Multiple verification in computational modeling of bone pathologies

We introduce a model checking approach to diagnose the emerging of bone pathologies. The implementation of a new model of bone remodeling in PRISM has led to an interesting characterization of osteoporosis as a defective bone remodeling dynamics with respect to other bone pathologies. Our approach allows to derive three types of model checking-based diagnostic estimators. The first diagnostic measure focuses on the level of bone mineral density, which is currently used in medical practice. In addition, we have introduced a novel diagnostic estimator which uses the full patient clinical record, here simulated using the modeling framework. This estimator detects rapid (months) negative changes in bone mineral density. Independently of the actual bone mineral density, when the decrease occurs rapidly it is important to alarm the patient and monitor him/her more closely to detect insurgence of other bone co-morbidities. A third estimator takes into account the variance of the bone density, which could address the investigation of metabolic syndromes, diabetes and cancer. Our implementation could make use of different logical combinations of these statistical estimators and could incorporate other biomarkers for other systemic co-morbidities (for example diabetes and thalassemia). We are delighted to report that the combination of stochastic modeling with formal methods motivate new diagnostic framework for complex pathologies. In particular our approach takes into consideration important properties of biosystems such as multiscale and self-adaptiveness. The multi-diagnosis could be further expanded, inching towards the complexity of human diseases. Finally, we briefly introduce self-adaptiveness in formal methods which is a key property in the regulative mechanisms of biological systems and well known in other mathematical and engineering areas.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Multi Agent Functional Bone Simulation: A theoretical study

In 200 A.D., Galen described bones as the fundamental system of body protection. Bones are highly dynamic, in constant renovation to preserve their properties. Understanding bone metabolism has become a relevant area of research. The most common bone disease is osteoporosis and is characterized by low bone mass and microarchitecture disturbances. The major consequence of osteoporosis are fragility fractures (fractures that occur with low impact trauma). Osteoporosis causes more than 8.9 million fractures each year worldwide. Several therapies are effective in preventing fractures and treating osteoporosis. However, there is an enormous difficulty in predicting osteoporosis related fractures and understanding who needs these therapies in order to prevent bone loss. In practical clinic, it becomes essential to have a model describing the bone remodeling process and the impact of the different cellular mediators in the bone metabolism. Although some mathematical models already describe the variation of the bone cells, they do it in a continuous and deterministic way with few cellular mediators. Many studies and experimental results have shown that cellular metabolism and birth-and-death processes in population dynamics are stochastic. Furthermore, mathematical models are reliable on describing a macro level, whereas multiagent simulation models are used to link micro and macro perspectives. In this thesis we have developed a multiagent stochastic model that simulates a timeline remodeling cycle. Our simulator reproduces the homeostatic process of remodeling with the different phases of it, which is time consistent with the real biological process. Our model includes the most relevant cellular mediators in the bone metabolism. Our model demonstrated to have great sensibility to predict bone loss caused by some chronic diseases such hyper and hypoparathyroidism, and excess of glucocorticoids, and also to the most known causes of osteoporosis: estrogen or vitamin D deficiency. Overall, this model provides a deeper understanding about bone metabolism and the pathologies associated with it.Em 200 A.D, Galen descreveu os ossos como o sistema fundamental de proteção do corpo. Os ossos são estruturas altamente dinâmicas e estão em constante remodelação para preservarem as suas propriedades. Compreender o metabolismo do osso tornou-se uma marcante área de pesquisa. A doença óssea mais comum é a osteoporose que causa mais de 8.9 milhões de fraturas em todo o mundo. Existem várias terapias eficazes em prevenir e tratar esta doença. Contudo, existe uma enorme dificuldade em prevê-la, bem como em entender quem necessita de terapêuticas para a retardar ou evitar a perda óssea. Na prática clínica, revelou-se importante existir um modelo que descreva o processo de remodelação óssea assim como o impacto dos diferentes mediadores celulares no metabolismo ósseo. Apesar de já existirem alguns modelos matemáticos que descrevem a variação das células ósseas na remodelação óssea, fazem-no de uma forma contínua e determinística e com poucos mediadores celulares. Bastantes estudos e resultados experimentais revelam que o metabolismo celular, bem como os processos de nascimento e morte em populações dinâmicas, são estocásticos. Para além disso, os modelos matemáticos são fidedignos em descrever um nível macro enquanto modelos de simulação de multiagentes são utilizados para conectar ambas as perspetivas, micro e macro. O modelo estocástico de multiagentes desenvolvido neste trabalho, simula um ciclo de remodelação ao longo do tempo. O nosso simulador reproduz o processo homeostático de remodelação com as diferentes fases deste, o que é consistente com o processo biológico real. Para além disso, o nosso modelo inclui os mediadores celulares mais relevantes no metabolismo ósseo. Os resultados do modelo demonstram ter sensibilidade em prever a perda óssea devido a algumas doenças crónicas como hiper e hipoparatiroidismo e o excesso de glucocorticoides, bem como das mais conhecidas causas de osteoporose: a deficiência de estrogénio e vitamina D. No geral, este modelo permite-nos ter um maior entendimento do metabolismo ósseo, bem como das patologias associadas a este

