Statistical methods for clinical verification of dose-response parameters related to esophageal stricture and AVM obliteration from radiotherapy

The purpose of this work is to provide some statistical methods for evaluating the predictive strength of radiobiological models and the validity of dose-response parameters for tumour control and normal tissue complications. This is accomplished by associating the expected complication rates, which are calculated using different models, with the clinical follow-up records. These methods are applied to 77 patients who received radiation treatment for head and neck cancer and 85 patients who were treated for arteriovenous malformation (AVM). The three-dimensional dose distribution delivered to esophagus and AVM nidus and the clinical follow-up results were available for each patient. Dose-response parameters derived by a maximum likelihood fitting were used as a reference to evaluate their compatibility with the examined treatment methodologies. The impact of the parameter uncertainties on the dose-response curves is demonstrated. The clinical utilization of the radiobiological parameters is illustrated. The radiobiological models (relative seriality and linear Poisson) and the reference parameters are validated to prove their suitability in reproducing the treatment outcome pattern of the patient material studied (through the probability of finding a worse fit, area under the ROC curve and chi2 test). The analysis was carried out for the upper 5 cm of the esophagus (proximal esophagus) where all the strictures are formed, and the total volume of AVM. The estimated confidence intervals of the dose-response curves appear to have a significant supporting role on their clinical implementation and use.     

Optimum parameters in a model for tumour control probability including interpatient heterogeneity

A model for computing tumour control probability (TCP) is studied which embodies a dependence on the size of the irradiated volume, the density of clonogenic cells and the dose received, together with the alpha and beta parameters of the linear quadratic model of cell kill. The model can be used to describe situations where both the dose and the clonogenic cell densities are inhomogeneously distributed; however there is still uncertainty about its radiobiological parameters and the author aims to establish parameters for four types of tumour. In its simplest form, when the volumes are spherical, the clonogenic cell density is considered constant throughout the volume and the dose is uniform, the model has been used (by D.J. Brenner, 1993) to predict the radiobiological parameter alpha which allows the model to best fit the observed clinical data for four types of tumour. Here a new set of fits to the data presented by Brenner is constructed using a model which includes the distribution of radiosensitivity across a heterogeneous patient population. It is shown that this leads to a different set of optimum radiobiological parameters when the clonogenic cell density is of the order of 107 cells cm-3.     

Possible fractionated regimens for image-guided intensity-modulated radiation therapy of large arteriovenous malformations

The aim of this study was to estimate a plausible alpha/beta ratio for arteriovenous malformations (AVMs) based on reported clinical data, and to design possible fractionation regimens suitable for image-guided intensity-modulated radiation therapy (IG-IMRT) for large AVMs based on the newly obtained alpha/beta ratio. The commonly used obliteration rate (OR) for AVMs with a three year angiographic follow-up from many institutes was fitted to linear-quadratic (LQ) formalism and the Poisson OR model. The determined parameters were then used to calculate possible fractionation regimens for IG-IMRT based on the concept of a biologically effective dose (BED) and an equivalent uniform dose (EUD). The radiobiological analysis yields a alpha/beta ratio of 2.2 +/- 1.6 Gy for AVMs. Three sets of possible fractionated schemes were designed to achieve equal or better biological effectiveness than the single-fraction treatments while maintaining the same probability of normal brain complications. A plausible alpha/beta ratio was derived for AVMs and possible fractionation regimens that may be suitable for IG-IMRT for large AVM treatment are proposed. The sensitivity of parameters on the calculation was also studied. The information may be useful to design new clinical trials that use IG-IMRT for the treatment of large AVMs.     

A mathematical approach for evaluating the influence of dose heterogeneity on TCP for prostate cancer brachytherapy treatment

The low-dose-rate brachytherapy technique has proven suitable for the management of prostate cancer. However, published data generally report the clinical outcome and the minimum peripheral dose (mPD) to the target volume and not the actual dose distribution in patients. To this end, modern guidelines recommend the use of specific dose and volume indices describing dose distribution throughout the target. The introduction of a method, based on the standard linear quadratic model and Poisson statistics, entitled the F-factor allows the TCP from different DVHs to be calculated, by using the TCP from a uniform dose distribution as the reference. The F-factor sensitivity against radiobiological parameters and influence of the DVH were evaluated. We applied the F-formula on the post-plan DVHs of 58 patients treated with (125)I permanent seed implant brachytherapy for localized prostate cancer. F shows a strong correlation with dosimetric parameters already reported as significant predictors of the biochemical outcome.     

