Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided. The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

Soft tissue modelling for applications in virtual surgery and surgical robotics

Soft tissue modelling has gained a great deal of importance, for a large part due to its application in surgical training simulators for minimally invasive surgery (MIS). This article provides a structured overview of different continuum-mechanical models that have been developed over the years. It aims at facilitating model choice for specific soft tissue modelling applications. According to the complexity of the model, different features of soft biological tissue will be incorporated, i.e. nonlinearity, viscoelasticity, anisotropy, heterogeneity and finally, tissue damage during deformation. A brief summary of experimental methods for material characterisation and an introduction to methods for geometric modelling are also provided.

The overview is non-exhaustive, focusing on the most important general models and models with specific biological applications. A trade-off in complexity must be made for enabling real-time simulation, but still maintaining realistic representation of the organ deformation. Depending on the organ and tissue types, different models with emphasis on certain features will prove to be more appropriate, meaning the optimal model choice is organ and tissue-dependent.     

Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo

The mechanical properties of human soft tissue are crucial for impact biomechanics, rehabilitation engineering, and surgical simulation. Validation of these constitutive models using human data remains challenging and often requires the use of non-invasive imaging and inverse finite element (FE) analysis. Post-processing data from imaging methods such as tagged magnetic resonance imaging (MRI) can be challenging. Digital image correlation (DIC), however, is a relatively straightforward imaging method. DIC has been used in the past to study the planar and superficial properties of soft tissue and excised soft tissue layers. However, DIC has not been used to non-invasive study of the bulk properties of human soft tissue in vivo. Thus, the goal of this study was to assess the use of DIC in combination with FE modelling to determine the bulk material properties of human soft tissue. Indentation experiments were performed on a silicone gel soft tissue phantom. A two camera DIC setup was then used to record the 3D surface deformation. The experiment was then simulated using a FE model. The gel was modelled as Neo-Hookean hyperelastic, and the material parameters were determined by minimising the error between the experimental and FE data. The iterative FE analysis determined material parameters (μ=1.80 kPa, K=2999 kPa) that were in close agreement with parameters derived independently from regression to uniaxial compression tests (μ=1.71 kPa, K=2857 kPa). Furthermore the FE model was capable of reproducing the experimental indentor force as well as the surface deformation found (R²=0.81). It was therefore concluded that a two camera DIC configuration combined with FE modelling can be used to determine the bulk mechanical properties of materials that can be represented using hyperelastic Neo-Hookean constitutive laws.     

Computational modelling and optimisation of soft tissue outcome in cranio-maxillofacial surgery planning

Cranio-maxillofacial (CMF) surgery operations are associated with rearrangement of facial hard and soft tissues, leading to dramatic changes in facial geometry. Often, correction of the aesthetical patient's appearance is the primary objective of the surgical intervention. Due to the complexity of the facial anatomy and the biomechanical behaviour of soft tissues, the result of the surgical impact cannot always be predicted on the basis of surgeon's intuition and experience alone. Computational modelling of soft tissue outcome using individual tomographic data and consistent numerical simulation of soft tissue mechanics can provide valuable information for surgeons during the planning stage. In this article, we present a general framework for computer-assisted planning of CMF surgery interventions that is based on the reconstruction of patient's anatomy from 3D computer tomography images and finite element analysis of soft tissue deformations. Examples from our clinical case studies that deal with the solution of direct and inverse surgical problems (i.e. soft tissue prediction, inverse implant shape design) demonstrate that the developed approach provides a useful tool for accurate prediction and optimisation of aesthetic surgery outcome.     

Estimating joint kinematics from skin motion observation: modelling and validation

Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis. The most frequently used method in 3D human motion analysis involves placing markers on the skin of the analysed segment which is composed of the rigid bone and the surrounding soft tissues. Skin and soft tissue deformations introduce a significant artefact which strongly influences the resulting bone position, orientation and joint kinematics. For this study, we used a statistical solid dynamics approach which is a combination of several previously reported tools: the point cluster technique (PCT) and a Kalman filter which was added to the PCT. The methods were tested and evaluated on controlled human-arm motions, using an optical motion capture system (Vicon(TM)). The addition of a Kalman filter to the PCT for rigid body motion estimation results in a smoother signal that better represents the joint motion. Calculations indicate less signal distortion than when using a digital low-pass filter. Furthermore, adding a Kalman filter to the PCT substantially reduces the dispersion of the maximal and minimal instantaneous frequencies. For controlled human movements, the result indicated that adding a Kalman filter to the PCT produced a more accurate signal. However, it could not be concluded that the proposed Kalman filter is better than a low-pass filter for estimation of the motion. We suggest that implementation of a Kalman filter with a better biomechanical motion model will be more likely to improve the results.     

