VLSI Implementation of the Pacemaker Unit of the...

VLSI Implementation of the Pacemaker Unit of the Interstitial Cell of Cajal

Ganapathy Subramanium Sundar 1

Department of Bioengineering 2 University of California, San Diego 3

San Diego,CA-92093 4 5

Abstract 6

The digestion of the food in the gastro-intestinal tract is aided by the 7 peristaltic contractions of the gastric muscles. This gastric motility is a 8 result of the sponta- neous rhythmic pacemaker activity produced by the 9 interstitial cells of Cajal(ICC), which line the gastro-enteric system. The 10 interstitial cells of Cajal are a special- ized group of neuro-muscular cells 11 and are derived from fibroblasts. These cells generate periodic action 12 potentials termed as slow waves, which are responsible for gastric motility. 13 The objective of this project is to implement a VLSI model of a simple 14 ICC network capable of producing slow waves generated by the ICC 15 network of the stomach. The cells of the network are designed using a 16 mathematical model where the membrane voltage of the ICC is based on 17 the flow of C a2+ ions and N a+ ions. 18

19

1 Introduction: 20

21 The human digestive system has the tasks of ingestion, digestion, absorption and 22 assimilation of food. The food taken in is pushed through the alimentary canal by a series of 23 rhythmic contractions of the smooth muscles lining the gastro-intestinal(GI)l tract called 24 peristalsis. These contractions are caused by a set of electrical-signals called ”slow waves”. 25 The slow-waves, in turn, are generated by the Interstitial cells of Cajal which also line the GI 26 tract. 27 The slow waves are a summation of a large number of various functional cell membrane 28 fluctuations called “Unitary Potentials (UP)”. The unitary potentials are generated from a 29 group of cell organelles called "Pacemaker Unit (PU)". The UP is generated by the flow of 30 Ca

2+ ions through the Pacemaker Unit. 31

32 Abnormalities in the Interstitial Cells of Cajal could result in gastric diseases like Irritable 33 Bowel Syndrome and Pylorus Dysfunction. In this project, a VLSI model of the Pacemaker 34 Unit, which is the most fundamental unit of the ICC, is built using VHDL from a proven 35 biophysical model. 36 37 2 Biophysical Background: 38

2.1 The Interstitial Cell of Cajal: 39

The Interstitial Cells of Cajal were first isolated by Santiago Ramon y Cajal. These cells are 40 found along the entire gut -wall including the myenteric-plexus and at the interface between 41 the circular muscle and the submucosa. These cells are neither neurons nor muscular cells 42

and are supposed to be derived from fibroblasts. The ICC are electrically coupled to the 43 enteric muscle cells through gap junctions. The slow waves in the digestive system are 44 generated by a large group of these cells. 45

Each part of the digestive system has its own charactersitic slow-wave. For example, in the 46 human digestive system, the frequency of the slow-waves is 3 cycles per minute in the 47 stomach and 12 cycles per minute in the duodenum. This variation is largely attributed to the 48 difference in the ICC population in the various digestive organs. Figure 1 shows the different 49 population of the ICC in the rat stomach and the rat intestine. 50

51

Figure 1: ICC distribution along the murine stomach and murine intestine[2] 52

53

2 .2 The Pa ce ma ke r Un i t : 54

[2] suggests that the Interstitial Cell of Cajal is fundamentally made up of a number of small 55 functional units which are responsible for the generation of the slow wa ves. These units are 56 called the pacemaker units and essentially are made up of four components: 57

2.2.1 The Endoplasmic Reticulum(ER): 58

It is the intracellular Ca2+

store that cycles Ca2+

by release via the IP3R and is sequestered 59 back again by the sarcoeondoplasmic reticulum calcium ATPase (SERCA) pump proteins. 60

2.2.2 The Mitochondrial Subspace (MT) : 61 62 It regulates the cellular ATP production through the mitochondrial calcium uni- 63 porter(MCU) and the Mitrochondrial Sodium/Calcium Exchanger(NCX). 64 65 2.2.3 Cytosolic Subspace(S1 and S2): 66 67 These two form the reamining of the pacemaker unit and includes the Non-Selective 68 Cation conductance exchanger(NSCC) and the intracellular C a2+ fluxes(S1S2). 69 70 2.3 The Unitary Potential: 71 72 The Unitary Potential is generated in the Pacemaker Unit as a consequence of the flow of 73 C a2+ ions. Initially C a2+ ions flow into the S1 subspace which then diffuse to S2 74 .Sufficient C a2+ entry into S2 raises the IP3 R open probability causing a flow of C a2+ 75 from the Endoplasmic Reticulum. The mitochondria also gets activated through the MCU 76 channel, causing rapid mitochondrial C a2+ accumulation. To maintain ionic concentrations 77 in the ER, the ER takes up C a2+ ions though the SERCA pump. The deficiency in the ions 78 in S1 causes the NSCC channel to open up taking up both N a+ and C a2+ ions. This 79 depolarization is then followed by a repolarization where mitochondria releases the excess 80

Ca2+ ions through NCX and S1 releases N a+ ions into the extracellular space. This 81 process is cyclic and gives rise to a unitary potential cycle. 82

83

84 Figure 2: The schematic diagram of the Pacemaker Unit and the flow of ions. 85

86 2.4 The Model Framework: 87 88 [2] models the Unitary Potential as a state model of 5 differential equations governing 89 the basic parameters. The state variables are: 90 91

