INTEGROVANÉ MODELY FYZIOLOGICKÝCH SYSTÉMŮ

MUDr. Jiří Kofránek, CSc.

INTEGROVANÉ MODELY FYZIOLOGICKÝCH SYSTÉMŮ

Habilitační práce

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wyer, Hara, Thompson, Chan, & Berg, 2009). Trenažéry Laerdal se osvědčily nejen ve výuce lékařů, ale i ve výuce sester (Cason, Kardong-Edgren, Cazzell, Behan, & Mancini, 2009). Druhým úspěšným výrobcem je americká firma METI, jejíž robotizované trenažéry jsou velmi efektivní (i když nákladnou) výukovou pomůcka pro výcvik anesteziologů a zdravotnických týmů zejména v oblasti medicíny akutních stavů (Sethi, Peine, Mohammadi, & Sundaram, 2009; Ellaway, Kneebone, Lachapelle, & Topps, 2009). Pořídit si drahý simulátor k efektivní výuce samo o sobě ale nestačí. Jak, zvláště v poslední době, upozorňuje řada autorů, výuka se simulátorem klade citelně vyšší nároky na vyučujícího, než klasická výuka. Při správném využití simulátoru, je však pedagogický efekt velmi výrazný, zvláště v takových oblastech, kde je rychlé a správné rozhodování velmi důležité, například v medicíně akutních stavů a v anesteziologii (Binstadt, Walls, White, Nadel, Takavesu & Barker; Lammers, 2006; Day, 2006; Wayne, Didwania, Feniglass, Fudala, Barsuk & McGaghie, 2008; Rosen, 2008; Kobayashi, Patterson, Overly, Shapiro, Williams & Jay, 2008; Jones & Lorraine, 2008; McGaghie, Siddall, Mazmanian & Myers, 2009). Vzhledem k technologickým i personálním nárokům proto vznikla na řadě předních univerzit i mimo ně specializovaná simulační centra pro lékařskou výuku na simulátorech, např. na Harwardu existuje „Center for Medical Simulation“ - http://www.harvardmedsim.org/, v Oxfordu se problematikou lékařské výuky na simulátorech zabývá „Oxford Simulation Centre“ - http://www.oxsim.ox.ac.uk/, a v Izraeli vzniklo štětře dotované „Israel Center for Medical Simulation“ - http://www.msr.org.il/.

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0.001

1.211 RFN

AOM

0.9899

AMM

0.3333

CNR

RBF RBF

182

CN8

1.2 RFN

100

AUM

1

183 176

1

175 NOD

1.2 201

lower limit 0.35

PVO

1 s

CNZ

lower limit 0

40

AH1

u

158A

NOD

221

1

1

10

AHC

185

0.0785 187

AH2 6

AHM

GP3 upper limit 15.0 lower limit 0.4

1

249 512

HM 40

186 6

1

0.1 215

APD

202

AH4

216 1

AAR

243

122 8

VPF 0.0125

TVD 0.001003 0.009

AM

211

1.5 ARF

191

210

1

1

POM 0.08

PM5 PMO

0.5

2.86

0 190

0.01

GF3

1 s xo

VIM

196

0.5

250

244

P3O^3

233

2.8 8

7.999

GF3 197

TVD

lower limit 0

Z11 AHM

217

5 GF4

203 algebraic loop breaking

VIM

0.01095

4

Z10

219

0.301

P3O

242

200

POT

VV7

1

60

234 PVO

QO2

0.00333

232

194 STH

8.25

1.002

1000

1

GLP

31.67

VV7

VV1

62

1

OVA

40

POT

P1O

18 63

VV6 VV2 lower limit .005 251

248

193

1

STH

0.001008

1

209

PPC

51.66

33

POE

1

7.987

AAR

198

VUD 0.001

TRR

0.8

8.0001

1

BFN

272

252

P2O

241

OSA

255

HM

xo 271

1 s

0

AOM

1

8

upper limit 8

lower limit 0.0003

212

SRK 247

P2O

2400 Xo

235

RMO

192

POT

8

VUD

PFL

EVR

AAR

0.25

DVS

THIRST AND DRINKING 218

GFR

208

0.00781

61

2400 271

upper limit 8

1 xo s

206

0.125

1 s

1

253

199

-1

0.7

231

200

GFN 205

200 65

VV7

256 5

POT^3

1

PM4

1 s xo

OVA 225

DOB 264

u^3

236

QOM

BFM

MO2 265

0.15

KIDNEY DYNAMICS AND EXCRETION RR

1

64

5

OVA

P40^3

AMM 1 s xo

u^2

257 40

254

02A

246

P4O 8.0001

PM1^2

2500 230

POV

266

237 PK3

PK1

258

40

RDO 267

AU 1

lower limit .001 239

226

262

POT

245

PMO

800 229 5

RMO

5

PM3

240

PK2

227

POV

270

228

BFM

1 259

0.7

261

AOM 1

1 s xo

OSV

168

269

181

AU

AH8

1

lower_limit_0 1

NON-MUSCLE LOCAL BLOOD FLOW CONTROL

40 POV

277

278 1 s

POB

276

274

275

POD

273

ARM

AK1

1

POK

lower limit 0.2

1

40

AR1 1 s

xo

A2K

1

lower limit 0.5

1.6

VIM

1

1.014

0.495

2.86

0.00355

11520

lower limit 0.3

A3K

0.3 1

289

32

1 s

if (POD<0) {POJ=PODx3.3}

VAS

VBD

VVR

6

2.95

DVS 1 s

BFN

PGS

7

PVS

VVS

QVO

5

0

1

PLA 8 upper limit 8PA lower limit 4

293

3 298

297

EXE

P2O

EXC

Z12

0

QLO

1

A1B

when PA1<40: AUB=1.85718 AUB when 40>PA1<170: AUB=0.014286*(170-PA1) when PA1>=170: AUB=0

304

PLA

23

6

QPO 18

22 PGL

VPE

uv

316

0.21 0.85

1

314

1.001

312 AUL

AUV

VIF

1 xo s

12

3.454e-006 110

CIRCULATORY DYNAMICS

AUY

318

0.5

319

313

1

1.001

1

8 70

PPA

150

0.4667

146

AVE

1

0.55

137

AUM

0.4

151

138

0.375

PPD

0.0003

152

AU

5 0.5 1

PPI DFP 2-(0.15/u)

DFP 0 0.0125

142 VPF

PPI = 2 - (0.15/VPF)

0.01252

333

DHM

1

352

HPR 347

HM

57600

343

40

348

125

96

0.1 93

94

PGC

PGR

u^2

REK CHY^2

99

VG

1 344

VB

1

349

5 1

1 xo s

1

1

HPL

1 xo s

119 1 xo s

2130

0.1

CNA

118 NED

0.25

NAE

HMD HPR

90 CHY

HYL

-5.9

142.1

142 NID PGH PTS

89

57

CNA

116

PGP

HMD

334

117

PG2

95

PIF upper limit 1

PTC

VRC 2

0.00042

NOD

1 s

40

VRC

124

CKE

126

120

V2D

xo 1

57600

RKC

RC2

5

123

0.013332

VGD 100

0.4

100

VPF

1 xo s

75

KE

KOD

1 342

-4.842e-010

1 xo s

KID

11.4

0.00014

122 KED

140

AM

98

1600

335

0.0000058

143 PLF

1

121

0.0028

(u/12)^2

HM

141

1

HEART RATE AND STROKE VOLUME

PTT = (VTS/12)^2

0.0025

351

xo 336b

2 VRC

PFI

1

KCD

1 s

PP3^0.1

HPL

1 s

2 xo

11

40 HMD

u^0.625

1 s

144

0.0003

2850 KE1 CKE 5

xo 6

PP3

346

PA4^0.625

KIR

127

0.013

1

97

u^0.625

128

129 KIE

KCD

113

PTT

336

336c

RCD 332

PPO CPF

0 140

325

331 PLF 145

PPI 2 PRA

321

130 3550

VG

HM2

40

PLF

POS

322

323

324

xo

GPR

350

345

PPA4 341

RC1

PPC 139 32

327

10

101 85

POT

15

1

340 0.00092

POS

0

PPA

HSR 100

1

11.99 VTS

464e-7

330

7.866e-008

148

PPD

HR

337

POY

147

PPN

VIE

1 s

PTS = f(VIF)

VG

8

15

PA HSL

lower limit 0.2375

xo

AVE

100 1.5

VIC

1 xo s

KI

171 1 s

88 0

86

VTS 338

135

25

131

xo 0

12 VIM

0.333

1 s

0.000225

PCP

SVO

-6.3 112

0.9897

339 1

PO2 VPF

AUTONOMIC CONTROL

QLO

PTS

8.25

PPR

149

VIM

POT 329

PO1

CPN

CPP 28

136

15

PPC

320

VIF

GPD

xo 1 s

0 VVR

AUH

0 VID

0.01

CNA VIC

PIF 12

CCD

132

20

VVR PLA

2.949

AUH

1

1

133

CKI GP2 111

0.0005 87

VID VTD 84

2.95

0.7

1

VID 134

GPD

83

VTC

VV9

AU

AUD 315

326

IFP

VTL 0.002

1

DPI

DPL 0.1

0

VPA

3.159

0.3

0.15

0.07039

14

103

AUJÂUZ

AU9

328

0.005

1

ALDOSTERONE CONTROL GP1

102

0

AUN calculation

SVO

15 PRA 0.09925

0.38

PTT 20

DPC

0.04

PRA

1 s

VPA

0.0048

1 s 170 AMC xo lower limit 6

104

0.30625

15

1

1 s xo

169

60

166 KN1

CNA

109

CPI

PIF 0.25

VRA

AMT

AMR

200

165

CKE

5

9

1 s

lower limit 4

20 -4 QRN = f(PRA)

0.00352 7.8

0.04 -6.328

QRO

20

21 PPA

xo

AUJ

PTC

PRA VRA

19

15.22

PLA

RPT

QPO AUZ 310

311

171

-0.017

168 AM1

AMP = f(PA)

106 PIF

142 105

PR1

Z8

309

0

1

u

AM2 AM3

00

PLD 0.004 20.15 CPI

0.1 xo

QRN

AUH 51

0.026

PPA

AU

172 19.8

167

107

lower limit 5 108 DPL

0.002 5

DRA 13

0

xo

AUN AUN

173

AM5

AMP

DPL VTL

5.038

12

QRO

PPA

AU8

317

0.001899 VTL

HMD

15

1

RVM = f(PP2) RPT

0.03826

PTC

50

1

AUB calculation

AUM

QVO

1

0

AUH

1 s

AM

10

HSR HPR

16 0

PP2

308

AUN CALCULATION when PA1<50: AUN=6 when 20>PA1<50: AUN=0.2*(50-PA1) when PA1>=50: AUC=0

1 ANM 164

RVM

52

PL1

AU2

0.0005

20.039

174

AM

PA

100

HMD

55 RPV

0.0357

20 57

DAU AUK

AUB^3 305

AUB

PA1

PA1

1.002

1

11

1

56

1

0.4 DLA 24

301 u^3

AUB CALCULATION

ANGIOTENSIN CONTROL

DPC

VP

0.002

lower limit 0 307

1

303 AU6

ANT

0.0384 20

3

PR1

AUH

50 1.4

PP1

QLN = f(PLA) xo

302

15

3.004

49

RPA

20

-4

1 s

VLA AUC

0.1

DPC

0.04 VP

1 xo s

3

RVG

1

48

sqrt

AUC

AUC calculation

1

158

AN1

CPI

71 VPD

2.738

RVM 53

QLN VLA

25

AUC CALCULATION when PA1<40: AUC=1.2 when 40>PA1<80: AUC=0.03*(80-PA1) when PA1>=80: AUC=0

PA1

CPA 54

26 1.24

PA1

PLA

1 s xo

157

4

1

0.4

CNE

152

PVS

0.6 QRF

15

VLE

0.1 295

8

296

156

155

74

VTL

10

QLO

QLN

47

28

10 ANM

44 27

8

POQ

0 260 LVM = f(PA2)

0

100 294

45

46

0.02244

POT

POQ

142

(1.2/RFN)^3

CNE 154 CNA

CP1

0 PVS

10

CPP 75

70

DFP

VRA

PLA

5.085

QLO 291

74

PC^3

VUD

5 VPA

PA2

LVM

159

ANC

(1.2/u)^3

TVD

0.001

VVS VB

VLA

58

1.4

1

HMD HPL

QLO

0.001

59

HSL LVM QLN

QAO

0.042

RFN

1.2

69.77

60 VAS PA 29

5

30

8

PPC

160 AN2

u

10

153b 153a

u^3

0.001902

VTC

3.3 161

AN3 4.0 REK

0.4

1.6283e-007 CPK

DAS

292

73

0.002

3.7

AN5 lower limit 0.7

ANM 210

CPP

PVS

VAS3

28

VTC

lower limit 0.0001 0.0825 CV

VVE

0.007

PTC

162

163

1

1.004

1 s xo

16.81

9

VV8 0.3

2.8

100

8

PPC

69

-6.3

xo

3.25

PRP VP

CFC PIF

3.781

VVS

QVO

61

CPP

72

VP PVS

5

2

RSN

1

PA

VAE

xo

0.85

POZ

AR3

1 xo s

1

33

0.33

VV7

0

QAO

BFN

31 288

0.3229

ANM

80

70

62

VRC

RBF

99.96

284b

16.81 68

2

4

0.04 DPP

0.00047

PC

5.004

VVE

100

DPL DLP

LPK

CPR 17

VB

RVS 1.2

BFM

PA

POJ

5

PC 17

284 283

286

DP0

78

77 85 PC

VB

0.007

0

67 PVS

3.7

79

PPD

PVG

BFN 2.8

2.782

1 POC

66 1.6379 0

39 17

2.9

BFM

PGS

ANTIDIURECTIC HORMONE CONTROL

RVS

1 s xo

41

CAPILLARY MEMBRANE DYNAMICS

2.9

0.2

0.0212 CN2

RV1

17

34

AUM

41A

RV1

43

1

3

PAM

AUM

287

42

CN7 1.79 RVS

RSM

37 RAR AUM PAM

30.5 RAR

0.1

1

35

ANU VIM

PON

20

AR2

ARM

38

36 ANU AMM VIM RAM 96.3 AUM RAM

1

AR3

40

1

1

1 290

279

280

AVE

lower limit 0.95

ARM

POR

0.06

1

POA

281

282

285

ANM

1

0.9457 xo

AR1

algebraic loop breaking

91

PIF 92

STH

0.1

1

VIC 0.0125

VPF

114

115 VEC

39.99 VTW

PRM 3

VP

VTW

24.2

1

12

VTS

0.0125

PULMONARY DYNAMICS AND FLUIDS

LIST OF VARIABLES

AAR-afferent arteriolar resistance [torr/l/min] AHM-antidiuretic hormone multiplier, ratio of normal effect AM-aldosterone multiplier, ratio of normal effect AMC-aldosterone concentration AMM-muscle vascular constriction caused by local tissue control, ratio to resting state AMP-effect of arterial pressure on rate of aldosterone secretion AMR-effect of sodium to potassium ratio on aldosterone secretion rate AMT-time constant of aldosterone accumulation and destruction ANC-angiotensin concentration ANM-angiotensin multiplier effect on vascular resistance, ratio to normal ANN-effect of sodium concentration on rate of angiotensin formation ANP-effect of renal blood flow on angiotensin formation ANT-time constant of angiotensin accumulation and destruction ANU-nonrenal effect of angiotensin AOM-autonomic effect on tissue oxygen utilization APD-afferent arteriolar pressure drop [torr] ARF-intensity of sympathetic effects on renal function ARM-vasoconstrictor effect of all types of autoregulation AR1-vasoconstrictor effect of rapid autoregulation AR2-vasoconstrictor effects of intermediate autoregulation AR3-vasoconstrictor effect of long-term autoregulation AU-overall activity of autonomic system, ratio to normal AUB-effect of baroreceptors on autoregulation AUC-effect of chemoreceptors on autonomic stimulation AUH-autonomic stimulation of heart, ratio to normal

AUK-time constant of baroreceptor adaptation AUL-sensitivity of sympathetic control of vascular capacitance AUM-sympathetic vasoconstrictor effect on arteries AUN-effect of CNS ischemic reflex on auto-regulation AUV-sensitivity control of autonomies on heart function AUY-sensitivity of sympathetic control of veins AUZ-overall sensitivity of autonomic control AVE-sympathetic vasoconstrictor effect on veins AlK-time constant of rapid autoregulation A2K-time constant of intermediate autoregulation A3K-time constant of long-term autoregulation A4K-time constant for muscle local vascular response to metabolic activity BFM-muscle blood flow [l/min] BFN-blood flow in non-muscle, non-renal tissues [l/min] CA-capacitance of systemic arteries [l/torr] CCD-concentration gradient across cell membrane [mmol/l] CHY-concentration of hyaluronic acid in tissue fluids [g/l] CKE-extracellular potassium concentration [mmol/l] CKI-intracellular potassium concentration [mmol/l] CNA-extracellular sodium concentration [mmol/l] CNE-sodium concentration abnormality causing third factor effect [mmo/l] CPG-concentration of protein in tissue gel [g/l] CPI-concentration of protein in free interstitial fluid [g/l] CPN-concentration of protein in pulmonary fluids [g/l] CPP-plasma protein concentration [g/l] CV-venous capacitance [l/torr] DAS-rate of volume increase of systemic arteries [l/min] DFP-rate of increase in pulmonary free fluid [l/min] DHM-rate of cardiac deterioration caused by hypoxia DLA-rate of volume increase in pulmonary veins and left atrium [l/min]

RED CELLS AND VISCOSITY

DLP-rate of formation of plasma protein by liver [g/min] DOB-rate of oxygen delivery to non-muscle cells [ml O2/min] DPA-rate of increase in pulmonary volume [l/min] DPC-rate of loss of plasma proteins through systemic capillaries [g/min] DPI-rate of change of protein in free interstitial fluid [g/min] DPL-rate of systemic lymphatic return of protein [g/min] DPO -rate of loss of plasma protein [g/min] DRA-rate of increase in right atrial volume [l/min] DVS-rate of increase in venous vascular volume [l/min] EVR-postglomerular resistance [torr/l] EXC-exercise activity, ratio to activity at rest EXE-exercise effect on autonomic stimulation GFN-glomerular filtration rate of undamaged kidney [l/min] GFR-glomerular filtration rate [l/min] GLP-glomerular pressure [torr] GPD-rate of increase of protein in gel [l/min] GPR-total protein in gel [g] HM-hematocrit [%] HMD-cardiac depressant effect of hypoxia HPL-hypertrophy effect on left ventricle HPR-hypertrophy effect on heart, ratio to normal HR-heart rate [beats/min] HSL-basic left ventricular strength HSR-basic strength of right ventricle HYL-quantity of hyaluronic acid in tissues [g] IFP-interstitial fluid protein [g] KCD-rate of change of potassium concentration [mmol/min] KE-total extracellular fluid potassium [mmol] KED-rate of change of extracellular fluid potassium concentration [mmol/min] KI-total intracellular potassium concentration [mmol/l]

HEART HYPERTROPHY OR DETERIORATION

KID-rate of potassium intake [mmol/min] KOD-rate of renal loss of potassium [mmol/min] LVM-effect of aortic pressure on left ventricular output MMO-rate of oxygen utilization by muscle cells [ml/min] M02--rate of oxygen utilization by non-muscle cells [ml/min] NAE-total extracellular sodium [mmol] NED-rate of change of sodium in intracellular fluids [mmol/min] NID-rate of sodium intake [mmol/min] NOD-rate of renal excretion of sodium [mmol/min] OMM-muscle oxygen utilization at rest [ml/min] OSA-aortic oxygen saturation OSV-non-muscle venous oxygen saturation OVA-oxygen volume in aortic blood [ml O2/l blood] OVS-muscle venous oxygen saturation O2M-basic oxygen utilization in non-muscle body tissues [ml/min] PA-aortic pressure [torr] PAM-effect of arterial pressure in distending arteries, ratio to normal PC-capillary pressure [torr] PCD-net pressure gradient across capillary membrane [torr] POP-pulmonary capillary pressure [torr] PDO-difference between muscle venous oxygen PO2 and normal venous oxygen PO2 [torr] PFI-rate of transfer of fluid across pulmonary capillaries [l/min] PFL-renal filtration pressure [torr] PGC-colloid osmotic pressure of tissue gel [torr] PGH-absorbency effect of gel caused by recoil of gel reticulum [torr] PGL-pressure gradient in lungs [torr] PGP-colloid osmotic pressure of tissue gel caused by entrapped protein [torr] PGR-colloid osmotic pressure of interstitial gel caused by Donnan equilibrium [torr] PIF-interstitial fluid pressure [torr] PLA-left atrial pressure [torr]

TISSUE FLUIDS, PRESSURES AND GEL

PLD-pressure gradient to cause lymphatic flow [torr] PLF-pulmonary lymphatic flow [torr] PMO-muscle cell PO2 [torr] POD-non-muscle venous PO2 minus normal value [torr] POK-sensitivity of rapid system of autoregulation PON-sensitivity of intermediate autoregulation POS-pulmonary interstitial fluid colloid osmotic pressure [torr] POT-non-muscle cell PO2 [torr] POV-non-muscle venous PO2 [torr] POY-sensitivity of red cell production POZ-sensitivity of long-term autoregulation PO2-oxygen deficit factor causing red cell production PPA-pulmonary arterial pressure [torr] PPC-plasma colloid osmotic pressure [torr] PPD-rate of change of protein in pulmonary fluids PPI-pulmonary interstitial fluid pressure [torr] PPN-rate of pulmonary capillary protein loss [g/min] PPO-pulmonary lymph protein flow [g/min] PPR-total protein in pulmonary fluids [g] PRA-right atrial pressure [torr] PRM-pressure caused by compression of interstitial fluid gel reticulum [torr] PRP-total plasma protein [g] PTC-interstitial fluid colloid osmotic pressure [torr] PTS-solid tissue pressure [torr] PTT-total tissue pressure [torr] PGV-pressure from veins to right atrium [torr] PVG-venous pressure gradient [torr] PVO-muscle venous PO2 [torr] PVS-average venous pressure [torr] QAO-blood flow in the systemic arterial system [l/min]

QLN-basic left ventricular output [l/min] QLO-output of left ventricle [l/min] QOM-total volume of oxygen in muscle cells [ml] QO2-non-muscle total cellular oxygen [ml] QPO-rate of blood flow into pulmonary veins and left atrium [l/min] QRF-feedback effect of left ventricular function on right ventricular function QRN-basic right ventricular output [l/min] QRO-actual right ventricular output [l/min] QVO-rate of blood flow from veins into right atrium [l/min] RAM-basic vascular resistance of muscles [torr/l/min] RAR-basic resistance of non-muscular and non-renal arteries [torr/l/min] RBF-renal blood flow [l/min] RC1-red cell production rate [l/min] RC2-red cell destruction rate [l/min] RCD-rate of change of red cell mass [l/min] REK-percent of normal renal function RFN-renal blood flow if kidney is not damaged [l/min] RKC-rate factor for red cell destruction RM0-rate of oxygen transport to muscle cells [ml/min] RPA-pulmonary arterial resistance [torr/l/min] RPT-pulmonary vascular resistance [torr/l/min] RPV-pulmonary venous resistance [torr/l/min] RR-renal resistance [torr/l/min] RSM-vascular resistance in muscles [torr/l] RSN-vascular resistance in non-muscle, n/minon-renal tissues [torr/l/min] RVG-resistance from veins to right atrium [torr/l/min] RVM-depressing effect on right ventricle of pulmonary arterial pressure RVS-venous resistance [torr/l/min] SR-intensity factor for stress relaxation SRK-time constant for stress relaxation