Estimating joint kinematics from skin motion observation: modelling and validation

Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis. The most frequently used method in 3D human motion analysis involves placing markers on the skin of the analysed segment which is composed of the rigid bone and the surrounding soft tissues. Skin and soft tissue deformations introduce a significant artefact which strongly influences the resulting bone position, orientation and joint kinematics. For this study, we used a statistical solid dynamics approach which is a combination of several previously reported tools: the point cluster technique (PCT) and a Kalman filter which was added to the PCT. The methods were tested and evaluated on controlled human-arm motions, using an optical motion capture system (Vicon^TM).

The addition of a Kalman filter to the PCT for rigid body motion estimation results in a smoother signal that better represents the joint motion. Calculations indicate less signal distortion than when using a digital low-pass filter. Furthermore, adding a Kalman filter to the PCT substantially reduces the dispersion of the maximal and minimal instantaneous frequencies. For controlled human movements, the result indicated that adding a Kalman filter to the PCT produced a more accurate signal. However, it could not be concluded that the proposed Kalman filter is better than a low-pass filter for estimation of the motion. We suggest that implementation of a Kalman filter with a better biomechanical motion model will be more likely to improve the results.     

Modelling of non-linear elastic tissues for surgical simulation

Realistic modelling of the interaction between surgical instruments and human organs has been recognised as a key requirement in the development of high-fidelity surgical simulators. Primarily due to computational considerations, most of the past real-time surgical simulation research has assumed linear elastic behaviour for modelling tissues, even though human soft tissues generally possess non-linear properties. For a non-linear model, the well-known Poynting effect developed during shearing of the tissue results in normal forces not seen in a linear elastic model. Using constitutive equations of non-linear tissue models together with experiments, we show that the Poynting effect results in differences in force magnitude larger than the absolute human perception threshold for force discrimination in some tissues (e.g. myocardial tissues) but not in others (e.g. brain tissue simulants).     

Modelling and simulation of porcine liver tissue indentation using finite element method and uniaxial stress–strain data

We hypothesize that both compression and elongation stress–strain data should be considered for modeling and simulation of soft tissue indentation. Uniaxial stress–strain data were obtained from in vitro loading experiments of porcine liver tissue. An axisymmetric finite element model was used to simulate liver tissue indentation with tissue material represented by hyperelastic models. The material parameters were derived from uniaxial stress–strain data of compressions, elongations, and combined compression and elongation of porcine liver samples. in vitro indentation tests were used to validate the finite element simulation. Stress–strain data from the simulation with material parameters derived from the combined compression and elongation data match the experimental data best. This is due to its better ability in modeling 3D deformation since the behavior of biological soft tissue under indentation is affected by both its compressive and tensile characteristics. The combined logarithmic and polynomial model is somewhat better than the 5-constant Mooney–Rivlin model as the constitutive model for this indentation simulation.     

A Case Study on Human Upper Limb Modelling for Dynamic Simulation

Modelling consists of developing a representation of the properties of an object or a phenomenon with respect to the goals of its analysis. In this paper, the procedure presented is that followed in the CHARM project for human upper limb modelling with respect to the project constraints on the model implementation and simulation. The objective is to develop a Comprehensive Human Animation Resource Model allowing the simulation of human motion, including the finite element simulation of soft tissue deformation and muscular contraction. Generally, models are presented based on assumptions left for a fortiori validation. The a priori considerations which lead to these assumptions are rarely detailed. Here, the aim is to form a basis for the choices and assumptions which are to be made prior to the validation. The analysis is based on the general approach for the modelling of multi-body deformable systems as well as on previous studies on the human upper limb.     

A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

Anisotropic material behaviours of soft tissues in human trachea: an experimental study

BackgroundHuman trachea is a multi-component structure composed of cartilage, trachealis muscle, mucosa and submucosa membrane and adventitial membrane. Its mechanical properties are essential for an accurate prediction of tracheal deformation, which has a significant clinic relevance. Efforts have been made in quantifying the material behaviour of tracheal cartilage and trachealis muscle. However, the material behaviours of other components have been least investigated.MethodsThree human cadaveric trachea specimens were used in this study. Trachealis muscle, mucosa and submucosa membrane and adventitia membrane were excised to perform the uniaxial test in axial and circumferential directions. In total, 72 tissue strips were prepared and tested. Tangent modulus was used to quantified the stiffness of each tissue strip at various stretch levels.ResultsThe obtained results indicated that all types of tracheal soft tissues were highly non-linear and anisotropic. Trachealis muscle in the circumferential direction had the most excellent extensibility; and the adventitial collagen membrane in the circumferential direction was the stiffest.ConclusionThis study is helpful in understanding the material behaviour of trachea. Obtained results can be used for computational and analytic modelling to quantify the tracheal deformation.     

