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In IMRT treatment plan optimization there are various methods that try to regularize the variation of dose nonuniformity using purely dosimetric measures. However, although these methods can help in finding a good dose distribution, they do not provide any information regarding the expected treatment outcome. When a treatment plan optimization is performed using biological measures, the final goal should be some indication about the expected tumor control or normal tissue complications, which is the primary goal of treatment planning (the association of treatment configurations and dose prescription with the treatment outcome). In this study, this issue is analyzed distinguishing the dose-oriented treatment plan optimization from the response-oriented optimization. Three different dose distributions were obtained by using a dose-based optimization technique, an EUD-based optimization without applying any technique for regularizing the nonuniformity of the dose distribution, and an EUD-based optimization using a variational regularization technique, which controls dose nonuniformity. The clinical effectiveness of the three dose distributions was investigated by calculating the response probabilities of the tumors and organs-at-risk (OARs) involved in two head and neck and prostate cancer cases. The radiobiological models used are the linear-quadratic-Poisson and the Relative Seriality models. Furthermore, the complication-free tumor control probability and the biologically effective uniform dose (D) were used for treatment plan evaluation and comparison. The radiobiological comparison shows that the EUD-based optimization using L-curve regularization gives better results than the EUD-based optimization without regularization and dose-based optimization in both clinical cases. Concluding, it appears that the applied dose nonuniformity regularization technique is expected to improve the effectiveness of the optimized IMRT dose distributions. However, more patient cases are needed to validate the statistical significance of the results and conclusions presented in this paper.

In IMRT treatment plan optimization there are various methods that try to regularize the variation of dose nonuniformity using purely dosimetric measures. However, although these methods can help in finding a good dose distribution, they do not provide any information regarding the expected treatment outcome. When a treatment plan optimization is performed using biological measures, the final goal should be some indication about the expected tumor control or normal tissue complications, which is the primary goal of treatment planning (the association of treatment configurations and dose prescription with the treatment outcome). In this study, this issue is analyzed distinguishing the dose-oriented treatment plan optimization from the response-oriented optimization. Three different dose distributions were obtained by using a dose-based optimization technique, an EUD-based optimization without applying any technique for regularizing the nonuniformity of the dose distribution, and an EUD-based optimization using a variational regularization technique, which controls dose nonuniformity. The clinical effectiveness of the three dose distributions was investigated by calculating the response probabilities of the tumors and organs-at-risk (OARs) involved in two head and neck and prostate cancer cases. The radiobiological models used are the linear-quadratic-Poisson and the Relative Seriality models. Furthermore, the complication-free tumor control probability and the biologically effective uniform dose (D) were used for treatment plan evaluation and comparison. The radiobiological comparison shows that the EUD-based optimization using L-curve regularization gives better results than the EUD-based optimization without regularization and dose-based optimization in both clinical cases. Concluding, it appears that the applied dose nonuniformity regularization technique is expected to improve the effectiveness of the optimized IMRT dose distributions. However, more patient cases are needed to validate the statistical significance of the results and conclusions presented in this paper.

Not until the last decade has flexible intensity modulated three-dimensional dose delivery techniques with photon beams become a clinical reality, first in the form of heavy metal transmission blocks and other beam compensators, then in dynamic and segmented multileaf collimation, and most recently by scanning high-energy narrow electron and photon beams. The merits of various treatment unit and bremsstrahlung target designs for high-energy photon therapy are investigated theoretically for two clinically relevant target sites, a cervix and a larynx cancer both in late stages. With an optimized bremsstrahlung target it is possible to generate photon beams with a half-width of about 3 cm at a source to axis distance (SAD) of 100 cm and an initial electron energy of 50 MeV. By making a more compact treatment head and shortening the SAD, it is possible to reduce the half-width even further to about 2 cm at a SAD of 70 cm and still have sufficient clearance between the collimator head and the patient. One advantage of a reduced SAD is that the divergence of the beam for a given field size on the patient is increased, and thus the exit dose is lowered by as much as 1%/cm of the patient cross section. A second advantage of a reduced SAD is that the electron beam on the patient surface will be only about 8 mm wide and very suitable for precision spot beam scanning. It may also be possible to reduce the beamwidth further by increasing the electron energy up to about 60 MeV to get a photon beam of around 15 mm half-width and an electron beam as narrow as 5 mm. The compact machine will be more efficient and easy to work with, due to the small gantry and the reduced isocentric height. For a given target volume and optimally selected static multileaf collimator, it is no surprise that the narrowest possible scanned elementary bremsstrahlung beam generates the best possible treatment outcome. In fact, by delivering a few static field segments with individually optimized scan patterns, it is possible to combine the advantage of being able to fine tune the fluence distribution by the scanning system with the steeper dose gradients that can be delivered by a few static multileaf collimator segments. It is demonstrated that in most cases a few collimator segments are sufficient and often a single segment per beam portal may suffice when narrow scanned photon beams are employed, and they can be delivered sequentially with a negligible time delay. A further advantage is the increase of therapeutically useful photons and improved patient protection, since the pencil beam is only scanned where the leaf collimator is open. Consequently, some of the problems associated with dynamic multileaf collimation such as the tongue and groove and edge leakage effects are significantly reduced. Fast scanning beam techniques combined with good treatment verification systems allow interesting future possibilities to counteract patient and internal organ motions in real time.

