"# <center>Using Agent Based Models in Perfusion Kinetic Compartmental Modeling</center>\n",
"\n",
"<center>by Ethan Tu</center>"
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"Agent based modeling (ABM) is a simulation technique used to model the behavior of a collection of individuals called agents. Each agent has the ability to make decisions based on its knowledge of the surrounding environment. Thus, it is incredibly useful to model social behavior of humans, from workflow, to diffusion of information, to organizational structure, and market simulation. ABM is not limited to the simulation of human behavior, it is also particularly useful in modeling hive behavior, such as with bees or ants. More recently due to increased computing power, researchers have been able to use agent based modeling to represent individual epithelial cells to explore mechanisms of apoptosis, proliferation, and polarization.$^1$ Currently, agent based models are not used for perfusion kinetic models, where the gold standard has been ordinary differential equations based on compartments. However, there may be a way to combine the two since both techniques due to their complementary structures.\n",
"\n",
"As a quick reminder, compartmental models (CM) use ordinary differential equations to represent the change of discrete compartments over time. To use the classic SIR example of a disease outbreak, let’s assume a hypothetical situation where a coronavirus epidemic broke out in Wuhan, China. In this completely made up scenario, we have a coronavirus that can both infect and kill people. Our compartments will represent groups of people; susceptible/healthy, infected, recovering, and dead. Within each of the groups, we will have susceptible people becoming infected or dying, infected people recovering or dying, and recovering people becoming healthy or dying. Normally, to model the rate of which each compartment changes, we would use ODEs. But wait! We have compartments of human individuals. Individuals who can make decisions based on knowledge of the surrounding environment. Individuals who can be represented as an agent. Suddenly, we have a hybrid model. Bobashev et al., described this very model, where the hybrid uses ABM while the infected population is small and then switches to CM when the infected population is large and stable enough.$^2$ Combining both models produces a more accurate representation for early stages of development. More mathematically driven hybrid models such as the one developed by Kuhlman et al. uses ABM to calculate the unknown constants for the CM equations for each timestep.$^3$ While incredibly powerful, doing so severely increases computational burden and simulation time.\n",
"\n",
"Applying this theory to the problem of perfusion kinetics, we can perform a similar hybridization. In a two-compartment model, we have the plasma and the extracellular matrix (also called interstitial fluid). Within the plasma, we have individual molecules of tracer, hemoglobin, plasma, red blood cells, hormones, and more. However, the actions of molecules and hormones done through informed decisions, and therefore is inappropriate to think of them as agents. Instead, we would use cells as our agents. Red blood cells, epithelial cells, fat cells, junction cells, etc. are lie either in or between our two compartments and make decisions such as which genes to transcript, what molecules to uptake, or when to proliferate. We can use AM to model the cells within the compartment and solve for unknown parameters for the ODEs. This is purely theoretical and is most likely incredibly difficult in practice. While AM is already computationally heavy for thousands of agents, in this situation it would need to model millions of cells. Even with the HPCC, simulation times may take days, which might make diagnosis applications irrelevant. Additionally, some mechanisms of uptake may not be completely known. For example, the active transport pathway of iodine into epithelial cells is a black box. We know it happens, but not exactly how. While it may be possible, the added complexity may not be worth the potential increase in accuracy.\n"
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"---\n",
"# References\n",
"\n",
"1.\tTang, J. et al. Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling. Integr Biol (Camb) 3, 408–421 (2011).\n",
"2.\tBobashev, G. V., Goedecke, D. M., Feng Yu & Epstein, J. M. A Hybrid Epidemic Model: Combining The Advantages Of Agent-Based And Equation-Based Approaches. in 2007 Winter Simulation Conference 1532–1537 (2007). doi:10.1109/WSC.2007.4419767.\n",
"3.\tKuhlman, C. J., Ren, Y., Lewis, B. & Schlitt, J. Hybrid Agent-based modeling of Zika in the united states. in 2017 Winter Simulation Conference (WSC) 1085–1096 (2017). doi:10.1109/WSC.2017.8247857.\n"
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%% Cell type:markdown id: tags:
# <center>Using Agent Based Models in Perfusion Kinetic Compartmental Modeling</center>
<center>by Ethan Tu</center>
%% Cell type:markdown id: tags:
Agent based modeling (ABM) is a simulation technique used to model the behavior of a collection of individuals called agents. Each agent has the ability to make decisions based on its knowledge of the surrounding environment. Thus, it is incredibly useful to model social behavior of humans, from workflow, to diffusion of information, to organizational structure, and market simulation. ABM is not limited to the simulation of human behavior, it is also particularly useful in modeling hive behavior, such as with bees or ants. More recently due to increased computing power, researchers have been able to use agent based modeling to represent individual epithelial cells to explore mechanisms of apoptosis, proliferation, and polarization.$^1$ Currently, agent based models are not used for perfusion kinetic models, where the gold standard has been ordinary differential equations based on compartments. However, there may be a way to combine the two since both techniques due to their complementary structures.
