It is shown that tumour volume distributions can yield information on two aspects of cancer research: tumour induction and tumour control.
From the hypothesis that the intrinsic distribution of ...breast cancer volumes follows an exponential distribution, firstly the probability density function of tumour growth time was deduced via a mathematical transformation of the probability density functions of tumour volumes. In a second step, the distribution of tumour volumes was used to model the variation of the clonogenic cell number between patients in order to determine tumour control probabilities for radiotherapy patients.
Distribution of lag times, i.e. the time from the appearance of the first fully malignant cell until a clinically observable cancer, can be used to deduce the probability of tumour induction as a function of patient age. The integration of the volume variation with a Poisson-TCP model results in a logistic function which explains population-averaged survival data of radiotherapy patients.
The inclusion of tumour volume distributions into the TCP formalism enables a direct link to be deduced between a cohort TCP model (logistic) and a TCP model for individual patients (Poisson). The TCP model can be applied to non-uniform tumour dose distributions.
One goal of nanodosimetry is to determine statistical quantities of ionization distributions in nanometric volumes. It is hypothesized here that these quantities are related to the initial biological ...damages in DNA from ionizations. Thus nanodosimetric quantities will potentially complement or replace the concept of RBE-weighted absorbed dose and hence they could be applied in treatment planning systems, risk assessments for radiation protection and space radiation. The development of a compact and portable nanodosimeter detector available for clinical routine is a significant step towards that goal. We present extensive measurements to characterize the performance of the FIRE (Frequency of Ion REgistration) nanodosimeter detector. It operates on similar principles like the Gas Electron Multiplier (GEM). Contrary to GEMs the FIRE detector registers positive ions instead of electrons and operates at low pressures of 0.5 Torr to 2.5 Torr. In addition, the FIRE nanodosimeter capitalizes on the usage of a resistive cathode in order to suppress discharges. Moreover, the geometry of the FIRE detector is adapted to the low pressure by enlarging the typical dimensions of a GEM foil by two orders of magnitude.
The authors present two configurations of the compact FIRE nanodosimetry detector. The resistivities of the two configurations differ by six orders of magnitude. The lower resistivity should allow for faster removal of the charges attached to the wall inside the hole channel. Measurements of mean number of ions produced by 5MeV alpha particles in low pressure propane gas, mean number of dark counts, the ion arrival time, and the mean avalanche charge are presented. The dependency of these parameters on acceleration voltage, drift voltage, pressure and hole diameter were investigated.
Tumor control probability (TCP) models based on Poisson statistics characterize the distribution of surviving clonogens. Thus enabling the calculation of TCP for individuals. To mathematically ...describe clinically observed survival data of patient cohorts it is necessary to extend the Poisson TCP model. This is typically done by either incorporating variations of model parameters or by using an empirical logistic model. The purpose of this work is the development of an analytical population TCP model by mechanistic extension of the Possion model.
The frequency distribution of gross tumor volumes was used to incorporate tumor volume variations into the TCP model. Additionally the tumor cell density variation was incorporated. Both versions of the population TCP model were fitted to clinical data and compared to existing literature.
It was shown that clinically observed brain tumor volumes of dogs undergoing radiotherapy are distributed according to an exponential distribution. The average gross tumor volume size was 3.37 cm3. Fitting the population TCP model including the volume variation using linear-quadratic and track-event model yieldedα=0.36Gy−1a, β=0.045Gy−2, a=0.9yr−1, TD=5.0d,and p=.36Gy−1, q=0.48Gy−1, a=0.80yr−1, TD=3.0d, respectively. Fitting the population TCP model including both the volume and cell density variation yielded α=0.43Gy−1, β=0.0537Gy−2, a=2.0yr−1, TD=3.0d, σ=2.5,and p=.43Gy−1, q=0.55Gy−1, a=2.0yr−1, TD=2.0d, σ=3.0,respectively.
Two sets of radiobiological parameters were obtained which can be used for quantifying the TCP for radiation therapy of brain tumors in dogs. We established a mechanistic link between the poisson statistics based individual TCP model and the logistic TCP model. This link can be used to determine the radiobiological parameters of patient specific TCP models from published fits of logistic models to cohorts of patients.
When fractionation schemes for hypofractionation and stereotactic body radiotherapy are considered, a reliable cell survival model at high dose is needed for calculating doses of similar biological ...effectiveness. An alternative to the LQ-model is the track-event theory which is based on the probabilities for one- and two two-track events. A one-track-event (OTE) is always represented by at least two simultaneous double strand breaks. A two-track-event (TTE) results in one double strand break. Therefore at least two two-track-events on the same or different chromosomes are necessary to produce an event which leads to cell sterilization. It is obvious that the probabilities of OTEs and TTEs must somehow depend on the geometrical structure of the chromatin. In terms of the track-event theory the ratio ε of the probabilities of OTEs and TTEs includes the geometrical dependence and is obtained in this work by simple Monte Carlo simulations.