ELECTROLYTES AND CELL WATER

STH-effect of tissue hypoxia on salt and water intake SVO-stroke volume output [l] TRR-tubular reabsorption rate [l/min] TVD-rate of drinking [l/min] VAS-volume in systemic arteries [l] VB-blood volume [l] VEC-extracellular fluid volume [l] VG-volume of interstitial fluid gel [l] VGD-rate of change of tissue gel volumes [l/min] VIB-blood viscosity, ratio to that of water VIC-cell volume [l] VID-rate of fluid transfer between interstitial fluid and cells [l/min] VIE-portion of blood viscosity caused by red blood cells VIF-volume of free interstitial fluid [l] VIM-blood viscosity (ratio to normal blood) VLA-volume in left atrium [l] VP-plasma volume [l] VPA-volume in pulmonary arteries [l] VPD-rate of change of plasma volume [l] VPF-pulmonary free fluid volume [l] VRA-right atrial volume [l] VTC-rate of fluid transfer across systemic capillary membranes [l/min] VTD-rate of volume change in total interstitial fluid [l/min] VTL-rate of systemic lymph flow [l/min] VTW-total body water [l] VUD-rate of urinary output [l/min] VV7-increased vascular volume caused by stress relaxation [l] VVR-diminished vascular volume caused by sympathetic stimulation [l] VVS-venous vascular volume [l] Z8-time constant of autonomic response

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38

100

RAP GFR

227 .1

FF

0.3411

GP

88 .11

Renal artery pressure

100

AffC

Afferent artery conductance

6.25

GLOMERULUS

TubC

Normal proximal tubule conductance [ml /min /torr] 1189

RBF

INPUTS : RAP - Renal artery pressure [torr] Affc - Afferent artery conductance [mll /min /torr] TubC - Proximal tubule conductaqnce [ml /min /torr] RBF - Renal blood flow [ml /min ] RPF - Renal plasma flow APr - Plasma protein concentration (in afferent artery ) [g/ml ] GKf - Glomerular filtration coeffitient [ml /min /torr]

Reanl blood flow rate

665 .8

RPF

Renal plasma flow rate

0.07

OUTPUTS : GFR - Glomerular filtration rate [ml /min ] FF - Filtration fraction [relative number ] GP - Glomerulal pressure [torr] PTP - Proximal tubule pressure [torr] AVeCOP - Average colloid osmotic pressure [torr] NETP - Net pressure gradient in glomerulus [torr]

PTP

36 .33

AVeCCP

37 .58

NetP

14 .19

APr

Plasma protein cnoncentration [g/ml ] 16 Normal glomerular filtration coeffitient [ml /min /torr]

GKf

Glomerulus

!I;"6--2 .2F=!ABk6=6<7&%.-&+-82

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39

125 RAP


AffC

TubC

6.25 Normal proximal tubule conductance [ml /min /torr]

GFR

GLOMERULUS

29 .89

RBF

1189

3.643 0.1904

FF

NA TRIUM

MDNaFlow


RPF

APr

0.07 Plasma protein cnoncentration [g/ml ]

16

GFR

20 .29

100 .1

NetP

OUTPUTS : MDNaFlow - Sodium outflow [mmol /min ] PdxNaReab - Proximal sodium reabsorbrtion [mmol /l] PrxFNa - Proximal fractional sodium reabsorbtion [relative number ]

PrxFNaNorm

0.8 Normal Na proximal fractional reabsorbtion

Glomerulus

14 .37

LogA2

32 .21

AVeCCP

GKf

Normal glomerular filtration coeffitient [ml /min /torr]

INPUTS : PNa - Plasma sodium concentration [mmol /ml ] GFR - GLomerulal filtration rate [ml /min ] LogA 2 - Logarithm of plasma angiotensin concentration [pg / ml ] PrxFNaNorm - Normal value of sodium proximal PdxNaReab fractional reabsorbtion [relative number ]

60 .31

GP

PTP

665 .8

- P R O XI M A L T U B U L E

PNa

PrxFNa

0.7977

Calculation of proximal tubule sodium reabsorbtion

7.811 MYOGENIC RESPONSE

RENAL PERFUSION

AffC EffC

200 RenVenC

Venous conductance [ml /min /torr]

AP

7

VP

RAP

INPUTS : AffC - Afferent artery conductance [ml /min /torr] EffC Efferent artery conductance [ml /min /torr] RenVenC - Renal venous conductance [ml /min /torr] AP - Arterial pressure [torr] VP - Vena renalis pressure [torr] Hct - Hematocrit [relative number ] Clamp - Renal artery pressure drop caused by renal artery clamp [torr]

INPUT : RAP - Renal artery pressure [torr]

RAP

OUTPUT : AffC - Myogenic effect [ x Normal ]

Calculation of the myogenic response to changes in renal perfusion pressure (afferent conductance responds to changes in perfusion pressure , with pressure increases causing vasoconstriction )

RBF

1189

Vena renalis pressure [torr] OUTPUTS : RAP - Renal artery pressure [torr] RBF - Renal blood flow rate [ml /min ] RPF - Renal plasma flow rate [ml /min ]

Hct

0.44 Clamp

Hematocrit

0.9997

AffMyo 1

= _,` = _5

7 , #9 54 ^

RPF

665 .8

Calculation of renal artery pressure and renal blood flow rate

0 Renal artery pressure clamp drop [torr]

A F F E RE NT A RTE RY

29 .89

AffMyo

INPUTS : AffMyo - Myogenic effect [ x Nomal ] MDSig MDSig - Macula densa feedback signal [ x Normal ] AffNorm - Normal conductance in afferent artery [ml /min /torr]

AffC

OUTPUT : AffC - Vascular conductance [ml /min /torr]

AffNorm

30 Normal conductance of Afferent artery [ml /min /torr]

Calculates conductance of afferent artery

E F F E RE NT A RTE RY

AP

EffC

EffC

OUTPUT : EffC - Vascular conductance [ml /min /torr]

25 .1 A RTE RIA L P RE S S URE

ZNAE

INPUTS : ZNAE - ECF sodium content [mmol ] logA 2 - Logarithm of plasma angiotensin concentration [pG /ml ] APNorm - Normal value of arterial pressurel [torr]

LogA2

100

logA2

INPUTS : logA 2 - logarithm of angiotensin concentration MDSig MDSig - Macula densa feedback signal [ x Normal ] EffNorm - Normal conductance in afferent artery [ml /min /torr]

EffNorm

AP

25 Normal conductance of Efferent artery [ml /min /torr]

Calculates conductance of efferent artery AP

1.003

100 .1

OUTPUT : AP Arterial pressure [torr]

APNorm

MACULA DENSA

MDNaFlow

APNorm [torr] INPUTS : MDNaFlow - Macula densa sodium flow [mmol /min ] logA 2 - Logarithm of plasma angiotensin concentration [pG /ml ] MDNorm - Normal macula densa feedback signal [ x Normal ]

Control of arterial pressure by angiotensin and extracellular sodium content MDSig

OUTPUT : MDSig - Macula densa feedback signal

LogA2

0.9451 Scope 1

A2

MDSig

PRA

INPUTS : PRA - Plasma renin activity [ Units /ml ] CEAct - Converting enzyme activity [x Normal ] A 2Inf Angiotensin 2 infusion rate [nG /min ]

1.276 LogA2

logA2

Macula densa feedback signal calculation based on macula densa sodium flow and angiotensin concentration

RENIN

Scope A NGIOTE NS IN

18 .9

PRA

CEAct

OUTPUTS : A2 - Plasma angiotensin 2 concentration [ pG/ml ] LogA 2 - logarithm of plasma angiotensin concentration [ pG /ml ])

OUTPUT : PRA - Plasma renin activity

1 Converting Enzyme Activity

A2Inf

A LDOS TE RONE

logA2

INPUTS : logA 2 - Logarithm of plasma angiotensin concentration AldoInf - Aldosterone infusion rate [nG /min ] VTW - Total body water content [ml ] OUTPUT : Aldo - Plasma aldosterone concentration

1

INPUTS : MDSig - Macula densa feedback signal [ x Normal ] VECml - Ectracellular fluid volume

Normal macula densa feedback signal

VECml

[ Units /ml ]

Calculation of plasma renin activity

0 Angiotensin Infusion Rate

Calculation of plasma angiotensin concentration and logarithm of plasma angiotensin concentration (most of the action of angiotensin are logarithmic in nature : concentration changes at higher concentrations produce less of an effect than changes of the same size at lower concentrations )

Aldo

LogA2

MDNorm

[ x Normal ]

VECml

LogA2

[pG /ml ] AldoInf

0

1.789

Aldosteron Infusion Rate

NA TRIUM

- DIS T A L TUB ULE

VTWml

Calculation of plasma aldosterone concentration

-CTotasl body water content [ml ] Aldo

INPUTS : MDNaFlow - Sodium inflow [mmol /min ] Aldo - Plasma aldosterone level [pg /ml ] DisFNaNorm - Normal value of sodium distal fractional reabsorbtion [relative number ] DisNaReab

Aldo

6.867

0.5

DisFNaNorm

Normal distal fractional reabsorbtion for Na

DistNaFlow

DisNaFlow

MDNaFlow

[ nG/dl ]

OUTPUTS : DisNaFlow - Sodium outflow [mmol /min ] DisNaReab - Distal sodium reabsorbrtion [mmol /min ] DisFNa - Distal fractional sodium reabsorbtion [relative number ]

1.854

0.509

DisFNa

Calculation of distal tubule sodium reabsorbtion

2162 SIMPLE SODIUM BALANCE NaDiet ZNAE

0.1441

PNa

INPUTS : NaDIet - Dietary sodium intake [mmol /min ] NaUrine - Sodium urine outflow [mmol /min ] VECml - Extracellular fluid volume [ml ] OUTPUT : ZNAE - ECF sodium content [mmol ] PNa - Plasma sodium concentration [mmol /ml ]

Extracellular sodium quantity is the integral over time dietary sodium intake minus urinary sodium loss

0.125

0.1243

NaDiet [mmol /min ] NA TRIUM NaUrine

VECml

- COLLE CTING DUCT

NaUrine

INPUTS : DisNaFlow - Sodium inflow [mmol /min ] CDFNaNorm - Normal value of sodium distal fractional reabsorbtion [relative number ]

15000 1.664

Extracellular fluid volume [mmol /min ]1

0.9305

DisNaFlow

CDNaReab

CDFNa

OUTPUTS : NaUrine - Sodium urine outflow [mmol /min ] CDNaReab - Collecting duct sodium reabsorbrtion [mmol /min ] CDFNa - Collecting duct fractional sodium reabsorbtion [relative number ]

CDFNaNorm

0.93 Normal collecting duct fractional reabsorbtion for Na

Calculation of collecing duct sodium reabsorbtion

!IE"3 2 .2F=!ABk6=6<. .-&.%&c &+.-&+.-,72 .2,8 %X .5)

40


THIRST AND DRINKING

KIDNEY DYNAMICS AND EXCRETION

MUSCLE BLOOD FLOW CONTROL AND PO2

7.997

99.95 0.01251

40.01

HM

8

NON-MUSCLE OXYGEN DELIVERY OVA

40

POT

HM

INTPUTS: HM-hematocrit [% ] OVA-oxygen volume in aortic blood[ml O2/l blood] BFN-blood flow in non-muscle, non-renal tissues [l/min] AOM-autonomic effect on tissue oxygen utilization

200 OVA

1.01 BFM

OUTPUTS: POT-non-muscle cell PO2 [torr] POV-non-muscle venous PO2 [torr]

BFN

0.001

VVE

0.3

VIM

VV7

1

0

1.001

INTPUTS: PA- aortic pressure [torr] PPC - plasma colloid osmotic pressure [torr] VIM - blood viscosity(ratio to normal blood [torr min/ll] REK- percent of normal renal function [ratio to normal] CNE- sodium concentration abnormability causing third factor effect [mmol/l] AUM - sympathetic vasoconstrictor effect on arteries [ratio of normal effect ] AHM - antidiuretic hormone [ratio of normal effect ] AM - aldosterone multiplier [ratio of normal effect ]

0.9993

INTPUT: VVE - VVE - excess blood (stressed ) volume in the veins [l]

8 P2O

OUTPUT: VV7 - increased vascular volume caused by stress relaxation [l]

VIM

1 0.3 REK

1

REK

Vascular Stress Relaxation 0.9834

POV

AMM

AU

10

1

AU

1

1 STH 0.0009993

0

AHM

TVD

1.2 Thirst And Drinking

RBF

1.2 RBF

OUTPUTS: VUD - rate of urinary output [l/min] RBF- renal blood flow [l/min] RFN- renal blood flow if kidney is not damaged[l/min] NOD - rate of renal excretion of sodium [mmol/min]

CNE

1

AOM

1

AHM

9.843

40

CNE

AMM

AOM

VUD

KIDNEY DYNAMICS AND EXCRETION

0.01011

AOM

1.007

0.9987

PPC


0.3213

EXC

1 EXC

28

7.973 P2O

OUTPUTS: OVA- oxygen content of arterial blood [ml O2 STPD/l blood] AOM P2O - muscle cell PO2 [torr] AOM - autonomic effect on tissue oxygenation AMM - muscle vascular constriction caused by logical tissue control [multiplifier, ratio to normal]

40

POV

1.001

VUD

PPC

1 BFM

2.862

2.8 BFN

1.012

STH

INTPUT: POT - non muscle cells PO2 [torr] AHM - antidiurectical hormone effect to non renal vascular resistance , multiplifier (ratio to normal effect ) OUTPUT: STH - salt appetite multiplifier factor [ratio to normal] TVD - rate of intake of fluid by mouth TVD or otherwise [l/min]

8 POT

27.97

OVA INTPUTS: VPF - volume of free fluid in the pulmonary interstitium HM - hematocrit [% ] BFM - blood flow in muscles [l/min] EXC - Effect of excercise on the metabolic usage of oxygen by the muscles[ratio to resting state ] AU - overall activity of autonomic system

POT

0.00095

PA


200

MUSCLE BLOOD FLOW CONTROL AND PO 2 40.01

POT

198.8

PA

100 OVA

0.0125 VPF

7.997

THIRST AND DRINKING

198.8 VPF

HM

40 HM

Muscle Blood Flow Control And pO 2

1.2 RFN

1.006


1.2

AAR - afferent arteriolar resistance [torr min/l] EVR - postglomerular resistance [torr min/l] RR - renal resistance [torr min/l] GLP - glomerular pressure [torr] GFN- glomerular filtration rate of undamaged kidney [l/min] GFR- glomerular filtration rate [l/min]

AUM

1 AUM 0.9987

RFN


AHM

1

1.007

0.09615

AHM

NOD

AU

0.9943 AM

0.1

1

NOD

AU


1

0.09019

AM Kidney Dynamics and Excretion

PRA

0

INTPUT: AU - overall activity of autonomic system, ratio to normal PRA- right artial pressure CNA- extracellural sodium contrentration

0.9987 AHM

1

PRA

OUTPUT: AHM - antidiurectic hormone multiplifier, ratio of normal effect

142.2

AHM

CNA

142

NON-MUSCLE LOCAL BLOOD FLOW CONTROL

CNA Antidiurectic Hormone Control

CIRCULATORY DYNAMICS 0.9331

NON MUSCLE LOCAL BLOOD FLOW CONTROL INTPUT: POT - non-muscle cells PO 2 [torr]

40 POV

POV

ARM

0.9331

1.01

1.6

ARM

OUTPUT: ARM - vasoconstrictor effect of local blood flow autoregulation in non-muscle tissues [ratio to normal]

40

ARM

BFM

0.9993

1

1 VIM

ARM

BFM

1 VIM

Non-Muscle Local Blood Flow Control

ANGIOTENSIN CONTROL

1.006 2.789

1

AUM

1

RVS

2.9

AUM 0.9996

CAPILLARY MEMBRANE DYNAMICS

RVS

0.9996

REK

1 ANGIOTENSIN CONTROL

REK

ANM

1

0.00095 3.772

ANM 0.9834

16.84

VUD

0.001

PVS AMM

VUD

3.7

1

PC

RFN

2.789

PVS

AMM 1.003

RVS

17

1.2

PC

RFN

CIRCULATORY DYNAMICS

AVE

RBF

RBF

AUTONOMIC CONTROL

16.84 PC

17 PC

2.947

1.007

VVR

99.95

2.95 VVR

AU

0.01011

1

PA

100

AU VV7

1.002

2.947

POT

7.973 P2O

8 P2O

AUH

VVR

1 2.95

AUH

1

VVR

HMD

1

-6.337

-6.3 PIF

5.063

QLO PTC

5 99.95

PTC

1.289e-008

PA

2.999 VP

3 VP

0.03864 DPC

0.04 DPC

DFP

0

100

DFP

0.001

HPL

TVD

0.9996 70 CPP ANM

VTL

0.002

PPC

HSL

PPA

PA

PPC

PPD

20.25

15

5.001

PPA

HSL

0.03788

0.04

0

142.2

VTC

DPL

1 HPR

0.9943

1 AM

CKE 0.002

DPL

HPR

Autonomic Control

5

VTC

1 PLA

OUTPUT: AM - aldosterone multiplier, ratio of normal effect

CKE

0.001913

CPI

0.006167

AVE

1 AVE

AM

CPI

20

EXC

EXC

INTPUT: ANM - angiotensin multiplier effect on vascular resistance , ratio to normal PA- aortic pressure [torr] CKE- extracellural potassium concentration CNA- extracellural sodium concentration

PA

100

28

PPD

0 HSR

ALDOSTERONE CONTROL

-4.386e-006

15.18

1

1

99.95

27.97

VTL

1 HSR

ANM

1

2.8 BFN VB

1.003

ALDOSTERONE CONTROL

69.92 CPP

0.001871

BFN

4.999

OUTPUTS: PC - systemic capillary pressure [torr] PPC - plasma colloid osmotic pressure [torr] VTC - toral rate of movement of fluid out of systemic capillaries [l/min] VB - blood volume CPP - plasma protein concentration DPC - rate of loss of plasma protein through systemic capillaries

0.0009993 TVD

2.862

5 VB

AUM

CAPILLARY MEMBRANE DYNAMICS INTPUTS: PTC - colloid osmotic pressure of the tissue gel [torr] VTL - rate of return of fluid from the interstitium to the blood through the lymph[l/min] TVD - rate of intake of fluid by mounth or otherwise [l/min] RVS - venous resistance BFN- blood flow in non-muscle , non renal tissues PVS - average venous pressure VRC - volume of red blood cell VUD - rate of urinary output DFP- rate of increase in pulmonary free field PIF - intersticial fluid pressure PPD - rate od change of protein in pulmonary fluids CPI - concentration of protein in free intersticial fluid VP - plasma volume [l] DPL - rate of systemic lymphatic return of protela

VRC

2 VRC 5.072

5

1 HPL

AUM

1

2

0 PRA

1

1.006

Angiotensin Control

3.7 PVS

PRA

AUH

AUH

CNE

CNA

5 VB

3.772 PVS

PA

HMD

10

CNA

142 VB

1

1.002

OUTPUTs: AU - overall activity af autonomic system [ratio to normal] AUH- autonomic multilier effect on the heart output [ratio to normal] VVR - basic volume of venous tree(maximum volume at zero pressure ) [l] AUM - autonomic multipllier effect on arterial resistance [ratio to normal] AVE- autonomic multipllier effect on venous resistance [ratio to normal]

9.843 CNE

4.999 2.8 BFN

0.09019

PIF

AUTONOMIC CONTROL INTPUTS: PA- systemic arterial pressure torr POT - non-muscle cell PO2 [torr] P2O - muscle cell PO2 [torr] EXC - Effect of excercise on the metabolic usage of oxygen by the muscles [ratio to resting state ] AUZ- overall sensitivity of autonomic control [ratio to normal]

7.997

8

142.2

2.862 BFN

0.3 VVE

OUTPUTS: BFM - muscle blood flow [l/min] RVS - venous resistance [torr/l/min] PVS - average venous pressure [torr] VVE - excess blood (stressed ) volume in the systemic veins [l] PRA - right atrial pressure [torr] QLO - output of left ventricle [l/min] PA- aortic pressure [torr] BFN- blood flow in non-muscle, non-renal tissues [l/min] PRA- right atrial pressure [torr] PLA - left atrial pressure [torr]

0

POT

RVS

VVE

QLO

VV7

PA

0.3213

INTPUTS: ARM - vasoconstrictor effect of all types of autoregulation VIM - blood viscosity(ratio to normal blood) AUM - sympathetic vasoconstrictor effect on arteries ANM - angiotensin multiplier effect on vascular resistance , ratio to normal AMM - muscle vascular constriction caused by local tissue control, ratio to resting state AVE- sympathetic vasoconstrictor effect on veins RBF- renal blood flow [l/min] PC - capillary pressure [torr] VVR - diminished vascular volume caused by sympathetic stimulation[l] VV7 - increased vascular volume caused by stress relaxation [l] AUH- autonomic stimulation of heart, ratio to normal HMD - cardiac depresant effect of hypoxia HPL - hypertrophy effect on left ventricle [ratio to normal] HPL - hypertrophy effect of left heart [ratio to normal] VB - blood volume[l] HSR - basic strenght or right ventricle [ratio to normal] HPR - hypertrophy effect of right heart [ratio to normal]

1.2

1.2

1 ANM

OUTPUTS: ANM - angiotensin multilier factor on vascular resistance [ratio to normal] CNE- sodium concentration abnormality causing third factor effect

2.9 1 AVE

ANM

INTPUTS: REK- percent of normal renal function [ratio to normal] RFN- renal blood flow if kidney is not damaged[l/min] CNA- extracellural sodium concentration

1.2

CNA

PLA

142

Capillary Membrane Dynamics

CNA Circulatory Dynamics Aldosterone Control

TISSUE FLUIDS , PRESSURES AND GEL

ELECTROLYTES AND CELL WATER


0.001871

PULMONARY DYNAMICS AND FLUIDS RED CELLS AND VISCOSITY

15.18

1.007

1

1.289e-008

PPA

PA 0.9993

DFP

0.006167 1

0

INTPUTS: AUR- overall activity of autonomic system [ratio to normal] HMD - cardiac depresant effect of hypoxia, shock and other factors [ratio to normal] PRA- right atrial pressure [torr] QLO - output of left ventricle [l/min]

PLA

27.97

PPC

INTPUTS: PA- systemic arterial pressure [torr] PPA- pulmonary arterial pressure [torr] HSL - basic strenght or left ventricle [ratio to normal] POT - Non muscle cells PO2 [troo] HSR - basic strenght or right ventricle [ratio to normal]

40.01

VB

7.997

HM

1.012 STH

1 20.25

8

HM

POT

STH 0.01251

CPI

20

VPF

VPF 11.97 1

5 CKE

142.2

CNA

142 CNA

VP

12

3

VTS

VP

VID

1

0

HMD

CKE

2.999

VTS

8.074e-006 HMD

HSR

5.001

OUTPUTS: VID - rate of fluid transfer between interstitial fluid and cells [l/min] CKE- extracellular potassium concentration [mmol/l] CNA- extracellular sodium concentration [mmol/l] VTW - total body water [l]

