96.3% and *P*I = 1.1%.

10.5114/jcb.2010.16923).

plans are characterized by high quality.

Evaluation and Optimization of Prostate Cancer Radiotherapy 253

the complication-free tumor control then the *P*+ value becomes 95.2% for a *D*B of 32.2 Gy

The average COIN values, which were calculated with and without the inclusion of the organs at risk (OARs) for the 12 implants using HIPO with modulation restriction are 0.867 ± 0.019 and 0.870 ± 0.021, respectively. These values indicate that the examined treatment

Fig. 12. *Left diagram:* The average dose-response curves of the PTV (red), urethra (black), bladder (pink) and rectum (blue) are presented for the HDR treatment plans, which were optimized with modulation restriction, regarding different prescription doses. *Right diagram:* The average curves of the total tumor control probability, *P*B (green), total normal tissue complication probability, *P*I (red) and complication-free tumor control probability, *P*+ (black) are presented for the HDR treatment plans, regarding different radiobiological prescription doses. The total dose of 34.5 Gy delivered by three fractions of 11.5 Gy is considered to be the total prescription dose (100%) (Mavroidis et al. 2010) (published with permission from: Mavroidis et al. Radiobiological evaluation of the influence of dwell time modulation restriction in HIPO optimized HDR prostate brachytherapy implants. Journal of Contemporary Brachytherapy, Vol.2, pp. 126, 2010, Termedia sp.zo.o., DOI:

Non-uniform dose distributions, which may be as effective as equivalent uniform dose distributions, which means that a higher number of degrees-of-freedom can be taken advantage of by incorporating radiobiological measures in treatment plan optimization. In this sense, a radiobiologically based optimization algorithm could find dose distributions of smoother non-uniformity that irradiate the target as effectively as the physically optimized dose distributions without modulation restriction and at the same time optimize the dose fall-off towards the organs at risk. This is because the radiobiologically based HDR optimization would take into account the volume effect of all the involved organs at risk in the proximity of the target and optimize the dose fall-off accordingly. It has to be mentioned that radiobiologically based HDR optimization is characterized by more clinically relevant dose constraints for the OARs and normal tissue stroma, which could lead to better results than the HDR optimization without modulation restriction. However, the large hot spots produced in the target volume by this method would increase the risk for secondary cancer (Schneider et al 2006). Consequently, by deteriorating physical dose conformation, the HDR

optimization with MR provides slightly better biological conformation.

Fig. 11. The average cumulative DVHs of the PTV (prostate gland, red), urethra (black), bladder (pink) and rectum (blue) are presented for the HDR treatment plans, which were optimized with modulation restriction. Here, the total dose of 34.5 Gy delivered by three fractions of 11.5 Gy is considered to be the total prescription dose (100%) (Mavroidis et al. 2010) (published with permission from: Mavroidis et al. Radiobiological evaluation of the influence of dwell time modulation restriction in HIPO optimized HDR prostate brachytherapy implants. Journal of Contemporary Brachytherapy, Vol.2, pp. 126, 2010, Termedia sp.zo.o., DOI: 10.5114/jcb.2010.16923).

Fig. 11 illustrates the average DVHs of the dose distributions examined. Based on the DVHs and the results shown in Table 4, the HIPO optimization with MR has an acceptable variance coefficient, CV, (meaning dose inhomogeneity) inside the PTV. The average mean dose in the PTV in the HIPO with MR plans is 48.4 Gy and the corresponding control probability is 97.8%. Regarding the organs at risk, the HIPO optimization with MR plans deliver fairly low maximum doses in urethra, which results in a clinically acceptable response probability (3.8%) (Mavroidis et al. 2010).


Table 4. Summary of the dosimetric and radiobiological measures averaged over the 12 prostate cancer patients regarding the applied HDR technique.

A quantitative analysis of the dosimetric and radiobiological results of the different dose distributions shows that for the HDR optimization with MR at the clinical dose prescription the *P*+ value is 94.0% and the biologically effective uniform dose to the PTV, *D*B is 32.9Gy. The total control probability, *P*B is 97.8% and the total complication probability, *P*I is 3.8%, which mainly stems from the response probability of urethra (3.8%) (Mavroidis et al. 2010). However, if a different dose level of the dose distributions is selected in order to maximize

Fig. 11. The average cumulative DVHs of the PTV (prostate gland, red), urethra (black), bladder (pink) and rectum (blue) are presented for the HDR treatment plans, which were optimized with modulation restriction. Here, the total dose of 34.5 Gy delivered by three fractions of 11.5 Gy is considered to be the total prescription dose (100%) (Mavroidis et al. 2010) (published with permission from: Mavroidis et al. Radiobiological evaluation of the

Fig. 11 illustrates the average DVHs of the dose distributions examined. Based on the DVHs and the results shown in Table 4, the HIPO optimization with MR has an acceptable variance coefficient, CV, (meaning dose inhomogeneity) inside the PTV. The average mean dose in the PTV in the HIPO with MR plans is 48.4 Gy and the corresponding control probability is 97.8%. Regarding the organs at risk, the HIPO optimization with MR plans deliver fairly low maximum doses in urethra, which results in a clinically acceptable