Investigation of soft tissue movement during level walking: translations and rotations of skin markers

Skin marker-based stereophotogrammetry is the most widely used technique for human motion analysis but its accuracy is mainly limited by soft tissue artifact (STA) which reflects the non-rigidity of human body segments during activities. To compensate for the effects of STA and improve the accuracy of motion analysis, it is critical to understand the behavior and characteristics of soft tissue movement. By using a non-invasive approach, this study investigated the soft tissue movement on the thigh and shank of twenty healthy subjects during level walking which is one of the most important human daily activities and the basic content of clinical gait analysis. With the measurement of inter-marker translations and rotations on each segment, a 4D picture (3D space and time) of soft tissue deformation on the thigh and shank during walking was quantified in terms of the positional and orientational change between different skin locations. Soft tissue deformation showed nonuniform distribution at different locations as well as along different directions. The range of inter-marker movement was found to be up to 19.1mm/19.6 degrees on the thigh and 9.3mm/8.6 degrees on the shank. Results in this study provide useful information for understanding soft tissue movement behavior and exploring better marker configurations. Inter-marker movement exhibited similar patterns across subjects. This finding suggests the possibility that STA has inter-subject similarity, which is contrary to the prevailing opinion. This new insight may lead to more effective STA compensation strategies for skin marker-based motion analysis.     

Evaluation of accuracy of non-linear finite element computations for surgical simulation: study using brain phantom

In this paper, the accuracy of non-linear finite element computations in application to surgical simulation was evaluated by comparing the experiment and modelling of indentation of the human brain phantom. The evaluation was realised by comparing forces acting on the indenter and the deformation of the brain phantom. The deformation of the brain phantom was measured by tracking 3D motions of X-ray opaque markers, placed within the brain phantom using a custom-built bi-plane X-ray image intensifier system. The model was implemented using the ABAQUS(TM) finite element solver. Realistic geometry obtained from magnetic resonance images and specific constitutive properties determined through compression tests were used in the model. The model accurately predicted the indentation force-displacement relations and marker displacements. Good agreement between modelling and experimental results verifies the reliability of the finite element modelling techniques used in this study and confirms the predictive power of these techniques in surgical simulation.     

Fast Soft Tissue Deformation and Stump-Socket Interaction Toward a Computer-Aided Design System for Lower Limb Prostheses

Prosthetic technology is rapidly advancing but there's a catch. Regardless the technology or the material used, a minimum cost is still high. One of the problems relates to the fact that the conventional socket fabrication process is still used. This method is based on subjective estimations of the involved specialists and feedbacks of the patients. This process consumes remarkable amount of time, manpower and materials. Research works are needed to design new efficient and low-cost alternative techniques for the socket design. This technique should definitely be based on CAD-CAM methods. Therefore, the first step toward this objective is to establish an accurate numeric model for evaluating and optimizing the design process. In this present work, we developed a new approach to simulate the stump soft tissue deformation and stump-socket interaction using Mass-Spring System (MSS) approach and a point-to-surface contact formulation.A novel Mass-Spring System with corrective spring (MSS-CS) model was developed and evaluated. A node-to-surface contact formulation was also integrated and evaluated. The MSS-CS model and contact formulation were evaluated with primitive geometrical object and a stump-socket model. Moreover, a finite element model of the stump-socket interaction was also developed using Abaqus to evaluate the proposed approach.Obtained results show that the proposed contact formulation has a very good precision level and the contact pressures on the interface between the elastic and rigid bodies are very close to the analytical solutions. The comparison with Abaqus showed a qualitative concordance for the contact pressure. However, quantitative deviation remains high [25-50]% at the peak contact pressure due to different contact formulations. In particular, our MSS-CS approach is more efficient than Abaqus simulation in term of computational time and cost.A novel approach was proposed to model soft tissue deformation and stump-socket interaction in an efficient and accurate manner. As perspectives, this present approach for a real-time simulation of the stump-socket interaction could be used in a real-time CAD-CAM platform to provide a cost-effective socket manufacturing process.     

Explicit finite element modelling of heel pad mechanics in running: inclusion of body dynamics and application of physiological impact loads

Many heel pathologies including plantar heel pain may result from micro tears/trauma in the subcutaneous tissues, in which internal tissue deformation/stresses within the heel pad play an important role. Previously, many finite element models have been proposed to evaluate stresses inside the heel pad, but the majority of these models only focus on static loading boundary conditions. This study explored a dynamics modelling approach to the heel pad subjected to realistic impact loads during running. In this model, the inertial property and action of the body are described by a lumped parameter model, while the heel/shoe interactions are modelled using a viscoelastic heel pad model with contact properties. The impact force pattern, dynamic heel pad deformation and stress states predicted by the model were compared with published experimental data. Further parametrical studies revealed the model responses, in terms of internal stresses in the skin and fatty tissue, change nonlinearly when body dynamics changes. A reduction in foot's touchdown velocity resulted in a less severe impact landing and stress relief inside the heel pad, for example peak von-Mises stress in fatty tissue, was reduced by 11.3%. Applications of the model may be extendable to perform iterative analyses to further understand the complex relationships between body dynamics and stress distributions in the soft tissue of heel pad during running. This may open new opportunities to study the mechanical aetiology of plantar heel pain in runners.