Symmetric Expansion Research Articles

Effect of customized 3D-printed MARPE appliance on hard tissues, soft tissues, and airway: A prospective CBCT study.

The advances in technology have enabled the customization of appliances including mini-screw-assisted rapid palatal expansion (MARPE) appliances for skeletal expansion in young adult patients. The study assessed the short-term effects of customized MARPE appliances on the hard tissues, soft tissues, and airway volume over a period of 6 months. A total of 15 patients in the age range of 15 to 25 years were treated for transverse maxillary deficiency using a three-dimensional (3D) printed customized MARPE appliance. The changes in hard tissues, soft tissues, and airway volume were evaluated using cone beam computed tomography before expansion (T0) and at 6 months post-expansion (T1). The Digital Imaging and Communications in Medicine files were analyzed for post-expansion changes using the NemoCeph 3D and 3D Slicer 5.6.1 software. An effective skeletal expansion was observed with significant changes in intercanine, interpremolar, and intermolar width; and decreased mid-palatal suture density in the anterior region (P < .05). The changes in tooth inclination and alveolar bone thickness were mostly non-significant apart from a significant decrease in buccal bone thickness in the coronal third region (P < .05). There was no significant root resorption or change in airway volumes (P > .05). The philtrum height increased significantly by 1.17 mm (P = .019) with no significant change on right and left sides. Rapid palatal expansion with 3D-printed customized MARPE enables effective and symmetrical expansion with a significant increase in philtrum height and no significant adverse effects in terms of alveolar bone thickness, dental inclination, root resorption, and airway volumes.

Symmetric and Asymmetric Expansion of the Weibull Distribution: Features and Applications to Complete, Upper Record, and Type-II Right-Censored Data

This paper introduces a new continuous lifetime model called the Odd Flexible Weibull-Weibull (OFW-W) distribution, which features three parameters. The new model is capable of modeling both symmetric and asymmetric datasets, regardless of whether they are positively or negatively skewed. Its hazard rate functions can exhibit various behaviors, including increasing, decreasing, unimodal, or bathtub-shaped. The key characteristics of the OFW-W model are discussed, including the quantile function, median, reliability and hazard rate functions, kurtosis and skewness, mean waiting (residual) lifetimes, moments, and entropies. The unknown parameters of the model are estimated using eight different techniques. A comprehensive simulation study evaluates the performance of these estimators based on bias, mean squared error (MSE), and mean relative error (MRE). The practical usefulness of the OFW-W distribution is demonstrated through four real datasets from the fields of engineering and medicine, including complete data, upper record data, and type-II right-censored data. Comparisons with five other lifetime distributions reveal that the OFW-W model exhibits superior flexibility and capability in fitting various data types, highlighting its advantages and improvements. In conclusion, we anticipate that the OFW-W model will prove valuable in various applications, including human health, environmental studies, reliability theory, actuarial science, and medical sciences, among others.

Symmetrical and asymmetrical surface structure expansions of silver nanoclusters with atomic precision.

Controlling symmetrical or asymmetrical growth has allowed a series of novel nanomaterials with prominent physicochemical properties to be produced. However, precise and continuous size growth based on a preserved template has long been a challenging pursuit, yet little has been achieved in terms of manipulation at the atomic level. Here, a correlated silver cluster series has been established, enabling atomically precise manipulation of symmetrical and asymmetrical surface structure expansions of metal nanoclusters. Specifically, the C 3-axisymmetric Ag29(BDTA)12(PPh3)4 nanocluster underwent symmetrical and asymmetrical surface structure expansions via an acid-mediated synthetic procedure, giving rise to C 3-axisymmetric Ag32(BDTA)12(PPh3)10 and C 1-axisymmetric Ag33(BDTA)12(PPh3)11, respectively. In addition, structural transformations, including structural degradation from Ag32 to Ag29 and asymmetrical structural expansion from Ag32 to Ag33, were rationalized theoretically. More importantly, the asymmetrically structured Ag33 nanoclusters followed a chiral crystallization mode, and their crystals displayed high optical activity, derived from CD and CPL characterization. This work not only provides an important model for unlocking the symmetrical/asymmetrical size growth mechanism at the atomic level but also pioneers a promising approach to activate the optical activity of cluster-based nanomaterials.