0.0125

CPI

POT

40

Red Cells And Viscosity 0 PPD

0.1

5

OUTPUTs: PTC - total colloid osmotic pressure of the tissue gel] VTL - lymph flow rate [l/min] DPL - rate of return of protein to the circulatin by way of the lymph [g/min] CPI - concentration pf protein in the interstitium [g/l] VTS - total interstitial fluid volume [l]

DPC

HPL

INTPUTS: AM - aldosterone multiplier, ratio of normal effect REK- percent of normal renal function [ratio to normal] NOD - rate of excretion of sodium in the urine [mmol/min] STH - salt appetite multiplier factor [ratio to normal] VTS - systemic interstitial fluid volume [l] VP - plasma volume [l] VPF - pulmonary interstitial fluid volume [l]

NOD

PTC

PTC

DPC

0.04 1

5 VB -4.386e-006 PPD

CPP

70 CPP

INTPUTS: VTC - rate of fluid transfer across systemic intersticial fluid DPC -rate of influx protein into the interstitial fluid from plasma [g/min] VID - rate of fluid transfer between interstitial fluid and cells

0.03864 1 HPL

OUTPUTS: HPR - hypertrophy effect of right heart [ratio to normal] HPL - hypertrophy effect of left heart [ratio to normal] HMD - cardiac depresant effect of hypoxia, shock

ELECTROLYTES AND CELL WATER NOD

5.063


HSL

2 VRC

69.92 QLO

0.09615

DPL

PPA 2

OUTPUT: VIM - blood viscosity [ratio to normal] HM - hematocrit [% ] VRC - volume of red blood cells []

4.999

VPF

PPC

5.072

5 QLO

15

VIM

VRC

0.0125

72.48

HR

RED CELLS AND VISCOSITY INTPUT: POT - non-muscle cell PO 2 [torr] VB - volume of blood[l]

0.01251 VPF

OUTPUTs: DFP- rate of change of free fluid in the lungs [l/min] VPF - volume of free fluid in the pulmonary interstitium [l/min] PPD - rate of loss of protein through the pulmonary capillary membrane [g/min]

28

OUTPUTS: SVO - stroke volume [l] HT - heart rate

PRA

0 PRA

POT

8 POT

INTPUTS: PPA- pulmonary arterial pressure [torr] PLA - left atrial pressure [torr] PPC - plasma colloid osmotic pressure [torr] CPP - plasma protein concentration

PLA

0.09019

0 VID REK

0.04

TISSUE FLUIDS , PRESSURES AND GEL

PPA

1

1 REK

DPL

HPR VIM

PULMONARY DYNAMICS AND FLUIDS

0.06998

SVO


HMD

1 HMD

8.074e-006 VID

VTC

1

15.18

7.997

0 DFP

AM 0.03788

HPR

15 PPA AU

1

AM

1

0.002 VTL VTC

0.002

PA

100

AU

0.9943

VTL

0.001913 99.95


11.97

-6.337

39.95

VTW

VID

VTW

VTS

Heart Rate and Stroke Volume

12

PIF

Pulmonary Dynamics and Fluids

-6.3 Heart Hypertrophy or Deterioration

VTS

PIF Electrolytes and Cell Water Tissue Fluids, Pressures and Gel

!II"AgF -GH;))&++.-&+.-,A 5- - ruv 5) ..& &%5)-%&' 195.5

NON MUSCLE O 2 DELIVERY OVA

INTPUTS: OVA- oxygen content of arterial blood [ml O2 STPD/l blood] BFN- blood flow in non-muscle and non-renal tissues [l/min] HM - hematocrit [% ] AOM - autonomic effect on tissue oxygenation [ratio to normal] O2M - basic oxygen utilisation in non-muscle cells [ml O2 STPD/min]

2.869 BFN

40 HM

OUTPUTS: OSV - non-muscle venous oxygen saturation[% ] POV - non muscle venous PO2 [torr] POT - non muscle cell PO2 [torr] DOB - rate of oxygen delivery to non-muscle cells [ml O2 STPD/min] MO2 - rate of oxygen utilisation by non-muscle tissues [ml O2 STPD/min] QO2 - non-muscle total cellular oxygen [ml O2 STPD]

1.001 AOM

164.5

O2M

0.6903

OSV

POT

164.8

DOB

PC

0.02556 240

164.7

QO 2

2425

1

0.01182

195.5

0.9775

INTPUTS: OVA- oxygen content of arterial blood [ml O2 STPD/l blood] BFN- blood flow in muscles [l/min] HM - hematocrit [% ] AOM - autonomic effect on tissue oxygenation [ratio to normal] OMM - basic oxygen utilisation in muscles [ml O2 STPD/min] EXC - Effect of excercise on the metabolic usage of oxygen by the muscles [ratio to resting state ]

BFM

PULMONARY O2 DELIVERY

40

DOB

OSA

INTPUTS: VPF - volume of free fluid in the pulmonary interstitium [l/min] DOB - non-muscle oxygen usage[ml/min] RMO - muscle oxygen usage [ml/min] PO2DEF- normalised difussion coecficient for oxygen through the pulmonary membrane [at norma PO2DEF=1] PO2MAB - ambient oxygen pressure [torr] HM - hematocrit

RMO

1 PO2DFF

PO2DEF

150 PO2AMB

PO2AMB

HM

1.001 AOM

60

OUTPUTs: OSA - arterial oxygen saturation OVA- arterial blood oxygen content [ml O2/l blood]

OVA

OUTPUTS: OVS - muscle venous oxygen saturation [% ] PVO - muscle venous PO2 [torr] PMO - muscle cell PO2 [torr] RMO - rate of oxygen delivery to muscles [ml O2 STPD/min] MMO - rate of oxygen utilisation by muscles [ml O2 STPD/min] QOM - muscle total cellular oxygen [ml O2 STPPD]

OMM

OMM

1

HM

EXC

EXC 40

Pulmonary O2 Delivery

OUTPUT: MYOGRS- myogenic autoregulation effect on vascular resistance in muscle and in non-renal tissue [multiplier, ratio to normal]

INTPUTS: AUR- autonomic stimulation of heart rate [ratio to normal] HMD - cardiac depresant effect of hypoxia, shock and other factors [ratio to normal] PRA- right atrial pressure [torr] QLO - output of left ventricle [l/min]

QLO

OUTPUTS: HR - heart rate [beats/min] SVO - stroke volume [l]

72.45

HR

PPA

-0.1045 PLA

1.616

RPA

INTPUTS: PPA- pulmonary arterial pressure [torr] PLA- left atrial pressure [torr] QPO - rate of blood flow into pulmonary veins and left atrium[l/min]

1.408

RPV

3.024 RPT

OUTPUTS: RPA- pulmonary arterial resistance [torr min/l] RPV - pulmonary venous resistance [torr min/l] RPT - total pulmonary vascular resistance [torr min/l] PVP - pulmonary venous pressure [torr]

0.06768

SVO

QPO

PPA

TENSGN

11.24

PVP

Heart Rate and Stroke Volume Resistances in the Pulmonary Circulation and Pulmonary Venous Pressure

Myogenic Autoregulation 1.003

INPUTS: PRA AH7 PRA - riight atrial pressure [torr] ATRVHBM- sensitivity controller of volumereceptor feedback effect on change of basic of venous system [ATRVFB=AH7*ATRRVBM, no effect = 0] ATRRFBM- sensitivity controller of volumereceptor feedback effect on nonmuscle arterial resistance [ATRRFB =AH7*ATRRFBM , no effect = 0] ATRVFBM ATRVFB

MUSCLE O2 DELIVERY OVA

1.038 VPF

TENSGN

THE VOLUME RECEPTOR FEEDBACK MECHANISM

Delivery of Oxygen to the Non-muscleTtissues

60.09

PRA

HMD

MYOGRS

MYOGTAU

MYOGTAU

Non-muscle Local Blood Flow Control MO 2

INTPUTS: PA- systemic arterial pressure [torr] PC - capillary pressure [torr] MYOGTAU- time delay factor of myogenic response (in normal condition TENSTC = 240 min) TENSGN- factor of effectiveness of myogenic response

17.82

ARM

OUTPUT: ARM - vasoconstrictor effect of local blood flow autoregulation in non-muscle tissues [ratio to normal]

RESISTANCES IN THE PULMONARY CIRCULATION AND PULMONARY VENOUS PRESSURE

AUR

MYOGENIC AUTOREGULATION PA

1.026

INTPUT: POT - non-muscle cells PO 2 [torr]

8.075 POT

O2M

164.8

14.72

HEART RATE AND STROKE VOLUME 99.79 NON MUSCLE LOCAL BLOOD FLOW CONTROL

39.44

POV

OVS

0.6881

PVO

39.32

0 ATRVFBM

MUSCLE LOCAL BLOOD FLOW CONTROL INTPUT: PMO - muscle cells PO2 [torr]

8.143

ATRRFBM

1.051

AMM

OUTPUT: AMM - vasoconstrictor effect of local blood flow autoregulation in muscles [ratio to normal]

60.09

ATRRFBM

0

PMO

PMO

OUTPUTS: AH7 - effect of right atrial volume receptor reflex on ADH secretion [relative additive factor, normal value = 0] ATRVFB- change in basic volume of venous system caused by atrial volume receptor feedback ATRRFB- multiplier factor for the effect on muscle and non-renal vacular resistance of feedback from the atrial stretch receptors [multiplier, ratio to resting state ]

0.2582

OSA

0 PA 14.72

0.02556 4.903 PPA

1

PPA

AUH

The volume receptor feedback mechanism

OSA

RMO

HSR

Muscle Local Blood Flow Control

HEART HYPERTROPHY OR DETERIORATION QAO

2402

QOM

HSR

PA

60.09

MMO

PPA

Delivery of Oxygen to the Muscles HSR

1 HSR 1

HSL

HSL

HSL

RIGHT HEART PUMPING

PRA ATRRFB

HPR

HPR

INTPUTS: PA- systemic arterial pressure [torr] QAO - blood flow in the systemic arteriel system [l/min] PPA- pulmonary arterial pressure [torr] HSR - basic strenght or right ventricle [ratio to normal] HSL - basic strenght or left ventricle [ratio to normal] POT - Non muscle cells PO2 [troo]

HPR

HMD

1

HMD

QLO

1

HPL

INTPUTS: QRO PRA- right atrial pressure [torr] PPA- pulmonary arterial pressure [torr] AUH- autonomic stimulation of heart [ratio to normal] OSA - oxygen hemoglobin saturation HSR - basic strenght or right ventricle [ratio to normal] HPR - hypertrophy effect of heart [ratio to normal] HMD - cardiac depressant effect of hypoxia. shock QRN and other factors [ratio to normal] QLO - output of left ventricle [l/min] QLN - normalised output of the left heart [l/min]

LEFT HEART PUMPING

PLA

PA

INTPUTS: QLO PLA - left atrial pressure [torr] PA- systemic arterial pressure [torr] AUH- autonomic stimulation of heart [ratio to normal] OSA - oxygen hemoglobin saturation HSL - basic strenght or left ventricle (ratio to normal) HPL - hypertrophy effect of left heart [ratio to normal] QLN HMD - cardiac depressant effect of hypoxia, shock and other factors [ratio to normal]

PA

AUH

4.885 OSA

HSL

OUTPUTS: QRO - actual right ventricular output [l/min] QRN - normalised right ventricular output [l/min] RVM RVM - depressing effect on right ventricle of pulmonary arterial pressure [ratio to normal]

4.903

4.897

HSL

OUTPUTS: QLO - actual left ventricular output [l/min] QLN - normalised lwft ventricular output [l/min] LVM - depressing effect on left ventricle of pulmonary arterial pressure [ratio to normal]

HPL

1.004 HMD

0.9982

LVM

QLN

Left Heart Pumping

Right Heart Pumping

OUTPUTS: HPR - hypertrophy effect of right heart [ratio to normal] HPL - hypertrophy effect of left heart [ratio to normal] HMD - cardiac depresant effect of hypoxia, shock

HPL HMD

HMD

4.897

POT

1

4.903

Heart hypertrophy or deterioration

HM 99.79

2.948

DFP

UNSTRESSED SYSTEMIC VENOUS VOLUME

VVR PPA

AUTONOMIC CONTROL OF THE CIRCULATION

VPF

PULMONARY FLUID DYNAMICS

PLA

PA

-0.04597

PCP

8.075

INTPUTS: PPA- pulmonary arterial pressure [torr] PLA- left atrial pressure [torr] PPC - plasma colloid osmotic pressure [torr] CPF- pulmonary capillary filtration coeffitient [l/min/torr]

OUTPUTs: DFP - rate of change of free fluid in the lungs [l/min] VPF - volume of free fluid in the pulmonary interstitium [l/min] PFI PCP - pulmonary capillary pressure [torr] POS - osmotic pressure in pulmonary interstitial fluid pressure [torr] PPI - pulmonary interstitial fluid pressure [torr] PLF PFI - rate of fluid filtration out of pulmonary capillary [l/min] PLF - pulmonary lymph flow rate [l/min] CPN - concentration of protein in pulmonary interstitial fluid[g/l] PPN - protein leakage rate through the pulmonary capillary membrane [g/min] CPN CPP PPR - total quantity of protein in pulmonary interstitial fluid[g] PPD - rate of loss of protein through the pulmonary capillary membrane [g/min]

72

AUH

1 9.409e-005

-0

50.84

0.00476

PPN

0.6012

PPR

1

OUTPUTs: AU - overall activity af autonomic system [ratio to normal] AUH- autonomic multilier effect on the heart output [ratio to normal] AUR- autonomic multilier effect on heart rate EXC [ratio to normal] VVR - basic volume of venous tree(maximum volume at zero pressure ) [l] AUP - autonomic multipllier effect on ADH hormone excretion etc. [ratio to normal] ANUBR AOM - autonomic multipllier effect on tissue oxygen utilisation [ratio to normal] AUM - autonomic multipllier effect on arterial resistance [ratio to normal] AVE- autonomic multipllier effect on venous resistance AUZ [ratio to normal]

AUZ -2.404e-005

PPD

-0.2

VV 6

INTPUTS: VVE - excess blood volume in the veins [l]

1.003

ANY

ANY VV6

AUR

VVE

1.01

VVR

OUTPUTS: VV6 - increased venous vascular volume caused by long time stress realaxation [l] VV7 - - increased venous vascular volume caused by short time stress realaxation [l]

99.79

INPUTS: VVR - normal maximum volume of blood in the venous system at zero pressure [l] ANU - nonrenal effect of angiotensin [ratio to normal] ANY- sensitivity of large veins to effect of angiotensin [normal value = -0.2 l/unit of angiotensin] VV6, VV7 - changes in basic volume of venous system cauused by stress relaxation [l] ATRVFB- change in basic volume of venous system caused by atrial volume receptor feedback

ANU

0.0003989 VENOUS STRESS RELAXATION

PMO

CPF

CPF

0.9018

1.01

AU

2.948

9.421e-005

PPC

0.0003

8.143

-10.69

PPI

CPP

POT

20.34

POS

INTPUTS: PA- systemic arterial pressure torr POT - non-muscle cell PO2 [torr] PMO - muscle cells PO2 [torr] EXC - Effect of excercise on the metabolic usage of oxygen by the muscles [ratio to resting state ] ANUBR- direct effect of angiotensin on vasomotor center ["virtual" torr] AUZ- overall sensitivity of autonomic control [ratio to normal]

0

VV 7

QLO

VVS 0

OUTPUT: VVS0 - the maximum volume ov venous system at zero volume (so called unstressed venous volume) [l]

0.495 RESISTANCES IN THE SYSTEMIC CIRCULATION

Effect of stress relaxation on basic venous volume

96.3

0.003467

RAM RAR 1.008 1.008 AUM

1 1.002

AVE

0.9018

Autonomic Contorl of the Circulation

1

Pulmonary Fluid Dynamics 1 1.051

1.026 3.677 1

SYSTEMIC CAPILLARY PRESSURE

BFN

INTPUTS: PVS - average of systemic venous pressure [torr] BFN- blood flow in non-renal and non-muscle tissues [l/min] RVS - resistance in small veins [torr min/l]

VPA0

VPA0 RSN

0.4

VLA0

VLA0 0.00355

CAS

CAS 0.0825

CLA

0.01 CLA

RSN

RSM

3.024 RPT

2.754 RR RVS

OUTPUTS: RSN - vascular resistance in non-muscle and non-renal tissues [torr min/l] RSM - vascular resistrance in muscles [torr min/l] RVS - resistance in small veins [torr min/l]

VIM

0.8492 VAS

3.275

VVS

0.3033 VVE

VRA

VPA

0.1001 0.3769 0.399

VLA

FIS

0

4.903 4.903 2.869 1.038

0.9963 0 20.35 4.273 0.7273 6.871

MCP

FIS

PC

-0.1045 PLA

4.903

CPA

CPA

ANUVN

1 OUTPUT: PC - systemic caplillary pressure [torr]

14.72 PPA

OUTPUTS: QAO PA- arterial (aortic) pressure [torr] PVS - average venous pressure [torr] QVO PRA- right atrial pressure [torr] PPA- pulmonary arterial pressure [torr] QPO PLA- left atrial mpressure [torr] VAS - volume in systemic arteries [l] VVS - systemic venous vascular volume [l] BFN VVE - excess blood volume in the veins[l] VRA- right atrial volume [l] BFM VPA- volume in pulmonary arteries [l] VLA- volume in left atrium [l] RBF QAO - blood flow in the systemic arteriel system [l/min] QVO - rate of blood flow from veins into right atrium [l/min] QPO - rate of blood flow into pulmonary veins and left atrium[l/min] FISFLO BFN- blood flow in non muscle and non renal tissues[l/min] BFM - blood flow in muscles [l/min] RTP RBF- renal blood flow [l/min] FISFLO- blood flow through a fistula[l/min] VT0 RTP - total systemic peripheral resistance [torr min /l] VT0 - total unstressed blood volume [l] VE0 - total excess volume of blood in the vasculature [l] VE 0 MCP - mean circulatory pressure [torr]

CRA

CRA 0.0048

RSM

3.677 0.02556 PRA

CV

CV 0.005 92.6

AVE

1.002 17.82

PC

2.754 RVS

VRA0

VRA0 0.30625

RVSM

PVS

2.869 BFN

33.5

INTPUTS: PA- systemic arterial pressure [torr] RAM - basic vascular resistance of muscles [torr min/l] RAR RAR - basic vascular resistance of non-muscle and non-renal tissues [torr min/l] MYOGRS MYOGRS - myogenic autoregulation effect on vascular resistance in muscle and in non-renal tissue (multiplier, ratio to normal) AUM - sympathetic vasoconstrictor effect on arteries AUM in muscle and non-renal tissues [multiplier factor , ratio to normal] VIM - blood viscosity[ratio to normal] VIM ANU- nonrenal effect of angiotensin [ratio to normal] AHM - antidiuretic hormone effect to non renal vascular resistance , multiplier (ratio to normal effect ) ANU ATRRFB- multiplier factor for the effect on muscle and non-renal vacular resistance of feedback from the atrial AHMR stretch receptors [multiplier, ratio to resting state ] AMM - muscle vascular constriction caused by local tissue control [multiplier, ratio to resting state ) ATRRFB ARM - the degree of vasoconstrictor effect of autoregulation in non-muscle and non-renal tissues [multilier, ratio to normal] RVSM - basal systemic venous multiplier causes basal vascular AMM stretch in the venous system [ratio to normal] AVE- multiplier factor for the effect of the autonomic nervous system ARM on venous resistance [ratio to basal effect ] ANUVN multiplier factor for the effect of angiotensin on venous resistance [ratio to normal] RVSM PC - systemic caplillary pressure [torr] RAM

30.52

1.003

1.001

AOM

0.1

Unstressed volume in systemic venous tree

1.01

AUP

VAS0

VAS0

PA

PVS

INPUTS: VB - blood volume[l] QRO - actual right ventricular output l/min] QLO - output of left ventricle [l/min] VVS0 - unstressed venous systemic vascular volume [l] VVE - excess volume (stressed volume) in systemic veins [l] VAS0 - unstressed volume in systemic arteries [l] VRA0 - unstressed right atrial volume [l] VPA0 - unstressed volume in pulmonary arteries [l] VLA0 - unstressed volume in left atrium and pulmonary veins [l] CAS - capacitance of systemic arteries [l/torr] CV - capacitance of venous systemic volume [l/torr] CRA- capacitance of right atrium [l/torr] CPA- capacitance of pulmonary arteries [l/torr] CLA- capacitance of left atrium and pulmonary veins [l/torr] RSN - vascular resistance in non-muscle and non renal tissues [torr min /l] RSM - vascular resistance in muscles [torr min /l] RPT -pulmonary vascular resistance [torr min /l] RR - total renal resistance [torr min /l] ( VIM - blood viscosity(ratio to normal blood) FIS - conductance fot the fistula [l/min/torr]

QRO

ATRVFB

PA

CIRCULATORY DYNAMICS - FLOWS AND PRESSURES

VB

PA 2.971

VVS 0

VV7

Circulatory Dynamics - Flows And Pressures

17.82 Resistances in the Systemic Circulation

Systemic Capillary Pressure

99.79

GBL

PVS

30.17 AAR

PAR PAR

INTPUTS: PA- systemic arterial pressure [torr] GBL - pressure drop in renal artery caused renal arterial constriction [torr] PVS - average systemic venous pressure [torr] AAR - resistance in afferent arteriole [torr min/ll] EAR - resistance in efferent arteriole [torr min/ll] REK- percent of normal renal function [ratio to normal]

AAR

40 HM

30.66

RR

RR

REK

GFR RFN

30.17

96.47

PPC

MACULA DENSA

142.4 GLOMERULUS

0.9963 0.9963 RFN

41.21 EAR

74.79

74.79

RENAL PERFUSION PA

25 GBL

INTPUTS: PAR - renal perfusion pressure[torr] RFN- renal blood flow if kidney is not damaged[l/min] AAR - resistance in afferent arteriole [torr min/ll] HM - hematocrit PPC - plasma colloid osmotic pressure [torr] PXTP - back pressurein proximal tubule [torr] GLFC- glomerular filtration coefficient [l/torr/min] REK- percent of normal renal function [ratio to normal]

0.1238

INTPUTS: CNA- Extracellular sodium concentration [mmol/l] GFN- glomerular filtration rate if kidney is not damaged [l/min]

CNA

0.1238

8

PXTP

PXTP

0.9963

RBF

0.0208

GLFC

GLFC

Renal Perfusion

OUTPUTS: RNAUG1 - macula densa feedback signal [ratio to normal effect ] NAPT1 - delivery of sodium to the macula densa area [ratio to normal value]

GFN

REK

ANXM

INTPUTS: NAPT1 - delivery of sodium to the macula densa area [ratio to normal value] REK- percent of normal renal function [ratio to normal] ANXM - controls of degree of hypertrophy of the juxtaglomerulal apparatus [0 = no hypertrophy] ANG- excess of angiotensin concentration caused by infusion [ratio to normal level of angiotensin] ANUBRM- sensitivity contoller for the effect of angiotensin of the baroreceptor system ANUVM- sensitivity controller for the multiplier factor of the systemic veins

