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Radiobiological comparison of single and dual-isotope prostate seed implants

Published online by Cambridge University Press:  02 August 2012

Courtney Knaup ,
Panayiotis Mavroidis ,
Carlos Esquivel ,
Sotirios Stathakis ,
Gregory Swanson ,
Dimos Baltas  and
Nikos Papanikolaou
Courtney Knaup
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA
Panayiotis Mavroidis
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA Department of Medical Radiation Physics, Karalinska Institutet & Stockholm University, Stockholm, Sweden
Carlos Esquivel
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA
Sotirios Stathakis
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA
Gregory Swanson
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA
Dimos Baltas
Affiliation:
Dept. of Medical Physics and Eng., Offenbach Clinic, Offenbach, Germany Nuclear and Particle Physics Section, Physics Department, University of Athens, Greece
Nikos Papanikolaou*
Affiliation:
Department of Radiation Oncology, University of Texas Health Science Centre at San Antonio, San Antonio, TX, USA
*
Correspondence to: Niko Papanikolaou, PhD, Cancer Therapy & Research Center, University of Texas Health Science Center at San Antonio, 7979 Wurzbach Rd, San Antonio, TX 78229, USA, phone: +1 210-450-5664, e-mail: [email protected]
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Abstract

Purpose: Several isotopes are available for low dose-rate prostate brachytherapy. Currently most implants use a single isotope. However, the use of dual-isotope implants may yield an advantageous combination of characteristics such as half-life and relative biological effectiveness. However, the use of dual-isotope implants complicates treatment planning and quality assurance. Do the benefits of dual-isotope implants outweigh the added difficulty? The goal of this work was to use a linear-quadratic model to compare single and dual-isotope implants.

Materials & Methods: Ten patients were evaluated. For each patient, six treatment plans were created with single or dual-isotope combinations of 125I, 103Pd and 131Cs. For each plan the prostate, urethra, rectum and bladder were contoured by a physician. The biologically effective dose was used to determine the tumor control probability and normal tissue complication probabilities for each plan. Each plan was evaluated using favorable, intermediate and unfavorable radiobiological parameters. The results of the radiobiological analysis were used to compare the single and dual-isotope treatment plans.

Results: Iodine-125 only implants were seen to be most affected by changes in tumor parameters. Significant differences in organ response probabilities were seen at common dose levels. However, after adjusting the initial seed strength the differences between isotope combinations were minimal.

Conclusions: The objective of this work was to perform a radiobiologically based comparison of single and dual-isotope prostate seed implant plans. For all isotope combinations, the plans were improved by varying the initial seed strength. For the optimized treatment plans, no substantial differences in predicted treatment outcomes were seen among the different isotope combinations.

Keywords

ProstateBrachytherapyRadiobiological ModelingTreatment Planning
Type
Original Article
Information
Journal of Radiotherapy in Practice , Volume 12 , Issue 2 , June 2013 , pp. 154 - 162
Copyright
Copyright © Cambridge University Press 2012

INTRODUCTION

Low dose-rate (LDR) brachytherapy is a common radiotherapy technique used in the treatment of prostate cancer. Three isotopes are commonly used: Iodine-125 which has a half-life of 59.4 days and emits a 28 keV gamma ray, Palladium-103 which has a 17 day half-life and emits a 21 keV gamma ray and Cesium-131 which has a 9.7 day half-life and emits a 30 keV gamma ray. The choice of isotope is typically made based on cancer grade, patient geometry and physician preference. Some have considered the possibility of using dual-isotope implants. Currently however, most commercially available treatment planning systems do not allow the use of dual-isotope plans. Additionally, the dosimetric planning goals would vary depending on what isotopes are used, as well as the fraction of total dose delivered by each isotope. With the added complexity of dual-isotope implants, one wonders if they provide disease control superior to mono-isotope implants.

In this work, a 3D treatment plan evaluation tool, based on the radiobiological response of each voxel is used to compare single and dual-isotope plans. For each treatment plan the probability of injury to the tumour and organs at risk (OAR) was calculated for three prostate cancer risk groups.