Vm: Membrane Potential 92 C S1 : Ca

2+ concentration in S1 93

C S2 : Ca2+

concentration in S2 94 C ER : Ca

2+ concentration in ER 95

C MT : Ca2+

concentration in MT 96 N S1 : Na

+ concentration in S1 97

H: opening gate variable 98 Φ3: IP3R slow variable 99

The state equations are given by: 100 101

102

103

Where the Ji is the Ca2+ flux due to the particular channel i, φ1 and φ2 are the opening and 104 closing gate variables of I P3R and fm is the mitochondrial buffering rate. 105

106

3. System Implementation: 107

3.1 Basic Block Diagram: 108

The Pacemaker Unit's digital VLSI model has two inputs viz. the Clock and the Reset 109 and a 32 bit output for the output voltage generated. This is as shown in Figure 3 110

111

Figure 3: Black Box of Pacemaker Unit 112

113

Figure 4: Block Diagram of the Pacemaker Unit 114 115 The Pacemaker Unit's block diagram is shown in the following diagram. The constants 116 and the parameters are stored in a memory block in the 32 bit IEEE-754 format. The main 117 advantage of this format is that floating point numbers are easy to represent and compute. 118 The membrane voltage and the other state parameters are calculated in the computation 119 block. The system is a positive edge triggered system and consists of 32 bit floating point 120 multipliers, adders and subtractors. 121

To verify the accuracy of the model, the system was first simulated on MATLAB with a 122 initial resting potential of -70.1 mV. The system was also simulated in MATLAB to 123 determine the clock frequency required to run the system so as to obtain a unitary potential 124 of 3 cycles/minute as the case with most mammals. 125

The actual model was simulated using VHDL on Altera's FPGA software Quartus II. The 126 output waveforms were analyzed using ModelSim and the Register Transfer Level (RTL) 127 schematic was obtained. 128

129

4. Results: 130

Figure 5 shows the MATLAB simulation of the system using MATLAB's ode23 solver. By a 131 hit-and-trial method, the system was found to generate a unitary potential of the desired 132 frequency when the samples were spaced at 1.54 ms. Thus it was decided that the clock 133 frequency of the system to be at 6.4 kHz. Figure 6 shows the various Ca

2+ concentrations 134

across the different parts of the Pacemaker Unit. 135

136 Fig ure 5 : MAT LAB : U n i t a r y P o ten t i a l s ( Amp l i tud e 3 mV p k -p k) 137

138

139 Fig ure 6 : MAT LAB Ca

2 + i o n f lo w i n va r io u s c o mp o nent s o f t he P acemaker 140

Uni t 141 142 143 144

Fig ure 7 sho ws t he wa v e fo r m s i mu la t io n u s in g VHDL a t a c lo ck o f 6 .4 kHz . 145 T he s ys t e m was b u i l t u s in g t he b ehav io ura l mo d e l and emp lo yed t he Eule r ' s 146 met ho d fo r so lv i ng t he d i ffe r en t i a l eq ua t io n s . Ap p end i x A sho ws the RT L 147 sche mat i c s yn t hes i zed fo r the P acema ker Uni t . 148

149

Fig ure 7 : VHD L S i mu la t io n Outp u t o f t he P acemaker U ni t 150

151

5. Conclusion and Future Work: 152

T hus the V LSI mo d e l o f the P ace m a ker Un i t w as o b ta ined us i n g V H D L and 153 ve r i f i ed wi t h M AT LAB s i mula t io ns . T he In te r s t i t i a l Ce l l o f Ca j a l has mo re 154 t han o ne P ace maker U n i t . Hence the co l l ec t ive su mmat io n o f a l l t he 155 P acema ker u n i t s has to b e s tud ied . A l so the ga s t r i c wa l l i s l i ned wi t h mo re 156 t han o ne ICC. He nce i t i s neces sa r y to s t ud y t h e e ffec t s o f ma n y I CC s and 157 t he e ffec t o f t he ICC p o p ula t io n o n t he cha rac te r i s t i c s o f t he s lo w wa ve 158 gene ra ted . 159

References 160 [1] Sanders, K.M., T. Koh, S.D. and Ward., S.M., “Interstitial Cells of Cajal as pacemakers in 161 the gastrointestinal tract”, Annu Rev. Physiol. 68:307-343. 162 163 [2] Faville, R. , A. Pullan, K. Sanders and N. Smith.2008. A biophysically based mathematical model of 164 unitary potential activity in interstitial cells of Cajal.”,Biophysical Journal 95(1):88-104. 165 166 [3] Douglas L. Perry, VHDL- Programming by Example,McGraw-Hill 167 Publishers. 168

169

170

171

172

173

174

175

Appendix A 176

RTL Schematic of the Pacemaker Unit 177

178

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

D Q

PRE

ENA

CLR

SEL

DATAA

DATABOUT0

MUX21

0

1

0

0

1

0

1

0

1

0

1

<<A[23..0]

COUNT[6..0]

LEFT_SHIFT

<<A[23..0]

COUNT[6..0]

LEFT_SHIFT

0

1

0

1

0

1

0

1

0

1

<<A[23..0]

COUNT[6..0]

