**Use of Radiobiological Modeling in Treatment Plan Evaluation and Optimization of Prostate Cancer Radiotherapy**

Panayiotis Mavroidis1, Dimos Baltas2, Bengt K. Lind1 and Nikos Papanikolaou3 *1Department of Medical Radiation Physics Karolinska Institutet and Stockholm University 2Department of Medical Physics & Engineering, Strahlenklinik, Klinikum Offenbach GmbH 3Department of Radiological Sciences University of Texas Health Science Center, San Antonio, Texas 1Sweden 2Germany 3USA* 

#### **1. Introduction**

236 Prostate Cancer – Diagnostic and Therapeutic Advances

VROM. Recommendations: working with therapeutical doses of radionuclides, The Hague.

Wang C et al (2002) Reticulated platelets predict platelet count recovery following

chemotherapy. *Transfusion* 42 (3):368-374.

2005.

There are many tools available that are used to evaluate a radiotherapy treatment plan, such as isodose distribution charts, dose volume histograms (DVH), maximum, minimum and mean doses of the dose distributions as well as DVH point dose constraints. All the already mentioned evaluation tools are dosimetric only without taking into account the radiobiological characteristics of tumors or OARs. It has been demonstrated that although competing treatment plans might have similar mean, maximum or minimum doses they may have significantly different clinical outcomes (Mavroidis et al. 2001). For performing a more complete treatment plan evaluation and comparison the complication-free tumor control probability (*P*+) and the biologically effective uniform dose ( *D* ) have been proposed (Källman et al. 1992a, Mavroidis et al. 2000). The *D* concept denotes that any two dose distributions within a target or OAR are equivalent if they produce the same probability for tumor control or normal tissue complication, respectively (Mavroidis et al. 2001).

In this chapter, the importance of the *P D* diagrams is illustrated. These diagrams provide important information by combining the radiobiological data of the organs involved with the dosimetric information of the delivered dose distribution (Mavroidis et al. 2010). It would increase the flexibility and clinical application of the *P*+ index if in its original definition the different terms related to the tumor control and normal tissue complication probabilities were accompanied by some weighting factors, which could be adjustable by the clinicians depending on the important of the different clinical endpoints used (Mavroidis et al. 2011). In practice the *P*+ index finds the pure benefit from the treatment by subtracting the normal tissue complication probabilities from the tumor control probability.

Use of Radiobiological Modeling in Treatment Plan

irradiated to high doses (Debois et al. 1999).

Evaluation and Optimization of Prostate Cancer Radiotherapy 239

demonstrate the internal prostatic anatomy, prostatic margins and the extent of prostatic tumors (Chen et al. 2004, Parker et al. 2003, Rørvik et al. 1993, Villeirs et al. 2007). It has been shown that an important decrease in the inter-observer delineation variation, as well as a significant decrease in the clinical target volume (CTV) may be resulted in by the use of fused MRI-CT images (Villeirs et al. 2005). Using MRI for delineation, the reduced prostatetarget volume is associated with a reduction of the rectal wall being irradiated, which may result in fewer rectal and urological complications (Rasch et al. 1999). More specifically, the use of axial and coronal MR scans, in localized prostate carcinoma treatment planning results in a better coverage of the prostate and a reduction of the volume of the rectum

Fig. 1. The reference CT (left) and fused CT-MRI (right) slices of a prostate cancer patient is shown for the 3D-CRT (upper) and MLC-based IMRT (lower) treatment plans in the transverse plane. The delineations of the anatomical structures involved were performed based on the CT and MRI images and they are illustrated together with the dose distributions delivered to the patient (Tzikas et al. 2011) (published with permission from: Tzikas et al. Investigating the clinical aspects of using CT vs. CT-MRI images during organ delineation and treatment planning in prostate cancer radiotherapy. Technology in Cancer Research and

