Biomedical Engineering Reference
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chambers of the heart: atrium and ventricular. Atrium and ventricular are the right
atrium and the right ventricular. The atrium chamber uses the three operating modes;
AOO, AAI and AAT (see Table 9.1 ). Similarly, the ventricular chamber uses three
operating modes: VOO, VVI and VVT (see Table 9.1 ). In the part of two-electrode
pacemaker, there is only one branch for both chambers. Both chambers of the heart
use the five operating modes: DOO, DVI, DDI, VDD and DDD. In the abstract
model, we introduce the bradycardia operating modes of the pacemaker abstractly
with required properties. From first refinement to the last refinement, there is only
one branch in every operating mode of the pacemaker. In one and two-electrode
pacemaker, there are three refinements: first threshold refinement; second hysteresis
refinement; and third rate adaptive or rate modulation refinement. The subsequent
refinement models introduce new features or functional requirements for the result-
ing system. The triple dots ( ... ) in the hierarchical tree represents that there is no
refinement at that level, in particular, operating modes (AOO, VOO, DOO, etc.). In
the last refinement level, we have achieved the additional rate adaptive operating
modes (i.e. AOOR, AAIR, VVTR, DOOR, DDDR, etc.). These operating modes
are different from the previous levels of operating modes. This refinement structure
is very helpful to model the functional requirements of the cardiac pacemaker.
9.5 Development of the Cardiac Pacemaker Using Refinement
Chart
A formal specification serves as the central role of the development and evolu-
tion process. A refinement typically embodies a well-defined unit of programming
knowledge. Figures 9.5 and 9.6 present the diagrams of the most abstract modal sys-
tem for the one and two-electrode pacemaker system (A) and the resulting models
of three successive refinement steps (B to D). The diagrams use a visual notation to
represent the bradycardia operating modes of the pacemaker under functional and
parametric requirements. An operating mode is represented by a box with a mode
name; an operating mode transition is an arrow connecting two operating modes.
The direction of an arrow indicates the previous and next operating modes in a tran-
sition. Refinement is expressed by nesting boxes [ 53 ].
A refined diagram of an abstract mode is equivalent to a concrete mode. These
block wise refinements are similar to the hierarchical tree structure (see Fig. 9.4 )
of the bradycardia operating modes of the pacemaker. The nesting boxes in one-
and two-electrode pacemakers (Figs. 9.5 and 9.6 ) represent equivalent to every re-
finement level of the hierarchical tree structure (see Fig. 9.4 ). Special initiating and
terminating modes are on and off respectively of the pacemaker, which are omitted
here in the refinement chart block diagram. At the most abstract level, we introduce
pacing activity into single and both heart chambers. In Figs. 9.5 (A) and 9.6 (A), pac-
ing is represented by transitions Pace ON and Pace OFF for single chamber or both
chambers. It is the basic transitions for all bradycardia operating modes. During a
pacing cycle, it is ensured that no other pacing activity has occurred. The model in-
cludes: the state of pacing (on/off) modelled by a boolean flag Pacemaker_Actuator ;
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