Toward a Transportable Cell Culture Platform for Evaluating Radiotherapy Dose Modifying Factors.

The current tools for validating dose delivery and optimizing new radiotherapy technologies in radiation therapy do not account for important dose modifying factors (DMFs), such as variations in cellular repair capability, tumor oxygenation, ultra-high dose rates and the type of ionizing radiation used. These factors play a crucial role in tumor control and normal tissue complications. To address this need, we explored the feasibility of developing a transportable cell culture platform (TCCP) to assess the relative biological effectiveness (RBE) of ionizing radiation. We measured cell recovery, clonogenic viability and metabolic viability of MDA-MB-231 cells over several days at room temperature in a range of concentrations of fetal bovine serum (FBS) in medium-supplemented gelatin, under both normoxic and hypoxic oxygen environments. Additionally, we measured the clonogenic viability of the cells to characterize how the duration of the TCCP at room temperature affected their radiosensitivity at doses up to 16 Gy. We found that (78±2)% of MDA-MB-231 cells were successfully recovered after being kept at room temperature for three days in 50% FBS in medium-supplemented gelatin at hypoxia (0.4±0.1)% pO2, while metabolic and clonogenic viabilities as measured by ATP luminescence and colony formation were found to be (58±5)% and (57±4)%, respectively. Additionally, irradiating a TCCP under normoxic and hypoxic conditions yielded a clonogenic oxygen enhancement ratio (OER) of 1.4±0.6 and a metabolic OER of 1.9±0.4. Our results demonstrate that the TCCP can be used to assess the RBE of a DMF and provides a feasible platform for assessing DMFs in radiation therapy applications.

Assessing the DNA Damaging Effectiveness of Ionizing Radiation Using Plasmid DNA.

Plasmid DNA is useful for investigating the DNA damaging effects of ionizing radiation. In this study, we have explored the feasibility of plasmid DNA-based detectors to assess the DNA damaging effectiveness of two radiotherapy X-ray beam qualities after undergoing return shipment of ~8000 km between two institutions. The detectors consisted of 18 µL of pBR322 DNA enclosed with an aluminum seal in nine cylindrical cavities drilled into polycarbonate blocks. We shipped them to Toronto, Canada for irradiation with either 100 kVp or 6 MV X-ray beams to doses of 10, 20, and 30 Gy in triplicate before being shipped back to San Diego, USA. The Toronto return shipment also included non-irradiated controls and we kept a separate set of controls in San Diego. In San Diego, we quantified DNA single strand breaks (SSBs), double strand breaks (DSBs), and applied Nth and Fpg enzymes to quantify oxidized base damage. The rate of DSBs/Gy/plasmid was 2.8±0.7 greater for the 100 kVp than the 6 MV irradiation. The 100 kVp irradiation also resulted in 5±2 times more DSBs/SSB than the 6 MV beam, demonstrating that the detector is sensitive enough to quantify relative DNA damage effectiveness, even after shipment over thousands of kilometers.

Quantifying the DNA-damaging Effects of FLASH Irradiation With Plasmid DNA.

PURPOSE: To investigate a plasmid DNA nicking assay approach for isolating and quantifying the DNA-damaging effects of ultrahigh-dose-rate (ie, FLASH) irradiation relative to conventional dose-rate irradiation. METHODS AND MATERIALS: We constructed and irradiated phantoms containing plasmid DNA to nominal doses of 20 Gy and 30 Gy using 16 MeV electrons at conventional (0.167 Gy/s) and FLASH (46.6 Gy/s and 93.2 Gy/s) dose rates. We delivered conventional dose rates using a standard clinical Varian iX linear accelerator and FLASH dose rates (FDRs) using a modified Varian 21EX C-series linear accelerator. We ran the irradiated DNA and controls (0 Gy) through an agarose gel electrophoresis procedure that sorted and localized the DNA into bands associated with single strand breaks (SSBs), double strand breaks (DSBs), and undamaged DNA. We quantitatively analyzed the gel images to compute the relative yields of SSBs and DSBs and applied a mathematical model of plasmid DNA damage as a function of dose to compute the relative biological effectiveness (RBE) of SSB and DSB (RBESSB and RBEDSB) damage for a given endpoint and FDR. RESULTS: Both RBESSB and RBEDSB were less than unity with the FDR irradiations, indicating FLASH sparing. With regard to the more deleterious DNA DSB damage, the DSB RBEs of FLASH beams at dose rates of 46.6 Gy/s and 93.2 Gy/s relative to the conventional 16 MeV beam dose rate were 0.54 ± 0.15 and 0.55 ± 0.17, respectively. CONCLUSIONS: This study demonstrated the feasibility of using a DNA-based phantom to isolate and assess the FLASH sparing effect on DNA. We also found that FLASH irradiation causes less damage to DNA compared with a conventional dose rate. This result supports the notion that the protective effect of FLASH irradiation occurs at least partially via fundamental biochemical processes.