MATERIALS AND METHODS

Ten patients were used in this study. Treatment plans were created using 125I seeds (BARD, BrachySource model, Covington, GA, USA) to a D100 of 145 Gy; 103Pd seeds (Theragenics, model 200, Buford, GA, USA) to a D100 of 125 Gy; and 131Cs seeds (IsoRay, CS-1 Rev2, Richland, WA, USA) to a D100 of 115 Gy.Reference Nag, Beyer and Friedland1,Reference Bice, Prestidge and Kurtzman2 For each patient six treatment plans were created for the following configuration of isotopes: 125I only, 103Pd only, 131Cs only, 125I and 103Pd, 125I and 131Cs, 103Pd and131Cs. Pre-implant prostate volume studies were performed using transrectal ultrasound (TRUS). These ultrasound images were used for treatment planning on the Prowess Panther 3D Brachy Pro (Prowess, Concord, California, USA) system. Volumes for the prostate, urethra, rectum and bladder were contoured by the same physician for all plans. A single physician was used for consistent contouring. Prowess does not allow treatment plans using multiple isotopes, so for the dual-isotope implants, two plans were created and combined using our in-house software. For the dual-isotope plans, the prescription dose for the constituent single-isotope plans was one-half of that used in mono-isotope plans. When combining the plans, the seed locations were examined to ensure seeds were not overlapping and there were no more than three consecutive seeds.

The radiobiological response of the treatment was calculated using the linear-quadratic model. The physical dose was calculated from the American Association of Physicists in Medicine Task-Group 43 formalism, using the seed strengths and coordinates from Prowess.Reference Nath, Anderson and Luxton3 The in-house software dose calculation was validated by comparing point-doses and isodose distributions with Prowess, for a single-source geometry and a simple distribution of five seeds. The differences in the calculated doses between the in-house software and Prowess were less than one percent. Then, the organ contours for each ultrasound image slice was exported from Prowess to the in-house software. Based on the physical dose and type of tissue present in each voxel, the tumour control probability (TCP) was calculated.Reference Mavroidis, Lind and Brahme4

RESULTS

The calculated response probabilities for the prostate and OARs for the treatment plans using the standard prescriptions are shown in Table 1. Table 1 shows the tumour response determined using the favourable parameters, which were identical to the intermediate and unfavourable parameters at the standard prescription level.

Table 1. Response probabilities using original initial seed strengths and favorable tumour parameters reported as an average of all patients.

The tumour control probability was determined using equation 8. The OAR responses were calculated using equation 9 with appropriate biological parameters. Table 1 shows that TCP is high, but so are many of the OAR responses. The P+ values also vary greatly among the plans. This seemed to indicate that for the single-isotope implants a reduction in dose may be advantageous. For the dual-isotope implants this also indicates that a reduction in dose may be advantageous, but also a different weighting of the seed strengths may yield better plans. For each plan the initial seed strength was varied to determine the maximum P+, and therefore the optimal initial seed strength. Figure 1 shows the response of the tumour and OARs as a function of initial seed strength for the single-isotope plans. Figure 2 shows P+ for the dual-isotope plans as a function of the initial seed strengths.

Figure 1. Response curves as a function of initial seed strength for single-isotope plans.

Figure 2 shows that for all combinations, the shape of the curve is very similar. The large, mostly flat topped shoulder indicates that there is no best combination of seed strengths. Rather, there is simply a trade-off of the two seed strengths that yield similar results. Close inspection of the shoulder region shows that the apex is not flat, rather it slopes slightly. This tilt shows that P+ is slightly higher when the short-lived isotope delivers the majority of the dose. Hence the 125I and 131Cs graph was tilted the most and the 103Pd and 131Cs was tilted the least. From the initial seed strength analysis, the optimal strengths were determined and the response probabilities for these treatments are shown in Table 2. Since the optimal seed strengths are lower than those planned, the intermediate and unfavourable tumour parameters were also used to determine if the lower dose would compromise treatment effectiveness for a more resistant disease.

Figure 2. P+ as a function of initial seed strength for the dual-isotope combinations.

Table 2. Response probabilities using optimal initial seed reported as an average of all patients.

