Agent Based Pharmacometric and Physiologic Insights

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Agent Based Pharmacometric and Physiologic
Insights

• Meyer Katzper
• January 2007
• 2007 International Conference on
• Health Sciences Simulation

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Purpose To show some initial experiments with
Agent Based Computing (ABC) as applied to
diffusion, PK and PD Talk Content Motivation/Backg
round Explanation of ABC Demonstration of NetLogo
aspects Diffusion PK results PD
results Evaluation, Prospects and Challenges
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Motivation/Background Agent Based Computing (ABC)
assumes that there are many independent agents
who follow algorithmic rules of interaction with
each other and with different types of agents.
Such a scheme is attractive for modeling many
biological processes. Processes such as the
immune system defense of the body lend themselves
to such an approach. Sample references of such
applications are provided later. To familiarize
myself with the ABC system I eventually decided
to master, I decided to experiment with an area I
knew so as to be clear as to the strengths and
weaknesses of ABC. For this purpose I chose to
look at some PK and PD models. I was also
interested in attempting non-compartmental
models. Specifically, I desired to study
non-homogeneous spatial distribution which
otherwise would involve using partial
differential equations. Note --- The novel Prey
by Michael Crichton starts out discussing
software to coordinate the actions of large
groups of autonomous agents.
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Example of Agent Based Computing ABC more
generally known as Agent Based Programming. Taken
from http//www.red3d.com/cwr/boids/ This is the
BOIDS model as formulated by its creator The
basic Boids flocking model consists of three
simple steering behaviors which describe how an
individual boid maneuvers based on the positions
and velocities its nearby flockmates Separation
steer to avoid crowding local flockmates Alignme
nt steer towards the average heading of local
flockmates Cohesion steer to move toward the
average position of local flockmates Output is
not shown here. Scientific American Amateur
Scientist, November 2000 ARTIFICIAL LIFE Boids
of a Feather Flock Together Shawn Carlson
explains how to simulate simple organisms on your
computer
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Algorithmic underpinning of BOIDs
Separation steer to avoid crowding local
flockmates
Alignment steer towards the average heading of
local flockmates
Cohesion steer to move toward the average
position of local flockmates
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There are a number of free and freely available
programs which can implement agent-based modeling
like Boids. Some of these are Swarm MASON
NetLogo StarLogo visualbots
Software http//www.swarm.org/wiki/Tools_for_Agent
-Based_Modelling http//www.geosimulation.org/geos
im/abms.htmprogramming Papers http//www.swarm.or
g/wiki/Agent-Based_Models_in_Biology_and_Medicine
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Excerpt from In pixels and in health computer
modeling pushes the threshold of medical
research Science News, Jan 21, 2006 by Naila
Moreira Moment by moment, a movie captures the
action as a group of immune cells scrambles to
counter an invasion of tuberculosis bacteria.
Rushing to the site of infected lung tissue, the
cells build a complex sphere of active immune
cells, dead immune cells, lung tissue, and
trapped bacteria. Remarkably, no lung tissue or
bacterium was harmed in the making of this
film. Instead, each immune cell is a computer
simulation, programmed to fight virtual
tuberculosis bacteria on a square of simulated
lung tissue. In their computer-generated
environment, these warrior cells spontaneously
build a structure similar to the granulomas that
medical researchers have noted in human lungs
fighting tuberculosis. The simulation was
created by Denise Kirschner of the University of
Michigan in Ann Arbor.
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Gary An has published widely with this
approach An G. Concepts for developing a
collaborative in-silico model of the acute
inflammatory response using agent based modeling.
J Crit Care 2006 21(1) 105-110. An G.
Mathematical modeling in medicine A means not an
end. Crit Care Med 2005 33(1) 253-254.
(Editorial) Vodovotz Y, Clermont G, Chow C, An
G. Mathematical models of the acute inflammatory
response. Cur Opin Crit Care 2004
10383-390. An G. In-silico experiments of
existing and hypothetical cytokine-directed
clinical trials using agent based modeling. Crit
Care Med 2004 32(10) 2050-2060.. An G.
Agent-based computer simulation and SIRS
Building a bridge between basic science and
clinical trials. Shock 2001 16(4) 266-273. An
G, Lee I. Agent-Based Computer simulation (ABCS)
and the inflammatory response Building a tool to
study Systemic Inflammatory Response Syndrome
(SIRS).Simulation and Gaming 2001 32(3)
344-361. An G, Lee I. Complexity, Emergence and
Pathophysiology Using Agent Based Computer
Simulation to characterize the Non-Adaptive
Inflammatory Response. InterJournal Complex
Systems http//www.interjournal.org. Manuscript
344. May, 2000.
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D. Y. Wong, A. Qutub, and C. A. Hunt. "Modeling
Transport Kinetics with StarLogo." Proc. 26th
Annual International Conference IEEE Engineering
in Medicine and Biology Society (EMBS), Sept.
1-5, 2004.
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The following Netlogo interface shows a diffusion
of agents who started out uniformly at the
leftmost Y coordinate and are moving randomly.
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Data for histogram at given point in time. This
