Real-time Error Control for Surgical Simulation

Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

Robotics-Assisted Needle Steering for Percutaneous Interventions: Modeling and Experiments

Needle insertion and guidance plays an important role in medical procedures such as brachytherapy and biopsy. Flexible needles have the potential to facilitate precise targeting and avoid collisions during medical interventions while reducing trauma to the patient and post-puncture issues. Nevertheless, error introduced during guidance degrades the effectiveness of the planned therapy or diagnosis. Although steering using flexible bevel-tip needles provides great mobility and dexterity, a major barrier is the complexity of needle-tissue interaction that does not lend itself to intuitive control. To overcome this problem, a robotic system can be employed to perform trajectory planning and tracking by manipulation of the needle base. This research project focuses on a control-theoretic approach and draws on the rich literature from control and systems theory to model needle-tissue interaction and needle flexion and then design a robotics-based strategy for needle insertion/steering. The resulting solutions will directly benefit a wide range of needle-based interventions. The outcome of this computer-assisted approach will not only enable us to perform efficient preoperative trajectory planning, but will also provide more insight into needle-tissue interaction that will be helpful in developing advanced intraoperative algorithms for needle steering. Experimental validation of the proposed methodologies was carried out on a state of-the-art 5-DOF robotic system designed and constructed in-house primarily for prostate brachytherapy. The system is equipped with a Nano43 6-DOF force/torque sensor (ATI Industrial Automation) to measure forces and torques acting on the needle shaft. In our setup, an Aurora electromagnetic tracker (Northern Digital Inc.) is the sensing device used for measuring needle deflection. A multi-threaded application for control, sensor readings, data logging and communication over the ethernet was developed using Microsoft Visual C 2005, MATLAB 2007 and the QuaRC Toolbox (Quanser Inc.). Various artificial phantoms were developed so as to create a realistic medium in terms of elasticity and insertion force ranges; however, they simulated a uniform environment without exhibiting complexities of organic tissues. Experiments were also conducted on beef liver and fresh chicken breast, beef, and ham, to investigate the behavior of a variety biological tissues

A Novel Bio-Inspired Insertion Method for Application to Next Generation Percutaneous Surgical Tools

The use of minimally invasive techniques can dramatically improve patient outcome from neurosurgery, with less risk, faster recovery, and better cost effectiveness when compared to conventional surgical intervention. To achieve this, innovative surgical techniques and new surgical instruments have been developed. Nevertheless, the simplest and most common interventional technique for brain surgery is needle insertion for either diagnostic or therapeutic purposes. The work presented in this thesis shows a new approach to needle insertion into soft tissue, focussing on soft tissue-needle interaction by exploiting microtextured topography and the unique mechanism of a reciprocating motion inspired by the ovipositor of certain parasitic wasps. This thesis starts by developing a brain-like phantom which I was shown to have mechanical properties similar to those of neurological tissue during needle insertion. Secondly, a proof-of-concept of the bio-inspired insertion method was undertaken. Based on this finding, the novel method of a multi-part probe able to penetrate a soft substrate by reciprocal motion of each segment is derived. The advantages of the new insertion method were investigated and compared with a conventional needle insertion in terms of needle-tissue interaction. The soft tissue deformation and damage were also measured by exploiting the method of particle image velocimetry. Finally, the thesis proposes the possible clinical application of a biologically-inspired surface topography for deep brain electrode implantation. As an adjunct to this work, the reciprocal insertion method described here fuelled the research into a novel flexible soft tissue probe for percutaneous intervention, which is able to steer along curvilinear trajectories within a compliant medium. Aspects of this multi-disciplinary research effort on steerable robotic surgery are presented, followed by a discussion of the implications of these findings within the context of future work

The development of a soft tissue mimicking hydrogel: Mechanical characterisation and 3D printing