LEFT_SHIFT

0

1

C_ER_OUT0

fpresult~_OUT0 C_S1_OUT0

fpresult~_OUT0

C_S2_OUT0

fpresult~_OUT0 H_OUT0

fpresult~_OUT0

V_m_OUT0

fpresult~_OUT0 phi_3_OUT0

fpresult~_OUT0 C_MT_OUT0

fpresult~_OUT0

add~199_OUT0

exp~1943_OUT0

find_leftmost~11907_OUT0

orx~1924_OUT0orx~1925_OUT0



exp~2069_OUT0



exp~1796_OUT0

exp~1803_OUT0





sign~27_OUT0

ufract~254_OUT0

sign~28_OUT0

fpresult~_OUT0

LessThan4559_OUT

fracts~4934_OUT0


Result~4843_OUT0



find_leftmost~11283_OUT0find_leftmost~11289_OUT0

fracts~4936_OUT0

fract~65_OUT0

Result~4839_OUT0

Result~4851_OUT0

Result~4859_OUT0

fracts~4937_OUT0

Add825_OUT




ShiftLeft92_OUT



Add863_OUT




ShiftLeft96_OUT

fracts~4938_OUT0


LessThan1157_OUT

fracts~1234_OUT0




fracts~4939_OUT0

Result~4818_OUT0


fracts~1235_OUT0




fracts~4940_OUT0

Add776_OUT




ShiftLeft87_OUT


fracts~1236_OUT0


C_ER[8..-23]

clk

rst

C_S1[8..-23]

H[8..-23]

V_m[8..-23]

phi_3[8..-23]

C_MT[8..-23]

V_out[31..0]~reg0

V_out[31..0]

fpresult~[9121..9090]

32' h7F800001 --

find_leftmost~11907

orx~1925

find_leftmost~11985

find_leftmost~12459

orx~1951

exp~1803

orx~7797

find_leftmost~12537

orx~7823

sign~28

fracts~4934

find_leftmost~11909

Result~4843

find_leftmost~12461

find_leftmost~11211

find_leftmost~11289

fracts~4936

Result~4859

fracts~4937

ShiftLeft92

find_leftmost~11213

find_leftmost~11912

ShiftLeft96

fracts~4938

find_leftmost~12464

fracts~1234

find_leftmost~11253

orx~1929

find_leftmost~11991

fracts~4939

Result~4818

orx~1955

fracts~1235

orx~7801

find_leftmost~12543

orx~7827

fracts~4940

ShiftLeft87

find_leftmost~11216

fracts~1236

find_leftmost~11915

C_S2[8..-23]C_S2[8..-23]

179

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

<A[26..0]

B[26..0]

LESS_THAN

0

1

0

1

0

1

0

1

0

1

0

1

>>A[27..0]

COUNT[8..0]

RIGHT_SHIFT

0

1

1

0

1

0

1

C_S2_OUT0

C_ER_OUT0ufract~254_OUT0

fpresult~_OUT0

fracts~4941_OUT0



LessThan1157_OUT

fracts~1237_OUT0





orx~1930_OUT0

orx~1931_OUT0

fracts~4942_OUT0




fracts~1238_OUT0


Result~4851_OUT0


fracts~4943_OUT0



fracts~1239_OUT0

leftright~39_OUT0

sign~27_OUT0

fracts~4944_OUT0

fracts~1240_OUT0




orx~1932_OUT0

orx~1933_OUT0


fracts~4945_OUT0



fracts~1241_OUT0



fract~65_OUT0

fract~66_OUT0

LessThan4559_OUT

fracts~4946_OUT0

fracts~1242_OUT0

fpresult~_OUT0fp_sign~13_OUT0

fracts~4947_OUT0


sign~108_OUT0

ufract~1026_OUT0

sign~109_OUT0

fracts~1243_OUT0




fracts~4948_OUT0


Add1787_OUTShiftRight179_OUT

exp~1216_OUT0


fracts~1244_OUT0



fracts~4949_OUT0

ufract~254

fracts~4941

find_leftmost~12467

fracts~1237

find_leftmost~11955

find_leftmost~11295

orx~1931

fracts~4942

orx~1957

find_leftmost~12507

fracts~1238

orx~7803

Result~4851

orx~7829

fracts~4943

find_leftmost~11219

fracts~1239

fracts~4944

fracts~1240

find_leftmost~11919

find_leftmost~11259

orx~1933

find_leftmost~11997

fracts~4945

find_leftmost~12471

orx~1959

fracts~1241

orx~7805

find_leftmost~12549

LessThan4559

3' h0 --

3' h0 --

fracts~4946

fracts~1242

fp_sign~13

fracts~4947

find_leftmost~11223

sign~109

fracts~1243

find_leftmost~11961

find_leftmost~11301

orx~1935

fracts~4948

orx~1961

ShiftRight179

1' h0 --

3' h0 --

exp~1216

find_leftmost~12513

fracts~1244

find_leftmost~11923

orx~7807

fracts~4949

sign~27

180

SEL[4..0]

DATA[31..0]OUT

MUX

0

1

0

0

1

0

1

0

1

0

0

1

0

1

<A[26..0]

B[26..0]

LESS_THAN

0

1

0

0

1

0

1

0

1

0

0

1

0

1

0

1

0

0

1

>>A[27..0]

COUNT[8..0]

RIGHT_SHIFT

0

1

0

1

0

0

1

SEL[4..0]

