Seishin Takao

A Mathematical Study to Select Fractionation Regimen Based on Physical Dose Distribution and the Linear–Quadratic Model

PURPOSE Hypofractionated irradiation is often used in precise radiotherapy instead of conventional multifractionated irradiation. We propose a novel mathematical method for selecting a hypofractionated or multifractionated irradiation regimen based on physical dose distribution adding to biologic consideration. METHODS AND MATERIALS The linear-quadratic model was used for the radiation effects on tumor and normal tissues, especially organs at risk (OARs). On the basis of the assumption that the OAR receives a fraction of the dose intended for the tumor, the minimization problem for the damage effect on the OAR was treated under the constraint that the radiation effect on the tumor is fixed. RESULTS For an N-time fractionated irradiation regimen, the constraint of tumor lethality was described by an N-dimensional hypersphere. The total dose of the fractionated irradiations was considered for minimizing the damage effect on the OAR under the hypersphere condition. It was found that the advantage of hypofractionated or multifractionated irradiation therapies depends on the magnitude of the ratio of α/β parameters for the OAR and tumor in the linear-quadratic model and the ratio of the dose for the OAR and tumor. CONCLUSIONS Our mathematical method shows that multifractionated irradiation with a constant dose is better if the ratio of α/β for the OAR and tumor is less than the ratio of the dose for the OAR and tumor, whereas hypofractionated irradiation is better otherwise.

What is the appropriate size criterion for proton radiotherapy for hepatocellular carcinoma? A dosimetric comparison of spot-scanning proton therapy versus intensity-modulated radiation therapy

BackgroundWe performed a dosimetric comparison of spot-scanning proton therapy (SSPT) and intensity-modulated radiation therapy (IMRT) for hepatocellular carcinoma (HCC) to investigate the impact of tumor size on the risk of radiation induced liver disease (RILD).MethodsA number of alternative plans were generated for 10 patients with HCC. The gross tumor volumes (GTV) varied from 20.1 to 2194.5 cm3. Assuming all GTVs were spherical, the nominal diameter was calculated and ranged from 3.4 to 16.1 cm. The prescription dose was 60 Gy for IMRT or 60 cobalt Gy-equivalents for SSPT with 95% planning target volume (PTV) coverage. Using IMRT and SSPT techniques, extensive comparative planning was conducted. All plans were evaluated by the risk of RILD estimated using the Lyman-normal-tissue complication probability model.ResultsFor IMRT the risk of RILD increased drastically between 6.3–7.8 cm nominal diameter of GTV. When the nominal diameter of GTV was more than 6.3 cm, the average risk of RILD was 94.5% for IMRT and 6.2% for SSPT.ConclusionsRegarding the risk of RILD, HCC can be more safely treated with SSPT, especially if its nominal diameter is more than 6.3 cm.

Intrafractional Baseline Shift or Drift of Lung Tumor Motion During Gated Radiation Therapy With a Real-Time Tumor-Tracking System

PURPOSE To investigate the frequency and amplitude of baseline shift or drift (shift/drift) of lung tumors in stereotactic body radiation therapy (SBRT), using a real-time tumor-tracking radiation therapy (RTRT) system. METHODS AND MATERIALS Sixty-eight patients with peripheral lung tumors were treated with SBRT using the RTRT system. One of the fiducial markers implanted near the tumor was used for the real-time monitoring of the intrafractional tumor motion every 0.033 seconds by the RTRT system. When baseline shift/drift is determined by the system, the position of the treatment couch is adjusted to compensate for the shift/drift. Therefore, the changes in the couch position correspond to the baseline shift/drift in the tumor motion. The frequency and amount of adjustment to the couch positions in the left-right (LR), cranio-caudal (CC), and antero-posterior (AP) directions have been analyzed for 335 fractions administered to 68 patients. RESULTS The average change in position of the treatment couch during the treatment time was 0.45 ± 2.23 mm (mean ± standard deviation), -1.65 ± 5.95 mm, and 1.50 ± 2.54 mm in the LR, CC, and AP directions, respectively. Overall the baseline shift/drift occurs toward the cranial and posterior directions. The incidence of baseline shift/drift exceeding 3 mm was 6.0%, 15.5%, 14.0%, and 42.1% for the LR, CC, AP, and for the square-root of sum of 3 directions, respectively, within 10 minutes of the start of treatment, and 23.0%, 37.6%, 32.5%, and 71.6% within 30 minutes. CONCLUSIONS Real-time monitoring and frequent adjustments of the couch position and/or adding appropriate margins are suggested to be essential to compensate for possible underdosages due to baseline shift/drift in SBRT for lung cancers.

