guyton's diagram brought to life after revision -...

1

GUYTON'S DIAGRAM BROUGHT TO LIFE – FROM GRAPHIC CHART TO SIMULATION MODEL FOR

TEACHING PHYSIOLOGY Jiří Kofránek, Jan Rusz, Stanislav Matoušek

Laboratory of Biocybernetics, Department of Pathophysiology, 1st Faculty of Medicine, Charles University, Prague, Czech Republic

Abstract

Thirty five years ago, A.C. Guyton et al. published a description of a large model of physiological regulation in a form of a graphic schematic diagram. The authors brought this old large-scale diagram to life using Matlab/Simulink. The original layout, connections and description of individual blocks were saved. However, contrary to the old system analysis diagram, the new one is also a functional simulation model by itself, giving the user a possibility to study behaviour of all the variables in time. Furthermore, obvious and less obvious errors and omissions were corrected in the new Simulink diagram.

1 Introduction Prof. Arthur C. Guyton, T. G. Coleman and H. J.

Grand published the article [6] in the Annual Review of Physiology magazine 35 years ago. It was a completely different form of article than usual physiological articles published until that time. Its fundament was a large scheme, which at first sight evoked some electrotechnical device, but there were computing blocks shown (multipliers, dividers, summators, integrators, functional blocks) instead of electrotechnical components. They symbolized mathematical operations, which were applied on physiological quantities. Connecting wires between blocks represented complicated feedback connections of physiological quantifiers? Blocks were divided to eighteen groups, which have represented separate physiological subsystems. The central subsystem symbolized circulation dynamics – to which other blocks were connected (kidney, tissue fluid, electrolytes, hormonal control and autonomous nervous regulation) via feedback connections..

2 Schematic Diagram Instead of Verbal Description The article described a large-scale model of the circulatory system regulation in wider

perspective: The respiratory system is integrated into other subsystems of the organism that influence its function. Instead of giving the reader a set of mathematic equations, the article uses fully equivalent graphical representation. This syntax graphically illustrates the mathematical relationships in the form of the above mentioned blocks. The description of the model was given in the form of a principal graphical chart only (which was, however, fully illustrative), explicatory comments and reasoning behind the given formulas were very brief, e.g.: “Blocks 266 through 270 calculate the effect of cell pO2, autonomic stimulation, and basic rate of oxygen consumption by the tissues on the actual rate of oxygen consumption by the tissues.” Such a formulation required full concentration, as well as some physiological and mathematical knowledge for the reader to understand the meaning of the formalized relationships between the physiological entities. Later, in 1973, and in 1975 Arthur C. Guyton published monographs [7,8], where he explained most of the concepts in more length.

Guyton’s model represents the first large-scale mathematical description of the body's interconnected subsystems and their functioning. It was indeed a turning point – the impetus to start

Figure 1: Dr. Arthur C. Guyton, with medical students discussing his computer

model of cardiovascular system.

Technical Computing Prague 2007. 15th Annual Conference Proceedings. Prague, 2007

2

Figure 2: Overall regulation model of Circulation - original scheme by A.C.Guyton et al., 1972.

Reprinted, with permission, from the Annual Review of Physiology, Volume 34 (c)1972 by Annual Reviews www.annualreviews.org

the research in the field known as integrative physiology. Using the system analysis of the physiological regulation, the model was for the first time in history able to depict the simultaneous dynamics of the circulatory, excretory, respiratory and homeostatic regulation.

The group of A. C. Guyton kept upgrading and extending the model later on, and upon request they even provided the FORTRAN source code of the model realization to the ones interested. In 1982, the “Human” model appeared [4], representing yet another milestone in the simulation model development. It gave the possibility to simulate a number of pathological conditions on a virtual patient (cardiac, respiratory, kidney failure, etc.) and the therapeutic influence of various drugs, infusions of electrolytes, blood transfusion, etc. Furthermore, the effect of the artificial organ use on normal physiological functions could have been simulated (artificial heart, artificial ventilator, dialysis, etc.). Its current interactive web implementation is available from this addresshttp://venus.skidmore.edu/human.

The latest work results from Guyton's colleagues and students are Quantitative Circulatory Physiology and Quantitative Human Physiology simulators [1]. Models can be downloaded from this address http://physiology.umc.edu/themodelingworkshop/.

3 Pioneer of the Systemic Approach in Physiology Arthur C. Guyton (Fig. 1) was among the pioneers of system analysis in the inquiry of

physiological regulation. He introduced many fundamental concepts regarding short and long time regulation of the circulation and its connection with the regulation of circulating volume, osmolarity and ionic composition of bodily fluids. He worked up a great many original experimental procedures – for instance, he was the first one to measure the value of pressure in the interstitial fluid. However, he was not only an innovative experimenter, but also a brilliant analyst and creative synthesizer. He was able to draw out new conclusions for the dynamics of processes in the body from the experimental

ISBN 987-80-7080-658-6, CD ROM Proceedings, http://www.humusoft.cz/akce/matlab07

3

results and thus explain the physiological basis of a number of regulatory processes in the organism as a whole. Guyton’s research has shown, for example, that it is not only the heart as a pump that controls the cardiac output; but that an equally important roles are played by the regulation of tissue perfusion, dependent on the oxygen supply, as well as on the filling of the vessels and the compliance of great veins. It was A.C. Guyton who proved that the long-term regulation of blood pressure is done by kidneys [9].

When you study the dynamism of regulatory processes, verbal description and common sense are often not sufficient. Prof. Guyton realized this already in the mid sixties, when he studied the factors influencing blood pressure. Hence, he has searched a more exact way of expressing relationships; first using connected graphs and finally also computer models. He created his first computer models, together with his long-term colleague Thomas Coleman, in 1966. As an erudite physiologist and a hand-minded person at the same time, he was engaged in biomedical engineering in times, when this specialization did not yet officially exist.

Remarkably, Guyton did not intend to engage in theoretical medicine at first. His original aim was to work in the clinical field. After he graduated from Harvard University in 1943, he began his surgical internship at Massachusetts General Hospital. His surgical carrier was interrupted by war. He was called into the Navy. However, he worked in bacteriological warfare research during most of this period. After the war, he returned to the surgery, but only for a short while. In 1946, overworked, he suffered a bout of poliomyelitis that left serious consequences – paralysis of the left arm and leg had bound him either to a wheelchair or crutches for the rest of his life. However, his creative spirit did not leave him in this period of hardship, and he invented an electric wheelchair controlled by “a joystick”, as well as a special hoist for easy transfer of disabled people from bed to the wheelchair. Later, he received a Presidential Citation for his invention. The physical handicap ended Guyton’s carrier in cardiac surgery and steered him into the theoretical research. In spite of having job offers at Harvard University, he returned back to his hometown Oxford, Mississippi, where he first taught pharmacology at a two-year medical school; however, not long after that, he became head of the Department of Physiology at The University of Mississippi. He established a world famous physiological school in what used to be a rather provincial institute (on an American scale). Here, he wrote his world-famous textbook of physiology, originally a monograph that has seen its eleventh edition already, as well as more than 600 articles and 40 other books. He has trained many generations of medical students and more than 150 Ph.D. students. In 1989, he passed on the leadership of the institute to his disciple J.E. Hall and as a professor emeritus devoted himself to research and teaching. He died tragically in an automobile accident in 2003.