DATA[31..0]OUT

MUX

0

1

0

1

1

0

1

0

1

0

1

C_ER_OUT0



Add1787_OUT

fract~65_OUT0 Mux162_OUT

exp~1217_OUT0

C_S2_OUT0

fracts~1245_OUT0

fpresult~_OUT0

LessThan4559_OUT

fracts~4950_OUT0

Result~4839_OUT0

Result~4843_OUT0

Result~4851_OUT0

Result~4836_OUT0

exp~1218_OUT0

fracts~1246_OUT0






fracts~4951_OUT0

exp~1224_OUT0

LessThan1157_OUT



exp~1219_OUT0

fracts~1247_OUT0



fracts~4952_OUT0

exp~1220_OUT0

fracts~1248_OUT0



fracts~4953_OUT0


exp~1221_OUT0

fracts~1249_OUT0





fracts~4954_OUT0

ufract~1026_OUT0


exp~1222_OUT0


fracts~1250_OUT0


Mux42_OUT

Result~17454_OUT0

fracts~4955_OUT0


exp~1223_OUT0

fracts~1251_OUT0

fracts~1252_OUT0





leftright~147_OUT0

sign~108_OUT0

find_leftmost~12483_OUT0find_leftmost~12475

Mux162

5' h00 --

3' h0 --

exp~1217

fracts~1245

fracts~4950

Result~4836

exp~1218

fracts~1246

find_leftmost~11265

orx~1937

find_leftmost~12003

fracts~4951

LessThan1157

3' h0 --

3' h0 --

find_leftmost~11227

exp~1219

fracts~1247

orx~7809

find_leftmost~12555

fracts~4952

exp~1220

fracts~1248

find_leftmost~11927

fracts~4953

find_leftmost~12479

exp~1221

fracts~1249

find_leftmost~11967

find_leftmost~11307

orx~1939

fracts~4954

ufract~1026

orx~7785

exp~1222

find_leftmost~12519

fracts~1250

orx~7811

Mux42

5' h00 --

3' h0 --

fracts~4955

find_leftmost~11231

exp~1223

fracts~1251

fracts~1252

find_leftmost~11931

find_leftmost~11271

orx~1941

find_leftmost~12009

sign~108

find_leftmost~12483

ShiftRight48

1' h0 --

3' h0 --

Result~17454

181

0

1

0

1

0

1

0

1

0

1

1

0

1

0

0

1

1

0

1

0

0

1

0

0

1

0

0

1

0

0

1

1

0

1

0

0

1

0

0

1

0

0

1

0

0

1

0

0

1

0

0

1

0

C_ER_OUT0


C_S2_OUT0

LessThan1157_OUT

fracts~1253_OUT0




fracts~1254_OUT0



fracts~1255_OUT0










fracts~1256_OUT0


exp~1943_OUT0

exp~1944_OUT0









exp~1945_OUT0




exp~2069_OUT0

exp~2070_OUT0

exp~1946_OUT0

exp~2071_OUT0

exp~1947_OUT0





exp~2072_OUT0


exp~1796_OUT0

exp~1797_OUT0

exp~1948_OUT0




exp~2073_OUT0

exp~1798_OUT0

exp~1949_OUT0

exp~2074_OUT0

exp~1799_OUT0

exp~1950_OUT0




orx~7787

fracts~1253

orx~7813

find_leftmost~12561

fracts~1254

find_leftmost~11235

fracts~1255

orx~1917

find_leftmost~11973

find_leftmost~11313

orx~1943

orx~7789

find_leftmost~12525

fracts~1256

orx~7815

exp~1944

find_leftmost~11937

find_leftmost~11277

orx~1919

orx~1945

find_leftmost~12015

find_leftmost~12489

exp~1945

orx~7791

orx~7817

find_leftmost~12567

exp~2070

exp~1946

exp~2071

exp~1947

find_leftmost~11241

orx~1921

find_leftmost~11979

find_leftmost~11319

exp~2072

orx~1947

exp~1797

exp~1948

orx~7793

find_leftmost~12531

orx~7819

exp~2073

exp~1798

exp~1949

exp~2074

exp~1799

exp~1950

find_leftmost~11943

find_leftmost~11283

orx~1923

182

0

1

0

0

1

0

0

1

1

0

1

0

0

1

0

0

1

1

0

1

0

0

1

0

1

1

0

1

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

0

1

1

0

1

0

0

1

00

1

10

1

00

1

10

1

00

1

10

1

00

1

10

1

00

1

10

1

0

C_ER_OUT0

exp~2069_OUT0

exp~2075_OUT0



exp~1796_OUT0

exp~1800_OUT0



exp~1951_OUT0


Result~4839_OUT0



exp~2076_OUT0

exp~1801_OUT0

exp~2077_OUT0

exp~1802_OUT0


fpresult~_OUT0

LessThan4559_OUT

fracts~4933_OUT0


exp~1804_OUT0

fracts~4935_OUT0







Result~4836_OUT0

Classfp~_OUT0

Result~17454_OUT0

Classfp~_OUT0

Classfp~_OUT0

Classfp~_OUT0

fpresult~_OUT0

add~25_OUT0

fpresult~_OUT0

fract~65_OUT0

C_S2_OUT0

exp~1224_OUT0

LessThan1157_OUT

Equal9_OUT

fractc~_OUT0

fract~66_OUT0

Equal36_OUT

fractc~_OUT0

ShiftLeft96_OUT

ShiftLeft92_OUT

ShiftLeft87_OUT

multiply~156_OUT0

fractr~_OUT0

exp~1943_OUT0












exp~2075

orx~1949

find_leftmost~12021

exp~1800

find_leftmost~12495

exp~1951

orx~7795

Result~4839

orx~7821

find_leftmost~12573

exp~2076

exp~1801

exp~2077

exp~1802

find_leftmost~11247

fracts~4933

find_leftmost~11325

exp~1804

fracts~4935

find_leftmost~11949

orx~1927

orx~1953

find_leftmost~12501

orx~7799

orx~7825

Classfp~[563..559]

2' h0 --

3' h0 --

Classfp~[833..832]

2' h0 --

Classfp~[879..878]