1

0.9673 ANM

GLPC

PTC

SODIUM EXCRETION INTPUTS: NAPT1 - delivery of sodium to the macula densa area [ratio to normal] RFAB- the multiplier factor for the effect of renal hemodynamics on reabsorbtion of sodium and potassium in the distal tubule collecting duct [ratio to normal] VUDN- rate of urinary output if kidney is not damaged [l/min] AMNA- aldosterone for control of sodium reabsorbtion [ratio to normal effect ] AHM - antidiuretic hormone [ratio to normal effect ] REK- percent of normal renal function [ratio to normal] DIURET- effect of diuretic on the distal tubule collecting duct [ratio to normal - without diuretics]

1.57

0.0007051 MYOGENIC AUTOREGULATION OF AFFERENT ARTERIOLE PAR

-0 240

MYOGTAU

0

1 TENSG

TENSGN

REK

1 1.57

0.9963

PERITUBULAR CAPILLARIES RFN

OUTPUTS: AMK - effect of aldosterone on potassium secretion [ratio to normal] AMNA- aldosterone for control of sodium reabsorbtion AMC - aldosterone concentration [ratio to normal]/n

OUTPUTS: RFAB- the multiplier factor for the effect of renal hemodynamics on reabsorbtion of sodium and potassium in the distal tubule collecting duct [ratio to normal] RCPRS- renal capillary pressure around the tubular systewm [torr]

DIURET

0.5388 DTNAI

RNAUG 1

1.024

ANM 1.034

ANM

0.9673

AUP

ANM

99.79 PA

0.2582 AH7

0

ADH

ADH 0 AHMRM

AHC1 1.008

VIM

1

0.9673

43.333

RNAUG 1

0

EFARF

EFARF

0 DPR

1.003

VUDN

PLURC

0.1238 GFN

1 2

1 BLOOD VISCOSITY

HM

INTPUT: HM - hematocrit [% ]

VIM

OUTPUT: VIM - blood viscosity[ratio to normal] Blood viscosity

0.24

URFORM

0.05128 NODN

0.05073 41.21

ANM

DR 0 0.05073

KOD

KODN

DR

INTPUTS: POT - non-muscle cell PO 2 [torr] AHC1 - antidiuretic hormone concentration factor in the circulating body fluids[ratio to normal] ANM - angiotensin multilier effect to vascular resistance [ratio to normal] AMK - effect of aldosterone on potassium secretion [ratio to normal] DR - forced input of fluid over and above the natural drinking desire (it may be used for intravenous infusion as well) [l/min] STHENABLED- switching variable: if STHENABLED <=0, then STH is not calcultated and STH=1 TVDENABLED- switching variable: if TVDENABLED<=0 then TVD is not calculated and TVD=DR

STHENABLED

STHENABLED

-2.682

PGH

1

TVDENABLED

UROD

71.95

INTERSTITIAL TISSUE FLUIDS , PRESSURES AND PROTEIN DYNAMICS

UREA

OUTPUTs: PGH - hydrostatic pressure in tissue gel [torr] PTC - total colloid osmotic pressure of the tissue gel] DPC PTT VTL - lymph flow rate [l/min] DPL - rate of return of protein to the circulatin by way of the lymph [g/min] CPI - concentration pf protein in the interstitium [g/l] PIF PTT - total interstitial tissue pressure [torr] PIF - pressurte in the free interstitial fluid [torr] PTS - solid tissue pressure [torr] PTS VIF - free interstitial fluid volume[l] VG - tissue gel volume[l] TSP - total interstitial tissue proteins [g] VIF

0.2364

UROD

OUTPUTS: UROD- urea excretion rate [mmol/min] VUDN- rate of urinary output if kidney id not damaged[l/min] VUDN- rate of urinary output [l/min]

VUDN

0.0007051

278.6

VPF

0.1 NID

NID

STH

1.006 NOD

-4.676 0.06 5.682

KID

KID

0.05073 KOD

0.6016

0.9825 AMK

Interstitial Tissue Fluids, Pressures and Gel Dznamics

VG

11.42

TSP

279.1

4.02

160.3

0.001019

VP

0.101

TSP0

TSP0

0.0007051 VUD

PLUR

Urea

TVD

OUTPUTS: STH - salt appetite multiplier factor [ratio to normal] TVD - actual rate of fluid intake [l/min]

0.004351

23.22

OUTPUTS: PLURC- concentration of urea in body fluids[mmol/l] PLUR- total body urea content[mmol/l]

PLURCNORM

TVDENABLED

VTS

INTPUTS: VTS - total interstitial fluid volume [l] DPL DPC -rate of influx protein into the interstitial fluid from plasma [g/min] TSP0 - initial value of total interstitial tissue proteins [g]

PLURC INTPUTS: URFORM- rate of urea metabolic production [mmol/min] UROD-rate of urea excretion [mmol/min] VTW - total body water volume [l] PLURCNORM- normal value of urea concentration in body fluids[4 mmol/l]

VTW

10.51

VTL

0.2364

4 PLURCNORM

VTS CKU

UREA AND WATER EXCRETION INTPUTS: PLURC- concentration of urea in body fluids[mmol/l] GFN- glomerular filtration rate if kidney is not damaged [l/min] NADT- the normalized delivery of sodium to the distal tubular system [ratio to normal] NODN- sodium excretion rate if kidney is not damaged [mmol/min] KODN- potassium excretion rate if kidney is not damaged [mmol/min] DTNAI - rate of sodium entry into the distal tubular system [mmol/min] AHM - antidiuretic hormone [ratio to normal] REK- percent of normal renal function [ratio to normal]

1

STH

Thirst, Drinking and Salt Appetite OUTPUTS: KODN- potassium excretion rate if kidney is not damaged [mmol/min] KOD - potassium excretion rate [mmol/min] CKU- concentration of potassium in urine [mmol/l]

1.115

1

THIRST,DRINKING AND SALT APPETITE

POT

0

1 ALCLK 25 VICnorm

ACLK

VICNorm

ECF AND ICF ELECTROLYTES AND VOLUMES INTPUTS: VP - plasma volume [l] VTS - systemic interstitial fluid volume [l] VPF - pulmonary interstitial fluid volume [l] NID - normal rate of sodium intake [mmol/min] STH - salt appetite multiplier factor [ratio to normal] NOD - rate of excretion of sodium in the urine [mmol/min] KID - rate of intake of potassium [mmol/min] KOD - rate of excretion of potassium in the urine [mmol/min] AMK - aldosterone multiplier factor for the effect of aldosterone on the transport of potassium through the cell membrane [ratio of normal effect ] ACLK- sensitivity control of the effect of the aldosterone on cellular membrane transport of potassium [ratio of normal effect ] VICnorm - normal value of the intracellular fluid volume [l] OUTPUTS: VEC- volume of extracellular fluid [l] VIC - volume of intracellular fluid [l] VTW - total body water [l] VID - rate of fluid transfer between interstitial fluid and cells [l/min] NAE- total extracellular sodium content [mmol] CNA- extracellular sodium concentration [mmol/l] CKE- extracellular potassium concentration [mmol/l] KI - total intracellular potassium content [mmol] CKI - intracellular potassium concentration [mmol/l] KCD- rate of transferof potassium from the interstitial fluid into the intracellular fluid [mmol/min]

VEC

VIC

14.96

24.92

39.88

VTW

VID

-0.0001418

NAE

2131

142.4

CNA

5.076

CKE

KI

3550

CKI

142.4

KCD

0.005006

Extracellular and Intracellular Fluid Electrolytes and Volumes

REK

1

REK

Red cells production and destruction

8.075

0.05073

Potassium Excretion

EAR

RC2

1.2 RFN

40

-0.01006

DPR

1.034 KODN

4.02

OUTPUT: AAR- afferent arteriolar resistance [torr l/min]

1.16e-005

3 VP

RFN

73.18

CPP

Plasma Protein Dynamics

CPI

INTPUTS: AARK- normal resistance in efferent arteriole [torr min/l RNAUG1 - macula densa feedback signal to efferent arteriole [ratio to normal] EAFRF- sensitivity contoller of macula densa feedback signal to efferent arteriole ANM - angiotensin multiplier effect on vascular resistance [ratio to normal] VIM - blood viscosity[ratio to normal blood]

RC1

PPD

Capillary Membrane Fluid Dynamics

30.17

AHM

0.9673

OUTPUTs: PPC - plasma colloid osmotic pressure [torr] DPC - rate of influx of protein into interstitial fluid from plasma [g/min] CPP - plasma protein concentration [g/l] DPL - net rate of protein exchange between liver and plasma [g/min]

VP

VIM

OUTPUTS: VRC - volume of red blood cells [l] VB - volume of blood[l] HM - hematocrit [% ] RC1 - red cells production rate [l/min] RC2 - red cells destruction rate [l/min]

VTSN

OUTPUT: AAR - afferent arteriolar resistance [torr l/min]

ANM

ANM

VIM

The control Functions of Antitiuretic Hormone

REK

AAR

OSA

RED CELLS PRODUCTION AND DESTRUCTION INTPUTS: OSA - arterial oxygen saturation [ratio to full saturation] VP - plasma volume [l] VIM - blood viscosity[ratio to normal blood] RFN- renal blood flow (if kidney is not damaged) [l/min] REK- fraction of normal kidney mass [ratio to normal]

0.1042

DLP

PTC

1

EARK

EARK

ANM

AHRM

AHMRM

LPPR

LPPR

0.9764

POTASSIUM EXCRETION INTPUTS: CKE- extracellular potassium concentration [mmol/l] CNA- extracellular sodium concentration [mmol/l] NADT- the normalized delivery of sodium to the distal tubular system [ratio to normal] DTNAI - rate of sodium entry into the distal tubular system [mmol/min] ANM - angiotensin multilier effect to vascular resistance [ratio to normal] AMK - effect of aldosterone on potassium secretion [ratio to normal] RFAB- the multiplier factor for the effect of renal hemodynamics on reabsorbtion of sodium and potassium in the distal tubule collecting duct [ratio to normal] REK- percent of normal renal function [ratio to normal] VUDN- rate of urinary output if kidney is not damaged[l/min]

0.0007051

EFFERENT ARTERIOLE

1

AHRM

1.57

AFFERENT ARTERIOLE INTPUTS: AARK- normal resistance in afferent arteriole [torr min/l] RNAUG1 - macula densa feedback signal [ratio to normal] AUM - sympathetic vasoconstrictor effect on arteries [ratio to normal] ANM - angiotensin multiplier effect on vascular resistance [ratio to normal] VIM - blood viscosity[ratio to normal blood]

Afferent Arteriole

1.115

AHMR

VTSREL

VTSN

0.03

0.004738

HM

72.73

CNU

AUM

AHM

OUTPUTS: AHC1 - antidiuretic hormone concentration in the circulating body fluids[ratio to normal] AHM - antidiuretic hormone multiplier [ratio to normal effect ] AHMR- effect of antidiuretic on systemic arterial resistance [ratio to normal effect ] ANUBRM- sensitivity contoller for the effect of angiotensin of the baroreceptor system ANUVM- sensitivity controller for the multiplier factor of the systemic veins

VPN 11.98

0.004025

RFAB

The control Functions of Aldosterone

0.9673

0.05128

NOD

VPN

1.152e-005

URFORM

NADT

ANM

AHC1

CFC

AHC1

CNA

1.078

0.9825

AARK

AARK MYOGRSAA

THE CONTROL FUNCTIONS OF ANTIDIURETIC HORMONE INTPUTS: CNA- Concentration of sodium in extracelullar fluid [mmol/l] AUP- autonomic multipllier effect on ADH hormone excretion etc. [ratio to normal] ANM - angiotensin multiplier effect [ratio to normal] PA- systemic arterial pressure [torr] H7 - effect of right atrial volume receptor reflex on ADH secretion [relative additive factor, normal value = 0] AHMRM- sensitivity coefficient for the effect of ADH on systemic arterial resistance .

3

HM

PLASMA PROTEINS DYNAMICS

INTPUTS: VP - plasma volume [l] VTCLP - rate of leakage of whole plasma through DPL DPC the capillary membrane [l/min] DPL - rate of return of protein to the circulation through the lymph[g/min] CPI - concentration of protein in the interstitium [g/l] [torr] LPPR - rate of production of protein by the liver[g/min] CPI PPD - rate of loss of protein through the pulmonary capillary membrane [g/min] DPR - rate of loos of protein through the kidney[g/min]

5.076

Peritubular Capillaries

40

VID

CFC

5 VTCLP

DIURET

142.4

19.88

0.958

0.9807

AMC

142.4 CNA

DFP

VID 0.01167

0.0007136

12.02

RFAB

RCPRS

AMNA

0.7392

1.01

VUD

1.138e-007

0 0.05128

NODN

OUTPUTS: NADT- the normalized delivery of sodium to the distal tubular system [ratio to normal] DTNAI- rate of sodium entry into the distal tubular system [mmol/min] NODN- sodium excretion rate if kidney is not damaged [mmol/min] NOD - sodium excretion rate [mmol/min] CNU- concentration of sodium in urine [mmol/l]

CKE

GLPC

AMK

ALD

0 ALD

TVD

0.0007051 0.5388

DTNAI

VB

30.66

PPC

INTPUTS: PC - systemic capillary pressure [torr] VTCLP PGH - hydrostatic pressure in the tissue gel [torr] PPC - plasma colloid osmotic pressure [torr] PTC - colloid osmotic pressure of the tissue gel [torr] VTL - rate of return of fluid from the interstitium to the blood through the lymph[l/min] VTS TVD - rate of intake of fluid by mounth or otherwise [l/min] VUD - loss of fluid into the urine [l/min] DFP- loss of fluid from the pulmonary capillaries [l/min] VID - rate of transfer of fluid into the cells [l/min] CFILTR CFC- capillary filtration coefficient [l/min/torr] (normal value CFC=0.01167) VPN - normal value of plasma volume [l] VTSN - normal value of interstitital fluid volume [l]/n OUTPUTS: VTC VP - plasma volume [l] VTS - total interstitial fluid volume [l] VTCPL - rate of leakage of whole plasma through the capillary membrane [l/min] CFILTR- rate of filtration from the systemic capillaries [l/min] VPREL VTC - toral rate of movement of fluid out of systemic capillaries [l/min] VPR - plasma volume [ratio to normal] VTS - total interstitial fluid volume [ratio to normal]

Sodium Excretion

INTPUTS: RFN- renal blood flow if kidney is not damaged[l/min] GLPC- average glomerular plasma colloid osmotic pressure [torr]

44.73

AMK

INTPUTS: ANM - angiotensin multiplier effect on vascular resistance [ratio to normal value] CKE- extracelullar fluid potassium concentrastion [mmol/l] ALD- rate of infusion of aldosterone [relative to normal rate of aldosterone secretion ]

1

OUTPUT: MYOGRSAA- myogenic autoregulation effect on vascular resistance in afferent arteriole [multiplier, ratio to normal effect ]

0.7036

0.9825 THE CONTROL FUNCTIONS OF ALDOSTERONE

CKE

1.115

Myogenic Autoregulation of Afferent Arteriole

The control Functions of Angiotensin

0.9673

5.076

AMNA

0.7392

AHM

ANUVM1

ANM

VUDN

0.958

MYOGRSAA

0.001019

1.078

NADT

ANUBR

OUTPUTS: ANM - angiotensin multilier factor on vascular resistance [ratio to normal] ANUVN ANU- angiotensin multilier factor on peripheral arteriolar resistance [ratio to normal] ANUBRM ANUBR- angiotensin multilier factor for the effect in controlling the sensitivity of the baroreceptor system[ratio to normal] ANUVM- angiotensin multilier factor for the constriction ANC of systemic veins [ratio to normal] ANC ANC- angiotensin concentration in blood[ratio to normal] ANUVM

0

INTPUTS: PAR - renal perfusion pressure [torr] PC - capillary pressure [torr] MYOGTAU- time delay factor of myogenic response (in normal condition TENSTC = 240 min) TENSGN- factor of effectiveness of myogenic response

MYOGTAU1

ANG

ANUBRM

RFAB

Glomerulus

74.79

ANU

VTL

NAPT1

5.949

VP

VP

CAPILLARY MEMBRANE FLUID DYNAMICS PPC

10.51 0.004351

1.005

PFL

VRC

PC

-2.682

30.78

ANM 0.9018

ANU

1 0 ANG

17.82 1.024

RNAUG 1

Macula densa

OUTPUTS: GFR- glomerular filtration rate [l/min] GFN- glomerular filtration rate if kidney is not damaged [l/min] GLP - glomerular pressure [torr] GLPC- average glomerular plasma colloid osmotic pressure [torr] PFL - net pressure gradient in glomerulus [torr]

REK

THE CONTROL FUNCTIONS OF ANGIOTENSIN NAPT1

1

2 2.929

0.1238 44.73 GLP

1.005

1 REK

ANXM

1.005

NAPT1

GFN

PGH

OUTPUTS: PAR - renal perfusion pressure [torr] RFN- renal blood flow if kidney is not damaged[l/min] RBF- renal blood flow [l/min] RR - renal resistance [torr min/l]

Efferent Arteriole Urea and Water Excretion

!IJ"1F &-GML & -&+.-,1& . - %-- 2 & .& & A ,& &&_ 7&%. X - & . w& &% X &_ .&- - '-%& . -'-('-&%. )5 .& +. )2 .--, ,+. &%2'8c+ - &2 ,& & . '-+. & .,-.>?@@.@)

41

1 Atrial pressure [mmHg ]

p(n) p(n)

left ventricle p - V diagram

p(n+2)

p(n+1)

p(n+1)

LEFT HEART

Q(n) Q(n) Q(n-1)

2 Left ventricular pressure

Q(n-1)

V

LEFT ATRIUM

p(n)

p(n)

p(n+1)

Q(n-1)

Q(n)

V

Q(n-1)

Q(n-1)

V Terminator 2

Q(n)

Q(n)

Q(n-1) V Terminator 3

V

V Terminator 4

RE a 2

RLE a 1

p(n) p(n+1)

p(n+1)

Q(n)

Q(n-1)

Scope 3

[ml ]

p(n)

p(n+1)

Q(n)

3 Left ventricular volume

LEFT VENTRICLE

p(n)

p(n+1)

[mmHg ]

V

Terminator

Terminator 6

Terminator 5

RE a3

RLE v 2

RE v1

SYSTEMIC CIRCUIT

p(n) p(n) p(n+2)

p(n+1)

p(n+1) Q(n)

RIGHT HEART

Q(n) Q(n-1)

V

Terminator 7 RIGHT ATRIUM

RIGHT VENTRICLE

p(n)

p(n) p(n+1)

Q(n)

V Terminator 12

Q(n-1) V

V

V Terminator 11

Terminator 9

Terminator 10

RE p 2

Q(n)

Q(n)

Q(n-1)

Q(n-1)

V

p(n) p(n+1)

Q(n)

Q(n-1)

RLE p 1

p(n) p(n+1)

p(n+1)

Q(n)

Right ventricle p - V diagram

p(n)

p(n+1)

Q(n-1)

Scope 4

Q(n-1)

V

Terminator 8

RE l 1

RE p 3

RLE l 2

PULMONARY CIRCUIT

1 p(n+2) systemic pressure [mmHg]

R

Pn+1

system resistance

1 p(n+1) next block pressure [mmHg]

2 p(n+1) atrial pressure [mmHg]

1 s Product

R

1 s

2 Q(n-1) inflow [ml/t]

L inductance

current volume

V

4 V current volume [ml]

Product 1

resistance

2 Qn outflow [ml/s]

1 s

3 V current volume [ml]

current volume

3 Q (n) outflow [ml/t]

Valve backflow condition

0

2 Q(n-1) inflow [ml/s]

-1

Integrator 1

phi (t)1

1 s

>= Vbmax Compare To Constant

Saturation >0

Memory

Compare To Zero

1 s L

V0

1 p(n) current pressure [mmHg]

E elastance

zero pressure volume

Pn

1 p(n)

RLE function block (according to Ottesen et al ., Applied Mathematical Models in Human Physiology ), 6th chapter , SIAM 2004

1 pi

sin

.9

2*pi

sin

.25

V0 zero pressure volume [ml ]

Elastance function Ev [phi (t)]

by O.Vacek, http ://patf -biokyb .lf1.cuni .cz Repeating Sequence

phi (t)

Ventricle function block (according to Ottesen et al ., Applied Mathematical Models in Human Physiology ), 6th chapter , SIAM 2004 by O.Vacek, http ://patf -biokyb .lf1.cuni .cz

Emin

Emax Emax

Product 3

!IL"<2 2.

&)(-% .5-c -- & &+2 .2,-.&cTx
&+ . & .A- L-.! 7!> !5y= ;WWI8 &,- !1-

*,.

$ * *'$* '$* #$ ! - *+* +#- $ @! , *# C! !-#( * -(+ *'$+ ', EIIIJG . -+ ** & * $/ \ '$

** + @! *# II ** $ -+ *# M R 2 * *(+ %, +. ! $* *'$ '! -* ' (* + , ( , E' !$+ -# G $# %,* ! $* $ #* #. / - #$ < % *,. *$

! C! I-$$ *'$+ ' E$# $ *#$ , , , '$* '$* ! * EILG )+ -* $# !.$ % *-

42

PercentVDi VA exp BTPS PercentQsh

A L V E Q - Alveolar Equilibrium Set of N Alveolar-Blood unit(s).

INPUTS: PercentVDi - Dead Space = how many percent of inspired air (VTi) is not participating in the blood gase exchange in the lungs [%] VTi BTPS PercentQsh - Shunts = how many percent of blood (QCO) is not participating in the blood gase exchange in the lungs [%] VTi BTPS - total insp. ventilation = alveolar ventil.+ death space [l BTPS/min] VAi distrib. - vector of VAi distribution relative weights[-] VAi distrib. FiO2 - fractional concentration of O2 in inspired gas [-] FiCO2 - fractional concentration of CO2 in inspired gas [-] QCO - minute cardiac output = perfusion of lungs + shunts [l/min] FiO2 Q distrib. - vector of Q distribution relative weights[-] CvO2 - O2 content in inflowing mixed venous blood[l/l] CvCO2 - CO2 content in inflowing mixed venous blood[l/l] BEox - Base excess in fully oxygenated blood [mmol/l] FiCO2 PB - Barometric pressure [torr] temp - body temperature [ôC] XHb - coefficients derived from blood hemoglobin concentration Number N - THE NUMBER OF ALVEOLAR UNITS QCO

Q distrib.

