An Example of Modeling and Simulation of Large-Scale Complex Systems, Processes, and Behaviors

Mark A. Johnson, The Aerospace Corporation, USA,

Abstract

Experiences in modeling and simulating large-scale complex systems, process, and behaviors are presented. Specific emphasis is on the bone-fracture healing process and the digestive system in humans. Also, an approach to autonomic organism behavior modeling is presented. Methods and tools used are applicable in any arena where large-scale complex environments are being addressed. Results presented are representative of the information used to develop the models.

Keywords: Large-scale, complex, bone, biomedical, systems, processes, behaviors.

  1. Introduction

Often, the only way to predict capabilities and performance of large-scale complex systems is through the use of modeling, simulation, and analysis. The human organism is representative of a large-scale complex system. Figure 1 depicts a unified modeling language representation of an organism from a physiological systems perspective. The organism is described from an organ systems level, organ level, tissue level, cell level, and atomic level (which could be extended to include intermediate and lower system levels).

Figure 1. Integrated Organism Model Architectural Elements

The biofunction of bone mineral homeostasis is shown with its connections to the respective organ systems involved. Each organ system is composed of organs that make up each system. For instance, the bones and cartilages are the organs making up the skeletal organ system with the tibia as an instantiation of a bone. The bone mineral homeostasis cooperative/goal coordinator is comprised of a multi-objective decision process integrated with the large-scale systems methods of interaction prediction and goal coordination [1]. The bone mineral regulation system model consists of the organ systems used to monitor and invoke the biofunctional behavior. Therefore, it is easy to see that organisms are comprised of complex, large-scale systems of systems with processes and behaviors embedded and interacting with the multiple and diverse systems.

In modeling large-scale complex systems, one uses a standard approach to modeling (shown in Figure 2). It is used iteratively for each component, system, process, and behavior. The Unified Modeling Language (UML), developed and managed by the Object Management Group (OMG) is the current preferred approach to implementing modeling. Although the UML provides a structure within which to perform the modeling, breadth and depth of knowledge concerning the components, systems, processes, behaviors and their interactions is necessary. This paper provides a brief overview of the development of an integrated model of the bone fracture healing process and the digestive system model with sample simulation results.



2. Integrated Bone Fracture Healing Process Model

The problem statement used to guide the development of an integrated model of the bone fracture healing process is, “can soft computing methodologies be used to identify and develop an integrated bioelectrical, biomechanical, and biochemical organ level model of the bone fracture healing process from information found in the open literature?” Many disciplines are involved in realizing the solution of this multi-faceted problem. Representative (not all inclusive) disciplines are: biochemistry, biomechanics, bioelectricity, orthopaedics, physiology, endocrinology, large scale systems, soft computing, object oriented systems engineering, control, and systems integration. Our perusal of the engineering, modeling, and medical literature revealed the existence of not one integrated model of the bone fracture healing process. Some computational biomechanical models dealing with cellular and/or tissue level processes existed; however, biochemical and bioelectrical models were either descriptive in nature or nonexistent.

For model development, the tibia is chosen since it represents a typical long bone and information exists in the literature concerning its electrical and mechanical properties and processes. Systemic properties and processes are used to realize the biochemical system and components. Bioelectrical, biochemical, and biomechanical systems and their processes were developed using model-based architectures was the overall environment in which the systems reside. This was needed since both the complete large-scale system or systems and the individual systems needed reference models of “normal” to guide their processes and behaviors when subjected to the severe disturbance of a bone fracture. It should be noted that all the methods and tools used in developing the overall model exist in the open literature except for the method of multi-objective cooperative/goal coordination.

An integrated bone fracture healing process model is shown in Figure 3. Note that it includes an adaptation component to enable emulation of external osteogenic stimulation and observe the effects on both the normal homeostatic processes as well as the healing process. Once this complex system of systems model was finished it was integrated into a bone mineral regulation system (another complex system of systems). Next the cooperative/goal coordinators were developed and integrated among the systems. These enabled the realization of the biofunctional behavior of organism calcium regulation during times of calcium intake surplus and shortages. For surpluses, the excess calcium is excreted by the digestive system. However, shortages can cause organism distress where the calcium shortage is made up by taking it from the bones. A depiction of the final architecture is shown in Figure 4.

