Relaxation Schemes for the $M_1$ Model with Space-Dependent Flux: Application to Radiotherapy Dose Calculation

Because of stability constraints, most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the $M_1$ system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the $M_1$ system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the $M_1$ system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.     

Numerical Bifurcation Methods and Their Application to Fluid Dynamics: Analysis Beyond Simulation

We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated withthese transitions, popularly referred to as 'tipping points', is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.     

In Vivo Intraoperative Radiotherapy: A Novel Approach to Radiotherapy for Early Stage Breast Cancer

Introduction Intraoperative radiotherapy (IORT) has the potential to eliminate the access problems associated with standard 6-week post-operative external beam radiotherapy for patients with breast cancer. However, accurate delivery of the IORT dose for breast cancer has been problematic due to difficulty estimating the tumor bed after tumor removal and tissue reapproximation. We are investigating the feasibility of partial breast irradiation using a single fraction of IORT delivered to the tumor in vivo prior to surgical resection. Methods In a trial, approved by the University of North Carolina School of Medicine Institutional Review Board, patients ≥55 years old with infiltrating ductal carcinoma without an extensive intraductal component with an overall tumor size ≤3.0 cm receive a single dose of IORT in place of standard post-operative radiotherapy. Results All patients undergo preoperative ultrasonography to define the target volume. In a standard operating room, the tumor is exposed through a standard partial mastectomy incision. IORT is then delivered using a mobile, self-shielded, magnetron-driven X-band linear accelerator (Intraop Corp, Santa Clara, CA, USA). 15 Gy is delivered to the 90% isodose line covering the tumor with a 1 cm margin anterior–posterior and 2 cm margins laterally. After IORT, partial mastectomy is performed in the usual manner. Conclusions IORT for breast cancer, delivered to the exposed tumor in vivo, is feasible and allows accurate estimation of the tumor bed. Further follow-up is ongoing to determine the efficacy of this approach. Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Adaptive Bayesian Inference for Discontinuous Inverse Problems,Application to Hyperbolic Conservation Laws

Various works from the literature aimed at accelerating Bayesian inference in inverse problems. Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution. These representations are efficient because they allow affordable simulation of a large number of samples from the posterior distribution. Unfortunately, they do not perform well when the forward model exhibits strong nonlinear behavior with respect to its input.In this work, we first relate the fast (exponential) $L^2$-convergence of the forward approximation to the fast (exponential) convergence (in terms of Kullback-Leibler divergence) of the approximate posterior. In particular, we prove that in case the prior distribution is uniform, the posterior is at least twice as fast as the convergence rate of the forward model in those norms. The Bayesian inference strategy is developed in the framework of a stochastic spectral projection method. The predicted convergence rates are then demonstrated for simple nonlinear inverse problems of varying smoothness.We then propose an efficient numerical approach for the Bayesian solution of inverse problems presenting strongly nonlinear or discontinuous system responses. This comes with the improvement of the forward model that is adaptively approximated by an iterative generalized Polynomial Chaos-based representation. The numerical approximations and predicted convergence rates of the former approach are compared to the new iterative numerical method for nonlinear time-dependent test cases of varying dimension and complexity, which are relevant regarding our hydrodynamics motivations and therefore regarding hyperbolic conservation laws and the apparition of discontinuities in finite time.     

A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations

A concept of "static reconstruction" and "dynamic reconstruction" was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a "hybrid reconstruction" approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as "dynamic reconstruction"), while the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.     

A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations

We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2×2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.     

Ability to Detect Change in Patient Function: Responsiveness Designs and Methods of Calculation

In hand clinics, the goal of enabling patient improvement is fostered by the use of assessments with the ability to detect change (responsiveness). Thus, for commonly used assessments, investigations are needed to determine a standardized change index, the amount of change exceeding error estimates (minimal detectable change or MDC), and the amount of change shown to make a clinically relevant difference (clinically important difference or CID). The purpose of study was to serve as an introduction for hand therapists to responsiveness designs and indices and to highlight their application within the clinical setting. The study design used was a narrative review. Method papers and research studies addressing responsiveness were selected and summarized. Currently, several good studies of responsiveness have been conducted. However, there is a need to move beyond the calculation of standardized change indices to include the calculation of clinically meaningful values. For many of the assessments used in hand clinics, there is still a call for investigation of the amount of change, which exceeds error estimates (MDC) and the amount of change shown to make a clinically relevant difference (CID).Level of EvidenceN/A.     