4 Fixing Errors in Guyton's Chart Guyton was among the first proponents of the formalized description of physiological reality.

Formalization means converting a purely verbal description of a relevant array of relationships into a description in the formalized language of mathematics. Guyton's diagram from 1972 (Fig 2) is a formalized description of results of one of the first significant systemic analysis of physiological functions.

Graphic notation for description of quantitative and structural relations in physiological systems suggested by Guyton was adopted by other authors in the seventies and eighties. For example, in 1977 [2] they used a slightly modified Guyton's notation in their monograph, covering the system analysis of interconnection between physiological regulation systems, [11] formulated, in Guyton's notation, their model of overall regulation of body fluids, etc.

Later on, means of simulation development tools were used for graphic notation of the structure of physiological regulation relations, for example; Simulink by the Mathworks company or open source free software package for teaching physiological modelling and research JSIM [16, 17] (see http://www.physiome.org/jsim/), or recently, graphic means of expression of simulation language Modelica [5].

Simulink diagrams are very similar to the thirty five year old notation used in the original model of A.C.Guyton. Therefore we decided to revive the old model by means of a modern software instrument. We tried to keep the resemblance identical as it was in the original pictorial diagram - the layout, the disposition of wires and the quantity labels are the same.


4

+

+

Corrected

Figure 4: The error in the Non-Muscle Oxygen Delivery subsystem.

The realization of the old diagram is not as smooth as it might seem at first sight, because, there are errors and omissions in the original scheme. In a hand-drawn picture, it does not matter so much, because the overall meaning is still valid (most of the errors are present just on the paper, not in the original FORTRAN implementation). However, if we try to bring the model to life in Simulink, the errors show up. The model either behaves inadequately or even becomes unstable, values start to oscillate and the model complex collapses. There were a few errors – changed signs, a multiplier instead of a divider, changed connection between blocks, missing decimal point, wrong initial conditions, etc. – but it was enough for a wrong functioning of the model. Being acquainted with physiology and system analysis, we could have avoided the mistakes with a little effort.

An easily detectable error in the diagram is, for instance, wrong marking of flow direction in the summation block no. 5 in subsystem Circulatory Dynamics (Fig 3). It is obvious, that the rate of increase in systemic venous vascular blood volume (DVS) is the subtraction (not the summation) between all rates of inflows and rates of outflows. Inflow is a blood flow from systemic arterial system – its rate is denoted as QAO, outflow rate from systemic veins is a blood flow rate from veins into the

right atrium (QVO). The rate change of filling of the vascular system as the blood volume changes (VBD) is calculated from the difference between summation of overall capacity of vascular blood compartments and blood volume – therefore VBD is the outflow rate and not the inflow rate, and in the summator it must have a negative sign.

In subsystem Non-Muscle Oxygen Delivery, there is a wrong depiction of connection in integrative block no. 260 (Fig.4). If the model was programmed exactly as depicted in the original

+QAO DVS

QVO

5 6

0VVS3.257

5

+QAO DVS

QVO

5 6

0VVS3.257

5

Corrected

Figure 3: The error in the Circulatory Dynamics subsystem.


5

RCD3320

331RC1

++

RCD3320

331RC1

-+

Corrected

HM40

336 HMK1600

HM2

HKM

VIE1.5337

HM40

336HMK

1600

HM2

HKM

VIE1.5337

-+

40

400 HM 40

336HMK0.8 HM2

HKM

VIE 1.5337

-

+

90

50

Corrected (A) Corrected (B)

Figure 5: The errors in the Red Cells and Viscosity subsystem.

diagram, the value of non-muscle venous oxygen saturation (OSV) would constantly rise and the model would become unstable very quickly. Besides, there would be an algebraic loop in the model. Correction is simple, input to summator no. 258 is the value of OSV, and therefore it is sufficient to move feedback input to summator behind the integrator as it is indicated in the picture.

Small and simple subsystem Red Cells and Viscosity includes two errors (Fig 5). The first is visible at first sight. It is obvious that the rate of change of red cell mass (RCD) is the subtraction (not the summation) between red cell mass production rate (RC1) and red cell mass destruction rate (RC2). The second error is obvious as well. During calculation of a portion of the blood viscosity caused by red blood cells (VIE) from value of hematocrit (HK) according to the diagram, the viscosity would have to constantly rise, because the value of quantity HM2 would incessantly rise (HK is the input to the integrator). According to the diagram, the value of a variable HM2 is equal to 1600 - in a stable situation and under normal conditions. If we divide this value by a constant parameter HKM (=0.000920), we should arrive at a normal value VIE. Normal value VIE should be 1.5 (formulated as a ratio to viscosity of water). We can find out, by simple calculation, that it is not so, and we will arrive at the correct calculation if we multiply the value HM2 by constant HKM instead of using division. Thus it is obvious, that block no. 337 should be a multiplier unit and not a dividing unit. In order to have the value of a variable HM2 in stable situation constant (and under normal conditions equal to value 1600), the input to integrator must have zero value (block no. 336). Therefore, it is apparent, that the depiction of feedback has been omitted in the diagram. The corrected diagram is shown in picture 6 as "Corrected (A)". Viscosity is proportionate to hematocrit and the integrator acts here as a dampening element. It can be from the experimental data that dependence of viscosity of blood on hematocrit is not linear proportionate [7]. Therefore in a later realization of the model (according to source text in Fortran language) the relation between hematocrit (HK) and portion of blood viscosity was caused by red blood cells (VIE) formulated as follows:

HKMHMHMK

HMVIE)( −

= (1)


6

Corrected

185

158A

.14184

1183

.3333

1 AHC

AH +

185 158A

.14184

1183

.3333

1AHC

AH +

Figure 6: The error in the Antidiuretic Hormone Control subsystem.

Where: 90=HMK

and 3333.5=HKM which is shown in a diagram in fig. 6, marked as Corrected (B). If we compare this picture with the original chart, the integrator no. 336 is replaced with dividing and summator units (and the value of HKM constant is quite different). Maybe, this exact structure should have been originally drawn in the original diagram, and (by mistake, the integrator was drawn instead of divider and summator) a label HKM on the left side next to integrator no. 336 indicates this situation.

An error in Antidiuretic Hormone Control subsystem is not visible at first sight (Fig. 6). According to graphic diagram, the following should hold true:

During stable conditions, according to data on the graphic diagram under normal conditions, the values should be: : 1333.0 =AH , 1=AHC .

Then the integrator 185 will have no zero value and the system will not be in stable condition.

Where is the error?