CvO2

CvCO2

BEox

PB

temp

XHb

OUTPUTS (all vectors) VAexp BTPS- (expired) alveolar ventilation [l BTPS/min] VAi BTPS - (inspired) alveolar ventilation [l BTPS/min] VDi BTPS - (inspired) dead space [l BTPS/mi] Qp - pulmonary perfusion [l/min] Qsh - right-to-left perfusion shunts [l/min] VO2 - rate of oxygen comsumption [l STPD/min] VCO2 - rate of carbon dioxide production [l BTPS/min] cepcO2 - O2 contents in end pulmonary capillary blood [l STPD/l] cepcCO2 - CO2 contents in end pulmonary capillary blood [l STPD/l] PAO2t - alveolar O2 partial pressures at body temperature [torr] PACO2t - alveolar CO2 partial pressures at body temperature [torr] sO2pct - saturations in end pulm. capilary blood at body temp. [-] pHpct - pH in end pulm.cap.blood at body temp.[-] HCO3pc - bicarbonate conc. in end pulm.cap.blood at body temp.[mmol/l] HCO3stpc - standard bicarbonat conc. in end pulm.cap.blood [mmol/l] BEpc - base excess in end pulm.cap.blood [mmol/l] cO2a - O2 content in mixed arterial blood [l/l] cCO2a - CO2 content in mixed arterial blood [l/l] pO2a - O2 partial press. in mixed arterial blod at body temp [torr] pCO2a - CO2 partial press. in mixed arterial blod at body temp [torr] SO2a - saturation in mixed arterial blod at body temp [-] pHa - pH in mixed arterial blod at body temp [-] HCO3a - bicarb. concentration in mixed arterial blod at body temp [mmol/l] HCO3st -standard bicarb. concentration in mixed arterial blod [mmol/l] BEa - Base Excess in mixed arterial blod at body temp [mmol/l]

VO2 VCO2 cepcO2 cepcCO2 pAO2t pACO2t sO2pct pHpct HCO3pc HCO3stpc BEpc Qp QSh VAi VDi cO2a cCO2a pO2a pCO2a sO2a pHa HCO3a HCO3sta BEa

Number N

ALVEQ

!IH"<2 2 ..-% - -+& $& 2 D -2& - 2 .2g=1Bn-.&cTx
43

cO2a pHt

17

XHb XH Hb

cO2 shunt mixing Mixing Concentrations MIXING Q[i] INPUTS : Q[i] - volumesCmix C[i] concentrations C[i] [i] OUTPUTS : Mixing Cmix C mix i - mixed miConcentrations xed d concen concentration concentrati concentrat t stiio ion on n MIXING Q[i] INPUTS TS S: Q[i] - vvolumes olume olum olu l es esCmix C[i]] - cconcentrations oncen once nt tions ntrat ntra ntr nt C[i] [i] OUTPUTS OUT OUTP TPUTS : TPU TP Cmix Cm C m mix iix x - mixed miixed mix d concentration t ti cCO2 cCO cC CO2 shunt mixing

cO2pc mixing1 Mixing Concentrations MIXING Q[i] INPUTS : Q[i] - volumes Cmix C[i] - concentrations C[i] [i] OUTPUTS : Mixing Cmix C i - mixed iConcentrations d concentration t ti MIXING Q[i] INPUTS : Q[i] - volumes Cmix C[i] - concentrations C[i] [i] OUTPUTS : Cmix C i -cO2pc mixed i d mixing4 concentration t ti

Blood Gases Tensions at Body Temperature ABINVT pCO2t

INPUTS : XHb - coefficients derived from hemoglobin concentration O2 - blood O2 content [l STPD/l] CO2 - blood CO2 content [l STPD/l BEox - Base Excess in fully oxygenated blood [mmol/l] temp - body temperature [ôC]

O2

CO2

BEox

18 cCO2a temp

20 pC CO2a CO pCO2a

pO2t

19 9 pO 2 2a pO2a

SO2t

21 2 sO2a sO a

HCO3

23 2 3 HCO3a HCO O3a

OUTPUTS : 9?27k %+- 9Z>;2) pH37 - pHt at body temperature

PCO2t - pCO2 [torr] at body temperature PO2t - pO2 [torr] at body temperature SO2t - oxyhemoglobin saturation at body temperature [expressed as ratio from 0 to 1] HCO3 - actual bicarbonate concentration [mmol/l] at body temperature HCO3st - standard bicarbonate concentration [mmol/l] BE - current value of blood Base Excess [mmol/l]

22 pHa

HCO3st

B BE

24 4 HCO3sta HCO3 3sta 25 5 BEa BEa

ABINVTemp at body temperature [mmol/l] ACBCB 7 BE

pH37

Hb

Blood Gases Tensions ABINV BE

INPUTS : XHb - coefficients derived from hemoglobin concentration O2 - blood O2 content [l STPD/l] CO2 - blood CO2 content [l STPD/l BEox - Base Excess in fully oxygenated blood [mmol/l]

2IN IN

pH37 37

TEMP37T

OUTPUTS : pH37 - pH at 37 ôC PCO237 - pCO2 [torr] at 37 ôC PO237 - pO2 [torr] at 37 ôC SO237 - O2 hemoglobin saturation at 37 ôC BE - blood Base Excess

O2IN

Eox ox

PCO23 7 PCO237

PCO237

PO237

9Z>;) %+- )7
PO237 SO237

SO237

OUTPUTS : plasm ma pH at body temperature pHt - plasma pCO2 [torr] at body temperature PCO2t - pCO2 PO2t - pO2 {torr] at body temperature

BEox

1

pHt

INPUTS : pH37 - plasma pH at 37 ôC PCO237 - pCO2 [torr] at 37 ôC PO237 - pO2 [torr] at 37 ôC SO237 - oxyhemoglobin saturation [expressed as ratio from 0 to 1] at 37ôC BEox - BE in fully oxygenated blood [mmol/l] temp - body temperature

pHt

2

pCO2t

pCO2

3

pO 2t pO2t

pO2

ABINV

tem p temp

TEMP37T PH37T

pH37

1 pH37

INPUTS : pH37 - plasma pH at 37 ôC BEox - BE in fully oxygenated blood temp - patient temperature

BEox

5 BEox

pHt

1 pHt

OUTPUT : pHt - plasma pH at body temperature

temp

PH37T

SO237

SAT37T PCO237T

PCO237 PC CO237

2 PCO237

INPUTS : PCO237 - pO2 [torr] at 37 ôC temp - body temperature

pCO2t

2

)7
6 temp

pCO2t

OUTPUT : PCO2t - pCO2 [torr] at body temperature

PO2t

PCO237T

XHb

3 PO237

PO237T

simulation chip: A B I N V T PO237 PO O237

SO SO237

4 SO237 SO237

temp te

INPUTS : PO237 - pO2 [torr] at 37 ôC SO237 - oxyhemoglobin saturation PO2t [expressed as ratio from 0 to 1] at 37ôC temp - body temperature

%?

SO237 37 - oxyhemoglobin saturation [expressed sssed as ratio form 0 to 1] at 37ôC O2 - blood O2 2 content [expressed in l CO2 STPD/l] PO2t - pO2 [torr] at body temperature Hb - coefficients derived from XHb entration of hemoglobin in blood concentration temp - body temperature

SO2t

4 S SO2

OUTPUT : OUTPUT bin saturation (expressed (exp pressed as ratio from 0 to 1) SO2t - oxyhemoglobin at body temperature

temp 3 pO2t

SATUR37T

OUTPUT : PO2t - pO2 {torr] at body temperature PO237T

I& & $I&

INPUTS :

O2

&!X!#!Y <

!"!&!!X#Y

bG <

<

# <&

><

bG <

><

I&

2 $ ('

$ L"R

!IM"T.-% 2 .2g=1Bn1 &+2 -+& $$ 4&

44

'$+ ', !. (+ *#! =%(* ** '$* #* - #.

# *. ++ #$ *'$+ ', EIHIMG -# +#I- *# *+ *&#$ * #+ #- .

! (+ *'$+ %, -(+ *#+

* #) DE#FGFAHIHE ! )$ ' -", ("' )+ 8*'$ '! - *. #

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) + ** - %+- . #-( i# + *# (+ ! *, ( %! ##* " " R.

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45

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46

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47

)

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48

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49

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51

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52

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53

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54

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55

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*# 8* - '/ * ! +! A[8>"?>ZQ9Q[ - - V B # # +c dd444+!*d*+ <# 8* * ++ \ . -# (+ (+ -(+ *(+ %, *$-$$+ '! L( *# - ( - -# ++! #( *( % E& LWG -+ V/B %-$ *# U -(* *(* %! -$ -# %! *, ELG A+ -# (+ %, -$ %! %! *# -* & %!! * ! ! 2 * .#+ % - ! (*! + $+ ( $+ *(+ !$+ -# +. - !-#! --+ +# ! -$ -# (+ %, - * - ! & - *# .! $ * *& +! - ! ! -(+ %, * +,* - *. Simulation time

SIMTIME ZUR XURE YURU ZMNE XMNE YMNU VA GFR ALD ADH THDF STPG YTA YTA1 PHU YNH4 YCO3 YCO3R PICO XPIF ZPIF ZPP XPP PPCO ZPO4E XPO4 YPO4 ZSO4E XSO4 YSO4 ZORGE XORGE YORG OSMP UCO2V UO2V PCO2A FCO2A PO2A FO2A YNU YNH YND XNE ZNE YNHI YKHI ZKI ZKE YKU YKD XKE PIF QLF QWD QWU OSMU ZCLE XCLE YCLU QCO PAP PAS PC PVS PVP ZCAE XCAE YCA ZMGE XMGE YMG HB HT VB VP VEC VIF VTW VIC YINT YGLS YKGLI ZGLE XGLE YGLU A STBC BE AH PHA SO2A XCO3 UCO2A UO2A BEOX BEEC

TBEOX YCO3IN YHIN MRH ZBEEC0 BEOX0 TYINT XGL0 CGL1 CGL2 YINS CGL3 YGLI YINT0 ZGLE0 QIN QVIN QIWL QMWP CFC CSM VRBC XHBER VIN0 VP0 VIF0 VIC0 YCAI YMGI ZCAE0 ZMGE0 RTOT RTOP KL KR DEN KRAN YCLI ZCLE0 QLF0 CPR YNIN CBFI CHEI ZKI0 CKEI YKIN ZNE0 ZKE0 ZHI0 MRCO2 MRO2 PBA FCO2I VAL FO2I UCO2V0 UO2V0 FCO2A0 FO2A0 YPO4I YSO4I YORGI ZPO4E0 ZSO4E0 ZORGE0 YPLIN ZPG0 ZPIF0 ZPP0 ZPLG0 TPHA1 YTA0 TPHU2 TPHU1 YNH40 PHA0 PHU20 PHU10 VA0 YURI YMNI ZUR0 ZMNE0

1 SIMTIME

TBEOX

1

TBEOX 2

(=8.0)

YCO3IN

<XURE>

3 YHIN

YHIN

(=0)

4

MRH <XMNE>

MRH (=0.0405)

6

(=0)

BEOX0

7 TYINT 8 XGL0

9 CGL1

10 CGL2

TYINT

11 YINS 12 CGL3

7 YMNU 8 VA

(=15) XGL0

(=108)

CGL1

9 GFR 10 ALD

(=1)

CGL2

11 ADH

(=1)

5 ZMNE 6

(=0)

BEOX0

3

4 YURU

XMNE

ZBEEC0

5 ZBEEC0

2 ZUR

XURE

YCO3IN (=0)

YINS

12 THDF

(=0) CGL3 <STPG>

(=0.03)

13 STPG

13 YGLI

14 YINT0

15

YGLI

(=0)

17 QVIN

18

(=0) ZGLE0

(=66)

ZGLE0

YINT0

QVIN

(=0.01)

QIWL

QIWL (=5e-4)

19

20 CFC

PHU 17 YNH4 18 YCO3 19 YCO3R 20 PICO

QMWP

(=5e-4)

QMWP

14 YTA 15 YTA1 16

<XPIF>

CFC

(=0.007)

21 XPIF 22 ZPIF

21 CSM

CSM

(=3e-4)

23 ZPP

22 VRBC

VRBC

<XPP>

(=1.8)

23 XHBER

XHBER

(=33.34)

24 XPP 25 PPCO 26 ZPO4E

24 VIN0

<XPO4>

VIN0

(=0.01)

25 VP0

26 VIF0

27 VIC0

28 YCAI

29 YMGI

VP0 <XSO4>

(=8.8) VIC0

(=20)

30

(=0.007) YMGI

ZORGE 33

ZMGE0

32 RTOT 33

RTOT

34 KL

35 KR

UO2V 38

36

KL

KR

(=0.3)

KRAN

<XNE>

37 KRAN (=5.93)

38 YCLI

39 ZCLE0

40 QLF0

41 CPR

42 YNIN

43

CBFI 44 CHEI

45

ZKI0

46 CKEI

YCLI

(=0.1531)

ZCLE0

(=1144) QLF0

(=0.002) CPR

(=0.2) YNIN

(=0.106) CBFI

(=1e-9) CHEI

<XKE>

(=5) ZKI0

(=2800) CKEI

(=0.001)

47

YKIN 48

ZNE0

49 ZKE0

YKIN

(=0.047) ZNE0

<XCLE>

(=1540)

41 FO2A 42 YNU 43

44 YND 45 XNE 46 ZNE 47 YNHI 48 YKHI 49 ZKI 50 ZKE 51 YKU 52 YKD 53 XKE 54 PIF 55 QLF 56 QWD 57 QWU 58 OSMU 59 ZCLE 60

XCLE 61

YCLU 62

ZKE0

(=49.5)

FCO2A 40 PO2A

YNH

DEN(=1)

DEN

36 UCO2V 37

PCO2A 39

(=0.2)

35 OSMP

XORGE 34 YORG

(=20) RTOP

RTOP (=3)

31

<XORGE>

(=0.008)

31 ZMGE0 (=33)

30 XSO4

YSO4 32

ZCAE0

(=55)

29 ZSO4E

YCAI

ZCAE0

28 YPO4

(=2.2)

VIF0

27 XPO4

QCO 50 ZHI0

ZHI0

(=100)

MRCO2

51 MRCO2 (=0.2318)

52 MRO2

53 PBA

MRO2

(=0.2591) PBA

(=760)

55 VAL

56 FO2I

FCO2I

(=3)

XMGE 73 YMG

UO2V0

(=0.155)

FCO2A0

59 FCO2A0 (=0.0561)

60 FO2A0

FO2A0

(=0.1473)

61

YPO4I

62 YSO4I

63 YORGI

64 ZPO4E0

65 ZSO4E0

66

ZORGE0 67 YPLIN

68 ZPG0

YPO4I

(=0.05) YSO4I

(=0.04) YORGI

(=0.01) ZPO4E0

(=24.2) ZSO4E0

69 ZPIF0 70 ZPP0

(=0)

71

ZPLG0 72 TPHA1

73 YTA0

74 TPHU2

ZPLG0

(=70)

<SO2A>

TPHA1

(=200) YTA0

<XCO3>

(=0.0068) TPHU2

(=20)

75 TPHU1

76 YNH40

77

PHA0 78 PHU20

79 PHU10

80 VA0

TPHU1

YGLU 88 A 89 STBC 90 BE 91 AH 92 PHA 93 SO2A 94 XCO3 95 UCO2A 96 UO2A 97 BEOX

(=300) YNH40

81 VIC 82

83 YGLS 84 YKGLI 85

XGLE 87

ZPP0

(=154)

79 VIF

(=20) ZPIF0

(=176)

VB 77 VP 78 VEC

80 VTW

ZGLE 86

YPLIN

ZPG0

HT 76

<XGLE>

(=66.0)

<STBC>

74 HB 75

YINT

(=22) ZORGE0

71

(=0.21)

58 UO2V0

69

ZMGE 72

UCO2V0

68

70 YCA

<XMGE>

57 (=0.52) UCO2V0

PC 66

67 PVP

XCAE

(=0.0003)

VAL

FO2I

64 PAS 65

ZCAE <XCAE>

54 FCO2I

63 PAP

PVS

98 BEEC

(=0.024) PHA0

(=7.4) PHU20

(=6) PHU10

(=6) VA0

(=5) YURI

81 YURI (=0.15) YMNI 82 (=0) YMNI ZUR0 83 (=77.5) ZUR0

GOLEM

ZMNE0

84 ZMNE0 (=0) 16 QIN

QIN

(=0.001)

!LW"A '-+ - +- F &- ..-+-&+- - +20& %-.&cTx?@@999 .@.8<& - - -+2

56

XHB TBEox

BEOX

ACID BASE METABOLIC BALANCE

A

9L>= Z987 <7)9Z"?>L Z9?9;L7

VEC

yTA

yNH4

yCO3

yKHi

yNHi

Z?""= 9L>= Z987 Z9?9;L7

yHin

HB

BEOX

BE

U(E) U

A

AH

UO2A

yINT <XGL0>

BE

Z?""= @?L"87 L";)Q"?

CGL2

yINS

SO2A

XCO3 UCO2A

UO2A

CGL3

BEEC

BEEC

yKGLI

vEC

GFR

zGLE

xGLE

21.8.2001

yGLU

YGLS

YKGLI

ZGLE

XGLE

YINT 0

Scope2

ZBEEC 0

ZGLE 0

YGLU

Blood Glucose Control

BEOX 0

yGLS

OUTPUTS: yINT - insulin secretion [unit/min] yGLS - glucose flow rate from ECF into cells [mEq/min] yKGLI - K flow rate from ECF to ICF accompanying secretion of insulin [mEq/min] zGLE - ECF glucose content [mEq] xGLE - ECF glucose concentration [mEq] yGLU - renal excretion rate of glucose [mEq/min]

yGLI

Blood Acid Base Balance

YINT

BLOOD GLUCOSE CONTROL INPUTS: TYINT - time constant of insulin secretion xGL0 - reference value of ECF glucose concentration CGL1 - parameter of glucose metabolism CGL2 - parameter of glucose metabolism yINS - intake rate of insulin[unit/min] CGL3 - parameter of glucose metabolism yGLI - intake rate of glucose [g/min] vEC - ECF volume [l] GFR - glomerular filtration rate [l/min]

CGL1

PHA

xGL0

AH

MRH

<MRH>

TYINT

Selector STBC

OUTPUTS: PHA XHB - Vector of coefficients derived from hemoglobin concentration STBC - Standard bicarbonate concentration [mmol/l] BE - Base Excess concentration in arterial blood SO2A AH - Hydrogen ions concentration [nmol/l] PHA - arterial plasma pH XCO3A SO2A - Oxygen hemoglobin saturation in arterial blood (expressed as ratio from 0 to 1) XCO3 - Actual bicarbonate concentration in arterial blood UCO2A - Content of CO2 in arterial blood [l STPD/l] UCO2A UO2A-Content of O2 in arterial blood [l STPD/l] PO2A PCO2A

OUTPUTS: BEox (** Base excess in fully oxygenated blood [mEq/l]*) BEEC (*ECF Base excess concentration

yCO3in

BEox

INPUTS: TBEOX - (*Time constant*) VB (*Blood Volume [l]*) HB (fore XHB) (*Blood hemoglobin concentration [g/100 ml]*) A [11] - (* vector of coeficients, see "Blood Acid Base Balance" *) pCO2A (*CO2 tension in arterial blood [Torr]*) VEC (*Extracelular fluid volume [l]*) yTA (*Renal excretion rate of titratable acid [mEq/min]*) yNH4 (*Renal excretion rate of ammonium [mEq/min]*) yCO3 (*Renal excretion rate of bicarbonate [mEq/min]*) yKHi (*Potassium ions flow rate from ECF into ICF exchanged with hydrogen ions [mEq/min]*) yNHi (*Hydrogen ions flow rate from ECF into ICF exchanged with sodium ions [mEq/min]*)

pCO2A

STBC

INPUTS: BEOX - Base Excess in fully oxygenated blood [mmol/l] HB - Hemoglobin concentration [g/dl] PCO2A - CO2 tension in arterial blood [torr] PO2A - Oxygen tension in arterial blood [torr]

HB

XHB

BLOOD ACID BASE BALANCE

VB

Scope Acid Base Metabolic Balance1 Acid base metabolic balance

Scope1

Blood acid base balance

Scope3

Blood glucose control

qIN

HB

qVIN

HB

vEC

zCaE

ZCAE

VB

QCO

QCO

qIWL

CALCIUM AND MAGNESIUM BALANCE

BODY FLUID VOLUME BALANCE qMWP

qWU

qLF

CFC

pICO

pPCO

pC

pIF

CSM

xNE

<XNE>

xKE

<XKE>

INPUTS: qIN - drinking rate [l/min] qVIN - intravenous water input [l/min] qIWL - insensible water loss [l/min] qMWP - metabolic water production [l/min] qWU - urine output [l/min] qLF - lymph flow rate [l/min] CFC - capillary filtration coefficient [l/min/torr] pICO - interstitial colloid osmotic pressure [torr] pPCO - plasma colloid osmotic pressure [torr] pC - capillary pressure [torr] pIF - interstitial pressure [torr] CSM - transfer coeff. of water from ECF to ICF xNE - ECF Na concentration [mEq/l] xKE - ECF K concentration [mEq/l] xGLE - ECF glucose conc. [mEq/l] zKI - ICF K content [mEq] vRBC - volume of red blood cells [l] xHBER - hemoglobin concentration in the red blood cells [g/100 ml]

Z"=[ O?>= 2"?<7 Z9?9;L7

zKI

vRBC

xHBER

<XHBER>

vB

VB

vP

VP

yCaI

xCaE

INPUTS: vEC - ECF volume [l] yCaI - calcium intake [mEq/min] yMgI -magnesium intake [mEq/min] GFR - glomerular filtration rate [l/min]

XCAE

L9?L>< 9;= <9@;78>< Z9?9;L7 GFR

yCa

OUTPUTS: zCaE - ECF calcium content [mEq] xCaE - ECF calcium contentration [mEq/l] yCa - calcium renal excretion rate [mEq/min] zMgE - ECF magnesium content [mEq] xMgE - ECF magnesium contentration [mEq/l] yMg - magnesium renal excretion rate [mEq/min]

yMgI

zMgE

INITIAL CONDITIONS: zCaE0 - ECF calcium content [mEq] zMgE0 - ECF magnesium content [mEq]

zCaE0

xMgE

zMgE0

yMg

VIF

L9Q=>"298L?9Q Z?"L

RTOP

KL

XMGE

YMG

PAS

OUTPUTS: QCO - Cardiac output [l/min] PAP - Pulmonary arterial pressure [torr] PAS - Systemic arterial pressure [torr] pC - Capillary pressure [Torr] PVS - Central venous pressure [torr] PVP - Pulmonary venous pressure [torr]

KR

PAP

INPUTS: VB - Blood volume [l] RTOT - Total resistance in systemic circulation [Torr * Min / l] (norm.=20) RTOP - Total resistance in pulmonary circulation [Torr * Min /l] (norm. =3) KL - Parameter of the left heart performance [l/min/torr] (norm.=0.2) KR - Parameter of the right heart performance [l/min/torr] (norm.=0.3) DEN - Proportional constant between QCO AND VB [1/min] (norm.=1) KRAN - Parameter of capillary pressure (norm.=5.93)

ZMGE

vTW

CARDIOVASCULAR BLOCK

RTOT

YCA

30.7.2001

VEC

vIF

24.8.2001

VIN 0

HT

vEC

OUTPUTS: HB - blood hemoglobin concentration [g/100 ml] HT - hematocrit vB - blood volume [l] vP -plasma volume [l] vEC - ECF volume [l] vIF - interstitial fluid volume [l] vTW - total body fluid volume [l] vIC - ICF volume [l]

xGLE

<XGLE>

HT

DEN

pC

PVS

24.8.2001 edited by Tom Kripner

KRAN

PVP

Calcium and Magnesium Balance

PAP

PAS

PC

PVS

PVP

Cardiovascular Block

VTW

VP 0

VIF 0

Scope5

vIC

Scope4

VIC

VIC 0

Body Fluid Volume Balance Scope6

Body fluid volume balance Calcium and magnesium balance

Cardiovascular block

vEC

>;)7Q8)>)>9? Q788Q7 9;= ?[
ADH

DIURESIS AND URINE OSMOLARITY

yCLI zCLE

CHLORIDE BALANCE

INPUTS: vEC - ECF volume [l] yCLI - chloride intake [mEq/min] yKU yNU - Na renal excretion rate [mEq/min] yKU - K renal excretion rate [mEq/min] yNH4 - ammonium renal excretion rate [mEq/min] yNH4 yCa - calcium renal excretion rate [mEq/min] yMg - magnesium renal excretion rate [mEq/min] xCLE yCa ySO4 - sulphate renal excretion rate [mEq/min] yCO3 - bicarbonate excretion rate [mEq/min] STPG - summary renal excretion rate of phosphates and org. acids yMg related to arterial pH [mEq/min]