Purpose: To investigate the clinical efficacy and effectiveness of 3D‐Conformal radiotherapy,Intensity Modulated Radiotherapy(IMRT) using Multileaf Collimators(MLC) and Helical Tomotherapy (HT), by evaluating dosimetric and radiobiological measures of a lungcancer case. Method and Materials: A typical case of lungcancer has been investigated by developing a 3D‐Conformal treatment plan, a linac MLC‐based step‐and‐shoot IMRT plan and a Helical Tomotherapy plan. The treatment plans of the 3D‐Conformal and the MLC‐based IMRT were developed on the Philips treatment planning station using the Pinnacle 7.6 software release while the dedicated Tomotherapy treatment planning station was used for the HT plan. With the use of the complication‐free tumorcontrol probability, P + and the biologically effective uniform dose,D concept as the common prescription point of the plans, the three different treatment plans were compared based on radiobiological measures. Results: The applied plan evaluation method shows that in this lungcancer case the MLC‐based IMRT and the HT treatment plans are almost equivalent over the clinically useful dose prescription range, whereas the 3D‐Conformal plan appears to be quite inferior than the other two modalities. More specifically, the 3D‐Conformal, MLC‐based IMRT and HT treatment plans give a P + of 55.4%, 72.9% and 66.9%, for a D to the target volume of 57.0Gy, 66.9Gy and 64.0Gy, respectively. If a higher than 5% risk for complications could be allowed, the complication‐free tumorcontrol could be increased by almost 5% compared to the initial dose prescription. Conclusion: In comparison to 3D‐Conformal radiotherapy, both the MLC based‐IMRT and HT can better encompass the often large ITV while minimizing the volume of the OARs receiving high dose. The use of P ‐ D diagrams can compliment the traditional tools of evaluation such as DVHs, in order to compare and effectively evaluate different treatment plans.

A very flexible iterative method for simultaneous optimization of dynamic multileaf collimation, scanning patterns and compensation filters has been developed. The algorithm can account for and optimize almost all the degrees of freedom available in a modern radiation therapy clinic. The method has been implemented for three dimensional treatment planning. The algorithm has been tested for a number of cases where both traditional wedge filters and block collimators, and modern equipment such as scanned beams and multileaf collimators are available. It is shown that the algorithm can improve heavily on traditional uniform dose plans with respect to the probability of achieving tumor control without causing severe complications (P +) simply by finding the optimal beam weights and block collimator settings. By allowing more complex equipment to deliver the dose and by accounting for their increased flexibility during the optimization, the dose plan can be substantially improved with respect to the applied objective functions. It is demonstrated that flexible lateral collimation combined with compensators or scanned beams in most cases allow close to optimal dose delivery. Here both the calculation time and the amount of primary computer memory needed has been reduced by performing the dose calculations in a cone beam coordinate system allowing the use of approximately spatially invariant energy deposition kernels. A typical calculation time for optimization of a two‐field technique in a three dimensional volume is about 20 s per iteration step on a Hewlett‐Packard 735 workstation. A well converged solution is normally obtained within about 50–100 iterations or within 15–30 min.

An iterative pencil beam algorithm for optimization of multidimensional radiation therapy dose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time-dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavitary and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.