A parametric modeling concept for predicting biomechanical compatibility in total hip arthroplasty

This work attempts to predict the long-term outcome of total hip arthroplasty based on available patient-specific information and possible installation positions of the prosthesis. For this purpose, a holistic modeling approach for the numerical simulation of osseointegration and long-term stability of endoprostheses, including possible prosthesis positions, is developed. In addition, new, efficient, and reliable methods for the numerical description of adaptive bone remodeling and osseointegration are proposed: The adaptive bone remodeling is described as a geometric-linear, material-nonlinear finite element model, following thermodynamically consistent material modeling guidelines. The resulting constitutive equations are expanded to describe osseointegration and transferred into a contact interface between bone and prosthesis. Finally, the results are projected to an imaging format that is easier to interpret for medical professionals, using a newly developed simulation for X-ray images. The inclusion of possible prosthesis positions spans an infinite-dimensional event space. Therefore, the model is reduced to a finite-dimensional surrogate model sampled with an adaptive sparse-grid collocation method. Without clinical validation, reliable statements cannot be made, and therefore the numerical examples given in this thesis can be regarded as proof of correct implementation and feasibility studies. This dissertation thus provides an answer to how much computational effort is required to provide a real digital decision aid in orthopedic surgery

Bone orthotropic remodeling as a thermodynamically-driven evolution

International audienceIn this contribution we present and discuss a model of bone remodeling set up in the framework of the theory of generalized continuum mechanics and first introduced by DiCarlo et al.[1]. Bone is described as an orthotropic body experiencing remodeling as a rotation of its microstruc-ture. Thus, the complete kinematic description of a material point is provided by its position in space and a rotation tensor describing the orientation of its microstructure. Material motion is driven by energetic considerations , namely by the application of the Clausius-Duhem inequality to the microstructured material. Within this framework of orthotropic re-modeling, some key features of the remodeling equilibrium configurations are deduced in the case of homogeneous strain or stress loading conditions. First, it is shown that remodeling equilibrium configurations correspond to energy extrema. Second, stability of the remodeling equilibrium configurations is assessed in terms of the local convexity of the strain and complementary energy functionals hence recovering some classical energy theorems. Eventually, it is shown that the remodeling equilibrium configurations are not only highly dependent on the loading conditions, but also on the material properties

Applied Analysis and Synthesis of Complex Systems: Proceedings of the IIASA-Kyoto University Joint Seminar, June 28-29, 2004