Accurate tissue phantoms are difficult to design due to the complex hyperelastic, viscoelastic and biphasic properties of real soft tissues. The aim of this work is to demonstrate the tissue mimicking ability of a composite hydrogel (CH), constituting of poly(vinyl alcohol) (PVA) and phytagel (PHY), as a soft tissue phantom over a range mechanical properties, for a variety of biomedical and tissue engineering applications. Its compressive stress-strain behaviour, relaxation response, tensile impact stresses and surgical needle-tissue interactions were mapped and characterised with respect to its constituent hydrogel formulation. The mechanical characterisation of biological tissues was also investigated and the results were used as the ground truth for mimicking. The best mimicking hydrogel compositions were determined by combining the most relevant mechanical properties for each desired application. This thesis demonstrates the use of the tissue mimicking composite hydrogel formulations as tissue phantoms for various surgical procedures, including convection enhanced drug delivery, and traumatic brain injury studies. To expand the applications of the CH, a preliminary biological evaluation of the hydrogel was performed using human dermal fibroblasts. Cell seeded on the collagen-coated composite hydrogel showed good attachment and viability. Finally, a novel fabrication method with the aim of creating samples that replicate the anisotropic properties of biological tissues was developed. A cryogenic 3D printing method utilising the liquid to solid phase change of the composite hydrogel ink was achieved by rapidly cooling the ink solution below its freezing point. The setup was able to successfully create complex 3D brain mimicking material. The method was validated by showing that the mechanical and microstructural properties of the 3D printed material was well matched to its cast-moulded equivalent. This greatly widens the applications of the CH as a mechanically accurate tool for in-vitro testing and also demonstrates promise for future mechanobiology and tissue engineering studies.Open Acces

Development of an online progressive mathematical model of needle deflection for application to robotic-assisted percutaneous interventions

A highly flexible multipart needle is under development in the Mechatronics in Medicine Laboratory at Imperial College, with the aim to achieve multi-curvature trajectories inside biological soft tissue, such as to avoid obstacles during surgery. Currently, there is no dedicated software or analytical methodology for the analysis of the needle’s behaviour during the insertion process, which is instead described empirically on the basis of experimental trials on synthetic tissue phantoms. This analysis is crucial for needle and insertion trajectory design purposes. It is proposed that a real-time, progressive, mathematical model of the needle deflection during insertion be developed. This model can serve three purposes, namely, offline needle and trajectory design in a forward solution of the model, when the loads acting on needle from the substrate are known; online, real-time identification of the loads that act on the needle in a reverse solution, when the deflections at discrete points along the needle length are known; and the development of a sensitivity matrix, which enables the calculation of the corrective loads that are required to drive the needle back on track, if any deviations occur away from a predefined trajectory. Previously developed mathematical models of needle deflection inside soft tissue are limited to small deflection and linear strain. In some cases, identical tip path and body shape after full insertion of the needle are assumed. Also, the axial load acting on the needle is either ignored or is calculated from empirical formulae, while its inclusion would render the model nonlinear even for small deflection cases. These nonlinearities are a result of the effects of the axial and transverse forces at the tip being co-dependent, restricting the calculation of the independent effects of each on the needle’s deflection. As such, a model with small deflection assumptions incorporating tip axial forces can be called “quasi-nonlinear” and a methodology is proposed here to tackle the identification of such axial force in the linear range. During large deflection of the needle, discrepancies between the shape of the needle after the insertion and its tip path, computed during the insertion, also significantly increase, causing errors in a model based on the assumption that they are the same. Some of the models developed to date have also been dependent on existing or experimentally derived material models of soft tissue developed offline, which is inefficient for surgical applications, where the biological soft tissue can change radically and experimentation on the patient is limited. Conversely, a model is proposed in this thesis which, when solved inversely, provides an estimate for the contact stiffness of the substrate in a real-time manner. The study and the proposed model and techniques involved are limited to two dimensional projections of the needle movements, but can be easily extended to the 3-dimensional case. Results which demonstrate the accuracy and validity of the models developed are provided on the basis of simulations and via experimental trials of a multi-part 2D steering needle in gelatine.Open Acces