Purpose: Proton's physical properties offer the maximum radiationdose to the target volume, which is an advantage in the radiotherapy development. The aim of this study is the clinical derivation of the dose‐response relations regarding urinary complications from combined photon and proton prostate radiotherapy.Material and Methods: 189 patients were treated for prostate cancer at Uppsala's Academic Hospital, Sweden from 2002 to 2006. The patients were treated with a proton boost of 20 Gy given in 5 Gy, followed by a X‐ray treatment of 50 Gy in 2 Gy fractions. The dose distribution delivered to the organs of interest and the clinical treatment outcomes (24 months follow‐up time) were available for 72 patients. The delineated regions of interest were the urinary bladder and the region of the lower 3 cm part of the bladder. The photon and protondoses were calculated with the BED (biologically effective dose) concept. Additionally, an RBE of 1.1 was used for protons. The radiobiological parameter acquisition of D 50 and γ was performed for the Poisson, Binomial and Probit models applying the Maximum Likelihood method. Results: Of the 72 patients, 15 (21%) showed urinary complications, whereas 57 (79%) didn't. The best estimated values of the parameters for the whole bladder and bladder 3 cm are D 50=104.0 Gy, γ =0.7 and D 50=88.4 Gy, γ =1.3 for Poisson,D 50=108.0 Gy, γ=0.6 and D 50=88.6 Gy, γ=1.3 for Binomial, whereas for Probit are D 50=97.0 Gy, γ=1.0 and D 50=85.6 Gy, γ=1.8, respectively. The analysis of the mean cumulative DVHs proves that the urinary complications were mainly due to the photontreatment.Conclusions: The dose‐response relations are described well by the estimated parameters of the Poisson, Binomial and Probit models. The results are necessary for a prospective estimation of the clinical effectiveness of radiation therapy using combinations of different radiation modalities.

Purpose Recent advances in radiation therapy have provided the possibility of combining different modalities in different parts of the treatment. The purpose of this study was the determination of the parameters D 50 and γ for the prostate adenocarcinoma using different radiobiological models, when proton and photon beams are combined. Material and Methods In this study 100 patients, who were treated for prostate cancer at the Academic Hospital in Uppsala, Sweden from 2002 to 2006, were used. The patients were treated with a conventional photon beam configuration to a dose of 50 Gy in 2 Gy fractions. Additionally, a proton boost of 20 Gy in 5 Gy fractions was applied. The photon and protondoses were corrected for the fractionation effects using the BED (biologically effective dose) concept. In the calculation of the protondose, we considered RBE=1.1. For each patient, the clinical treatment outcome (follow‐up of 24 months) and the 3D dose distribution delivered to the target were available. The best estimates of the parameters D 50 and γ of the Binomial, Poisson and Probit models were determined by applying a maximum likelihood fitting. Results Of the 100 patients, 94 had tumor control (94.0%) whereas 6 patients had treatment failure (6.0%). The mean doses in the prostate in these two groups of patients were 72.97Gy and 62.60Gy, respectively. The estimated values of the parameters for the Poisson and Binomial models are D 50=49.6Gy (68%CI=47.1–51.9Gy) and γ=2.25 (68%CI=1.83–2.75), whereas for the Probit model they are D 50=47.3Gy (68%CI=45.1–49.4Gy) and γ=1.31 (68%CI=1.11–1.52). Conclusions The estimated parameters are able to describe the dose‐response relation of prostate adenocarcinoma. Since there are very limited data on radiation therapy using combinations of photon and proton beams, the determined parameters can be useful in estimating the expected clinical outcome during treatment planning and perform optimization of the delivered treatment.