2' h0 --

Classfp~[1926..1925]

2' h0 --

fpresult~[3937..3906]

32' h7F800001 --

fractc~[887..864]fractc~[911..888]

fractc~[3479..3456]fractc~[3503..3480]

fractr~[551..480]

exp~1943

find_leftmost~11908

find_leftmost~11910

find_leftmost~11911find_leftmost~11914





find_leftmost~11960

Classfp~[837..834]

2' h0 --

1' h0 --

1' h0 --

183

184

185

186

187

188

189 190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

0

1

10

1

00

1

10

1

00

1

10

1

00

1

10

1

00

1

10

1

00

1

1

SEL

DATAA

DATABOUT0

MUX210

1

1

0

1

1

+A[4..0]

B[4..0]

ADDER

0

1

1

0

1

1

0

1

1

+A[4..0]

B[4..0]

ADDER

+A[10..0]

B[10..0]

ADDER

+A[10..0]

B[10..0]

ADDER

+A[7..0]

B[7..0]

ADDER

+A[9..0]

B[9..0]

ADDER

+A[9..0]

B[9..0]

ADDER

+A[9..0]

B[9..0]

ADDER

+A[12..0]

B[12..0]

ADDER

SEL

DATAA

DATAB

OUT0

MUX21

+A[8..0]

B[8..0]

ADDER

<

CIN

A[9..0]

B[9..0]

LESS_THAN

1

SEL

DATAA

DATAB

OUT0

MUX21

<

CIN

A[9..0]

B[9..0]

LESS_THAN

1

SEL

DATAA

DATABOUT0

MUX21

>>A[27..0]

COUNT[11..0]

RIGHT_SHIFT

<A[11..0]

B[11..0]

LESS_THAN

+A[13..0]

B[13..0]

ADDER

+A[14..0]

B[14..0]

ADDER

SEL

DATAA

DATABOUT0

MUX21

xA[23..0]

B[23..0]

MULTIPLIER

0

1

0

1

0

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

0

1

0

1

0

1




















Add825_OUT










Add776_OUT

Classfp~_OUT0

multiply~156_OUT0

exp~1803_OUT0

exp~1804_OUT0

Add826_OUT

Add827_OUT

exp~1797_OUT0

exp~1798_OUT0

exp~1799_OUT0

exp~1800_OUT0

exp~1801_OUT0

exp~1802_OUT0

Add782_OUT

Add780_OUT

LessThan1689_OUT

LessThan1688_OUT

Result~6995_OUT0

Add786_OUT

Add785_OUT

ShiftLeft88_OUT

sfract~_OUT0

fractr~_OUT0

Mult16_OUT

orx~2921_OUT0

exp~1831_OUT0

exp~1830_OUT0

exp~1829_OUT0

exp~1828_OUT0

exp~1827_OUT0

expon_out~_OUT0

rexp~_OUT0

fract_out~_OUT0

rfract~_OUT0

exp~_OUT0

exp~1834_OUT0

exp~1833_OUT0

exp~1832_OUT0






find_leftmost~12026

shifty~[237..224]

14' h0000 --

find_leftmost~12025

find_leftmost~12024

Add825

1' h1 --

5' h05 --

find_leftmost~11330

find_leftmost~11329

find_leftmost~11328

Add776

1' h1 --

5' h05 --

multiply~156

Add778

1' h1 --

1' h1 --

Add827

1' h1 --

1' h1 --

Add777

8' hFD --

Add779

10' h001 --

Add783

10' h07F --

Add782

Add784

1' h1 --

13' h0001 --

shiftr~[1556..1545]

Add781

1' h1 --

9' h0F9 --

LessThan1689

9' h169 --1' h1 --

shiftr~[1568..1557]

LessThan1688

1' h1 --

9' h180 --

shiftr~[1580..1569]

Result~6995

ShiftRight70

LessThan1691

11' h000 --

1' h0 --Add786

1' h1 --

14' h1FFD --

Add785

1' h1 --

15' h0001 --

sfract~[1155..1130]Mult16

24' h9D4952 --

stickyx~67

Result~6968

stickyx~66

check_round~75

Result~6997

rexp~[359..352]

rfract~[1034..1012]

exp~1834

exp~1833

exp~1832

207

0

1

0

1

0

1

0

1

0

1

SEL

DATAA

DATAB

OUT0

MUX21

0

11

0

11

0

11

0

11

0

11

0

11

0

11

0

11

0

10

0

10

0

11

SEL

DATAA

DATAB

OUT0

MUX21

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

SEL

DATAA

DATABOUT0

MUX21

exp~_OUT0

Add782_OUT

Result~6995_OUT0

exp~1831_OUT0

exp~1830_OUT0

exp~1829_OUT0

exp~1828_OUT0

exp~1827_OUT0

exp~1834_OUT0

exp~1833_OUT0

exp~1832_OUT0

Add787_OUT

Result~7019_OUT0

expon_out~_OUT0

rexp~_OUT0

infres~88_OUT0

infres~89_OUT0

zerores~88_OUT0

Result~7050_OUT0

Result~7049_OUT0

Result~7048_OUT0

Result~7047_OUT0

Result~7046_OUT0

Result~7045_OUT0

Result~7044_OUT0

Result~7043_OUT0

Result~7042_OUT0

Result~7041_OUT0

Result~7040_OUT0

Result~7039_OUT0

Result~7038_OUT0

Result~7037_OUT0

Result~7036_OUT0

Result~7035_OUT0

Result~7034_OUT0

Result~7033_OUT0

Result~7032_OUT0

Result~7031_OUT0

Result~7030_OUT0

Result~7029_OUT0

Result~7028_OUT0

Classfp~_OUT0

multiply~155_OUT0

add~25_OUT0

fpresult~_OUT0

exp~1831

exp~1830

exp~1829

exp~1828

exp~1827

expon_out~[359..352]

