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 /

High Fidelity Haptic Rendering for Deformable Objects Undergoing Topology Changes

International audienceThe relevance of haptic feedback for minimally invasive surgery has been demonstrated at numerous counts. However, the proposed methods often prove inadequate to handle correct contact computation during the complex interactions or topological changes that can be found in surgical interventions. In this paper, we introduce an approach that allows for accurate computation of contact forces even in the presence of topological changes due to the simulation of soft tissue cutting. We illustrate this approach with a simulation of cataract surgery, a typical example of microsurgery

Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.The research leading these results has received funding from the European Union’s Seven Framework Program managed by REA Research Executive agency http://ec.europa.eu/research/rea (FP7/2007-2013) under Grant Agreement n° FP7-SME-2013 606634 and the Spanish Ministry of Economy and Competitiveness (DPI2011-27939-C02-01)

Identification of corneal mechanical properties using optical tomography and digital volume correlation

This work presents an effective methodology for measuring the depth-resolved 3D full-field deformation of semitransparent, light scattering soft tissues such as vertebrate eye cornea. This was obtained by performing digital volume correlation on optical coherence tomography volume reconstructions of silicone rubber phantoms and porcine cornea samples. Both the strip tensile tests and the posterior inflation tests have been studied. Prior to these tests, noise effect and strain induced speckle decorrelation were first studied using experimental and simulation methods. The interpolation bias in the strain results has also been analyzed. Two effective approaches have been introduced to reduce the interpolation bias. To extract material constitutive parameters from the 3D full-field deformation measurements, the virtual fields method has been extended into 3D. Both manually defined virtual fields and the optimized piecewise virtual fields have been developed and compared with each other. Efforts have also been made in developing a method to correct the refraction induced distortions in the optical coherence tomography reconstructions. Tilt tests of different silicone rubber phantoms have been implemented to evaluate the performance of the refraction correction method in correcting the distorted reconstructions

Corneal biomechanical properties : Measurement, modification and simulation

Esta tesis aborda la medición de las propiedades biomecánicas de la córnea. Se desarrollaron técnicas para medir la rigidez de la córnea in vitro con el fin de estudiar el comportamiento de la córnea como una función de diferentes factores (tales como la hidratación, la geometría, la presión intraocular y la rigidez de la córnea). Los datos experimentales se utilizaron para construir modelos numéricos capaces de reproducir la respuesta biomecánica observada de la córnea. Se aplicaron modelos numéricos para recuperar los parámetros biomecánicos de mediciones de deformación in vivo y para estudiar el efecto de la implantación de segmentos de anillos intraestromales. En particular, se utilizaron el método de inflación en ojos enteros y botones córneales, la extensiometría bídimensional, un soplo de aire combinado con tomografía de coherencia óptica (OCT), microscopía de Brillouin y OCT-vibrografía para las mediciones experimentales. Para el análisis numérico, se construyeron modelos de elementos finitos para estudiar la inflación de ojos enteros y botones córneales, la respuesta de la córnea después de un soplo de aire, el comportamiento del ojo bajo vibración y los cambios refractivos después de la implantación de anillos intraestromales. This thesis addresses the measurement of the corneal biomechanical properties. Techniques were developed to measure the corneal stiffness in vitro in order to study the corneal behavior as a function of different factors (such as hydration, geometry, intraocular pressure, corneal stiffness). Experimental data were used to build numerical models, which were able to reproduce the observed biomechanical response of the cornea. Numerical models were applied to retrieve biomechanical parameters from in vivo deformation measurements and to study the outcome with implantation of intrastromal ring segments. In particular whole-eye / corneal inflation, 2D extensiometry, an air-puff technique combined with optical coherence tomography (OCT), Brillouin microscopy and OCT-vibrography were used for the experimental measurements. For the numerical analysis, finite element models were built for eye inflation, corneal response following an air-puff, ocular vibration behavior and refractive changes after ICRS implantation

A virtual training simulator for learning cataract surgery with phacoemulsification

Author name used in this publication: Fu-Lai Chung2009-2010 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Biomechanics of Eye Globe and Methods of Its Study

