AGENT BASED MODELING – PLUG-IN FOR BIOUML PLATFORM

1. Motivation Agent based modeling and simulation is a new fast developing approach to modeling systems consisting of autonomous interacting agents. Being initially devised to model social processes in human societies, it is now applied to a variety of domains from modeling stock markets to predicting the spread of contagious diseases. This approach is also well suited for studying of complex biological systems. Agent’s autonomy makes it possible to work with biological submodels such as human organs or cells and simulate their functioning independently. Flexibility of agent interaction mechanism allows simple connection of such submodels to each other. Water intake agent Neuro-Humoral Control System agent Averager agent Venous System agent Tissue Metabolism System agent Capillary System agent AGENT BASED MODELING – PLUG-IN FOR BIOUML PLATFORM Methods We chose Ascape [1] as a platform for creating agent-based models because of its power and flexibility. On Ascape’s base we have developed plugin for agent based modeling and simulation for open source integrated Java framework BioUML (Biological Universal Modeling Language). In our concept, agent represents part of complex systems functioning independently but sharing variables. Composite model engine developed for BioUML allows us to create easily models by drawing diagrams and then make connections between them. Each agent has its own mathematical model and simulator. Also we add to our agent model special agents which represent plots on diagram, so we can record and observe graphics during simulation. Main part of plugin is the scheduler which maintains parameters sharing and execution of agents. For the scheduler agents are just some abstract entities with ability to take a step in time and provide access to their inner variables. This concept allows us to easily combine models incompatible otherwise: ODE, PDE, stochastic and others without even knowing their inner realizations. On each simulation step agents send and receive messages about changes via shared variables. The message consists of timestamp at which agent starts, timestamp at which agent finished, and variable changing during step. For each sharing variable scheduler stores history of messages so we can interpolate value at requested time point. This engine allows us to use agents with different steps, but precision of such simulation directly depends on step sizes. Legend: P – Pressure. R – Resistance. Q – Blood Flow. V – Volume. • Application • Mathematical studying of human cardiovascular system is the actual problem in modern medicine. Currently there are many mathematical models describing whole system or it parts on different levels and using different mathematical apparatus. It is very interesting task to build complex model which can describe both global processes in system and particular parts without loosing of accuracy. Agent-based approach is promising method to accomplish this task. • Using our plug-in we build agent model on the base of three different models: • Solodyannikov heart model (ODE)[2], • Karaaslan kidney model (ODE, long time)[3] • 1D hydrodynamic arterial tree model (PDE) [4]. • At first, we decompose heart model to 6 logical parts which we present as independent agents (fig 3.). Each agent specifies necessary input parameters and possible output parameters. Next step is to adjust blocks independently and create different combinations of them basing only on those parameters. Then we are replacing Arterial System from Solodyannikov model by Arterial Tree. To connect between each other models with different time scales we created special adaptor agent: Averager which takes one parameter as input and output its average value in a given period of time. In this diagram, it is needed to connect kidney model to renal vessel from arterial tree. I.N. Kiselev1, 2,*, B.V. Semisalov2,3 ,F.A. Kolpakov1,2, , 1Technological Institute of Digital Techniques SB RAS, Novosibirsk, Russia 2Institute of Systems Biology, Novosibirsk, Russia 3Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia *Corresponding author: axec@developmentontheedge.com Simulation Engine Simulation step is performed as follows: An agent with minimum current time is picked up. This agent receives messages about changes in its variables occurred since its last execution from scheduler The agent takes a step in time. The agent sends messages about changes in its variables to the scheduler. If this agent reaches its final time point, it dies. If all agents are dead, then simulation ends, else go to 1. Schematically engine is given on figure 1. Figure 2. Agent model of human cardiovascular system. Consists of 13 agents: Heart, Arterial System, Venous System, Capillary System, Neuro-Humoral control system, Tissue Metabolism system, Averager (collects information about arterial pressure and calculates average pressure), Water intake (liquid input flow into organism), Kidney and 4 plot agents (provide visualization of parameters changing in time) Figure 3. ODE agents from model of human cardiovascular system. This kidney model consists of simple sigmoid function which generates output blood flow from organism. But because of agent structure we can replace it by more complicated variance in future. Results of simulation are presented on figure 5. Conclusions We developed a plug-in for the framework of formal description of biological systems BioUML on the base of Ascape platform. This plug-in provides easy way to construct (by simply drawing diagrams) and connect different models, experimenting with them by replacing different blocks and even integrate models incompatible in usual ways (in our example DAE heart model and PDE hemodynamics model). Using plugin we build complex model of human cardiovascular system comprising three different models (heart, arterial tree and kidney) which allows us to observe processes both in large scales and for example in each particular vessel. This model can be improved in the future by adding new agents or advancing already existed. Figure 1. Agent simulation engine. Currently Agent 1 is active it will be chosen by Scheduler as active agent and take steps in time until he will not surpass Final time point at which Agent 2 will become active. (Scheduler always pick as active agent with smallest current time) • Availability • Software is freely available as a part of BioUML on websites: • http://www.biouml.org/ (workbench version). • http://server.biouml.org/bioumlweb/index.html# (web version). Acknowledgements This work was supported by Interdisciplinary project SBRAS No. 91. References Inchiosa, M.E. and M.T. Parker, 2002. Overcoming Design and Development Challenges in Agent-based Modeling Using Ascape. PNAS, 99: Suppl. 3, pp. 7304-7308. Proshin A. P. and Solodyannikov Yu.V., 2006. Mathematical modeling of blood circulation system and its practical application. AvtomatikaiTelemekhanika, No. 2, pp. 174–188. Karaaslan F. et al., 2005. Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion. Ann Biomed Eng., 33(11), pp. 1607-1630. Leonova T. et al., 2010. Numerical Analysis Of The Complex Model Of Human Cardio-Vascular System Using 1D Hemodynamic Mode. This abstract book. Figure 4. Arterial Tree PDE agent from model of human cardiovascular model Figure 5. Simulation Results