  1. Digestive System Model Development

The problem statement used to guide the development of an integrated model of the bone fracture healing process is, “can soft computing methodologies be used to identify and develop an organ system level process model of the digestion of the bone minerals or calcium, phosphorus, and magnesium from information found in the open literature?” The model given here is of the calcium digestion component of the digestive system process model.

Originally developed as part of the bone mineral regulation model it is used to provide calcium inputs/outputs used in the bone fracture healing biochemical component model. The model is based upon evidence found in the open clinical and research literature. The model is developed to realize dietary bone mineral intake versus absorption, resorption, and fecal outputs that are reactive to variations in serum 1,25 dihydroxyvitamin D3 levels. The absorbed/resorbed bone minerals of calcium, phosphorus, and magnesium are then used to adjust their levels in serum in the cardiovascular model shown in Figure 1. One rendition of the digestive system model is shown in Figure 5.







The digestive system model consists of eight meal processors, each of which contain calcium, phosphorus, and magnesium absorption/resorption processes for the stomach, jejunum, …, and duodenum. A calcium meal processor is shown in Figure 5. Eight meal and several snack processors are used since it takes around 2500 – 3000 minutes to fully digest a food bolus with an assumption of three meals a day. The principle variable, among several, that control the absorption/reabsorption of calcium in the digestive system is serum levels of 1,25 dihydroxyvitamin D3.

4. Simulation Results

Figure 6 provides an example of the integrated output from the bone fracture healing model when external osteogenic stimulation is not in use. The solid line indicates the overall healing progress for a traverse tibial fracture at mid-diaphysis with no complications. The other lines depict the bioelectrical, biochemical and biomechanical indicators of fracture healing process progress.

Figure 7 shows the absorption of calcium for three days of three meals and one snack with a total calcium intake per day of 800 mg for two different levels of serum 1,25 dihydroxyvitamin D3. The higher amount is in the normal range, as is the amount absorbed while lower amount of vitamin D3 and its related absorption is considered to be below normal.





  1. Summary

The methods used to model and simulate large-scale, complex systems are presented with representative results. Modeling of large-scale, complex systems of systems, processes, and behaviors is not difficult when a consistent process is applied to each individual component used in the realization of an integrated model. An example of one system of one large system of systems of the overall systems and process is provided in the digestive systems model. This gives some insight into the nature of developing model(s) of large-scale complex, systems of systems.

  1. Acknowledgements

The author would like to thank the following for their support during various portions of the above work. An American Indian Science and Technology and Engineering Consortium (AISTEC) Fellowship, NASA Research Assistant Position, and The Aerospace Corporation. The author desires to thank Dr. Jamshidi for his support and guidance throughout the entire endeavor.

6. References

[1] M. Jamshidi, Large-Scale Systems: Modeling, Control, and Fuzzy Logic, Prentice Hall TR, Upper Saddle River, New Jersey, 1996.

[2] M. A. Johnson, “Bone Fracture Healing Process Identification, Modeling, and Control Using Soft Computing,” Dissertation, The University of New Mexico, Albuquerque, NM, USA, 2002.

Mark A Johnson, graduated in 2002, dissertation titled, “Bone Fracture Healing Process Identification, Modeling, and Control Using Soft Computing”. Dr. Johnson has over 36 years of space technology; communications and cryptographic systems; systems engineering; research and development; modeling, simulation, and analysis; acquisition; operations; program, cost, and schedule risk analysis and management; and test and evaluation experience with the USAF, NASA, and Aerospace. His diverse research interests include: application of soft computing to large-scale complex, systems of systems identification, modeling, simulation and analysis; behavioral and intelligent decision making; biomedicine; and physics. Dr. Johnson is currently a Senior Project Engineer with The Aerospace Corporation.