Biomedical Engineering Reference
In-Depth Information
3.8.3.2 Combinatorial Operation of a Binary Multiplexer
he author's laboratory at the University of Washington in Seattle has extended the design of the
Quake multiplexer to doormat microvalves and shown that its use can be broadened to create
combinations
of compounds. (In Quake's original implementation, only one input was selected.)
his “combinatorial operation” is depicted in
Figure 3.56
. he device has 16 inlets (named A,
B,…through P) controlled by eight multiplexing lines of valves (named V
1
, V
2
,…through V
8
).
Line V
1
must be opened to turn on any of the eight letmost channels A through H and line V
2
must be opened to turn on any of the eight rightmost channels I through P; the V
1
and V
2
valves
are said to be a “complementary pair” of valves; V
3
(which is necessary to open the irst and last
four channels) is complementary of V
4
(which is necessary to open the middle eight channels),
and so on. he “state” of the multiplexer is denoted by the state of its valves,
V
= {V
1
,V
2
, V
3
,V
4
,
V
5
,V
6
, V
7
,V
8
}, with
V
i
taking the values of 0 (closed) or 1 (open); note that, for clarity, a space is
written between each pair of complimentary bits. To open a single inlet, one (and only one) valve
from each complementary valve pair needs to be opened. For example, to open inlet
M
, valves
V
2
, V
3
, V
6
, and V
8
need to be opened, but V
1
, V
4
, V
5
, and V
7
are “forbidden” and must be closed
(
V
= {01 10 01 01};
Figure 3.56b
).
It is crucial to note that the original implementation of Quake's multiplexer (i.e., selection of
a single input) is based on respecting the “complementarity rule,” in other words, none of the
forbidden valves may be open. However, this operation is not a design constraint—it is only an
operational constraint to ensure that the multiplexer is maintained in a “single-inlet state.” If,
(a)
16 Inlets
(b)
A B C D E F G
H
I J K L M N O P
A B C D E F G
H
I J K L M N O P
V
1
V
3
V
5
V
7
V
1
V
3
V
5
V
7
V
2
V
4
V
6
V
8
V
2
V
4
V
6
V
8
V = {V
1
,V
2
,V
3
,V
4
,V
5
,V
6
,V
7
,V
8
}
V = {01 10 01 01}
(c)
(d)
A B C D E F G
H
I J K L
M N O P
A B C D E F G
H
I J K L M N O P
V
1
V
3
V
5
V
7
V
1
V
3
V
5
V
7
V
2
V
4
V
6
V
8
V
2
V
4
V
6
V
8
V = {01 10 01 11}
V = {01 10 11 11}
M,N,O,P
I,J,M,N
A,C,E,G,J,L,N,P
I,J,K,L,M,N,O,P
(e)
(f )
(g)
(h)
2 mm
V = {01 10 11 11}
V = {01 11 01 11}
V = {11 11 11 10}
V = {01 11 11 11}
FIGURE 3.56
Combinatorial.operation.of.a.binary.multiplexer..(From.Gregory.A..Cooksey,.Christopher.
G..Sip,.and.Albert.Folch,.“A.multi-purpose.microluidic.perfusion.system.with.combinatorial.choice.
of.inputs,.mixtures,.gradient.patterns,.and.low.rates,”.
Lab Chip
.9,.417-426,.2009..Reproduced.
with.permission.from.The.Royal.Society.of.Chemistry.)