LA?"Q>=7 Z9?9;L7

yKD

yGLU

XCLE

yURU

yMNU

=>Q78>8 9;= Q>;7 Z9?9;L7

qWU

VIF0

QWD

yKU

yCLU

YCLU

PIF

PIF

OUTPUTS: pIF - interstitial pressure [torr] qLF - lymph flow rate [l/min]

QWU

QLF

OUTPUTS: qWD - rate of urinary excretion in distal tubule [l/min] qWU - urine output [l/min] OSMU - urine osmolality [mOsm/l]

Scope7

STPG

INTERSTITIAL PRESSURE AND LYMPH FLOW RATE

INPUTS: vIF0 - normal interstitial fluid volume [l] vIF - interstitial fluid volume [l] qLF - normal lymph flow rate [l/min]

VIF

16.8.2001

QLF0

QLF

Interstitial Pressure and Lymph Flow Rate

17.8.2001

yNU

yCO3

30.7.2001 <STPG>

INPUTS: ADH - effect of antidiuretic hormone [x normal] OSMP - plasma osmolality [mOsm/l] yND - sodium excretion rate in distal tubule [mEq/min] yKD - potassium excretion rate in distal tubule [mEq/min] yGLU - renal excretion rate of glucose [mEq/min] yURU - renal excretion rate of urea [mEq/min] yMNU - renal excretion rate of mannitol [mEq/min] yNU - sodium renal excretion rate [mEq/min] yKU - potassium renal excretion rate [mEq/min]

yND

OUTPUTS: zCLE - ECF chloride content [mEq] xCLE - ECF chloride concentration [mEq/l] yCLU - chloride renal excretion rate [mEq/min]

ySO4

qWD

OSMP

ZCLE

yNU

OSMU

OSMU

Diuresis and Urine Osmolarity

ZCLE 0

Chloride Balance

Scope8 Scope9 Diuresis and urine osmolarity

Interstitial pressure and lymph flow rate

mrCO2

<MRCO2>

uCO2A

yTA1

yNU

8"=>< 9;= ")988>< Z9?9;L7

CHEI

yNH

xNE

zKI0 CKEI yKIN vEC ZNE 0 ZKE 0

YND

QCO

PBA

XNE

ZNE

VAL

VA

YNHI

fO2i

yKHI

YKHI

zKI

zKE

yKU

yKD

ZKI

ZKE

<XMNE> UCO2V <XURE>

uO2V

"R 9;= L"R 7}LA9;@7

fCO2i

zNE

yNHI

OUTPUTS: yNU - Na renal excretion rate [mEq/min] yNH - Na excretion in Henle loop [mEq/min] yND - Na excretion rate in distal tubule [mEq/min] xNE - ECF Na concentration [mEq/l] zNE - ECF Na content[mEq] yNHI - H ions flow rate from ECF to ICF (exchanged w. Na) [mEq/min] yKHI - K flow rate from ECF to ICF (exchanged w. H) [mEq/min] zKI - ICF K content [mEq] zKE - ECF K content [mEq] yKU - K renal excretion rate [mEq/min] yKD - K excretion rate in distal tubule [mEq/min] xKE - ECF K concentration [mEq/l]

yKGLI

uO2A

yND

INPUTS: mrCO2 - (*Metabolic production rate of CO2 [l STPD/min]*) uCO2A (*Content of CO2 in arterial blood [l STPD/l]*) VTW (*Total body fluid volume [l]*) mrO2 - (*Metabolic consumption rate of O2 [l STPD/min]*) uO2A (*Content of CO2 in arterial blood [l STPD/l]*) QCO (*Cardiac output [l/min]*) PBA - (*Barometric pressure*) fCO2i - (*Volume fraction of CO2 in dry inspired gas*) VAL - (*Total alveolar volume (BTPS)*) VA (*Alveolar ventilation [l BTPS/min]*) fO2i - (*Volume fraction of O2 in dry inspired gas*)

mrO2

<MRO2>

YNH

uCO2V

O2 and CO2 EXCHANGE VTW

INPUTS: yTA1 - Arterial pH dependent portion of titrable acid excretion rate yNH4 - ammonium renal excretion rate [mEq/min] ALD yCO3R - bicarbonate reabsorption rate [mEq/min] ALD - aldostrone effect [x normal] GFR GFR - glomerular filtration rate [l/min] CPR - excretion ratio of filterd load after proximal tubule CPR THDF - effect of 3rd factor (natriuretic horm.) [x normal] yNIN - sodium intake [mEq/min] THDF PHA - Arterial blood pH CBFI - Parameter of intracellular buffer capacity yNIN CHEI - Transfer coeff. of H ions from ECF to ICF yKGLI - K flow rate from ECF to ICF accompanying secretion of insulin [mEq/min] PHA zKI0 - normal ICF K content [mEq] CKEI - Transfer coeff. of K ions from ECF into ICF (exchanged with H ions) yKIN - K intake [mEq/min] CBFI vEC - ECF volume [l] yCO3

YNU

SODIUM AND POTASSIUM BALANCE

yNH4

pCO2A

fCO2A

OUTPUTS: (** Content of CO2 in venous blood [l STPD/l]*) (** Content of O2 in venous blood [l STPD / l*) pCO2A (*CO2 tension alveoli [Torr]*) fCO2A (*Volume fraction of CO2 in dry alveoli gas*) pO2A (*O2 tension in alveoli [Torr]*) fO2A (*Volume fraction of O2 in dry alveoli gas*)

UO2V

xMNE

?98<9 "8<"?9Q>)[ PLASMA OSMOLARITY

xURE

xGLE

<XGLE>

xNE

<XNE> PCO2A

INPUTS : XMNE - ECF mannitol concentration [mmol/l] XURE - ECF urea concentration [mmol/l XGLE - ECF glucose concentration [mmol/l] XNE - ECF sodium concentration [mmol/l] XKE - ECF potassium concentration [mmol/l]

OSMP

OSMP

OUTPUT : OSMP - plasma osmolarity

xKE

<XKE>

Plasma osmolarity calculation

FCO2A

uCO2V uO2V -

UCO2V 0

pO2A

PO2A

UO2V 0

8.10.2001 fO2A

FCO2A 0

FO2A

FO2A 0

O2 and CO2 Exchange

YKU

YKD

27.7.2001 xKE

ZHI 0

XKE

Scope12 Na & K Balance Scope11

Sodium and potassium balance

Scope10 O2 and CO2 exchange Plasma osmolarity

zPO4E

vEC

ZPO4E

A"8A9)7 9;= "Q@9;>L 9L>=8 Z9?9;L7 PHOSPHATE, SULPHATE AND ORGANIC ACIDS BALANCE

xPO4

yPO4I

INPUTS: vEC - ECF volume [l] yPO4I - phosphate intake [mEq/min] ySO4I - sulphate intake [mEq/min] yORGI - organic acids intake [mEq/min] GFR - Glomerular filtration rate [l/min]

ySO4I

yORGI

GFR

ZPO4E 0

OUTPUTS: zPO4E - ECF phosphate content [mEq] xPO4 - ECF phosphate contentration [mEq/l] yPO4 - Phosphate renal excretion rate [mEq/min] zSO4E - ECF sulphate content [mEq] xSO4 - ECF sulphate contentration [mEq/l] ySO4 - sulphate renal excretion rate [mEq/min] zORGE - ECF organic acids content [mEq] xORGE - ECF organic acids contentration [mEq/l] yORG - organic acids renal excretion rate [mEq/min]

ZSO4E 0

30.7.2001

ZORGE 0

yPO4

zSO4E

xSO4

ySO4

zORGE

xORGE

yORG

pICO

vIF

STPG

XSO4

pC YPLIN vP ZPG 0 ZPIF 0

YSO4

ZPP 0

INPUTS: vIF interstitial fluid volume [l] qLF - lymph flow rate [l/min] pC - capillary pressure [torr] YPLIN - rate of intravenous plasma protein input [g/min] vP -plasma volume [l]

Q")7>; Z9?9;L7 OUTPUTS: pICO - interstitial colloid osmotic pressure [torr] xPIF - interstitial protein concentration [g/l] zPIF - interstitial protein content[g] zPP - plasma protein content [g] xPP - plasma protein concentration [g/l] pPCO - plasma colloid osmotic pressure [torr]

xPIF

XPIF

zPIF

ZPIF

zPP

ZPP

xPP

XPP

10.7.2001

ZORGE

STPG

PHA

qLF

YPO4

ZSO4E

TPHA1

PICO

PROTEIN BALANCE

XPO4

ZPLG 0

pPCO

PPCO

Protein Balance

XORGE

YORG

Phosphate, Sulphate and Organic Acids Balance

ano XCO3

<XCO3>

yORG

RENAL ACID BASE CONTROL yPO4

Q7;9? 9L>= Z987 L";)Q"?

INPUTS: TPHA1 - Time constant of titratable acid [1/min] PHA - arterial pH yORG - Renal excretion rate of organic acid [mEq/min] yPO4 - Renal excretion rate of phosphate [mEq/min] yTA0 - Normal value of renal excretion rate of titratable acid [mmol/min] ALD - Aldosterone effect [x normal] TPHU1 - Time constant of ammonium secretion [1/min] TPHU2 - Time constant of titratable acids secretion [1/min] yNH40 - Normal value of ammonium renal excretion rate [mmol/min] TPHU1 qWU - Urine output [l/min] pCO2A - Alveolar pCO2 [torr] GFR - Glomerular filtration rate [l/min] yNH40 xCO3 - Actual bicarbonate concentration [mmol/l] yTA0 ALD

TPHU2

yTA

yTA1

PHU

YTA

YTA1

PHU

qWU OUTPUT VARIABLES: STPG - summary renal excretion rate of titratable acids, phosphate and org. acids [mmol/mi yNH4 yTA - renal excretion rate of titratable acids [mmol/min] pCO2A YNH4 yTA1 - on arterial pH dependent portion of titratable acid secretion rate [mmol/min] PHU - urine pH GFR YNH4 - Ammonium renal excretion rate [mmol/min] YCO3 - Bicarbonate excretion rate [mmol/min] YCO3R - Bicarbonate reabsorption rate [mmol/min] xCO3 yCO3

YCO3

24.7.2001

PHA 0 PHU2 0 yCO3R

Phosphate sulphate and organic acids balance Protein balance

vEC

CONTROLLER OF RENAL FUNCTION

<XKE>

GFR

L";)Q"??7Q "O Q7;9? O;L)>"; pAS

xKE

yNH

pVP

INPUTS: vEC - ECF volume [l] pAS - systemic arterial pressure [torr] xKE - ECF K concentration [mEq/l] yNH - Na excretion in Henle loop [mEq/min] pVP - pulmonary venous pressure [torr] OSMP - plasma osmolality [mOsm/l] pPCO - plasma colloid osmotic pressure [torr]

ALD

HIDDEN CONSTANTS: vEC0 - normal ECF volume [l] GFR0 - normal glomerular filtration rate [l/min] ___

VA0

ALD

RESPIRATION CONTROL

Q78>Q9)>"; L";)Q"?

pO2A

pCO2A

pHA

INPUTS: VA0 - normal value of alveolar ventilation [l BTPS/min] pO2A - O2 partial pressure in alveoli [Torr] pCO2A - CO2 partial pressure in alveoli Torr] pHA - arterial blood pH AH - concentration of hydrogen ions in arterial blood [nM/l]

VA

vTW

yURI

VA

OUTPUTS: VA - alveolar ventilation [l BTPS/min]

GFR

4.10.2001

AH

yMNI

Respiration Control

ADH

Scope15

YCO3R

vEC

zUR

ZUR

UREA AND MANNITOL BALANCE xURE

Q79 9;= <9;>)"? Z9?9;L7 INPUTS: vTW - total body fluid volume [l] yURI - intake rate of urea [mEq/min] GFR - glomerular filtration rate [l/min] yMNI - intake rate of mannitol [mEq/min] vEC - ECF volume [l]

OUTPUTS: zUR - total body-fluid urea content [mEq] xURE - ECF urea concentration [mEq/l] yURU - renal excretion rate of urea [mEq/min] zMNE - ECF mannitol content [mEq] xMNE - ECF mannitol concentration [mEq] yMNU - renal excretion rate of mannitol [mEq/min]

yURU

XURE

YURU Urea and mannitol balance

zMNE

ZMNE

21.8.2001

xMNE

OSMP

ZUR 0

17.8.2001 THDF

Renal Acid Base Control

GFR

OUTPUTS: GFR - glomerular filtration rate [l/min] ALD - aldosterone effect [x normal] ADH - effect of antidiuretic hormone [x normal] THDF - effect of 3rd factor (natriuretic horm.) [x normal]

ADH

Scope14

Scope13

PHU1 0

THDF

pPCO

ZMNE 0

yMNU

XMNE

YMNU

Urea and Mannitol Balance Controller of Renal Function

Scope16

Scope17 Scope18

Respiration control Controller of renal function Renal acid base control

Chloride balance

INPUTS

!L"1 - -&%. - . F - M -, &+.5)-+. %, .$& &+ 21 - -N=!!agCaNg
57

XHB

BEOX

XHB

BLOOD ACID BASE BALANCE STBC


HB

A

U(E) U Selector

STBC

BE

BE

AH

AH

OUTPUTS: PHA XHB - Vector of coefficients derived from hemoglobin concentration STBC - Standard bicarbonate concentration [mmol/l] BE - Base Excess concentration in arterial blood SO2A PCO2A AH - Hydrogen ions concentration [nmol/l] PHA - arterial plasma pH XCO3A SO2A - Oxygen hemoglobin saturation in arterial blood (expressed as ratio from 0 to 1) XCO3 - Actual bicarbonate concentration in arterial blood UCO2A - Content of CO2 in arterial blood [l STPD/l] UCO2A UO2A-Content of O2 in arterial blood [l STPD/l] PO2A

PHA SO2A XCO3 UCO2A

UO2A

UO2A


1 XHB

Hemoglobin Coefficients ABCNST 2 HB

Blood hemoglobin concentration

Hb

Standard Bicarbonate Concentration STBCB

XHb

INPUT : Hb - blood hemoglobin concentration [g/dl]

INPUTS : STBC XHb - coefficients derived from hemoglobin concentration BE -blood Base Excess [mmol/l]

XHb

OUTPUTS : XHb - coefficients derived from hemoglobin concentration

2 STBC

HCO3st

BE

OUTPUT : HCO3st - standard bicarbonate concentration [mmol/l]

c[1]..c[10] a[1]..a[11]

5 PHA

ST BCB pH From Base Excess BEINV

XHb

ABCNST

pH37 INPUTS : XHb - coefficients derived from concentration of hemoglobin in blood BEox - Base Excess in fully oxygenated blood [mmol/l] SO237 - oxyhemoglobin saturation [expressed as ratio form 0 to 1] SO237 PCO237 - pCO2 [torr] in blood at 37 °C

PHA PHA

Actual Bicarbonate Concentration ACBCB

pHt

BEox

1 BEOX SO2A Memory PCO2A

PCO237

OUTPUTS : pH37 - plasma pH at standard temperature (37 °C) BE- current value of blood Base Excess [mmol/l]

PCO2A

INPUTS : pHt - plasma pH at patient temperature PCO2t - PCO2 [torr] at body temperature temp - body temperature [°C]

PCO2t

Fcn

4 AH 7 XCO3A

XCO3A

OUTPUT : HCO3 - actual bicarbonate concentration at body temperature

BE

37

10^(9-u);

HCO3

temp

Constant AC BCB

pH From BE

SO2A

3 BE CO2 Blood Content CARB

XHb

PCO2A

INPUTS : XHb - coefficients derived from conentration of hemoglobin in blood PCO237 - pCO2 [torr] in blood at 37 °C SO237 - oxyhemoglobin saturation [expressed as ratio form 0 to 1] pH37 - pH of plasma at 37 °C

PCO237

PHA

SO2A PO2A

4 PO2A PO2A

PO237

pH37

3 PCO2A PCO2A

pCO237

Oxyhemoglobin Saturation SATUR INPUTS : PO237 - pO2 [torr] in blood at 37 °C PCO237 - pCO2 [torr] in blood at 37 °C pH37 - pH of plasma at 37 °C

PHA

SO237

SO2A

SO237

CO2

8 UCO2A

OUTPUT : CO2 - blood CO2 content [expressed in l CO2 STPD/l ]

pH37

SO2A

CARB

PCO2A

OUTPUT : SO237 - oxyhemoglobin saturation (expressed as ratio form 0 to 1)

SO2A

SO2A

SO2A

6 SO2A

SATUR XHb

SO2A

SO2A

PO2A

SO237

PO237

O2 Blood Content OXY INPUTS : XHb - coefficient derived from concentration of hemoglobin in blood SO237 - oxyhemoglobin saturation 37 °C (expressed as ratio form 0 to 1) PO237 - pO2 (torr) in blood at 37 °C

O2

9 UO2A

OUTPUT : O2 - blood O2 content [expressed in l CO2 STPD)/l ] OXY

SIMULATION CHIP: BLOOD ACID BASE BALANCE

u[1] CO2 - part1 ( u[2]*u[26] + u[3] ) / (u[26]*u[26])

1

CO2 - part2

XHb

u[4]*u[25]/u[26] 2

CO2 - part3

PCO237 u[5]* ( 1-u[24] ) / ( (u[26]/u[25])^2 + u[26]*u[6] / u[25] + u[7] * u[23] ) [7.0388002E-3 3.6447450E-4 7.9099077 -2.0113444E-1 -1.4790526 ]

CO2 - part4

X0 ... X4

u[8]* u[24] / ( (u[26]/u[25])^2 + u[26]*u[9] / u[25] + u[10] * u[23] ) CO2 - part5

3 SO237

4

SO2 >= 10^ -13

f(u)

1 CO2

D

0.02226 X0=7.0388002E-3 ; X1=3.6447450E-4 ; X2=7.9099077 ; X3=-2.0113444E-1 ; X4=-1.4790526 ; % if SO237==0 % SO237=1E-13; % end;

D=X0*(SO237^X1)*(pH37^X2) *exp(X3*SO237+X4*pH37);

pH37

10^( 9 - u )

AH

AH=10^(9-pH37);

CO2=

Const

D=X0*(SO237^X1)*(pH37^X2)*exp(X3*SO237+X4*pH37); AH=10^(9-pH37);

SIMULATION CHIP: CARB

CO2 = 0.02226*PCO237*(XHb(1)+(XHb(2)*AH+XHb(3))/(AH*AH)+XHb(4)*D/AH ... +XHb(5)*(1-SO237)/((AH/D)^2+AH*XHb(6)/D+XHb(7)*PCO237) ... +XHb(8)*SO237 /((AH/D)^2+AH*XHb(9)/D+XHb(10)*PCO237));

!L;"+ - + & F & & ..- +. & +.-&+.-,K. %&'& &+5)-+ %< - -&%2

& '-%& . & & $ ..-%4&#- -& -N=!!agCaNg
-&- X.2 %.&-& $.& 2

-

58

#

(* V$*B ++! (+ *(+ %, ) -+% $ P %$ * '$ $ $ -$$ $ * *& (' ! # *# EL;G L( *# +! %! - I '/ * +! A[8>"?>ZQ9Q[ 1# %! #-$ !.$

* -(+ *#+ 8. -* %! *# %! *#* -$$ -$* #C(+ , % #$* ,%+ ( , .#* * ! .* % +! *,. ! *

#

-+ +$ 2 - #$ % - *#( %! * #%- ' $ (+ * *&(+ +, E JWG A $" = " " = ! ACT>9U>'L<= W0

*:>#) / 8* * ++! #+ *+ % - +#(* -* #% * # $* . +! * ! $ (+ * ( *#, * % '$ 8*'$ - C*! < +4 - &. '! ! %.+ . ( + *'$* *#* - V+ B $ +#$ > #!. #$ + -, - *. *

* $-* . +$ #$ ! + *# X ! " E * + !.#- * # G %! # ## C ! *'$+ *# m *

$ * ' -+ . + +$ -+. #$ - +! E - # ! *#$! G # - $ . #$ < % 8* )% *# % * - # #$ P+! :/* (- *# - & (* % * * $ .(( + '$-$$ # $* ' * ELEG (- * -* !. - (- #! . < % 8* ' * +$ $ . %(+ 54(+ -$+ E ! 1 =+ 2 Lnn -G -* +# " $! %" E*$$+ P # $,G 2#! * # $* #,#! 10 # " # $$! % +* '$

E -,- $ C ' '$ #% % G *. $ -,- $+ *(+ #

E- ,*! *$$ P #G I +* -##+(* ,%* E&* '$ '$* f$, +$* + #G *'$ *# #

E%#% - $ $#$ - + G R ,*! $#$$ '$ - N"= " " ; #$ # (+ $ # *( ('

*,. +$ ## !$ C *-$ % * (' ! ,*!(+ $#$$+ '$+ $+ %! ! $ . C !$ (#, "%#% *! '( %+ *# #$ * - - #,. ( - +$ *# -+ C* . * +$ W #$* #,. (* #,#* ' -* + 54* - ,*! - .#! +& # - --+. *$ !$--$ ,*! $#$$ - %! # ! $ . %(+ *$+ -, ; -, # ,*!(+ $ - * + * 1-+ ! - * #$ # %(+ 54(+ -, # * ! 1#$* $(+ (-(+ -, #$ J#4 - (- #$ ?%24 # *+ (% ;&

59

XHB TBEox

BEOX

STBC


HB

ACID BASE METABOLIC BALANCE

A

BEox

VEC

yTA

yNH4

yCO3

yKHi

yNHi

yHin

BE

U(E) U

A

yINT <XGL0>

BE

<MRH>

CGL2

yINS

SO2A

XCO3 UCO2A

UO2A

CGL3

yGLI

vEC

BEEC

BEEC

yGLS

yKGLI

OUTPUTS: yINT - insulin secretion [unit/min] yGLS - glucose flow rate from ECF into cells [mEq/min] yKGLI - K flow rate from ECF to ICF accompanying secretion of insulin [mEq/min] zGLE - ECF glucose content [mEq] xGLE - ECF glucose concentration [mEq] yGLU - renal excretion rate of glucose [mEq/min]

ZBEEC 0

Scope Acid Base Metabolic Balance1 Acid base metabolic balance

zGLE

xGLE

GFR

21.8.2001

YGLS

YKGLI

ZGLE

XGLE

YINT 0

Scope2

BEOX 0

YINT

BLOOD GLUCOSE CONTROL INPUTS: TYINT - time constant of insulin secretion xGL0 - reference value of ECF glucose concentration CGL1 - parameter of glucose metabolism CGL2 - parameter of glucose metabolism yINS - intake rate of insulin[unit/min] CGL3 - parameter of glucose metabolism yGLI - intake rate of glucose [g/min] vEC - ECF volume [l] GFR - glomerular filtration rate [l/min]

