System Dynamics and Dynamic Systems Integration in Regulatory Environments Leeza Osipenko John Farr, PhD, PE Stevens Institute of Technology SEEM Dept. Burchard Bld. Hoboken, NJ 07030 tel. (1) 973 851 7114 fax (1) 201 216 5541 [email protected] [email protected] Abstract System Dynamics evolved from Dynamic Systems often associated with classical mechanical engineering. However, today System Dynamics (SD) and Dynamic Systems (DS) are differentiated in theory and application. We believe that the link between SD and DS shall be reemphasized if not re-established in certain fields in order to advance system development and understanding. In some regulatory environments (e.g. energy, medicine, ecology, aviation), the integration of SD and DS techniques can be especially beneficial. Many systems and simulations developed in these fields omit important parameters, modeling a specific problem or task. We believe that the combination of system dynamics and dynamic systems can provide for a higher level of precision in the system building process. In this paper, using an example of clinical trials, we attempt to demonstrate how SD and DS can be used together to yield more sophisticated models. Key words: system dynamics, dynamic systems, modeling techniques, regulatory environments, pharmaceutics. 1 Table of Contents Introduction……………………………………………………………………………………..…3 Background SD and DS in System Theory……………………………………………………….…….3 Dynamic Systems………………………………………………………………………….5 System Dynamics………………………………………………………………………….5 Regulatory Framework……………………………………………………………………………6 Clinical Trials Example Pre-Clinical Stage………………………………………………………………..………..7 Clinical Trials……………………………………………………………………..……….9 SD-DS Modeling Technique………………………………………………..……………………11 Limitations…………………………………………………………………..…………………...11 Conclusion……………………………………………………………………………..………...12 Future Work……………………………………………………………………..…….…12 References……………………………………………………………………..…………………14 List of Figures Figure 1 Systems Theory………………………………………………………...……………….4 Figure 2 Simple Regulatory Framework…………………………………………………..……..6 Figure 3 Basic Components of the PK Model………………………………………….…….…..8 Figure 4 DS Model in SD Environment.………………………………………….………………8 Figure 5 Clinical Trials within the Basic Regulatory Framework………………………………..9 Figure 6 A Part of a Casual Loop Diagram of the Clinical Trials Process…….………………..10 . 2 Introduction Over the past fifty years, modeling and simulation (M&S) has become widespread almost in the entire spectrum of sciences and engineering. In most disciplines, it has replaced traditional “build and break” methods of design. In the myriad of modern computer-based modeling techniques, System Dynamics (SD) finds most of its applications in social sciences, while exact sciences continue to rely heavily upon the Dynamic Systems (DS) modeling. There are logical explanations to this: SD, using a holistic approach, involves complex feedback systems and affects soft variables producing models often used for policy recommendations, whereas, DS model a specific problem generally restricted by the exact mathematical equations. Despite the fact that SD and DS are being used for different purposes and in general by different research communities, DS are imbedded into the development of SD and the SD theory is often used to explain the principles upon which dynamic systems are being built. The developers of system dynamics models are not always highly trained mathematicians and in certain cases they do not see the need for DS applications within their models. In turn, engineers, physicists and mathematicians working on their DS models often do not look beyond the exact mathematical solution to a given problem. The integration of SD and DS is a complex process and it is very important to emphasize that this linking is probably beneficial only for fields involving policy, decision and complex DS models. For instance, medicine, ecology, energy, and aviation are associated with high risk and are controlled by strict engineering and governmental regulations. Most M&S in these fields are being built according to many specific parameters dictated by the industry, the government, the economic policy, and scientific calculations. The application of SD and DS separately presents only half of the picture necessary to reflect the relationships in the regulatory environments. We believe that the incorporation of both methods should allow for addressing quantifiable and non- quantifiable parameters and building models, which better portray the real world. The incorporation of SD and DS modeling techniques has been applied to a certain degree in some disciplines. For example, the Everglades Landscape Model (ELM) is a complex simulation in ecology built using several fundamental sub-models each operating at different spatial scales. These sub-models are built using the dynamic equations and then ecological process feedbacks are modeled with the help of system dynamics [5]. Also some transportation networks, spatial economics and logistics models attempted combining system dynamics and dynamic systems. In this paper we are proposing a modeling methodology based on the integration of SD and DS. Using an example of pharmaceutical clinical trials we suggest that the SD-DS modeling technique can be feasible, efficient and necessary to produce better models in the regulatory environments. Background SD and DS in System Theory Systems theory naturally brings together SD and DS. The Systems Theory is a trans-disciplinary study of the abstract organization of phenomena, independent of their substance, type, or spatial 3 or temporal scale of existence. It investigates both the principles common to all complex entities, and the (usually mathematical models), which can be used to describe them [22]. As we’ll see from the information presented further in this paper, the above definition incorporates features related to SD, DS and Chaos - three parts of the systems theory. Chaos is not addressed in this work, thus we’ll omit it from the discussion simply admitting the fact that, if necessary, it can be incorporated into the proposed methodology if described as a set of complex non-linear equations, which represent a Dynamic System. System Dynamics and Dynamic Systems share common roots and basic principles. Figure 1 shows the “evolution” of SD and DS in its simplest form. People have been studying dynamics since ancient times, as well as building systems, which incorporate dynamic principles. With the development of mathematics, physics, and mechanical engineering, the development of many dynamic systems and control theory became possible. System Dynamics originated in the 1960s and J. Forrester is regarded to be the father of basic principles of the modern SD theory [26]. Around the same time DS evolved dramatically with the growth of computing power. Personal computers facilitated the modeling process as well as made possible the application of SD and DS to various fields. The separation between SD and DS happened very fast and very naturally since SD found its applications in social sciences, while dynamic systems predominantly remained within the scope of exact sciences and engineering. Before we address the differences of each modeling technique in greater detail, let’s sum up the commonalities between SD and DS. Besides sharing common roots, SD and DS are the tools for designing a system, which is a whole (set, group, network), which consists of entities or elements, which are connected with each other according to certain rules or principles (interrelated, interdependent, organized, interacted, etc). Figure 1 Systems Theory SD is primarily focused on the dynamics of the system behavior while DS studies the dynamics of its parts. Since the behavior of the system is distinct from the behavior of its elements [13], 4 SD and DS carry on different missions modeling these behaviors. System Dynamics and Dynamic Systems are used to build models for forecasting, which produces policy recommendations or physical prototypes. Both techniques are involved with modeling, which is an intermediary (not a final answer!) for deriving hopefully helpful information if the model is well designed and implemented. SD and DS use similar model design methodologies (but different techniques) and a very similar nomenclature. The process of model building presents a risk of unmanageable complexity in both cases. Dynamic System is a system described by differential and/or difference equations [18]. In dynamic systems the present output depends on past input and the output changes with time if it’s not in a state of equilibrium [18]. In order to build a dynamic system, a modeler should define specifications to be met, apply synthesis techniques if available, build a mathematical model of the system, simulate the model on a computer to test the effect of various inputs and disturbances on the behavior of the resulting system. Then, if the initial system configuration is not satisfactory, the system must be redesigned and the corresponding analysis completed. The process of design and analysis is repeated until a satisfactory system is found, then the prototype of a physical system is constructed [21]. The above description of the modeling process shows that DS are primarily involved with modeling a system. Most of the time, but not always, it’s a system, which can be physically represented in the form of a prototype. DS have holistic features but are grounded in the reductionism theory by using mathematical description of dynamic