This two-day seminar aimed at introducing the new development of the COE by Kyoto University to IIASA and discussing general modeling methodologies for complex systems consisting of many elements, mostly via nonlinear, large-scale interactions. We aimed at clarifying fundamental principles in complex phenomena as well as utilizing and synthesizing the knowledge derived out of them. The 21st Century COE (Center of Excellence) Program is an initiative by the Japanese Ministry of Education, Culture, Science and Technology (MEXT) to support universities establishing discipline-specific international centers for education and research, and to enhance the universities to be the world's apex of excellence with international competitiveness in the specific research areas. Our program of "Research and Education on Complex Functional Mechanical Systems" is successfully selected to be awarded the fund for carrying out new research and education as Centers of Excellence in the field of mechanical engineering in 2003 (five-year project), and is expected to lead Japanese research and education, and endeavor to be the top in the world. The program covers general backgrounds in diverse fields as well as a more in-depth grasp of specific branches such as complex system modeling and analysis of the problems including: nonlinear dynamics, micro-mesoscopic physics, turbulent transport phenomena, atmosphere-ocean systems, robots, human-system interactions, and behaviors of nano-composites and biomaterials. Fundamentals of those complex functional mechanical systems are macroscopic phenomena of complex systems consisting of microscopic elements, mostly via nonlinear, large-scale interactions, which typically present collective behavior such as self-organization, pattern formation, etc. Such phenomena can be observed or created in every aspect of modern technologies. Especially, we are focusing upon; turbulent transport phenomena in climate modeling, dynamical and chaotic behaviors in control systems and human-machine systems, and behaviors of mechanical materials with complex structures. As a partial attainment of this program, IIASA and Kyoto University have exchanged Consortia Agreement at the beginning of the program in 2003, and this seminar was held to introduce the outline of the COE program of Kyoto University to IIASA researchers and to deepen the shared understandings on novel complex system modeling and analysis, including novel climate modeling and carbonic cycle management, through joint academic activities by mechanical engineers and system engineers. In this seminar, we invited a distinguished researcher in Europe as a keynote speaker and our works attained so far in the project were be presented by the core members of the project as well as by the other contributing members who participated in the project. All IIASA research staff and participants of YSSP (Young Scientist Summer Program) were cordially invited to attend this seminar to discuss general modeling methodologies for complex systems

Generalised S-System-Type Equation: Sensitivity of the deterministic and stochastic models for bone mechanotransduction

The formalism of a bone cell population model is generalised to be of the form of an S-System. This is a system of nonlinear coupled ordinary differential equations (ODEs), each with the same structure: the change in a variable is equal to a difference in the product of a power-law functions with a specific variable. The variables are the densities of a variety of biological populations involved in bone remodelling. They will be specified concretely in the cases of a specific periodically forced system to describe the osteocyte mechanotransduction activities. Previously, such models have only been deterministically simulated causing the populations to form a continuum. Thus, very little is known about how sensitive the model of mechanotransduction is to perturbations in parameters and noise. Here, we revisit this assumption using a Stochastic Simulation Algorithm (SSA), which allows us to directly simulate the discrete nature of the problem and encapsulate the noisy features of individual cell division and death. Critically, these stochastic features are able to cause unforeseen dynamics in the system, as well as completely change the viable parameter region, which produces biologically realistic results

Computational Modeling, Formal Analysis, and Tools for Systems Biology.

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Extension of Generalized Modeling and Application to Problems from Cell Biology