Initiating Mechanical Ventilation in Critically Ill Patients: Case-based Clinical Review

Abstract Mechanical Ventilation continues to be an integral part of critical care on which patients with respiratory failure often depend on for their survival. Specific criteria that need to be met to justify initiating MV include a patient dependency assessment, a clinical indication as well as the ventilator settings that are most appropriate. Hypoxemic respiratory failure, hypercapnic respiratory failure and the need for airway protection are the common indications to initiate MV. This review uses case-based to discuss the initiation of MV. Some of the clinical use settings include Acute Respiratory Distress Syndrome (ARDS), Pneumonia, Chronic Obstructive Pulmonary Disease (COPD) exacerbations, Trauma with altered mental status. Specific scenarios of patients, clinical management and intervention measures are described for every condition to help with the best approach. The review placed special focus on assessment before intubation, the type of mechanical ventilation to choose-VCV or PCV, and the settings to be used: TVs, RR, PEEP and FiO2. Further, it highlights the topic of focussed monitoring, common ventilator problems, and the Weaning phase from MV. The review outlines certain well-documented antecedent knowledge failures of young medicos and also intensivists that need to be corrected in their curriculums for enhancing their ventilator management competencies. Knowledge of MV initiation, strict supervision, and preparation for the cessation of MV is important in order to enhance the results of the patients within the Intensive Care Unit. It is mandatory and more important to see clinical signs like bilateral symmetric chest expansion than looking at the values on the ventilator alone. The presented case-based examples provide practical translation of theoretical information into the clinical practice and enhance the development of the clinical decision-making in the framework of critical care medicine. We definitely need a curriculum integration to decrease the phobia among the new entrants to the intensive care unit whether its medical or paramedical personnel.

Intrinsic Muscle Stem Cell Dysfunction Contributes to Impaired Regeneration in the mdx Mouse.

Duchenne muscular dystrophy (DMD) is a devastating disease characterized by progressive muscle wasting that leads to diminished lifespan. In addition to the inherent weakness of dystrophin-deficient muscle, the dysfunction of resident muscle stem cells (MuSC) significantly contributes to disease progression. Using the mdx mouse model of DMD, we performed an in-depth characterization of disease progression and MuSC function in dystrophin-deficient skeletal muscle using immunohistology, isometric force measurements, transcriptomic analysis and transplantation assays. We examined the architectural and functional changes in mdx skeletal muscle from 13 and 52 weeks of age and following acute cardiotoxin (CTX) injury. We also studied MuSC dynamics and function under homeostatic conditions, during regeneration post-acute injury, and following engraftment using a combination of histological and transcriptomic analyses. Dystrophin-deficient skeletal muscle undergoes progressive changes with age and delayed regeneration in response to acute injury. Muscle hypertrophy, deposition of collagen and an increase in small myofibres occur with age in the tibialis anterior (TA) and diaphragm muscles in mdx mice. Dystrophic mdx mouse TA muscles become hypertrophic with age, whereas diaphragm atrophy is evident in 1-year-old mdx mice. Maximum tetanic force is comparable between genotypes in the TA, but maximum specific force is reduced by up to 38% between 13 and 52 weeks in the mdx mouse. Following acute injury, myofibre hyperplasia and hypotrophy and delayed recovery of maximum tetanic force occur in the mdx TA. We also find defective MuSC polarity and reduced numbers of myocytes in mdx muscle following acute injury. We observed a 50% and 30% decrease in PAX7+ and MYOG+ cells, respectively, at 5 days post CTX injury (5 dpi) in the mdx TA. A similar decrease in mdx progenitor cell proportion is observed by single cell RNA sequencing of myogenic cells at 5 dpi. The global expression of commitment-related genes is also reduced at 5 dpi. We find a 46% reduction in polarized PARD3 in mdx MuSCs. Finally, mdx MuSCs exhibit elevated PAX7+ cell engraftment with significantly fewer donor-derived myonuclei in regenerated myofibres. Our study provides evidence that dystrophin deficiency in MuSCs and myofibres together contributes to progression of DMD. Ongoing muscle damage stimulates MuSC activation; however, aberrant intrinsic MuSC polarity and stem cell commitment deficits due to the loss of dystrophin impair muscle regeneration. Our study provides invivo validation that dystrophin-deficient MuSCs undergo fewer asymmetric cell divisions, instead favouring symmetric expansion.