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

We propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions. Since the derivation is based on a semi-implicit time discretization, this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method. As an interesting application of the numerical approach, we propose a new variational approach for extracting limit cycles in dynamical systems. The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles. Further, we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.     

Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

We present quantum numerical methods for the typical initial boundaryvalue problems (IBVPs) of convection-diffusion equations in fluid dynamics. The IBVPis discretized into a series of linear systems via finite difference methods and explicittime marching schemes. To solve these discrete systems in quantum computers, wedesign a series of quantum circuits, including four stages of encoding, amplification,adding source terms, and incorporating boundary conditions. In the encoding stage,the initial condition is encoded in the amplitudes of quantum registers as a state vectorto take advantage of quantum algorithms in space complexity. In the following threestages, the discrete differential operators in classical computing are converted into unitary evolutions to satisfy the postulate in quantum systems. The related arithmeticcalculations in quantum amplitudes are also realized to sum up the increments fromthese stages. The proposed quantum algorithm is implemented within the open-sourcequantum computing framework Qiskit [2]. By simulating one-dimensional transientproblems, including the Helmholtz equation, the Burgers’ equation, and Navier-Stokesequations, we demonstrate the capability of quantum computers in fluid dynamics.     

Rapid Tracheal Intubation with Rocuronium: A probability Approach to Determining Dose

Background: Rapid tracheal intubation with rocuronium has not been studied using a probability-based approach. The authors aimed to predict doses of rocuronium giving 90% and 95% probability of intubation within 60 s and to estimate their durations of action.

Methods: After premedication with midazolam, 2 mg, anesthesia was induced in 80 subjects with fentanyl, 2 [micro sign]g/kg, followed 3 min later by propofol, 2 mg/kg. Patients received randomly rocuronium, 0.0, 0.4, 0.8, or 1.2 mg/kg (n = 20/dose). Laryngoscopy began 40 s later, aiming for intubation at 60 s, and conditions were graded perfect, acceptable, or unacceptable, with the first two conditions being successful intubation. Anesthesia was maintained with isoflurane 0.5-1.0% (end-tidal) and fentanyl. Duration of action was time until reappearance of the first tactile train-of-four response. The dose versus fraction of patients with successful intubation was analyzed by logistic regression. Doses giving 90% and 95% (D (90) and D95) probability of successful intubation were calculated.

Results: Intubation was successful in 7, 11, 18, and 19 patients in the 0.0, 0.4, 0.8, and 1.2 mg/kg groups, respectively. The D90 and D95 doses (95% confidence limits in parentheses) were 0.83 (0.59-1.03) and 1.04 (0.76-1.36) mg/kg, respectively. Estimated time until first tactile train-of-four response after D90 and D95 doses was 32 and 46 min, respectively.     

Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls

We propose and analyse finite volume Godunov type methods based on discontinuous flux for a 2×2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The problem considered here is the so-called partially open table problem where sand is blocked by a wall (of infinite height) on some part of the boundary of the table. The novelty here is the corresponding modification of boundary conditions for the standing and the rolling layers and generalization of the techniques of the well-balancedness proposed in [1]. Presence of walls may lead to unbounded or discontinuous surface flow density at equilibrium resulting in solutions with singularities propagating from the extreme points of the walls. A scheme has been proposed to approximate efficiently the Hamiltonians with the coefficients which can be unbounded and discontinuous. Numerical experiments are presented to illustrate that the proposed schemes detect these singularities in the equilibrium solutions efficiently and comparisons are made with the previously studied finite difference and Semi-Lagrangian approaches by Finzi Vita et al.     

Assessment of Heat Flux Prediction Capabilities of Residual Distribution Method: Application to Atmospheric Entry Problems

In the present contribution we evaluate the heat flux prediction capabilities of second-order accurate Residual Distribution (RD ) methods in the context of atmospheric (re-)entry problems around blunt bodies. Our departing point is the computation of subsonic air flows (with air modeled either as an inert ideal gas or as chemically reacting and possibly out of thermal equilibrium gas mixture) around probe-like geometries, as those typically employed into high enthalpy wind tunnels. We confirm the agreement between the solutions obtained with the RD method and the solutions computed with other Finite Volume (FV ) based codes.However, a straightforward application of the same numerical technique to hypersonic cases involving strong shocks exhibits severe deficiencies even on a geometry as simple as a 2D cylinder. In an attempt to mitigate this problem, we derive new variants of RD schemes. A comparison of these alternative strategies against established ones allows us to derive a diagnose for the shortcomings observed in the traditional RD schemes.     