Biological effect of dose distortion by fiducial markers in spot-scanning proton therapy with a limited number of fields: A simulation study

PURPOSE In accurate proton spot-scanning therapy, continuous target tracking by fluoroscopic x ray during irradiation is beneficial not only for respiratory moving tumors of lung and liver but also for relatively stationary tumors of prostate. Implanted gold markers have been used with great effect for positioning the target volume by a fluoroscopy, especially for the cases of liver and prostate with the targets surrounded by water-equivalent tissues. However, recent studies have revealed that gold markers can cause a significant underdose in proton therapy. This paper focuses on prostate cancer and explores the possibility that multiple-field irradiation improves the underdose effect by markers on tumor-control probability (TCP). METHODS A Monte Carlo simulation was performed to evaluate the dose distortion effect. A spherical gold marker was placed at several characteristic points in a water phantom. The markers were with two different diameters of 2 and 1.5 mm, both visible on fluoroscopy. Three beam arrangements of single-field uniform dose (SFUD) were examined: one lateral field, two opposite lateral fields, and three fields (two opposite lateral fields + anterior field). The relative biological effectiveness (RBE) was set to 1.1 and a dose of 74 Gy (RBE) was delivered to the target of a typical prostate size in 37 fractions. The ratios of TCP to that without the marker (TCP(r)) were compared with the parameters of the marker sizes, number of fields, and marker positions. To take into account the dependence of biological parameters in TCP model, α∕β values of 1.5, 3, and 10 Gy (RBE) were considered. RESULTS It was found that the marker of 1.5 mm diameter does not affect the TCPs with all α∕β values when two or more fields are used. On the other hand, if the marker diameter is 2 mm, more than two irradiation fields are required to suppress the decrease in TCP from TCP(r) by less than 3%. This is especially true when multiple (two or three) markers are used for alignment of a patient. CONCLUSIONS It is recommended that 1.5-mm markers be used to avoid the reduction of TCP as well as to spare the surrounding critical organs, as long as the markers are visible on x-ray fluoroscopy. When 2-mm markers are implanted, more than two fields should be used and the markers should not be placed close to the distal edge of any of the beams.

Proton-induced x-ray fluorescence CT imaging

PURPOSE To demonstrate the feasibility of proton-induced x-ray fluorescence CT (pXFCT) imaging of gold in a small animal sized object by means of experiments and Monte Carlo (MC) simulations. METHODS First, proton-induced gold x-ray fluorescence (pXRF) was measured as a function of gold concentration. Vials of 2.2 cm in diameter filled with 0%-5% Au solutions were irradiated with a 220 MeV proton beam and x-ray fluorescence induced by the interaction of protons, and Au was detected with a 3 × 3 mm(2) CdTe detector placed at 90° with respect to the incident proton beam at a distance of 45 cm from the vials. Second, a 7-cm diameter water phantom containing three 2.2-diameter vials with 3%-5% Au solutions was imaged with a 7-mm FWHM 220 MeV proton beam in a first generation CT scanning geometry. X-rays scattered perpendicular to the incident proton beam were acquired with the CdTe detector placed at 45 cm from the phantom positioned on a translation/rotation stage. Twenty one translational steps spaced by 3 mm at each of 36 projection angles spaced by 10° were acquired, and pXFCT images of the phantom were reconstructed with filtered back projection. A simplified geometry of the experimental data acquisition setup was modeled with the MC TOPAS code, and simulation results were compared to the experimental data. RESULTS A linear relationship between gold pXRF and gold concentration was observed in both experimental and MC simulation data (R(2) > 0.99). All Au vials were apparent in the experimental and simulated pXFCT images. Specifically, the 3% Au vial was detectable in the experimental [contrast-to-noise ratio (CNR) = 5.8] and simulated (CNR = 11.5) pXFCT image. Due to fluorescence x-ray attenuation in the higher concentration vials, the 4% and 5% Au contrast were underestimated by 10% and 15%, respectively, in both the experimental and simulated pXFCT images. CONCLUSIONS Proton-induced x-ray fluorescence CT imaging of 3%-5% gold solutions in a small animal sized water phantom has been demonstrated for the first time by means of experiments and MC simulations.

