A Finite Model Property for Gödel Modal Logics

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, and indeed co-NP-completeness for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classes of formulas.

Purchase decision-making is modulated by vestibular stimulation

Purchases are driven by consumers’ product preferences and price considerations. Using caloric vestibular stimulation (CVS), we investigated the role of vestibular-affective circuits in purchase decision-making. CVS is an effective noninvasive brain stimulation method, which activates vestibular and overlapping emotional circuits (e.g., the insular cortex and the anterior cingulate cortex (ACC)). Subjects were exposed to CVS and sham stimulation while they performed two purchase decision-making tasks. In Experiment 1 subjects had to decide whether to purchase or not. CVS significantly reduced probability of buying a product. In Experiment 2 subjects had to rate desirability of the products and willingness to pay (WTP) while they were exposed to CVS and sham stimulation. CVS modulated desirability of the products but not WTP. The results suggest that CVS interfered with emotional circuits and thus attenuated the pleasant and rewarding effect of acquisition, which in turn reduced purchase probability. The present findings contribute to the rapidly growing literature on the neural basis of purchase decision-making.

Dosimetric properties of an amorphous silicon EPID for verification of modulated electron radiotherapy

Purpose: To investigate the dosimetric properties of an electronic portal imaging device (EPID) for electron beam detection and to evaluate its potential for quality assurance (QA) of modulated electron radiotherapy (MERT). Methods: A commercially available EPID was used to detect electron beams shaped by a photon multileaf collimator (MLC) at a source-surface distance of 70 cm. The fundamental dosimetric properties such as reproducibility, dose linearity, field size response, energy response, and saturation were investigated for electron beams. A new method to acquire the flood-field for the EPID calibration was tested. For validation purpose, profiles of open fields and various MLC fields (square and irregular) were measured with a diode in water and compared to the EPID measurements. Finally, in order to use the EPID for QA of MERT delivery, a method was developed to reconstruct EPID two-dimensional (2D) dose distributions in a water-equivalent depth of 1.5 cm. Comparisons were performed with film measurement for static and dynamic monoenergy fields as well as for multienergy fields composed by several segments of different electron energies. Results: The advantageous EPID dosimetric properties already known for photons as reproducibility, linearity with dose, and dose rate were found to be identical for electron detection. The flood-field calibration method was proven to be effective and the EPID was capable to accurately reproduce the dose measured in water at 1.0 cm depth for 6 MeV, 1.3 cm for 9 MeV, and 1.5 cm for 12, 15, and 18 MeV. The deviations between the output factors measured with EPID and in water at these depths were within ±1.2% for all the energies with a mean deviation of 0.1%. The average gamma pass rate (criteria: 1.5%, 1.5 mm) for profile comparison between EPID and measurements in water was better than 99% for all the energies considered in this study. When comparing the reconstructed EPID 2D dose distributions at 1.5 cm depth to film measurements, the gamma pass rate (criteria: 2%, 2 mm) was better than 97% for all the tested cases. Conclusions: This study demonstrates the high potential of the EPID for electron dosimetry, and in particular, confirms the possibility to use it as an efficient verification tool for MERT delivery.

Risk of Second Malignant Neoplasms Following Proton Arc Therapy and Volumetric Modulated Arc Therapy for Prostate Cancer

The risk of second malignant neoplasms (SMNs) following prostate radiotherapy is a concern due to the large population of survivors and decreasing age at diagnosis. It is known that parallel-opposed beam proton therapy carries a lower risk than photon IMRT. However, a comparison of SMN risk following proton and photon arc therapies has not previously been reported. The purpose of this study was to predict the ratio of excess relative risk (RRR) of SMN incidence following proton arc therapy to that after volumetric modulated arc therapy (VMAT). Additionally, we investigated the impact of margin size and the effect of risk-minimized proton beam weighting on predicted RRR. Physician-approved treatment plans were created for both modalities for three patients. Therapeutic dose was obtained with differential dose-volume histograms from the treatment planning system, and stray dose was estimated from the literature or calculated with Monte Carlo simulations. Then, various risk models were applied to the total dose. Additional treatment plans were also investigated with varying margin size and risk-minimized proton beam weighting. The mean RRR ranged from 0.74 to 0.99, depending on risk model. The additional treatment plans revealed that the RRR remained approximately constant with varying margin size, and that the predicted RRR was reduced by 12% using a risk-minimized proton arc therapy planning technique. In conclusion, proton arc therapy was found to provide an advantage over VMAT in regard to predicted risk of SMN following prostate radiotherapy. This advantage was independent of margin size and was amplified with risk-optimized proton beam weighting.