AH*0.3333 is a normalized rate of antidiuretic hormone creation (ratio of current rate of creation according to the norm). AHC is a normalized concentration of this hormone (according to the norm). How is the normalized concentration of substance from normalized rate of substance creation calculated? The classic compartment approach will answer our question.

In subsystems of conducting ADH creation, aldosterone and angiotensin are calculated in the model from the rate of hormone inflow (normalized as a relative number according to the norm) and hormone concentration (again normalized as a relative number according to the norm).


7

We come out of a simple compartment approach - into a whole-body compartment inflow the hormone at the rate Fi (it is synthesised) and outflows at the rate Fo. Quantity of hormone M in whole-body compartment depends on the balance between inflow and outflow of the hormone.

dtdMFF oi =− . (2)

Rate of depletion of hormone Fo is proportional to its concentration c: ckFo = . (3)

Concentration of hormone c depends on overall quantity of hormone M and on the capacity of distribution area V:

VMc = . (4)

Thus after inserting:

dtdM

VMkFi =− . (5)

Provided that the capacity of distribution area V is constant, we will substitute ratio k/V for constant k1:

Vkk =1 . (6)

We arrive at:

dtdMMkFi =− 1 . (7)

In the model, Guyton calculated the concentration of hormone c0 normalized as a ratio of current concentration c to its normal value cnorm:

normccc =0 . (8)

At invariable distribution area V ratio of concentrations is the same as a ratio of current overall quantity of hormone M to overall quantity of hormone under normal conditions Mnorm:

normnorm MM

ccc ==0

. (9)

If we formulate the rate of flows in a normalized way (as a ratio to normal rate), then under normal conditions: 1=iF ,

0=dt

dM norm .

Therefore: 01 1 =− normMk . (10)

Normal quantity of hormone Mnorm will be:

1

1k

M norm = . (11)

Hence, the relative concentration of hormone c0 can be formulated:

MkM

Mcnorm

10 == . (12)

Thus:

1

0

kcM = . (13)


8

After inserting into differential equation we arrive at:

dtkcd

kckFi

⎟⎟⎠

⎞⎜⎜⎝

⎛

=− 1

0

1

01 , (14)

i.e.:

dt

dck

cFi0

10

1⎟⎟⎠

⎞⎜⎜⎝

⎛=− . (15)

Thus:

( )dt

dckcFi0

10 =− . (16)

According to this equation, the normalized concentration of the hormone c0 is calculated from the normalized inflow of the hormone Fi. In original Guyton's chart, the normalized concentration of aldosterone and angiotensin is calculated in this way. In case of ADH, there is an error in the chart.

The normalized rate of inflow in case of ADH:

AHFi 3333.0= . (17)

The normalized concentration of the hormone is: AHCc =0 , (18)

Coefficient 14.01 =k .

Instead of ( )dt

dckcFi0

10 =− , there is a graphic representation of relation dt

dckcFi0

10 =− .

Correct relation in case of ADH should be:

( )dt

dAHCAHCAH =− 14.03333.0 . (19)

This relation corresponds to a correct part of diagram shown in fig. 6

Quoted examples of errors in the original graphic depiction of Guyton's model do not mean at all that the actual implementation of the model did include the above-mentioned errors. The model was implemented in Fortran language and it functioned flawlessly. What was incorrect was only the graphic depiction of the mathematical relations that did not correspond to the model.

If somebody implemented the model exactly according to the depiction, without thinking over and understanding the meaning of mathematical relations between physiological quantities, then such a model would not function correctly on a computer.

It is interesting, that this complicated schematic diagram was many times overprinted in several publications and nobody made an effort to fix these errors. After all, at the time, when picture schemes were created, no appropriate application had existed yet – pictures arose like a complicated drawing – and to handle redoing such a complicated drawing isn’t so easy. Maybe the authors didn't even want to correct the errors – the ones who took the pain over the analysis of the model easily uncovered the diagrams mistakes, the ones who just wanted to blindly copy, failed.

After all, at that time, the authors even used to send round the program source files in Fortran language, so if somebody wanted to just test the behaviour of the model, s/he did not have to program anything (at the most they had to routinely convert the Fortran program into other programming languages).

5 Results After the correction of errors in the original Guyton's chart, we realized its Simulink

implementation. In the Simulink diagram, we tried to maintain the same distribution of all the individual elements, as in the original diagram.


9

OVA

BFN

271

AOM

02M

P4O

P1O POT QO2

DOB

MO2

RDO

POT

OSV

POV

255

256

257

258

259

267

266

265

272

271

264

263

262

270

260

261

268

269

NON-MUSCLE OXYGEN DELIVERY

2 POV

1 POT

upper limit 8

lower limit 50

2400

0.7

u^3 POT^3

u^3 P40^3

1s

xo

1s xo

512

5

5

0.00333

57.14

8.0001

2688

168

1

4AOM

3 BFN

1 HM

+- +

+

Figure 7: The pictorial block scheme of the original A.C.Guyton's model on the left and the model block diagram in the Simulink software tool. Analogically positioned and numbered blocks represent

the same mathematical operations. Multipliers and dividers: blocks 255, 257, 259, 261, 263, 268 ,272, 270 ; sum blocks: 256, 258, 262, 264, 266, 269; integrator blocks: 260 a 271; function blocks (cubic

function): 265 a 267; high level saturation: between blocks 272 and 286, low level saturation: between blocks 265 and 180. The switches can either be set to receive the input values from other

subsystems, or directly from the user, thus disconnecting the block from the rest of the model.

The only difference is in the graphic shapes of the individual elements - e.g. in Simulink, the multiplier/ divider is represented as a square unlike the "piggy" symbol in Guyton's notation (See Fig. 7). The integrator does not have the sign of integral on itself but the expression "1/ s" (being related to the transcription of Laplace transformation).

In the Simulink model, we also used switches, by which we could couple or uncouple individual subsystems and control loops.

Resultant chart of Simulink model is depicted in Fig 8.

We can transform individual physiological subsystems of the model into the form of Simulink subsystems. The graphic chart of the whole model looks rather better arranged (Fig. 9). Then the diagram of the model resembles the interconnected network of electronic chips – instead of electric signals; however, there is a flow of information in individual conductors - data of the model.

Physiological subsystems are represented by "simulation chips" – conductors with input data are connected to their individual input, and signals with information about the value of individual physiological quantities are distributed from their output “pins” to other “simulation chips”.

Models formulated through the network of "simulation chips" are also the appropriate tools for team collaboration between branches of study [13]. Such a chart is much more legible also for an experimental physiologist who does not have to understand the complicated mathematical structure of a computational network inside a "simulation chip", however s/he understands the structure and functions of physiological relations. S/he can study the behaviour of a model in individual simulation chips on virtual displays and oscilloscopes, which are standard components of the Simulink environment.

In fig. 10, there is a Simulink implementation of a Guyton-Coleman model from 1986, formulated with the help of interconnected "simulation chips". When the reader compares it to a previous picture, s/he can imagine how the model has expanded in the past 14 years.


10

.


