Meshfree and Particle Methods in Biomechanics: Prospects and Challenges

The use of meshfree and particle methods in the field of bioengineering and biomechanics has significantly increased. This may be attributed to their unique abilities to overcome most of the inherent limitations of mesh-based methods in dealing with problems involving large deformation and complex geometry that are common in bioengineering and computational biomechanics in particular. This review article is intended to identify, highlight and summarize research works on topics that are of substantial interest in the field of computational biomechanics in which meshfree or particle methods have been employed for analysis, simulation or/and modeling of biological systems such as soft matters, cells, biological soft and hard tissues and organs. We also anticipate that this review will serve as a useful resource and guide to researchers who intend to extend their work into these research areas. This review article includes 333 references

Thermal ablation of biological tissues in disease treatment: A review of computational models and future directions

Percutaneous thermal ablation has proved to be an effective modality for treating both benign and malignant tumors in various tissues. Among these modalities, radiofrequency ablation (RFA) is the most promising and widely adopted approach that has been extensively studied in the past decades. Microwave ablation (MWA) is a newly emerging modality that is gaining rapid momentum due to its capability of inducing rapid heating and attaining larger ablation volumes, and its lesser susceptibility to the heat sink effects as compared to RFA. Although the goal of both these therapies is to attain cell death in the target tissue by virtue of heating above 50 oC, their underlying mechanism of action and principles greatly differs. Computational modelling is a powerful tool for studying the effect of electromagnetic interactions within the biological tissues and predicting the treatment outcomes during thermal ablative therapies. Such a priori estimation can assist the clinical practitioners during treatment planning with the goal of attaining successful tumor destruction and preservation of the surrounding healthy tissue and critical structures. This review provides current state-of- the-art developments and associated challenges in the computational modelling of thermal ablative techniques, viz., RFA and MWA, as well as touch upon several promising avenues in the modelling of laser ablation, nanoparticles assisted magnetic hyperthermia and non- invasive RFA. The application of RFA in pain relief has been extensively reviewed from modelling point of view. Additionally, future directions have also been provided to improve these models for their successful translation and integration into the hospital work flow

Thermal-mechanical response modelling and thermal damage prediction of soft tissues during thermal ablation

During thermal ablation, target soft tissue responses both thermally and mechanically simultaneously. However, current thermal ablation treatment mainly relies on the quantitative temperature indication to evaluate tissue behaviours and control the delivered thermal energy, which is ineffective and inaccurate. Based on these, our research study focuses on: bioheat transfer theory, linear and nonlinear elasticity of soft tissues at varied temperatures, as well as thermal damage prediction theory, and the whole program was developed in Netbeans IDE 8.1. The main contributions of our research work lie in the following aspects: Firstly, considering a situation where soft tissue’s mechanical deformation during thermal ablation is only caused by thermal loading, it is reasonable to assume that the generated strain value is within the linear range of stress-strain relationship characterisation which is also thermal stable (nearly temperature independent). Therefore, we propose our first model by integrating the heating process with thermally-induced mechanical deformations of soft tissues for simulation and analysis of the thermal ablation process. This method combines classical Fourier based bioheat transfer and constitutive elastic mechanics derived from the method of multiplicative decomposition of thermal mechanical deformation gradient, as well as non-rigid motion dynamics. The 3D governing equations are discretised spatially using finite difference scheme and temporally using implicit time integration scheme and the obtained linear system of equations are subsequently solved using a Gauss-Seidel iterative solver. Simulation implement based on proposed method can serve as a visible assistance for relevant surgeons on analysing soft tissue’s behaviours from both thermal and mechanical deformation fields rather than from just determined temperature distribution. Secondly, we present a method to characterize soft tissue thermal damage by taking into account of thermal mechanical interactions during thermal ablation, concerning stored energy by both thermal and mechanical effects can affect the energy barrier for macromolecular transitions, leading to further or the reverse damage to treated biological tissues. To do this, traditional tissue damage model of Arrhenius integration is improved by including the thermally and mechanically induced strain energy term. Simulations and comparison analysis based on different types of soft tissues are also performed to study its influences. Our findings may provide more reliable guidelines for relevant surgeons to control the tissue damage zone during thermal ablation practice. Thirdly, thermal relaxation time used to describe heating process in homogeneous substance is usually referred to as the characteristic time in non-homogeneous biological materials, which is needed to accumulate enough energy to transfer to the nearest point. Such non-Fourier thermal behaviour has also been experimentally observed in biological tissues. Our second model is presented by integrating non-Fourier bioheat transfer and constitutive elastic mechanics derived from the method of multiplicative decomposition of thermal mechanical deformation gradient, as well as non-rigid motion of dynamics to predict and analyse thermal distribution, thermal-induced mechanical deformation and tissue damage under purely thermal loads. The simulation performances are compared between two numerical methods: Finite Difference Method and Finite Element Method, from perspectives of accuracy and computing efficiency, and also against available existed experimental data and other commercialized analysis tools. Finally, our research moves on to nonlinear range characterization of tissue deformation under combined thermal and mechanical loads. Basically, the contribution of our proposed nonlinear thermal mechanical model is by extending the finite strain framework of Neo-Hookean energy function to the heating process of soft tissues during thermal ablation. Meanwhile, our nonlinear thermal mechanical model also considers the effect of collagen fibre bundles as embedded in many biological tissues. Separating free energy density modelling into isotropic and anisotropic parts, it is assumed that the anisotropy is due to the collagen fibre bundles behaviour, while the ground substance, behaves in an isotropic manner can be modelled using selected nonlinear biomaterial model. The necessary ingredients for the finite element method implementation including: weak form and time integration are also included in this chapter. Keywords: Thermal ablation, soft tissue, non-Fourier bioheat transfer, thermal mechanical deformation, anisotropic nonlinear, tissue damage