For this work it was assumed that the anchors of loop forming chromatin are most sensitive to radiation induced cell deaths. Therefore two adjacent tetranucleosomes representing the loop anchors were digitized. The probability ratio ε of OTEs and TTEs was factorized into a radiation quality dependent part and a geometrical part: ε = εion ∙ εgeo. εgeo was obtained for two situations, by applying Monte Carlo simulation for DNA on the tetranucleosomes itself and for linker DNA. Low energy electrons were represented by randomly distributed ionizations and high energy electrons by ionizations which were simulated on rays. εion was determined for electrons by using results from nanodosimetric measurements. The calculated ε was compared to the ε obtained from fits of the track event model to 42 sets of experimental human cell survival data.
When the two tetranucleosomes are in direct contact and the hits are randomly distributed εgeo and ε are 0.12 and 0.85, respectively. When the hits are simulated on rays εgeo and ε are 0.10 and 0.71. For the linker-DNA εgeo and ε for randomly distributed hits are 0.010 and 0.073, and for hits on rays 0.0058 and 0.041, respectively. The calculated ε fits the experimentally obtained ε = 0.64±0.32 best for hits on the tetranucleosome when they are close to each other both, for high and low energy electrons.
The parameter εgeo of the track event model was obtained by pure geometrical considerations of the chromatin structure and is 0.095 ± 0.022. It can be used as a fixed parameter in the track-event theory.
(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor ...diameter is. This paper presents a method to derive tumor volume distributions from tumor diameter distributions. (2) Methods: The hypothesis is made that tumor maximum diameters d are Weibull distributed, and tumor volume is proportional to dk, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k = 2.14 ± 0.36 (from Weibull distribution of d) and 2.21 ± 0.25 (from tumor volume). The tumor diameter data from the SEER database were fitted to a Weibull distribution, and the resulting parameters were used to calculate the corresponding exponential tumor volume distributions with an average volume obtained from the diameter fit. (4) Conclusions: The agreement of the fitted k using independent data supports the presented methodology to obtain tumor volume distributions. The method can be used to obtain tumor volume distributions when only maximum tumor diameters are available.
A simple model for cell survival which is valid also at high dose has been developed. The model parameters can be traced back to measurable quantities from nanodosimetry. It is assumed that a cell is ...killed by an event which is defined by two or more double strand breaks in differently sized lethal interaction volumes (LIVs). Two different mechanisms can produce events, one-track events by one-particle track and two-track events by two. One- and two-track events are statistically independent. From the stochastic nature of cell killing which is described by the Poisson distribution, the cell survival probability was derived. The ratio of the number of one- and two-track events can be directly expressed in terms of nanodosimetry by the probability F2 that at least two ionizations are produced in a basic interaction volume (5-10 base pairs). From the model, relative biological effectiveness (RBE) can be derived which depends only on F2 and the size of the LIV. The expression for RBE fits experimental data with satisfying quality.
A radiation action model based on nanodosimetry is presented. It is motivated by the finding that the biological effects of various types of ionizing radiation lack a consistent relation with ...absorbed dose. It is postulated that the common fundamental cause of these effects is the production of elementary sublesions (DSB), which are created at a rate that is proportional to the probability to produce more than two ionisations within a volume of 10 base pairs of the DNA. The concepts of nanodosimetry allow for a quantitative characterization of this process in terms of the cumulative probability
F
2
. The induced sublesions can interact in two ways to produce lethal damage. First, if two or more sublesions accumulate in a locally limited spherical volume of 3–10 nm in diameter, clustered DNA damage is produced. Second, consequent interactions or rearrangements of some of the initial damage over larger distances (~ µm) can produce additional lethal damage. From the comparison of theoretical predictions deduced from this concept with experimental data on relative biological effectiveness, a cluster volume with a diameter of 7.5 nm could be determined. It is shown that, for electrons, the predictions agree well with experimental data over a wide energy range. The only free parameter needed to model cell survival is the intersection cross-section which includes all relevant cell-specific factors. Using ultra-soft X-rays it could be shown that the energy dependence of cell survival is directly governed by the nanodosimetric characteristics of the radiation track structure. The cell survival model derived in this work exhibits exponential cell survival at a high dose and a finite gradient of cell survival at vanishing dose, as well as the dependence on dose-rate.
Planning organ at risk volume (PRV) estimates have been reported as methods for sparing organs at risk (OARs) during radiation therapy, especially for hypofractioned and/or dose‐escalated protocols. ...The objectives of this retrospective, analytical, observational study were to evaluate peri‐ocular OAR shifts and derive PRVs in a sample of dogs undergoing radiation therapy for periocular tumors. Inclusion criteria were as follows: dogs irradiated for periocular tumors, with 3D‐image‐guidance and at least four cone‐beam CTs (CBCTs) used for position verification, and positioning in a rigid bite block immobilization device. Peri‐ocular OARs were contoured on each CBCT and the systematic and random error of the shifts in relation to the planning CT position computed. The formula 1.3×Σ+0.5xσ was used to generate a PRV of each OAR in the dorsoventral, mediolateral, and craniocaudal axis. A total of 30 dogs were sampled, with 450 OARs contoured, and 2145 shifts assessed. The PRV expansion was qualitatively different for each organ (1‐4 mm for the dorsoventral and 1‐2 mm for the mediolateral and craniocaudal axes). Maximal PRV expansion was ≤4 mm and directional for the majority; most pronounced for corneas and retinas. Findings from the current study may help improve awareness of and minimization of radiation dose in peri‐ocular OARs for future canine patients. Because some OARs were difficult to visualize on CBCTs and/ or to delineate on the planning CT, authors recommend that PRV estimates be institution‐specific and applied with caution.