269

268

261

260

270

262

263

264

271

272

265

266

267

259

258

257

256

255

POV

OSV

POT

RDO

MO2

DOB

QO2POTP1O

P4O

02M

AOM

271

MUSCLE BLOOD FLOW CONTROL AND PO2

227

226

225

224

223

228

229

230

231

232

233

234

235

238236

237239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

OSA

OVA

BFM

RMO

BFM

PK1

PK2

DVS

PVO

PMO

PM5

RMO

QOM

PMO

PM3

PK3

PM4

P2O

P3O

EXC

AOM

02A

AUAMM

POE

POM

PDO

PVO

POV

POT

OVA

P2O

AOM

AMM

HM

BFN

VPFHM

OVA

upper limit 8

upper limit 8

lower limit 50

lower limit .005

lower limit .001

2400

0.7

0.7

1

2400Xo

u^3 POT^3

u^2PM1^2

u^3 P40^3

u^3P3O^3

1s xo

1s xo

1s

xo

1s

xo

1s xo

0.9864

2.859

0.9999

40

7.983

198.7

8

512

5

5

0.00333

57.14

8.0001

2688

1

1

8

200

8

40

168

1

1

1

400.0125

200

2.8

40

1

800

2500

122

1

57.14

5

0.5

1

840

0.08

51

0.25

0.15

1

60

1

512

8.0001

-1

51


269

268

261

260

270

262

263

264

271

272

265

266

267

259

258

257

256

255

POV

OSV

POT

RDO

MO2

DOB

QO2POTP1O

P4O

02M

AOM

271

NON-MUSCLE LOCAL BLOOD FLOW CONTROL

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

278 277 276 275 274 273

285 282 281 280 279

290

284

283284b286287

288

289

AR1

AK1

POB

POK

POD

POV

ARM

AR1AR3

PON

POA

A2K

AR2

POJ

POZ

POC

A3K

AR3

POR

VASCULAR STRESS

RELAXATION

65

64

63

6261

VV7

VV7

VV1

VV2

VVE

SRK

VV6

195

196

197

198

199

200

201

202

203

205206

207

208

209

210

211

212

213 214

215

216

217

218

219

220

221

222

KIDNEY DYNAMICS AND EXCRETIONTHIRST AND DRINKING

192 193 194

190 191

Z10 Z11

STH

TVD

POT

ANTIDIURECTIC HORMONE CONTROL

181

180179178177

175 176 182183

184

185

158A

186

187

188189

AHM AH4

AH2 AH1

AHC

AH

CNZ

CN8

CNR

CNA

PRAAHZ

AH7

AHY

AH8AU

CIRCULATORY DYNAMICS

VIM

AUM

AUM

VIM

AUM

BFN12

3

4

36

35

31

3233

PGS

RSM

38

34

37

RVS

43

42 41A

41

40

39

VBD

VVE

5 6

7 8 9

DAS

QAO30

QLO

LVM

HPLHMD

QLN

2959

58

28

50

16

PA2

60

PLA

24

25

26

27

VVS

QLO

AUH

HMD

QRO

QRO

AUH

VPEPPA

PL1

PPA

RPV

RPT

RPT

PP1

5453

5556

57

52

51

2322 21

2019 18

4849

4645

47

44

10

11

12

13

1415

LVM

CAPILLARY MEMBRANE DYNAMICS66

67

68

69

70 71

7473

6261

80

79

7877

75

74

72

RVS

BFNPVG

PVS

VB

VP

VRC

PTC

PPCPIF

CFC

VPDVUD

DFP

TVD

VP

CPKCPI

CP1

CPP

CPP PRP

VP

CPRLPK

DLP

PPD

DP0

DPL

DPP

DPC

ANGIOTENSIN CONTROL

154 155 156 157 158

159

160161

162163

153b153a

CNA CNEANM

AN1

ANT

ANC

AN2AN3

AN5ANM

REK

RFN

TISSUE FLUIDS, PRESSURES AND GEL

105PTC

108

107

106

109

104

110

103102

112

113

98

97

96

99

92919089

9394 95

100

101

86

85

84

8387

88

111

DPL

VTL

CPI

PIF

PLD

PTT

GP1

GPD

GPR

VG

VIF PTS

PIF

GPD

DPL

VTC

VTL

VID

VTS

VTD

PTT

DPIVIF

IFP

GP2

VGD

VG

V2D

PG2PGC

PTC

PIF

PIFPTS

PRMCHY

HYL

VG

PGR

PGP

PGH

ALDOSTERONE CONTROL

165 166

167

164

168

169

170

171

172173174AM AM5

AM3AM2

AMC

AMT

AM1AMP

KN1CKE

CNA

ANM

AMR

ELECTROLYTES AND CELL WATER

114 115

116

117 118119

120

121

126

125

122123 124

127

128129130

131

135134133

132CKI CCD

CNAVIC

VIDVIC

KI

KCD KIE KIR

KE1

AM

CKEKEKED

KCD

KID

KOD

REK

NEDNAE

CNA

VTW

VIC

VEC

STHNID

VP

VPF

VTS

HEART HYPERTROPHY OR DETERIORATION

340

341

342

343

344 349

348

347

346

345

350

351

352

PA

PPA4

HPLHPR

PP3

PPAHSL HSR

POT

DHM

HMD

RED CELLS AND VISCOSITY

329

330

331

332

333334

335

337

338

339POT

PO1

POY

PO2

RC1

RCD

VRC

RKC

RC2VRC

VB

HM

VIE

VIM

PULMONARY DYNAMICS AND FLUIDS

PLA

136

137

138

139

140

141

142

143

144

145152

146

147

148

149

150

151

PPA

PCP

PPC

POS

PPI

CPF

PFI

PLF

DFP VPF

PPI

PLF

PLF

PPO

POS

CPN

VPFPPR

PPD

PPN

PPC

CPP

AUTONOMIC CONTROL

292291

294293

296297298

295

307303302

301

305

304308

309

310311

312

313

315

314

316317

318319

320

POQPOT

PA

EXE

POQP2O

Z12EXC

AUCPA1

A1B

AUB

AUN

AU8

AUK AU2

AU6

DAU

Z8

AUJ

AULVV9

VVR

AUH

AUM

AVE

AUY

AUD

AUVAU9

AU

HEART RATE AND STROKE VOLUME

328327 323

322

321324325326

SVO

QLO

HR

PRA

AUHMD


227

226

225

224

223

228

229

230

231

232

233

234

235

238236

237239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

OSA

OVA

BFM

RMO

BFM

PK1

PK2

DVS

PVO

PMO

PM5

RMO

QOM

PMO

PM3

PK3

PM4

P2O

P3O

EXC

AOM

02A

AUAMM

POE

POM

PDO

PVO

POV

POT

ARM

OVA

P2O

AOM

AMM

AMM

VVE

VV7

VUD

RBF

RFN

NOD

AU

VVR

AUH

AUM

AVE

SVO

HM

BFN

VPFHM

OVA

PPCREK

CNEAUM AHM

AM

AHM

PA

NOD

DPC

AUZ

ARM

VIM

AUM

ANMAVE

RBF

PC

VVR

VV7

AUH

HMD

HSR

HPR

STH

TVD

VTL

AHM

ANM

CNE

AM

VID

CKE

CNA

VTW

PCVB

VP

DPC

CPP

VTC

VTL

DPL

PTC

CPI

VTS

PIF

HPR

HPL

HMD

VIM

HM

VRC

DFP

VPF

PPD

BFN

BFM

RVS

PVS

PRA

QLOPLA

PPA

PA

HSL

PPCVTC

PC

GP3APD

algebraic loop

breaking

algebraic loop

breaking