**Tissues CTV Urethra Bladder Rectum P (%)** 97.8 3.8 0.0 0.02 *D***mean (Gy)** 48.4 33.0 9.2 14.4 *CV* **(%)** 30.5 18.2 46.5 33.3 *D* **(Gy)** 32.9 34.2 22.3 22.8 *D***max (Gy)** 136.6 41.4 27.6 27.6 *D***min (Gy)** 23.5 11.0 2.8 2.8 Table 4. Summary of the dosimetric and radiobiological measures averaged over the 12

A quantitative analysis of the dosimetric and radiobiological results of the different dose distributions shows that for the HDR optimization with MR at the clinical dose prescription the *P*+ value is 94.0% and the biologically effective uniform dose to the PTV, *D*B is 32.9Gy. The total control probability, *P*B is 97.8% and the total complication probability, *P*I is 3.8%, which mainly stems from the response probability of urethra (3.8%) (Mavroidis et al. 2010). However, if a different dose level of the dose distributions is selected in order to maximize

influence of dwell time modulation restriction in HIPO optimized HDR prostate brachytherapy implants. Journal of Contemporary Brachytherapy, Vol.2, pp. 126, 2010,

Termedia sp.zo.o., DOI: 10.5114/jcb.2010.16923).

response probability (3.8%) (Mavroidis et al. 2010).

prostate cancer patients regarding the applied HDR technique.

the complication-free tumor control then the *P*+ value becomes 95.2% for a *D*B of 32.2 Gy having *P*B = 96.3% and *P*I = 1.1%.

The average COIN values, which were calculated with and without the inclusion of the organs at risk (OARs) for the 12 implants using HIPO with modulation restriction are 0.867 ± 0.019 and 0.870 ± 0.021, respectively. These values indicate that the examined treatment plans are characterized by high quality.

Fig. 12. *Left diagram:* The average dose-response curves of the PTV (red), urethra (black), bladder (pink) and rectum (blue) are presented for the HDR treatment plans, which were optimized with modulation restriction, regarding different prescription doses. *Right diagram:* The average curves of the total tumor control probability, *P*B (green), total normal tissue complication probability, *P*I (red) and complication-free tumor control probability, *P*+ (black) are presented for the HDR treatment plans, regarding different radiobiological prescription doses. The total dose of 34.5 Gy delivered by three fractions of 11.5 Gy is considered to be the total prescription dose (100%) (Mavroidis et al. 2010) (published with permission from: Mavroidis et al. Radiobiological evaluation of the influence of dwell time modulation restriction in HIPO optimized HDR prostate brachytherapy implants. Journal of Contemporary Brachytherapy, Vol.2, pp. 126, 2010, Termedia sp.zo.o., DOI: 10.5114/jcb.2010.16923).

Non-uniform dose distributions, which may be as effective as equivalent uniform dose distributions, which means that a higher number of degrees-of-freedom can be taken advantage of by incorporating radiobiological measures in treatment plan optimization. In this sense, a radiobiologically based optimization algorithm could find dose distributions of smoother non-uniformity that irradiate the target as effectively as the physically optimized dose distributions without modulation restriction and at the same time optimize the dose fall-off towards the organs at risk. This is because the radiobiologically based HDR optimization would take into account the volume effect of all the involved organs at risk in the proximity of the target and optimize the dose fall-off accordingly. It has to be mentioned that radiobiologically based HDR optimization is characterized by more clinically relevant dose constraints for the OARs and normal tissue stroma, which could lead to better results than the HDR optimization without modulation restriction. However, the large hot spots produced in the target volume by this method would increase the risk for secondary cancer (Schneider et al 2006). Consequently, by deteriorating physical dose conformation, the HDR optimization with MR provides slightly better biological conformation.

Use of Radiobiological Modeling in Treatment Plan

Radiobiological treatment plan evaluation

fractionation effects that are introduced by the clinical protocol:

the relative seriality model for normal tissues (Lind et al. 1999).

is expressed as follows (Källman et al. 1992b, Lind et al. 1999):

I

of merit for a treatment.

**7. Appendix** 

and 

for 

where I

and 

Evaluation and Optimization of Prostate Cancer Radiotherapy 255

increased by the use of therapeutic indices such as *P*+ and *D* , which can be used as figures

In the present radiobiological treatment plan evaluation method, the Linear-Quadratic-Poisson model is used to describe the dose-response relation of the tumours and normal tissues (Källman et al. 1992b, Ågren et al. 1990). This model takes into account the

/ ln ln 2 <sup>50</sup> ( ) exp *e DD e PD e*

where *P(D)* is the probability to control a tumour or induce a certain injury to a normal tissue that is irradiated uniformly with a dose *D*. *D*50 is the dose, which gives a 50% response

is the maximum normalized dose-response gradient. The parameters *D*50 and

specific for every organ and type of clinical endpoint and they are derived directly from clinical data (Emami et al. 1991, Eriksson et al. 2000, Gagliardi et al. 2000, Jackson et al. 1995, Mavroidis et al. 2003, 2005, Roesink et al. 2001, Willner et al. 2002, Ågren 1995). The uncertainties that are associated with these parameters are of the order of 5% for *D*50, 30%

 and 90% for *s*. These uncertainties define the confidence interval of the entire doseresponse curve around its best estimate (Deasy 1997). The response of the entire organ to a non-uniform dose distribution is given by an expanded version of Eq. (1) for tumours and