DISCUSSION

Table 1 shows that for the common prescription levels used here, the effectiveness of different isotopes varies considerably. The response probabilities of the tumour and OARs are consistent with those commonly observed in the clinic. The differences between P+ values were thought to arise primarily from high prescription dose levels rather than from inherent isotope differences. To further explore this, different initial seed combinations were evaluated to determine the optimal seed strengths, and therefore the best treatment that the particular isotope could provide. By comparing the optimal plans, the different isotopes may be compared on a more even level.

Figure 1 shows that differences in TCP at a given dose level, for different tumour types, varies significantly for 125I, and minimally for 103Pd and 131Cs implants. This is consistent with the practice of using short-lived isotopes to maintain high TCP in high-grade tumours.Reference Stock, Stone and Tabert5,Reference Armpilia, Dale and Coles6,Reference Nag, Beyer and Friedland1Figures 1 and 2 indicate that for favourable, intermediate and unfavourable tumours, there is a wide therapeutic window between the tumour and OAR responses. This suggests the possibility that reducing dose levels may significantly reduce OAR toxicity without adversely affecting TCP. Indeed, many investigators have similarly concluded that a reduction of dose prescriptions may be warranted.7,Reference Todor, Barani and Lin8Table 2 shows the response probabilities for the plans using the optimal initial seed strengths. These show that the toxicity to the OARs may be significantly reduced with no discernible reduction in TCP.

The major limitation of this analysis stems from the use of specific radiobiological parameters, which are known to vary somewhat between patients and even within the same organ. Thus, the probabilities calculated should only be considered as estimates of the response for a typical patient. However, this limitation is also shared by all the common radiobiological and dosimetric quantifiers, because the degree of radiation induced effect for a specified dose level is also variable within a patient population. Additional factors not considered in this work may also contribute to the radiobiological response. Hypoxic cells, for example, have been shown to dominate the response of the tumour. However, in practice the imaging information of the location of those hypoxic cells is not available and the whole tumour is considered to have a homogeneous radiosensitivity. In this way, the effective radiobiological values representing the radiosensitivity of the whole tumour are determined. The use of such parameters may be acceptable for evaluating similar treatment plans, but may be insufficient for performing a full scale plan optimization.Reference Nahum, Movsas and Horwitz9 While the specific parameters may vary, Table 2 shows for cancer grades that vary substantially, the calculated responses are comparable. Furthermore, the wide plateau seen in figures 1 and 2 indicate that modest changes in the radiobiological parameter would have little effect on the calculated response.

Comparing the responses in Table 2 for the different seed combinations, one sees that there is little difference. P+ for the 125I implants was the lowest of all the combinations evaluated. P+ for the dual-isotope combination of 125I and 131Cs was the highest. While the results of this work suggest that use of short-lived isotopes are preferred in treating high-grade tumours, the benefits of dual-isotope implants were not seen. A difference may be seen if significant prostate edema is present. However, edema is difficult to model and varies considerably between patients. Considering the energies of the isotopes, 103Pd may be slightly more susceptible to volume changes due to edema. Therefore, one might expect the addition of 125I and 131Cs to 103Pd implants to reduce the effects of edema. More research is needed before models of prostate edema can be included in treatment planning.Reference Waterman and Dicker10,Reference Waterman, Yue and Reisinger11It is also important to note that this work treated the tumour as homogeneous in risk. Using dual-isotopes to boost disease foci may yield more effect than single-isotope implants.Reference Todor, Barani and Lin8

CONCLUSION

The rationale for the use of dual-isotope prostate seed implants is to combine the favourable characteristics of different isotopes to obtain a better clinical outcome for the patient. The goal of this work was to perform a radiobiologically-based comparison of single and dual-isotope prostate seed implants. The results of this work indicate that there is room for optimisation within a given plan. However, comparison of different isotope combinations showed that all were nearly equivalent, even when considering favourable, intermediate and unfavourable cancer risk groups.

Acknowledgment

This work supported by Cancer Center Support Grant (P30CA054174).