Is a 3-mm intrafractional margin sufficient for daily image-guided intensity-modulated radiation therapy of prostate cancer?

PURPOSE: To determine whether a 3-mm isotropic target margin adequately covers the prostate and seminal vesicles (SVs) during administration of an intensity-modulated radiation therapy (IMRT) treatment fraction, assuming that daily image-guided setup is performed just before each fraction. MATERIALS AND METHODS: In-room computed tomographic (CT) scans were acquired immediately before and after a daily treatment fraction in 46 patients with prostate cancer. An eight-field IMRT plan was designed using the pre-fraction CT with a 3-mm margin and subsequently recalculated on the post-fraction CT. For convenience of comparison, dose plans were scaled to full course of treatment (75.6 Gy). Dose coverage was assessed on the post-treatment CT image set. RESULTS: During one treatment fraction (21.4+/-5.5 min), there were reductions in the volumes of the prostate and SVs receiving the prescribed dose (median reduction 0.1% and 1.0%, respectively, p<0.001) and in the minimum dose to 0.1 cm(3) of their volumes (median reduction 0.5 and 1.5 Gy, p<0.001). Of the 46 patients, three patients' prostates and eight patients' SVs did not maintain dose coverage above 70 Gy. Rectal filling correlated with decreased percentage-volume of SV receiving 75.6, 70, and 60 Gy (p<0.02). CONCLUSIONS: The 3-mm intrafractional margin was adequate for prostate dose coverage. However, a significant subset of patients lost SV dose coverage. The rectal volume change significantly affected SV dose coverage. For advanced-stage prostate cancers, we recommend to use larger margins or improve organ immobilization (such as with a rectal balloon) to ensure SV coverage.

Assessment of Collimator Jaw Optimization in Reducing Normal Tissue Irradiation with Intensity Modulated Radiation Therapy

Purpose: To evaluate normal tissue dose reduction in step-and-shoot intensity-modulated radiation therapy (IMRT) on the Varian 2100 platform by tracking the multileaf collimator (MLC) apertures with the accelerator jaws. Methods: Clinical radiation treatment plans for 10 thoracic, 3 pediatric and 3 head and neck patients were converted to plans with the jaws tracking each segment’s MLC apertures. Each segment was then renormalized to account for the change in collimator scatter to obtain target coverage within 1% of that in the original plan. The new plans were compared to the original plans in a commercial radiation treatment planning system (TPS). Reduction in normal tissue dose was evaluated in the new plan by using the parameters V5, V10, and V20 in the cumulative dose-volume histogram for the following structures: total lung minus GTV (gross target volume), heart, esophagus, spinal cord, liver, parotids, and brainstem. In order to validate the accuracy of our beam model, MLC transmission measurements were made and compared to those predicted by the TPS. Results: The greatest change between the original plan and new plan occurred at lower dose levels. The reduction in V20 was never more than 6.3% and was typically less than 1% for all patients. The reduction in V5 was 16.7% maximum and was typically less than 3% for all patients. The variation in normal tissue dose reduction was not predictable, and we found no clear parameters that indicated which patients would benefit most from jaw tracking. Our TPS model of MLC transmission agreed with measurements with absolute transmission differences of less than 0.1 % and thus uncertainties in the model did not contribute significantly to the uncertainty in the dose determination. Conclusion: The amount of dose reduction achieved by collimating the jaws around each MLC aperture in step-and-shoot IMRT does not appear to be clinically significant.