As a quick reminder, compartmental models (CM) use ordinary differential equations to represent the change of discrete compartments over time. To use the classic SIR example of a disease outbreak, let’s assume a hypothetical situation where a coronavirus epidemic broke out in Wuhan, China. In this completely made up scenario, we have a coronavirus that can both infect and kill people. Our compartments will represent groups of people; susceptible/healthy, infected, recovering, and dead. Within each of the groups, we will have susceptible people becoming infected or dying, infected people recovering or dying, and recovering people becoming healthy or dying. Normally, to model the rate of which each compartment changes, we would use ODEs. But wait! We have compartments of human individuals. Individuals who can make decisions based on knowledge of the surrounding environment. Individuals who can be represented as an agent. Suddenly, we have a hybrid model. Bobashev et al., described this very model, where the hybrid uses ABM while the infected population is small and then switches to CM when the infected population is large and stable enough.$^2$ Combining both models produces a more accurate representation for early stages of development. More mathematically driven hybrid models such as the one developed by Kuhlman et al. uses ABM to calculate the unknown constants for the CM equations for each timestep.$^3$ While incredibly powerful, doing so severely increases computational burden and simulation time.
Applying this theory to the problem of perfusion kinetics, we can perform a similar hybridization. In a two-compartment model, we have the plasma and the extracellular matrix (also called interstitial fluid). Within the plasma, we have individual molecules of tracer, hemoglobin, plasma, red blood cells, hormones, and more. However, the actions of molecules and hormones done through informed decisions, and therefore is inappropriate to think of them as agents. Instead, we would use cells as our agents. Red blood cells, epithelial cells, fat cells, junction cells, etc. are lie either in or between our two compartments and make decisions such as which genes to transcript, what molecules to uptake, or when to proliferate. We can use AM to model the cells within the compartment and solve for unknown parameters for the ODEs. This is purely theoretical and is most likely incredibly difficult in practice. While AM is already computationally heavy for thousands of agents, in this situation it would need to model millions of cells. Even with the HPCC, simulation times may take days, which might make diagnosis applications irrelevant. Additionally, some mechanisms of uptake may not be completely known. For example, the active transport pathway of iodine into epithelial cells is a black box. We know it happens, but not exactly how. While it may be possible, the added complexity may not be worth the potential increase in accuracy.
%% Cell type:markdown id: tags:
---
# References
1. Tang, J. et al. Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling. Integr Biol (Camb) 3, 408–421 (2011).
2. Bobashev, G. V., Goedecke, D. M., Feng Yu & Epstein, J. M. A Hybrid Epidemic Model: Combining The Advantages Of Agent-Based And Equation-Based Approaches. in 2007 Winter Simulation Conference 1532–1537 (2007). doi:10.1109/WSC.2007.4419767.
3. Kuhlman, C. J., Ren, Y., Lewis, B. & Schlitt, J. Hybrid Agent-based modeling of Zika in the united states. in 2017 Winter Simulation Conference (WSC) 1085–1096 (2017). doi:10.1109/WSC.2017.8247857.
