Objectives: To evaluate the outcomes and prognosis of high-intensity focused ultrasound (HIFU) therapy for patients with localized prostate cancer, and identify suitable candidates for this therapy by investigating th...Objectives: To evaluate the outcomes and prognosis of high-intensity focused ultrasound (HIFU) therapy for patients with localized prostate cancer, and identify suitable candidates for this therapy by investigating the predictive factors. Methods: The 224 patients (low 54, intermediate 111 and high-risk patients 59) with T1-2 stage were treated using the Sonablate device and followed for over 12 months after treatment. Recurrence was determined based on histological findings, prostate-specific antigen (PSA) failure and local or distant metastasis. The factors which are predicting variables with potential effects were investigated by Kaplan-Meier and multivariate analysis. Results: A total of 255 treatment sessions (193 with one, 31 with two) were performed. No patients died of prostate cancer, but 15 died of other causes and 14 patients were lost during follow-up. The 7-year recurrence-free survival (RFS) rates in all patients were 75%, and 5-year RFS rates were 98%, 84% and 59% in the low, intermediate and high-risk patients respectively. In the 216 patients who underwent histological examination at 6 months or later after HIFU, 25 (12%) were positive. In 77 patients with recurrence after first-HIFU, the second treatments were hormonal therapy and HIFU. Of the 31 patients who underwent a second HIFU, the 5-year RFS rates were 64%, and 5-year RFS rates were 100%, 74% and 33% in the low, intermediate and high-risk patients. The significant predictor for recurrence was risk-group, T-stage (T1 vs T2), Gleason score (≤3 + 4 and ≥4 + 3), pretreatment PSA (Conclusions: Prognosis of HIFU for Patients with localized prostate cancer was good, and the low and intermediate-risk patients with T1-staging are suitable indications for HIFU. Effective predictors for outcomes were risk-group, T-stage, Gleason score, pretreatment PSA and nadir PSA.展开更多
In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian(ALE)one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimension...In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian(ALE)one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes.A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in[25].For that purpose,a new element-local weak formulation of the governing PDE is adopted on moving space-time elements.The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes.Moreover,a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element.To maintain algorithmic simplicity,the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges.This is possible in the ALE framework,which allows a local mesh velocity that is different from the local fluid velocity.We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.展开更多
This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Ku...This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.展开更多
In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtain...In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.展开更多
文摘Objectives: To evaluate the outcomes and prognosis of high-intensity focused ultrasound (HIFU) therapy for patients with localized prostate cancer, and identify suitable candidates for this therapy by investigating the predictive factors. Methods: The 224 patients (low 54, intermediate 111 and high-risk patients 59) with T1-2 stage were treated using the Sonablate device and followed for over 12 months after treatment. Recurrence was determined based on histological findings, prostate-specific antigen (PSA) failure and local or distant metastasis. The factors which are predicting variables with potential effects were investigated by Kaplan-Meier and multivariate analysis. Results: A total of 255 treatment sessions (193 with one, 31 with two) were performed. No patients died of prostate cancer, but 15 died of other causes and 14 patients were lost during follow-up. The 7-year recurrence-free survival (RFS) rates in all patients were 75%, and 5-year RFS rates were 98%, 84% and 59% in the low, intermediate and high-risk patients respectively. In the 216 patients who underwent histological examination at 6 months or later after HIFU, 25 (12%) were positive. In 77 patients with recurrence after first-HIFU, the second treatments were hormonal therapy and HIFU. Of the 31 patients who underwent a second HIFU, the 5-year RFS rates were 64%, and 5-year RFS rates were 100%, 74% and 33% in the low, intermediate and high-risk patients. The significant predictor for recurrence was risk-group, T-stage (T1 vs T2), Gleason score (≤3 + 4 and ≥4 + 3), pretreatment PSA (Conclusions: Prognosis of HIFU for Patients with localized prostate cancer was good, and the low and intermediate-risk patients with T1-staging are suitable indications for HIFU. Effective predictors for outcomes were risk-group, T-stage, Gleason score, pretreatment PSA and nadir PSA.
基金the European Research Council(ERC)under the European Union’s Seventh Framework Programme(FP7/2007-2013)with the research project STiMulUs,ERC Grant agreement no.278267.
文摘In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian(ALE)one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes.A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in[25].For that purpose,a new element-local weak formulation of the governing PDE is adopted on moving space-time elements.The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes.Moreover,a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element.To maintain algorithmic simplicity,the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges.This is possible in the ALE framework,which allows a local mesh velocity that is different from the local fluid velocity.We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.
基金This work was partially supported by the Special Project on High-performance Computing under the National Key R&D Program(No.2016YFB0200603)Science Challenge Project(No.JCKY2016212A502)the National Natural Science Foundation of China(Nos.91330205,91630310,11421101).
文摘This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.
基金the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013)under the research project STiMulUs,ERC Grant agreement no.278267.
文摘In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.
