The goal of the simulation is to predict the size of the RFA lesion based on the patient 3D model, RFA needle position and a simulated RFA protocol.

Our simulation is based on the Penne's bioheat model, whereas finite element method is used for numerical discretization. The major advantage of our simulation software is the speed up and the accuracy.

The fast RFA simulation software uses the advanced heterogeneous GPU computing. The CPU part receives the data such as mesh, needle position and patient-specific parameters. The CPU reads the mesh, finds the neighbours and generates a CSR (compressed Sparse Row) matrix. The GPU receives the required data from the CPU and computes the following:

  • Heat source or Point source values (each thread → each node)
  • Shape function and Assembly matrix (each thread → each element)
  • Solution of the linear system (CUBLAS and CUSPARSE library)
  • Prediction of the cell death values (each thread → each node)

Our optimized code avoids the explicit numerical integration while computing the stiffness matrix and it assembles the stiffness matrix to the global matrix with the help of an efficient neighbour mapping algorithm.

Once the GPU computes and sends the data back to the CPU, the CPU computes the thermocouple values and loops again through GPU-CPU cycle until a certain criteria to stop the simulation becomes true. Also, the GPU saves the lesion values in a vtp file at a regular interval.

Lesion Growth and Temperature Changes

Lesion Growth in Liver


The simulation workflow is divided into three phases to closely match with the clinical workflow.

Pre-interventional or Pre-processing Phase
During the pre-interventional or pre-processing phase, the liver, tumour, hepatic artery, hepatic vein and portal vein are segmented from CT scan images. The surface mesh of each segmentation is saved in the Visualization Toolkit (VTK) file format. A standalone volumetric mesher, such as CGAL (Computational Geometry Algorithms), Gmsh or some other meshing package, is used to generate a finite element mesh which includes tetrahedra and triangles. An adaptive mesh refinement strategy is employed to generate a high-resolution mesh around the tumour.
Peri-interventional or Co-processing Phase
The lesion prediction is sensitive to patient- and device-specific parameters such as liver perfusion, ablation protocol, needle positions, power, target temperature, density of the liver etc. On the day of treatment or peri-interventional or co-processing phase, the perfusion values are estimated and the exact needle positions are segmented from contrast enhanced CT scan images. Next the mesh and other input parameters are passed to the simulation solver. Based on the volumetric mesh, the simulation generates a CSR matrix depending on the neighbours of each node in the volumetric mesh. The required arrays are generated for the GPU device and the simulation is then fully performed on the GPU. The solver calculates the temperature distribution due to the RF power by solving the Penne’s bioheat equation. Depending on the temperature distribution, a two-state cell model is used to identify dead cells. In the case of a multiple ablation protocol, the simulation waits for the next inputs and then resumes the calculation. The CPU acts as a co-processor and extracts the predicted lesion, the collection of dead nodes shown in red below, and then saves them in the VTK format.
Pre-interventional Phase
During the pre-interventional stage, the software provides an additional option to use a virtual needle to answer “what kind of protocol could be useful for this treatment”? One month after the treatment, during the post-interventional or post-processing phase, a CT scan is performed to obtain a more accurate segmented lesion without any of the tissue swelling commonly observed just after treatment. This real segmented lesion is compared with the simulated lesion and the accuracy of the treatment is studied based on a set of evaluation metrics. The volume (80%) and surface deviation (3mm) between both the real and simulated lesion allows us to decide on the treatment success.