APPENDIX

The value of TCP is based on a calculation of biologically effective dose (BED), which is calculated for the tumour and normal tissues using equations 1a and 1b, respectively.Reference Yu, Anderson and Li12,Reference Zaider and Hanin13

(1a)
BED_{tum} = D_{eff} \{ {RBE + [ {{{R_O } \over {( {\mu + \lambda } )( {\alpha /\beta } )_{tum} }}} ]*A*( {B - C} )} \} + {K \over \lambda }\ln ( {{K \over {RBE*R_O }}} )
(1b)
\vskip 2pt \scale 95% {BED_{NT} = D_{eff} \{ {RBE + {{R_O } \over {(\mu + \lambda )*(\alpha /\beta )_{NT} }}} \}

where,

A = {1 \over {1 - e^{ - \lambda T_{eff} } }}
B = {{1 - e^{ - 2\lambda T_{eff} } } \over {2\lambda }}
C = {{1 - e^{ - T_{eff} (\mu + \lambda )} } \over {\mu + \lambda }}

In equations 1a and 1b, R0 is the initial dose-rate and λ is the decay constant (for 125I λ = 0.01166 day−1, 103Pd λ = 0.04079 day−1, 131Cs λ = 0.07144 day−1). The sublethal damage repair constant (μ) was calculated using equation 2.

(2)
\mu = {{\ln (2)} \over {T_{1/2} }}

This factor accounts for the decrease in cell kill as the cell repairs damage. Here, a general repair half-life of 15 minutes was assumed for both tumour and normal tissues, making μ = 2.8 hour−1.Reference Wang, Guerrero and Li14,Reference Brenner and Hall15 The tumour repopulation factor (K) accounts for the growth of new tumour cells during treatment and is calculated from equation 3.Reference Armpilia, Dale and Coles6,Reference Wang, Guerrero and Li14Prostate cancer is considered to be a slow growing cancer. The potential doubling time (Tpot) reported in the literature for favourable tumours and used in this report was 42 days. Resulting in a repopulation factor of 0.11 Gy/day, which is consistent with a slow growing disease. Models of repopulation often assume a “kick-off” time for repopulation to occur.Reference Fowler16 Equation 1a, which is widely used, does not assume any kick-off time. However, even in the case of such a biological mechanism, the effective value of the potential doubling time would incorporate its effects, since Tpot is determined from retrospective clinical data. Especially in the case of seed implants, where the treatment follows a certain treatment time pattern, this issue plays no role.

(3)
K = {{\ln (2)} \over {\alpha T_{pot} }}

The effective dose (D eff) was calculated using equation 4. The effective treatment time (T eff) was determined from equation 5. The endpoint for brachytherapy has been defined as the point where the rate of cell kill is equal to the tumour repopulation factor.Reference Antipas, Dale and Coles17 For normal tissues it is assumed that Teff = ∞, hence the effective dose is taken to be equal to the total physical dose accumulated over the lifetime of the seeds.

(4)
D_{eff} = D( {1 - e^{ - \lambda T_{eff} } } )
(5)
T_{eff} = - {1 \over \lambda }\ln ( {{K \over {R_O *RBE}}} )

The relative biological effectiveness (RBE) for 125I, 103Pd and 131Cs used in this study were 1.45, 1.75 and 1.45, respectively.Reference Antipas, Dale and Coles17,Reference Wuu and Zaider18. The RBE for 131Cs has been assumed to be the same as for 125I, based on their similar decay energy. The specific radiobiological parameters α/β, D 50 and γ used for each tissue are given in Table 3. D 50 is the dose which gives a 50% response and γ is the maximum normalised dose-response gradient. In this study, three sets of parameters were evaluated for each plan representing favourable, intermediate and unfavourable cancer risk groups, indicating increasing radioresistance, as suggested by King et al.Reference King, DiPetrillo and Wazer19 The α/β indicates the proportion of the process of cell kill that are related to the α and β parameters. However, the level of this ratio is determined by the value of the α parameter, which expresses the cell radiosensitivity. So as it can be seen in Table 3, although favourable tumours have α/β similar to that of dose-limiting normal tissues, which indicates a similar dependence on dose-rate, their α value indicates that they are radiosenesitive. Both α and β parameters are intrinsic for each tumour and they are determined from clinical trials. The use of a high α/β for favourable group and a low α/β for the unfavourable group could possibly play some role on the results of this study, but since this is not indicated by the clinical studies that determined those parameters, the authors did not examine this scenario.