Impact of a 1.5 T magnetic field on DNA damage in MRI-guided HDR brachytherapy.

PURPOSE: Some studies have suggested that the presence of a static magnetic field (SMF) during irradiation alters biological damage. Since MRI-guided radiotherapy is becoming increasingly common, we constructed a DNA-based detector to assess the effect of a 1.5 T SMF on DNA damage during high dose rate (HDR) brachytherapy irradiation. METHODS: Block phantoms containing a small cavity for the placement of plasmid DNA (pBR322) samples were 3-D printed with biocompatible tissue equivalent material. The phantom was CT scanned and an HDR brachytherapy treatment plan was designed to deliver 20 Gy and 30 Gy doses to the DNA samples in the presence and absence of a 1.5 T SMF. Relative yields of single- and double-strand breaks (SSBs and DSBs, respectively) were computed from gel electrophoresis images of the DNA band intensities and averaged over sample sizes ranging from 12 to 30. Radiation dose was also measured in the presence and absence of the 1.5 T SMF using GafChromic™ EBT3 film placed in the coronal, sagittal, and axial planes. RESULTS: The average yield of DNA with SSBs and DSBs in the presence and absence of the SMF showed no statistically significant differences (all p ≥ 0.17). Differences in the net optical densities of the EBT3 films for each plane were within experimental uncertainty, suggesting no dose difference in the presence and absence of the SMF. CONCLUSIONS: HDR irradiation in the presence of the 1.5 T SMF did not alter dose deposition to the DNA cavity nor change SSB and DSB DNA damage.

Experimental validation of a kV source model and dose computation method for CBCT imaging in an anthropomorphic phantom.

We present an experimental validation of a kilovoltage (kV) X-ray source characterization model in an anthropomorphic phantom to estimate patient-specific absorbed dose from kV cone-beam computed tomography (CBCT) imaging procedures and compare these doses to nominal weighted CT-dose index (CTDIw) dose estimates. We simulated the default Varian on-board imager 1.4 (OBI) default CBCT imaging protocols (i.e., standard-dose head, low-dose thorax, pelvis, and pelvis spotlight) using our previously developed and easy to implement X-ray point-source model and source characterization approach. We used this characterized source model to compute absorbed dose in homogeneous and anthropomorphic phantoms using our previously validated in-house kV dose computation software (kVDoseCalc). We compared these computed absorbed doses to doses derived from ionization chamber measurements acquired at several points in a homogeneous cylindrical phantom and from thermoluminescent detectors (TLDs) placed in the anthropomorphic phantom. In the homogeneous cylindrical phantom, computed values of absorbed dose relative to the center of the phantom agreed with measured values within ≤2% of local dose, except in regions of high-dose gradient where the distance to agreement (DTA) was 2 mm. The computed absorbed dose in the anthropomorphic phantom generally agreed with TLD measurements, with an average percent dose difference ranging from 2.4% ± 6.0% to 5.7% ± 10.3%, depending on the characterized CBCT imaging protocol. The low-dose thorax and the standard dose scans showed the best and worst agreement, respectively. Our results also broadly agree with published values, which are approximately twice as high as the nominal CTDIw would suggest. The results demonstrate that our previously developed method for modeling and characterizing a kV X-ray source could be used to accurately assess patient-specific absorbed dose from kV CBCT procedures within reasonable accuracy, and serve as further evidence that existing CTDIw assessments underestimate absorbed dose delivered to patients.

A measurement-based X-ray source model characterization for CT dosimetry computations.