Limitations of a TCP model incorporating population heterogeneity

The variation between individuals in their dose-response characteristics complicates attempts to extract estimates of radiobiological parameters (e.g. alpha, beta, etc) from fits to clinical dose-response data. The use of 'population' dose-response models that explicitly account for this variability is necessary to avoid obtaining skewed parameter estimates. In this work, we evaluated an example of a 'population' tumour control probability (TCP) model in terms of its ability to provide reliable parameter estimates. This was accomplished by performing fits of this population model to 'pseudo' data sets, which were generated with Monte Carlo techniques and based on preset values for the various radiobiological parameters. The fitting exercises illustrated considerable correlations between the model parameters. Especially significant was the large correlation observed between the parameter mu=alpha/sigmaalpha used to characterize the level of population heterogeneity in radiosensitivity and the alpha/beta parameter typically used to describe the response to fractionation. The results imply that fits to clinical data may not be able to distinguish between tumours exhibiting a high degree of heterogeneity and a strong beta-mechanism and those containing little heterogeneity and having a weak beta-mechanism. One implication is that basing the design of optimal fractionation regimes on such fitting results may be error-prone. If in vitro assays are to be used to independently determine biologically reasonable ranges for parameter values, an accurate knowledge of the relationship between in vitro and in vivo dose-response characteristics is required.     

The impact of different dose-response parameters on biologically optimized IMRT in breast cancer

The full potential of biologically optimized radiation therapy can only be maximized with the prediction of individual patient radiosensitivity prior to treatment. Unfortunately, the available biological parameters, derived from clinical trials, reflect an average radiosensitivity of the examined populations. In the present study, a breast cancer patient of stage I-II with positive lymph nodes was chosen in order to analyse the effect of the variation of individual radiosensitivity on the optimal dose distribution. Thus, deviations from the average biological parameters, describing tumour, heart and lung response, were introduced covering the range of patient radiosensitivity reported in the literature. Two treatment configurations of three and seven biologically optimized intensity-modulated beams were employed. The different dose distributions were analysed using biological and physical parameters such as the complication-free tumour control probability (P(+)), the biologically effective uniform dose (D), dose volume histograms, mean doses, standard deviations, maximum and minimum doses. In the three-beam plan, the difference in P(+) between the optimal dose distribution (when the individual patient radiosensitivity is known) and the reference dose distribution, which is optimal for the average patient biology, ranges up to 13.9% when varying the radiosensitivity of the target volume, up to 0.9% when varying the radiosensitivity of the heart and up to 1.3% when varying the radiosensitivity of the lung. Similarly, in the seven-beam plan, the differences in P(+) are up to 13.1% for the target, up to 1.6% for the heart and up to 0.9% for the left lung. When the radiosensitivity of the most important tissues in breast cancer radiation therapy was simultaneously changed, the maximum gain in outcome was as high as 7.7%. The impact of the dose-response uncertainties on the treatment outcome was clinically insignificant for the majority of the simulated patients. However, the jump from generalized to individualized radiation therapy may significantly increase the therapeutic window for patients with extreme radio sensitivity or radioresistance, provided that these are identified. Even for radiosensitive patients a simple treatment technique is sufficient to maximize the outcome, since no significant benefits were obtained with a more complex technique using seven intensity-modulated beams portals.     

An analysis of the relationship between radiosensitivity and volume effects in tumor control probability modeling

The dependence of local tumor control probability (tcp) on tumor volume is analyzed and discussed with the help of radiobiological modeling; in particular the impact of possible correlations between mean tumor radiosensitivity and tumor dimensions on the tcp volume dependence is explored. The linear-quadratic Poissonian tumor control probability (tcp) model was modified to account for the possible dependence of clonogenic cell density and radiosensitivity parameters on tumor volume; then the original and modified versions of the model were fitted to published clinical and laboratory tumor control data. These different versions of the tcp model often fitted tumor control data equally well, because of the high degree of correlation between the parameters. Nevertheless the results were very different from a physical point of view and we suggest that sometimes it is possible to choose between equally good fits on the basis of physical considerations. Possible links between the volume dependence of the mean radiosensitivity and the degree of tumor hypoxia were also analyzed through a comparison of the results of the tcp fit to published measurements of oxygen tension in tumors.     

