Biomedical Engineering Reference
In-Depth Information
principles and techniques for various systems. For example, fluid conservation prin-
ciples are also applicable to electrical circuits as described in Chapter 4. A water
tank stores energy in the form of water raised to a particular height. Similarly, a
capacitor stores energy in the form of electrons at a particular voltage. The larger
the capacitance, the more energy must be stored to achieve a desired voltage. Defi-
brillator storage capacitor employs a very thin plastic film dielectric with metallic
layer deposited on one side, which acts as the plates for the capacitor. In the cardio-
vascular system, the pressure drop from the ventricle to the atrium is equal to the
pressure at the ventricle.
An analogy between an electrical system and a mechanical system is the resist-
ance of hydraulic systems, similar to the resistance of electrical systems. If velocity
is analogous to voltage, force will be analogous to current.
Mobility
=
Velocity/Force is analogous to Impedance
=
Voltage/Current
Any lumped damped mass-spring vibration (viscoelastic models described in
Chapter 5) system is turned into a lumped resitance-impedence-capacitance system
and is solved by a circuit analysis. The advantage of transforming it into a circuit is
to use the advanced tools developed for circuit analysis. Thus using these analogies,
one can: (1) capture the essential dynamic behavior of the system, (2) employ a unit
system so that quantitative statements can be made, and (3) identify pathways and
storage compartments of mass, charge, and energy.
10.2.4 Multicompartmental Models
Compartmental models can accommodate mathematical descriptions for different
clearance patterns and entrance conditions. Metabolic elimination of a drug by
chemical modification could be a constant mass; that is, a linear decrease in drug
concentration, proportional to the concentration still remaining in the compart-
ment (referred as first order kinetics) or enzyme-controlled like many biological
processes and could obey the Michaelis-Menten type kinetics(described in Chapter
7). Enzymatic activity is generally high in the liver and may convert the therapeutic
agent into a more potent drug or a toxic component.
Therapeutic agents could be administered by different routes such as an in-
stantaneous bolus administration through intravenous injection, a constant rate
infusion through intravenous infusion, an exponentially decreasing first order oral
administration, a diffusion controlled transdermal route, or a complex process like
hepatic metabolism-dependent. If the drug is delivered orally, then the drug will
dissolve in the digestive cavity before entering the systemic circulation and local-
izing in the area of therapeutic need. This scenario is identical to Figure 10.3 with
two tanks in series: tank 1 is the digestive track and tank 2 is the systemic circula-
tion. Since the effectiveness of the drug is determined by the amount circulating in
the systemic circulation, understanding the time-dependent concentration change
in the plasma (or in circulating blood) is necessary. In that case, the changes in the
digestive track are lumped into one parameter,
k
1
and incorporated as an exponen-
tial decay function into the second compartment. Thus the first tank is assumed not
to exist (shown with dotted line) in Figure 10.4. In other words, (10.8) can be used