Purpose The purpose of this study was the determination of the parameters D 50 and γ for the rectum and penile bulb using different radiobiological models, when proton and photon beams are combined. Material and Methods In this study, 98 patients were included with localized adenocarcinoma of the prostate. The patients were treated with a conventional photon beam configuration to a dose of 50 Gy in 2 Gy fractions. Additionally, a proton boost of 20 Gy in 5 Gy fractions was applied. In some patients, the distance between prostate and rectum was increased during proton therapy by retraction of the rectum in the dorsal direction by the use of a cylindrical rod of Perspex inside the rectum. In the calculation of the protondose, we considered RBE=1.1. The best estimates of the parameters D 50 and γ of the Binomial, Poisson and Probit models were determined by applying a maximum likelihood fitting. Results 33 of the patients produced rectal dysfunction (33.7%). The analysis shows that the treatment plans with rectal retraction significantly reduces the dose in the rectum and as a consequence the responders of the treatment (27.3% vs. 36.9% with and without the rod, respectively). The estimated parameters values for the Poisson and Binomial models are D 50=61.2Gy (68%CI=57.5–65.2Gy) and γ =0.8 (68%CI=0.6–1.0) for the rectum. The estimated values for the Probit model are D 50=60.5Gy (68%CI=56.9–64.1Gy) and γ=1.0 (68%CI=0.7–1.3) for the rectum. Of the 89 patients used in the penile bulb analysis, 25 had sexual dysfunction (28.1%) with mean doses for the responders and non‐responders of 55.5 Gy and 54.2 Gy, respectively. Conclusions The additional use of the cylindrical rod in the protontreatment appears to reduce rectal side effects. The determined parameters can be useful in estimating the expected clinical outcome during treatment planning and perform optimization of the delivered treatment.

Purpose The majority of complications occur in patients with large AVM volumes being treated with high doses. For large intracranial arteriovenous malformations, the special characteristics of high ionization density light ion beams offer several advantages over photon and proton beams for high dose stereotactic radiation therapy. These include a better depth dose‐distribution in tissue, negligible lateral scattering, a sharper penumbra, a steep dose fall‐off beyond the Bragg peak and a higher probability of vascular response. Material and Methods Peripheral doses and dose volume histograms (DVHs) of large AVMs were collected from different centers. Based on these data and using a maximum likelihood fitting, dose‐response parameters were derived for the Binomial model. A comparison was performed for different radiation modalities taking also into account their radiobiological differences. Results Light ion Bragg peak dose delivery has the precision required for treating very large AVMs, as well as for delivering extremely sharp focused beams to irregular lesions. For stereotactic radiosurgery with light ions, a better angiographic obliteration rate was observed. Furthermore, a lower complication rate and lower white matter necrosis was simultaneously achieved, which composed a more favorable overall clinical outcome. In patients treated by helium ion beams, a sharper dose‐response gradient was observed, which is probably related to a more homogenous radiosensitivity of the AVM nidus to ion beamradiation.Conclusion Based on this study of linear energy transfer of different therapeuticion beams19 (H, He, Li, C), Helium or Lithium ions may be most suitable for AVM's up to 10 cm3 and for larger AVMs Lithium to carbon ions may be more appropriate. The unique physical characteristics of light ion beams are of considerable advantage for the treatment of AVMs located in front of or adjacent to sensitive and functionally important brain structures.

Purpose: Significant discrepancies in dose delivery can contribute to underdosage of the tumor or overdosage of normal tissue. To study the impact of patient positioning and internal organ motion in breast cancerradiotherapy, the setup and breathing uncertainties characterizing three different irradiation techniques are employed. Method and Materials: Fifteen breast cancer patients (5 resected with negative nodes (R−), 5 resected with positive nodes (R+) and 5 ablated), who were treated with three different irradiation techniques are examined. The positioning uncertainties in the anteroposterior (AP) and the craniocaudal (CC) directions are approximated by Gaussian distributions and breathing is assumed to be linear. The combined frequency distributions of the positioning and breathing distributions are obtained by convolution. The three radiation techniques are compared by using the complication‐free tumorcontrol probability, P + and the biologically effective uniform dose (BEUD). Results: For the R− case, at the optimum dose levels of the two dose distributions, the P + values are 97.9% and 97.3%, respectively. The respective total control probabilities, P B are 99.3% and 99.1%, whereas the corresponding total complication probabilities, P I are 1.4% and 1.8%. For the R+ case, the P + values are 94.2% and 93.0%, respectively. The P B values are 97.5% and 96.3%, whereas the P I values are 3.3% and 3.3%. For the Ablation case, the P + values are 96.9% and 89.4%, respectively. The P B values are 99.0% and 96.5%, whereas the P I values are 2.1% and 7.2%. In this case, for lungradiation pneumonitis Grade 1–2 the P + values would change to 69.3% and 37.7%, respectively. Conclusion: The combined effects of positioning uncertainties and breathing motion can introduce a significant deviation between the planned and delivered dose distributions to the lung in breast cancerradiotherapy. This inaccuracy in the delivered dose may lead to a significant underestimation of the expected lung complications.