The purpose of this study was to show that the nominal peak tube voltage potential (kVp) and measured half-value layer (HVL) can be used to generate energy spectra and fluence profiles for characterizing a computed tomography (CT) X-ray source, and to validate the source model and an in-house kV X-ray dose computation algorithm (kVDoseCalc) for computing machine- and patient-specific CT dose. Spatial variation of the X-ray source spectra of a Philips Brilliance and a GE Optima Big Bore CT scanner were found by measuring the HVL along the direction of the internal bow-tie filter axes. Third-party software, Spektr, and the nominal kVp settings were used to generate the energy spectra. Beam fluence was calculated by dividing the integral product of the spectra and the in-air NIST mass-energy attenuation coefficients by in-air dose measurements along the filter axis. The authors found the optimal number of photons to seed in kVDoseCalc to achieve dose convergence. The Philips Brilliance beams were modeled for 90, 120, and 140 kVp tube settings. The GE Optima beams were modeled for 80, 100, 120, and 140 kVp tube settings. Relative doses measured using a Capintec Farmer-type ionization chamber (0.65 cc) placed in a cylindrical polymethyl methacrylate (PMMA) phantom and irradiated by the Philips Brilliance, were compared to those computed with kVDoseCalc. Relative doses in an anthropomorphic thorax phantom (E2E SBRT Phantom) irradiated by the GE Optima were measured using a (0.015 cc) PTW Freiburg ionization chamber and compared to computations from kVDoseCalc. The number of photons required to reduce the average statistical uncertainty in dose to < 0.3% was 2 × 105. The average percent difference between calculation and measurement over all 12 PMMA phantom positions was found to be 1.44%, 1.47%, and 1.41% for 90, 120, and 140 kVp, respectively. The maximum percent difference between calculation and measurement for all energies, measurement positions, and phantoms was less than 3.50%. Thirty-five out of a total of 36 simulation conditions were within the experimental uncertainties associated with measurement reproducibility and chamber volume effects for the PMMA phantom. The agreement between calculation and measurement was within experimental uncertainty for 19 out of 20 simulation conditions at five points of interest in the anthropomorphic thorax phantom for the four beam energies modeled. The source model and characterization technique based on HVL measurements and nominal kVp can be used to accurately compute CT dose. This accuracy provides experimental validation of kVDoseCalc for computing CT dose.

A rapid noninvasive characterization of CT x-ray sources.

PURPOSE: The aim of this study is to generate spatially varying half value layers (HVLs) that can be used to construct virtual equivalent source models of computed tomography (CT) x-ray sources for use in Monte Carlo CT dose computations. METHODS: To measure the spatially varying HVLs, the authors combined a cylindrical HVL measurement technique with the characterization of bowtie filter relative attenuation (COBRA) geometry. An apparatus given the name "HVL Jig" was fabricated to accurately position a real-time dosimeter off-isocenter while surrounded by concentric cylindrical aluminum filters (CAFs). In this geometry, each projection of the rotating x-ray tube is filtered by an identical amount of high-purity (type 1100 H-14) aluminum while the stationary radiation dose probe records an air kerma rate versus time waveform. The CAFs were progressively nested to acquire exposure data at increasing filtrations to calculate the HVL. Using this dose waveform and known setup geometry, each timestamp was related to its corresponding fan angle. Data were acquired using axial CT protocols (i.e., rotating tube and stationary patient table) at energies of 80, 100, and 120 kVp on a single CT scanner. These measurements were validated against the more laborious conventional step-and-shoot approach (stationary x-ray tube). RESULTS: At each energy, HVL data points from the COBRA-cylinder technique were fit to a trendline and compared with the conventional approach. The average relative difference in HVL between the two techniques was 1.3%. There was a systematic overestimation in HVL due to scatter contamination. CONCLUSIONS: The described method is a novel, rapid, accurate, and noninvasive approach that allows one to acquire the spatially varying fluence and HVL data using a single experimental setup in a minimum of three scans. These measurements can be used to characterize the CT beam in terms of the angle-dependent fluence and energy spectra along the bowtie filter direction, which can serve as input for accurate CT dose computations.

Modeling a superficial radiotherapy X-ray source for relative dose calculations.

