VLSI Implementation of the Pacemaker Unit of
the Interstitial Cell of Cajal
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Ganapathy Subramanium Sundar
Department of Bioengineering
University of California, San Diego
San Diego,CA-92093
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Abstract
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The digestion of the food in the gastro-intestinal tract is aided by the
peristaltic contractions of the gastric muscles. This gastric motility is a
result of the sponta- neous rhythmic pacemaker activity produced by the
interstitial cells of Cajal(ICC), which line the gastro-enteric system. The
interstitial cells of Cajal are a special- ized group of neuro-muscular cells
and are derived from fibroblasts. These cells generate periodic action
potentials termed as slow waves, which are responsible for gastric motility.
The objective of this project is to implement a VLSI model of a simple
ICC network capable of producing slow waves generated by the ICC
network of the stomach. The cells of the network are designed using a
mathemat- ical model where the membrane voltage of the ICC is based on
the flow of C a2+ ions and N a+ ions.
1
In trod u cti on :
The human digestive system has the tasks of ingestion, digestion, absorption and
assimilation of food. The food taken in is pushed through the alimentary canal by a series of
rhythmic contractions of the smooth muscles lining the gastro-intestinal(GI)l tract called
peristalsis. These contractions are caused by a set of electrical-signals called ”slow waves”.
The slow-waves, in turn, are generated by the Interstitial cells of Cajal which also line the GI
tract.
The slow waves are a summation of a large number of various functional cell membrane
fluctuations called “Unitary Potentials (UP)”. The unitary potentials are generated from a
group of cell organelles called "Pacemaker Unit (PU)". The UP is generated by the flow of
Ca2+ ions through the Pacemaker Unit.
Abnormalities in the Interstitial Cells of Cajal could result in gastric diseases like Irritable
Bowel Syndrome and Pylorus Dysfunction. In this project, a VLSI model of the Pacemaker
Unit, which is the most fundamental unit of the ICC, is built using VHDL from a proven
biophysical model.
2
B i op h ysi cal B ack grou n d :
2.1
The Interstitial Cell of Cajal:
The Interstitial Cells of Cajal were first isolated by Santiago Ramon y Cajal. These cells are
found along the entire gut -wall including the myenteric-plexus and at the interface between
the circular muscle and the submucosa. These cells are neither neurons nor muscular cells
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and are supposed to be derived from fibroblasts. The ICC are electrically coupled to the
enteric muscle cells through gap junctions. The slow waves in the digestive system are
generated by a large group of these cells.
Each part of the digestive system has its own charactersitic slow-wave. For example, in the
human digestive system, the frequency of the slow-waves is 3 cycles per minute in the
stomach and 12 cycles per minute in the duodenum. This variation is largely attributed to the
difference in the ICC population in the various digestive organs. Figure 1 shows the different
population of the ICC in the rat stomach and the rat intestine.
Figure 1: ICC distribution along the murine stomach and murine intestine[2]
2 . 2 T h e P a c e ma k e r U n i t :
[2] suggests that the Interstitial Cell of Cajal is fundamentally made up of a number of small
functional units which are responsible for the generation of the slow wa ves. These units are
called the pacemaker units and essentially are made up of four components:
2.2.1
The Endoplasmic Reticulum(ER):
It is the intracellular Ca 2+ store that cycles Ca 2+ by release via the IP 3R and is sequestered
back again by the sarcoeondoplasmic reticulum calcium ATPase (SERCA) pump proteins.
2.2.2
The Mitochondrial Subspace (MT) :
It regulates the cellular ATP production through the mitochondrial calcium uniporter(MCU) and the Mitrochondrial Sodium/Calcium Exchanger(NCX).
2.2.3 Cytosolic Subspace(S1 and S2):
These two form the reamining of the pacemaker unit and includes the Non-Selective
Cation conductance exchanger(NSCC) and the intracellular C a2+ fluxes(S1S2).
2.3
The Unitary Potential:
The Unitary Potential is generated in the Pacemaker Unit as a consequence of the flow of
C a2+ ions. Initially C a2+ ions flow into the S1 subspace which then diffuse to S2
.Sufficient C a2+ entry into S2 raises the IP3 R open probability causing a flow of C a2+
from the Endoplasmic Reticulum. The mitochondria also gets activated through the MCU
channel, causing rapid mitochondrial C a2+ accumulation. To maintain ionic concentrations
in the ER, the ER takes up C a2+ ions though the SERCA pump. The deficiency in the ions
in S1 causes the NSCC channel to open up taking up both N a+ and C a2+ ions. This
depolarization is then followed by a repolarization where mitochondria releases the excess
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Ca2+ ions through NCX and S1 releases N a+ ions into the extracellular space. This
process is cyclic and gives rise to a unitary potential cycle.
Figure 2: The schematic diagram of the Pacemaker Unit and the flow of ions.
2.4 The Model Framework:
[2] models the Unitary Potential as a state model of 5 differential equations governing
the basic parameters. The state variables are:
Vm: Membrane Potential
C S1 : Ca2+ concentration in S1
C S2 : Ca2+ concentration in S2
C ER : Ca2+ concentration in ER
C MT : Ca2+ concentration in MT
N S1 : Na+ concentration in S1
H: opening gate variable
Φ3: IP3R slow variable
The state equations are given by:
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Where the Ji is the Ca2+ flux due to the particular channel i, φ1 and φ2 are the opening and
closing gate variables of I P3R and fm is the mitochondrial buffering rate.
