Reference Approach Modelling methods Soft-tissue types Tissue behaviors Computation time/speed Geometry discretization Hardware configurations Cotin et al. [12 ] MD Precomputation-based FEM (pre-comp FEM) approximated by linear functions The human liver Linear elasticity 7 ms (force feedback) 1400 N Dec AlphaStation 400 MHz Berkley et al. [14 ] MD Linearized FEM (L-FEM) The human skin Linear elasticity 1 kHz (force feedback) 863 N 1 GHz Athelon CPU Audette et al. [18 ] MI Multirate FEM (MR-FEM) The human brain Linear elasticity 10 kHz (force feedback) NI Dual Pentium PC Sedef et al. [19 ] MD Precomputation-based FEM (pre-comp FEM) using linear viscoelastic formulations The soft-tissue cube Linear viscoelasticity 1 kHz (force feedback) 51 N Pentium IV 2.4 GHz dual CPU Sela et al. [20 ] MD Precomputation-based FEM (pre-comp FEM) using discontinuous free form deformations The human skin Linear elasticity 1 kHz (force feedback and model cutting) 12,108 polygons P4-2.8 GHz CPU, 1 GB RAM Karol Miller et al. [16 ] MD Total Lagrangian explicit dynamic (TLED) FEM NI Nonlinear elasticity 16 ms (model deformation) 6000 E 3.2 GHz Pentium IV García et al. [21 ] MD Matrix system reduction FEM (MSR-FEM) NI Linear elasticity 3.8 ms–35.7 ms (solving the system) From 266 N–1,579 E to 110 N–587 E 2.4 GHz Pentium IV CPU, 1 GB Joldes et al. [22 ] MD Total Lagrangian (TL) FEM NI Nonlinear elasticity 2.1 ms (one system time step) 2,200 E-2535 N CPU Taylor et al. [17 ] MI Total Lagrangian explicit dynamic (TLED) FEM The human brain Nonlinear elasticity From 14.0 to 10.7 times faster than CPU From 11,168 E to 46,655 E 3.2 GHz P4 CPU, 2 GB RAM Joldes et al. [15 ] MD Total Lagrangian explicit dynamic FEM (TLED-FEM) The human brain Hyperelasticity (neo-Hookean) 12 ms (model deformation) 15,050 E, 16,710 N 3 GHz Intel Core Duo CPU Joldes et al. [23 ] MI FEM (NL-FEM) implemented on GPU The human brain Nonlinear elasticity 3.54 s (3000 system time step running) 16,825 E-12,693 N GPU NVIDIA CUDA Tesla C1060 (240 1.296 GHz cores, 4 GB high-speed memory) Wittek et al. [24 ] MI Total Lagrangian explicit dynamic FEM (TLED-FEM) implemented on GPU The human brain Nonlinear elasticity <4 s (deformation prediction) 18,000 N–30,000 E GPU NVIDIA CUDA tesla C870 (128 600 MHz cores, 1.5 GB memory) Peterlík et al. [3 ] MD Precomputation-based FEM (pre-comp FEM) using radial basic functions (RBF) The human liver Nonlinear elasticity 0.54 s 1,777 E–501 N AMD Opteron 2 GHz CPU, 8 GB RAM Lapeer et al. [25 ] MI Total Lagrangian FEM (TL-FEM) The human skin Hyperelasticity (general polynomial, reduced polynomial, and ogden formulation) >1 kHz (haptic feedback) 100 E–50,000 E GPU Marchesseau et al. [26 ] MD Multiplicative Jacobian energy decomposition FEM (MJED-FEM) The human liver Porohyperelasticity, Viscohyperelasticity 13 FPS (model deformation) 20,700 E–4,300 N CPU Courtecuisse et al. [27 ] MI Linearized FEM (L-FEM) The human cataract Linear elasticity combined with a corotational method 1.4 FPS (model computing model on CPU) 41,000 N GPU Turkiyyah et al. [28 ] MD Discontinuous basic function FEM (DBF-FEM) The human skin Linear elasticity 13.9 ms (model computing and mesh updating) 31,008 N CPU Niroomandi et al. [29 ] MD Order reduction method (ORM) FEM The human cornea Nonlinear elasticity 20 Hz (model and graphic updating) 7,182 E–8,514 N 2 GHz CPU, 2 GB RAM Wu et al. [30 ] MD Finite element method (FEM) The superficial fascia in a face Nonlinear elasticity NI 560 E–1180 N CPU Morooka et al. [31 ] MD Precomputation-based FEM (pre-comp FEM) using neuro networks The phantom liver NI NI 15,616 E-4,804 N CPU Mafi and Sirouspour [32 ] MI Element-by-element precondition conjugate gradient FEM (EbE PCG-FEM) The human stomach Linear elasticity 10 times faster than CPU for model computing 6361 E–13,3784 E NDIVIDA GTX 470 Courtecuisse et al. [33 ] MI Precondition FEM (pre-cond FEM) The heterogeneous soft tissues Linear elasticity combined with a corotational method 70 FPS (system iteration) 1,300 tetrahedral elements 256 core GPU Strbac et al. [34 ] MI Total Lagrangian explicit dynamic (TLED) FEM A general cube mesh Hyperelasticity (neo-Hookean) 0.309 s–163.402 s (one solution time step) 125 E–91,125 E NVIDIA GTX460 GPU Karami et al. [35 ] MD Finite element modelling method (FEM) The extraocular muscles (EOMs) in an eye Linear elasticity 20 ms (model deformation) Eyeball: CPU Martínez et al. [36 ] MD Precomputation-based FEM (pre-comp FEM) using artificial neuro networks The human breast Hyperelastic (Mooney-Rivlin) <0.2 s (model compression) 313,000 E-62,000 N 2.6 GHz Intel (R) Xeon (R) CPU Lorente et al. [8 ] MD Precomputation-based FEM (pre-comp FEM) using artificial neuro networks The human liver Nonlinear elasticity 2.89 s (model computing using machine learning) From 379,800 N to 420,690 N 3.4 GHz Intel Core i7, 8 GB RAM, OS X El Capitan Tonutti et al. [7 ] MD Precomputation-based FEM (pre-comp FEM) using artificial neuro networks and support vector regression The brain tumor Nonlinear elasticity <10 ms (model prediction using neural network) 6,442 N-1,087 E Core i7 2.9 GHz CPU Luboz et al. [37 ] MD Precomputation-based FEM (pre-comp FEM) using the reduced order modelling method The butt area Nonlinear elasticity <1 s (strain field computing) 27,649 E CPU