Biological optimization of heterogeneous dose distributions in systemic radiotherapy

The standard computational method developed for internal radiation dosimetry is the MIRD (medical internal radiation dose) formalism, based on the assumption that tumor control is given by uniform dose and activity distributions. In modern systemic radiotherapy, however, the need for full 3D dose calculations that take into account the heterogeneous distribution of activity in the patient is now understood. When information on nonuniform distribution of activity becomes available from functional imaging, a more patient specific 3D dosimetry can be performed. Application of radiobiological models can be useful to correlate the calculated heterogeneous dose distributions to the current knowledge on tumor control probability of a homogeneous dose distribution. Our contribution to this field is the introduction of a parameter, the F factor, already used by our group in studying external beam radiotherapy treatments. This parameter allows one to write a simplified expression for tumor control probability (TCP) based on the standard linear quadratic (LQ) model and Poisson statistics. The LQ model was extended to include different treatment regimes involving source decay, incorporating the repair "micro" of sublethal radiation damage, the relative biological effectiveness and the effective "waste" of dose delivered when repopulation occurs. The sensitivity of the F factor against radiobiological parameters (alpha, beta, micro) and the influence of the dose volume distribution was evaluated. Some test examples for 131I and 90Y labeled pharmaceuticals are described to further explain the properties of the F factor and its potential applications. To demonstrate dosimetric feasibility and advantages of the proposed F factor formalism in systemic radiotherapy, we have performed a retrospective planning study on selected patient case. F factor formalism helps to assess the total activity to be administered to the patient taking into account the heterogeneity in activity uptake and dose distribution, giving the same TCP of a homogeneous prescribed dose distribution. Animal studies and collection of standardized clinical data are needed to ascertain the effects of nonuniform dose distributions and to better assess the radiobiological input parameters of the model based on LQ model.     

Evaluation of dose-response models and parameters predicting radiation induced pneumonitis using clinical data from breast cancer radiotherapy

The purpose of this work is to evaluate the predictive strength of the relative seriality, parallel and LKB normal tissue complication probability (NTCP) models regarding the incidence of radiation pneumonitis, in a large group of patients following breast cancer radiotherapy, and furthermore, to illustrate statistical methods for examining whether certain published radiobiological parameters are compatible with a clinical treatment methodology and patient group characteristics. The study is based on 150 consecutive patients who received radiation therapy for breast cancer. For each patient, the 3D dose distribution delivered to lung and the clinical treatment outcome were available. Clinical symptoms and radiological findings, along with a patient questionnaire, were used to assess the manifestation of radiation-induced complications. Using this material, different methods of estimating the likelihood of radiation effects were evaluated. This was attempted by analysing patient data based on their full dose distributions and associating the calculated complication rates with the clinical follow-up records. Additionally, the need for an update of the criteria that are being used in the current clinical practice was also examined. The patient material was selected without any conscious bias regarding the radiotherapy treatment technique used. The treatment data of each patient were applied to the relative seriality, LKB and parallel NTCP models, using published parameter sets. Of the 150 patients, 15 experienced radiation-induced pneumonitis (grade 2) according to the radiation pneumonitis scoring criteria used. Of the NTCP models examined, the relative seriality model was able to predict the incidence of radiation pneumonitis with acceptable accuracy, although radiation pneumonitis was developed by only a few patients. In the case of modern breast radiotherapy, radiobiological modelling appears to be very sensitive to model and parameter selection giving clinically acceptable results in certain cases selectively (relative seriality model with Seppenwoolde et al and Gagliardi et al parameter sets). The use of published parameters should be considered as safe only after their examination using local clinical data. The variation of inter-patient radiosensitivity seems to play a significant role in the prediction of such low incidence rate complications. Scoring grades were combined to give stronger evidence of radiation pneumonitis since their differences could not be strictly associated with dose. This obviously reveals a weakness of the scoring related to this endpoint, and implies that the probability of radiation pneumonitis induction may be too low to be statistically analysed with high accuracy, at least with the latest advances of dose delivery in breast radiotherapy.     