A Two-Dimensional Planar Fracture Network Model for Broken Rock Mass Based on Packer Test and Fractal Dimension

Broken rock masses with the complexity and concealment widely exist in nature such as underground mine, collapse column, and zone. It is extremely difficult to model fracture networks and to simulate water diffusion for broken rock masses. To explore a reasonable fracture network model for broken rock masses, a new method for modeling a two-dimensional planar fracture network model is proposed in this paper. It includes packer test, empirical relationship, fractal width description, and symmetric expansion modeling. Then, the fluid-solid coupling is used to simulate the diffusion properties of water in the two-dimensional planar fracture network model. It is found that the diffusion velocities vmax and vmin do not appear in the fracture widths λmax and λmin. It indicates that the fracture widths λmax and λmin in the fracture network model for broken rock mass have little impact on the diffusion velocity. Furthermore, the fracture distribution pattern in the fracture network model is an important factor affecting the diffusion velocities vmax and vmin. The simulation results of water diffusion in the currently proposed model are almost consistent with the actual process of the packer test. Also, the validity of the two-dimensional planar fracture network model is verified by comparing the simulation results with the existing research.

On a New Two-Point Taylor Expansion With Applications

A new two-point Taylor series expansion is proposed. The expansion is slightly different than the classical definition. The coefficients are calculated as recursive relations in a general form. The two-point Taylor expansion is applied to several functions which are odd, even, neither odd nor even. Functions having finite interval of convergence or infinite interval of convergence are investigated. The conditions for convergence are derived and the results are compared with the results of single-point Taylor expansions as well as two-point Taylor expansions reported in the literature. It is found that for a finite radius of convergence, two-point Taylor expansions can have a single convergence interval as well as two separate convergence intervals. Generally speaking, two-point Taylor expansions better represent the real function when the series is truncated. The new two-point expansion and the classical two-point expansion produced identical results for all the problems treated. Based on the results of this analysis, the asymmetric two-point Taylor expansion presented here does not have an advantage compared to the classical symmetric expansion. An application of the series to solution of a variable coefficient differential equation is also treated.

Disruption Mechanisms of Enveloped Viruses by Ionic and Nonionic Surfactants.

The world has witnessed multiple pandemics and endemics caused by enveloped viruses in the past century. To name a few, the ongoing COVID-19 pandemic and other pandemics/endemics caused by coronaviruses, influenza viruses, HIV-1, etc. The external and topical applications of surfactants have been effective in limiting the spread of viruses. While it is well-known that surfactants inactivate virus particles (virions), the mechanism of action of surfactants against enveloped virions has not yet been established. In this work, we have evaluated the surfactant-induced disruption mechanism of a cocktail of enveloped viruses containing particles of mumps, measles, and rubella viruses. We applied the total internal reflection fluorescence microscopy technique to trace the temporal changes in the fluorescence signal from single virions upon the addition of a surfactant solution. We report that surfactants solubilize either the viral lipid membrane, proteins, or both. Ionic surfactants, depending on their charge and interaction type with the viral lipids and proteins, can cause bursting or perforation of the viral envelope, whereas a nonionic surfactant can cause either symmetric expansion or perforation of the viral envelope depending on the surfactant concentration.

Delta and Theta Operator Expansions

Abstract We give an elementary symmetric function expansion for the expressions $M\Delta _{m_\gamma e_1}\Pi e_\lambda ^{\ast }$ and $M\Delta _{m_\gamma e_1}\Pi s_\lambda ^{\ast }$ when $t=1$ in terms of what we call $\gamma $ -parking functions and lattice $\gamma $ -parking functions. Here, $\Delta _F$ and $\Pi $ are certain eigenoperators of the modified Macdonald basis and $M=(1-q)(1-t)$ . Our main results, in turn, give an elementary basis expansion at $t=1$ for symmetric functions of the form $M \Delta _{Fe_1} \Theta _{G} J$ whenever F is expanded in terms of monomials, G is expanded in terms of the elementary basis, and J is expanded in terms of the modified elementary basis $\{\Pi e_\lambda ^\ast \}_\lambda $ . Even the most special cases of this general Delta and Theta operator expression are significant; we highlight a few of these special cases. We end by giving an e-positivity conjecture for when t is not specialized, proposing that our objects can also give the elementary basis expansion in the unspecialized symmetric function.