Result~7020

Result~7021

Result~7022

Result~7023

Result~7024

Result~7025

Result~7026

Result~7027

infres~89

Result~7051

zerores~89

fpresult~[3557..3527]

31' h7F800000 --

Result~7081

Result~7080

Result~7079

Result~7078

Result~7077

Result~7076

Result~7075

Result~7074

Result~7073

Result~7072

Result~7071

Result~7070

Result~7069

Result~7068

Result~7067

Result~7066

Result~7065

Result~7064

Result~7063

Result~7062

Result~7061

Result~7060

Result~7059

Result~7058

Result~7057

Result~7056

Result~7055

Result~7054

Result~7053

Result~7052

multiply~155

fpresult~[3588..3558]

31' h7F800001 --

208

0

1

0

1

0

1

1

0

1

0

0

1

0

0

1

0

0

1

0

0

1

0

0

1

0

0

1

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

>>A[27..0]

COUNT[8..0]

RIGHT_SHIFT

0

1

SEL[4..0]

DATA[31..0]OUT

MUX

0

1

0

1

Classfp~_OUT0add~25_OUT0

fpresult~_OUT0

C_S1_OUT0

LessThan1746_OUT

fracts~1801_OUT0

Result~7106_OUT0

fracts~1803_OUT0



exp~1835_OUT0

exp~1836_OUT0

Result~7154_OUT0



exp~1837_OUT0

exp~1838_OUT0

exp~1839_OUT0



exp~1840_OUT0

exp~1841_OUT0

exp~1842_OUT0



exp~1843_OUT0





fracts~1782_OUT0



fracts~1783_OUT0

fracts~1784_OUT0

fracts~1785_OUT0



fracts~1786_OUT0

fracts~1787_OUT0

fracts~1788_OUT0


fracts~1789_OUT0

Result~7088_OUT0

fracts~1790_OUT0

fracts~1791_OUT0



fracts~1792_OUT0

Mux64_OUT

fracts~1793_OUT0

fracts~1794_OUT0

add~25

fracts~1801

Result~7106

fracts~1803

orx~2976

orx~3002

exp~1836

orx~2978

orx~3004

exp~1837

exp~1838

Result~7134

exp~1839

orx~2980

orx~3006

exp~1840

exp~1841

Result~7138

exp~1842

orx~2982

orx~3008

exp~1843

orx~2984

orx~3010

orx~2986

orx~3012

Result~7146

fracts~1782

orx~2988

orx~3014

fracts~1783

fracts~1784

fracts~1785

orx~2990

orx~3016

fracts~1786

fracts~1787

fracts~1788

orx~2992

fracts~1789

Result~7088

fracts~1790

fracts~1791

ShiftRight72

1' h0 --

3' h0 --

orx~2994

fracts~1792

Mux64

5' h00 --

3' h0 --

fracts~1793

fracts~1794

Result~7154

209

<A[26..0]

B[26..0]

LESS_THAN

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATAB

OUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

SEL

DATAA

DATABOUT0

MUX21

0

1

=A[8..0]

B[8..0]

EQUAL

SEL

DATAA

DATABOUT0

MUX21

>>A[27..0]

COUNT[8..0]

RIGHT_SHIFT

<A[8..0]

B[8..0]

LESS_THAN

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

0

10

fpresult~_OUT0

orx~2995_OUT0

orx~2996_OUT0

fract~46_OUT0

C_S1_OUT0

exp~1835_OUT0

LessThan1746_OUT

Result~7113_OUT0

orx~2971_OUT0

orx~2972_OUT0

orx~2997_OUT0

orx~2998_OUT0

orx~2973_OUT0

orx~2974_OUT0

orx~2999_OUT0

orx~3000_OUT0

fpresult~_OUT0

Result~7106_OUT0

Classfp~_OUT0

fractc~_OUT0

fractc~_OUT0

LessThan1720_OUT

fractc~_OUT0

fracts~1803_OUT0

fracts~1801_OUT0

fracts~1794_OUT0

fracts~1793_OUT0

fracts~1792_OUT0

fracts~1791_OUT0

fracts~1790_OUT0

fracts~1789_OUT0

fracts~1788_OUT0

fracts~1787_OUT0

fracts~1786_OUT0

fracts~1785_OUT0

fracts~1784_OUT0

fracts~1783_OUT0

fracts~1782_OUT0

ShiftRight72_OUT

LessThan1747_OUT

Add789_OUT

Equal13_OUT

fracts~_OUT0

Add790_OUT

LessThan1721_OUT

fracts~1889_OUT0

fracts~1891_OUT0

fracts~1892_OUT0

fracts~1893_OUT0

fracts~1894_OUT0

fracts~1895_OUT0

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

fracts~1912_OUT0

fracts~1913_OUT0

orx~2996

fracts~1795

Result~7113

fracts~1796

fracts~1797

orx~2972

orx~2998

fracts~1798

fracts~1799

fracts~1800

orx~2974

orx~3000

fracts~1802

fracts~1804

Classfp~[813..809]

2' h0 --

3' h0 --

fractc~[1271..1248]

fractc~[1319..1296]

fractc~[1343..1320]

fracts~[1860..1833]

3' h0 --

1' h0 --

fracts~[1832..1805]