Elastocapillary Phenomena in Soft Elastic Solids

Soft elastic solids play an important role in a wide range of applications such as in tissue scaffolds to grow artificial organs, in wearable contact lenses, as adhesives, in soft robotics and even as prototypical models to understand the mechanics of growth and morphology of organs. For a soft elastic material like hydrogel with its shear modulus in the range of tens of pascals, its surface tension also contributes to the mechanics of its deformation in addition to its elasticity. As opposed to a hard solid that is very difficult to deform, for the case of these soft solids, even a weak force like gravity can bring about significant deformation. Many of these aspects of the deformation and behavior of these ultrasoft materials are still not very well understood. Thus, the objectives of this dissertation were to understand the role of elastocapillarity (i.e, joint roles of solid surface tension and elasticity) and elastobuoyancy (i.e, joint roles of gravity and elasticity) that manifest in such solids. In this dissertation, we studied the role elastocapillarity in adhesion-induced instability in thin elastic films bonded to rigid substrates and also in surface oscillation modes of soft gel spheres set to vibration; the elastobuoyancy effect; elasticity mediated interaction of particles in soft solids as well as on thin films supported over a pool of liquid. We also presented some new results on how soft spherical gels undergo restricted spreading on rigid substrates with varying surface energies. In the first section, we studied how a thin confined layer of a soft elastic film loses adhesion from a rigid substrate by forming interfacial instabilities when a tensile stress is applied to it. We performed experiments to quantify the characteristic lengthscale of the patterns formed and found that they were significantly larger than the wavelengths of purely elastic instabilities. A linear stability analysis of the elastic field equations by taking into account the role of surface tension showed that the amplification of the wavelength is due to the role of elastocapillarity where the surface tension, elasticity, and film thickness contribute jointly in a non-trivial way. In addition, we found experimentally as well as theoretically that the stress required to adhesively fracture these films is much larger than Griffith’s fracture stress for stiffer elastic films, which is also due to the effect of elastocapillarity. We also studied the surface fluctuation of sessile hydrogel spheres subjected to mechanically-induced Gaussian white noise to understand the role of elastocapillarity in their oscillation modes. An important finding of this study is that they give a direct evidence that the surface tension of these elastic hydrogels is almost like that of water, which is the integral solvent in the swollen network of the polymeric gel. In the subsequent section, we introduced the new phenomenon of Elastobuoyancy. When a rigid sphere is placed on the surface of an ultrasoft hydrogel, it plunges into the soft substrate to an equilibrium depth where the elastic strain energy of the surrounding medium balances its weight. We refer to this state of the sphere as ‘Elastobuoyant’. By performing systematic experiments where we varied the sphere size and the elasticity of the substrate, we obtained scaling laws of the depth as a function of the radii, elastic modulus and the spheres buoyant weight, which were also supported by asymptotic analyses of the same. Following the section on elastobuoyancy, we reported a new set of principles to design self-assembly of particles by using the combined roles of surface tension, elasticity, and gravity in soft substrates. We used three different systems to study this elastic interaction macroscopically: (i) elastobuoyant assembly of particles suspended inside a soft elastic gel, (ii) elastocapillary assembly of particles floating on the surface of soft gels analogous to capillary attraction of objects on the surface of liquids, and (iii) assembly of particles on the surface of thin elastic membranes supported over a viscous liquid. In the second last chapter in this thesis, we presented some results on how soft elastic gel spheres spread on rigid substrates with different surface energies. Our observations indicate that their contact angles are slightly greater than those of equivalent liquid drops on similar substrates. The contact angles of these gel spheres increase as a function of elasticity and decrease when surface energy increases. We derived an expression for the excess elastic tension in the gel spheres at the crack tip by using an approach that is similar to estimating the viscous dissipation at the contact line during spreading of liquids. By using a general constitutive law where the elastic energy is not limited to the square of the strains, the singularity at the crack tip is artificially removed thereby forcing the gel to assume a liquid-like behavior. Our experimental results agreed reasonably well with the model. In the last chapter, we summarized the doctoral research and presented suggestions for future investigations. There are several appendices in this thesis that have interesting observations from partially completed projects that need additional research and analysis in the future

Force Sensing Surgical Scissor Blades using Fibre Bragg Grating Sensors

This thesis considers the development and analysis of unique sensorised surgical scissor blades for application in minimally invasive robotic surgery (MIRS). The lack of haptic (force and tactile) feedback to the user is currently an unresolved issue with modern MIRS systems. This thesis presents details on smart sensing scissor blades which enable the measurement of instrument-tissue interaction forces for the purpose of force reflection and tissue property identification. A review of current literature established that there exists a need for small compact, biocompatible, sterilisable and robust sensors which meet the demands of current MIRS instruments. Therefore, the sensorised blades exploit the strain sensing capabilities of a single fibre Bragg grating (FBG) sensor bonded to their surface. The nature and magnitude of the strain likely to be experienced by the blades, and consequently the FBG sensor, while cutting soft tissue samples were characterised through the use of an application specific test-bed. Using the sensorised blades to estimate fracture properties is proposed, hence two methods of extracting fracture toughness information from the test samples are assessed and compared. Investigations were carried out on the factors affecting the transfer of strain from the blade material to the core of the FBG sensor for surface mounted or partially embedded arrangements. Results show that adhesive bond length, thickness and stiffness need to be carefully specified when bonding FBG sensors to ensure effective strain transfer. Calibration and dynamic cutting experiments were carried out using the characterisation test-bed. The complex nature of the blade interaction forces were modelled, primarily for the purpose of decoupling the direct, lateral, friction and fracture strains experienced by the bonded FBG sensor during cutting. The modelled and experimental results show that the approach taken in sensorising the blade enables detailed cutting force data to be obtained and consequently leads to a unique method in estimating the kinetic friction coefficient for the blades. The forces measured using the FBG are validated against a commercial load cell used in the test-bed. This research work demonstrates that this unique approach of placing a single optical fibre onto the scissor blades can, in an unobtrusive manner, measure interblade friction forces and material fracture properties occurring at the blade-tissue interface

