Development of Techniques for Modeling the Static Buckling of Euler Beam and Dynamic Response of Kirchhoff Rods: Application to Surgical Simulation and Training

In this dissertation, we present novel schemes for a static simulation of a buckled Euler beam with curve channel constraints in two dimensional space and simulation of the dynamic response of a soft Kirchhoff rod in three dimension space at real time rate. The aim of this model is to provide a robust and fast means for simulating endoscopes and surgical threads for training and surgical simulation purposes. Finding a static configuration of a buckled cantilever elastic beam constrained in a curved solid channel subject to end forces is a simple model of endoscopy and it is posed as the minimization of an energy functional. We solve it by a novel technique, a variant of a dynamic programming approach called the Viterbi algorithm. The core idea of this approach is to discretize the variables describing the potential energy and to construct a set of admissible configurations of the beam. The Viterbi algorithm is then employed to search through the set of possible beam configurations and locate the one with the minimum potential energy in a very computationally efficient way. The new approach does not require any gradient computations and could be considered as a direct search method, and thus can be guaranteed to find the global minimum potential energy. Also the constraints can be automatically satisfied by constructing the proper set of all the possible configurations. The approach can also be used to find feasible starting configurations associated with conventional minimizing algorithms. We also discuss a novel scheme based on discrete variational integrators to study the dynamics of an inextensible thin Kirchhoff rod which is a model for a surgical thread. The benefits of such approach are that it is a very efficient scheme that guarantees conservation of momentum and energy over very long times so that a real time simulator can be operated over long periods of time. In addition, we report on an innovative technique to capture the inextensibility as well as the internal dissipation of the rod efficiently. Finally, a new collision avoidance scheme based on a continuous penalty force is employed to simulate the interaction of the rod with the surrounding medium. The simulations performed capture the formation of plectoneme, i.e. a loop of helices twisted together. Lastly, the scheme is employed to simulate the tying of a square knot. This model can be used to simulate surgical threads at real time rate

Simulation Guidée par l’Image pour la Réalité Augmentée durant la Chirurgie Hépatique

The main objective of this thesis is to provide surgeons with tools for pre and intra-operative decision support during minimally invasive hepaticsurgery. These interventions are usually based on laparoscopic techniques or, more recently, flexible endoscopy. During such operations, the surgeon tries to remove a significant number of liver tumors while preserving the functional role of the liver. This involves defining an optimal hepatectomy, i.e. ensuring that the volume of post-operative liver is at least at 55% of the original liver and the preserving at hepatic vasculature. Although intervention planning can now be considered on the basis of preoperative patient-specific, significant movements of the liver and its deformations during surgery data make this very difficult to use planning in practice. The work proposed in this thesis aims to provide augmented reality tools to be used in intra-operative conditions in order to visualize the position of tumors and hepatic vascular networks at any time.L’objectif principal de cette thèse est de fournir aux chirurgiens des outils d’aide à la décision pré et per-opératoire lors d’interventions minimalement invasives en chirurgie hépatique. Ces interventions reposent en général sur des techniques de laparoscopie ou plus récemment d’endoscopie flexible. Lors de telles interventions, le chirurgien cherche à retirer un nombre souvent important de tumeurs hépatiques, tout en préservant le rôle fonctionnel du foie. Cela implique de définir une hépatectomie optimale, c’est à dire garantissant un volume du foie post-opératoire d’au moins 55% du foie initial et préservant au mieux la vascularisation hépatique. Bien qu’une planification de l’intervention puisse actuellement s’envisager sur la base de données pré-opératoire spécifiques au patient, les mouvements importants du foie et ses déformations lors de l’intervention rendent cette planification très difficile à exploiter en pratique. Les travaux proposés dans cette thèse visent à fournir des outils de réalité augmentée utilisables en conditions per-opératoires et permettant de visualiser à chaque instant la position des tumeurs et réseaux vasculaires hépatiques

Image-Based Force Estimation and Haptic Rendering For Robot-Assisted Cardiovascular Intervention