The radiosensitivity of T and B lymphocytes in mice.

The radiosensitivity of T and B lymphocytes in spleens of specific pathogen-free C3Hf/HeMs male mice was studied by the direct and indirect immunofluorescence technique. It was found that the radiobiological parameters characterizing the survival curve of Bpsi lymphocytes were DO = 200 R and n = 1-00. The T lymphocytes, on the other hand, were shown to consist of two distinct subpopulations with respect to their radiosensitivity. The radiobiological parameters of the radiosensitive fraction of T lymphocytes were Dq = 185 R, DO =195 R and n = 2-50. The DO value of the radioresistant T lymphocyte subpopulation was practically unmeasurable. It was estimated that approximately 8 per cent of the T lymphocytes present in the spleen of normal C3Hf mice belonged to this radioresistant subpopulation.     

RBE-dose relations for neutrons and pions.

From cellular radiosensitivity parameters and theoretical particle-energy spectra in tissue, of the secondary particles from neutron and negative pion irradiations, RBE-Dose relations have been calculated. The theoretical results are compared with clinical and radiobiological data for normal tissue, tumours and cells in culture. Formulae for calculation, cellular parameters and the needed properties of equivalent 'track-segment bombardments' are given, for several mammalian cells irradiated with pions and with neutrons of several energies.     

Biologically effective uniform dose (D) for specification, report and comparison of dose response relations and treatment plans.

Developments in radiation therapy planning have improved the information about the three-dimensional dose distribution in the patient. Isodose graphs, dose volume histograms and most recently radiobiological models can be used to evaluate the dose distribution delivered to the irradiated organs and volumes of interest. The concept of a biologically effective uniform dose (D) assumes that any two dose distributions are equivalent if they cause the same probability for tumour control or normal tissue complication. In the present paper the D concept both for tumours and normal tissues is presented, making use of the fact that probabilities averaged over both dose distribution and organ radiosensitivity are more relevant to the clinical outcome than the expected number of surviving clonogens or functional subunits. D can be calculated in complex target volumes or organs at risk either from the 3D dose matrix or from the corresponding dose volume histograms of the dose plan. The value of the D concept is demonstrated by applying it to two treatment plans of a cervix cancer. Comparison is made of the D concept with the effective dose (Deff ) and equivalent uniform dose (EUD) that have been suggested in the past. The value of the concept for complex targets and fractionation schedules is also pointed out.     

A NTCP approach for estimating the outcome in radioiodine treatment of hyperthyroidism

Radioiodine has been in use for over 60 years as a treatment for hyperthyroidism. Major changes in clinical practice have led to accurate dosimetry capable of avoiding the risks of adverse effects and the optimization of the treatment. The aim of this study was to test the capability of a radiobiological model, based on normal tissue complication probability (NTCP), to predict the outcome after oral therapeutic 131I administration. Following dosimetric study, 79 patients underwent treatment for hyperthyroidism using radioiodine and then 67 had at least a one-year follow up. The delivered dose was calculated using the MIRD formula, taking into account the measured maximum uptake of administered iodine transferred to the thyroid, U0, and the effective clearance rate, Teff and target mass. The dose was converted to normalized total dose delivered at 2 Gy per fraction (NTD2). Furthermore, the method to take into account the reduction of the mass of the gland during radioiodine therapy was also applied. The clinical outcome and dosimetric parameters were analyzed in order to study the dose-response relationship for hypothyroidism. The TD50 and m parameters of the NTCP model approach were then estimated using the likelihood method. The TD50, expressed as NTD2, resulted in 60 Gy (95% C.I.: 45-75 Gy) and 96 Gy (95% C.I.: 86-109 Gy) for patients affected by Graves or autonomous/multinodular disease, respectively. This supports the clinical evidence that Graves' disease should be characterized by more radiosensitive cells compared to autonomous nodules. The m parameter for all patients was 0.27 (95% C.I.: 0.22-0.36). These parameters were compared with those reported in the literature for hypothyroidism induced after external beam radiotherapy. The NTCP model correctly predicted the clinical outcome after the therapeutic administration of radioiodine in our series.     