AAR-afferent arteriolar resistance [torr/l/min]AHM-antidiuretic hormone multiplier, ratio of normal effectAM-aldosterone multiplier, ratio of normal effectAMC-aldosterone concentrationAMM-muscle vascular constriction caused by local tissue control, ratio to resting stateAMP-effect of arterial pressure on rate of aldosterone secretionAMR-effect of sodium to potassium ratio on aldosterone secretion rateAMT-time constant of aldosterone accumulation and destructionANC-angiotensin concentrationANM-angiotensin multiplier effect on vascular resistance, ratio to normalANN-effect of sodium concentration on rate of angiotensin formationANP-effect of renal blood flow on angiotensin formationANT-time constant of angiotensin accumulation and destructionANU-nonrenal effect of angiotensinAOM-autonomic effect on tissue oxygen utilizationAPD-afferent arteriolar pressure drop [torr]ARF-intensity of sympathetic effects on renal functionARM-vasoconstrictor effect of all types of autoregulationAR1-vasoconstrictor effect of rapid autoregulationAR2-vasoconstrictor effects of intermediate autoregulationAR3-vasoconstrictor effect of long-term autoregulationAU-overall activity of autonomic system, ratio to normalAUB-effect of baroreceptors on autoregulationAUC-effect of chemoreceptors on autonomic stimulationAUH-autonomic stimulation of heart, ratio to normal

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 restEXE-exercise effect on autonomic stimulationGFN-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 hypoxiaHPL-hypertrophy effect on left ventricleHPR-hypertrophy effect on heart, ratio to normalHR-heart rate [beats/min]HSL-basic left ventricular strengthHSR-basic strength of right ventricleHYL-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]

KID-rate of potassium intake [mmol/min]KOD-rate of renal loss of potassium [mmol/min]LVM-effect of aortic pressure on left ventricular outputMMO-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 saturationOSV-non-muscle venous oxygen saturationOVA-oxygen volume in aortic blood [ml O2/l blood]OVS-muscle venous oxygen saturationO2M-basic oxygen utilization in non-muscle body tissues [ml/min]PA-aortic pressure [torr] PAM-effect of arterial pressure in distending arteries, ratio to normalPC-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]

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 autoregulationPON-sensitivity of intermediate autoregulationPOS-pulmonary interstitial fluid colloid osmotic pressure [torr]POT-non-muscle cell PO2 [torr]POV-non-muscle venous PO2 [torr]POY-sensitivity of red cell productionPOZ-sensitivity of long-term autoregulationPO2-oxygen deficit factor causing red cell productionPPA-pulmonary arterial pressure [torr]PPC-plasma colloid osmotic pressure [torr]PPD-rate of change of protein in pulmonary fluidsPPI-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 functionQRN-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 functionRFN-renal blood flow if kidney is not damaged [l/min]RKC-rate factor for red cell destructionRM0-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 pressureRVS-venous resistance [torr/l/min]SR-intensity factor for stress relaxationSRK-time constant for stress relaxation

STH-effect of tissue hypoxia on salt and water intakeSVO-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 waterVIC-cell volume [l]VID-rate of fluid transfer between interstitial fluid and cells [l/min]VIE-portion of blood viscosity caused by red blood cellsVIF-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

AUK-time constant of baroreceptor adaptationAUL-sensitivity of sympathetic control of vascular capacitanceAUM-sympathetic vasoconstrictor effect on arteriesAUN-effect of CNS ischemic reflex on auto-regulationAUV-sensitivity control of autonomies on heart functionAUY-sensitivity of sympathetic control of veinsAUZ-overall sensitivity of autonomic controlAVE-sympathetic vasoconstrictor effect on veinsAlK-time constant of rapid autoregulationA2K-time constant of intermediate autoregulationA3K-time constant of long-term autoregulationA4K-time constant for muscle local vascular response to metabolic activityBFM-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 hypoxiaDLA-rate of volume increase in pulmonary veins and left atrium [l/min]

LIST OF VARIABLES

336

HM2

336b

HMK

upper limit 8

upper limit 8lower limit 4

upper limit 8

upper limit 15.0lower limit 0.4

upper limit 1

lower_limit_0

lower limit 6

lower limit 50

lower limit 5

lower limit 4

lower limit 3

lower limit 0.95

lower limit 0.7lower limit 0.5

lower limit 0.3

lower limit 0.2375

lower limit 0.2

lower limit 0.0003

lower limit 0.0001

lower limit 0

lower limit 0

lower limit .005

lower limit .001

12

12

171

3

210

90

1

0

2

2400

1

1

1

75

25

2130

3550

1

11.4

0.7

0

1

0.7

1

1

2400Xo

00

1.4

50RVM = f(PP2)

30.5

RAR

96.3

RAM

0-4

15

20

QRN = f(PRA)

0.6

QRF

0-4

15

20

QLN = f(PLA)

(u/12)^2PTT = (VTS/12)^2

00

20

10PTS = f(VIF)

2-(0.15/u) PPI = 2 - (0.15/VPF)

u^0.625 PP3^0.1

u^3 POT^3

0.33

u^2PM1^2

u^3

PC^3

u^0.625 PA4^0.625

u^3 P40^3

u^3P3O^3

10u

10u

sqrt

10u

00

1.4

260LVM = f(PA2)

