System dynamics was founded in 1956 by Professor Jay W. Forrester from the Sloan School of Management, Massachusetts Institute of Technology. Forrester mentioned the¡uLevel equation is also known as a first-order differential equation in the branch of mathematics¡K¡K¡v in the book of Principles of Systems. Hence fundamentally system dynamics is a dynamic model in the mathematical model itself, which can also be expressed as a differential equation model. Since the 17th century, differential equation has evolved to become a powerful tool for analyzing the natural processes, and it has developed several research and observation methods, such as the resolution analysis, qualitative analysis and numerical analysis. System dynamics can be applied to solve those kind of problems about high-order, nonlinear, time delay and causal feedback, and these problems are difficult to transform into mathematical models. However, researchers have already addressed many modeling approaches using the basis of system dynamics. In this study, a new transformation method is studied using system dynamics model and transforms it into differential equation model with the aid of mathematical software, applying qualitative analysis and numerical analysis to observe and analyze the differential equation model in order to understand the structure and behavior of the system dynamics model.

<p>Injuries to the neck, or cervical region, are very importantsince there is a potential risk of damage to the spinal cord.Any neck injury can have devastating if not life threateningconsequences. High-speed transportation as well as leisure-timeadventures have increased the number of serious neck injuriesand made us increasingly aware of its consequences.Surveillance systems and epidemiological studies are importantprerequisites in defining the scope of the problem. Thedevelopment of mechanical and clinical tools is important forprimary prevention of neck injuries.</p><p>Thus, the main objectives of the present doctoral thesisare:- To illustrate the dimension of cervical injuries inSweden,- To develop a Finite Element (FE) model of the uppercervical spine, and- To study spinal stability for cervical injuries.</p><p>The incidence studies were undertaken with data from theinjury surveillance program at the Swedish National Board ofHealth and Welfare. All in-patient data from Swedish hospitals,ranging over thirteen years from 1987 to 1999, were analyzed.During this period 14,310 nonfatal and 782 fatal cervicalinjuries occurred. The lower cervical spine is the mostfrequent location for spinal trauma, although, this changeswith age so that the upper cervical spine is the most frequentlocation for the population over 65 years of age. The incidencefor cervical fractures for the Swedish population decreased forall age groups, except for those older than 65 years of age.The male population, in all age groups, has a higher incidencefor neck fractures than females. Transportation relatedcervical fractures have dropped since 1991, leaving fallaccidents as the sole largest cause of cervical trauma.</p><p>An anatomically detailed FE model of the human uppercervical spine was developed. The model was validated to ensurerealistic motions of the joints, with significant correlationfor flexion, extension, lateral bending, axial rotation, andtension. It was shown that an FE-model could simulate thecomplex anatomy and mechanism of the upper cervical spine withgood correlation to experimental data. Three studies wereconducted with the FE model. Firstly, the model of the uppercervical spine was combined with an FE model of the lowercervical spine and a head model. The complete model was used toinvestigate a new car roof structure. Secondly, the FE modelwas used for a parameter study of the ligament materialcharacteristics. The kinematics of the upper cervical spine iscontrolled by the ligamentous structures. The ligaments have tomaintain spinal stability while enabling for large rotations ofthe joints. Thirdly, the FE-model was used to study spinalinjuries and their effect on cervical spinal stability inflexion, extension, and lateral bending. To do this, the intactupper cervical spine FE model was modified to implementruptures of the various spinal ligaments. Transection of theposterior atlantooccipital membrane, the ligametum flavum andthe capsular ligament had the most impact on flexion, while theanterior longitudinal ligament and the apical ligamentinfluenced extension.</p><p>It is concluded that neck injuries in Sweden is a problemthat needs to be address with new preventive strategies. It isespecially important that results from the research on fallaccidents among the elderly are implemented in preventiveprograms. Secondly, it is concluded that an FE model of thecervical region is a powerful tool for development andevaluation of preventive systems. Such models will be importantin defining preventive strategies for the future. Lastly, it isconcluded that the FE model of the cervical spine can increasethe biomechanical understanding of the spine and contribute inanalyses of spinal stability.</p>

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 100-104). Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 151-159). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 100-104). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaf 177). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaf 177). Also available on the Internet.

Thesis (M.S.)--Florida State University, 2003. / Advisor: Michael Mascagni, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed Mar. 2, 2004). Includes bibliographical references.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Available via ProQuest Digital Dissertations. Title from first page of PDF file (viewed March 12, 2010). Includes bibliographical references (p. 122-126). Also issued in print.