Biomedical Engineering Reference
In-Depth Information
the solution to the preceding equation during the first 100 seconds after drug administration,
assuming an initial dose of 1000 milligrams, a plasma volume of 6000 ml, an elimination constant of
0.4, and a
dt
of 0.1 seconds, appears as:
DOSE = 1000
PLASMA VOLUME = 6000
T = 0
K = 0.4
DT = 0.1
FOR INDEX = 1 TO 1000
DO
CONCENTRATION = (DOSE/plasma volume) x EXP(-K x T)
T = T + DT
LOOP
This differential equation is solved by advancing time in relatively small increments
dt
and
recomputing the continuous variable
concentration
at each step. Larger steps may be taken to
decrease computation time at the expense of greater approximation error. Termination of the
program occurs after 1000 iterations of the DO LOOP. However, termination could also be linked to a
maximum runtime, or a maximum or minimum concentration, or some combination of the two. The
drug concentration, as described in the preceding differential equation, isn't limited to integer values,
but is instead most accurately expressed in real values, such as 3.457 mg per ml. When run, the
output of the simulation results in a plasma drug concentration that initially decreases rapidly and
then more slowly as the concentration approaches zero.
Discrete Simulation
A discrete event simulation perspective lends itself to modeling systems in which an object or process
arrives at a stage, waits in a queue until it receives attention, and then moves on to the next stage.
Discrete event simulation is characterized by relatively large quantities of time during which the
underlying system doesn't change. Advancing the simulation from one event to the next simulates
time. Another characteristic of discrete methods is that the progress of objects or processes moving
through the system are typically measured as integers.
Hybrid Simulation
Hybrid simulation methods are useful when the system to be modeled displays a variety of behaviors,
some of which lend themselves to discrete event methods, and some of which are more easily solved
through continuous simulation techniques. Consider the challenges faced by a modeler attempting to
simulate a complex neuromuscular system involving individual packets of neurotransmitter
substances, receptor sites, and resulting muscular contraction. Describing the release, transport, and
subsequent absorption of neurotransmitter packets might be most easily mapped in a discrete event
model. The resulting time-varying contraction, however, is likely to be most easily described in terms
of differential equations within a continuous simulation model.
In general, any system can be simulated with models adhering to continuous, discrete, or hybrid
perspectives. However, the perspective that most closely maps to the actual system characteristics
will minimize development effort. The optimal modeling perspective is also a function of the
characteristic of the system to be modeled. For example, a system can be modeled with discrete and
continuous methods, with each method answering a different question. In addition, in extremely
complex simulations, computation consideration may dictate the most appropriate perspective. For
example, it's often more economical, in terms of computational time and hardware requirements, to
approximate an event-driven system with a continuous simulation.
Numeric Considerations