1sxo

1sxo

1sxo

1s

xo

1s

xo

1s

xo

1sxo

1s

xo

1s xo

1s

xo

1s

xo1s

xo

1s xo

1sxo

1s xo

1s xo

1s xo

1s xo

1s

xo

1s xo

1s

1s

1sxo

1sxo

1s

xo

1s

xo

1s xo

1s

5

GF4

0.01028

0.3216

0.9864

2.859

100

0.9999

15.18

0.014535.07

0.09477

3.774

2.781

1.011

2.859

-9.648e-008

0.01252

40

-1.154e-008

2

40

0.999

1

1

1

-6.334

11.98

20.18

7.983

5.045

0.037910.001879

0.001879

16.7969.76

0.03824

3.002

5.00216.79

198.7

39.97

142.1

5

8.154e-006

0.9984

10

1.004

0.9996

0.0009964

1

0.9387

0.07026

0.9997

0.9994

0.9998

2.949

0.9993

0.1024

1.2

1.2

0.001022

8

0.0005

4.0

3.3

0.042

150.1152

1.6379

0.00047

85

512

0.007

1.6283e-007

0.007 0.4

0.1

1.79

0.4

0.4

0.003550.495

5

2.738

1

0.026

1

0.035720

0.85

0.00480.30625

3.25

5

1717

1

0.38

0.0050.1

0.1

100

1

0.0007

0.00333

2

1

139

0.3333

0.0785

6

0.14

6

8.25 4

57.14

0.009

0.01

1

1

1

0.125

0.00781

1851.66

31.67

8.0001

0.0250.001

1000

0.8

1

33

0.5

11

15

0

5

100

1

2.8

0

0.301

0.3

2.9

3.7

28

517

0.002

0.04

70

3

0.3

1

1

2.95

1

1

1

0

0

0.0125

40

0.1

2688

1

2

1 1

1

20

-6.3

0.04

0.002

5

1

12

142

5

0

1

10

1

1

0

1

20

1.2

1.2

0.1

0.001

0

1

0.04

20

0

0.002

1

0.001

0

5

-6.3

2

3.72.8

2.9

0.001

1

0.06

1

51

1

1

1

0

2.95

17

1.2

40

1

1

1

1

1

1.6

40

1

1

8

1

8

100

5

0

1

1

70

28

0

15

1

5

8

8

8

200

15100

0.04

0

0.002

1

12

3

0.0125

1

0.1

8

1

142

5

100

11520

1

1.2

142

401

8

142

0

1

1

1

168

1

1

10

1

128

100

0.3

1

1

1

1

400.0125

200

2.8

40

1

800

2500

122

1

57.14

5

0.5

1

840

0.08

51

0.25

0.15

1

32

0.5 1

40

2

0.21

6

0.0005

1

1

1.24

1

8

3

1

0.5

1

0.85

0.15

0.7

60

0.3

3.159

8

0.4

0.375

0.000225

0.0003

11

0.0003

0.4667

1

0.0125

0.550.333

1.5

0.5333

8.25

100

0.0000058

464e-7

512

0.0025

6

57600

15

57600

100

2850

0.01

140

0.013

8.0001

0.0028

0.00014

0.00042

0.1

0.00352

20.039

19.8

-0.017

60

9

-1

0.25

24.2

-5.9

57

0.4

0.1

0.0047.8

0.25

0.013332

51

0.0825

CV

6

CNY

2.5

CNX

0.2

CN7

0.0212

CN2

u^2 CHY^2

PA1 AUN

AUN CALCULATION

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

when PA1>=50: AUC=0

AUN calculation

uv

AUJ^AUZ

PA1 AUC

AUC CALCULATION

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

when PA1>=80: AUC=0

AUC calculation

u^3 AUB^3

PA1 AUB

AUB CALCULATION

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

when PA1>=170: AUB=0

AUB calculation

1.5

ARF

0 0

4

200AMP = f(PA)

1

(1.2/u)̂ 3

(1.2/RFN)^3

1s

xo

VVS

1s

xo

VRA

1s

xo

VPA

1s

xo

VLA

1sxo

1s

xo

1s

xo

VAS31sxo

1s xo

1s xo

lower limit 0.35

lower limit 0

VIM

VIM

AAR

AAR

AAR

RR

RFN

GLP

PPC

PFL

GFN

GFR

TRR

VUD

AHM

AM

AM

NOD

EVR

RBF

ANU

ANU

RAR

VAS

VAS VAE

PA

PA

PAMPAM

RAM

PGSRSN

BFM

QAO

RV1

RV1

VVS VV8

PVS

PVS

PVS

PVS

QVO

QVO

QVO

DVS

QLO

QLN

QLN

DLA

VLA

VLA

VLE

PLA

PLA

PLA

VB

RVM

RVM

QRN

RVG

DRA

VRA

VRA

PRA

PRA

PR1

PR1

PP2

VPA

VPAPGL

QPO

QPO

RPA

CPA

RFN

GF3

GF3

Figure 8: Guyton's overall regulation model of Circulation - implementation in Matlab/Simulink. The layout and block numbering is exactly the same as in the original Guyton's scheme (Fig. 2). The difference is, that

this scheme is also a fully functional simulation model.


11

Simulink implementation of the (corrected) Guyton's model made by us is available for

download from the address http://physiome.cz/Guyton to anyone interested. At the same address, our Simulink implementation of a much complex sequel of the model from 1986 can be found too. Further, there is also a detailed description of all mathematical relations used with their reasoning (however, for the present time it is in the Czech language only).

6 From Simulink Diagram to Simulation Games During Physiological Teaching We use Simulink implementation of Guyton's model as an educational tool to teach physiology

to undergraduate and postgraduate students at the Czech Technical University (ČVUT). This structure of Simulink diagram (in a form of "simulation chips") is however, too abstract for medical students. It is ideal, if their teaching models have the form of schematic pictures to which they are accustomed, for example from the Atlas of Physiology [18]. Unlike the book, these pictures can be interactive, and

AMM

AOM

P2O

OVA

AU

EXC

BFM

HM

VPF

NON-MUSCLE OXYGEN DELIVERY MUSCLE BLOOD FLOW CONTROL AND PO2

40

POV

8

POT

200

OVA

HM

OVA

BFN

AOM

POT

POV


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

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

POV-non-muscle venous PO2 [torr]


VPF

HM

BFM

EXC

AU

OVA

P2O

AOM

AMM


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

OUTPUTS: OVA - oxygen content of arterial blood

[ml O2 STPD/l blood] P2O -

AOM - autonomic effect on tissue oxygenation AMM - muscle vascular constriction caused by logical tissue control

[multiplifier, ratio to normal]