EVALUATION OF INTENSITY MODULATED RADIATION THERAPY (IMRT) DELIVERY ERROR DUE TO IMRT TREATMENT PLAN COMPLEXITY AND IMPROPERLY MATCHED DOSIMETRY DATA

Intensity modulated radiation therapy (IMRT) is a technique that delivers a highly conformal dose distribution to a target volume while attempting to maximally spare the surrounding normal tissues. IMRT is a common treatment modality used for treating head and neck (H&N) cancers, and the presence of many critical structures in this region requires accurate treatment delivery. The Radiological Physics Center (RPC) acts as both a remote and on-site quality assurance agency that credentials institutions participating in clinical trials. To date, about 30% of all IMRT participants have failed the RPC’s remote audit using the IMRT H&N phantom. The purpose of this project is to evaluate possible causes of H&N IMRT delivery errors observed by the RPC, specifically IMRT treatment plan complexity and the use of improper dosimetry data from machines that were thought to be matched but in reality were not. Eight H&N IMRT plans with a range of complexity defined by total MU (1460-3466), number of segments (54-225), and modulation complexity scores (MCS) (0.181-0.609) were created in Pinnacle v.8m. These plans were delivered to the RPC’s H&N phantom on a single Varian Clinac. One of the IMRT plans (1851 MU, 88 segments, and MCS=0.469) was equivalent to the median H&N plan from 130 previous RPC H&N phantom irradiations. This average IMRT plan was also delivered on four matched Varian Clinac machines and the dose distribution calculated using a different 6MV beam model. Radiochromic film and TLD within the phantom were used to analyze the dose profiles and absolute doses, respectively. The measured and calculated were compared to evaluate the dosimetric accuracy. All deliveries met the RPC acceptance criteria of ±7% absolute dose difference and 4 mm distance-to-agreement (DTA). Additionally, gamma index analysis was performed for all deliveries using a ±7%/4mm and ±5%/3mm criteria. Increasing the treatment plan complexity by varying the MU, number of segments, or varying the MCS resulted in no clear trend toward an increase in dosimetric error determined by the absolute dose difference, DTA, or gamma index. Varying the delivery machines as well as the beam model (use of a Clinac 6EX 6MV beam model vs. Clinac 21EX 6MV model), also did not show any clear trend towards an increased dosimetric error using the same criteria indicated above.

Identification of the signal pathways modulated by expression of p210$\rm\sp{bcr-abl}$ and the inhibition of p210$\rm\sp{bcr-abl}$ transforming activity by polypeptides interacting with p210$\rm\sp{bcr-abl}$ in murine myeloid 32D cells