Mathematical modeling is an important tool in improving the understanding of complex biological processes. However, mathematical models are often faced with challenges that arise due to the limited knowledge of the underlying biological processes and the high number of parameters for which exact values are unknown. The method of generalized modeling is an alternative modeling approach that aims to address these challenges by extracting information about stability and bifurcations of classes of models while making only minimal assumptions on the specific functional forms of the model. This is achieved by a direct parameterization of the Jacobian in the steady state, introducing a set of generalized parameters which have a biological interpretation. In this thesis, the method of generalized modeling is extended and applied to different problems from cell biology. In the first part, we extend the method to include also the higher derivatives at the steady state. This allows an analysis of the normal form of bifurcations and thereby a more specific description of the nearby dynamics. In models of gene-regulatory networks, it is shown that the extended method can be applied to better characterize oscillatory systems and to detect bistable dynamics. In the second part, we investigate mathematical models of bone remodeling, a process that renews the human skeleton constantly. We investigate the connection between structural properties of mathematical models and the stability of steady states in different models. We find that the dynamical system operates from a stable steady state that is situated in the vicinity of bifurcations where stability can be lost, potentially leading to diseases of bone. In the third part of this thesis, models of the MAPK signal transduction pathway are analyzed. Since mathematical models for this system include a high number of parameters, statistical methods are employed to analyze stability and bifurcations. Thereby, the parameters with a strong influence on the stability of steady states are identified. By an analysis of the bifurcation structure of the MAPK cascade, it is found that a combination of multiple layers in a cascade-like way allows for additional types of dynamic behavior such as oscillations and chaos. In summary, this thesis shows that generalized modeling is a fruitful alternative modeling approach for various types of systems in cell biology.Mathematische Modelle stellen ein wichtiges Hilfmittel zur Verbesserung des Verständnisses komplexer biologischer Prozesse dar. Sie stehen jedoch vor Schwierigkeiten, wenn wenig über die zugrundeliegende biologischen Vorgänge bekannt ist und es eine große Anzahl von Parametern gibt, deren exakten Werte unbekannt sind. Die Methode des Verallgemeinerten Modellierens ist ein alternativer Modellierungsansatz mit dem Ziel, diese Schwierigkeiten dadurch anzugehen, dass dynamische Informationen über Stabilität und Bifurkationen aus Klassen von Modellen extrahiert werden, wobei nur minimale Annahmen über die spezifischen funktionalen Formen getätigt werden. Dies wird erreicht durch eine direkte Parametrisierung der Jacobimatrix im Gleichgewichtszustand, bei der neue, verallgemeinerte Parameter eingeführt werden, die eine biologische Interpretation besitzen. In dieser Arbeit wird die Methode des Verallgemeinerten Modellierens erweitert und auf verschiedene zellbiologische Probleme angewandt. Im ersten Teil wird eine Erweiterung der Methode vorgestellt, bei der die Analyse höherer Ableitungen im Gleichgewichtszustand integriert wird. Dies erlaubt die Bestimmung der Normalform von Bifurkationen und hierdurch eine spezifischere Beschreibung der Dynamik in deren Umgebung. In Modellen für genregulatorische Netzwerke wird gezeigt, dass die so erweiterte Methode zu einer besseren Charakterisierung oszillierender Systeme sowie zur Erkennung von Bistabilität verwendet werden kann. Im zweiten Teil werden mathematische Modelle zur Knochenremodellierung untersucht, einem Prozess der das menschliche Skelett kontinuierlich erneuert. Wir untersuchen den Zusammenhang zwischen strukturellen Eigenschaften verschiedener Modelle und der Stabilität von Gleichgewichtszuständen. Wir finden, dass das dynamische System von einem stabilen Zustand operiert, in dessen Nähe Bifurkationen existieren, welche das System destabilisieren und so potentiell Knochenkranheiten verursachen können. Im dritten Teil werden Modelle für den MAPK Signaltransduktionsweg analysiert. Da mathematische Modelle für dieses System eine hohe Anzahl von Parametern beinhalten, werden statistische Methoden angewandt zur Analyse von Stabilität und Bifurkationen. Zunächst werden Parameter mit einem starken Einfluss auf die Stabilität von Gleichgewichtszuständen identifizert. Durch eine Analyse der Bifurkationsstruktur wird gezeigt, dass eine kaskadenartige Kombination mehrerer Ebenen zu zusätzliche Typen von Dynamik wie Oszillationen und Chaos führt. Zusammengefasst zeigt diese Arbeit, dass Verallgemeinertes Modellieren ein fruchtbarer alternativer Modellierungsansatz für verschiedene zellbiologische Probleme ist