NTCP modeling analysis of acute hematologic toxicity in whole pelvic radiation therapy for gynecologic malignancies : A dosimetric comparison of IMRT and spot-scanning proton therapy (SSPT)

PURPOSE This treatment planning study was conducted to determine whether spot scanning proton beam therapy (SSPT) reduces the risk of grade ⩾3 hematologic toxicity (HT3+) compared with intensity modulated radiation therapy (IMRT) for postoperative whole pelvic radiation therapy (WPRT). METHODS AND MATERIALS The normal tissue complication probability (NTCP) of the risk of HT3+ was used as an in silico surrogate marker in this analysis. IMRT and SSPT plans were created for 13 gynecologic malignancy patients who had received hysterectomies. The IMRT plans were generated using the 7-fields step and shoot technique. The SSPT plans were generated using anterior-posterior field with single field optimization. Using the relative biological effectives (RBE) value of 1.0 for IMRT and 1.1 for SSPT, the prescribed dose was 45Gy(RBE) in 1.8Gy(RBE) per fractions for 95% of the planning target volume (PTV). The homogeneity index (HI) and the conformity index (CI) of the PTV were also compared. RESULTS The bone marrow (BM) and femoral head doses using SSPT were significantly lower than with IMRT. The NTCP modeling analysis showed that the risk of HT3+ using SSPT was significantly lower than with IMRT (NTCP=0.04±0.01 and 0.19±0.03, p=0.0002, respectively). There were no significant differences in the CI and HI of the PTV between IMRT and SSPT (CI=0.97±0.01 and 0.96±0.02, p=0.3177, and HI=1.24±0.11 and 1.27±0.05, p=0.8473, respectively). CONCLUSION The SSPT achieves significant reductions in the dose to BM without compromising target coverage, compared with IMRT. The NTCP value for HT3+ in SSPT was significantly lower than in IMRT.

Optimization of the fractionated irradiation scheme considering physical doses to tumor and organ at risk based on dose–volume histograms

PURPOSE Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose-volume histograms for tumor and normal tissues of organs around the tumor. METHODS Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose-volume histogram. RESULTS It was found that the optimization of fractionation scheme incorporating the dose-volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8-32 fractions with a daily dose of 2.2-6.3 Gy. CONCLUSIONS It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose-volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.

Graphical representation of the effects on tumor and OAR for determining the appropriate fractionation regimen in radiation therapy planning

PURPOSE The authors propose a graphical representation of the relation between the effect on the tumor and the damage effect on an organ at risk (OAR) against the irradiation dose, as an aid for choosing an appropriate fractionation regimen. METHODS The graphical relation is depicted by the radiation effect on the tumor E(1) versus that on an OAR E(0). By observing the features of the E(1) vs E(0) relation curve, i.e., convex or concave shape, one can judge whether multifractionation is better or not. This method is applied to the linear-quadratic model (with α and β parameters) as an example. Further, the method is extended to the general case for nonuniform dose distribution to the OAR, which is frequently seen in clinical situations. RESULTS The criterion for selecting multi- or hypofractionation is based on the relation between the dose for the OAR and the α∕β ratio of the OAR to the tumor. It is also shown that the graphical relation enables us to estimate the final effect after multifractionated treatment by plotting a tangent line on the curve. CONCLUSIONS The graphical representation method is of use for improving planning in radiotherapy by determining the effective fractionation scheme.

