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Suturing in Surgical Simulations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
: Härdning i kirurgiska simuleringar (Swedish)
Abstract [en]

The goal of this project is to develop virtual surgical simulation software in order to simulate the suturing and knot tying processes associated with surgical thread. State equations are formulated using Lagrangian mechanics, which is useful for the conservation of energy. Solver methods are developed with theory based in Differential Algebraic Equations (DAEs) which concern governing Ordinary Differential Equations (ODEs) that are constraint with Algebraic Equations (AE). An implicit integration scheme and Newton's method is used to solve the system in each step. Furthermore, a collision response process based on the Linear Complementarity Problem (LCP) is implemented to handle collisions and measure their forces. Models have been developed to represent the different types of objects. A spline model is used to represent the suture and mass-spring model for the tissue. They were both selected for their efficiency and base on real physical properties. The spline model was also chosen as it is continuous and can be evaluated at any point along the length. Other objects are also defined such as rigid bodies. The Lagrangian multiplier method is used to define the constraints in the model. This allows for the construction of complex models. An important constraint is the suturing constraint, which is created when a sufficient force is applied by the suture tip on to the tissue. This constraint allows only a sliding point along the suture to pass through a specific point on the tissue. This results in a virtual suturing model which can be built on for use in surgical simulations. Further investigations would be interesting to increase performance, accuracy and scope of the simulator.

Abstract [sv]

Det här projektet syftar till att utveckla mjukvara för virtuell simulering av kirurgi som involverar knytande av suturtråd. Lagranges ekvationer används för att härleda energibevarande tillståndsekvationer. Lösningsmetoderna grundar sig i teori från området Differential-Algebraiska Ekvationer (DAEer), som avser att kontrollera Ordinära Differentialekvationer (ODEer) med algebraiska bivillkor. Ett implicit integrationsschema och Newtons metod används för att lösa systemet i varje steg. Utöver det så implementeras en kollisionsrespons-process baserad på det linjära komplementaritetsproblemet (LCP) för att hantera kollisioner och mäta deras krafter. Modeller har utvecklats för att representera olika typer av objekt. En spline-modell används för att representera suturtråden och ett mass-fjäder system för vävnaden. Valet baserades på deras höga prestanda samt starka anknytning till objektens fysiska egenskaper. Spline-modellen valdes också då dess kontinuitet innebär att den går att evaluera för en godtycklig punkt inom dess domän. Andra objekt, såsom stela kroppar, finns också definierade. Lagrangemultiplikator används för att definiera bivillkor i modellen. Detta tillåter konstruktionen av komplexa modeller. Ett viktigt bivillkor är sutur-bivillkoret som uppstår när tillräcklig kraft från spetsen på den kirurgiska nålen appliceras på vävnaden. Detta bivillkor tillåter att endast en glidande punkt längsmed suturen passerar genom en specifik punkt på vävnaden. Detta resulterar i en virtuell modell för stygn som kan byggas vidare på för användning i kirurgiska simulationer. Det vore intressant med ytterligare undersökningar för att förbättra prestandan, precisionen och simulatorns omfattning.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:359
Keywords [en]
Surgical suturing, spline model, Lagrange constraints, multibody dynamics, differential algebraic equations
Keywords [sv]
Kirurgisk suturering, spline-modell, Lagrange-begränsningar, multikroppsdynamik, differentiella algebraiska ekvationer
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-260254OAI: oai:DiVA.org:kth-260254DiVA, id: diva2:1357926
External cooperation
SenseGraphics AB
Subject / course
Scientific Computing
Educational program
Master of Science - Computer Simulation for Science and Engineering
Supervisors
Examiners
Available from: 2019-10-04 Created: 2019-10-04 Last updated: 2019-10-04Bibliographically approved

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