The purpose of this study was to empirically characterize and validate a kilovoltage (kV) X-ray beam source model of a superficial X-ray unit for relative dose calculations in water and assess the accuracy of the British Journal of Radiology Supplement 25 (BJR 25) percentage depth dose (PDD) data. We measured central axis PDDs and dose profiles using an Xstrahl 150 X-ray system. We also compared the measured and calculated PDDs to those in the BJR 25. The Xstrahl source was modeled as an effective point source with varying spatial fluence and spectra. In-air ionization chamber measurements were made along the x- and y-axes of the X-ray beam to derive the spatial fluence and half-value layer (HVL) measurements were made to derive the spatially varying spectra. This beam characterization and resulting source model was used as input for our in-house dose calculation software (kVDoseCalc) to compute radiation dose at points of interest (POIs). The PDDs and dose profiles were measured using 2, 5, and 15 cm cone sizes at 80, 120, 140, and 150 kVp energies in a scanning water phantom using IBA Farmer-type ionization chambers of volumes 0.65 and 0.13 cc, respectively. The percent difference in the computed PDDs compared with our measurements range from -4.8% to 4.8%, with an overall mean percent difference and standard deviation of 1.5% and 0.7%, respectively. The percent difference between our PDD measurements and those from BJR 25 range from -14.0% to 15.7%, with an overall mean percent difference and standard deviation of 4.9% and 2.1%, respectively - showing that the measurements are in much better agreement with kVDoseCalc than BJR 25. The range in percent difference between kVDoseCalc and measurement for profiles was -5.9% to 5.9%, with an overall mean percent difference and standard deviation of 1.4% and 1.4%, respectively. The results demonstrate that our empirically based X-ray source modeling approach for superficial X-ray therapy can be used to accurately compute relative dose in a homogeneous water-equivalent medium. They also show limitations in the accuracy of theBJR 25 PDD data.

Fractal analysis of nuclear histology integrates tumor and stromal features into a single prognostic factor of the oral cancer microenvironment.

BACKGROUND: The lack of prognostic biomarkers in oral squamous cell carcinoma (OSCC) has hampered treatment decision making and survival in OSCC remains poor. Histopathological features are used for prognostication in OSCC and, although useful for predicting risk, manual assessment of histopathology is subjective and labour intensive. In this study, we propose a method that integrates multiple histopathological features of the tumor microenvironment into a single, digital pathology-based biomarker using nuclear fractal dimension (nFD) analysis. METHODS: One hundred and seven consecutive OSCC patients diagnosed between 1998 and 2006 in Calgary, Canada were included in the study. nFD scores were generated from DAPI-stained images of tissue microarray (TMA) cores. Ki67 protein expression was measured in the tumor using fluorescence immunohistochemistry (IHC) and automated quantitative analysis (AQUA®). Lymphocytic infiltration (LI) was measured in the stroma from haematoxylin-eosin (H&E)-stained TMA slides by a pathologist. RESULTS: Twenty-five (23.4%) and 82 (76.6%) patients were classified as high and low nFD, respectively. nFD was significantly associated with pathological tumor-stage (pT-stage; P = 0.01) and radiation treatment (RT; P = 0.01). High nFD of the total tumor microenvironment (stroma plus tumor) was significantly associated with improved disease-specific survival (DSS; P = 0.002). No association with DSS was observed when nFD of either the tumor or the stroma was measured separately. pT-stage (P = 0.01), pathological node status (pN-status; P = 0.02) and RT (P = 0.03) were also significantly associated with DSS. In multivariate analysis, nFD remained significantly associated with DSS [HR 0.12 (95% CI 0.02-0.89, P = 0.04)] in a model adjusted for pT-stage, pN-status and RT. We also found that high nFD was significantly associated with high tumor proliferation (P < 0.0001) and high LI (P < 0.0001), factors that we and others have shown to be associated with improved survival in OSCC. CONCLUSIONS: We provide evidence that nFD analysis integrates known prognostic factors from the tumor microenvironment, such as proliferation and immune infiltration, into a single digital pathology-based biomarker. Prospective validation of our results could establish nFD as a valuable tool for clinical decision making in OSCC.

Digital differentiation of non-small cell carcinomas of the lung by the fractal dimension of their epithelial architecture.