CGL1

PHA

xGL0

AH

UO2A

MRH

TYINT

Selector STBC

AH

OUTPUTS: PHA XHB - Vector of coefficients derived from hemoglobin concentration STBC - Standard bicarbonate concentration [mmol/l] SO2A BE - Base Excess concentration in arterial blood AH - Hydrogen ions concentration [nmol/l] PHA - arterial plasma pH XCO3A SO2A - Oxygen hemoglobin saturation in arterial blood (expressed as ratio from 0 to 1) XCO3 - Actual bicarbonate concentration in arterial blood UCO2A UCO2A - Content of CO2 in arterial blood [l STPD/l] UO2A-Content of O2 in arterial blood [l STPD/l] PO2A PCO2A


OUTPUTS: BEox (** Base excess in fully oxygenated blood [mEq/l]*) BEEC (*ECF Base excess concentration

yCO3in

HB

BEOX

INPUTS: TBEOX - (*Time constant*) VB (*Blood Volume [l]*) HB (fore XHB) (*Blood hemoglobin concentration [g/100 ml]*) A [11] - (* vector of coeficients, see "Blood Acid Base Balance" *) pCO2A (*CO2 tension in arterial blood [Torr]*) VEC (*Extracelular fluid volume [l]*) yTA (*Renal excretion rate of titratable acid [mEq/min]*) yNH4 (*Renal excretion rate of ammonium [mEq/min]*) yCO3 (*Renal excretion rate of bicarbonate [mEq/min]*) yKHi (*Potassium ions flow rate from ECF into ICF exchanged with hydrogen ions [mEq/min]*) yNHi (*Hydrogen ions flow rate from ECF into ICF exchanged with sodium ions [mEq/min]*)

pCO2A

XHB

BLOOD ACID BASE BALANCE

VB

yGLU

ZGLE 0

YGLU

Blood Glucose Control

Scope1

Blood acid base balance

Scope3

Blood glucose control

qIN

HB

qVIN

HB

vEC

zCaE

ZCAE

VB

QCO

QCO

qIWL

CALCIUM AND MAGNESIUM BALANCE

BODY FLUID VOLUME BALANCE qMWP

INPUTS: qIN - drinking rate [l/min] qVIN - intravenous water input [l/min] qIWL - insensible water loss [l/min] qMWP - metabolic water production [l/min] qWU - urine output [l/min] qLF - lymph flow rate [l/min] CFC - capillary filtration coefficient [l/min/torr] pICO - interstitial colloid osmotic pressure [torr] pPCO - plasma colloid osmotic pressure [torr] pC - capillary pressure [torr] pIF - interstitial pressure [torr] CSM - transfer coeff. of water from ECF to ICF xNE - ECF Na concentration [mEq/l] xKE - ECF K concentration [mEq/l] xGLE - ECF glucose conc. [mEq/l] zKI - ICF K content [mEq] vRBC - volume of red blood cells [l] xHBER - hemoglobin concentration in the red blood cells [g/100 ml]

qWU

qLF

CFC

pICO

pPCO

pC

pIF

CSM

xNE

<XNE>

xKE

<XKE>

zKI

vRBC

xHBER

<XHBER>

vB

yCaI

GFR

yMg

KL

VIF

vTW

PAS

OUTPUTS: QCO - Cardiac output [l/min] PAP - Pulmonary arterial pressure [torr] PAS - Systemic arterial pressure [torr] pC - Capillary pressure [Torr] PVS - Central venous pressure [torr] PVP - Pulmonary venous pressure [torr]

KR

pC

PVS

YMG

vIF

RTOP

XMGE

zMgE0

PAP

INPUTS: VB - Blood volume [l] RTOT - Total resistance in systemic circulation [Torr * Min / l] (norm.=20) RTOP - Total resistance in pulmonary circulation [Torr * Min /l] (norm. =3) KL - Parameter of the left heart performance [l/min/torr] (norm.=0.2) KR - Parameter of the right heart performance [l/min/torr] (norm.=0.3) DEN - Proportional constant between QCO AND VB [1/min] (norm.=1) KRAN - Parameter of capillary pressure (norm.=5.93)

ZMGE

xMgE

30.7.2001

VEC

CARDIOVASCULAR BLOCK

RTOT

YCA

zMgE

INITIAL CONDITIONS: zCaE0 - ECF calcium content [mEq] zMgE0 - ECF magnesium content [mEq]

zCaE0

XCAE

yCa

OUTPUTS: zCaE - ECF calcium content [mEq] xCaE - ECF calcium contentration [mEq/l] yCa - calcium renal excretion rate [mEq/min] zMgE - ECF magnesium content [mEq] xMgE - ECF magnesium contentration [mEq/l] yMg - magnesium renal excretion rate [mEq/min]

yMgI

VP

xCaE

INPUTS: vEC - ECF volume [l] yCaI - calcium intake [mEq/min] yMgI -magnesium intake [mEq/min] GFR - glomerular filtration rate [l/min]

VB

vP

24.8.2001

VIN 0

HT

vEC

OUTPUTS: HB - blood hemoglobin concentration [g/100 ml] HT - hematocrit vB - blood volume [l] vP -plasma volume [l] vEC - ECF volume [l] vIF - interstitial fluid volume [l] vTW - total body fluid volume [l] vIC - ICF volume [l]

xGLE

<XGLE>

HT

DEN

24.8.2001 edited by Tom Kripner

KRAN

PVP

Calcium and Magnesium Balance

PAP

PAS

PC

PVS

PVP

Cardiovascular Block

VTW

VP 0

VIF 0

Scope5

vIC

Lnn

Scope4

VIC

VIC 0

Body Fluid Volume Balance Scope6

Body fluid volume balance Calcium and magnesium balance

Cardiovascular block

vEC

ADH

DIURESIS AND URINE OSMOLARITY

yCLI zCLE

CHLORIDE BALANCE

INPUTS: vEC - ECF volume [l] yCLI - chloride intake [mEq/min] yNU - Na renal excretion rate [mEq/min] yKU - K renal excretion rate [mEq/min] yNH4 - ammonium renal excretion rate [mEq/min] yCa - calcium renal excretion rate [mEq/min] yMg - magnesium renal excretion rate [mEq/min] xCLE ySO4 - sulphate renal excretion rate [mEq/min] yCO3 - bicarbonate excretion rate [mEq/min] STPG - summary renal excretion rate of phosphates and org. acids related to arterial pH [mEq/min]

yKU

yNH4

yCa

yMg

qWD

INPUTS: ADH - effect of antidiuretic hormone [x normal] OSMP - plasma osmolality [mOsm/l] yND - sodium excretion rate in distal tubule [mEq/min] yKD - potassium excretion rate in distal tubule [mEq/min] yGLU - renal excretion rate of glucose [mEq/min] yURU - renal excretion rate of urea [mEq/min] yMNU - renal excretion rate of mannitol [mEq/min] yNU - sodium renal excretion rate [mEq/min] yKU - potassium renal excretion rate [mEq/min]

yND

yKD

yGLU

qWU

VIF0

VIF

QWD

XCLE

yURU

PIF

16.8.2001

QLF0

QLF

Interstitial Pressure and Lymph Flow Rate

17.8.2001 yNU

OSMU

OSMU

yKU

YCLU

Scope7

STPG

PIF

OUTPUTS: pIF - interstitial pressure [torr] qLF - lymph flow rate [l/min]

OUTPUTS: qWD - rate of urinary excretion in distal tubule [l/min] qWU - urine output [l/min] OSMU - urine osmolality [mOsm/l]

yMNU

yCO3 yCLU

INTERSTITIAL PRESSURE AND LYMPH FLOW RATE INPUTS: vIF0 - normal interstitial fluid volume [l] vIF - interstitial fluid volume [l] qLF - normal lymph flow rate [l/min]

QWU

QLF

OUTPUTS: zCLE - ECF chloride content [mEq] xCLE - ECF chloride concentration [mEq/l] yCLU - chloride renal excretion rate [mEq/min]

ySO4

30.7.2001 <STPG>

OSMP

ZCLE

yNU

Diuresis and Urine Osmolarity

ZCLE 0

Chloride Balance

Scope8 Scope9 Diuresis and urine osmolarity

Interstitial pressure and lymph flow rate

mrCO2

<MRCO2>

uCO2A

yTA1

yNU

yNH

yND

xNE

zKI0 CKEI yKIN vEC ZNE 0 ZKE 0

YND

QCO

PBA

XNE

fCO2i

zNE

ZNE

VAL

YNHI

YKHI

zKI

zKE

yKU

yKD

ZKI

ZKE

PLASMA OSMOLARITY

OUTPUTS: (** Content of CO2 in venous blood [l STPD/l]*) (** Content of O2 in venous blood [l STPD / l*) pCO2A (*CO2 tension alveoli [Torr]*) fCO2A (*Volume fraction of CO2 in dry alveoli gas*) pO2A (*O2 tension in alveoli [Torr]*) fO2A (*Volume fraction of O2 in dry alveoli gas*)

xGLE

<XGLE>

pCO2A

INPUTS : XMNE - ECF mannitol concentration [mmol/l] XURE - ECF urea concentration [mmol/l XGLE - ECF glucose concentration [mmol/l] XNE - ECF sodium concentration [mmol/l] XKE - ECF potassium concentration [mmol/l]

xURE

UO2V

xNE

<XNE>

OSMP

OSMP

OUTPUT : OSMP - plasma osmolarity

PCO2A

( Y$

xKE

<XKE>

Plasma osmolarity calculation

FCO2A

uCO2V uO2V -

fO2i

yKHI

xMNE

<XMNE>

<XURE> uO2V

fCO2A

VA

yNHI

OUTPUTS: yNU - Na renal excretion rate [mEq/min] yNH - Na excretion in Henle loop [mEq/min] yND - Na excretion rate in distal tubule [mEq/min] xNE - ECF Na concentration [mEq/l] zNE - ECF Na content[mEq] yNHI - H ions flow rate from ECF to ICF (exchanged w. Na) [mEq/min] yKHI - K flow rate from ECF to ICF (exchanged w. H) [mEq/min] zKI - ICF K content [mEq] zKE - ECF K content [mEq] yKU - K renal excretion rate [mEq/min] yKD - K excretion rate in distal tubule [mEq/min] xKE - ECF K concentration [mEq/l]

yKGLI

uO2A

CHEI

INPUTS: mrCO2 - (*Metabolic production rate of CO2 [l STPD/min]*) uCO2A (*Content of CO2 in arterial blood [l STPD/l]*) VTW (*Total body fluid volume [l]*) mrO2 - (*Metabolic consumption rate of O2 [l STPD/min]*) uO2A (*Content of CO2 in arterial blood [l STPD/l]*) QCO (*Cardiac output [l/min]*) PBA - (*Barometric pressure*) fCO2i - (*Volume fraction of CO2 in dry inspired gas*) VAL - (*Total alveolar volume (BTPS)*) VA (*Alveolar ventilation [l BTPS/min]*) fO2i - (*Volume fraction of O2 in dry inspired gas*)

mrO2

<MRO2>

YNH

ALD

UCO2V

VTW

INPUTS: yTA1 - Arterial pH dependent portion of titrable acid excretion rate yNH4 - ammonium renal excretion rate [mEq/min] yCO3R - bicarbonate reabsorption rate [mEq/min] ALD - aldostrone effect [x normal] GFR GFR - glomerular filtration rate [l/min] CPR - excretion ratio of filterd load after proximal tubule CPR THDF - effect of 3rd factor (natriuretic horm.) [x normal] yNIN - sodium intake [mEq/min] THDF PHA - Arterial blood pH CBFI - Parameter of intracellular buffer capacity yNIN CHEI - Transfer coeff. of H ions from ECF to ICF yKGLI - K flow rate from ECF to ICF accompanying secretion of insulin [mEq/min] PHA zKI0 - normal ICF K content [mEq] CKEI - Transfer coeff. of K ions from ECF into ICF (exchanged with H ions) CBFI yKIN - K intake [mEq/min] vEC - ECF volume [l] yCO3

uCO2V

O2 and CO2 EXCHANGE

YNU

SODIUM AND POTASSIUM BALANCE

yNH4

UCO2V 0

pO2A

PO2A

UO2V 0

8.10.2001 fO2A

FCO2A 0

FO2A

FO2A 0

O2 and CO2 Exchange

YKU

YKD

27.7.2001 xKE

ZHI 0

XKE

Scope12 Na & K Balance Scope11

Sodium and potassium balance

Scope10 O2 and CO2 exchange Plasma osmolarity

zPO4E

vEC

ZPO4E

pICO

vIF

xPO4

yPO4I

INPUTS: vEC - ECF volume [l] yPO4I - phosphate intake [mEq/min] ySO4I - sulphate intake [mEq/min] yORGI - organic acids intake [mEq/min] GFR - Glomerular filtration rate [l/min]

ySO4I

yORGI

GFR

ZPO4E 0

yPO4

XPO4

xSO4

ySO4

STPG

pC YPLIN

INPUTS: vIF interstitial fluid volume [l] qLF - lymph flow rate [l/min] pC - capillary pressure [torr] YPLIN - rate of intravenous plasma protein input [g/min] vP -plasma volume [l]

xPIF

XPIF

zPIF

ZPIF

ZSO4E

XSO4

vP ZPG 0 ZPIF 0

YSO4

zORGE

OUTPUTS: pICO - interstitial colloid osmotic pressure [torr] xPIF - interstitial protein concentration [g/l] zPIF - interstitial protein content[g] zPP - plasma protein content [g] xPP - plasma protein concentration [g/l] pPCO - plasma colloid osmotic pressure [torr]

zPP

XPP

30.7.2001

xORGE

10.7.2001 pPCO

PPCO

Protein Balance

XORGE

ZORGE 0

yORG

RENAL ACID BASE CONTROL yPO4 yTA0 ALD TPHU2 TPHU1

ZPP 0 ZPLG 0

ZSO4E 0

yORG

ZPP

xPP

ZORGE

STPG

PHA

qLF

YPO4

zSO4E

OUTPUTS: zPO4E - ECF phosphate content [mEq] xPO4 - ECF phosphate contentration [mEq/l] yPO4 - Phosphate renal excretion rate [mEq/min] zSO4E - ECF sulphate content [mEq] xSO4 - ECF sulphate contentration [mEq/l] ySO4 - sulphate renal excretion rate [mEq/min] zORGE - ECF organic acids content [mEq] xORGE - ECF organic acids contentration [mEq/l] yORG - organic acids renal excretion rate [mEq/min]

TPHA1

PICO

PROTEIN BALANCE PHOSPHATE, SULPHATE AND ORGANIC ACIDS BALANCE

YORG

Phosphate, Sulphate and Organic Acids Balance

ano XCO3

<XCO3>

yNH40

INPUTS: TPHA1 - Time constant of titratable acid [1/min] PHA - arterial pH yORG - Renal excretion rate of organic acid [mEq/min] yPO4 - Renal excretion rate of phosphate [mEq/min] yTA0 - Normal value of renal excretion rate of titratable acid [mmol/min] ALD - Aldosterone effect [x normal] TPHU1 - Time constant of ammonium secretion [1/min] TPHU2 - Time constant of titratable acids secretion [1/min] yNH40 - Normal value of ammonium renal excretion rate [mmol/min] qWU - Urine output [l/min] pCO2A - Alveolar pCO2 [torr] GFR - Glomerular filtration rate [l/min] xCO3 - Actual bicarbonate concentration [mmol/l]

yTA

yTA1

PHU

YTA

YTA1

PHU

qWU OUTPUT VARIABLES: STPG - summary renal excretion rate of titratable acids, phosphate and org. acids [mmol/mi yNH4 yTA - renal excretion rate of titratable acids [mmol/min] pCO2A YNH4 yTA1 - on arterial pH dependent portion of titratable acid secretion rate [mmol/min] PHU - urine pH GFR YNH4 - Ammonium renal excretion rate [mmol/min] YCO3 - Bicarbonate excretion rate [mmol/min] YCO3R - Bicarbonate reabsorption rate [mmol/min] xCO3 yCO3

YCO3

24.7.2001

PHA 0 PHU2 0 yCO3R

Phosphate sulphate and organic acids balance Protein balance

vEC

CONTROLLER OF RENAL FUNCTION

GFR

<XKE>

pAS

xKE

yNH

pVP

INPUTS: vEC - ECF volume [l] pAS - systemic arterial pressure [torr] xKE - ECF K concentration [mEq/l] yNH - Na excretion in Henle loop [mEq/min] pVP - pulmonary venous pressure [torr] OSMP - plasma osmolality [mOsm/l] pPCO - plasma colloid osmotic pressure [torr]

ALD

VA0

pO2A

pCO2A

pHA

RESPIRATION CONTROL INPUTS: VA0 - normal value of alveolar ventilation [l BTPS/min] pO2A - O2 partial pressure in alveoli [Torr] pCO2A - CO2 partial pressure in alveoli Torr] pHA - arterial blood pH AH - concentration of hydrogen ions in arterial blood [nM/l]

VA

vTW

yURI

VA

OUTPUTS: VA - alveolar ventilation [l BTPS/min]

AH

GFR

yMNI

Respiration Control ADH

HIDDEN CONSTANTS: vEC0 - normal ECF volume [l] GFR0 - normal glomerular filtration rate [l/min] ___

Scope15

YCO3R

PHU1 0

zUR

ADH

vEC

ZUR

UREA AND MANNITOL BALANCE INPUTS: vTW - total body fluid volume [l] yURI - intake rate of urea [mEq/min] GFR - glomerular filtration rate [l/min] yMNI - intake rate of mannitol [mEq/min] vEC - ECF volume [l]

xURE

yURU

4.10.2001

OUTPUTS: GFR - glomerular filtration rate [l/min] ALD - aldosterone effect [x normal] ADH - effect of antidiuretic hormone [x normal] THDF - effect of 3rd factor (natriuretic horm.) [x normal]

OUTPUTS: zUR - total body-fluid urea content [mEq] xURE - ECF urea concentration [mEq/l] yURU - renal excretion rate of urea [mEq/min] zMNE - ECF mannitol content [mEq] xMNE - ECF mannitol concentration [mEq] yMNU - renal excretion rate of mannitol [mEq/min]

XURE

YURU Urea and mannitol balance

zMNE

ZMNE

21.8.2001 xMNE

OSMP

ZUR 0

XMNE

17.8.2001 THDF

ALD

Renal Acid Base Control

GFR

Scope14

Scope13

THDF

pPCO

yMNU

ZMNE 0

YMNU

Urea and Mannitol Balance Controller of Renal Function

Scope16

Scope17 Scope18

Respiration control Controller of renal function Renal acid base control

Chloride balance

INPUTS

< $

< $

!LE"#& && . & %4.30 &&+-2 & &55)-% & & '(- '-%.

&& . &+&&~9&c-$ . 4.&.%& & c & F &$ & & A @<- !+ --VV$& -%. & &&~9&% | ,&2% &,&+. . .-

> * ' !.$ *(+ #

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+K =, ! ! * % ,*!(+ $ * T%)%FV'MW, ( # (+ * + *( 54 (* * ! - - *+* . $ -* (- ((+ *'$+ $ 54( - $ '&

*B$)$ ) 7! K8 V8

E& )- GB \ V]# E ' !GB - -#* *$* ' #+ # % (+ 54+ - 2 ]# - * #*( $ (+ (%, # (-* - ( Y$ #$! $

60

S!?,K

&0 !& "! * ("& !

,

("& !

"!& - !LI"1 &,&%-& |-- & & .&+ .-,2 @ - .)

S ?,K!! %>%! ,QD! %<

$% %> > ,adi virtuální mící/ídící karty

Vstupní kanály Výstupní kanály

1 GFR

GL O M ER ULUS

RAP

0 .1 4 4

Simulátor v Control Control Webu

Zdrojový text programu v jazyce j C/C++

GFR

INP UTS : RAP - Re n a l a r te r y pr e s s ure [to rr ] Affc - Affe r e nt a rte r y c onduc ta nc e [m ll/m in/to rr ] FF T ubC - P r ox im a l tubule c onduc ta qnc e [m l/m in/to rr ] RBF - Re n a l blo od flow [m l/m in] RP F - Re n a l pla s m a flow GP AP r - P la s m a p rote in c onc e ntra tion (in a ffe r e nt a r te r y) [g/m l] GKf - Glom e r ula r filtr a tion c oe ffitie n t [m l/m in /tor r]

Cloc k

2 FF

T ubC

6 .2 5

RBF

0 .0 7

RPF

OUTP UTS : GFR - Glom e r ula r filtr a tion ra te [m l/m in ] FF - Filtra tion fr a c tion [re la tive num be r ] AV eCCP GP - Glom e r ula l pr e s s ur e [tor r ] P TP - P rox im a l tub ule pr e s s u re [to rr ] AV e COP - Ave r a ge c o lloid os m otic pre s s ur e [tor r] Ne tP NETP - Ne t p re s s ure gr a die nt in glo m e ru lus [tor r ]

A Pr

16 3 GKf

GKf

8 RAP

M DNaFlo w

Pd xNaRe ab

AP - Arte r ia l pr e s s ur e [tor r ] VP - V e na r e na lis pr e s s ur e [tor r ] Hc t - He m a toc r it [r e la tive n um be r ] Cla m p - Re na l a rte r y pr e s s ur e dr op c a us e d by r e na l a rte r y c la m p [to rr ]

AP VP

Pr xFNaNo r m

OUTP UTS : M DNa Flow - S odiu m outflow [m m ol/m in] P dx Na Re a b - Pr ox im a l s o dium r e a bs orb rtion [m m ol/l] P rx FNa - P r ox im a l fr a c tiona l s odiu m r e a bs or btion [r e la tive num be r]

1 4 .3 9 Pr xFNa

C lam p

21 P r x FNa

7 .8 1 5 Ca lc ula tion o f pro x im a l tubule s odium re a bs or btion 0 .7 9 9 1 14 AffM yo

A ffM y o 1

0 .8

Ca lc ula tion of the m yoge nic re s pons e to c ha nge s in re na l p e rfu s ion pr e s s ure (a ffe re n t c onduc ta nc e r e s po nds to c ha ng e s in pe r fu s ion p re s s ure , w ith pr e s s ur e inc r e a s e s c a us ing va s oc ons tr ic tio n) 1186

9 RBF

RBF

O UTP UTS : RAP - Re n a l a r te r y pr e s s u re [torr ] RBF - Re na l b lood flow r a te [m l/m in] RP F - Re na l pla s m a flow r a te [m l/m in ]

Hct

20 P dx Na Re a b

LogA2

11 P rx FNa Nor m

O UTP UT : AffC - M yog e nic e ffe c t [ x Nor m a l]

Re n V e n C Re n Ve nC - Re na l ve nou s c ond uc ta nc e [m l/m in/torr ]

6 Htc 7 Cla m p

- P RO X IM AL TUBUL E

INP UTS : P Na - P la s m a s odium c onc e ntr a tion [m m ol/m l] GFR - GLom e r ula l filtr a tion r a te [m l/m in] LogA2 - L oga r ithm of pla s m a a ngiote n s in c o nc e ntr a tion [pg/m l] P r x FNa Nor m - No rm a l va lue of s o dium p rox im a l fra c tiona l re a bs or btion [r e la tive n um be r ]

GFR

3 2 .2 2 6 Ne tP

Glo m e ru lus M YOGENIC RES P O NS E INP UT : RAP - Re na l a rte r y pre s s ur e [tor r]

RA P

RAP

INP UT S : AffC - Affe r e nt a rte r y c onduc ta nc e [m l/m in/tor r ] EffC Effe re nt a r te ry c ond uc ta nc e [m l/m in/torr ]