Boundary Element Modeling and Simulation Algorithm for Fractional Bio-Thermomechanical Problems of Anisotropic Soft Tissues

The main purpose of this chapter is to propose a novel boundary element modeling and simulation algorithm for solving fractional bio-thermomechanical problems in anisotropic soft tissues. The governing equations are studied on the basis of the thermal wave model of bio-heat transfer (TWMBT) and Biot’s theory. These governing equations are solved using the boundary element method (BEM), which is a flexible and effective approach since it deals with more complex shapes of soft tissues and does not need the internal domain to be discretized, also, it has low RAM and CPU usage. The transpose-free quasi-minimal residual (TFQMR) solver are implemented with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner to solve the linear systems arising from BEM. Numerical findings are depicted graphically to illustrate the influence of fractional order parameter on the problem variables and confirm the validity, efficiency and accuracy of the proposed BEM technique

A New Boundary Element Technique For One- And Two-Temperature Models Of Biothermomechanical Behavior Of Anisotropic Biological Tissues

The main objective of this paper is to develop a novel boundary element technique for describing the three-dimensional (3D) biothermomechanical behavior of anisotropic biological tissues. The governing equations are studied on the basis of the dual phase lag bioheat transfer and Biot's theory for oneand two-temperature models. Because of the benefits of CQBEM, such as not being restricted by the complex shape of biological tissues and not requiring discretization of the interior of the treated region, it can cope with complex bioheat models and has low use of RAM and CPU. CQBEM is therefore a flexible and efficient tool for modeling the distribution of bioheat in anisotropic biological tissues and associated deformation. The resulting linear equations arising from CQBEM are solved by the generalized modified shift-splitting (GMSS) iterative method which reduces the number of iterations and the total time of the CPU. Numerical findings show the validity, efficacy and consistency of the proposed technique

Development of Gradient Smoothing Operations and Application to Biological Systems

Ph.DDOCTOR OF PHILOSOPH

Mechanical characterisation and FEM modelling of biological deformation for surgical simulation