Purpose: In order to estimate better the clinical effectiveness of the Helical Tomotherapy and MLC‐based IMRT radiation modalities a radiobiological assessment was performed. This was achieved by employing additional physical and radiobiological criteria. Method and Materials: Two brain and cranio‐spinal cancers were investigated. For each cancer type, a linac MLC‐based step‐and‐shoot IMRT plan and a Helical Tomotherapy plan were developed. The treatment plans of the MLC‐based IMRT were developed on the Philips treatment planning station (Pinnacle 7.6 software release), whereas the dedicated Tomotherapy treatment planning station was used for the HT plans. The different treatment plans were compared using dosimetric criteria and the biologically effective uniform dose (BEUD) together with the complication‐free tumor control probability (P +). Results: The applied plan evaluation method shows that in the braincancer case the HT treatment gives similar results with the MLC‐based IMRT (P + of 66.0% and 63.4%, respectively). The total control probabilities, P B are 79.5% and 76.6%, whereas the total complication probabilities, P I are 13.4% and 13.1%. In both cases, the dose limiting tissue is the Speech Area. In the cranio‐spinal cancer case, the HT treatment plan is much better than the MLC‐based IMRT plan with P + values of 84.1% and 28.4%, respectively. The P B values are 86.4% and 51.3%, whereas the P I values are 2.3% and 23.0%. In the case of HT, the lung is the dose limiting tissue (1.7%) whereas in the case of MLC‐based IMRT the dose limiting tissues are the lung (8.1%) and the left kidney (14.2%). Conclusion: Both MLC based‐IMRT and HT are suitable for treating often large PTVs while minimizing the volume of the organs at risk receiving high dose. However, in certain more complex clinical cases the HT radiation modality may show clearly better properties in producing very conformal and clinically effective dose distributions.

Purpose: Regularization techniques for determining the optimal dose distribution have been proposed because the dose distributions produced by different IMRTtreatment planningoptimization algorithms are highly non‐uniform in the target volume. In the present work, an analysis is made about the relation of the DVH gradient and the dose to the PTV and normal tissues.Method and Materials: In this study, two head & neck and prostate cancer cases treated with IMRT were employed. Three different dose distributions were obtained by using a dose‐basedoptimization technique, an EUD‐based optimization without regularization of non‐uniformity and an EUD‐based optimization using a variational regularization technique. The clinical effectiveness of the three dose distributions was investigated by using the complication‐free tumor control probability, P + and the biologically effective uniform dose.Results: In the head & neck case, for the dose‐basedoptimization, the P + value is 32.9%, the total control probability P B is 79.6% and the total complication probability P I is 49.0%. For the EUD‐based no‐reg optimization, the P + value is 56.4%, the P B value is 71.9% and the P I value is 15.5%. For the EUD‐based reg optimization, the P + value is 67.3%, the P B value is 87.4% and the P I value is 20.1%. In the prostate case, for the dose‐basedoptimization, the P + value is 94.8%, the P B value is 97.8% and the P I value is 3.0%. For the EUD‐based no‐reg optimization, the P + value is 86.0%, the P B value is 97.3% and the P I value is 11.3%. For the EUD‐based reg optimization, the P + value is 95.3%, the P B value is 98.4% and the P I value is 3.1%. Conclusion: The radiobiological comparison shows that the EUD‐based optimization with regularization gives better results than the EUD‐based optimization without regularization and dose‐basedoptimization in both clinical cases, which indicates better clinical effectiveness.