In the present analysis, the respective CT and MRI images at treatment position were acquired for 10 prostate cancer patients (Tzikas et al. 2011). For each patient the separate CT and MRI images were used to delineate the Clinical Target Volume (CTV), which includes the prostate gland and the seminal vehicles. During treatment planning, the MRI and CT images were fused. The PTV was produced by adding to the CTV 1.0 cm margin in all directions apart from that towards rectum, which was 0.6 cm. So, 2 PTVs were produced for each patient based on the CT and MRI images. The comparison of the prostate cancer treatment plans in terms of isodose lines and dose volume histograms (DVH) is shown in

Treatment, Vol.10, pp. 235 and 236, 2011, Adenine Press, http://www.tcrt.org).

In clinical practice, there are not different weighting factors that are applied but there are risk thresholds (usually 5-10%) for every organ at risk, which should not be exceeded (Mavroidis et al. 2011). So, in order to classify the different treatment plans one can select the dose level that satisfies these demands imposed by the normal tissues risk thresholds and compare the expected tumor control rates at this dose level.

By using the *D* concept on the dose axis, the control and complication probabilities of the target and OARs can be examined individually. Due to the fact that different plans generally deliver different mean doses to the target for the same control rate, the use of the target mean dose as a dose scaling basis is not suitable since the expected response rates induced by the treatment to the rest of the involved organs cannot be easily compared using this scale. The major advantage is that the *D* concept forces the total control probabilities of different plans to coincide and the comparison of the response curves becomes much simpler than when the mean target dose is used (Mavroidis et al. 2001).

The results and conclusions of this chapter are strongly dependent on the accuracy of the radiobiological models and the parameters describing the dose-response relation of the different tumours and normal tissues (Mavroidis et al. 2007). However, it is known that all the existing models are based on certain assumptions or take into account certain only biological mechanisms. Furthermore, the determination of the model parameters expressing the effective radiosensitivity of the tissues is subject to uncertainties imposed by the inaccuracies in the patient setup during radiotherapy, lack of knowledge of the inter-patient and intra-patient radiosensitivity and inconsistencies in treatment methodology (Buffa et al. 2001, Fenwick & Nahum 2001). Consequently, the determined model parameters and the corresponding dose-response curves are characterized by confidence intervals. In the present analysis, most of the tissue response parameters have been taken from recently published clinical studies, where these parameter confidence intervals has been reduced significantly (e.g. uncertainty of around 5% in the determination of *D*50). So, the expected response of a tissue is known with some uncertainty, which can be considered clinically acceptable (Mavroidis et al. 2007).

In this chapter, the treatment plans were optimized using conventional physical criteria like dose volume histograms, isodose charts, DVH point constraints, target prescribed doses and OAR tolerance doses. However, the developed treatment plans were evaluated radiobiologically using the radiation sensitivities of the respective organs involved in each case. The expected normal tissue complications were estimated against the optimum target dose using radiobiological plots. Just as a dose volume histogram is a good illustration of the volumetric dose distribution delivered to the target and OAR in the patient, so is the radiobiological evaluation plot as a measure of the expected clinical outcome. The doseresponse diagrams in conjunction with the dosimetric diagrams provide a more thorough viewpoint of the examined treatment plans.

#### **2. Organ delineation and treatment planning using CT vs. CT-MRI images during in prostate cancer radiotherapy**

Traditionally, targets and organs-at-risk (OAR) are anatomically delineated on computed tomography (CT)-images in prostate cancer treatment planning. However, in CT the sensitivity of visualizing extracapsular involvement is lower than in magnetic resonance imaging (MRI), which provides much more detailed information. MRI can superbly

In clinical practice, there are not different weighting factors that are applied but there are risk thresholds (usually 5-10%) for every organ at risk, which should not be exceeded (Mavroidis et al. 2011). So, in order to classify the different treatment plans one can select the dose level that satisfies these demands imposed by the normal tissues risk thresholds