This thesis sought to explore the use of minimally invasive surgery via biomechanical simulation of soft tissue deformation and needle path planning insertion. When surgeons are placed under mechanical stress, human brain cells exhibit the viscoelastic behaviour of solid structures. However, the behavioural mechanisms of tissues/cells are not yet fully understood, and more information is needed to reliably calculate tissue/cell deformation. The research objectives and methodologies were: First, to objectively investigate and characterise the mechanical properties of biological tissues/cells by using experimental atomic force microscopy (AFM) data (see CHAPTER 3). This method was used to analyse the cell's mechanical behaviours with a developed numerical algorithm. The difference between two human brain cells (normal HNC-2 and U87 cancer cells) was studied to determine their mechanical properties so that these could then be applied to our proposed 3D model (see CHAPTER 5). Second, using the measured experimental AFM data, a system identification of AFM characterisation was implemented in another chapter (CHAPTER 4), which for comparison, was based on a MATLAB algorithm. The results showed that the model that was identified for AFM matched the measured experimental AFM data. Third, to establish a finite element method (FEM) for real-time modelling of nonlinear soft tissue deformation behaviours using a three-dimensional (3D) dynamic nonlinear FEM; this method was developed to establish the large-range deformation of tissue/cells with second- order Piola-Kirchhoff stress (CHAPTER 5). A Newmark numerical process was implemented to solve the partial differential equations (PDEs) that resulted from the FEM. Experimental analysis of biological human brain cells was conducted to verify and validate the nonlinear FEM for simulating deformation. Fourth, to establish a method for real-time motion plan modelling of nonlinear needle deflection during needle insertion using the third objective to implement the nonlinear FEM for needle path planning. Last, to use an application of bio-heat transfer of potential needle tip path planning by applying a bioheat transfer-based method (CHAPTER 6); this method was established for optimal path planning for needle insertion in the presence of soft tissue deformation. A bio- heat transfer was used to develop a temperature distribution for path planning to reach the target and avoid obstacles in cubic, liver and brain cell models. The algorithm defines the optimal path for needle tip placement; the needle tip placement is determined by the temperature distribution, which in turn, is based on soft tissue deformation that occurs in the process of needle insertion. When force was applied during the needle penetration process, the deflection accrued was based on the geometry of nonlinear material. Based on our simulation of 3D FEM discretisation of the Pennes' Bio-heat Transfer Equation, the distribution of the temperature from single point temperature sources was performed to determine the degree of transient thermal. Furthermore, the distribution was used to model thermal stresses and strains within the cell/tissue, which result from the heat source. The main contribution to this field is building a new conceptual design methodology for characterisation of the mechanical properties of biological cells by extracts of the mechanical properties of two biological human brain cells (normal HNC-2 and cancer U87 MG cells), and the experimental use of AFM for the first time. Also, linear FEM for soft tissue/needle insertion with large deformation is developed and adapted to our three-dimensional dynamic FEM soft tissue/cell modelling using numerical integration methods. Verification of the experimental work and the proposed method is examined mathematically and systematically using a system identification schema. Moreover, bio-heat transfer for needle insertion is implemented based on the proposed FEM soft tissue deformation modelling to represent path planning. The investigation of needle insertion into soft tissue/cell deformation using bioheat transfer FEM has not been done before

Robust GPU-based Virtual Reality Simulation of Radio Frequency Ablations for Various Needle Geometries and Locations

Purpose: Radio-frequency ablations play an important role in the therapy of malignant liver lesions. The navigation of a needle to the lesion poses a challenge for both the trainees and intervening physicians. Methods: This publication presents a new GPU-based, accurate method for the simulation of radio-frequency ablations for lesions at the needle tip in general and for an existing visuo-haptic 4D VR simulator. The method is implemented real-time capable with Nvidia CUDA. Results: It performs better than a literature method concerning the theoretical characteristic of monotonic convergence of the bioheat PDE and a in vitro gold standard with significant improvements (p < 0.05) in terms of Pearson correlations. It shows no failure modes or theoretically inconsistent individual simulation results after the initial phase of 10 seconds. On the Nvidia 1080 Ti GPU it achieves a very high frame rendering performance of >480 Hz. Conclusion: Our method provides a more robust and safer real-time ablation planning and intraoperative guidance technique, especially avoiding the over-estimation of the ablated tissue death zone, which is risky for the patient in terms of tumor recurrence. Future in vitro measurements and optimization shall further improve the conservative estimate.Comment: 18 pages, 14 figures, 1 table, 2 algorithms, 2 movie