Simulators for virtual surgery training need to perform complex calculations very quickly to provide realistic haptic and visual interactions with a user. The complexity is further increased by the addition of cuts to virtual organs, such as would be needed for performing tumor resection. A common method for achieving large performance improvements is to make use of the graphics hardware (GPU) available on most general-use computers. Programming GPUs requires data structures that are more rigid than on conventional processors (CPU), making that data more difficult to update. We propose a new method for structuring graph data, which is commonly used for physically based simulation of soft tissue during surgery, and deformable objects in general. Our method aligns all nodes of the graph in memory, independently from the number of edges they contain, allowing for local modifications that do not affect the rest of the structure. Our method also groups memory transfers so as to avoid updating the entire graph every time a small cut is introduced in a simulated organ. We implemented our data structure as part of a simulator based on a meshless method. Our tests show that the new GPU implementation, making use of the new graph structure, achieves a 10 times improvement in computation times compared to the previous CPU implementation. The grouping of data transfers into batches allows for a 80-90% reduction in the amount of data transferred for each graph update, but accounts only for a small improvement in performance. The data structure itself is simple to implement and allows simulating increasingly complex models that can be cut at interactive rates.

Abstract Soft body deformation models are commonly used in surgery simulations. However, cutting those models can have a severe impact on computation times and affects the interactivity of the simulation. We propose a novel method for modeling topology and introducing cuts in a meshless soft body simulated on a background grid, as well a way to progressively update the visual aspect of the object by adding a small number of triangles to the surface mesh to cover the cut area. We determine that the accuracy of the deformation is preserved after cutting by comparing our method to a finite element method. Tests show that this new method achieves interactive simulation rates with more than 10,000 elements while cutting the model and reconstructing the mesh. Our separation of the visual and physical aspects of the simulation allows for more flexibility when tuning the performance of the simulation. Topology modifications have little impact on computation times for either physical or visual changes.

Virtual reality has become a viable tool for training surgeons for specific operations. In order to be useful, such a simulation need to be as realistic as possible so that a user can believe what they experience and act upon the virtual objects. We focus on simulating surgical operations that require cutting virtual organs. They offer a particular set of challenges with respect to simulation stability, performance, robustness and immersion.

In proton therapy, Monte Carlo simulations are desirable to accurately predict the delivered dose. This paper introduces and benchmarks pGPUMCD, a GPU-based Monte Carlo code implementing the physical processes required for proton therapy applications. In pGPUMCD, the proton transport is carried out in a voxelized geometry with a class II condensed history scheme. For this purpose, the equivalent restricted stopping power formalism (Leq formalism), the Fermi-Eyges scattering theory and the discrete electromagnetic/nuclear interactions were considered. pGPUMCD was compared to Geant4 in a validation study where the physical processes were validated one after the other. Dose differences between pGPUMCD and Geant4 were smaller than 1% in the Bragg peak region and up to 3% in its distal fall-off. Moreover, a voxelwise dose difference below 1% was observed for 99.5% of calculation positions. The pGPUMCD 80% falloff positions matched with those of Geant4 within 0.1%. The pGPUMCD computation times were inversely proportional to the voxel size, with one million protons transported in less than 0.5 s with mm3 voxels. pGPUMCD, based on the Leq formalism variance reduction technique, is therefore an attractive candidate for integration in a clinical treatment planning system.

The purpose of this study was to evaluate the impact of numerical errors caused by the floating point representation of real numbers in a GPU-based Monte Carlo code used for dose calculation in radiation oncology, and to identify situations where this type of error arises. The program used as a benchmark was bGPUMCD. Three tests were performed on the code, which was divided into three functional components: energy accumulation, particle tracking and physical interactions. First, the impact of single-precision calculations was assessed for each functional component. Second, a GPU-specific compilation option that reduces execution time as well as precision was examined. Third, a specific function used for tracking and potentially more sensitive to precision errors was tested by comparing it to a very high-precision implementation. Numerical errors were found in two components of the program. Because of the energy accumulation process, a few voxels surrounding a radiation source end up with a lower computed dose than they should. The tracking system contained a series of operations that abnormally amplify rounding errors in some situations. This resulted in some rare instances (less than 0.1%) of computed distances that are exceedingly far from what they should have been. Most errors detected had no significant effects on the result of a simulation due to its random nature, either because they cancel each other out or because they only affect a small fraction of particles. The results of this work can be extended to other types of GPU-based programs and be used as guidelines to avoid numerical errors on the GPU computing platform.

The aim of this study was to evaluate the potential of bGPUMCD , a Monte Carlo algorithm executed on Graphics Processing Units (GPUs), for fast dose calculations in permanent prostate implant dosimetry. It also aimed to validate a low dose rate brachytherapy source in terms of TG-43 metrics and to use this source to compute dose distributions for permanent prostate implant in very short times. The physics of bGPUMCD was reviewed and extended to include Rayleigh scattering and fluorescence from photoelectric interactions for all materials involved. The radial and anisotropy functions were obtained for the Nucletron SelectSeed in TG-43 conditions. These functions were compared to those found in the MD Anderson Imaging and Radiation Oncology Core brachytherapy source registry which are considered the TG-43 reference values. After appropriate calibration of the source, permanent prostate implant dose distributions were calculated for four patients and compared to an already validated Geant4 algorithm. The radial function calculated from bGPUMCD showed excellent agreement (differences within 1.3%) with TG-43 accepted values. The anisotropy functions at r = 1 cm and r = 4 cm were within 2% of TG-43 values for angles over 17.5°. For permanent prostate implants, Monte Carlo-based dose distributions with a statistical uncertainty of 1% or less for the target volume were obtained in 30 s or less for 1 × 1 × 1 mm 3 calculation grids. Dosimetric indices were very similar (within 2.7%) to those obtained with a validated, independent Monte Carlo code (Geant4) performing the calculations for the same cases in a much longer time (tens of minutes to more than a hour). bGPUMCD is a promising code that lets envision the use of Monte Carlo techniques in a clinical environment, with sub-minute execution times on a standard workstation. Future work will explore the use of this code with an inverse planning method to provide a complete Monte Carlo-based planning solution.

A new hybrid imaging-treatment modality, the MRI-Linac, involves the irradiation of the patient in the presence of a strong magnetic field. This field acts on the charged particles, responsible for depositing dose, through the Lorentz force. These conditions require a dose calculation engine capable of taking into consideration the effect of the magnetic field on the dose distribution during the planning stage. Also in the case of a change in anatomy at the time of treatment, a fast online replanning tool is desirable. It is improbable that analytical solutions such as pencil beam calculations can be efficiently adapted for dose calculations within a magnetic field. Monte Carlo simulations have therefore been used for the computations but the calculation speed is generally too slow to allow online replanning. In this work, GPUMCD, a fast graphics processing unit (GPU)-based Monte Carlo dose calculation platform, was benchmarked with a new feature that allows dose calculations within a magnetic field. As a proof of concept, this new feature is validated against experimental measurements. GPUMCD was found to accurately reproduce experimental dose distributions according to a 2%-2 mm gamma analysis in two cases with large magnetic field-induced dose effects: a depth-dose phantom with an air cavity and a lateral-dose phantom surrounded by air. Furthermore, execution times of less than 15 s were achieved for one beam in a prostate case phantom for a 2% statistical uncertainty while less than 20 s were required for a seven-beam plan. These results indicate that GPUMCD is an interesting candidate, being fast and accurate, for dose calculations for the hybrid MRI-Linac modality.