Purpose: The aim of this study is to determine the parameters that describe the dose‐response relations of spinal cord regarding the endpoints of radiation myelopathy in the thoracic and cervical parts. This can be critical information since spinal cord is known for its serial behaviour. Method and Materials: In the present study, the clinical data of 43 patients treated for lungcarcinoma and 248 patients treated for head and neck cancer are analyzed. The two datasets were fitted by the relative seriality model regarding thoracic and cervical spinal cord radiation myelitis. The respective best estimates of the model parameters were determined together with their 68% confidence intervals by applying the maximum likelihood method to fit the clinical data. Results: The parameter values of D 50 = 75.5 Gy , γ = 1.13, s = 36.0, describe the dose‐response relation of thoracic myelopathy, whereas the dose‐response relation of cervical myelopathy can be adequately described by the parameters D 50 = 55.9 Gy , γ = 6.88, s = 0.13. Regarding the cervical radiation myelopathy, 10 of the 12 responders had received a uniform dose in the whole circumference of the irradiated vertebrae (83.3%). Furthermore, only 18 of the 248 patients had received a uniform dose in the anterior and posterior parts of the irradiated vertebrae. 10 of those 18 patients (55.6%) showed complications. Conclusion: The high relative seriality, s value of the thoracic part and the quite low s value of the cervical part are the major findings of the present analysis. According to our observations, when a larger portion of cervical spinal cord was irradiated, considerably more patients showed cervical myelopathy. This indicates that the manifestation of radiation myelitis is clearly related with a dose cutoff and volume effect in the cervical part of spinal cord.

Purpose: In radiotherapy for breast cancer, it is very important to estimate the expected lung complications. In this study, it is examined whether the Dose Mass Histogram (DMH) concept can be better associated with the expected lung complications than the widely used Dose Volume Histogram (DVH) concept. Method and Mataerials: The problem was investigated theoretically by applying two hypothetical dose distributions (Gaussian and Semi‐Gaussian shaped) on two lungs of uniform and varying densities. Furthermore, a group of breast cancer patients was used to clinically quantify the difference between DVHs and DMHs. These patients were treated with resection and irradiation with two tangential fields. The influence of the deviation between DVHs and DMHs on the clinical endpoint of radiation pneumonitis is estimated by using the Relative Seriality and LKB models. The biological equivalent of the corresponding difference in their mean doses was estimated by the Biologically Effective Uniform Dose (BEUD) and Equivalent Uniform Dose (EUD) concepts, respectively. Results: The relation of the DVHs and DMHs varies depending on the underlying cell density distribution and the applied dose distribution. The range of their deviation in terms of expected clinical outcome was large both for the theoretical and the clinical studies. For the group of patients, according to the DVH, lung receives 9.82 Gy, whereas according to the DMH it receives 8.06 Gy (1.76 Gy difference). Interpreting these figures in terms of lung response, DVH gives 0.30% probability for lung complications compared to 0.10% given by DMH for the Relative Seriality model. Similarly, for the LKB model the corresponding values are 2.62% and 1.85%, respectively. Conclusion: Concluding, the expected lung complications appear to be overestimated when using the DVH concept, whereas the effectiveness of the dose distribution is closer related to the radiation effects when using the DMH concept.

Purpose: The aim of this study is to calculate the average penetration depth, zav , and detour factors of 10–10 000 eV electrons in water using an in‐house Monte Carlo track structure code. These low electrons are known to be the most toxic in sense of radiation damage and the calculation of their true depth of penetration and energy depositions is required in areas such as radiation therapy, to be able to calculate the correlation between ion tracks and the potential cell damage. Method and Materials: The CSDA‐range largely overestimates the range of electrons of energies between 10–10000 eV because of the high amount of elastic scattering. Up to 50% of the interactions can be elastic for energies below 100 eV. This phenomena will shorten the longitudinal distribution, average penetration depth zav , but @@ elongate the transverse distribution 〈x 2 +y 2 〉 av . Several definition of the detour factor can be found in the literature. In this work is the detour factor defined as in ICRU (1993): d = z av /r o , were ro is the CSDA‐range. The zav is computed according to: z av = 1 N Σz abs , were N is the number of histories and zabs is the depth of absorption of every primary electron.ro is calculated by integrating the stopping power, which is extracted from the MC track structure code. Results: The calculated zav is shorter for low energies compared to Wilson et al(2004) and slightly higher for energies around 10 keV. zav is substantially shorter than the calculated CSDA‐range for energies below 1 keV, which results in a small Detour factor. The sigmoid shape of the Detour curve decompose at very low energies around 10 eV due to a drastically reduction of the ionization cross section and a still increasing elastic cross section. Conclusion: The results show that the CSDA‐range should be used with caution at these low energies.

