Hardware Reference
In-Depth Information
In order to design the layout for a PCR biochip with devices d 1n on it,
we
must determine the
coordinates for all
the devices (written as .x 1 ;y 1 /,
.x 2 ;y 2 /; :::; .x n ;y n /), such that:
q .x i x j / 2 C .y i y j / 2
C
.d i ;d j /; 8 i; j:
5.3.2
Objective Function for Device Placement
The objective function assesses the quality of the results of device placement. We
consider the following two metrics in the objective function:
The area of the PCR biochips. The fabrication cost of the biochip increases with
area. For a given device placement G, assume that the coordinates of all of the
devices can be written as .x 1 ;y 1 /, .x 2 ;y 2 /; :::; .x n ;y n /. The area of the biochip
can be estimated as follows:
Area D Πmax .x 1 ;x 2 ; :::; x n / min .x 1 ;x 2 ; :::; x n /
Πmin .y 1 ;y 2 ; :::; y n / min .y 1 ;y 2 ; :::; y n /:
(5.6)
The average of the distances from the heater to the reservoirs on the biochip.
As discussed in Sect. 5.3.1 , relatively high temperature around the heater may
lead to degradation of the samples in the reservoirs. If the constraint concerning
the minimum distance between the reservoirs and the heater is not violated, the
overheating of the liquid in the reservoirs can be avoided. However, in order to
further guarantee the quality of the biochemical samples in the reservoirs, it is
preferable to place the reservoirs as far away from the heater as possible. For a
given device placement result G, assume that all the N r reservoirs can be labeled
as .x r 1 ;y r 1 /, .x r 2 ;y r 2 /; :::; .x r N r ;y r N r / in coordinates, and the coordinates of
the heater are .x h ;y h /. Then, the average distance between the heater and the
reservoirs can be estimated as follows:
i D1
N r
Œ.x r i x h / 2 C .y r i y h / 2 2
(5.7)
D avg D
:
N r
For a given device placement result G, the objective function for the optimization
of biochip design (F.G/) can be computed as follows:
ˇ
D avg .G/
F.G/ D ˛Area C
(5.8)
 
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