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3. System Implementation:
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3.1 Basic Block Diagram:
The Pacemaker Unit's digital VLSI model has two inputs viz. the Clock and the Reset
and a 32 bit output for the output voltage generated. This is as shown in Figure 3
Figure 3: Black Box of Pacemaker Unit
Figure 4: Block Diagram of the Pacemaker Unit
The Pacemaker Unit's block diagram is shown in the following diagram. The constants
and the parameters are stored in a memory block in the 32 bit IEEE-754 format. The main
advantage of this format is that floating point numbers are easy to represent and compute.
The membrane voltage and the other state parameters are calculated in the computation
block. The system is a positive edge triggered system and consists of 32 bit floating point
multipliers, adders and subtractors.
To verify the accuracy of the model, the system was first simulated on MATLAB with a
initial resting potential of -70.1 mV. The system was also simulated in MATLAB to
determine the clock frequency required to run the system so as to obtain a unitary potential
of 3 cycles/minute as the case with most mammals.
The actual model was simulated using VHDL on Altera's FPGA software Quartus II. The
output waveforms were analyzed using ModelSim and the Register Transfer Level (RTL)
schematic was obtained.
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4. Results:
Figure 5 shows the MATLAB simulation of the system using MATLAB's ode23 solver. By a
hit-and-trial method, the system was found to generate a unitary potential of the desired
frequency when the samples were spaced at 1.54 ms. Thus it was decided that the clock
frequency of the system to be at 6.4 kHz. Figure 6 shows the various Ca 2+ concentrations
across the different parts of the Pacemaker Unit.
F i g u r e 5 : M AT L A B : U n i t a r y P o t e n t i a l s ( A m p l i t u d e 3 m V p k - p k )
F i g u r e 6 : M AT L A B C a 2 + i o n f l o w i n v a r i o u s c o m p o n e n t s o f t h e P a c e m a k e r
Unit
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Figure 7 shows the waveform simulation using VHDL at a clock of 6.4 kHz.
T he syste m was b uilt using the behavioural model and emplo yed the Euler's
m e t h o d f o r s o l v i n g t h e d i f f e r e n t i a l e q u a t i o n s . A p p e n d i x A s h o w s t h e RT L
sche matic synthesized for the Pacema ker Unit.
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Figure 7: VHDL Simulation Output of the Pacemaker Unit
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5.
Con cl u si on and Fu tu re Wo rk :
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R e f e re n c e s
T hus the V LSI model o f the Pace m a ker Unit w as obtained using V H D L and
v e r i f i e d w i t h M AT L A B s i m u l a t i o n s . T h e I n t e r s t i t i a l C e l l o f C a j a l h a s m o r e
than o ne Pace maker U nit. Hence the collective summation of all the
P a c e m a k e r u n i t s h a s t o b e s t u d i e d . A l s o t h e g a s t r i c wa l l i s l i n e d w i t h m o r e
t h a n o n e I C C . H e n c e i t i s n e c e s s a r y t o s t u d y t h e e ff e c t s o f m a n y I C C s a n d
the e ffect of t he ICC p opulation on t he charac teristics of t he slo w wa ve
generated.
[1] Sanders, K.M., T. Koh, S.D. and Ward., S.M., “Interstitial Cells of Cajal as pacemakers in
the gastrointestinal tract”, Annu Rev. Physiol. 68:307-343.
[2] Faville, R. , A. Pullan, K. Sanders and N. Smith.2008. A biophysically based mathematical model of
