A GPU Accelerated Finite Differences Method of the Bioheat Transfer Equation for Ultrasound Thermal Ablation

Abstract

Over the years, high intensity focused ultrasound (FUS) therapy has become a promising therapeutic alternative for non-invasive tumor treatment. The basic idea of FUS therapy is the elevation of the tissue temperature by the application of focused ultrasound beams to focal spot in the tumor. Biothermal modeling is utilized to predict dynamic temperature distributions generated and altered by the therapeutic heating modality, tissue energy storage and dissipation, and blood flow. Implementation of biothermal modeling in the planning, monitoring, control and evaluation of MR guided Focused Ultrasound (MRgFUS) therapies can help to minimize treatment time, maximize efficacy, and ensure the safety of healthy normal tissues, while increasing clinical confidence in MRgFUS treatments. Fast calculations of thermal doses can support in planning, conduction, and monitoring of such treatments. In the current study a GPU-based method in Matlab is proposed, for fast calculations of the temperature and cumulative equivalent minutes at 43°( CEM 43°) based on the bioheat equation. The performance of our proposed method was assessed with three GPUs (GTX 750, GTX 770 and Tesla C2050) for five grid sizes. The maximum speedup was achieved with the Tesla C2050 (*29) while GTX 750 demonstrated the lower performance (*15).

Fast computation of soft tissue thermal response under deformation based on fast explicit dynamics finite element algorithm for surgical simulation

“…The classical PBHT exists certain simplifications and assumptions. The blood flow in the capillaries is assumed isotropic and hence the directional-dependent blood flow heat transfer is not modelled [19,54]. The physical processes such as water evaporation and transport of vapor are not captured in the classical PBHT [25,37,55]; however, the phase change occurs when tissue temperature elevates beyond the vaporisation threshold 𝑇 𝑡ℎ𝑟𝑒𝑠 (𝑇 𝑡ℎ𝑟𝑒𝑠 = 100℃ [36]), but the maximum temperature reached in the present work is less than 𝑇 = 65℃ (see Fig.…”

“…Various methods were reported for fast solutions of bio-heat transfer models; however, the study on fast thermal analysis under tissue deformation is very limited. Studies were focused on facilitating the computational efficiency by using parallel alternating direction explicit scheme [15] based on finite difference method (FDM) [16], spatial filter method based on Fast Fourier Transform (FFT) [17], fast FFT method [18], Graphics Processing Unit (GPU)-accelerated FDM [19,20], GPU-accelerated finite element methodology (FEM) [21], cellular neural network [22], multi-grid technique based on finite volume method (FVM) [23,24], dynamic mode decomposition based on meshless point collocation method [25] and model order reduction based on FDM [26]. Despite the improved computational effort by the above methods, they all consider solving the bio-heat transfer equation on a static non-moving state of soft tissue.…”

Real-time computation of bio-heat transfer in the fast explicit dynamics finite element algorithm (FED-FEM) framework

“…The heat transfer in soft biological tissue may be characterised by various bio-heat transfer models, among which the most well-known is the Pennes bio-heat transfer model by Harry H. Pennes [37], which mathematically describes the heat transfer process in living biological tissue composed of solid tissue and blood flow [38]. The Pennes bio-heat transfer model can provide suitable temperature predictions in the whole body, organ, and tumour analyses [39], and therefore it has been widely used in the modelling of thermal ablation for cancer treatment [16,23,30,40] and other biomedical research areas [12,21,41,42].…”

“…Schwenke et al [20] studied a Graphics Processing Unit (GPU)-accelerated FDM to achieve fast simulation of focused ultrasound treatment via a parallel execution of the solution procedure on GPU; however, FDM requires a regular computation grid to approximate spatial derivatives, but human organs/tissue are irregular shapes with curvilinear boundaries, resulting in inaccuracy for accommodating soft tissue material properties and enforcing boundary conditions. He and Liu [21] developed a parallel alternating direction explicit (ADE) scheme based on FDM to solve the bio-heat equation; Carluccio et al [22] devised a spatial filter method based on Fast Fourier Transform (FFT) with FDM to reduce computation time; Kalantzis et al [23] studied a GPU-accelerated FDM for fast simulation of focused ultrasound thermal ablation; Dillenseger and Esneault [24] also studied an FFT-based FDM method; Chen et al [25] presented a GPU-accelerated microwave imaging method based on FDM to monitor temperature in thermal therapy; Johnson and Saidel [26] studied an FDM-based methodology for fast simulation of radiofrequency tumour ablation; and Niu et al [27] employed cellular neural networks (CNN) based on FDM for efficient estimation of tissue temperature field. Despite the improved computational performance by the above methods, they all suffer from the inaccuracy in describing the thermal effects of irregular boundary conditions due to using FDM for computation grid.…”

A 3D Approach Using a Control Algorithm to Minimize the Effects on the Healthy Tissue in the Hyperthermia for Cancer Treatment

“…Since solving a partial differential equation (PDE) in a three-dimensional domain requires significant computational time, even with simplified models, combining DE with Pennes’ three-dimensional model significantly impacts performance. To reduce computational time and obtain solutions within a reasonable timeframe, we used general-purpose computing on graphics processing units (GPGPU) via the Compute Unified Device Architecture (CUDA) parallel computing platform to parallelize the implementation of the bioheat model [ 11 , 28 , 29 , 30 ], i.e., minimize the time spent evaluating the objective function.…”