INTRODUCTION: In recent years, differences have emerged in the treatment of squamous and non-squamous non-small cell lung carcinomas (NSCLCs). This highlights the importance of accurate histopathologic classification. However, there remains inter-observer disagreement when making diagnoses based on histology. Fractal dimension (FD) is a mathematical measure of irregularity and complexity of shape. We hypothesize that the FD of carcinoma epithelial architecture can assist in differentiating adenocarcinoma (ADC) from squamous cell carcinoma (SCC) of the lung. METHODS: 134 resected (88 ADC and 46 SCC) cases of resected early-stage NSCLC were analyzed. Tissue micro arrays were generated from formalin-fixed paraffin-embedded tissue, stained with pan-cytokeratin, and digitally imaged and the FD of the epithelial structure calculated. Mean FD of ADC and SCC were compared using the independent t-test, partial correlations, and receiver operating characteristic (ROC) analyses. RESULTS: A statistically significant difference (p<0.001) between the mean FD of ADC (M=1.70, SD=0.07) and SCC (M=1.78, SD=0.07) was found. Significance remained (p<0.001) when controlling for several possible confounders. ROC analysis demonstrated an area-under-the-curve of 0.81 (p<0.001). CONCLUSIONS: The epithelial structure FD of NSCLC has potential as a reproducible and automated measure to help subtype NSCLCs into ADC and SCC. With further image analysis algorithm improvements, fractal analysis may be a component in computerized histomorphological assessments of lung cancer and may provide an adjunct test in differentiating NSCLCs.

Experimental validation of a kilovoltage x-ray source model for computing imaging dose.

PURPOSE: To introduce and validate a kilovoltage (kV) x-ray source model and characterization method to compute absorbed dose accrued from kV x-rays. METHODS: The authors propose a simplified virtual point source model and characterization method for a kV x-ray source. The source is modeled by: (1) characterizing the spatial spectral and fluence distributions of the photons at a plane at the isocenter, and (2) creating a virtual point source from which photons are generated to yield the derived spatial spectral and fluence distribution at isocenter of an imaging system. The spatial photon distribution is determined by in-air relative dose measurements along the transverse (x) and radial (y) directions. The spectrum is characterized using transverse axis half-value layer measurements and the nominal peak potential (kVp). This source modeling approach is used to characterize a Varian(®) on-board-imager (OBI(®)) for four default cone-beam CT beam qualities: beams using a half bowtie filter (HBT) with 110 and 125 kVp, and a full bowtie filter (FBT) with 100 and 125 kVp. The source model and characterization method was validated by comparing dose computed by the authors' inhouse software (kVDoseCalc) to relative dose measurements in a homogeneous and a heterogeneous block phantom comprised of tissue, bone, and lung-equivalent materials. RESULTS: The characterized beam qualities and spatial photon distributions are comparable to reported values in the literature. Agreement between computed and measured percent depth-dose curves is ⩽ 2% in the homogeneous block phantom and ⩽ 2.5% in the heterogeneous block phantom. Transverse axis profiles taken at depths of 2 and 6 cm in the homogeneous block phantom show an agreement within 4%. All transverse axis dose profiles in water, in bone, and lung-equivalent materials for beams using a HBT, have an agreement within 5%. Measured profiles of FBT beams in bone and lung-equivalent materials were higher than their computed counterparts resulting in an agreement within 2.5%, 5%, and 8% within solid water, bone, and lung, respectively. CONCLUSIONS: The proposed virtual point source model and characterization method can be used to compute absorbed dose in both the homogeneous and heterogeneous block phantoms within of 2%-8% of measured values, depending on the phantom and the beam quality. The authors' results also provide experimental validation for their kV dose computation software, kVDoseCalc.

Scale-specific multifractal medical image analysis.

Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter rather than a single number. We describe this approach in the context of the more generalized Rényi entropy, in which we can also compute the information and correlation dimensions of images. In addition, we describe and validate a computational improvement to box-counting fractal analysis. This improvement is based on integral images, which allows the speedup of any box-counting or similar fractal analysis algorithm, including estimation of scale-dependent dimensions. Finally, we applied our technique to images of invasive breast cancer tissue from 157 patients to show a relationship between the fractal analysis of these images over certain scale ranges and pathologic tumour grade (a standard prognosticator for breast cancer). Our approach is general and can be applied to any medical imaging application in which the complexity of pathological image structures may have clinical value.

FracMod: a computational tool for assessing IMRT field modulation.