case is for all elements starting centrally and
diffusing outward randomly.
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Histogram in netlogo based on the data shown.
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If initially all particles are at some asymmetric
location but they move randomly for sufficient
time in a confined area they become fairly
uniformly distributed. For a well distributed
system the histogram gives a reasonable
representation of the location of the particles.
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If however one starts with an unsymmetrical
concentration, say at the top right corner
(without wrapping) the evolution of the particle
positions is quite different. However, the
histogram still provides a reasonable
representation of what is occurring in the system.
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If the particles are arranged in a circle, the
histogram gives a completely wrong impression of
the particle distribution.
The lower representation looks better but is
probably and artifact of scale and grouping
interval.
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If we let the particles diffuse, the histogram
continues to give an erroneous representation of
particle position.
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PK and PD are long established disciplines that
use lumped parameter models to approximate drug
concentration and effect versus time. In the
simplest PK case the entire body is considered
one compartment from which a given drug is
cleared in proportion to its concentration. If we
call the proportionality constant K the governing
differential equation is dC/dt - KC where C
is the concentration. In our agent based approach
we will specify N, the number of particles. N/V
would give the concentration.
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Clearance experiments with NetLogo Initial study
of clearance of drug dose as a form of predation
with destructive agents taking the place of
physiologic processes which eliminate drugs. Look
at drug administration as an introduction of N
particles into a fixed volume. Look at clearance
as effected by M agents also randomly moving in
the same volume and eliminating any drug particle
they encounter. Experiment Fix the drug dose
(N100). Vary M the eliminating agents. Track
dose half life T1/2 as F(M). As will be seen
there is a large degree of randomness in this
process.
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NetLogo results. Drug entities are the white
circles. Clearance entities are the black
triangles
Early in elimination process, Later in
elimination process,
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Demo of dose elimination. T 1/2 is a more stable
measure than the endpoint which has great
variability Dose of 100 and dose clearance agents
20 in this case. Here T 1/2 is 98 time
interaction units. Graph shows concentration vs
time.
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Dose 100. Agents 20. Stochastic nature of
clearance versus time is demonstrated by this
sample of 4 identically specified runs.
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Demonstration of dose independence of T ½ in this
model. Statistics for only one hundred runs each
for dose 100 and dose 200. 20 dose clearance
agents used in each case.
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The frequency graph below is for one hundred runs
with each run for dose 100 with 20 dose clearance
agents.
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The frequency graph below is for five hundred
runs each run for dose 100 with 20 dose
clearance agents. Y axis is the frequency of T1/2
values which are shown on the X axis.
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With more clearance agents clearance will be
quicker.
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Two samples of initial distributions for
simulation run of a model of a drug to eliminate
germs. Dose of 100. 20 Clearance agents. 240 germ
patches.
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Drug eliminates germ patches. Clearance agents
eliminate drug. Graph shows time course up to
this point. This case is a highly effective
antibiotic. Picture is for the last time point
in the graph.
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Drug eliminates germ patches. Clearance agents
eliminate drug. Graph shows time course up to
this point. This case is a highly ineffective
antibiotic.
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Germ elimination ½ life for drug N 100 Clearers
N 20 Frequency count from 100 NetLogo runs.
Time units NetLogo ticks.
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Time for ½ the germ burden to vanish a a function
of dose. Note In diseases like HIV data on
viral load and dose are available.
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Time for ½ the germ burden to vanish a a function
of dose. Two sets of runs with doses from 10 to
100.
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Evaluation, Prospects and Challenges Our models
are metaphors for reality. With the agent based
metaphor we can examine reality in another way.
This exercise was intended to explore the
strengths and weaknesses of the NetLogo agent
based modeling platform. I have compared it with
other platforms and found it to be the most user
friendly. I intend to explore metabolic and
immunologic questions using NetLogo. The effects
of non-uniform distributions of substances can
also be studied. How feasible and how much effort
this will take remains to be seen. After the
challenge of formulating the model there is the
challenge of transforming the observations to
match the classical values that are in current
use.