Muscle stem cell dysfunction in rhabdomyosarcoma and muscular dystrophy.

Muscle stem cells (MuSCs) are crucial to the repair and homeostasis of mature skeletal muscle. MuSC dysfunction and dysregulation of the myogenic program can contribute to the development of pathology ranging from cancers like rhabdomyosarcoma (RMS) or muscle degenerative diseases such as Duchenne muscular dystrophy (DMD). Both diseases exhibit dysregulation at nearly all steps of myogenesis. For instance, MuSC self-renewal processes are altered. In RMS, this leads to the creation of tumor propagating cells. In DMD, impaired asymmetric stem cell division creates a bias towards producing self-renewing stem cells instead of committing to differentiation. Hyperproliferation of these cells contribute to tumorigenesis in RMS and symmetric expansion of the self-renewing MuSC population in DMD. Both diseases also exhibit a repression of factors involved in terminal differentiation, halting RMS cells in the proliferative stage and thus driving tumor growth. Conversely, the MuSCs in DMD exhibit impaired differentiation and fuse prematurely, affecting myonuclei maturation and the integrity of the dystrophic muscle fiber. Finally, both disease states cause alterations to the MuSC niche. Various elements of the niche such as inflammatory and migratory signaling that impact MuSC behavior are dysregulated. Here we show how these seemingly distantly related diseases indeed have similarities in MuSC dysfunction, underlying the importance of considering MuSCs when studying the pathophysiology of muscle diseases.

Numerical investigation on self-propelled hydrodynamics of squid-like multiple tentacles with synergistic expansion

Cephalopods, such as squids, have versatile swimming mechanisms that allow them to adapt to complex underwater environments. Their primary means of propulsion are funnel jets, whereas coordinating soft wrists are often overlooked. The purpose of this study is to provide tentacles at the end of a squid-like robot with a circular symmetric expansion based on the traveling wave motion law and analyze the effects of the number, frequency and expansion amplitude of tentacles on its self-propelled performance. The geometry of the aquatic squid and flexible posterior segment including three joints are considered to be the key features. Overlapping grids of hole cutting technique are applied to manipulate virtual swimmers and simulate incompressible viscous flow. The results indicate that the three-tentacled squid has the best propulsion performance, and excessive tentacles cannot unilaterally enhance propulsion. The increase in frequency can be effectively mapped as an increase in the steady-state velocity coefficient and propulsion efficiency, whereas the maximum amplitude of the tentacle bending could only be raised within a certain range, and excessive bending may be counterproductive. The corresponding flow structure can indirectly reveal the evolution process of the multi-tentacled expansion performance.

Double neutron star formation via consecutive type II supernova explosions

ABSTRACT Since the discovery of the first double neutron star (DNS) system, the number of these exotic binaries has reached 15. Here we investigate a channel of DNS formation in binary systems with components above the mass limit of Type II supernova explosion (SN II), that is, 8M⊙. We apply a spherically symmetric homologous envelope expansion model to account for mass-loss, and follow the dynamical evolution of the system numerically with a high-precision integrator. The first SN occurs in a binary system whose orbital parameters are pre-defined, then, the homologous expansion model is applied again in the newly formed system. Analysing 1 658 880 models we find that DNS formation via subsequent SN II explosions requires a fine-tuning of the initial parameters. Our model can explain DNS systems with a separation greater than 2.95 au. The eccentricity of the DNS systems spans a wide range thanks to the orbital circularization effect due to the second SN II explosion. The eccentricity of the DNS is sensitive to the initial eccentricity of the binary progenitor and the orbital position of the system preceding the second explosion. In agreement with the majority of the observations of DNS systems, we find the system centre-of-mass velocities to be less than 60 km s−1. Neutron stars that become unbound in either explosion gain a peculiar velocity in the range of 0.02 − 240 km s−1. In our model, the formation of tight DNS systems requires a post-explosion orbit-shrinking mechanism, possibly driven by the ejected envelopes.