Clinical studies have indicated that the loss of haptic perception is the prime limitation of robot-assisted cardiovascular intervention technology, hindering its global adoption. It causes compromised situational awareness for the surgeon during the intervention and may lead to health risks for the patients. This doctoral research was aimed at developing technology for addressing the limitation of the robot-assisted intervention technology in the provision of haptic feedback. The literature review showed that sensor-free force estimation (haptic cue) on endovascular devices, intuitive surgeon interface design, and haptic rendering within the surgeon interface were the major knowledge gaps. For sensor-free force estimation, first, an image-based force estimation methods based on inverse finite-element methods (iFEM) was developed and validated. Next, to address the limitation of the iFEM method in real-time performance, an inverse Cosserat rod model (iCORD) with a computationally efficient solution for endovascular devices was developed and validated. Afterward, the iCORD was adopted for analytical tip force estimation on steerable catheters. The experimental studies confirmed the accuracy and real-time performance of the iCORD for sensor-free force estimation. Afterward, a wearable drift-free rotation measurement device (MiCarp) was developed to facilitate the design of an intuitive surgeon interface by decoupling the rotation measurement from the insertion measurement. The validation studies showed that MiCarp had a superior performance for spatial rotation measurement compared to other modalities. In the end, a novel haptic feedback system based on smart magnetoelastic elastomers was developed, analytically modeled, and experimentally validated. The proposed haptics-enabled surgeon module had an unbounded workspace for interventional tasks and provided an intuitive interface. Experimental validation, at component and system levels, confirmed the usability of the proposed methods for robot-assisted intervention systems

Realtime Simulation of Stiff Threads for microsurgery training simulation

This thesis introduces the physical simulation of surgical thread for usage in a microsurgical training simulator for the education of medical students. To allow interactive simulation the thread must be real time capable. Importantly, in the simulation, the thread must behave in a way that it looks like a real thread to the user. The user can then "dive into" the simulation, because for the user, the simulation of the thread appears real. We refer to this "diving into" the simulation as "immersion". The physical model of the thread is a mass-spring model based on the Kirchhoff theory for elastic rods. One challenge is the stiffness constraint of the thread. A real world thread does not change it's length signiffcantly even under high stress. In a mass-spring model this property can be obtained by using high spring constants. But if an explicit integration method is applied the so called "overshooting" effect presents a problem. It causes the system to diverge when the spring constants are too high. In this thesis the problem is addressed by applying an implicit integration method. A key property of implicit integration methods is that it is unconditionally stable and thereby allows a large time step in the numerical integration. But it also requires that a linear system of size equal to the number of degrees of freedom in the system is solved. If the number of degrees of freedom is high this conflicts with the real-time requirement of the simulation. In this work it is shown that for the case of the thread the matrix in the linear system is banded and can therefore be solved in linear time. Another advantage of the implicit integration is that forces are propagated along the complete thread within one time step. For the simulation of microsurgical sutures knots have to be modeled. A knot causes numerous contacts of the thread with itself. The contact forces are modeled and calculated using a physical model. Because all forces propagate along the whole thread within one time step all contacts interact with each other. A force applied at one contact affects all other contacts. Because of this all contact forces have to be solved for simultaneously. The interaction of the contacts due to the implicit integration are calculated resulting in a linear system which describes the relation between the contact forces and the relative movement of the thread at the contacts. Physically correct contact forces have to be found with this linear system. Similar to the simulation of rigid bodies, a linear complementary problem or a nonlinear complementary problem results depending on the model that is used for the contact forces. In case of rigid body simulation the "projected Gauss-Seidel" is a proven method for solving the problem. In this thesis the nonlinear conjugate gradient (NNCG) method from Silcowitz-Hansen et al. is applied. This method was originally developed for rigid body simulations. The thread has been integrated into the microsurgical training simulator "MicroSim". Which is to say, interactions between the thread and tissue and forceps have been modeled and incorporated into "MicroSim". These interactions have to be compatible with the implicit integration of the thread. In a joint work with Sismanidis and Schuppe a training module for MicroSim has been developed. This training module allows for training of a microsurgical anastomosis of blood vessels