unitary potential activity in interstitial cells of Cajal.”,Biophysical Journal 95(1):88-104.
[3] Douglas L. Perry, VHDL- Programming by Example,McGraw-Hill
Publishers.
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Appendix A
177
RTL Schematic of the Pacemaker Unit
V_out[31..0]~reg0
PRE
fpresult~_OUT0
D
Q
V_out[31..0]
ENA
sign~27_OUT0
ufract~254_OUT0
CLR
V_m[8..-23]
PRE
D
Q
V_m_OUT0
ENA
CLR
add~199_OUT0
fpresult~[9121..9090]
C_ER[8..-23]
SEL
fpresult~_OUT0
0
PRE
DATAA
32' h7F800001 --
OUT0
D
Q
sign~28_OUT0
1
DATAB
sign~28
ENA
MUX21
CLR
ShiftLeft96
A[23..0]
<<
ShiftLeft96_OUT
COUNT [6..0]
Add863_OUT
find_leftmost~12576_OUT0
find_leftmost~12577_OUT0
find_leftmost~12578_OUT0
LEFT_SHIFT
ShiftLeft92
A[23..0]
<<
ShiftLeft92_OUT
COUNT [6..0]
Add825_OUT
find_leftmost~12024_OUT0
find_leftmost~12025_OUT0
find_leftmost~12026_OUT0
LEFT_SHIFT
ShiftLeft87
A[23..0]
<<
ShiftLeft87_OUT
COUNT [6..0]
Add776_OUT
find_leftmost~11328_OUT0
find_leftmost~11329_OUT0
find_leftmost~11330_OUT0
LEFT_SHIFT
fract~65_OUT0
Result~4839_OUT0
Result~4843
Result~4859
Result~4859_OUT0
Result~4851_OUT0
Result~4818
Result~4818_OUT0
phi_3[8..-23]
PRE
fpresult~_OUT0
D
Q
phi_3_OUT0
ENA
CLR
orx~7827
orx~7827_OUT0
orx~7826_OUT0
orx~7823
orx~7823_OUT0
orx~7822_OUT0
orx~7801
orx~7801_OUT0
orx~7800_OUT0
orx~7797
orx~7797_OUT0
orx~7796_OUT0
orx~1955
orx~1955_OUT0
orx~1954_OUT0
orx~1951
orx~1951_OUT0
orx~1950_OUT0
orx~1929
orx~1929_OUT0
orx~1928_OUT0
orx~1925
orx~1925_OUT0
orx~1924_OUT0
H[8..-23]
PRE
fpresult~_OUT0
D
Q
ENA
CLR
0
H_OUT0
ufract~254
C_S2_OUT0
C_ER_OUT0
ufract~254_OUT0
ufract~1026_OUT0
sign~108_OUT0
0
sign~109_OUT0
1
sign~109
leftright~39_OUT0
0
sign~27_OUT0
1
sign~27
1' h0 --
ShiftRight179
A[27..0]
3' h0 --
>>
COUNT [8..0]
Add1787_OUT
ShiftRight179_OUT
RIGHT_SHIFT
Result~4851
Result~4851_OUT0
orx~7829
orx~7829_OUT0
orx~7828_OUT0
orx~7807
orx~7807_OUT0
orx~7806_OUT0
orx~7805
orx~7805_OUT0
orx~7804_OUT0
orx~7803
orx~7803_OUT0
orx~7802_OUT0
orx~1961
orx~1961_OUT0
orx~1960_OUT0
orx~1959
orx~1959_OUT0
orx~1958_OUT0
orx~1957
orx~1957_OUT0
orx~1956_OUT0
orx~1935
orx~1935_OUT0
orx~1934_OUT0
orx~1933
orx~1933_OUT0
orx~1931
fract~65_OUT0
orx~1932_OUT0
orx~1930_OUT0
fract~66_OUT0
fpresult~_OUT0
LessThan4559
orx~1931_OUT0
A[26..0]
3' h0 -B[26..0]
<
0
3' h0 --
LESS_THAN
1
fracts~4949_OUT0
fracts~4949
0
1
fracts~4948_OUT0
fracts~4948
0
1
fracts~4947_OUT0
fracts~4947
0
1
fracts~4946_OUT0
fracts~4946
0
1
fracts~4945_OUT0
fracts~4945
0
1
fracts~4944_OUT0
fracts~4944
0
1
fracts~4943_OUT0
fracts~4943
0
1
fracts~4942_OUT0
fracts~4942
0
1
fracts~4941_OUT0
fracts~4941
0
1
fracts~1244_OUT0
fracts~1244
0
1
fracts~1243_OUT0
fracts~1243
0
1
fracts~1242_OUT0
fracts~1242
0
1
fracts~1241_OUT0
fracts~1241
0
1
fracts~1240_OUT0
fracts~1240
0
1
fracts~1239_OUT0
fracts~1239
0
1
LessThan1157_OUT
fracts~1238
0
fracts~1238_OUT0
ufract~1026
ufract~1026_OUT0
leftright~147_OUT0
0
sign~108_OUT0
1
sign~108
1' h0 --
ShiftRight48
A[27..0]
3' h0 --
>>
ShiftRight48_OUT
COUNT [8..0]
Add534_OUT
RIGHT_SHIFT
Result~17454
Result~17454_OUT0
Result~4839_OUT0
Result~4843_OUT0
Result~4836
Result~4836_OUT0
Result~4851_OUT0
orx~7811
orx~7811_OUT0
orx~7810_OUT0
orx~7809
orx~7809_OUT0
orx~7808_OUT0
orx~7785
orx~7785_OUT0
orx~7784_OUT0
orx~1941
orx~1941_OUT0
orx~1940_OUT0
orx~1939
orx~1939_OUT0
orx~1938_OUT0
orx~1937
orx~1937_OUT0
orx~1936_OUT0
Mux162
Add1787_OUT
SEL[4..0]
5' h00 --
fract~65_OUT0
C_ER_OUT0
OUT
Mux162_OUT
OUT
Mux42_OUT
DATA[31..0]
3' h0 --
MUX
Mux42
SEL[4..0]
5' h00 -DATA[31..0]
3' h0 --
MUX
0
1
fracts~4955_OUT0
fracts~4955
0
1
fracts~4954_OUT0
fracts~4954
0
1
fracts~4953_OUT0
fracts~4953
0
1
fracts~4952_OUT0
fracts~4952