有限元分析中软组织力学参数的设定及验证

目的提供软组织超弹性材料参数并探讨优化方法,为有限元分析(finite element analysis,FEA)冲击研究中软组织显式求解的准确模拟提供参考。方法测定6具足底软组织标本抗压性能,以实验数据计算FEA材料参数,利用泊松比对材料参数进行优化。设置与体外实验相同工况的FEA模型进行模拟。利用实验及文献报道数据对模拟结果进行验证。结果软组织体外实验中力-位移曲线呈指数增长。FEA模拟与实验结果相比,压缩率≤45%时,结果相一致;在压缩率>45%时,材料泊松比愈接近0.5,FEA模拟的准确性越高。泊松比为0.497时,FEA模拟与体外实验结果有较强线性相关关系(R2=0.9923)。结论本研究中材料参数模拟效果良好。在较低压缩率下,计算结果与体外实验的结果相一致;在较高压缩率下,提高材料泊松比可增加FEA模拟准确性。     

Multivariate approach to differential diagnosis of acute meningitis

A previously reported statistical model based on a combination of four parameters (total polymorphonuclear cell count in cerebrospinal fluid (CSF), CSF/blood glucose ratio, age and month of onset) appeared effective in differentiating acute viral meningitis (AVM) from acute bacterial meningitis (ABM). The objectives of this study were to validate this model on a large independent sample of patients with acute meningitis and to build and validate a new model based on this sample. Of 500 consecutive cases of community-acquired meningitis reviewed retrospectively, 115 were ABM, 283 were AVM and 102 were of uncertain etiology. For each of the ABM and AVM cases, the probability of ABM versus AVM (pABM) was calculated for both models. Sensitivity, specificity and predictive values as well as areas under the receiver operating characteristic (ROC) curves were calculated for both models. The original model proved an accurate and reliable diagnostic test. Its area under the ROC curve was 0.981. For pABM=0.1, its negative and positive predictive values were 0.99 and 0.68, respectively. The new model retained four slightly different independent variables: CSF protein level, total CSF polymorphonuclear cell count, blood glucose level and leukocyte count. Its area under the ROC curve was 0.991 and, for pABM=0.1, its negative and positive predictive values were 0.99 and 0.85, respectively. In conclusion, both models provide a valuable aid in differentiating AVM from ABM. They should be further evaluated in a prospective appraisal of their contribution to therapeutic decision making.     

Dose planning with comparison to in vivo dosimetry for epithermal neutron irradiation of the dog brain

Boron neutron capture therapy (BNCT) is an experimental type of radiotherapy, presently being used to treat glioblastoma and melanoma. To improve patient safety and to determine the radiobiological characteristics of the epithermal neutron beam of Finnish BNCT facility (FiR 1) dose-response studies were carried on the brain of dogs before starting the clinical trials. A dose planning procedure was developed and uncertainties of the epithermal neutron-induced doses were estimated. The accuracy of the method of computing physical doses was assessed by comparing with in vivo dosimetry. Individual radiation dose plans were computed using magnetic resonance images of the heads of 15 Beagle dogs and the computational model of the FiR 1 epithermal neutron beam. For in vivo dosimetry, the thermal neutron fluences were measured using Mn activation foils and the gamma-ray doses with MCP-7s type thermoluminescent detectors placed both on the skin surface of the head and in the oral cavity. The degree of uncertainty of the reference doses at the thermal neutron maximum was estimated using a dose-planning program. The estimated uncertainty (+/-1 standard deviation) in the total physical reference dose was +/-8.9%. The calculated and the measured dose values agreed within the uncertainties at the point of beam entry. The conclusion is that the dose delivery to the tissue can be verified in a practical and reliable fashion by placing an activation dosimeter and a TL detector at the beam entry point on the skin surface with homogeneous tissues below. However, the point doses cannot be calculated correctly in the inhomogeneous area near air cavities of the head model with this type of dose-planning program. This calls for attention in dose planning in human clinical trials in the corresponding areas.