By using the *D* concept on the dose axis, the control and complication probabilities of the target and OARs can be examined individually. Due to the fact that different plans generally deliver different mean doses to the target for the same control rate, the use of the target mean dose as a dose scaling basis is not suitable since the expected response rates induced by the treatment to the rest of the involved organs cannot be easily compared using this scale. The major advantage is that the *D* concept forces the total control probabilities of different plans to coincide and the comparison of the response curves becomes much

The results and conclusions of this chapter are strongly dependent on the accuracy of the radiobiological models and the parameters describing the dose-response relation of the different tumours and normal tissues (Mavroidis et al. 2007). However, it is known that all the existing models are based on certain assumptions or take into account certain only biological mechanisms. Furthermore, the determination of the model parameters expressing the effective radiosensitivity of the tissues is subject to uncertainties imposed by the inaccuracies in the patient setup during radiotherapy, lack of knowledge of the inter-patient and intra-patient radiosensitivity and inconsistencies in treatment methodology (Buffa et al. 2001, Fenwick & Nahum 2001). Consequently, the determined model parameters and the corresponding dose-response curves are characterized by confidence intervals. In the present analysis, most of the tissue response parameters have been taken from recently published clinical studies, where these parameter confidence intervals has been reduced significantly (e.g. uncertainty of around 5% in the determination of *D*50). So, the expected response of a tissue is known with some uncertainty, which can be considered clinically

In this chapter, the treatment plans were optimized using conventional physical criteria like dose volume histograms, isodose charts, DVH point constraints, target prescribed doses and OAR tolerance doses. However, the developed treatment plans were evaluated radiobiologically using the radiation sensitivities of the respective organs involved in each case. The expected normal tissue complications were estimated against the optimum target dose using radiobiological plots. Just as a dose volume histogram is a good illustration of the volumetric dose distribution delivered to the target and OAR in the patient, so is the radiobiological evaluation plot as a measure of the expected clinical outcome. The doseresponse diagrams in conjunction with the dosimetric diagrams provide a more thorough

**2. Organ delineation and treatment planning using CT vs. CT-MRI images** 

Traditionally, targets and organs-at-risk (OAR) are anatomically delineated on computed tomography (CT)-images in prostate cancer treatment planning. However, in CT the sensitivity of visualizing extracapsular involvement is lower than in magnetic resonance imaging (MRI), which provides much more detailed information. MRI can superbly

and compare the expected tumor control rates at this dose level.

simpler than when the mean target dose is used (Mavroidis et al. 2001).

acceptable (Mavroidis et al. 2007).

viewpoint of the examined treatment plans.

**during in prostate cancer radiotherapy** 

demonstrate the internal prostatic anatomy, prostatic margins and the extent of prostatic tumors (Chen et al. 2004, Parker et al. 2003, Rørvik et al. 1993, Villeirs et al. 2007). It has been shown that an important decrease in the inter-observer delineation variation, as well as a significant decrease in the clinical target volume (CTV) may be resulted in by the use of fused MRI-CT images (Villeirs et al. 2005). Using MRI for delineation, the reduced prostatetarget volume is associated with a reduction of the rectal wall being irradiated, which may result in fewer rectal and urological complications (Rasch et al. 1999). More specifically, the use of axial and coronal MR scans, in localized prostate carcinoma treatment planning results in a better coverage of the prostate and a reduction of the volume of the rectum irradiated to high doses (Debois et al. 1999).

Fig. 1. The reference CT (left) and fused CT-MRI (right) slices of a prostate cancer patient is shown for the 3D-CRT (upper) and MLC-based IMRT (lower) treatment plans in the transverse plane. The delineations of the anatomical structures involved were performed based on the CT and MRI images and they are illustrated together with the dose distributions delivered to the patient (Tzikas et al. 2011) (published with permission from: Tzikas et al. Investigating the clinical aspects of using CT vs. CT-MRI images during organ delineation and treatment planning in prostate cancer radiotherapy. Technology in Cancer Research and Treatment, Vol.10, pp. 235 and 236, 2011, Adenine Press, http://www.tcrt.org).