Performance of double expansion ramp nozzle

Additional thrust gained by expanding the supersonic stream emerging from a convergent–divergent (C–D) nozzle through a symmetric double expansion ramp nozzle (DERN) connected to the nozzle is experimentally investigated. Thrust augmentation caused by the DERN of design Mach number 3.5 attached to a full and a half convergent–divergent (C–D) nozzle of design Mach number 1.5 is studied. The nozzle pressure ratios (NPRs) studied are 3, 4, 5, 5.45, and 6. The ramp angles of the symmetric double expansion ramp nozzle studied were 18° and 22°. It is found that an additional thrust of around 44% can be derived with the DERN in the presence of a favorable gradient of +36%, corresponding to NPR 5.

GCCSwin-UNet: Global Context and Cross-Shaped Windows Vision Transformer Network for Polyp Segmentation

Accurate polyp segmentation is of great importance for the diagnosis and treatment of colon cancer. Convolutional neural networks (CNNs) have made significant strides in the processing of medical images in recent years. The limited structure of convolutional operations prevents CNNs from learning adequately about global and long-range semantic information interactions, despite the remarkable performance they have attained. Therefore, the GCCSwin-UNet framework is suggested in this study. Specifically, the model utilizes an encoder–decoder structure, using the patch-embedding layer for feature downsampling and the CSwin Transformer block as the encoder for contextual feature extraction. To restore the feature map’s spatial resolution during upsampling operations, a symmetric decoder and patch expansion layer are also created. In order to help the backbone module to do better feature learning, we also create a global context module (GCM) and a local position-enhanced module (LPEM). We conducted extensive experiments on the Kvasir-SEG and CVC-ClinicDB datasets, and compared them with existing methods. GCCSwin-UNet reached remarkable results with Dice and MIoU of 86.37% and 83.19% for Kvasir-SEG, respectively, and 91.26% and 84.65% for CVC-ClinicDB, respectively. Finally, quantitative analysis and statistical tests are applied to further demonstrate the validity and plausibility of our method.

Stochastic fate decisions of HSCs after transplantation: early contribution, symmetric expansion, and pool formation

AbstractHematopoietic stem cells (HSCs) are assumed to be rare, infrequently dividing, long-lived cells not involved in immediate recovery after transplantation. Here, we performed unprecedented high-density clonal tracking in nonhuman primates and found long-term persisting HSC clones to actively contribute during early neutrophil recovery, and to be the main source of blood production as early as 50 days after transplantation. Most surprisingly, we observed a rapid decline in the number of unique HSC clones, while persisting HSCs expanded, undergoing symmetric divisions to create identical siblings and formed clonal pools ex vivo as well as in vivo. In contrast to the currently assumed model of hematopoietic reconstitution, we provide evidence for contribution of HSCs in short-term recovery as well as symmetric expansion of individual clones into pools. These findings provide novel insights into HSC biology, informing the design of HSC transplantation and gene therapy studies.

Study of maximum electron energy of sub-PeV pulsar wind nebulae by multiwavelength modelling

ABSTRACTRecently, the Large High Altitude Air Shower Observatory (LHAASO) reported the discovery of 12 ultrahigh-energy (UHE; ε ≥ 100 TeV) gamma-ray sources located in the Galactic plane. A few of these UHE gamma-ray emitting regions are in spatial coincidence with pulsar wind nebulae (PWNe). We consider a sample of five sources: two of them are LHAASO sources (LHAASO J1908+0621 and LHAASO J2226+6057) and the remaining three are GeV–TeV gamma-ray emitters. In addition, X-rays, radio observations, or upper limits are also available for these objects. We study multiwavelength radiation from these sources by considering a PWN origin, where the emission is powered by spin-down luminosity of the associated pulsars. In this Leptonic emission model, the electron population is calculated at different times under the radiative (synchrotron and inverse-Compton) and adiabatic cooling. We also include the onset of the reverberation phase for the PWN, by assuming radially symmetric expansion. However, in this work, we find that multiwavelength emission can be interpreted before the onset of this phase. The maximum energy of the electrons based on the spectral fit is found to be above 0.1 PeV and close to 1 PeV. For LHAASO J2226+6057, using its observations in radio to UHE gamma-rays, we find that UHE gamma-rays can be interpreted using electrons with maximum energy of 1 PeV. We estimate the upper limits on the minimum Lorentz factor of the electrons and it also infers the minimum value of the pair-multiplicity of charged pairs.