LessThan4559_OUT
fpresult~_OUT0
0
1
fracts~4951_OUT0
fracts~4951
0
LessThan1157
A[26..0]
3' h0 --
exp~1224_OUT0
C_S2_OUT0
B[26..0]
<
1
fracts~4950
0
fracts~4950_OUT0
orx~7819
orx~7819_OUT0
orx~7818_OUT0
orx~7817
orx~7817_OUT0
orx~7816_OUT0
orx~7815
orx~7815_OUT0
orx~7814_OUT0
orx~7813
orx~7813_OUT0
orx~7812_OUT0
orx~7793
orx~7793_OUT0
orx~7792_OUT0
orx~7791
orx~7791_OUT0
orx~7790_OUT0
orx~7789
orx~7789_OUT0
orx~7788_OUT0
orx~7787
C_ER_OUT0
orx~7786_OUT0
orx~7787_OUT0
orx~1947
orx~1947_OUT0
orx~1946_OUT0
orx~1945
orx~1945_OUT0
orx~1944_OUT0
orx~1943
orx~1943_OUT0
orx~1942_OUT0
orx~1923
orx~1923_OUT0
orx~1922_OUT0
orx~1921
orx~1921_OUT0
orx~1920_OUT0
orx~1919
orx~1919_OUT0
orx~1918_OUT0
orx~1917
orx~1917_OUT0
orx~1916_OUT0
0
1
fracts~1256_OUT0
fracts~1256
0
1
fracts~1255_OUT0
fracts~1255
0
1
fracts~1254_OUT0
fracts~1254
LessThan1157_OUT
C_S2_OUT0
0
1
find_leftmost~12561
fracts~1253_OUT0
fracts~1253
find_leftmost~12567
find_leftmost~12567_OUT0
find_leftmost~12555_OUT0
find_leftmost~12531
find_leftmost~12525
find_leftmost~12531_OUT0
find_leftmost~12519_OUT0
find_leftmost~12489
find_leftmost~12489_OUT0
find_leftmost~12483_OUT0
find_leftmost~12015
find_leftmost~12015_OUT0
find_leftmost~12009_OUT0
find_leftmost~11979
find_leftmost~11973
find_leftmost~11979_OUT0
find_leftmost~11967_OUT0
find_leftmost~11943
find_leftmost~11937
find_leftmost~11943_OUT0
find_leftmost~11931_OUT0
find_leftmost~11319
find_leftmost~11313
find_leftmost~11319_OUT0
find_leftmost~11307_OUT0
find_leftmost~11283
find_leftmost~11277
find_leftmost~11283_OUT0
find_leftmost~11271_OUT0
find_leftmost~11241
find_leftmost~11235
find_leftmost~11241_OUT0
find_leftmost~11231_OUT0
0
0
1
exp~2074_OUT0
exp~2074
0
0
1
exp~2073_OUT0
exp~2073
0
0
1
exp~2072_OUT0
exp~2072
0
0
exp~2071_OUT0
Result~17454_OUT0
Classfp~[837..834]
fractr~[551..480]
SEL
Result~4836_OUT0
SEL
Classfp~[833..832]
2' h0 --
DATAA
exp~1943
SEL
C_ER_OUT0
OUT0
1' h0 --
DATAA
DATAA
OUT0
2' h0 --
DATAB
OUT0
fractr~_OUT0
1' h0 --
DATAB
DATAB
MUX21
find_leftmost~11907_OUT0
LessThan4559_OUT
Equal36_OUT
MUX21
MUX21
fractc~[3503..3480]
fractc~[3479..3456]
SEL
SEL
DATAA
fract~65_OUT0
fpresult~_OUT0
fract~66_OUT0
DATAA
OUT0
OUT0
fractc~_OUT0
DATAB
DATAB
MUX21
exp~1943_OUT0
MUX21
LessThan1157_OUT
fractc~[911..888]
fractc~[887..864]
SEL
SEL
DATAA
DATAA
C_S2_OUT0
exp~1224_OUT0
OUT0
OUT0
fractc~_OUT0
DATAB
DATAB
MUX21
fpresult~[3937..3906]
MUX21
find_leftmost~11909_OUT0
fpresult~_OUT0
SEL
DATAA
OUT0
find_leftmost~11915_OUT0
find_leftmost~11923_OUT0
find_leftmost~11931_OUT0
find_leftmost~11937_OUT0
find_leftmost~11955_OUT0
add~25_OUT0
Equal9_OUT
ShiftLeft96_OUT
ShiftLeft92_OUT
ShiftLeft87_OUT
multiply~156_OUT0
32' h7F800001 --
fpresult~_OUT0
DATAB
MUX21
Classfp~[1926..1925]
SEL
DATAA
OUT0
2' h0 --
Classfp~_OUT0
DATAB
MUX21
Classfp~[879..878]
SEL
2' h0 --
DATAA
OUT0
DATAB
Classfp~_OUT0
MUX21
Classfp~[563..559]
SEL
DATAA
2' h0 --
OUT0
Classfp~_OUT0
3' h0 -DATAB
MUX21
Result~4839
Result~4839_OUT0
orx~7825
orx~7825_OUT0
orx~7824_OUT0
orx~7821
orx~7821_OUT0
orx~7820_OUT0
orx~7799
orx~7799_OUT0
orx~7798_OUT0
orx~7795
orx~7795_OUT0
orx~7794_OUT0
orx~1953
orx~1953_OUT0
orx~1952_OUT0
orx~1949
orx~1949_OUT0
orx~1948_OUT0
orx~1927
orx~1927_OUT0
orx~1926_OUT0
0
1
fracts~4935_OUT0
fracts~4935
0
1
fracts~4933_OUT0
fracts~4933
find_leftmost~12573
find_leftmost~12573_OUT0
find_leftmost~12567_OUT0
find_leftmost~12501
find_leftmost~12495
find_leftmost~12501_OUT0
find_leftmost~12489_OUT0
find_leftmost~12021
find_leftmost~12015_OUT0
find_leftmost~12021_OUT0
find_leftmost~11949
find_leftmost~11949_OUT0
find_leftmost~11943_OUT0
0
1
0
1
0
1
find_leftmost~11927_OUT0