The Bcr-Abl fusion oncogene which resulted from a balanced reciprocal translocation between chromosome 9 and 22, t(9;22)(q11, q34), encodes a 210 KD elevated tyrosine specific protein kinase that is found in more than 95 percent of chronic myelogenous leukemia patients (CML). Increase of level of phosphorylation of tyrosine is observed on cell cycle regulatory proteins in cells overexpressing the Bcr-Abl oncogene, which activates multiple signaling pathways. In addition, distinct signals are required for transforming susceptible fibroblast and hematopoietic cells, and the minimal signals essential for transforming hematopoietic cells are yet to be defined. In the present study, we first established a tetracycline repressible p210$\rm\sp{bcr-abl}$ expression system in a murine myeloid cell line 32D c13, which depends on IL3 to grow in the presence of tetracycline and proliferate independent of IL3 in the absence of tetracycline. Interestingly, one of these sublines does not form tumors in athymic nude mice suggesting that these cells may not be completely transformed. These cells also exhibit a dose-dependent growth and expression of p210$\rm\sp{bcr-abl}$ at varying concentrations of tetracycline in the culture. However, p210$\rm\sp{bcr-abl}$ rescues IL3 deprivation induced apoptosis in a non-dose dependent fashion. DNA genotoxic damage induced by gamma-irradiation activates c-Abl tyrosine kinase, the cellular homologue of p210$\rm\sp{bcr-abl},$ and leads to activation of p38 MAP kinase in the cells. However, in the presence of p210$\rm\sp{bcr-abl}$ the irradiation failed to activate the p38 MAP kinase as examined by an antibody against phosphorylated p38 MAP kinase. Similarly, an altered tyrosine phosphorylation of the JAK1-STAT1 pathways was identified in cells constitutively overexpressing p210$\rm\sp{bcr-abl}.$ This may provided a molecular mechanism for altered therapeutic response of CML patients to IFN-$\alpha.$^ Bcr-Abl oncoprotein has multiple functional domains which have been identified by the work of others. The Bcr tetramerization domain, which may function to stabilize the association of the Bcr-Abl with actin filaments in p210$\rm\sp{bcr-abl}$ susceptible cells, are essential for transforming both fibroblast and hematopoietic cells. We designed a transcription unit encoding first 160 amino acids polypeptide of Bcr protein to test if this polypeptide can inhibit the transforming activity of the p210$\rm\sp{bcr-abl}$ oncoprotein in the 32D c13 cells. When this vector was transfected transiently along with the p210$\rm\sp{bcr-abl}$ expression vector, it can block the transforming activity of p210$\rm\sp{bcr-abl}.$ On the other hand, the retinoblastoma tumor suppressor protein (Rb), a naturally occurring negative regulator of the c-Abl kinase, the cellular homologue of Bcr-Abl oncoprotein, binds to and inhibits the c-Abl kinase in a cell cycle dependent manner. A polypeptide obtained from the carboxyl terminal end of the retinoblastoma tumor suppressor protein, in which the nuclear localization signal was mutated, was used to inhibit the kinase activity of the p210$\rm\sp{bcr-abl}$ in the cytoplasm. This polypeptide, called Rb MC-box, and its wild type form, Rb C-box, when overexpressed in the 32D cells are mainly localized in the cytoplasm. Cotransfection of a plasmid transcription unit coding for this polypeptide and the gene for the p210$\rm\sp{bcr-abl}$ resulted in reduced plating efficiency of p210$\rm\sp{bcr-abl}$ transfected IL3 independent 32D cells. Together, these results may lead to a molecular approach to therapy of CML and an in vitro assay system to identify new targets to which an inhibitory polypeptide transcription unit may be directed. ^

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Hennessy-Milner property. Complete characterizations are obtained in the case of many-valued modal logics based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], including crisp Lukasiewicz, Gödel, and product modal logics.

A critical evaluation of secondary cancer risk models applied to Monte Carlo dose distributions of 2-dimensional, 3-dimensional conformal and hybrid intensity-modulated radiation therapy for breast cancer

The comparison of radiotherapy techniques regarding secondary cancer risk has yielded contradictory results possibly stemming from the many different approaches used to estimate risk. The purpose of this study was to make a comprehensive evaluation of different available risk models applied to detailed whole-body dose distributions computed by Monte Carlo for various breast radiotherapy techniques including conventional open tangents, 3D conformal wedged tangents and hybrid intensity modulated radiation therapy (IMRT). First, organ-specific linear risk models developed by the International Commission on Radiological Protection (ICRP) and the Biological Effects of Ionizing Radiation (BEIR) VII committee were applied to mean doses for remote organs only and all solid organs. Then, different general non-linear risk models were applied to the whole body dose distribution. Finally, organ-specific non-linear risk models for the lung and breast were used to assess the secondary cancer risk for these two specific organs. A total of 32 different calculated absolute risks resulted in a broad range of values (between 0.1% and 48.5%) underlying the large uncertainties in absolute risk calculation. The ratio of risk between two techniques has often been proposed as a more robust assessment of risk than the absolute risk. We found that the ratio of risk between two techniques could also vary substantially considering the different approaches to risk estimation. Sometimes the ratio of risk between two techniques would range between values smaller and larger than one, which then translates into inconsistent results on the potential higher risk of one technique compared to another. We found however that the hybrid IMRT technique resulted in a systematic reduction of risk compared to the other techniques investigated even though the magnitude of this reduction varied substantially with the different approaches investigated. Based on the epidemiological data available, a reasonable approach to risk estimation would be to use organ-specific non-linear risk models applied to the dose distributions of organs within or near the treatment fields (lungs and contralateral breast in the case of breast radiotherapy) as the majority of radiation-induced secondary cancers are found in the beam-bordering regions.

Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods

PURPOSE This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). METHODS As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. RESULTS The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V95% increased from 90% to 96% and V107% decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. CONCLUSIONS MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.