Objective: Patient-specific musculoskeletal models have emerged as a reliable method to study how tibiofemoral joint (TFJ) morphology influences anterior cruciate ligament (ACL) injuries. However, there are no such models for adolescent populations that can be scaled to accommodate growth. To serve as the foundation for such models, the objective of this thesis was therefore to i) build a patient-specific model of natural knee motion in an ACL-injured (ACLi) adolescent sample using joint congruency and ii) to attempt to reconstruct patient-specific simplified articular contacts using principal component analysis (PCA). Design: Twelve magnetic resonance images (MRI) of ACi adolescents were segmented and used to generate spheres of simplified TFJ articulations. A congruence-based optimization algorithm was used to determine the envelope of tibiofemoral configurations that optimize joint congruency. Descriptive statistics were used to compare model outputs to existing literature. Combinations of marker trajectories and anthropometrics were used to determine the feasibility of reconstructing articular sphere simplifications using PCA. Root-mean squared error (RMSE) was used to compare predicted sphere contacts to MRI-extracted contacts. Results: Average knee joint anglesof the femur with respect to the tibia was slightly abducted and externally rotated, with a range of motion (ROM) of 1.60º ± 0.66 and 7.64 º ± 2.34 across 102° of flexion respectively. The percent elongation of the posterior cruciate ligament (PCL) varied the most across participants (8.65 ± 6.2%) compared to the ACL (2.34 ± 2.1%), MCL (1.41 ± 0.5%) and LCL (1.75 ± 1.6%) respectively. The combination of femur markers and anthropometrics was able to reconstruct simplified tibiofemoral articulations the best, but not within 5 mm of RMSE. Conclusion: Inter-subject variability in passive kinematic motion derived from patient-specific morphology highlights the need for personalized and accessible musculoskeletal models in growing populations. Furthermore, simplified distal femur morphology can be reconstructed from anthropometrics and marker positions, but proximal tibia morphology requires more information.

<div>Excessive deformation and stress of skin following reconstructive surgery plays a crucial role in wound healing, often leading to complications. Yet, despite of this concern, surgeries are still planned and executed based on each surgeon's training and experience rather than quantitative engineering tools. The limitations of current treatment planning and execution stem in part from the difficulty in predicting the mechanical behavior of skin, challenges in directly measuring stress in the operating room, and inability to predict the long term adaptation of skin following reconstructive surgery. Computational modeling of soft tissue mechanics has emerged as an ideal candidate to determine stress contours over sizable skin regions in realistic situations. Virtual surgeries with computational mechanics tools will help surgeons explore different surgeries preoperatively, make prediction of stress contours, and eventually aid the surgeon in planning for optimal wound healing. While there has been significant progress on computational modeling of both reconstructive surgery and skin mechanical and mechanobiological behavior, there remain major gaps preventing computational mechanics to be widely used in the clinical setting. At the preoperative stage, better calibration of skin mechanical properties for individual patients based on minimally invasive mechanical tests is still needed. One of the key challenges in this task is that skin is not stress-free in vivo. In many applications requiring large skin flaps, skin is further grown with the tissue expansion technique. Thus, better understanding of skin growth and the resulting stress-free state is required. The other most significant challenge is dealing with the inherent variability of mechanical properties and biological response of biological systems. Skin properties and adaptation to mechanical cues changes with patient demographic, anatomical location, and from one individual to another. Thus, the precise model parameters can never be known exactly, even if some measurements are available. Therefore, rather than expecting to know the exact model describing a patient, a probabilistic approach is needed. To bridge the gaps, this dissertation aims to advance skin biomechanics and computational mechanics tools in order to make virtual surgery for clinical use a reality in the near future. In this spirit, the dissertation constitutes three parts: skin growth and its incompatibility, acquisition of patient-specific geometry and skin mechanical properties, and uncertainty analysis of virtual surgery scenarios.</div><div>Skin growth induced by tissue expansion has been widely used to gain extra skin before reconstructive surgery. Within continuum mechanics, growth can be described with the split of the deformation gradient akin to plasticity. We propose a probabilistic framework to do uncertainty analysis of growth and remodeling of skin in tissue expansion. Our approach relies on surrogate modeling through multi-fidelity Gaussian process regression. This work is being used calibrate the computational model against animal model data. Details of the animal model and the type of data obtained are also covered in the thesis. One important aspect of the growth and remodeling process is that it leads to residual stress. It is understood that this stress arises due to the nonhomogeneous growth deformation. In this dissertation we characterize the geometry of incompatibility of the growth field borrowing concepts originally developed in the study of crystal plasticity. We show that growth produces unique incompatibility fields that increase our understanding of the development of residual stress and the stress-free configuration of tissues. We pay particular attention to the case of skin growth in tissue expansion.