find_leftmost~11912_OUT0
1
0
1
find_leftmost~11960
0
0
0
find_leftmost~11960_OUT0
1
1
find_leftmost~11954
1
find_leftmost~11948
find_leftmost~11942
find_leftmost~11936
find_leftmost~11930
0 0
1
find_leftmost~11926
1 0
1
find_leftmost~11922
1
find_leftmost~11918
1
find_leftmost~11914
find_leftmost~11911
find_leftmost~11908
0
1
0
1
find_leftmost~11919_OUT0
0
0
0
0
0
0
find_leftmost~12495_OUT0
1
1
1
0
0
1
find_leftmost~11910_OUT0
find_leftmost~11910
find_leftmost~11325
find_leftmost~11325_OUT0
find_leftmost~11319_OUT0
find_leftmost~11247
find_leftmost~11247_OUT0
find_leftmost~11241_OUT0
1
0
1
exp~2077_OUT0
exp~2077
0
0
1
exp~2069_OUT0
exp~2076_OUT0
exp~2076
0
0
1
exp~2075_OUT0
exp~2075
1
0
1
exp~1951_OUT0
exp~1951
1
0
1
exp~1804_OUT0
exp~1804
0
0
1
exp~1802_OUT0
exp~1802
0
0
1
exp~1796_OUT0
exp~1801_OUT0
exp~1801
0
0
1
exp~1800_OUT0
exp~1800
182
Classfp~_OUT0
183
184
185
186
187
188
Mult16
ShiftRight70
A[23..0]
24' h9D4952 -B[23..0]
fractr~_OUT0
10' h001 --
Add781
+
B[9..0]
+
9' h0F9 --
SEL
Add784
1' h1 -B[12..0]
13' h0001 --
rfract~[1034..1012]
1
SEL
DATAA
OUT0
DATAB
SEL
DATAA
OUT0
LessThan1691
DATAA
DATAB
OUT0
DATAB
DATAB
11' h000 -B[11..0]
1' h0 --
<
MUX21
0
check_round~75
Add786
1
MUX21
ADDER
ADDER
stickyx~67
1' h1 -B[13..0]
14' h1FFD --
+
Add786_OUT
Add782
LessThan1689
A[9..0]
B[9..0]
Add777
0
1
1
0
1
find_leftmost~11966
1
0
1' h1 -B[14..0]
15' h0001 --
Add778
1' h1 -B[10..0]
DATAA
0
+
Add785_OUT
ADDER
+
1
1
1' h1 --
1
find_leftmost~12026
0 0
1
find_leftmost~12020
1 0
1
find_leftmost~12014
0 0
1
find_leftmost~12008
1 0
1
find_leftmost~12002
0 0
1
find_leftmost~11996
1
find_leftmost~11990
1
find_leftmost~11984
find_leftmost~11978
find_leftmost~11972
ADDER
LessThan1688
CIN
1
A[9..0]
OUT0
<
1' h1 -B[9..0]
DATAB
9' h180 --
LessThan1688_OUT
Mult16_OUT
LESS_THAN
rexp~[359..352]
0
MUX21
find_leftmost~12019_OUT0
9' h169
1' h1 --
A[14..0]
0
0
0
Add785
<
A[10..0]
SEL
14' h0000 -1
0
1
find_leftmost~11960_OUT0
1
A[9..0]
LESS_THAN
shifty~[237..224]
ADDER
find_leftmost~11961_OUT0
find_leftmost~12015_OUT0
+
ADDER
+
B[7..0]
CIN
B[9..0]
A[7..0]
8' hFD --
SEL
0
1
exp~1834_OUT0
1
find_leftmost~12025
1
exp~1834
0
DATAA
OUT0
find_leftmost~12018_OUT0
find_leftmost~11973_OUT0
find_leftmost~11967_OUT0
find_leftmost~12022_OUT0
find_leftmost~12023_OUT0
A[13..0]
LESS_THAN
MUX21
ADDER
exp~1797_OUT0
exp~1798_OUT0
exp~1799_OUT0
exp~1800_OUT0
exp~1801_OUT0
exp~1802_OUT0
find_leftmost~12021_OUT0
MUX21
rfract~_OUT0
sfract~_OUT0
MUX21
A[11..0]
OUT0
+
0
OUT0
RIGHT_SHIFT
DATAA
A[12..0]
ADDER
0
Result~6997
SEL
DATAA
DATAB
shiftr~[1580..1569]
SEL
ADDER
+
B[8..0]
shiftr~[1556..1545]
Add783
A[9..0]
10' h07F --
A[8..0]
1' h1 --
>>
COUNT [11..0]
shiftr~[1568..1557]
Add779
A[9..0]
B[9..0]
Add780_OUT
sfract~[1155..1130]
A[27..0]
x
MULTIPLIER
1
rexp~_OUT0
find_leftmost~12024
DATAB
Add825
A[4..0]
Result~6995
1' h1 --
MUX21
+
B[4..0]
5' h05 --
Result~6995_OUT0
ADDER
find_leftmost~11325_OUT0
1
find_leftmost~11324_OUT0
0
1
find_leftmost~11330
1
find_leftmost~11323_OUT0
0
1
find_leftmost~11329
1
find_leftmost~11322_OUT0
0
1
find_leftmost~11328
find_leftmost~11326_OUT0
find_leftmost~11327_OUT0
Add776
A[4..0]
1' h1 -B[4..0]
5' h05 --
+
ADDER
Result~6968
multiply~156
Classfp~_OUT0
stickyx~66
orx~2921_OUT0
exp~_OUT0
find_leftmost~11979_OUT0
find_leftmost~11985_OUT0
find_leftmost~11991_OUT0
find_leftmost~11997_OUT0
find_leftmost~12003_OUT0
find_leftmost~12009_OUT0
Add826_OUT
0
exp~1833_OUT0
1
exp~1833
0
1
exp~1832
Add827
A[10..0]
1' h1 -B[10..0]
exp~1803_OUT0
exp~1804_OUT0
expon_out~_OUT0
1' h1 --
+
Add827_OUT
ADDER
LessThan1689_OUT
exp~1832_OUT0
Add782_OUT
find_leftmost~12026_OU