Table 3. Radiobiological parameters for the tumour.

Voxel response probability (P) was determined using equation 6, where BED becomes BEDTum or BEDNT depending on whether the given voxel belongs to the tumour or an OAR.Reference Strigari, Orlandini and Andriani20,Reference Li, Wang and Stewart21Reference Haworth, Ebert and Waterhouse,22 The overall response probability for the tumour and normal tissues is calculated using equations 7a and 7b, respectively.

(6)
P = \exp ( - \exp (\exp (1)*\gamma - \alpha *BED))
(7a)
P_{Tum} (D,V) = \prod\limits_{i = 1}^N {TCP(D_i )^{\Delta v_i}}
(7b)
\scale 95% {P_{NT} (D,V) = [ {1 - \prod\limits_{i = 1}^N {(1 - TCP(D_i ,V_i )^S )^{\Delta V_i } } } ]^{1/S}}

Where N is the total number of voxels in the organ, s is the tissue-specific relative seriality parameter and Δvi is the fractional subvolume of the organ irradiated. The overall probability of tumour control (PB), the overall probability of injury to the involved normal tissues (P I) and the complication-free tumour control probability (P+) for the treatment were calculated using equations 8, 9 and 10, respectively. The biologically effective uniform dose (\bar \bar D) which is the uniform dose that causes the same tumour control as the actual dose distribution for a given treatment, was calculated from equation 11.

(8)
P_B = \prod\limits_{j = 1}^{N_{tumors} } {P_{Tum}^j}
(9)
P_I = 1 - \prod\limits_{j = 1}^{N_{organs} } {(1 - P_{NT}^j )}
(10)
P_ + = P_B - P_I
(11)
P(\vec D) \equiv P(\bar \bar D)

The biologically effective uniform dose (\bar \bar D) calculates the uniform dose that would provide the same clinical outcome as the inhomogeneous dose distribution. It is a function of physical dose and tissue specific radiobiological parameters. The general expression of \bar \bar D is derived numerically from the first part of the following equation, where for a tissue of uniform radiosensitivity, \bar \bar D is given from the analytical formula of the second part of equation 12.

(12)
\scale 95% {P(\vec D) \equiv P(\bar \bar D) \Rightarrow \bar \bar D = {{e\gamma - \ln ( - \ln (P(\bar \bar D)))} \over {e\gamma - \ln ( - \ln 2)}}}

where \vec D denotes the 3-dimensional dose distribution delivered to the tissue and P(\vec D) is the response probability of the tissue. The second part of the equation has been derived using the Poisson model (4).