Development of A Kinetic Model For Loop-Free Colonoscopy Technology

The colonoscope is an important tool in diagnosis and management of diseases of the colon. One of the ongoing challenges with this device is that the colonoscope may form a loop together with the colon during the procedure. The result of the loop is that further insertion of the scope in the colon may not be possible. The loop may also cause risks of perforation of the colon and pain in the patient. There are currently several existing devices to overcome loop formation in colonoscopy, some of which have been introduced in clinical work. However, empirical assessment shows that these devices do not work very well. This is the motivation for the research presented in this thesis. In this thesis, a new paradigm of thinking, “doctor-assisted colonoscopy,” is proposed to overcome loop formation. In this new approach, the physician’s role is enhanced with new information that is acquired by sensors outside the human body and inferred from the mathematical model. It is referred to as a kinetic model due to the fact that this model describes the kinetic behaviour of the scope. This thesis is devoted to development of this kinetic model. In this study, the model of the colonoscope and the model of the colon are developed based on the Timoshenko beam theory, and parameters in both models are determined by the experiments. The following conclusions then are made: (1) self-locking of the colonoscope is the most basic cause for a loop to occur, while structural instability of the colonsocope is dependent on the self-locking; (2) both the scope and the colon can be well represented with the Timoshenko beam elements and the Linear Complementary Problem (LCP) formulation derived from Signorini’s law, and Coulom’s law for representation of interactions between the colon and scope is adequate; (3) there are effects from the location, looping, and tip deflection of the scope on flexural rigidity of the scope. Approximately, the flexural rigidity of the CF-Q160L colonoscope ranges from 300 to 650 N•cm2, and its accuracy is proven by a good agreement between the model predicted result and experimental result; (4) Rayleigh damping for the CF-Q160L colonoscope depends more on the mass matrix [M] of the colonoscope than the stiffness matrix [K], which is evident by the large coefficient value of “alpha” (0.3864) and the small coefficient value of “beta” (0.0164). The contributions of this thesis are: (1) the finding that the main cause of the loop is not structural instability of the colonoscope but rather self-locking of the colonoscope, which could lead to design of a “new-generation” colonoscope to avoid the loop; (2) a systematic evaluation of the existing colonoscopy technologies based on the well-proven Axiomatic Design Theory (ADT), which will serve as a guideline for the development of future new colonoscopes in future; (3) an approach to developing a kinetic model of the colonoscope useful to modeling similar objects such as a catheter guide-wire; (4) a novel ex-vivo colonoscopy test-bed with the kinetic and kinematic measurements useful for validation of new designs in colonoscopy technology and also useful for training physicians who perform the colonoscopy procedure; and (5) a new paradigm of thinking for colonoscopy called “doctor-assisted colonoscopy,” which has potential applications to other medical procedures such as catheter-based procedures

Shear-promoted drug encapsulation into red blood cells: a CFD model and μ-PIV analysis

The present work focuses on the main parameters that influence shear-promoted encapsulation of drugs into erythrocytes. A CFD model was built to investigate the fluid dynamics of a suspension of particles flowing in a commercial micro channel. Micro Particle Image Velocimetry (μ-PIV) allowed to take into account for the real properties of the red blood cell (RBC), thus having a deeper understanding of the process. Coupling these results with an analytical diffusion model, suitable working conditions were defined for different values of haematocrit

Contact non-localisé entre poutres avec des sections droites circulaires et elliptiques

Numerous materials and structures are aggregates of slender bodies. We can, for example, refer to struts in metal foams, yarns in textiles, fibers in muscles or steel wires in wire ropes. To predict the mechanical performance of these materials and structures, it is important to understand how the mechanical load is distributed between the different bodies. If one can predict which slender body is the most likely to fail, changes in the design could be made to enhance its performance. As the aggregates of slender bodies are highly complex, simulations are required to numerically compute their mechanical behaviour. The most widely employed computational framework is the Finite Element Method in which each slender body is modeled as a series of beam elements. On top of an accurate mechanical representation of the individual slender bodies, the contact between the slender bodies must often be accurately modeled. In the past couple of decades, contact between beam elements has received wide-spread attention. However, the focus was mainly directed towards beams with circular cross-sections, whereas elliptical cross-sections are also relevant for numerous applications. Only two works have considered contact between beams with elliptical cross-sections, but they are limited to point-wise contact, which restricts their applicability. In this Ph.D. thesis, different frameworks for beams with elliptical cross-sections are proposed in case a point-wise contact treatment is insufficient. The thesis also reports a framework for contact scenarios where a beam is embedded inside another beam, which is in contrast to conventional contact frameworks for beams in which penetrating beams are actively repelled from each other. Finally, two of the three contact frameworks are enhanced with frictional sliding, where friction not only occurs due to sliding in the beams’ longitudinal directions but also in the transversal directions

Catheter Localization Utilizing a Sensor-Enabled Guidewire: Design of a Proof-of-Concept System

The purpose of this thesis project was to develop a proof-of-concept system for tracking the tip of a catheter without an embedded electromagnetic sensor by utilizing a sensor enabled guidewire. The motivation for the project was a reduction fluoroscopy radiation dose for clinicians in the interventional cardiology lab and the extension of navigation technology to be used with a wider variety of interventional devices through the implementation of expanded capabilities of the Abbott MediGuide system. The focus of the project was on the development of a proof-of-concept system capable of using an external device to track relative guidewire and catheter motion and apply that to a calculated position in the vasculature. The research conducted covered multiple disciplines from mechanical design to software algorithms. A prototype system was developed that functions alongside the MediGuide system to provide a three dimensional depiction of catheter location and a measurement of the relative linear displacement separating the distal tip of the guidewire and the distal tip of the catheter. The system consists of an electromechanical device to measure relative motion and software to communicate with the device, interpret recorded guidewire position data into a representative trajectory, and display the results to the user. The hardware and software components of the project were evaluated to determine accuracy and precision. The prototype device was determined to be accurate to 0.7±0.03% of total displacement. In a simulated use procedure the device was determined to be accurate to 1.4±0.53mm. The software algorithms to generate a simulated guidewire path were evaluated and tuned to generate the best response to the data sets available. In summary, the work performed here shows the possibility of implementing a device and software system that can provide localization information to the operator about the catheters used in an interventional procedure without the need for a sensor in the catheter

