Biomedical Engineering Reference
In-Depth Information
tains the dynamic part. The context uses sets and constants to define axioms and
theorems. Axioms and theorems represent the logical theory of the elements of a
system. The logical theory lists the static properties of constants related to the sys-
tem and provides an axiomatisation of the system environment. The context can be
extended by other contexts and referenced by a set of machines, while a machine
can be refined by other machines.
We need to choose electrical features for modelling the heart system. To model
the heart system, we identify a set of electrical impulse propagation nodes Conduc-
tionNode of the heart conduction network (see Fig. 8.4 (a)). These nodes are basic
landmarks, which enable expression of the normal and abnormal behaviour of the
heart system. These landmarks were identified through a literature survey [ 24 , 30 ]
and fruitful discussions with a cardiologist and a physiologist. Three constants de-
fine the impulse propagation time, namely ConductionTime , impulse propagation
path ConductionPath and impulse propagation velocity ConductionSpeed . Static
properties are defined in the context model to specify the electrical impulse propa-
gation network of the heart system, the impulse propagation time for each landmark
node and the impulse propagation speed for every path. Paths are represented by a
set of pairs of landmark nodes (see Definition 1 , Properties 1 and 2 and Tables 8.1
and 8.2 ).
axm 1
:
partition(ConductionNode,
{
A
}
,
{
B
}
,
{
C
}
,
{
D
}
,
{
E
}
,
{
F
}
,
{
G
}
,
{
H
}
)
axm 2
:
ConductionTime
ConductionNode
→ P
( 0 .. 230 )
axm 3
:
ConductionPath
ConductionNode
×
ConductionNode
axm 4
:
ConductionSpeed
ConductionPath
→ P
( 5 .. 400 )
As you see axioms are extracted from the definitions and are validated by cardi-
ologist and physiologist.
8.5.2 Abstract Model
We define an abstract model for indicating the heart state according to the observa-
tion impulse propagation on the conduction nodes. The machine model represents a
dynamic behaviour of the heart system through the step-wise impulse propagation
into the atria and ventricular chambers. To define the dynamic properties, we have
introduced four variables ConductionNodeState , CConductionTime , CConduction-
Speed and HeartState in invariants. The variable ConductionNodeState is defined as
a function, which shows boolean states of the landmark nodes. When the electrical
impulse passes through the landmark nodes (see Fig. 8.4 (b)), then the visited nodes
become TRUE and the unvisited landmark nodes are represented by FALSE .The
variables CConductionTime and CConductionSpeed represent current impulse prop-
agation time and velocity in the conduction network. The last variable HeartState
represents a boolean state TRUE or FALSE . TRUE represents the normal condition
of the heart while FALSE represents an abnormal condition of the heart.
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