The authors develop and investigate a user-friendly computational tool (FracMod) to quantify modulation complexity in planned IMRT fields. FracMod comprises a graphical user interface and variogram fractal dimension (FD) analysis tool developed by the authors using MATLAB(®), and made freely available at http://www.medphysfiles.com/index.php. FracMod is investigated for its ability to identify overly-modulated dynamic IMRT fields designed for prostatic carcinoma treatments. A set of 5 prostate alone plans and 5 prostate plus pelvic node plans were used to choose FD cut-points that ensure no false positives in distinguishing between moderate and high field modulation. IMRT quality control (QC) was performed on all the treatment fields using Varian(®) Portal Dosimetry and MapCHECK™. Receiver operating characteristic analysis was used to quantitatively compare the classification performance of FD and the number of monitor units (MUs). The effect of dose rate on the average leaf pair opening (ALPO) and the number of MUs delivered was also investigated. The variogram FD performed better than the number of MUs in identifying overly-modulated fields. FD thresholds >2.15 for prostate alone and >2.20 for prostate plus pelvic nodes correctly identified 75% and 100% of the high modulation fields, respectively, with no false positives. With appropriate cut-points, MapCHECK™ identified the most highly modulated IMRT fields, whereas Varian(®) Portal Dosimetry could not. As expected, ALPO decreases with increasing modulation and increasing dose rate. FracMod is a user-friendly tool that allows one to accurately quantify and identify overly-modulated IMRT fields at the treatment planning stage before they are sent for patient-specific QC.

A simplified approach to characterizing a kilovoltage source spectrum for accurate dose computation.

PURPOSE: To investigate and validate the clinical feasibility of using half-value layer (HVL) and peak tube potential (kVp) for characterizing a kilovoltage (kV) source spectrum for the purpose of computing kV x-ray dose accrued from imaging procedures. To use this approach to characterize a Varian® On-Board Imager® (OBI) source and perform experimental validation of a novel in-house hybrid dose computation algorithm for kV x-rays. METHODS: We characterized the spectrum of an imaging kV x-ray source using the HVL and the kVp as the sole beam quality identifiers using third-party freeware Spektr to generate the spectra. We studied the sensitivity of our dose computation algorithm to uncertainties in the beam's HVL and kVp by systematically varying these spectral parameters. To validate our approach experimentally, we characterized the spectrum of a Varian® OBI system by measuring the HVL using a Farmer-type Capintec ion chamber (0.06 cc) in air and compared dose calculations using our computationally validated in-house kV dose calculation code to measured percent depth-dose and transverse dose profiles for 80, 100, and 125 kVp open beams in a homogeneous phantom and a heterogeneous phantom comprising tissue, lung, and bone equivalent materials. RESULTS: The sensitivity analysis of the beam quality parameters (i.e., HVL, kVp, and field size) on dose computation accuracy shows that typical measurement uncertainties in the HVL and kVp (±0.2 mm Al and ±2 kVp, respectively) source characterization parameters lead to dose computation errors of less than 2%. Furthermore, for an open beam with no added filtration, HVL variations affect dose computation accuracy by less than 1% for a 125 kVp beam when field size is varied from 5 × 5 cm(2) to 40 × 40 cm(2). The central axis depth dose calculations and experimental measurements for the 80, 100, and 125 kVp energies agreed within 2% for the homogeneous and heterogeneous block phantoms, and agreement for the transverse dose profiles was within 6%. CONCLUSIONS: The HVL and kVp are sufficient for characterizing a kV x-ray source spectrum for accurate dose computation. As these parameters can be easily and accurately measured, they provide for a clinically feasible approach to characterizing a kV energy spectrum to be used for patient specific x-ray dose computations. Furthermore, these results provide experimental validation of our novel hybrid dose computation algorithm.

Fractal analysis for assessing the level of modulation of IMRT fields.