Accurate Analysis of the Change in Volume, Location, and Shape of Metastatic Cervical Lymph Nodes During Radiotherapy

PURPOSE To establish a method for the accurate acquisition and analysis of the variations in tumor volume, location, and three-dimensional (3D) shape of tumors during radiotherapy in the era of image-guided radiotherapy. METHODS AND MATERIALS Finite element models of lymph nodes were developed based on computed tomography (CT) images taken before the start of treatment and every week during the treatment period. A surface geometry map with a volumetric scale was adopted and used for the analysis. Six metastatic cervical lymph nodes, 3.5 to 55.1 cm(3) before treatment, in 6 patients with head and neck carcinomas were analyzed in this study. Three fiducial markers implanted in mouthpieces were used for the fusion of CT images. Changes in the location of the lymph nodes were measured on the basis of these fiducial markers. RESULTS The surface geometry maps showed convex regions in red and concave regions in blue to ensure that the characteristics of the 3D tumor geometries are simply understood visually. After the irradiation of 66 to 70 Gy in 2 Gy daily doses, the patterns of the colors had not changed significantly, and the maps before and during treatment were strongly correlated (average correlation coefficient was 0.808), suggesting that the tumors shrank uniformly, maintaining the original characteristics of the shapes in all 6 patients. The movement of the gravitational center of the lymph nodes during the treatment period was everywhere less than ±5 mm except in 1 patient, in whom the change reached nearly 10 mm. CONCLUSIONS The surface geometry map was useful for an accurate evaluation of the changes in volume and 3D shapes of metastatic lymph nodes. The fusion of the initial and follow-up CT images based on fiducial markers enabled an analysis of changes in the location of the targets. Metastatic cervical lymph nodes in patients were suggested to decrease in size without significant changes in the 3D shape during radiotherapy. The movements of the gravitational center of the lymph nodes were almost all less than ±5 mm.

Lifetime attributable risk of radiation-induced secondary cancer from proton beam therapy compared with that of intensity-modulated X-ray therapy in randomly sampled pediatric cancer patients

Abstract To investigate the amount that radiation-induced secondary cancer would be reduced by using proton beam therapy (PBT) in place of intensity-modulated X-ray therapy (IMXT) in pediatric patients, we analyzed lifetime attributable risk (LAR) as an in silico surrogate marker of the secondary cancer after these treatments. From 242 pediatric patients with cancers who were treated with PBT, 26 patients were selected by random sampling after stratification into four categories: (i) brain, head and neck, (ii) thoracic, (iii) abdominal, and (iv) whole craniospinal (WCNS) irradiation. IMXT was replanned using the same computed tomography and region of interest. Using the dose–volume histograms (DVHs) of PBT and IMXT, the LARs of Schneider et al. were calculated for the same patient. All the published dose–response models were tested for the organs at risk. Calculation of the LARs of PBT and IMXT based on the DVHs was feasible for all patients. The means ± standard deviations of the cumulative LAR difference between PBT and IMXT for the four categories were (i) 1.02 ± 0.52% (n = 7, P = 0.0021), (ii) 23.3 ± 17.2% (n = 8, P = 0.0065), (iii) 16.6 ± 19.9% (n = 8, P = 0.0497) and (iv) 50.0 ± 21.1% (n = 3, P = 0.0274), respectively (one tailed t-test). The numbers needed to treat (NNT) were (i) 98.0, (ii) 4.3, (iii) 6.0 and (iv) 2.0 for WCNS, respectively. In pediatric patients who had undergone PBT, the LAR of PBT was significantly lower than the LAR of IMXT estimated by in silico modeling. Although a validation study is required, it is suggested that the LAR would be useful as an in silico surrogate marker of secondary cancer induced by different radiotherapy techniques.