Knowledge of biomechanical properties of eye globe is necessary both for correct selection of candidates for refractive surgery and right choice of operative intervention parameters. No less important, it is for corneal ectatic disease diagnostics and monitoring. Also it gives inestimable contribution for interpretation of intraocular pressure (IOP) indices especially in cases with irregular eye shape or after past corneal surgical procedures. Moreover, it allows studying injury mechanism by glaucoma process on optic nerve head fibers. Above it, scleral biomechanical properties research is necessary for the investigation of pathophysiologic factors of myopia manifestation and progression. This chapter is devoted to review of existed to date methods of study of eye fibrous tunic biomechanical properties. It describes mathematical, experimental, and clinical models provided evaluation of unsearchable by direct measurement parameters. It also observes effective technics of impact on both sclera and cornea with the aim of correction of its biomechanical condition

Numerical simulation of the eye structure under endoscopic treatment

Tato magisterská diplomová práce vznikla pro České vysoké učení technické, dále ČVUT. Univerzita ČVUT patří mezi přední univerzity technického zaměření v České republice, a je situována v jejím hlavním m ěstě, v Praze. Účelem této diplomové práce byl výzkum napětí a deformací lidského oka a hlavice endoskopu průběhu endoskopických lékařských zákroků. Výsledky výpočtů budou dále použity při vývoji dalších lékařských nástrojů užívaných k oftalmologickým operačním zákrokům. V průběhu vývoje nového, kompaktnějšího lékařského endoskopu, který by disponoval lepší rozlišovací schopností se vynořil problém potýkající se odolností samotného endoskopického nástroje. Mohlo by se stát, že nástroj by nemusel být dostatečně odolný k tomu, aby zvládl některé extrémní podmínky zatížení, které mohou nastat v průběhu operace vedené volnou rukou oftalmochirurga. Právě z tohoto důvodu bylo třeba provést výzkum, který by zodpověděl otázky, jaké zatížení mohou ony kritické části nástroje unést v průběhu operace tak, aby bylo možné optimalizovat jejich navržení bez toho, aniž bychom museli dělat kompromis mezi požadovanými kvalitami a pevností nástroje. V průběhu oftalmologického operačního zákroku je lidské oko penetrováno jemnou jehlou endoskopu, a to za účelem vizuálního prozkoumání vnitřních části oční bulvy. Výkonný operatér potřebuje v tento moment pohybovat endoskopem uvnitř oka, a to všemi směry tak, aby mohl jasně vidět všechny kritické části orgánu, které z pohledu operatéra potřebuje. Ačkoliv je lidské oko velice křehký orgán, a proto potřebuje výjimečně obezřetnou péči při operacích, mohou se uvnitř oční bulvy vyskytovat takové síly, které jsou dostatečně vysoké na to, aby došlo k mechanickému poškození nejjemnějších součástek struktury operačního nástroje - endoskopu. Jedním ze stěžejních problémů tohoto výzkumu byl fakt, že samotný nástroj je využívaný napřímo rukou operatéra, a proto byl rozsah provozního zatížení velice široký a těžko definovatelný. Tato diplomová práce je rozdělena do šesti hlavních kapitol. V první části se nachází zevrubný a obsažný úvod do problematiky tohoto tématu. V části druhé je pokryta teorie matematického modelu lidského oka, resp. oční bulvy. Ve třetí části je shrnut konkrétní model se všemi jeho detaily, zatímco ve čtvrté části jsou již popisovány výsledky samotného modelování. V páté části jsou popsány výsledky modelací a výsledky dosažené měřením. V šesté, závěrečné části jsou srovnávány naše dosažené výsledky s dříve publikovanými výsledky v související odborné literatuře.This thesis work was assigned by Czech Technical University in Prague, further CTU. It is a leading technical University in the Czech Republic, located in the capital of the country, Prague. The purpose of this study was to investigate the stresses and displacements in the human eye and instrument during endoscopy. The results of the calculations will be used on developing the instrument for ophthalmic operations. While developing a new, more compact instrument with a better resolution image, a new problem aroused from the endurance point of view. The instrument might be not robust enough to handle some extreme conditions while being operated freehand by the surgeon. Therefore, there was a need to study how much the critical parts can hold a load during the operation in order to optimise the design without having to compromise between the wanted qualities and strength. During the ophthalmic operation, the eye is penetrated by a needle-like endoscope to visually study the inner parts of the eye. The surgeon needs to move the endoscope inside the eye in all directions in order to see all the critical parts for the operational point of view. Even though the human eye is a very fragile organ and therefore requires extreme care during the surgical procedure, there might occur some forces high enough to damage the weakest parts of the instrument structure. One of the main problems in this study was that the tool is operated directly by the surgeon's hand, and therefore, the range of operational loading was wide and hard to define. This work is divided into six main sections. First part encloses the introduction to the topic. The second part covers the theory of building the mathematical model of the human eye. The third part reviews the actual model and its details, while the fourth part is dedicated to the experimental measurements. Results of the modelling and measurements are presented in the fifth part. In the sixth part, we discuss the results and compare them to the previously published results in related literature