In the present analysis, the respective CT and MRI images at treatment position were acquired for 10 prostate cancer patients (Tzikas et al. 2011). For each patient the separate CT and MRI images were used to delineate the Clinical Target Volume (CTV), which includes the prostate gland and the seminal vehicles. During treatment planning, the MRI and CT images were fused. The PTV was produced by adding to the CTV 1.0 cm margin in all directions apart from that towards rectum, which was 0.6 cm. So, 2 PTVs were produced for each patient based on the CT and MRI images. The comparison of the prostate cancer treatment plans in terms of isodose lines and dose volume histograms (DVH) is shown in

Use of Radiobiological Modeling in Treatment Plan

90.2%, whereas the average *P*I = 15.4%.

the horizontal crossed bar.

individual patients.

while the average *P*I would remains the same.

Gy having an average *P*B = 80.6% and an average *P*I by 33.8%.

Evaluation and Optimization of Prostate Cancer Radiotherapy 241

complication-free tumor control gets optimum, for the CT-based treatment plans, the *P*<sup>+</sup> value becomes 42.5% for a *D*B of 86.4 Gy having average *P*B = 80.0% and average *P*I = 37.4%, whereas for the CT-MRI-based treatment plans, the *P*+ value becomes 46.7% for a *D*B of 86.7

For the treatment plans of the IMRT treatment modality, which were produced based on the CT images, at the clinical dose prescription, the *P*+ value is 52.5% for *D*CTV = 81.0 Gy and *D*B = 80.8 Gy. The average *P*B is 57.1% and the average *P*I is 4.7%. Similarly, for the CT-MRIbased treatment plans, the *P* value is 53.4% for *D*CTV = 80.8 Gy and *D*B = 80.5 Gy. The average *P*B = 58.6% and the average *P*I = 5.2%. However, at the dose level that maximizes the complication-free tumor control for the CT-based plans, the *P*+ value becomes 74.7% for a *D*B of 91.5Gy having *P*B = 90.0% and *P*I = 15.3%, whereas for the CT-MRI-based plans, the *P* value remains the same for a higher *D*B by 0.6 Gy. The corresponding average *P*B =

If the CT-based treatment plans were applied to calculate the dose in target and OARs that were produced using the fused CT-MRI images then the average differences would be almost zero in the case of CRT radiation modality, whereas in the case of IMRT radiation modality the *P*+ value would become 2.1% lower, the average *P*B would be lower by 2.1%

Observing the diagrams in Fig. 3 it is apparent that the clinically established dose prescription, which corresponds to a certain uniform dose in the CTV deviates from the optimal dose level that is indicated by the radiobiological evaluation. For example, the clinically prescribed dose level is lower than the optimum level by *D* = 8-14 Gy. According to these findings, it is expected that a small increase in the dose prescription will slightly increase the complication rate but it will also be accompanied by a significant increase in the control rate. As shown in Fig. 3, a margin of improvement can be observed while the individual normal tissue responses are kept below the limit of 10% as indicated by

Fig. 3. The dose-response curves of the CTV / total control probability, *P*B, bladder, rectum, total complication probability, *P*I and complication-free tumor control probability, *P*+ are presented for the CRT and IMRT treatment plans, which were optimized based on the CT and fused CT-MRI images, separately. The horizontal crossed bar indicates the 5-10% response probability region. The vertical lines represent the prescribed dose levels of the

Figs. 1 and 2. Furthermore, individual dose-response curves and *P*+ - *D*B plots of the CT and CT-MRI based treatment plans are presented in Fig. 3 for the CRT (left) and IMRT (right) radiation modalities, respectively.

Fig. 2. The dose volume histograms (DVHs) of the CTV, rectum and bladder are presented in the upper, middle and lower diagrams, respectively for the CRT (left) and IMRT (right) treatment plans, which were optimized based on the CT and fused CT-MRI images, separately.

