The ability to predict patient-specific soft tissue deformations is key for computer-integrated surgery systems and the core enabling technology for a new era of personalized medicine. Element-Free Galerkin (EFG) methods are better suited for solving soft tissue deformation problems than the finite element method (FEM) due to their capability of handling large deformation while also eliminating the necessity of creating a complex predefined mesh. Nevertheless, meshless methods based on EFG formulation, exhibit three major limitations: i) meshless shape functions using higher order basis cannot always be computed for arbitrarily distributed nodes (irregular node placement is crucial for facilitating automated discretization of complex geometries); ii) imposition of the Essential Boundary Conditions (EBC) is not straightforward; and, iii) numerical (Gauss) integration in space is not exact as meshless shape functions are not polynomial. This paper presents a suite of Meshless Total Lagrangian Explicit Dynamics (MTLED) algorithms incorporating a Modified Moving Least Squares (MMLS) method for interpolating scattered data both for visualization and for numerical computations of soft tissue deformation, a novel way of imposing EBC for explicit time integration, and an adaptive numerical integration procedure within the Meshless Total Lagrangian Explicit Dynamics algorithm. The appropriateness and effectiveness of the proposed methods is demonstrated using comparisons with the established non-linear procedures from commercial finite element software ABAQUS and experiments with very large deformations. To demonstrate the translational benefits of MTLED we also present a realistic brain-shift computation.

We proposed an inverse planning method based on dose-volume histogram optimization and Monte Carlo dosimetry. We compared plans calculated using our proposed method with clinical plans calculated using the TG-43 dosimetry formalism. We demonstrated that our method can provide plans with higher prostate dose homogeneity (up to 6.1%) and lower urethral dose (up to 4.0%) compared with the clinical plans. The computational time (37.5 AE 3.2 s) complies with intraoperative time restrictions.Purpose: Inverse planning is an integral part of modern low-dose-rate brachytherapy. Current clinical planning systems do not exploit the total dose information and largely use the American Association of Physicists in Medicine TG-43 dosimetry formalism to ensure clinically acceptable planning times. Thus, suboptimal plans may be derived as a result of TG-43-related dose overestimation and nonconformity with dose distribution requirements. The purpose of this study was to propose an inverse planning approach that can improve planning quality by combining dose-volume information and precision without compromising the overall execution times. Methods and Materials: The dose map was generated by accumulating precomputed Monte Carlo (MC) dose kernels for each candidate source implantation site. The MC computational burden was reduced by using graphics processing unit acceleration, allowing accurate dosimetry calculations to be performed in the intraoperative environment. The proposed dose-volume histogram (DVH) fast simulated annealing optimization algorithm was evaluated using clinical plans that were delivered to 18 patients who underwent low-dose-rate prostate brachytherapy. Results: Our method generated plans in 37.5 AE 3.2 seconds with similar prostate dose coverage, improved prostate dose homogeneity of up to 6.1%, and lower dose to the urethra of up to 4.0%. Conclusions: A DVH-based optimization algorithm using MC dosimetry was developed. The inclusion of the DVH requirements allowed for increased control over the optimization outcome. The optimal plan's quality was further improved by considering tissue heterogeneity.

The monodomain model is widely used in in‐silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi‐implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting‐based methods.