Computational planning tools in ophthalmology: Intrastromal corneal ring surgery

This thesis addresses the problem of the simulation of intrastromal corneal ring segment surgery for the reduction of myopia and astigmatism, as well as the stabilisation of keratoconus (KC). This disease causes high myopia, irregular astigmatism and reduction of the patient's visual acuity to the point of blindness. Therefore there are several techniques to try to stabilise it and, thus, prevent its progression. For mild keratoconus, it is enough to use special spectacles or lenses to try to correct it, but in more advanced cases it would be necessary to use refractive surgery to try to stop the progression of the disease. The most common ones to avoid the cornea transplant (PK) are the cross-linking and the additive surgery of intrastromal rings. The current planning tools are empirical, based on the nomograms of the ring manufactures, and rely on the experience of the surgeon. Unfortunately, deterministic tools able to estimate the postsurgical visual results of this treatment do not exist. Therefore, the aim of the current thesis is to establish a realistic numerical framework to simulate intrastromal ring surgeries and estimate the mechanical and optical postsurgical outcomes. There are different types of rings depending on their angle and cross-section. There are two large groups of rings: segments which have an angle of less than 360º and those that cover the entire circumference. In the first group we find rings of triangular section such as the Keraring (Mediaphacos, BeloHorizonte, Brazil) and the Ferrara (AJL Ophthalmic Ltd, Spain) and rings of hexagonal section like the Intacs (Additional Technology Inc.). In the second group we can find the MyoRing (Dioptex, GmbH.) whose cross-section is the combination of a parabola and a circumference and the Intacs SK whose section is oval. Due to the complexity of the simulation, since multiple variables are involved, such as the type of rings, the model of the corneal material, the contact conditions between them, etc., two methodologies arised which simulated the insertion of the rings. Both are based on generating a hole in the corneal stroma, introducing the ring and closing the hole with the ring inside, establishing contact until the simulation is completed. In the first of the methodologies the hole was generated by introducing a pressure, while the second was used to an auxiliary tool, such as balloon angioplasty to introduce endovascular stents, which is displaced generating enough hole to insert the rings. As with all numerical simulations, they were not exempt of limitations, although with the first of the methodologies only circular cross--section rings were simulated and in some configurations, there was pressure inside the hole, so it was decided to focus on the second. Nevertheless, interesting conclusions were obtained: the greatest correction was obtained by placing the rings with the largest section near the apex, and whether the ring is located near the epithelium, the stresses generated in the stroma can cause the ring to extrude. With the second methodology based on a displacement control, it was possible to simulate most of the cross-sections and very interesting studies were carried out that gave conclusive results. The most important were: i) the most influential parameter is the depth of insertion; ii) considering the physiological depth of the surgery, the greater optical change is provided by the diameter of the ring, and the fine adjusted is reached with the size of the implant cross--section, i.e the diameter of the implant and the size of the cross--section are the key on regulating the refractive correction; iii) the friction between ring and stroma is important to consider it because a prediction of 2 or 3 diopters could be lost; iv) whether the KC progression is stress-driven, only MyoRing can stop its progression; v) when the covered arc of the segments is more than 320º, axisymmetric model could be used instead of tridimensional model, saving computational time; vi) the anisotropy of the model does not play an important role because the rings are much stiffer than corneal tissue; vii) the implants cannot consider such as second limbus since they act as a dynamic pivot that moves along the circadian cycles of intraocular pressure (IOP); viii) preliminary nomograms is built which allow the estimation of the optical outputs according to the size and typology of the ring and optical zone of implantation.Additionally, a characterisation of ring material was carried out by means two complementary methods: uncertainty analysis and iFEM optimisation, concluding that the manufacturing process of the rings could be the cause of the alteration of the material between the raw PMMA and the ring already prepared for its insertion.<br /