</div><div>Patient-specific geometry and material properties are the focus on the second part of the thesis. Minimally invasive mechanical tests based on suction have been developed which can be used in vivo, but these tests offer only limited characterization of an individual's skin mechanics. Current methods have the following limitations: only isotropic behavior can be measured, the calibration problem is done with inverse finite element methods or simple analytical calculations which are inaccurate, the calibration yields a single deterministic set of parameters, and the process ignores any previous information about the mechanical properties that can be expected for a patient. To overcome these limitations, we recast the calibration problem in a Bayesian framework. To sample from the posterior distribution of the parameters for a patient given a suction test, the method relies on an inexpensive Gaussian process surrogate. For the patient-specific geometry, techniques such as magnetic resonance imaging or computer tomography scans can be used. Such approaches, however, require specialized equipment and set up and are not affordable in many scenarios. We propose to use multi-view stereo (MVS) to capture patient-specific geometry.</div><div>The last part of the dissertation focuses on uncertainty analysis of the reconstructive procedure itself. To achieve uncertainty analysis in the clinical setting we propose to create surrogate and reduced order models, especially principal component analysis and Gaussian process regression. We first show the characterization of stress profiles under uncertainty for the three most common flap designs. For these examples we deal with idealized geometries. The probabilistic surrogates enable not only tasks such as fast prediction and uncertainty quantification, but also optimization. Based on a global sensitivity analysis we show that the direction of anisotropy of skin with respect to the flap geometry is the most important parameter controlled by the surgeon, and we show hot to optimize the flap in this idealized setting. We conclude with the application of the probabilistic surrogates to perform uncertainty analysis in patient-specific geometries. In summary, this dissertation focuses on some of the fundamental challenges that needed to be addressed to make virtual surgery models ready for clinical use. We anticipate that our results will continue to shape the way computational models continue to be incorporated in reconstructive surgery plans.</div>

Se cree que la medicina in silico supondrá uno de los cambios más disruptivos en el futuro próximo. A lo largo de la última década se ha invertido un gran esfuerzo en el desarrollo de modelos computacionales predictivos para mejorar el poder de diagnóstico de los médicos y la efectividad de las terapias. Un punto clave de esta revolución, será la personalización, que conlleva en la mayoría de los casos, la creación de modelos computacionales específicos de paciente, también llamados gemelos digitales. Esta práctica está actualmente extendida en la investigación y existen en el mercado varias herramientas de software que permiten obtener modelos a partir de imágenes. A pesar de eso, para poderse usar en la práctica clínica, estos métodos se necesita reducir drásticamente el tiempo y el trabajo humano necesarios para la creación de los modelos numéricos. Esta tésis se centra en la propuesta de la versión basada en imágenes del Cartesian grid Finite Element Method (cgFEM), una técnica para obtener de forma automática modelos a partir de imágenes y llevar a cabo análisis estructurales lineales de huesos, implantes o materiales heterogéneos. En la técnica propuesta, tras relacionar la escala de los datos de la imágen con valores de propiedades mecánicas, se usa toda la información contenida en los píxeles para evaluar las matrices de rigidez de los elementos que homogenizan el comportamiento elástico de los grupos de píxeles contenidos en cada elemento. Se h-adapta una malla cartesiana inicialmente uniforme a las características de la imágen usando un procedimiento eficiente que tiene en cuenta las propiedades elásticas locales asociadas a los valores de los píxeles. Con eso, se evita un suavizado excesivo de las propiedades elásticas debido a la integración de los elementos en áreas altamente heterogéneas, pero, no obstante, se obtienen modelos finales con un número razonable de grados de libertad. El resultado de este proceso es una malla no conforme en la que se impone la continudad C0 de la solución mediante restricciones multi-punto en los hanging nodes. Contrariamente a los procedimientos estandar para la creación de modelos de Elementos Finitos a partir de imágenes, que normalmente requieren la definición completa y watertight de la geometrá y tratan el resultado como un CAD estandar, con cgFEM no es necesario definir ninguna entidad geométrica dado que el procedimiento propuesto conduce a una definición implícita de los contornos. Sin embargo, es inmediato incluirlas en el modelo en el caso de que sea necesario, como por ejemplo superficies suaves para imponer condiciones de contorno de forma más precisa o volúmenes CAD de dispositivos para la simulación de implantes. Como consecuencia de eso, la cantidad de trabajo humano para la creación de modelos se reduce drásticamente. En esta tesis, se analiza en detalles el comportamiento del nuevo método en problemas 2D y 3D a partir de CT-scan y radiográfias sintéticas y reales, centrandose en tres clases de problemas. Estos incluyen la simulación de huesos, la caracterización de materiales a partir de TACs, para lo cual se ha desarrollado la cgFEM virtual characterisation technique, y el análisis estructural de futuros implantes, aprovechando la capacidad del cgFEM de combinar fácilmente imágenes y modelos de CAD. / Es creu que la medicina in silico suposarà un dels canvis més disruptius en el futur pròxim. Al llarg de l'última dècada, s'ha invertit un gran esforç en el desenvolupament de models computacionals predictius