multiply~156_OUT0
Add776_OUT
find_leftmost~11328_OU
find_leftmost~11329_OU
find_leftmost~11330_OU
Add825_OUT
find_leftmost~12024_OU
find_leftmost~12025_OU
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
exp~1831_OUT0
exp~1830_OUT0
exp~1829_OUT0
exp~1828_OUT0
exp~1827_OUT0
ShiftLeft88_OUT
fract_out~_OUT0
Result~6995_OUT0
zerores~88_OUT0
fpresult~[3557..3527]
0
1
1
zerores~89
multiply~155
Classfp~_OUT0
SEL
0
0
1
Result~7081
Result~7049_OUT0
0
0
1
Result~7080
Result~7048_OUT0
0
0
1
Result~7079
Result~7047_OUT0
Result~7050_OUT0
fpresult~[3588..3558]
0
0
1
SEL
DATAA
Result~7078
OUT0
DATAA
31' h7F800001 --
Result~7046_OUT0
OUT0
DATAB
fpresult~_OUT0
0
0
1
MUX21
Result~7077
Result~7045_OUT0
exp~1831_OUT0
0
0
0
1
0
Result~7076
Result~7044_OUT0
1
Result~7058
0
0
1
Result~7075
0
0
1
Result~7053
Result~7043_OUT0
31' h7F800000 --
0
0
Result~7074
Result~7042_OUT0
MUX21
0
0
1
Result~7073
Result~7041_OUT0
0
0
1
Result~7072
Result~7040_OUT0
0
0
1
Result~7071
Result~7039_OUT0
0
0
1
Result~7070
Result~7038_OUT0
0
0
1
Result~7069
Result~7037_OUT0
0
0
1
Result~7068
Result~7036_OUT0
0
0
1
Result~7067
Result~7035_OUT0
0
0
1
Result~7066
Result~7034_OUT0
0
0
1
Result~7065
Result~7033_OUT0
0
0
1
Result~7064
Result~7032_OUT0
0
0
1
Result~7063
Result~7031_OUT0
0
0
1
Result~7062
Result~7030_OUT0
0
0
1
Result~7061
Result~7029_OUT0
0
0
1
Result~7060
Result~7028_OUT0
0
0
infres~88_OUT0
0
0
1
Result~7059
1
0
infres~89
1
1
Result~7027
0
0
1
1
0
Result~7026
1
Result~7057
0
0
1
1
0
Result~7025
1
Result~7056
0
0
1
DATAB
1
1
0
Result~7024
1
Result~7055
1' h0 --
ShiftRight72
A[27..0]
3' h0 --
>>
COUNT [8..0]
Add789_OUT
ShiftRight72_OUT
RIGHT_SHIFT
Result~7134
fpresult~_OUT0
Result~7138
Result~7154
Result~7154_OUT0
Result~7146
Result~7106
Result~7106_OUT0
Result~7088
Result~7088_OUT0
orx~3016
orx~3016_OUT0
orx~3015_OUT0
orx~3014
orx~3014_OUT0
orx~3013_OUT0
orx~3012
orx~3012_OUT0
orx~3011_OUT0
orx~3010
orx~3010_OUT0
orx~3009_OUT0
orx~3008
orx~3008_OUT0
orx~3007_OUT0
orx~3006
orx~3006_OUT0
orx~3005_OUT0
orx~3004
orx~3004_OUT0
orx~3003_OUT0
orx~3002
orx~3002_OUT0
orx~3001_OUT0
orx~2994
orx~2994_OUT0
orx~2993_OUT0
orx~2992
orx~2992_OUT0
orx~2991_OUT0
orx~2990
orx~2990_OUT0
orx~2989_OUT0
orx~2988
orx~2988_OUT0
orx~2987_OUT0
orx~2986
orx~2986_OUT0
orx~2985_OUT0
orx~2984
orx~2984_OUT0
orx~2983_OUT0
orx~2982
orx~2982_OUT0
orx~2981_OUT0
orx~2980
orx~2980_OUT0
orx~2979_OUT0
orx~2978
LessThan1721
1' h0 -A[8..0]
Add789_OUT
<
B[8..0]
fractc~[1319..1296]
fractc~[1343..1320]
8' h00 -LESS_THAN
SEL
DATAA
SEL
OUT0
DATAA
DATAB
OUT0
DATAB
fract~46_OUT0
C_S1_OUT0
LessThan1746
A[26..0]
3' h0 -B[26..0]
exp~1835_OUT0
fpresult~_OUT0
MUX21
<
fractc~[1271..1248]
LESS_THAN
3' h0 --
fractc~_OUT0
MUX21
SEL
DATAA
OUT0
fractc~_OUT0
DATAB
fracts~1787_OUT0
Result~7106_OUT0
fracts~1786_OUT0
fracts~1785_OUT0
fpresult~_OUT0
fracts~1784_OUT0
fracts~1783_OUT0
fracts~1782_OUT0
fracts~1803_OUT0
MUX21
Classfp~[813..809]
SEL
DATAA
2' h0 --
OUT0
Classfp~_OUT0
3' h0 -DATAB
fracts~1801_OUT0
fracts~1794_OUT0
fracts~1793_OUT0
fracts~1792_OUT0
fracts~1791_OUT0
fracts~1790_OUT0
fracts~1789_OUT0
fracts~1788_OUT0
orx~2995_OUT0
orx~2971_OUT0
orx~2973_OUT0
orx~2997_OUT0
orx~2999_OUT0
fractc~_OUT0
MUX21
Result~7113
Result~7113_OUT0
orx~3000
orx~3000_OUT0
LessThan1747_OUT
fracts~[1832..1805]
fracts~[1860..1833]
orx~2998
SEL
ShiftRight72_OUT
SEL
DATAA
OUT0
28' h0000000 --
orx~2998_OUT0
DATAA
DATAB
3' h0 --
orx~2996
0
MUX21
Equal13
orx~2996_OUT0
1
fracts~1804
orx~2974
A[8..0]
B[8..0]
9' h000 --
=
orx~2974_OUT0
0
1
EQUAL
orx~2972
fracts~1802
orx~2972_OUT0
fracts~[1888..1861]
1' h0 -0
ShiftRight71
A[27..0]
3' h0 --