Preliminary Evaluation of PTV Margins for Online Adaptive Radiation Therapy of the Prostatic Fossa

In modern trials, traditional planning target volume (PTV) margins for postoperative prostate radiation therapy have been large (7-10 mm) to account for both daily changes in patient positioning and target deformation. With daily adaptive radiation therapy, these interfractional changes could be minimized, potentially reducing the margins required for treatment and improving adjacent normal-tissue dosimetry. A single-center retrospective study was conducted from March 2021 to November 2021. Patients receiving conventionally fractionated postoperative radiation therapy (PORT) for prostate cancer with pretreatment and posttreatment cone beam computed tomography (CBCT) imaging (pre-CBCT and post-CBCT, respectively) were included (248 paired images). Pretreatment and posttreatment clinical target volumes (pre-CTVs and post-CTVs) were contoured by a single observer on all CBCTs and verified by a second observer. Motion was calculated from pre-CTV to that of the post-CTV, and predicted margins were calculated with van Herk's formula. Adequate coverage of the proposed planning target volume (PTV) margin expansions (pre-PTV) were verified by determining overlap with post-CTV. In a smaller cohort (25 paired images), dosimetric changes with the proposed online adaptive margins were compared with conventional plans in the Ethos emulator environment. The estimated margins predicted to achieve ≥95% CTV coverage for 90% of the population were 1.6 mm, 2.0 mm, and 2.2 mm (x-, y-, and z -xes, respectively), with 95% of the absolute region of interest displacement being within 1.9 mm, 2.8 mm, and 2.1 mm. After symmetrically expanding all pre-CTVs by 3 mm, the percentage of paired images achieving ≥95% CTV coverage was 97.1%. When comparing adaptive plans (3-mm margins) with scheduled plans (7-mm margins), rectum dosimetry significantly improved, with an average relative reduction in V40Gy[cc] of 59.2% and V65Gy[cc] of 79.5% (where V40Gy and V65Gy are defined as the volumes receiving 40 Gy and 65 Gy or higher dose, respectively). Online daily adaptive radiation therapy could significantly decrease PTV margins for prostatic PORT and improve rectal dosimetry, with a symmetrical expansion of 3 mm achieving excellent coverage in this cohort. These results need to be validated in a larger prospective cohort.

Asymmetric deformation of the Earth’s magnetosphere under low Alfvén Mach number solar wind: Observations and MHD simulation

AbstractThe density of the solar wind plasma near the Earth’s magnetosphere sometimes decreases to only several per cent of the usual value, and such density extrema result in a significant reduction of the dynamic pressure and Alfvén Mach number ($$M_A$$ M A ) of the solar wind flow. While a symmetric expansion of the Earth’s magnetosphere by the low dynamic pressure was assumed in previous studies, a global magnetohydrodynamic (MHD) simulation study predicted a remarkable dawn-dusk asymmetry of the magnetospheric shape under low-density solar wind and Parker-spiral interplanetary magnetic field (IMF) configuration. Here, we present observations consistent with the asymmetric deformation of the magnetosphere under low-$$M_A$$ M A solar wind and Parker-spiral IMF conditions, focusing on the significant expansion of the dawn-flank magnetosphere detected by the Geotail spacecraft. A global MHD simulation reproduced the dawnward expansion of the near-Earth magnetosphere, which was consistent with the observation by Geotail. The solar wind flow had a non-negligible dusk-to-dawn component and partly affected the dawnward expansion of the magnetosphere. Local, roughly Alfvénic sunward acceleration of magnetosheath ions at the dawn flank magnetopause suggests magnetosheath plasma entry into the magnetosphere through open field lines generated by magnetic reconnection at the dayside magnetopause. At the same time, Cluster 1 and 3, located near the southern polar cusp, also detected continuous antisunward ion jets and occasional sunward jets, which are consistent with the occurrence of magnetic reconnection near the southern cusp. These observations suggest that enhanced plasma acceleration at the dayside magnetopause operates under the low-$$M_A$$ M A solar wind and Parker spiral IMF conditions and that plasma influx across the dawnside magnetopause is at work under such a low-$$M_A$$ M A condition. These results can be helpful in understanding interactions between low-$$M_A$$ M A solar/stellar winds and celestial objects, such as inner planets and exoplanets. Graphic Abstract