Purpose: Due to the highly conformal distributions that can be obtained with intensity modulated radiation therapy(IMRT), any discrepancy between the intended and delivered distributions would likely affect the clinical outcome. Consequently, there is a need for a measure that would quantify those differences in terms of a change in the expected clinical outcome. Material and Methods: To evaluate such a measure, the case of a cervix cancer was used where the bladder and rectum, are proximal and partially overlapping with the internal target volume. A solid phantom simulating the pelvic anatomy was fabricated and a treatment plan was developed to deliver the prescribed dose to the phantom. The phantom was then irradiated with films positioned in several transverse planes. The racetrack microtron at 50MV was used in the treatment planning and delivery processes. The dose distribution delivered was analyzed based on the film measurements and compared against the treatment plan. The differences in the measurements were evaluated using both physical and biological criteria. Results: For the computerized treatment plan, the maximum value of P + was 84.1%, for a mean dose to the ITV of D = 93.3Gy, associated relative standard deviation σ D /D = 16.8% and biologically effective uniform dose,D ITV of 89.2 Gy. The delivereddose distribution from all the beams produced a P + value of 77.0% for D ITV = 93.2 Gy , σ D /D = 19.0% and D ITV of 83.5 Gy. Discussion and Conclusions: Whereas the physical comparison of dose distributions can assess the geometric accuracy of delivery, it does not reflect the clinical impact of any measured dose discrepancies. With highly conformal IMRT, the accuracy of the patient setup and treatmentdelivery, are critical for the success of the treatment. A method is proposed to evaluate the precision of the delivered plan based on changes in complication and control rates as they relate to uncertainties in dosedelivery.

Purpose: Presently, the radiobiological parameters of the different tumours and normal tissues are typically not taken into account during dose prescription and optimization of a treatment plan. In this study, to investigate a more comprehensive treatment plan evaluation, the biologically effective uniform dose (D) is applied together with the complication‐free tumour control probability (P +). Material and Methods: Three different cancer types at different anatomical sites were investigated: head & neck, lung and prostate cancers. For each cancer type, a linac MLC‐based step‐and‐shoot IMRT plan and a Helical Tomotherapy plan were developed. By using D as the common prescription point of the treatment plans and plotting the tissue response probabilities vs. D for a range of prescription doses, a number of plan trials can be compared based on radiobiological measures. Results: The applied plan evaluation method shows that in the head & neck cancer case the HT treatment gives better results than the MLC‐based IMRT (P + of 62.2% and 46.0%, D to the internal target volume (ITV) of 72.3Gy and 70.7Gy, respectively). In the lungcancer and prostate cancer cases, the MLC‐based IMRT plans are better. For the lungcancer case, the HT and MLC‐based IMRT plans give a P + of 66.9% and 72.9%, D to the ITV of 64.0Gy and 66.9Gy, respectively. Similarly, for the prostate cancer case, the two radiation modalities give a P + of 68.7% and 72.2%, D to the ITV of 86.0Gy and 85.9Gy, respectively. Discussion and Conclusions: Both MLC based‐IMRT and HT can encompass the often large ITV required while they minimize the volume of the organs at risk receiving high dose. There may exist clinical cases, which may look dosimetrically similar but in radiobiological terms may be quite different. In such situations, traditional dose based evaluation tools can be complemented by the use of P + − D diagrams to compare treatment plans.

Purpose: To describe software for biological optimization of fractionated IMRT where the fluence profiles are not restricted to be identical for all fractions and to investigate the impact of fractionated time-dependent response functions on the optimization result. Method and Materials: If the fluence profiles of all beams in every fraction are optimized the number of variables is proportional to the number of fractions. Each new fraction consumes memory and slows down the optimization. In order to reduce the number of variables similar fractions are assigned to the same fraction group. The same fluence profile is delivered for every fraction in a fraction group. To test the method the Poisson-LQ model is extended with a time-dependent bi-exponential repair model. Results: In all tests the NTCP was minimized while the TCP was kept constant. If the time between consecutive fractions is long enough to cause complete repair there is not much gain in optimizing several fraction groups. In the case of incomplete repair, the NTCP was reduced by assigning Monday morning and Friday afternoon to a second fraction group. Adding more fraction groups did not improve the response significantly. Conclusion: The use of fraction groups enables an efficient implementation of IMRT-optimization of a fractionated treatment and makes it possible to study time-dependent biological models. In the case of Poisson-LQ with repair, two fraction groups can improve the biological response. This is only true in the case of incomplete repair and the impact of the fractionation depends on the repair half times. Conflict of Interest: Some of the authors are employees and some are stock owners of the submitting company.