Add790_OUT
>>
1
SEL
OUT0
fracts~1800
DATAA
DATAB
COUNT [8..0]
OUT0
RIGHT_SHIFT
0
DATAB
0
0
1
fracts~1913_OUT0
fracts~1913
1
MUX21
fracts~_OUT0
LessThan1746_OUT
fracts~1799
0
1
fracts~1798
0
1
1' h0 --
fracts~1797
MUX21
0
1
fracts~1796
0
1
fracts~1795
0
1
fracts~1781
0
0
1
fracts~1912_OUT0
fracts~1912
0
0
1
fracts~1911_OUT0
fracts~1911
0
0
1
fracts~1910_OUT0
fracts~1910
0
0
1
fracts~1909_OUT0
fracts~1909
0
0
1
fracts~1908_OUT0
fracts~1908
0
0
1
fracts~1907_OUT0
fracts~1907
0
0
1
fracts~1906_OUT0
fracts~1906
0
0
1
fracts~1905_OUT0
fracts~1905
0
0
1
fracts~1904_OUT0
fracts~1904
0
0
1
fracts~1903
fracts~1903_OUT0
LessThan1720
1' h1 --
1' h0 --
Add792
A[8..0]
Add789_OUT
A[28..0]
<
B[8..0]
4' h1 -B[28..0]
8' hE5 --
+
0
LESS_THAN
ufract~368
0
0
1
1
ADDER
ufract~369
fracts~1890
C_S1_OUT0
fpresult~_OUT0
0
1
ufract~370
fracts~1896_OUT0
fracts~1897_OUT0
fracts~1898_OUT0
fracts~1899_OUT0
fracts~1900_OUT0
fracts~1901_OUT0
fracts~1902_OUT0
fracts~1903_OUT0
fracts~1904_OUT0
fracts~1905_OUT0
fracts~1906_OUT0
fracts~1907_OUT0
fracts~1908_OUT0
fracts~1909_OUT0
fracts~1910_OUT0
fracts~1911_OUT0
0
1
ufract~371
0
1
ufract~372
0
1
ufract~373
0
1
fracts~_OUT0
ufract~374
0
0
1
ShiftRight73
fracts~1917
fracts~1914
1' h1 --
0
A[27..0]
1
COUNT [10..0]
>>
ShiftRight73_OUT
ufract~375
0
0
RIGHT_SHIFT
1
0
fracts~1915
1
ufract~376
0
0
1
0
fracts~1916
1
ufract~377
0
1
ufract~378
0
1
ufract~379
0
1
ufract~380
Add791
1' h0 -A[24..0]
fractc~_OUT0
fracts~1889_OUT0
sticky~55_OUT0
fracts~1891_OUT0
fracts~1892_OUT0
fracts~1893_OUT0
fracts~1894_OUT0
fracts~1895_OUT0
B[24..0]
0
1
+
ADDER
ufract~381
0
1
ufract~382
0
1
ufract~383
0
1
ufract~384
Result~7181
Mux65
Result~7181_OUT0
0
1
ufract~385
SEL[4..0]
4' h0 --
0
1
ufract~386
fracts~1912_OUT0
fracts~1913_OUT0
0
1
LessThan1777
ufract~387
A[11..0]
12' h01B -B[11..0]
Add799_OUT
<
0
1
LESS_THAN
LessThan1778
ufract~388
orx~3022
OUT
DATA[31..0]
0
orx~3018
B[11..0]
<
orx~3019
0
orx~3022_OUT0
orx~3021_OUT0
0
1
A[11..0]
12' h01A --
orx~3020
1
orx~3021
1
LESS_THAN
find_leftmost~11475_OUT0
ufract~389
0
1
ufract~390
0
1
ufract~391
0
1
MUX
ufract~392
0
1
ufract~393
0
1
ufract~394
0
1
ufract~395
0
ShiftLeft89
1
A[27..0]
Add798_OUT
<<
ufract~396
COUNT [12..0]
ShiftLeft89_OUT
LEFT_SHIFT
shiftr~_OUT0
find_leftmost~11475
1
0
1
find_leftmost~11476
210
211
212
find_leftmost~11476_OUT0
ufract~391_OUT0
ufract~392_OUT0
ufract~393_OUT0
ufract~394_OUT0
ufract~395_OUT0
ufract~396_OUT0
ufract~390_OUT0
ufract~389_OUT0
ufract~388_OUT0
ufract~387_OUT0
ufract~386_OUT0
ufract~385_OUT0
ufract~384_OUT0
ufract~383_OUT0
ufract~382_OUT0
ufract~381_OUT0
ufract~380_OUT0
ufract~379_OUT0
ufract~378_OUT0
ufract~377_OUT0
ufract~376_OUT0
ufract~375_OUT0
ufract~374_OUT0
ufract~373_OUT0
ufract~372_OUT0
ufract~371_OUT0
LessThan1720_OUT
ufract~368_OUT0
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
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250
251
252
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254
255
256
257
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261
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263
264
265
266
267
Appendix B
VHDL Code for the Pacemaker Unit
library IEEE;
use IEEE.std_logic_1164.all;
use IEEE.std_logic_arith.all;
use IEEE.math_real.all;
--library IEEE_PROPOSED;
--use IEEE_PROPOSED.fixed_float_types.all;
--use IEEE_PROPOSED.fixed_pkg.all;
--use IEEE_PROPOSED.float_pkg.all;
entity Pace_Unit is
port (clk,rst:in STD_LOGIC;V_out:out STD_LOGIC_VECTOR(31 downto 0));
end Pace_Unit;
architecture PU of Pace_Unit is
-- UP Model Parameters
constant g_Ca : real := 0.01;
constant E_NSCC : real := 0.0;
constant g_capNSCC_Ca : real := 0.12;
