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.
Search WWH ::
Custom Search