For the treatment plans of the CRT treatment modality, which were produced based on the CT images, at the clinical dose prescription the average *P*+ value is 15.9% for a mean dose ( *D*CTV ) and a biologically effective uniform dose ( *D*<sup>B</sup> ) to the CTV of 75.5 Gy. The average total control probability, *P*B is 26.5% and the average total complication probability, *P*I is 10.5%. Similarly, for the treatment plans that were produced based on the fused CT-MRI images, the average *P*+ value is 17.5% for the same *D*CTV and *D*<sup>B</sup> . The average *P*B the same with that of the treatment plans that were produced using CT images alone (26.5%) and the average *P*I is 8.9%. However, at the dose level of the individual dose distributions that the

Figs. 1 and 2. Furthermore, individual dose-response curves and *P*+ - *D*B plots of the CT and CT-MRI based treatment plans are presented in Fig. 3 for the CRT (left) and IMRT (right)

Fig. 2. The dose volume histograms (DVHs) of the CTV, rectum and bladder are presented in the upper, middle and lower diagrams, respectively for the CRT (left) and IMRT (right) treatment plans, which were optimized based on the CT and fused CT-MRI images,

For the treatment plans of the CRT treatment modality, which were produced based on the CT images, at the clinical dose prescription the average *P*+ value is 15.9% for a mean dose ( *D*CTV ) and a biologically effective uniform dose ( *D*<sup>B</sup> ) to the CTV of 75.5 Gy. The average total control probability, *P*B is 26.5% and the average total complication probability, *P*I is 10.5%. Similarly, for the treatment plans that were produced based on the fused CT-MRI images, the average *P*+ value is 17.5% for the same *D*CTV and *D*<sup>B</sup> . The average *P*B the same with that of the treatment plans that were produced using CT images alone (26.5%) and the average *P*I is 8.9%. However, at the dose level of the individual dose distributions that the

radiation modalities, respectively.

separately.

complication-free tumor control gets optimum, for the CT-based treatment plans, the *P*<sup>+</sup> value becomes 42.5% for a *D*B of 86.4 Gy having average *P*B = 80.0% and average *P*I = 37.4%, whereas for the CT-MRI-based treatment plans, the *P*+ value becomes 46.7% for a *D*B of 86.7 Gy having an average *P*B = 80.6% and an average *P*I by 33.8%.

For the treatment plans of the IMRT treatment modality, which were produced based on the CT images, at the clinical dose prescription, the *P*+ value is 52.5% for *D*CTV = 81.0 Gy and *D*B = 80.8 Gy. The average *P*B is 57.1% and the average *P*I is 4.7%. Similarly, for the CT-MRIbased treatment plans, the *P* value is 53.4% for *D*CTV = 80.8 Gy and *D*B = 80.5 Gy. The average *P*B = 58.6% and the average *P*I = 5.2%. However, at the dose level that maximizes the complication-free tumor control for the CT-based plans, the *P*+ value becomes 74.7% for a *D*B of 91.5Gy having *P*B = 90.0% and *P*I = 15.3%, whereas for the CT-MRI-based plans, the *P* value remains the same for a higher *D*B by 0.6 Gy. The corresponding average *P*B = 90.2%, whereas the average *P*I = 15.4%.

If the CT-based treatment plans were applied to calculate the dose in target and OARs that were produced using the fused CT-MRI images then the average differences would be almost zero in the case of CRT radiation modality, whereas in the case of IMRT radiation modality the *P*+ value would become 2.1% lower, the average *P*B would be lower by 2.1% while the average *P*I would remains the same.

Observing the diagrams in Fig. 3 it is apparent that the clinically established dose prescription, which corresponds to a certain uniform dose in the CTV deviates from the optimal dose level that is indicated by the radiobiological evaluation. For example, the clinically prescribed dose level is lower than the optimum level by *D* = 8-14 Gy. According to these findings, it is expected that a small increase in the dose prescription will slightly increase the complication rate but it will also be accompanied by a significant increase in the control rate. As shown in Fig. 3, a margin of improvement can be observed while the individual normal tissue responses are kept below the limit of 10% as indicated by the horizontal crossed bar.