Classical radiation protocols are guided by physical dose delivered homogeneously over the target. Protocols are chosen to keep normal tissue complication probability (NTCP) at an acceptable level. ...Organs at risk (OAR) adjacent to the target volume could lead to underdosage of the tumor and a decrease of tumor control probability (TCP). The intent of our study was to explore a biology-based dose escalation: by keeping NTCP for OAR constant, radiation dose was to be maximized, allowing to result in heterogeneous dose distributions.
We used computed tomography datasets of 25 dogs with brain tumors, previously treated with 10x4 Gy (40 Gy to PTV D50). We generated 3 plans for each patient: A) original treatment plan with homogeneous dose distribution, B) heterogeneous dose distribution with strict adherence to the same NTCPs as in A), and C) heterogeneous dose distribution with adherence to NTCP <5%. For plan comparison, TCPs and TCP equivalent doses (homogenous target dose which results in the same TCP) were calculated. To enable the use of the generalized equivalent uniform dose (gEUD) metric of the tumor target in plan optimization, the calculated TCP values were used to obtain the volume effect parameter a.
As intended, NTCPs for all OARs did not differ from plan A) to B). In plan C), however, NTCPs were significantly higher for brain (mean 2.5% (SD±1.9, 95%CI: 1.7,3.3), p<0.001), optic chiasm (mean 2.0% (SD±2.2, 95%CI: 1.0,2.8), p=0.010) compared to plan A), but no significant increase was found for the brainstem. For 24 of 25 of the evaluated patients, the heterogenous plans B) and C) led to an increase in target dose and projected increase in TCP compared to the homogenous plan A). Furthermore, the distribution of the projected individual TCP values as a function of the dose was found to be in good agreement with the population TCP model.
Our study is a first step towards risk-adaptive radiation dose optimization. This strategy utilizes a biologic objective function based on TCP and NTCP instead of an objective function based on physical dose constraints.
•Heterogeneous dose escalation differs from existing techniques•Biology-based optimization surpasses physical dose constraints.•Heterogeneous plans enhance target dose and TCP.
Purpose:
The full benefit of the increased precision of contemporary treatment techniques can only be exploited if the accuracy of the patient positioning is guaranteed. Therefore, more and more ...imaging modalities are used in the process of the patient setup in clinical routine of radiation therapy. The improved accuracy in patient positioning, however, results in additional dose contributions to the integral patient dose. To quantify this, absorbed dose measurements from typical imaging procedures involved in an image-guided radiation therapy treatment were measured in an anthropomorphic phantom for a complete course of treatment. The experimental setup, including the measurement positions in the phantom, was exactly the same as in a preceding study of radiotherapy stray dose measurements. This allows a direct combination of imaging dose distributions with the therapy dose distribution.
Methods:
Individually calibrated thermoluminescent dosimeters were used to measure absorbed dose in an anthropomorphic phantom at 184 locations. The dose distributions from imaging devices used with treatment machines from the manufacturers Accuray, Elekta, Siemens, and Varian and from computed tomography scanners from GE Healthcare were determined and the resulting effective dose was calculated. The list of investigated imaging techniques consisted of cone beam computed tomography (kilo- and megavoltage), megavoltage fan beam computed tomography, kilo- and megavoltage planar imaging, planning computed tomography with and without gating methods and planar scout views.
Results:
A conventional 3D planning CT resulted in an effective dose additional to the treatment stray dose of less than 1 mSv outside of the treated volume, whereas a 4D planning CT resulted in a 10 times larger dose. For a daily setup of the patient with two planar kilovoltage images or with a fan beam CT at the TomoTherapy unit, an additional effective dose outside of the treated volume of less than 0.4 mSv and 1.4 mSv was measured, respectively. Using kilovoltage or megavoltage radiation to obtain cone beam computed tomography scans led to an additional dose of 8–46 mSv. For treatment verification images performed once per week using double exposure technique, an additional effective dose of up to 18 mSv was measured.
Conclusions:
Daily setup imaging using kilovoltage planar images or TomoTherapy megavoltage fan beam CT imaging can be used as a standard procedure in clinical routine. Daily kilovoltage and megavoltage cone beam computed tomography setup imaging should be applied on an individual or indication based protocol. Depending on the imaging scheme applied, image-guided radiation therapy can be administered without increasing the dose outside of the treated volume compared to therapies without image guidance.
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