28' h0000000 --

fracts~1781

Equal13

9' h000 --

fracts~[1888..1861]

ShiftRight71

1' h0 --

3' h0 --

LessThan17211' h0 --

8' h00 --

fracts~1889

fracts~1891

fracts~1892

fracts~1893

fracts~1894

fracts~1895

fracts~1896

fracts~1897

fracts~1898

fracts~1899

fracts~1900

fracts~1901

fracts~1902

fracts~1903

fracts~1904

fracts~1905

fracts~1906

fracts~1907

fracts~1908

fracts~1909

fracts~1910

fracts~1911

fracts~1912

fracts~1913

LessThan1746

3' h0 --

3' h0 --

210

211

212

0

10

0

10

0

10

0

10

<A[8..0]

B[8..0]

LESS_THAN

+A[28..0]

B[28..0]

ADDER

+A[24..0]

B[24..0]

ADDER

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

0

1

>>A[27..0]

COUNT[10..0]

RIGHT_SHIFT

<<A[27..0]

COUNT[12..0]

LEFT_SHIFT

0

1

1

SEL[4..0]

DATA[31..0]OUT

MUX

0

1

<A[11..0]

B[11..0]

LESS_THAN 0

1

<A[11..0]

B[11..0]

LESS_THAN

fracts~_OUT0

Add789_OUT

LessThan1720_OUT

fractc~_OUT0

fracts~1889_OUT0

fracts~1891_OUT0

fracts~1892_OUT0

fracts~1893_OUT0

fracts~1894_OUT0

fracts~1895_OUT0

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

fracts~1912_OUT0

fracts~1913_OUT0

sticky~55_OUT0

ufract~371_OUT0

ufract~372_OUT0

ufract~373_OUT0

ufract~374_OUT0

ufract~375_OUT0

ufract~376_OUT0

ufract~377_OUT0

ufract~378_OUT0

ufract~379_OUT0

ufract~380_OUT0

ufract~381_OUT0

ufract~382_OUT0

ufract~383_OUT0

ufract~384_OUT0

ufract~385_OUT0

ufract~386_OUT0

ufract~387_OUT0

ufract~388_OUT0

ufract~389_OUT0

ufract~390_OUT0

ufract~391_OUT0

ufract~392_OUT0

ufract~393_OUT0

ufract~394_OUT0

ufract~395_OUT0

ufract~396_OUT0

C_S1_OUT0

fpresult~_OUT0

ufract~368_OUT0

shiftr~_OUT0

ShiftRight73_OUT

Add798_OUTShiftLeft89_OUT



Result~7181_OUT0

Add799_OUT

orx~3021_OUT0

orx~3022_OUT0

fracts~1914

fracts~1915

fracts~1916

fracts~1890

LessThan17201' h1 --

8' hE5 --

Add7921' h0 --

4' h1 --

1' h1 --

Add7911' h0 --

fracts~1917

ufract~369

ufract~370

ufract~371

ufract~372

ufract~373

ufract~374

ufract~375

ufract~376

ufract~377

ufract~378

ufract~379

ufract~380

ufract~381

ufract~382

ufract~383

ufract~384

ufract~385

ufract~386

ufract~387

ufract~388

ufract~389

ufract~390

ufract~391

ufract~392

ufract~393

ufract~394

ufract~395

ufract~396

ufract~368

orx~3018

ShiftRight73

ShiftLeft89

find_leftmost~11475

find_leftmost~11476

Result~7181Mux65

4' h0 --

orx~3019

LessThan1777

12' h01B --

orx~3020

orx~3021

LessThan1778

12' h01A --

orx~3022

Appendix B 213

VHDL Code for the Pacemaker Unit 214 library IEEE; 215 use IEEE.std_logic_1164.all; 216 use IEEE.std_logic_arith.all; 217 use IEEE.math_real.all; 218 --library IEEE_PROPOSED; 219 --use IEEE_PROPOSED.fixed_float_types.all; 220 --use IEEE_PROPOSED.fixed_pkg.all; 221 --use IEEE_PROPOSED.float_pkg.all; 222 223 entity Pace_Unit is 224 port (clk,rst:in STD_LOGIC;V_out:out STD_LOGIC_VECTOR(31 downto 0)); 225 226 end Pace_Unit; 227 architecture PU of Pace_Unit is 228 -- UP Model Parameters 229 constant g_Ca : real := 0.01; 230 constant E_NSCC : real := 0.0; 231 constant g_capNSCC_Ca : real := 0.12; 232 constant g_capNSCC_Na :real := 220.0; 233 constant K_NSCC :real := 0.12; 234 constant h_NSCC :real := 3.0; 235 constant g_PM :real := 420.0; 236 constant K_PM :real := 1.0; 237 constant g_Na :real := 15000.0; 238 constant K_Na :real := 10000.0; 239 constant h_Na :real := 4.0; 240 constant V_SERCA :real := 100000.0; 241 constant A_2 :real := 0.0006; 242 constant A_4 :real := 3.57; 243 constant A_5 :real := 0.000027; 244 constant A_6 :real := 0.0000231; 245 constant V_MCU :real := 800.0; 246 constant K_MCU :real := 10.0; 247 constant K_INH :real := 10.0; 248 constant h_INH :real := 4.0; 249 constant V_NCX :real := 0.5; 250 constant K_NCX :real := 0.3; 251 constant u_S1S2 :real := 0.04; 252 constant k_IPR :real := 2000.0; 253 constant k_1 :real := 0.0; 254 constant k_min1 :real := 6.4; 255 constant k_2 :real := 4.0; 256 constant r_2 :real := 200.0; 257 constant r_min2 :real := 0.0; 258 constant r_4 :real := 750.0; 259 constant R_1 :real := 36.0; 260 constant R_3 :real := 300.0; 261 constant g_alpha :real := 0.02; 262 constant g_beta :real := 300.0; 263 constant K_beta :real :=2.0; 264 constant h_beta :real := 2.0; 265 constant K_m :real := 0.01; 266 constant B_m :real := 100.0; 267