Real-time simulation of surgery by Proper Generalized Decomposition techniques

La simulación quirúrgica por ordenador en tiempo real se ha convertido en una alternativa muy atractiva a los simuladores quirúrgicos tradicionales. Entre otras ventajas, los simuladores por ordenador consiguen ahorros importantes de tiempo y de costes de mantenimiento, y permiten que los estudiantes practiquen sus habilidades quirúrgicas en un entorno seguro tantas veces como sea necesario. Sin embargo, a pesar de las capacidades de los ordenadores actuales, la cirugía computacional sigue siendo un campo de investigación exigente. Uno de sus mayores retos es la alta velocidad a la que se tienen que resolver complejos problemas de mecánica de medios continuos para que los interfaces hápticos puedan proporcionar un sentido del tacto realista (en general, se necesitan velocidades de respuesta de 500-1000 Hz).Esta tesis presenta algunos métodos numéricos novedosos para la simulación interactiva de dos procedimientos quirúrgicos habituales: el corte y el rasgado (o desgarro) de tejidos blandos. El marco común de los métodos presentados es el uso de la Descomposición Propia Generalizada (PGD en inglés) para la generación de vademécums computacionales, esto es, metasoluciones generales de problemas paramétricos de altas dimensiones que se pueden evaluar a velocidades de respuesta compatibles con entornos hápticos.En el caso del corte, los vademécums computacionales se utilizan de forma conjunta con técnicas basadas en XFEM, mientras que la carga de cálculo se distribuye entre una etapa off-line (previa a la ejecución interactiva) y otra on-line (en tiempo de ejecución). Durante la fase off-line, para el órgano en cuestión se precalculan tanto un vademécum computacional para cualquier posición de una carga, como los desplazamientos producidos por un conjunto de cortes. Así, durante la etapa on-line, los resultados precalculados se combinan de la forma más adecuada para obtener en tiempo real la respuesta a las acciones dirigidas por el usuario. En cuanto al rasgado, a partir de una ecuación paramétrica basada en mecánica del daño continuo, se obtiene un vademécum computacional. La complejidad del modelo se reduce mediante técnicas de Descomposición Ortogonal Propia (POD en inglés), y el vademécum se incorpora a una formulación incremental explícita que se puede interpretar como una especie de integrador temporal.A modo de ejemplo, el método para el corte se aplica a la simulación de un procedimiento quirúrgico refractivo de la córnea conocido como queratotomía radial, mientras que el método para el rasgado se centra en la simulación de la colecistectomía laparoscópica (la extirpación de la vesícula biliar mediante laparoscopia). En ambos casos, los métodos implementados ofrecen excelentes resultados en términos de velocidades de respuesta y producen simulaciones muy realistas desde los puntos de vista visual y háptico.The real-time computer-based simulation of surgery has proven to be an appealing alternative to traditional surgical simulators. Amongst other advantages, computer-based simulators provide considerable savings on time and maintenance costs, and allow trainees to practice their surgical skills in a safe environment as often as necessary. However, in spite of the current computer capabilities, computational surgery continues to be a challenging field of research. One of its major issues is the high speed at which complex problems in continuum mechanics have to be solved so that haptic interfaces can render a realistic sense of touch (generally, feedback rates of 500–1 000 Hz are required). This thesis introduces some novel numerical methods for the interactive simulation of two usual surgical procedures: cutting and tearing of soft tissues. The common framework of the presented methods is the use of the Proper Generalised Decomposition (PGD) for the generation of computational vademecums, i. e. general meta-solutions of parametric high-dimensional problems that can be evaluated at feedback rates compatible with haptic environments. In the case of cutting, computational vademecums are used jointly with XFEM-based techniques, and the computing workload is distributed into an off-line and an on-line stage. During the off-line stage, both a computational vademecum for any position of a load and the displacements produced by a set of cuts are pre-computed for the organ under consideration. Thus, during the on-line stage, the pre-computed results are properly combined together to obtain in real-time the response to the actions driven by the user. Concerning tearing, a computational vademecum is obtained from a parametric equation based on continuum damage mechanics. The complexity of the model is reduced by Proper Orthogonal Decomposition (POD) techniques, and the vademecum is incorporated into an explicit incremental formulation that can be viewed as a sort of time integrator. By way of example, the cutting method is applied to the simulation of a corneal refractive surgical procedure known as radial keratotomy, whereas the tearing method focuses on the simulation of laparoscopic cholecystectomy (i. e. the removal of the gallbladder). In both cases, the implemented methods offer excellent performances in terms of feedback rates, and produce.<br /