Random Walk
Contaminant Spread
By Parrish Myers
DSES-6620 Simulation Modeling and Analysis
Spring 2002
Median Lethal-Dose
Acute Toxicity
• Procedure Modeled after EPA SOP #2024
• Data Obtained from EPA
Organism: Delphia Magna
small freshwater crustacean
Contaminant: Methyl Parathion
insecticide LC50 = 0.14 ppb
EC50 = 0.09 – 0.2 ppb
Simulation
Assumptions
• 2d
• Contaminant spread: random walk of constant step size
and not drift
• The contaminant starts at the center of the system (0,0)
• The contaminant is assumed discrete, containing N groups
of molecules
• Exits for molecule groups:
• wander beyond system boundary
• collision with an organism
• Stochastic susceptibility for organisms
• The organisms are stationary
State Variables
Modifiable
• Number of Molecule Groups
• Number of Organisms
• Size of System
System
• System Time
• Number of Dead Organisms
• Number of Remaining Contaminant Molecule Groups
• Radius of Contaminant
System Area
Organism
Contaminant
Simulation
Controls
Amount of
Contaminant
Number of
Organisms
Size of System
State Variables
State of Simulation
RWCS
Simulation Procedure
1. Keep system size at 50.0 and the number of organisms at
10
2. Start with an amount of contaminant small enough to
have minimal effect
3. Record the number of dead organisms at:
1-Hour, 24-Hours, and 48-Hours
4. Increase the amount of contaminant and repeat step 3.
5. When organism mortality becomes 80%-90% STOP!
6. Tally data and find LD50.
Simulation Results
9
EC50 Area
8
LC50
7
6
5
4
3
48 hours
24 hours
1 hour
2
1
Concentration (ppb)
0.
60
0.
57
0.
53
0.
49
0.
46
0.
42
0.
38
0.
35
0.
31
0.
27
0.
24
0.
20
0.
16
0.
13
0.
09
0.
05
0
0.
02
Number of Organisms Dead
Mortality of Delphia Magna