constant y_S1 :real := 100.0; 268 constant y_S2 :real := 1.0; 269 constant y_ER :real := 20.0; 270 constant y_MT :real := 200.0; 271 constant d_S :real := 26.0; 272 constant C_m :real := 20.0; 273 constant Z_Ca :real := 2.0; 274 constant Z_Na :real :=1.0; 275 constant V_t :real := 26.7; 276 constant C_O :real:= 1800.0; 277 constant P :real := 1.0; 278 signal V_m :real := -70.1; 279 signal C_S1 :real := 0.12; 280 signal C_S2 :real := 0.023; 281 signal C_ER :real := 203.0; 282 signal C_MT: real := 0.22; 283 signal N_S1 :real := 10100.0; 284 signal H : real := 0.0; 285 signal phi_3 :real := 0.306; 286 signal a_phi3,b_phi3,phi_1,phi_min1,phi_2,J_IPR,J_S1S2,J_NCX,J_MCU,J_SERCA : real := 0.0 287 ; 288 signal 289 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 : 290 real := 0.0 ; 291 signal l_MTS1,l_ERS1,l_ERS2,l_S1S2,l_MTS2 : real := 0.0 ; 292 begin 293 process(clk,rst) 294 begin 295 if rst = '1' and rising_edge(clk) then 296 V_out <= CONV_STD_LOGIC_VECTOR(INTEGER(V_m),32); 297 a_phi3 <= g_alpha; 298 b_phi3 <= g_beta*((C_S2**h_beta)/(K_beta**h_beta+C_S2**h_beta)); 299 phi_3 <= phi_3+ (a_phi3-b_phi3*phi_3);--IP3R Slow Rate Variable 300 --IP3R Constants 301 phi_1 <= (k_1*R_1+r_2*C_S2)/(R_1+C_S2); 302 phi_min1 <= ((k_min1+r_min2)*R_3)/(R_3+C_S2); 303 phi_2 <= (k_2*R_3+r_4*C_S2)/(R_3+C_S2); 304 J_IPR <=k_IPR*(((P*phi_1*H)/(P*phi_1+phi_min1))**4.0)*(C_ER-C_S2); 305 J_S1S2 <= u_S1S2*(C_S2-C_S1); 306 J_NCX <= V_NCX*(C_MT/(K_NCX+C_MT)); 307 J_MCU <= V_MCU*((C_S2**2.0)/(K_MCU**2.0+C_S2**2.0)); 308 J_SERCA <= V_SERCA*((C_S1-A_2*C_ER)/(1.0 309 +A_4*C_S1+A_5*C_ER+A_6*C_S1*C_ER)); 310 I_Na <= g_PM*(C_S1**h_Na/(K_Na**h_Na+C_S1**h_Na)); 311 g_NSCC_Ca <= 312 g_capNSCC_Ca*(K_NSCC**h_NSCC/(K_NSCC**h_NSCC+C_S1**h_NSCC)); 313 g_NSCC_Na <= 314 g_capNSCC_Na*(K_NSCC**h_NSCC/(K_NSCC**h_NSCC+C_S1**h_NSCC)); 315 I_NSCC_Ca <= g_NSCC_Ca*(V_m-E_NSCC); 316 I_NSCC_Na <= g_NSCC_Na*(V_m-E_NSCC); 317 E_Ca <= 0.5*V_t*log(C_O/C_S1); 318 I_Ca <= g_Ca*(V_m-E_Ca); 319 l_MTS1 <= y_MT/y_S1; 320 l_ERS1 <= y_ER/y_S1; 321 l_ERS2 <= y_ER/y_S2; 322 l_S1S2 <= y_S1/y_S2; 323

l_MTS2 <= y_MT/y_S2; 324 f_m <= 1.0/(1.0+(K_m*B_m/(K_m+C_MT**2.0))); 325 I_iNa <= I_NSCC_Na+I_Na; 326 I_iCa <= I_NSCC_Ca+I_Ca; 327 V_m <= V_m- ((I_iCa+I_iNa)/C_m); 328 C_S1 <= C_S1 + (J_S1S2+l_MTS1*J_NCX)- 329 ((d_S/Z_Ca)*I_iCa+l_ERS1*J_SERCA); 330 C_S2 <= C_S2 + (l_ERS2*J_IPR-(l_S1S2*J_S1S2+l_MTS2*J_MCU)); 331 C_ER <= C_ER + (J_SERCA-J_IPR); 332 C_MT <= C_MT + f_m*(J_MCU-J_NCX); 333 N_S1 <= N_S1 - ((d_S/Z_Na)*I_iNa); 334 H <= H+ ((phi_3*(1.0-H))- (((P*phi_1*phi_2)/(P*phi_1+phi_min1)*H))); 335 --V_out <= CONV_STD_LOGIC_VECTOR(INTEGER(V_m),32); 336 337 338 end if; 339 end process; 340 end PU; 341 342

343

344

345

346

VLSI Implementation of the Pacemaker Unit of the...

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Transcript of VLSI Implementation of the Pacemaker Unit of the...