constant g_capNSCC_Na :real := 220.0;
constant K_NSCC :real := 0.12;
constant h_NSCC :real := 3.0;
constant g_PM :real := 420.0;
constant K_PM :real := 1.0;
constant g_Na :real := 15000.0;
constant K_Na :real := 10000.0;
constant h_Na :real := 4.0;
constant V_SERCA :real := 100000.0;
constant A_2 :real := 0.0006;
constant A_4 :real := 3.57;
constant A_5 :real := 0.000027;
constant A_6 :real := 0.0000231;
constant V_MCU :real := 800.0;
constant K_MCU :real := 10.0;
constant K_INH :real := 10.0;
constant h_INH :real := 4.0;
constant V_NCX :real := 0.5;
constant K_NCX :real := 0.3;
constant u_S1S2 :real := 0.04;
constant k_IPR :real := 2000.0;
constant k_1 :real := 0.0;
constant k_min1 :real := 6.4;
constant k_2 :real := 4.0;
constant r_2 :real := 200.0;
constant r_min2 :real := 0.0;
constant r_4 :real := 750.0;
constant R_1 :real := 36.0;
constant R_3 :real := 300.0;
constant g_alpha :real := 0.02;
constant g_beta :real := 300.0;
constant K_beta :real :=2.0;
constant h_beta :real := 2.0;
constant K_m :real := 0.01;
constant B_m :real := 100.0;
268
269
270
271
272
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322
323
constant y_S1 :real := 100.0;
constant y_S2 :real := 1.0;
constant y_ER :real := 20.0;
constant y_MT :real := 200.0;
constant d_S :real := 26.0;
constant C_m :real := 20.0;
constant Z_Ca :real := 2.0;
constant Z_Na :real :=1.0;
constant V_t :real := 26.7;
constant C_O :real:= 1800.0;
constant P :real := 1.0;
signal V_m :real := -70.1;
signal C_S1 :real := 0.12;
signal C_S2 :real := 0.023;
signal C_ER :real := 203.0;
signal C_MT: real := 0.22;
signal N_S1 :real := 10100.0;
signal H : real := 0.0;
signal phi_3 :real := 0.306;
signal a_phi3,b_phi3,phi_1,phi_min1,phi_2,J_IPR,J_S1S2,J_NCX,J_MCU,J_SERCA : real := 0.0
;
signal
I_Na,I_PM,g_NSCC_Ca,g_NSCC_Na,I_NSCC_Ca,I_NSCC_Na,E_Ca,I_Ca,I_iCa,I_iNa,f_m :
real := 0.0 ;
signal l_MTS1,l_ERS1,l_ERS2,l_S1S2,l_MTS2 : real := 0.0 ;
begin
process(clk,rst)
begin
if rst = '1' and rising_edge(clk) then
V_out <= CONV_STD_LOGIC_VECTOR(INTEGER(V_m),32);
a_phi3 <= g_alpha;
b_phi3 <= g_beta*((C_S2**h_beta)/(K_beta**h_beta+C_S2**h_beta));
phi_3 <= phi_3+ (a_phi3-b_phi3*phi_3);--IP3R Slow Rate Variable
--IP3R Constants
phi_1 <= (k_1*R_1+r_2*C_S2)/(R_1+C_S2);
phi_min1 <= ((k_min1+r_min2)*R_3)/(R_3+C_S2);
phi_2 <= (k_2*R_3+r_4*C_S2)/(R_3+C_S2);
J_IPR <=k_IPR*(((P*phi_1*H)/(P*phi_1+phi_min1))**4.0)*(C_ER-C_S2);
J_S1S2 <= u_S1S2*(C_S2-C_S1);
J_NCX <= V_NCX*(C_MT/(K_NCX+C_MT));
J_MCU <= V_MCU*((C_S2**2.0)/(K_MCU**2.0+C_S2**2.0));
J_SERCA <= V_SERCA*((C_S1-A_2*C_ER)/(1.0
+A_4*C_S1+A_5*C_ER+A_6*C_S1*C_ER));
I_Na <= g_PM*(C_S1**h_Na/(K_Na**h_Na+C_S1**h_Na));
g_NSCC_Ca <=
g_capNSCC_Ca*(K_NSCC**h_NSCC/(K_NSCC**h_NSCC+C_S1**h_NSCC));
g_NSCC_Na <=
g_capNSCC_Na*(K_NSCC**h_NSCC/(K_NSCC**h_NSCC+C_S1**h_NSCC));
I_NSCC_Ca <= g_NSCC_Ca*(V_m-E_NSCC);
I_NSCC_Na <= g_NSCC_Na*(V_m-E_NSCC);
E_Ca <= 0.5*V_t*log(C_O/C_S1);
I_Ca <= g_Ca*(V_m-E_Ca);
l_MTS1 <= y_MT/y_S1;
l_ERS1 <= y_ER/y_S1;
l_ERS2 <= y_ER/y_S2;
l_S1S2 <= y_S1/y_S2;
324
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l_MTS2 <= y_MT/y_S2;
f_m <= 1.0/(1.0+(K_m*B_m/(K_m+C_MT**2.0)));
I_iNa <= I_NSCC_Na+I_Na;
I_iCa <= I_NSCC_Ca+I_Ca;
V_m <= V_m- ((I_iCa+I_iNa)/C_m);
C_S1 <= C_S1 + (J_S1S2+l_MTS1*J_NCX)((d_S/Z_Ca)*I_iCa+l_ERS1*J_SERCA);
C_S2 <= C_S2 + (l_ERS2*J_IPR-(l_S1S2*J_S1S2+l_MTS2*J_MCU));
C_ER <= C_ER + (J_SERCA-J_IPR);
C_MT <= C_MT + f_m*(J_MCU-J_NCX);
N_S1 <= N_S1 - ((d_S/Z_Na)*I_iNa);
H <= H+ ((phi_3*(1.0-H))- (((P*phi_1*phi_2)/(P*phi_1+phi_min1)*H)));
--V_out <= CONV_STD_LOGIC_VECTOR(INTEGER(V_m),32);
end if;
end process;
end PU;