PURPOSE: To investigate the potential of three fractal dimension (FD) analysis methods (i.e., the variation, power spectrum, and variogram methods) as metrics for quantifying the degree of modulation in planned intensity modulated radiation therapy (IMRT) treatment fields, and compare the most suitable FD method to the number of monitor units (MUs), the average leaf gap, and the 2D modulation index (2D MI) for assessing modulation. METHODS: The authors implemented, validated, and compared the variation, power spectrum, and variogram methods for computing the FD. Validation of the methods was done using mathematical fractional Brownian surfaces of known FD that ranged in size from 128 × 128 to 512 × 512. The authors used a test set consisting of seven head and neck carcinoma plans (50 prescribed treatment fields) to choose an FD cut-point that ensures no false positives (100% specificity) in distinguishing between moderate and high degrees of field modulation. The degree of field modulation was controlled by adjusting the fluence smoothing parameters in the Eclipse™ treatment planning system (Varian Medical Systems, Palo Alto, CA). The moderate modulation fields were representative of the degree of modulation used clinically at the authors' institution. The authors performed IMRT quality assurance (QA) on the 50 test fields using the MapCHECK™ device. The FD cut-point was applied to a validation set consisting of four head and neck plans (28 fields). The area under the curve (AUC) from receiver operating characteristic (ROC) analysis was used to compare the ability of FD, number of MUs, average leaf gap, and the 2D MI for distinguishing between the moderate and high modulation fields. RESULTS: The authors found the variogram FD method to be the most suitable for assessing the modulation complexity of IMRT fields for head and neck carcinomas. Pass rates as measured by the gamma criterion for the MapCHECK™ IMRT field measurements were higher for the moderately modulated fields, and a gamma criterion with 1 mm distance-to-agreement and 1% dose difference showed a clear separation between the 94% pass rates of the moderate and high modulation groups. From the ROC analysis of the test set, the authors found the AUC of the variogram FD, number of MUs, average leaf gap, and 2D MI methods to be 0.99 (almost perfect), 0.91 (excellent), 0.91 (excellent), and 0.92 (excellent), respectively. A cut-point of FD > 2.25 correctly identified 92.8% of the high modulation fields and 100% of the moderately modulated fields in the validation set, satisfying the condition of no false positives. CONCLUSIONS: Of the three FD methods investigated, the variogram method is the most accurate and precise metric for identifying high modulation treatment fields. It is also more accurate and precise than the number of MUs, the average leaf gap, and the 2D MI. Although MapCHECK™ IMRT QA does a reasonable job at identifying high modulation fields, the variogram FD method provides one with the opportunity to quantitatively and accurately assess modulation and adjust overly modulated fields at the treatment planning stage before they are sent to the treatment machine for QA or patient treatment.

A hybrid approach for rapid, accurate, and direct kilovoltage radiation dose calculations in CT voxel space.

PURPOSE: To develop and validate a fast and accurate method that uses computed tomography (CT) voxel data to estimate absorbed radiation dose at a point of interest (POI) or series of POIs from a kilovoltage (kV) imaging procedure. METHODS: The authors developed an approach that computes absorbed radiation dose at a POI by numerically evaluating the linear Boltzmann transport equation (LBTE) using a combination of deterministic and Monte Carlo (MC) techniques. This hybrid approach accounts for material heterogeneity with a level of accuracy comparable to the general MC algorithms. Also, the dose at a POI is computed within seconds using the Intel Core i7 CPU 920 2.67 GHz quad core architecture, and the calculations are performed using CT voxel data, making it flexible and feasible for clinical applications. To validate the method, the authors constructed and acquired a CT scan of a heterogeneous block phantom consisting of a succession of slab densities: Tissue (1.29 cm), bone (2.42 cm), lung (4.84 cm), bone (1.37 cm), and tissue (4.84 cm). Using the hybrid transport method, the authors computed the absorbed doses at a set of points along the central axis and x direction of the phantom for an isotropic 125 kVp photon spectral point source located along the central axis 92.7 cm above the phantom surface. The accuracy of the results was compared to those computed with MCNP, which was cross-validated with EGSnrc, and served as the benchmark for validation. RESULTS: The error in the depth dose ranged from -1.45% to +1.39% with a mean and standard deviation of -0.12% and 0.66%, respectively. The error in the x profile ranged from -1.3% to +0.9%, with standard deviations of -0.3% and 0.5%, respectively. The number of photons required to achieve these results was 1 x 10(6). CONCLUSIONS: The voxel-based hybrid method evaluates the LBTE rapidly and accurately to estimate the absorbed x-ray dose at any POI or series of POIs from a kV imaging procedure.

Angular dependence of the output of a kilovoltage X-ray therapy unit.