High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ("High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks", CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. One of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.     

Radiotherapy for nonfunctioning pituitary adenomas: from conventional to modern stereotactic radiation techniques

The initial management of nonfunctioning pituitary macroadenomas (NFAs) is usually surgery; however, a significant proportion of NFAs may require further treatment. Radiotherapy is currently used in patients with residual tumour and achieves excellent long-term control, but there are concerns about potential late toxicity. Stereotactic radiotherapy, both in the form of radiosurgery or fractionated stereotactic radiotherapy, has been developed as a more accurate technique of irradiation with more precise tumour localization and consequently a reduction in the volume of normal tissue, particularly the brain, irradiated to high radiation doses. A review of the literature suggests that new radiation techniques offer safe and effective treatment for recurrent or residual pituitary adenomas; however longer follow-up is necessary to confirm the excellent tumour control and the potential reduction of long-term radiation toxicity. Currently, radiotherapy has an important role in patients with residual or progressive disease after surgery. Patients with small or no residual tumours after surgery may generally continue on a policy of surveillance without immediate irradiation, in order to avoid the potential toxicity of treatment.     

Neoadjuvant Radiotherapy for Rectal Cancer: Adherence to Evidence-Based Guidelines in Clinical Practice

Background

Implementation of evidence-based standards is problematic. Level 1 evidence, largely predicated on the German Rectal Cancer Study, supports neoadjuvant treatment for patients with stage II/III rectal cancer. The purpose of this study was to determine to what extent this evidence has affected clinical practice.

Methods

Stage II/III rectal cancer patients undergoing surgery from 1998 to 2007 were identified in the SEER tumor registry. Variables were analyzed with SPSS software. Trends were evaluated with regression models. Survivals were compared with the log-rank test.

Results

A total of 22,136 patients were identified and 15,021 (67.8 %) were treated with adjuvant radiotherapy. A large percentage were >60 years old (64.4 %), white (83.0 %), male (58.8 %), at stage III (55.1 %), and treated with neoadjuvant radiotherapy (35.5 %). A significant increase in the use of neoadjuvant radiotherapy occurred: from 17 % in 1998 to 51 % in 2007 (p < 0.001). Scatter-plot best-fit lines for neoadjuvant and adjuvant radiotherapy intersected at approximately year 2002. Significant increases in preoperative radiotherapy were observed for all races and cancer stages (p < 0.001). On unadjusted analysis, race (p = 0.018), sex (p < 0.001), year of diagnosis (p < 0.001), age (p < 0.001), and stage (p < 0.001) were associated with increased likelihood of neoadjuvant radiotherapy. On logistic regression analysis, male sex [odds ratio (OR) 1.14, p < 0.001), year (OR 1.223, p < 0.001), and stage II (OR 1.39, p < 0.001) were predictors of neoadjuvant therapy.

Conclusions

When adjuvant radiotherapy was utilized, there was rapid adoption of a neoadjuvant approach. This trend predated publication of prospective randomized data.     

Surgery Combined with Radiotherapy to Treat Spinal Tumors: A Review of Published Reports

Spinal tumors result in high morbidity and a high rate of lower limb paralysis. Both surgical therapy and radiation therapy (RT) are used to treat spinal tumors; however, how best to combine these two therapies to maximize the benefits and minimize the risks is still being debated. It is also difficult to decide the optimal timing, course and dose of RT, especially in pregnant women and children. The aim of this review is to assist surgeons who are dealing with spinal tumors by providing comprehensive information about advanced techniques for administering RT with greater precision and safety, and about the impact of various ways of combining surgery and RT on therapeutic outcomes. We here review published reports about treating spinal tumors with a combination of these two forms of therapy and attempt to draw appropriate conclusions concerning selection of optimal treatment protocols. Our conclusion is that postoperative radiotherapy, especially with high‐precision, low‐dose and multiple fractions, and brachytherapy are promising therapies to combined with surgery.