per millorar el poder de diagnòstic dels metges i l'efectivitat de les teràpies. Un punt clau d'aquesta revolució, serà la personalització, que comporta en la majoria dels casos la creació de models computacionals específics de pacient. Aquesta pràctica està actualment estesa en la investigació i hi ha al mercat diversos software que permeten obtenir models a partir d'imatges. Tot i això, per a poder-se utilitzar en la pràctica clínica aquests métodes es necessita reduir dràsticament el temps i el treball humà necessaris per a la seva creació. Aquesta tesi es centra en la proposta d'una versió basada en imatges del Cartesian grid Finite Element Method (cgFEM), una técnica per obtenir de forma automàticament models a partir d'imatges i dur a terme anàlisis estructurals lineals d'ossos, implants o materials heterogenis. Després de relacionar l'escala del imatge a propietats macàniques corresponents, s'usa tota la informació continguda en els píxels per a integrar les matrius de rigidesa dels elements que homogeneïtzen el comportament elàstic dels grups de píxels continguts en cada element. Es emphh-adapta una malla inicialment uniforme a les característiques de la imatge usant un procediment eficient que té en compte les propietats elàstiques locals associades als valors dels píxels. Amb això, s'evita un suavitzat excessiu de les propietats elàstiques a causa de la integració dels elements en àrees altament heterogénies, però, tot i això, s'obtenen models finals amb un nombre raonable de graus de llibertat. El resultat d'aquest procés és una malla no conforme en la qual s'imposa la continuïtat C0 de la solució mitjançant restriccions multi-punt en els hanging nodes. Contràriament als procediments estàndard per a la creació de models d'Elements finits a partir d'imatges, que normalment requereixen la definició completa i watertight de la geometria i tracten el resultat com un CAD estàndard, amb cgFEM no cal definir cap entitat geométrica. No obstant això, és immediat incloure-les en el model en el cas que sigui necessari, com ara superfícies suaus per imposar condicions de contorn de forma més precisa o volums CAD de dispositius per a la simulació d'implants. Com a conseqüéncia d'això, la quantitat de treball humà per a la creació de models es redueix dràsticament. En aquesta tesi, s'analitza en detalls el comportament del nou métode en problemes 2D i 3D a partir de CT-scan i radiografies sintétiques i reals, centrant-se en tres classes de problemes. Aquestes inclouen la simulació d'ossos, la caracterització de materials a partir de TACs, per a la qual s'ha desenvolupat la cgFEM virtual characterisation technique, i l'anàlisi estructural de futurs implants, aprofitant la capacitat del cgFEM de combinar fàcilment imatges i models de CAD. / In silico medicine is believed to be one of the most disruptive changes in the near future. A great effort has been carried out during the last decade to develop predicting computational models to increase the diagnostic capabilities of medical doctors and the effectiveness of therapies. One of the key points of this revolution, will be personalisation, which means in most of the cases creating patient specific computational models, also called digital twins. This practice is currently wide-spread in research and there are quite a few software products in the market to obtain models from images. Nevertheless, in order to be usable in the clinical practice, these methods have to drastically reduce the time and human intervention required for the creation of the numerical models. This thesis focuses on the proposal of image-based Cartesian grid Finite Element Method (cgFEM), a technique to automatically obtain numerical models from images and carry out linear structural analyses of bone, implants or heterogeneous materials. In the method proposed in this thesis, after relating the image scale to corresponding elastic properties, all the pixel information will be used for the integration of the element stiffness matrices, which homogenise the elastic behaviour of the groups of pixels contained in each element. An initial uniform Cartesian mesh is h-adapted to the image characteristics by using an efficient refinement procedure which takes into account the local elastic properties associated to the pixel values. Doing so we avoid an excessive elastic property smoothing due to element integration in highly heterogeneous areas, but, nonetheless obtain final models with a reasonable number of degrees of freedom. The result of the process is non-conforming mesh in which C0 continuity is enforced via multipoint constraints at the hanging nodes. In contrast to the standard procedures for the creation of Finite Element models from images, which usually require a complete and watertight definition of the geometry and treat the result as a standard CAD, with cgFEM it is not necessary to define any geometrical entity, as the procedure proposed leads to an implicit definition of the boundaries. Nonetheless, they are straightforward to include in the model if necessary, such as smooth surfaces to impose the boundary conditions more precisely or CAD device volumes for the simulation of implants. As a consequence, the amount of human work required for the creation of the numerical models is drastically reduced. In this thesis, we analyse in detail the new method behaviour in 2D and 3D problems from CT-scans and X-ray images and synthetic images, focusing on three classes of problems. These include the simulation of bones, the material characterisation of solid foams from CT scans, for which we developed the cgFEM virtual characterisation technique, and the structural analysis of future implants, taking advantage of the capability of cgFEM to easily mix images and CAD models. / Giovannelli, L. (2018). Direct creation of patient-specific Finite Element models from medical images and preoperative prosthetic implant simulation using h-adaptive Cartesian grids [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/113644 / TESIS