Muscle Blood Flow Control And pO2

40

HM

39.96

198.5

2.857

0.9982 0.9996

0.01251

0.9982

198.5

8

0.9879

1.019

39.96

8.005

40 1

1

8

200

1

1

40

0.0125

1

2.8

BFN

1

AOM

PVS

RVS

BFN

BFM

PA

PPA

PRA

PLA

QLO

VVE

PC

VV7

VB

VVR

RBF

AVE

HPR

HMD

HPL

ANM

AMM

AUM

ARM

VIM

AUH

HSR

HSL

AMM

AOM

P2O

OVA

AU

EXC

BFM

HM

VPF

AUM

PPC

AM

CNE

AHM

VIM

REK

PA

AHM

POT

TVD

STH

AU

CNA

PRA

RFN

REK

CNACNE

ANM

RVS

VUD

BFN

PVS

VRC

PIF

PTC

DFP

TVD

VTL

PPD

CPI

DPL

VB

DPC

PC

VP

CPP

PPC

VTC

ANM

PA

CKE

CNA

AM

DPC

VTC

VID

CPI

PTC

DPL

VTL

VTS

PIF

PA

PPA

POT

HPR

HPL

HMD

POT

VB

HM

VIM

VRC

PPA

PLA

CPP

PPC

VPF

PPD

DFP

QLO

HMD

AU

PRA

AUM

AVE

AUH

VVR

AU

POT

EXC

P2O

PA

POVARM

VID

NOD

STH

VPF

VP

VTS

CNA

CKE

VTW

AM

REK

VUD

RBF

RFN

NOD

AHM

NON-MUSCLE OXYGEN DELIVERY MUSCLE BLOOD FLOW CONTROL AND PO2

VASCULAR STRESS RELAXATION

KIDNEY DYNAMICS AND EXCRETIONTHIRST AND DRINKING

ANGIOTENSIN CONTROL

ALDOSTERONE CONTROL

ANGIOTENSIN CONTROL

ELECTROLYTES AND CELL WATERTISSUE FLUIDS, PRESSURES AND GEL





AUTONOMIC CONTROL

NON-MUSCLE LOCAL BLOOD FLOW CONTROL


CAPILLARY MEMBRANE DYNAMICS

VVE VV7

VASCULAR STRESS RELAXATION

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

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

Vascular Stress Relaxation

VTC

DPC

VID

VTL

DPL

PTC

CPI

VTS

PIF

TISSUE FLUIDS, PRESSURES AND GEL

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

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]

Tissue Fluids, Pressures and Gel

POT

AHM

STH

TVD

THIRST AND DRINKING

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 or otherwise [l/min]

Thirst And Drinking

POT

VB

VIM

VRC

HM


INTPUT: POT - non-muscle cell PO2 [torr]

VB - volume of blood [l]

OUTPUT: VIM - blood viscosity [ratio to normal]

HM - hematocrit [%] VRC - volume of red blood cells []

Red Cells And Viscosity

PPA

PLA

PPC

CPP

DFP

VPF

PPD


INTPUTS: PPA - pulmonary arterial pressure [torr]

PLA - left atrial pressure [torr] PPC - plasma colloid osmotic pressure [torr]

CPP - plasma protein concentration

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]

Pulmonary Dynamics and Fluids

40

POV

8

POT

200

OVA

POV ARM

NON MUSCLE LOCAL BLOOD FLOW CONTROL

INTPUT: POT - non-muscle cells PO2 [torr]

OUTPUT:

ARM - vasoconstrictor effect of local blood flow autoregulation in non-muscle tissues

[ratio to normal]

Non-Muscle Local Blood Flow Control

HM

OVA

BFN

AOM

POT

POV


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

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

POV-non-muscle venous PO2 [torr]


VPF

HM

BFM

EXC

AU

OVA

P2O

AOM

AMM


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

OUTPUTS: OVA - oxygen content of arterial blood

[ml O2 STPD/l blood] P2O -

AOM - autonomic effect on tissue oxygenation AMM - muscle vascular constriction caused by logical tissue control

[multiplifier, ratio to normal]

Muscle Blood Flow Control And pO2

PA

PPC

VIM

REK

CNE

AUM

AHM

AM

VUD

RBF

RFN

NOD

KIDNEY DYNAMICS AND EXCRETION

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]

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]

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]

Kidney Dynamics and Excretion

AU

HMD

PRA

QLO

SVO


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]

OUTPUTS: SVO - stroke volume [l]

Heart Rate and Stroke Volume

PA

PPA

HSL

POT

HSR

HPR

HPL

HMD


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]

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

Heart Hypertrophy or Deterioration

40

HM

AM

REK

NOD

STH

VPF

VP

VTS

VID

CKE

CNA

VTW

ELECTROLYTES AND CELL WATER

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]

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]

Electrolytes and Cell Water

1

0.9988

0.9399

7.999

100

15.19

-6.334

11.96

0.001887

0.0385

0.01395

5.101

0.04

20.4

7.527e-006

0.001902

0.9925

39.95

5.001

142.2

11.96

15.19

3.001

0.01251

7.527e-006

1.005

0.09917

0.9925

142.2

0.9985

5.001

100

2.861

0.001887

0.001

-3.722e-007

5.101

-6.334

39.99

198.7

2.861

1

2

100

2.784

3.775

2.861

0.001902

27.99

69.97

3.001

16.82

0.03842

5.001

5.075

0.0385

20.4

-1.524e-006

0.0009778

0.9985

1.201

9.834

142.2

0.09827

142.2

0.09827

0.9995

1.003

1.0057.999

1.013

0.0010.9995

0.0009778

0.09917

1.201

0.3219

1.002

100

0.9988

0.9995

9.834

0.9925

1.201

27.99

0.010410.3219

3.775

0.9873

0.01251

1

198.7

7.982

5.075

0.09827

1.003

1

1.003

7.982

7.999

100

1

5.001

1

1

1.001

1.013

0.01041

2.948

16.82

1.201

1.001

0.9873

0.9985

1.002

40 0.9399

39.99

1.003

1.001

1.002

1.001

2.948

0.07019

-1.524e-006

0.01251

15.19

-3.722e-007

7.999

69.97

27.99

0.01395

7.999

39.99

2

0.9988

5.001

1

1

40

2.784

1

15

0

5

100

1

2.8

0

0.3

2.9

3.7

28

5

17

0.002

0.04

70

3

1

1

2.95

1

1

1

0

0

0.0125

40

1

21

1

1

20

-6.3

0.04

0.002

5

12

142

5

0

1

10

1

0

1

1.2

1.2

0.1

0.001

0

1

0.04

20

0

0.002

0.001

0

5

-6.3

2

3.7

2.8

2.9

0.001

1

1

5

1

1

1

1

0

2.95

17

1.2

1

1

1

1

1

1.6

40

1

8

8

100

5

0

1

1

70

28

0

15

5

8

8

8

200

15

100

0.04

0

0.002

12

3

0.0125

1

0.1

1

142

5

100

1

1.2

142

1

8

142

0

1

1

1

1

1

10

1

1

28

100

0.3

1

1

40

0.0125

1

1

1

ARM

VIM

AUM

ANM

AMM

AVE

RBF

PC

VVR

VV7

AUH

HMD

HPL

VB

HSR

HSL

HPR

BFM

RVS

PVS

VVE

PRA

QLO

PA

BFN

PPA

PLA


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 depressant effect of hypoxia

HPL - hypertrophy effect on left ventricle VB - blood volume [l]

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]

Circulatory Dynamics

VUD

RVS

BFN

PVS

VRC

PIF

PTC

DFP

TVD

VTL

PPD

CPI

DPL

PC

VB

VP

DPC

CPP

PPC

VTC

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

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

Capillary Membrane Dynamics

2.8

BFN

PA

POT

P2O

EXC

AU

VVR

AUH

AUM

AVE

AUTONOMIC CONTROL

INTPUTS: PA - systemic arterial pressure torr

POT - non-muscle cell PO2 [torr] P20 -

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]

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]

Autonomic Control

AU

PRA

CNA

AHM

ANTIDIURECTIC HORMONE CONTROL

INTPUT: AU - overall activity of autonomic system,

ratio to normal PRA - right artial pressure

CNA - extracellural sodium contrentration

OUTPUT: AHM - antidiurectic hormone multiplifier,

ratio of normal effect

Antidiurectic Hormone Control

REK

RFN

CNA

ANM

CNE

ANGIOTENSIN CONTROL

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

OUTPUTS: ANM - angiotensin multilier factor on vascular resistance

[ratio to normal] CNE - sodium concentration abnormality causing third factor effect

Angiotensin Control

ANM

PA

CKE

CNA

AM

ALDOSTERONE CONTROL

INTPUT: ANM - angiotensin multiplier effect on vascular resistance,

ratio to normal PA - aortic pressure [torr]

CKE - extracellural potassium concentration CNA - extracellural sodium concentration

OUTPUT:

AM - aldosterone multiplier, ratio of normal effect

Aldosterone Control

1

AOM

Figure 9: Guyton's overall regulation model of Circulation - implementation in Matlab/Simulink using

Simulink subsystem blocks as "simulation chips".