During the recommissioning of a Philips RT-250 kilovoltage X-ray unit, unexpected output variations with tube head rotation (cross-plane) and tube head tilt (in-plane) were observed. The measured output showed an increase of up to 7.3% relative to the neutral position (0? in-plane and 0? cross-plane) over the possible range of angles of in-plane rotation for 75 kVp (half-value layer, HVL = 1.84 mm Al). A less pronounced but noticeable output change (with respect to the neutral position) was observed for cross-plane rotation reaching 2% for the 225 kVp beam (HVL = 0.90 mm Cu). This output variation was observed while manually adjusting the current to maintain constancy according to the current meter gauge. In order to address the observed output dependence with head orientation, the dose rate monitor chamber of the kilovoltage unit was calibrated to monitor the beam output in real time. The dose rate was manually adjusted to maintain a constant dose rate (in r/min) as displayed on the r/min gauge. This approach resulted in maintaining beam output for the 75 kVp and the 225 kVp beams within +/- 2% for the in-plane angle variation and +/- 0.5% for the cross-plane angle variation. A daily output check that includes ion chamber-based measurements at the neutral position and an in-plane angle of 45? has been implemented using the constant dose rate approach to monitor the stability of the X-ray beams. As a result of the output variations with in/cross-plane rotation, the quality control (QC) procedures that are typically used for clinical setup have been modified to test the stability of the beams under the non-neutral positioning of the X-ray tube.

Morphologic complexity of epithelial architecture for predicting invasive breast cancer survival.

BACKGROUND: Precise criteria for optimal patient selection for adjuvant chemotherapy remain controversial and include subjective components such as tumour morphometry (pathological grade). There is a need to replace subjective criteria with objective measurements to improve risk assessment and therapeutic decisions. We assessed the prognostic value of fractal dimension (an objective measure of morphologic complexity) for invasive ductal carcinoma of the breast. METHODS: We applied fractal analysis to pan-cytokeratin stained tissue microarray (TMA) cores derived from 379 patients. Patients were categorized according to low (<1.56, N = 141), intermediate (1.56-1.75, N = 148), and high (>1.75, N = 90) fractal dimension. Cox proportional-hazards regression was used to assess the relationship between disease-specific and overall survival and fractal dimension, tumour size, grade, nodal status, estrogen receptor status, and HER-2/neu status. RESULTS: Patients with higher fractal score had significantly lower disease-specific 10-year survival (25.0%, 56.4%, and 69.4% for high, intermediate, and low fractal dimension, respectively, p < 0.001). Overall 10-year survival showed a similar association. Fractal dimension, nodal status, and grade were the only significant (P < 0.05) independent predictors for both disease-specific and overall survival. Among all of the prognosticators, the fractal dimension hazard ratio for disease-specific survival, 2.6 (95% confidence interval (CI) = 1.4,4.8; P = 0.002), was second only to the slightly higher hazard ratio of 3.1 (95% CI = 1.9,5.1; P < 0.001) for nodal status. As for overall survival, fractal dimension had the highest hazard ratio, 2.7 (95% CI = 1.6,4.7); P < 0.001). Split-sample cross-validation analysis suggests these results are generalizable. CONCLUSION: Except for nodal status, morphologic complexity of breast epithelium as measured quantitatively by fractal dimension was more strongly and significantly associated with disease-specific and overall survival than standard prognosticators.

Effects of image resolution and noise on estimating the fractal dimension of tissue specimens.

OBJECTIVE: To investigate the effects of imaging system noise and resolution on the ability to estimate and distinguish relative differences in the fractal dimension of tissue specimens. STUDY DESIGN: Mathematically derived test images of known fractal dimension mimicking the complexity of epithelial morphology were created. The box-counting method was used to compute fractal dimension. To study the effects of resolution on fractal dimension, the test images were convolved with Gaussian point spread functions (PSF), and effects of noise were studied by adding Poisson and Gaussian noise. Application of these findings was illustrated by measuring the resolution and noise for a typical optical microscope and digital camera (OMDC) system. RESULTS: Poor spatial resolution reduces the fractal dimension and has an increased adverse effect on higher dimensions. Fractal dimension can be estimated within 7% of the true dimension, and relative differences of 0.1 between dimensions are distinguishable provided the PSF of an imaging system has a full-width-at-half-maximum < or = 4 pixels and the contrast-to-noise ratio > 15. These conditions were satisfied by our OMDC. CONCLUSION: Effects of noise and resolution from a typical OMDC system do not significantly inhibit the ability to estimate and distinguish relative differences in the fractal dimension of tissue specimens.