References

Nag, S, Beyer, D, Friedland, J et al. , American Brachytherapy Society (ABS) recommendations for transperineal permanent brachytherapy of prostate cancer, Int J Radiat Oncol Biol Phys 1999; 4:789–799.CrossRefGoogle Scholar
Bice, W S, Prestidge, B R, Kurtzman, S M et al. , Recommendations for permanent prostate brachytherapy with (131)Cs: a consensus report from the Cesium Advisory Group, Brachytherapy 2008; 4:290–296.CrossRefGoogle Scholar
Nath, R, Anderson, L L, Luxton, G et al. , Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM Radiation Therapy Committee Task Group No. 43. American Association of Physicists in Medicine, Med Phys 1995; 2:209–234.CrossRefGoogle Scholar
Mavroidis, P, Lind, B K, and Brahme, A, Biologically effective uniform dose (D) for specification, report and comparison of dose response relations and treatment plans, Phys Med Biol 2001; 10:2607–2630.CrossRefGoogle Scholar
Stock, R G, Stone, N N, Tabert, A et al. , A dose-response study for I-125 prostate implants, Int J Radiat Oncol Biol Phys 1998; 1:101–108.CrossRefGoogle Scholar
Armpilia, C I, Dale, R G, Coles, I P et al. , The determination of radiobiologically optimized half-lives for radionuclides used in permanent brachytherapy implants, Int J Radiat Oncol Biol Phys 2003; 2:378–385.CrossRefGoogle Scholar
S G and MD M, Pd-103 dose de-escalation for early stage prostate cancer: A prospective randomized trial. Study NCT00247312, Wheeling, WV: Schiffler Cancer Center.Google Scholar
Todor, D A, Barani, I J, Lin, P S et al. , Moving toward focal therapy in prostate cancer: dual-isotope permanent seed implants as a possible solution, Int J Radiat Oncol Biol Phys 2011; 1:297–304.CrossRefGoogle Scholar
Nahum, A E, Movsas, B, Horwitz, E M et al. , Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: implications for the alpha/beta ratio, Int J Radiat Oncol Biol Phys 2003; 2:391–401.CrossRefGoogle Scholar
Waterman, F M and Dicker, A P, Impact of postimplant edema on V(100) and D(90) in prostate brachytherapy: can implant quality be predicted on day 0?, Int J Radiat Oncol Biol Phys 2002; 3:610–621.CrossRefGoogle Scholar
Waterman, F M, Yue, N, Reisinger, S et al. , Effect of edema on the post-implant dosimetry of an I-125 prostate implant: a case study, Int J Radiat Oncol Biol Phys 1997; 2:335–339.CrossRefGoogle Scholar
Yu, Y, Anderson, L L, Li, Z et al. , Permanent prostate seed implant brachytherapy: report of the American Association of Physicists in Medicine Task Group No. 64, Med Phys 1999; 10:2054–2076.CrossRefGoogle Scholar
Zaider, M and Hanin, L, Biologically-equivalent dose and long-term survival time in radiation treatments, Phys Med Biol 2007; 20:6355–6362.CrossRefGoogle Scholar
Wang, J Z, Guerrero, M, and Li, X A, How low is the alpha/beta ratio for prostate cancer?, Int J Radiat Oncol Biol Phys 2003; 1:194–203.CrossRefGoogle Scholar
Brenner, D J and Hall, E J, Conditions for the equivalence of continuous to pulsed low dose rate brachytherapy, Int J Radiat Oncol Biol Phys 1991; 1:181–190.CrossRefGoogle Scholar
Fowler, J F, Biological factors influencing optimum fractionation in radiation therapy, Acta Oncol 2001; 6:712–717.CrossRefGoogle Scholar
Antipas, V, Dale, R G, and Coles, I P, A theoretical investigation into the role of tumour radiosensitivity, clonogen repopulation, tumour shrinkage and radionuclide RBE in permanent brachytherapy implants of 125I and 103Pd, Phys Med Biol 2001; 10:2557–2569.CrossRefGoogle Scholar
Wuu, C S and Zaider, M, A calculation of the relative biological effectiveness of 125I and 103Pd brachytherapy sources using the concept of proximity function, Med Phys 1998; 11:2186–2189.CrossRefGoogle Scholar
King, C R, DiPetrillo, T A, and Wazer, D E, Optimal radiotherapy for prostate cancer: predictions for conventional external beam, IMRT, and brachytherapy from radiobiologic models, Int J Radiat Oncol Biol Phys 2000; 1:165–172.Google Scholar
Strigari, L, Orlandini, L C, Andriani, I et al. , A mathematical approach for evaluating the influence of dose heterogeneity on TCP for prostate cancer brachytherapy treatment, Phys Med Biol 2008; 18:5045–5059.CrossRefGoogle Scholar
Li, X A, Wang, J Z, Stewart, R D et al. , Dose escalation in permanent brachytherapy for prostate cancer: dosimetric and biological considerations, Phys Med Biol 2003; 17:2753–2765.CrossRefGoogle Scholar
Haworth, A, Ebert, M, Waterhouse, D et al. , Assessment of i-125 prostate implants by tumor bioeffect, Int J Radiat Oncol Biol Phys 2004; 5:1405–1413.CrossRefGoogle Scholar
Figure 0

Table 1. Response probabilities using original initial seed strengths and favorable tumour parameters reported as an average of all patients.

Figure 1

Figure 1. Response curves as a function of initial seed strength for single-isotope plans.

Figure 2

Figure 2. P+ as a function of initial seed strength for the dual-isotope combinations.

Figure 3

Table 2. Response probabilities using optimal initial seed reported as an average of all patients.

Figure 4

Table 3. Radiobiological parameters for the tumour.