Fig. 3. The dose-response curves of the CTV / total control probability, *P*B, bladder, rectum, total complication probability, *P*I and complication-free tumor control probability, *P*+ are presented for the CRT and IMRT treatment plans, which were optimized based on the CT and fused CT-MRI images, separately. The horizontal crossed bar indicates the 5-10% response probability region. The vertical lines represent the prescribed dose levels of the individual patients.

Use of Radiobiological Modeling in Treatment Plan

Evaluation and Optimization of Prostate Cancer Radiotherapy 243

For each of the examined patients, a Helical Tomotherapy plan was developed and subsequently the calculated dose distributions with and without patient setup correction were compared by using physical and radiobiological measures (Mavroidis et al. 2011). The corresponding cumulative dose distributions, which are determined by adding the delivered fractional dose distributions, are calculated for the entire course of radiation therapy (Fig. 4).

Fig. 4. The reference CT slices of a prostate cancer patient are shown in the transverse and coronal planes for the Helical Tomotherapy dose distributions with (left) and without (right) patient setup correction. In each case, the dose values of the isodose lines are also presented. In this investigation each patient has a reference kilovoltage CT (kVCT) that was used for the development of the treatment plan. For each fraction, a pre-treatment verification megavoltage CT (MVCT) was obtained in the tomotherapy unit to assess setup accuracy. In order to evaluate the dosimetric effect of setup correction in Helical Tomotherapy, two different cumulative dose distributions were analyzed for the examined clinical cases. One cumulative dose distribution was calculated by adding up the separate delivered fractional dose distributions with setup correction. In this set of merged images, a mutual information based registration (that considered translational and rotational only corrections) was performed between the reference kVCT and the pre-treatment MVCT for each fraction based on anatomical landmarks. The other cumulative dose distribution was computed by adding up the delivered fractional dose distributions as calculated on the daily MVCT, without applying any positional corrections from the daily MVCT-kVCT co-registration. The dose distributions with and without patient repositioning were computed and the final dose

volume histograms (DVHs) for both dose calculations were compared (Fig. 5).

It is worth of noticing that the OAR with the highest risk for complications is rectum in the case of CRT and bladder in the case of IMRT (Fig. 3). This observation confirms previous reports that one of the most important advantages of IMRT over 3D-CRT is the ability of sparing the rectal wall reducing the development of late toxicity. In Fig. 3, it is shown that the results vary considerably among the patients as indicated by the thin *P*+ lines.

For the CRT treatment plans, the response probabilities of CTV and bladder from the CT and fused CT-MRI based treatment plans do not differ significantly (p=0.87 and p=0.49, respectively), whereas those of rectum differ significantly (p=0.02) (Tzikas et al 2011). On the other hand, for the IMRT treatment plans, the response probabilities of all the structures (CTV, bladder and rectum) do not differ significantly between the two sets of plans (p=0.68, p=0.59 and p=0.34, respectively). The improvement that results in by the use of fused CT-MRI images in the overall effectiveness of the CRT plans is statistically significant (p=0.03), which is mainly caused by the statistically significant sparing of the OARs (p=0.03 for *P*I). In the IMRT treatment plans this improvement does not get statistically significant. This stems from the fact that IMRT radiation has to capability of producing highly conformal dose distributions that can spare already from the beginning very well the OARs.

In the future, target volumes could be reduced by both CT/MRI co-registration and dose painting using MR spectroscopy (Claus et al. 2004, Hou et al. 2009, Scheidler et al. 1999, Weinreb et al. 2009). These ongoing improvements and developments in radiotherapy treatment planning are leading to treatments which offer both better tumour volume coverage, and are minimizing the risk of treatment-related complications (Beasley et al. 2005). These changes should allow the escalation in dose delivered to the tumour volume with the potential for increased cure rates.