Locality and analyticity of the crossing symmetric dispersion relation

This paper discusses the locality and analyticity of the crossing symmetric dispersion relation (CSDR). Imposing locality constraints on the CSDR gives rise to a local and fully crossing symmetric expansion of scattering amplitudes, dubbed as Feynman block expansion. A general formula is provided for the contact terms that emerge from the expansion. The analyticity domain of the expansion is also derived analogously to the Lehmann-Martin ellipse. Our observation of type-II super-string tree amplitude suggests that the Feynman block expansion has a bigger analyticity domain and better convergence.

Comparison of Nodal CTV Coverage with Alignment to Bladder-Rectal Interface vs. Pelvic Bone in Post-Prostatectomy Radiotherapy

<h3>Purpose/Objective(s)</h3> In patients receiving post-prostatectomy radiation therapy (RT), daily image guidance is used to align to the bladder-rectal interface (BRI) which varies depending on bladder and rectal filling. Alignment to pelvic bone is often used for nodal irradiation targets. The impact of alignment prioritized to the BRI on coverage of concurrent nodal targets is unknown. We hypothesized that the nodal clinical target volume (CTVn) would remain within nodal planning target volume (PTV) expansions with alignment to BRI versus bone. <h3>Materials/Methods</h3> Cone-beam CTs (CBCT) from patients receiving prostate bed RT using a 6 degrees of freedom couch were analyzed using transformation matrices to calculate differences in offsets. The CBCTs with translational offsets of ≥5mm were further evaluated for impact on nodal coverage. The CTVn was contoured according to consensus guidelines and two PTVs generated, using 5 and 7mm symmetric expansions (PTV5=5mm and PTV7=7mm) on the treatment planning CT. Each CBCT of interest was extended superiorly to evaluate the full nodal volumes. Two separate registrations of each CBCT to the treatment planning CT were performed, one with alignment prioritized to the BRI and the other to pelvic bone. The CTVn and PTVs were copied to each CBCT registration (BRI and bone) for analysis (e.g., PTVn_BRI is where the planned nodal dose is delivered when the treatment is matched to BRI). The inclusion of the CTVn within each PTV was evaluated. Boolean functions were used to compare the overlap and intersections of the nodal volumes between alignment to BRI versus bone. <h3>Results</h3> A set of 139 CBCTs from 14 patients were initially evaluated, of which 13 CBCTs had maximal translational offsets of ≥5mm. The mean CTVn was 324.3cc, PTV5 was 655.2cc, and PTV7 was 801.4cc. When alignment to the BRI was prioritized, the CTVn was completely included within the PTV7 in 9 of 13 CBCTs. At least 95% of the CTVn was within the PTV5 or PTV7 in all but one CBCT in which 92% of the CTVn was within the PTV5. The volume of the CTVn outside the PTV5 ranged from 2.7-28.4cc (mean 2.6%, range 0.6-8%) and outside the PTV7 from 0-15.4cc (mean 0.7%, range 0-4.3%). The most common location for incomplete inclusion of the CTVn within the PTV was in the most caudal and posterior nodal regions (between the prostate bed and the presacral space), primarily occurring in the event of pitch related mismatch between BRI and bone alignment. When the intersection between PTV_(bone) and PTV_(BRI) was evaluated, the overlap ranged between 80-98% and did not differ between comparisons for 5 and 7mm expansions. <h3>Conclusion</h3> These data from CBCTs with translational offsets of ≥5mm suggest that even with larger disagreement between alignment to BRI versus bone, the vast majority of the CTVn remains encompassed within the PTV, particularly when a 7mm expansion is used. The predominant site of incomplete inclusion raises concern about use of smaller posterior nodal PTV margins. These results are informative for concurrent prostate bed and nodal irradiation.