The relative seriality model is a model that account for the volume effect. For a heterogeneous dose distribution, the overall probability of injury (*P*I) for a number of OARs

1 1

*N Mj*

*j i P P D* 

etc could also have been used with the appropriate response parameter set.

organs 1/

*<sup>j</sup> P* is the probability of injuring organ *j* and *N*organs is the total number of vital OARs. ( ) *<sup>j</sup> P Di* is the probability of response of the organ *j* having the reference volume and being irradiated to dose *Di* as described by Eq. (1). *Δvi = ΔVi / V*ref is the fractional sub-volume of the organ that is irradiated compared to the reference volume for which the values of *D*<sup>50</sup>

 were calculated. *Mj* is the total number of voxels or sub-volumes in the organ *j*, and *sj* is the relative seriality parameter that characterizes the internal organization of that organ. A relative seriality close to zero (*s* 0) corresponds to a completely parallel structure, which becomes non-functional when all its functional subunits are damaged, whereas *s* 1 corresponds to a completely serial structure which becomes non-functional when at least one functional subunit is damaged. It should be mentioned that other models such as the LKB (Burman et al. 1991, Kutcher et al. 1991, Kwa et al. 1998), parallel (Boersma et al. 1995)

Tumours are assumed to have a parallel structural organization since the eradication of all of the clonogenic cells is required. Furthermore, in complex multi-target cancer cases, the

*j s s v i*

(2)

1 1 [1 (1 ( ) ) ] *j j <sup>i</sup>*

 

(1)

are

#### **6. Conclusions**

This chapter demonstrates the use of radiobiological measures in prostate cancer treatment plan optimization may have a great impact on the clinical effectiveness of the applied treatment. Taking into account the dose-response relations of the irradiated tumors and normal tissues, a radiobiological dose delivery evaluation can be performed, which combines the information of a given dose distribution with the radiosensitivity map of the patient. The use of *P D* diagrams can complement the traditional tools of evaluation such as DVHs, in order to compare and effectively evaluate different treatment plans*.*

The findings show that the use of fused CT-MRI images produce dose distributions, which lead on average to better expected treatment outcome compared to the use of CT images alone. The extent of this improvement decreases as we move from conventional to IMRT treatments due to the fact that IMRT delivers already limited doses to OARs. Although 3D conformal radiotherapy techniques are not characterized by very high conformalities, the better knowledge of the CTV extension can considerably improve the effectiveness of their dose distributions. These findings were observed during treatment plan evaluation and comparison based on common dosimetric indices as well as on radiobiological measures.

The clinical effectiveness of delivered Helical Tomotherapy dose distributions with and without patient setup correction, which were evaluated using both physical and biological criteria, showed that the dose distributions with and without patient setup correction are very similar and the expected clinical outcome is not always better in the first case unless a radiobiological treatment plan optimization has been performed first. However, the effectiveness of a HT treatment plan can be considerably deteriorated if an accurate initial patient setup procedure is not available. The application of radiobiological measures on HT prostate cancer treatment plans with and without patient setup correction revealed minor or modest differences in the predicted therapeutic impact of using the MVCT method.

Radiobiological evaluation of treatment plans provides additional information about the fitness of a plan and a closer association of the delivered treatment with the clinical outcome. The simultaneous presentation of the radiobiological evaluation together with the physical data shows their complementary relation in analyzing a dose plan. The use of radiobiological parameters is necessary if a clinically relevant quantification of a plan is needed. The application of the *P*+ and *D* concepts on representative Helical Tomotherapy and MLC-based IMRT prostate cancer treatment plans revealed differences in the biological impact of the corresponding dose distributions. It can be concluded that for clinical cases, which may look dosimetrically similar, in radiobiological terms they can be quite different. Helical Tomotherapy and MLC-based IMRT can cover the target volume with the clinically prescribed dose while minimizing the volume of the organs at risk receiving high dose. Both radiation modalities have almost the same potential of producing treatment plans of equivalent clinical effectiveness in terms adequate irradiation of the tumor and sparing of the involved OARs.

At the maximum *P*+ dose prescription, it was proved that the different modulation restriction approaches do not affect significantly the proper coverage and eradication of the target and the sparing of rectum and bladder but they affect mainly the effective sparing of urethra. In this analysis, which was performed using both physical and radiobiological criteria, it is shown that the HDR optimization with MR can introduce a minor improvement in the effectiveness of the produced dose distribution compared to the HDR optimization without modulation restriction. The likelihood to accomplish a good treatment result can be increased by the use of therapeutic indices such as *P*+ and *D* , which can be used as figures of merit for a treatment.
