Automated approach for optimizing dynamic systems

The optimal design of nonlinear dynamic systems can be formulated as a multicriteria optimization problem. On the basis of a multibody system model integral type objective functions are defined evaluating the dynamic behavior of the system under consideration. Multicriteria optimization methods reduce the problem to nonlinear programming problems which can be solved with standard algorithms like the SQP method. The gradients required for such an efficient optimization procedure are computed by solving, additional differential equations resulting from an adjoint variable approach. The whole design process can be highly automated by using computer algebra packages

Development of a planar multi-body model of the human knee joint

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur can not be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous non-linear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as non-linear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.Fundação para a Ciência e a Tecnologia (FCT

A Bayesian approach in differential equation dynamic models incorporating clinical factors and covariates

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiretroviral (ARV) therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but may be easily affected by clinical factors such as drug exposures and drug resistance as well as baseline characteristics during the long-term treatment evaluation process. HIV dynamic studies have significantly contributed to the understanding of HIV pathogenesis and ARV treatment strategies. Viral dynamic models can be formulated through differential equations, but there has been only limited development of statistical methodologies for estimating such models or assessing their agreement with observed data. This paper develops mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy. In this model we not only incorporate clinical factors (drug exposures, and susceptibility), but also baseline covariate (baseline viral load, CD4 count, weight, or age) into a function of treatment efficacy. A Bayesian nonlinear mixed-effects modeling approach is investigated with application to an AIDS clinical trial study. The effects of confounding interaction of clinical factors with covariate-based models are compared using the deviance information criteria (DIC), a Bayesian version of the classical deviance for model assessment, designed from complex hierarchical model settings. Relationships between baseline covariate combined with confounding clinical factors and drug efficacy are explored. In addition, we compared models incorporating each of four baseline covariates through DIC and some interesting findings are presented. Our results suggest that modeling HIV dynamics and virologic responses with consideration of time-varying clinical factors as well as baseline characteristics may play an important role in understanding HIV pathogenesis, designing new treatment strategies for long-term care of AIDS patients.AIDS, baseline characteristics, Bayesian nonlinear mixed-effects models, long-term HIV dynamics, longitudinal data, time-varying drug efficacy,