Experimental and numerical analysis of conventional and ultrasonically-assisted cutting of bone

Bone cutting is widely used in orthopaedic, dental and neuro surgeries and is a technically demanding surgical procedure. Novel surgical methods are continually introduced in orthopaedic, neuro and dental surgeries and are aimed at minimising the invasiveness of the operation and allowing more precise cuts. One such method that utilises cutting with superimposed ultrasonic vibration is known as ultrasonically- assisted cutting (UAC). The main concern in bone cutting is the mechanical and thermal damage to the bone tissue induced by high-speed power tools. Recent technological improvements are concerned with the efforts to decrease the force required by the surgeon when cutting the bone as well as increases in surgery speed. A programme of experiments was conducted to characterise properties of a bone and get a basic understanding of the mechanics of bone cutting. The experiments included: (a) nanonindentation and tension tests to obtain the properties for the finite element (FE) bone cutting model, (b) high-speed filming to observe the chip formation process, which influences thermomechanics of the cutting process in conventional drilling (CD) and ultrasonically-assisted drilling (UAD) and, (c) plane cutting and drilling experiments to measure the levels of force and temperature rise in the bone tissue. Novel two-dimensional finite element (FE) models of cortical bone cutting were developed for conventional and ultrasonically-assisted modes with the MSC.MARC general FE code that provided thorough numerical analysis of thermomechanics of the cutting process. Mechanical properties such as the elastic modulus and strain-rate sensitivity of the bone material were determined experimentally and incorporated into the FE models. The influence of cutting parameters on the levels of stress, penetration force and temperature in the bone material was studied using conventional cutting (CC) and ultrasonically-assisted cutting (UAC). The temperature rise in the bone material near the cutting edge was calculated and the effect of cutting parameters on the level of thermal necrosis was analysed. The necrosis depth in bone was calculated as a distance from the cut surface to the point where the thermal threshold level was attained. Comparative studies were performed for the developed FE models of CC and UAC of bone and the results validated by conducting experiments and using data from scientific publications. The main outcome of the thesis is an in-depth understanding of the bone cutting process, and of its possible application in orthopaedics. Recommendations on further research developments are also suggested

Real-time Error Control for Surgical Simulation

International audienceObjective: To present the first real-time a poste-riori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA 1. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local h-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations. Index Terms—Finite element method, real-time error estimate, adaptive refinement, constraint-based interaction

Mechanical Understanding and Optimization of Template Guided Core Needle Biopsy

Prostate cancer is the second highest cause of cancer related deaths among men. According to the diagnostic pathway for prostate cancer, a prostate biopsy is performed if an individual showed signs of lesions through high prostate-specific antigen (PSA) concentration or suggestive digital rectal exam (DRE) results. The core biopsy mechanism involves inserting a beveled needle into the organ and removing a cylindrical fragment of tissue. Many factors affect the histological quality of the sample, including fragmentation, needle deflection, and needle insertion velocity. If a biopsy core is not clinically viable, an alternative core will need to be taken, resulting in increased patient trauma and potential risk of infection. Many of these relevant factors are impacted by sources of friction in the system. Prior studies have examined methods of decreasing the friction of the interactions between different components of the biopsy system to reduce the negative effects on histological sample quality. While scenarios have been explored that examine reducing the friction between the needle and tissue through sharpening and polishing techniques, the friction introduced by the needle guide in template guided core prostate biopsies has not been analyzed in the decades since its development. This study aims to introduce the biopsy guide as an additional source of friction which can be optimized to reduce friction force, while proposing and testing several configurations of the needle guide that would reduce the friction force of the system. A Finite Element Analysis (FEA) was conducted using SIMULA Abaqus modeling software, and the simulation was correlated with a derived equation that estimated friction force according to material properties. The study demonstrated that configurations for the internal surface of the needle guide which provided decreased contact surface compared to the control needle guide resulted in lower friction force between the needle and guide. Conditions which had contact points oriented parallel to the direction of insertion had the lowest recorded friction force. This suggests that the traditional biopsy needle guide may be optimized to introduce less friction force by reducing the contact area between the needle and guide inner surface. This has application in reducing the number of passes required to obtain a histologically viable core specimen, and therefore reducing the opportunity for patients to develop infection