**7. Appendix**

254 Prostate Cancer – Diagnostic and Therapeutic Advances

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

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

as DVHs, in order to compare and effectively evaluate different treatment plans*.*

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

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

**6. Conclusions** 

the involved OARs.

Radiobiological treatment plan evaluation

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 fractionation effects that are introduced by the clinical protocol:

$$P(D) = \exp\left(-e^{\varepsilon\gamma - \left(D \ne D\_{50}\right) \cdot \left(e\gamma - \ln\ln 2\right)}\right) \tag{1}$$

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 and is the maximum normalized dose-response gradient. The parameters *D*50 and are 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% for 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 for normal tissues (Lind et al. 1999).

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

$$P\_1 = 1 - \prod\_{j=1}^{N\_{\text{organs}}} \left( 1 - \left[ 1 - \prod\_{i=1}^{M\_j} (1 - P^j(D\_i)^{s\_j})^{\Delta v\_i} \right]^{1/s\_j} \right) \tag{2}$$

where I *<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> and 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) etc could also have been used with the appropriate response parameter set.

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

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eradication of all the clonogenic cells in tumours implies that every individual tumour has to be eradicated. This implication indicates a parallel organization fashion for the tumours. Taking this assumption into account the overall probability of tumour control (*P*B), is given by the expression (Lind et al. 1999, Mavroidis et al. 2000):

$$P\_{\rm B} = \prod\_{j=1}^{N\_{\rm tumours}} \left( \prod\_{i=1}^{M\_j} P^j(D\_i)^{\Delta v\_i} \right) \tag{3}$$

where B *<sup>j</sup> P* is the probability of eradicating tumour *j* and *N*tumours is the total number of tumours or targets involved in the clinical case.

To evaluate the effectiveness of the treatment plans, the concept of *P*+, which expresses the probability of achieving tumour control without causing severe damage to normal tissues (Källman et al. 1992a), was employed. Using the quantities *P*B and *P*I, which were defined above, the *P*+ can be estimated from the following expression:

$$P\_{\star} = P\_{\rm B} - P\_{\rm B \cap I} \approx P\_{\rm B} - P\_{\rm I} \tag{4}$$

This concept is based on the accuracy of the models to calculate the probabilities *P*B and *P*<sup>I</sup> and the radiobiological parameters, which describe the dose-response relations of the different tumours and normal tissues.

As a measure of the quality of a treatment plan, the mean doses and their standard deviations to the target volumes and organs at risk are usually reported, together with the minimum and maximum doses as well as some DVH-based constraints. In addition to those parameters, the present radiobiological treatment plan evaluation uses the *D* concept, which is defined as the dose that causes the same tumour control or normal tissue complication probability as the actual dose distribution given to the patient and it is derived numerically from the following expression (Mavroidis et al. 2000, 2001):

$$P\_{\mathcal{B}}(\vec{D}) \equiv P\_{\mathcal{B}}(\overline{\overline{D}}\_{\mathcal{B}}) \tag{5}$$

where *D* denotes the 3-dimensional dose distribution. This definition is a generalization of the effective uniform dose, *D*eff introduced by Brahme (Brahme 1984). By normalizing treatment plans to a common prescription point ( *D* ) and then plotting out the tissue response probability vs. *D* curves, a number of plan trials can be compared based on radiobiological endpoints.

#### **8. References**


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1 1

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**Part 4** 

**Medical Management and Its** 

**Therapeutic Implications** 