EffC

5 VP

6 0 .3 2

2 0 .2 9

5 AV e CCP

RENAL P ERFUS IO N

A ffC

4 Re n V e nC

19 M DNa Flow NA TRIUM

PNa

0 .1 9 0 8

3 GP 4 P TP

PT P

2 Apr

30 S im Tim e

125

A ffC

2 9 .9 6 1 TubC

10 RP F

RPF

6 6 4 .4

Ca lc ula tion of re n a l a r te r y pr e s s ure a nd r e na l blood flow ra te

Automatické generování zdrojového textu

1 .0 0 1 11 AFC

A FFER E N T A R T ER Y

A ffM yo

INPUT S : AffM yo - M yog e nic e ffe c t [ x Nom a l] M DS ig - M a c ula de ns a fe e dba c k s igna l [ x Nor m a l] M DSig AffNor m - Nor m a l c o nduc ta nc e in a ffe re nt a rte ry [m l/m in/tor r]

1 .0 0 2

A ffC

O UTP UT : AffC - V a s c u la r c ondu c ta nc e [m l/m in/to rr ]

2 9 .9 6

8 AffNo rm

A ffNo r m

Ca lc ula te s c onduc ta nc e of a ffe re nt a r te ry 30

2 5 .0 3 1 .2 9 1

E FFER E N T A R T ER Y AP EffC

ARTERIAL P RES S U RE

Z NA E

AP

lo g A 2

OUTP UT : EffC - V a s c ula r c ondu c ta nc e [m l/m in/to rr ]

M DSig

3 .6 1 7

9 EffNor m

EffNo r m

13 M DS ig

Ca lc ula te s c onduc ta n c e of e ffe re n t a rte ry

7 AP

AP Nor m - Nor m a l va lu e of a r te r ia l pre s s ur e l [tor r]

25

OUTP UT : AP Ar te r ia l p re s s ur e [tor r]

A PNo r m

INP UTS : logA2 - log a rith m of a ng iote ns in c onc e ntra tion M DSig - M a c ula d e ns a fe e dba c k s igna l [ x Nor m a l] EffNo rm - Norm a l c ond uc ta nc e in a ffe r e nt a rte r y [m l/m in/torr ]

EffC

12 EffC

INP UTS : ZNAE - ECF s o dium c o nte nt [m m ol] - L oga r ithm of p la s m a a ngiote n s in c on c e ntr a tion [pG/m l] A P L o glogA2 A2

10 AP Nor m

M ACULA DENSA

9 9 .9 3

Contro l of a r te r ia l pre s s ur e by a ngiote ns in a nd e x tr a c e llula r s od ium c on te nt M DSig

OUTP UT : M DSig - M a c ula d e ns a fe e dba c k s igna l [ x Nor m a l]

1 9 .5 6 ANGIO TENS IN 16 A2

INP UTS : P RA - P la s m a r e nin a c tivity [ Units /m l] CEAc t - Con ve r ting e n zym e a c tivity [x Norm a l] A2 Inf Ang iote ns in 2 infu s ion r a te [n G/m in]

lo g A 2

ALDO S T ERO NE

lo g A 2

INPUTS : logA2 - Loga r ithm o f pla s m a a ngio te ns in c onc e ntr a tion [pG/m l] Aldo Inf - Aldo s te ro ne infu s ion r a te [n G/m in] A ld o In f V TW - Tota l body w a te r c o nte nt [m l]

Log A2

O UTP UT : Aldo - P la s m a a ldos te ron e c onc e ntra tion [ nG/d l]

0 .9 7 7 8

V ECm l

3 .6 1 7 22 Dis tNa Flow

4 e +0 0 4

N ATRIU M - DIS T AL TUBU LE

M DNaFlo w

Aldo

A ld o

6 .9 4 5 12 Dis FNa No rm

Dis Na Flo w

Dis tNa Flow

INP UTS : M DNa Flow - S odium inflow [m m o l/m in] Aldo - P la s m a a ldos te ron e le ve l [pg/m l] Dis FNa Nor m - Nor m a l va lu e of s o dium dis ta l fr a c tiona l r e a bs or btion [re la tive num be r ] Dis Na Re a b

18 V TW

V TWm l

Ca lc ula tio n of pla s m a a ldos te r one c onc e ntr a tion

14 M DNor m

1

1 .5 e +0 0 4

0

0

17 AldoInf

A ld o

LogA2

M DNo r m

1 .0 0 2

Ca lc ula tion of pla s m a r e nin a c tivity

16 A2 Inf

Ca lc ula tion of pla s m a a ng iote ns in c onc e n tra tion a nd loga r ithm o f pla s m a a ngiote ns in c on c e ntr a tion (m os t of the a c tion o f a ngiote n s in a r e loga r ithm ic in na tur e : c onc e ntr a tion c ha ng e s a t highe r c onc e ntra tions pr odu c e le s s of a n e ffe c t tha n c ha nge s of the s a m e s iz e a t low e r c o nc e ntr a tions )

M DSig

V EC m l

O UTP UT : P RA - P la s m a r e nin a c tivity [ Units /m l]

1

1 .2 9 1

18 Ald o

INP UT S : M DS ig - M a c ula de ns a fe e dba c k s igna l [ x No rm a l] V ECm l - Ec tr a c e llula r fluid volum e

PRA

15 CEAc t

C EA c t

O UTP UT S : A2 - P la s m a a ngiote n s in 2 c onc e ntr a tion [ pG/m l] LogA2 - loga r ithm of pla s m a a ngio te ns in c onc e ntr a tion [ pG/m l]) A 2In f

M a c ula de ns a fe e dba c k s ign a l c a lc ula tio n ba s e d on m a c ula de ns a s o dium flow a nd a n giote ns in c onc e ntra tion

RENIN

15 P RA

P RA

A2

17 LogA2

M DNaFlo w

INP UTS : M DNa Flow - M a c ula de ns a s odium flow [m m o l/m in] logA2 - L oga r ithm of p la s m a a ngiote n s in c on c e ntr a tion [pG/m l] M DNor m - Nor m a l m a c ula de ns a fe e dba c k s igna l [ x Nor m a l]

L ogA2

Dis FNa No r m

O UT PUTS : Dis Na Flow - S od ium outflow [m m ol/m in] Dis Na Re a b - Dis ta l s odiu m r e a bs or br tion [m m ol/m in] Dis FNa - Dis ta l fr a c tiona l s o dium r e a bs orb tion [re la tive num be r ]

23 Dis tNa Re a b 1 .8 3 9 24 Dis tFNa

Dis FNa

0 .5 0 8 4 Ca lc ula tion of dis ta l tubule s odium re a b s or btion 0 .5

0 .1 2 5

2 160

28 ZNa e 1 .7 7 8 S IM P L E S OD IUM Z NA E

BALANCE

INPUT S : Na DIe t - Die ta r y s odium inta k e [m m ol/m in] Na Ur ine - S odium u rin e outflow [m m ol/m in] VECm l - Ex tr a c e llula r fluid vo lum e [m l]

29 P Na

O UTP UT : Z NAE - ECF s odium c onte nt [m m ol] P Na - P la s m a s odium c onc e ntra tion [m m o l/m l]

PNa

19 Na Die t

NaDie t

0 .1 2 2 6 25 Na Urin e

NATRIUM NaUr in e

NaUr in e

1 .6 5 6 V EC m l

20 V ECm l

Ex tr a c e llula r s od ium qua ntity is the inte gr a l ove r tim e die ta r y s od ium in ta k e m in us ur ina r y s odium los s 0 .1 4 4 1 .5 e +0 0 4

26 CDNa Re a b 0 .9 3 1 27 CDFNa

- CO LL ECT ING DUCT

INP UTS : Dis NaFlo w Dis Na Flow - S odium inflow [m m ol/m in] CDFNa Nor m - Nor m a l va lue of s odium dis ta l fr a c tiona l r e a bs or btion [re la tive num be r ]

C DNaRe ab

0 .9 3

O UTP UTS : Na Urin e - S odiu m ur ine ou tflow [m m o l/m in] CDNa Re a b - Colle c ting duc t s o dium r e a bs orb rtion

C DFNaNo r m [m m ol/m in] C DFNa CDFNa - Colle c ting duc t fr a c tion a l s od ium r e a bs o rbtion

13 CDFNa No rm

[r e la tive nu m be r ] Ca lc ula tion of c olle c ing duc t s odium re a bs or btion

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72

100

RAP GFR

227 .1

FF

0.3411

GP

88 .11


100

AffC


GLOMERULUS

6.25


TubC


RBF


665 .8


RPF


0.07

PTP

36 .33

AVeCCP

37 .58

NetP

14 .19

APr

Plasma protein cnoncentration [g/ml ] 16

GKf


GKf - Glomerular filtration coeffitient

7

Glomerulus

[ml /min /torr]

GKf

1

RAP - Renal artery pressure [torr]

RAP

GP - Glomerulal pressure

RAP 4

PAff - Afferent artery pressure [torr] RBF - Renal blood flow

[torr]

GKf

GP = RAP - PAff

@OQl@n;7)

[ml /min ] PAff

RBF


PAff=RBF*AffC

[ml /min /torr]

GP

GFR - Glomerular filtration rate NETP - Net pressure gradient in glomerulus

[ml /min ]

1

[torr]

GFR GFR = NETP *GKf

@

2 AffC

AffC - Afferent artery conductance

[ml /min /torr]

@OQ GFR - Glomerular filtration rate TubC - Tubule conductance

@ @OQ

PTP

PTPl@OQn)%L PTPl l@OQ O n) n)% %L L 92L 92 L" " 92L"

[ml /min ]

PTP - Proximal tubule pressure 3

[ml /min /torr]

)%L )%L

TubC

3 GP

4

PTP = GFR/TubC

[torr]

AVeCOP - Average colloid osmotic pressure

6

;7)l@ l@6 6PTP69 692 2L" L" ;7)l@6PTP692L" NetP

[torr] [torr rr] rr

NetP = GP - PTP - AVECOP 5 AVeCCP

92 92L L" " 92L"

@OQ

92L 92 L" " 92L" GFR - Glomerular filtration rate

[ml /min ] FF - Filtration fraction

RPF - Renal plasma flow

5

6

[relative number ]

[ml /min ]

2 FF

RPF

FF = GFR/RPF

APr - Afferent protein concentration

[g/ml ]

u

APr

2

(APr)^2 B * (Apr)^2

1160 B - Landis -Pappenheimer coeffitient [torr/g/ml ]1

ACOP - Afferent colloid osmotic pressure

[torr]

320 A - Landis -Pappenheimer coeffitient [torr/g/ml ]

ACOP = A *Apr + B *(APr)^2

A *Apr

EPr - Efferent protein concentration 1

[g/ml ]

u

2

(EPr)^2 1 - FF

EPr = APr / (1-FF)

B * (Epr)^2

ECOP - Efferent colloid osmotic pressure

[torr] ACOP +ECOP

ECOP = A *Epr + B *(EPr)^2

A*Epr

2 AVeCOP = (ACOP +ECOP )/2

! HI g) - - 2- 22- & & -&% -&% - % 22 .

. 22 F=!ABk6=6< F=!ABk6=6 ! < & & !HI"g)- 2 . 2

. ) ( 7F_k8

73

100

RAP GFR

227 .1

FF

0.3411

GP

88 .11


100

AffC


GLOMERULUS

6.25


TubC


RBF


665 .8


RPF


0.07

PTP

36 .33

AVeCCP

37 .58

NetP

14 .19

APr

Plasma protein cnoncentration [g/ml ] 16

GKf


Glomerulus

1 RAP

RAP

2 AffC

GFR

1 GFR

AffC FF

3 TubC

2 FF

TubC

4 RBF

3 GP

PTP

4 PTP

do { ... } while

RBF

5 RPF

GP

RPF

AVeCCP

6 APr

APr

7 GKf

GKf

5 AVeCCP

NetP

6 NetP

While Iterator Subsystem

cond

do { ... } while

5 number of iteration

While Iterator

|u| < Abs

1 RAP

RAP

2 AffC

AffC

3 TubC

TubC

4 RBF

RBF

5 RPF

RPF

OUTPUT : GFR - Glomerular filtration rate [ml /min ] FF - Filtration fraction [relative number ] GP - Glomerulal pressure [torr] PTP - Proximal tubule pressure [torr] AVeCOP - Average colloid osmotic pressure [torr] NETP - Net pressure gradient in glomerulus [torr]

APr

6 APr 0.01

GLOM E RULA R F ILTRA TION

GKf

7 GKf

GFR

1 GFR

FF

2 FF


GRFold

GP

3 GP

PTP

4 PTP

AVeCCP

5 AVeCCP

NetP

6 NetP

Calculation of glomerular filtration rate calculation

Saturation

Memory Memory Initial condition =120

Memory Initial condition =0 2

==

0

Switch threshold =0

Relational Operator Switch Threshold =0.1

Memory Initial condition =5


7

[ml /min /torr]

GKf

1

RAP - Renal artery pressure [torr]

RAP

GP - Glomerulal pressure

RAP 4

PAff - Afferent artery pressure [torr] RBF - Renal blood flow

[torr]

GKf

GP = RAP - PAff

[ml /min ] PAff

RBF


PAff=RBF*AffC

[ml /min /torr]

GP

GFR - Glomerular filtration rate NETP - Net pressure gradient in glomerulus

[ml /min ] 1

[torr]

GFR GFR = NETP *GKf

3 GP

2 AffC

AffC - Afferent artery conductance

[ml /min /torr] 4 PTP

8 GRFold 3

GFR - Glomerular filtration rate

[ml /min ] PTP - Proximal tubule pressure

TubC - Tubule conductance

[torr]

6

[ml /min /torr]

NetP

TubC

PTP = GFR/TubC AVeCOP - Average colloid osmotic pressure

[torr]

NetP = GP - PTP - AVECOP 5 AVeCCP

GFR - Glomerular filtration rate

[ml /min ] FF - Filtration fraction

RPF - Renal plasma flow

5

6

[relative number ]

[ml /min ]

2 FF

RPF

FF = GFR/RPF

APr - Afferent protein concentration

[g/ml ]

u

APr

2

(APr)^2 B * (Apr)^2

1160 B - Landis -Pappenheimer coeffitient [torr/g/ml ]1

ACOP - Afferent colloid osmotic pressure

[torr]

320 A - Landis -Pappenheimer coeffitient [torr/g/ml ]

ACOP = A *Apr + B *(APr)^2

A *Apr

EPr - Efferent protein concentration 1

[g/ml ]

u

2

(EPr)^2 1 - FF

EPr = APr / (1-FF)

B * (Epr)^2

ECOP - Efferent colloid osmotic pressure

[torr] ACOP +ECOP

A*Epr

ECOP = A *Epr + B *(EPr)^2

2 AVeCOP = (ACOP +ECOP )/2

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114

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+ & + +

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115

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? 6 * @+ L+

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#& c)5C_g< Y) F59 EWE:I;WWW E RWW6RSRG "0# * 7 8 g^Wh 1 2 ) ` Q EMMXG @* L* 8* +! O& 7

)+ ) 2 [ < )+ J L J ` ) 1 " E7# G =) 5; c)5 .|)< <'E S^X6SG 8 >77 8 8& g^Sh 1 2 ) 1# ` Q ER^^G = & # *

& 4 + @* \ *&*# * +! & 2 1 @ 9# ` < E7# G <' .T .A< ;WW E NX6TSG 8 = 8 ! L* 8*& > & 8*& L g^Nh 1 2 L 2 ) ` 1# ER^^G 2 & +

\ <&*# *& @* 2 ? Z# ` 7 " E7# G c)5 .B 5:=)=5)=)c'& E RRU6RWUG ?# ?# !

116

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# c)N.AN) MJ SWW6SN^ gUh ?4 ? < ` 8+e 1 ER^^G )+ 2 L 54 *

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117

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! * +! *# ** C KNC ;I S6NS gWXh ; ! A Z =6#4# ? 2 @ L J < ? = ? 9 8 1 Z = =* ) L* ER^^MG 9 #& # *# *& ! 6# # +! # + & %# & *# #

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118

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! * K5gc. G X^ gNh 8 #69# " EMTRG )+ A L"2 %# #6% * * # <K =C& S 8 TT 6R^ gNRh 8 #69# " EMXXG )+ 2 8! 7s& <K=C& 8 ST N6R^ gNWh 8 #69# " ER^^SG g .)5NBXEMMS6^N6W # R^^S6^6^NG !| = +c dd444 #6##d"9 + !"Z7+ *. gNSh 8 #69# " ER^^TG 9#6% %> ?

@1 8+ 8= E#G B 5k A >8Z; ^6R6SWUWT^6R 7 ? # R^^T N6^ - # # +c dd444 #6##d9#ZZ#. gNNh 8 #69# " `7 EMT^G 9 4 9#6Z * * 9 *# * +# + & +

%# #6% # <K=C& W XX6 UT gNTh 8 #69# " O +69# ; EMMNG Z 0 %e % E #eG * 6 ! #6% # % 9 9 + 8# WM 8 ^X RW6RU gNXh 8 #69# < ` 8 #69# " EMMNG "0! +* W 4 + * & g g .< EG <WH W6R^ gNUh 8 #69# " J*%! = O +69# ; @ + >A EMUUG <# # ## s&& 4 + *# A # %# s* & +* 4 + NS s& <K=C& SU 8 UM X6N gNMh 8% 8 ` = 9 ER^^W ' !#$ R^^SG #. c.)w2-% & ?g 5)2&- ET !#G 8 c @ )+* 2 ' !#$ + @# gT^h 8% 8 ` ? O EMMU ' !#$ R^^G #. c ..) 8 c @ )+* 2 ' !#$ + @# gTh 8 QZ # A& 9Z EMSUG 9 *# * +# + &*& # % + #6% % +* %#A7N'8 RX RRW6RSR gTRh 8 9 9 Q+# 9 ` @# Q < ER^^G 9#6% +! ! + #& # *# + g . JH WSU6WNT gTWh 8* + ; ) EMUXG < +*& <# # = %& >+& 9 +& 9 2 g .C.' E UX6UG 9c %+

119

gTSh 8* + ; ) ` 8 EMMNG L6%# + * K5g .7K8 G 6S gTNh 8* + ; ) 8 ` =# ) EMMTG L6%# + * 2 ># E7# G g .?C'5 .) E 6S E L= Q"8Z; ^SSS^^S^TU#+ !#$ ER^^MG * 1 9 7% J @E#G < 9 b X -5g:N gN) g ;WWG C
J7Z % *# #& * 2 Z : Q % ` 8 Z.' E7# G c)5 . L .B6k!Q +!* *# %#! f# +* # %# & ++ )& + Q! 8 ! WTT WXN6WMX gX^h ) << ER^^G C ' .)9 .A 9#* %+ Z R^^ >8Z; MXU6M6XMRW6MWTX6S gXh )6) < # < ` Z < ER^ÛG @*6%# + #! & 8# ? CD9=)#.)A a' 1 A W6N gXRh " * 9 ` " # ) O ER^^SG 7L@8>< & #! + kQ8) 4* T

G TN6TU gXWh 2 2 Z ; ` < 1 ER^^NG L& # f# * 2 C )'& c.) .c c Fg) E SW6TTG A* gXSh 2 2 2 EMUXG 8! *! * #! * #! *'- *# % E;989

+ & ;989 ))6R^RM 8! * * +# % ! # *#G c-2-) JJ 6RT 9 ( # - # ( # +c dd 444+!*dd;989~c6R^RM#. gXNh J+ ? < Z! < Z ) > =! 9 8 ` A ; @ ER^ÛG <9)?9Z ;& 9 > #& 8&C L*& <9)?9Z Z <9 9#* gXTh J! = =#4 9 O 1 O# < 1 Z 1 A ` <@ + J L ER^ÛG 8*&6%# #& * s ! # #

*

#* + + .

EE NT6T gXXh J+ Q 1 ` + 1 L ER^^TG )+ = 9 # *# # # % ! * %*# + # & g g ' LW RXW6RU^ gXUh J* Z ER^ÛG A~BXN. _ ' ># 8* gXMh JK+ : EMTMG <** !%&! E:#$ * #! ,%! $G + '%$ 0 ! !(+ O %+ $ 8; gU^h JK+ : = L ` 2( 9 EMXXG 3-%--%-'- + 9* gUh JK+ : ) 1 ` 9#$ < ER^^SG )+ *+ & -

120

* 6 <&*# *& #& 54 2 @ 9! ` [ A** E7# G c) 5 . J . B6k!<J+R^^S#. gURh JK+ : < P < ` 1 ER^^XG +! #% *# *# #& 2 Z : Q % ` 8 Z.' E7# G c)5 .L .B6k!<J+R^^X#. gUWh :# Q EMMNG = Z&** # Z670 EZ7 **dG N g . C &D<. . W^ 8 WT\U

121

# )! 1 ` Q 1 ER^^G Q & @! # * & + & % s& & +! *# #* c.) k. NM UMX6MÛ - # # +c dd444%*#d +!d#dNMdNM~UMX# . R 1 Q 1 ` < 8 ER^^XG @! = * Z +

? 6 * @+ L+

8*& <# )+ +! ! 2 Z! E7# G #. ') c);WWH O L=6Q"< # E 6WG + A*5 ` >& L+* )+ ! - # # +c dd444+!*dd)L^X#. W 1 3- - '-%.5)-+.5- 2&- 7(-gF -GML&52 .2, +&2 .. &<-8 % * %$ )+ L*& R^^X E+c dd#+ d~* %d* %^XG - $+ 1 Q 1 < 8 @! = * Z +

? 6 * @+ L+

8*& <# )+ +! !

S 1 < < ] Z O < 1 =+' 2 ( : Z# : @#+ 1 EMUUG 7& # ! & # +

+ & + +

*& *# & > 7 Q L ` g&

E W6WR^G ;4 [ * N 1 ER^^MG *0$ *# #% +! E9 L*0 *# #6% % X - # # +c dd444+!*dd*#5R^^M#%# *# - # +c dd444+!*d#%G 2 < : +* E7# G ABa## 2% 8 4 *# + #6% +* ! + %# * c)5 . C_g<A) N< 9% =* 9

R6S R^^M E RST6RN^G 9% - # # +c dd 444+!*dd9#Z>O9L^M#. U 1 9+ 2 ? = 8 A Q ` 2 ) ER^^G @"?7< \ <&*# * *# #& 2 ? Q Q ` Q A0 E7# G < T .#.)C5' US <7=>;O" R^^ # + ^ + J# L <# >*& ?# >"8 ^SR6 ^ST - # # +c dd444+!*dd<7=>;O"R^^#.

122

M 1 9#$ < ) ` < 1 ER^^RG O* *& + %*# * 2 9*% ` A < + E7# G A)<' ;WW;c)5L .B<'A'5 SW6SWT =* # 8L8 %+ A - # # +c dd444+!*d d7Q"8> AB_gDB# W E= 2#*$ <+ 8 ]/ 1* * = 8+4 ? ]# 7#G >& Z && # 9! <! ! R^^ >88; ^^S6RMT NR6MX - # # +c dd 444+!*dd* W#. 1 < 8 Q 1 8 # < - < )% < ER^G )+ 9 +! ! # ++! ! 4%6%# *&*# %# & *& A . c) N ER^G # ^^Td-*%R^^R^^X - # # +c dd44+!* dd*%R^#. R 1 < - < ` ER^G A*<# 6 ? 8 +! <# <# c)5M .C 'A5;W R &

123

INTEGROVANÉ MODELY FYZIOLOGICKÝCH SYSTÉMŮ

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