12

HSR

HPR

HPL

11.98

VTSN

0.1

VRA0

3

VPN

0.30625

VPA0

3VP

0.4

VLA0

0VID

25VICnorm

0.495

VAS0

PLURC

GFN

NODN

KODN

AHM

REK

UROD

VUDN

VUD

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]

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]

Urea and Water Excretion

URFORM

UROD

VTW

PLURCNORM

PLURC

PLUR

UREA

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]

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

PLUR - total body urea content[mmol/l]

Urea

VVR

ANU

ANY

VV6

VV7

ATRVFB

VVS0

UNSTRESSED SYSTEMIC VENOUS VOLUME

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

OUTPUT: VVS0 - the maximum volume ov venous system at zero volume

(so called unstressed venous volume) [l]

Unstressed volume in systemic venous tree

0.24

URFORMPOT

AHC1

ANM

DR

STHENABLED

TVDENABLED

STH

TVD

THIRST,DRINKING AND SALT APPETITE

INTPUTS: POT - non-muscle cell PO2 [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

OUTPUTS: STH - salt appetite multiplier factor [ratio to normal]

TVD - actual rate of fluid intake [l/min]

Thirst, Drinking and Salt Appetite

PRA

ATRVFBM

ATRRFBM

AH7

ATRVFB

ATRRFB

THE VOLUME RECEPTOR FEEDBACK MECHANISM

INPUTS: 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]

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]

The volume receptor feedback mechanism

CNA

AUP

ANM

PA

AH7

ADH

AHMRM

AHC1

AHM

AHMR

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.

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

The control Functions of Antitiuretic Hormone

NAPT1

REK

ANXM

ANG

ANUBRM

ANUVM

ANM

ANU

ANUBR

ANUVN

ANC

THE CONTROL FUNCTIONS OF ANGIOTENSIN

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

OUTPUTS: ANM - angiotensin multilier factor on vascular resistance [ratio to normal]

ANU - angiotensin multilier factor on peripheral arteriolar resistance [ratio to normal]

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

of systemic veins [ratio to normal] ANC - angiotensin concentration in blood [ratio to normal]

The control Functions of Angiotensin

ANM

CKE

ALD

AMK

AMNA

AMC

THE CONTROL FUNCTIONS OF ALDOSTERONE

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]

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

The control Functions of Aldosterone

1

TVDENABLED

278.6TSP0

1

TENSGN

1TENSG

PVS

BFN

RVS

PC

SYSTEMIC CAPILLARY PRESSURE

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]

OUTPUT: PC - systemic caplillary pressure [torr]

Systemic Capillary Pressure

NAPT1

RFAB

VUDN

AMNA

AHM

REK

DIURET

NADT

DTNAI

NODN

NOD

CNU

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]

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]

Sodium Excretion

1

STHENABLED

PRA

PPA

AUH

OSA

HSR

HPR

HMD

QLO

QLN

QRO

QRN

RVM

RIGHT HEART PUMPING

INTPUTS: 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

and other factors [ratio to normal] QLO - output of left ventricle [l/min]

QLN - normalised output of the left heart [l/min]

OUTPUTS: QRO - actual right ventricular output [l/min]

QRN - normalised right ventricular output [l/min] RVM - depressing effect on right ventricle of pulmonary

arterial pressure [ratio to normal]

Right Heart Pumping

PA

RAM

RAR

MYOGRS

AUM

VIM

ANU

AHMR

ATRRFB

AMM

ARM

RVSM

AVE

ANUVN

PC

RSN

RSM

RVS

RESISTANCES IN THE SYSTEMIC CIRCULATION


RAM - basic vascular resistance of muscles [torr min/l] RAR - basic vascular resistance of non-muscle and non-renal

tissues [torr min/l] MYOGRS - myogenic autoregulation effect on vascular resistance

in muscle and in non-renal tissue (multiplier, ratio to normal) AUM - sympathetic vasoconstrictor effect on arteries

in muscle and non-renal tissues [multiplier factor, ratio to normal]

VIM - blood viscosity [ratio to normal] ANU - nonrenal effect of angiotensin [ratio to normal]

AHM - antidiuretic hormone effect to non renal vascular resistance, multiplier (ratio to normal effect)

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] AMM - muscle vascular constriction caused by local

tissue control [multiplier, ratio to resting state) 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

stretch in the venous system [ratio to normal] AVE - multiplier factor for the effect of the autonomic nervous system

on venous resistance [ratio to basal effect] ANUVN multiplier factor for the effect of angiotensin

on venous resistance [ratio to normal] PC - systemic caplillary pressure [torr]

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]

Resistances in the Systemic Circulation

PPA

PLA

QPO

RPA

RPV

RPT

PVP

RESISTANCES IN THE PULMONARY CIRCULATION AND PULMONARY VENOUS PRESSURE


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

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]

Resistances in the Pulmonary Circulation and Pulmonary Venous Pressure

PA

GBL

PVS

AAR

EAR

REK

PAR

RFN

RR

RBF

RENAL PERFUSION

INTPUTS: PA - systemic arterial pressure[torr] GLB - 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]

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]

Renal Perfusion

OSA

VP

VIM

RFN

REK

VRC

VB

HM

RC1

RC2

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]

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]

Red cells production and destruction

1RVSM

1.2RFN

1

REK

30.52

RAR

96.3

RAM

VPF

DOB

RMO

PO2DEF

PO2AMB

HM

OSA

OVA

PULMONARY O2 DELIVERY

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

OUTPUTs:

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

Pulmonary O2 Delivery

PPA

PLA

PPC

CPP

CPF

DFP

VPF

PCP

POS

PPI

PFI

PLF

CPN

PPN

PPR

PPD

PULMONARY FLUID DYNAMICS


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] PCP - pulmonary capillary pressure [torr]

POS - osmotic pressure in pulmonary interstitial fluid pressure [torr] PPI - pulmonary interstitial fluid pressure [torr]

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]

PPR - total quantity of protein in pulmonary interstitial fluid [g] PPD - rate of loss of protein through the pulmonary capillary

membrane [g/min]

Pulmonary Fluid Dynamics

CKE

CNA

NADT

DTNAI

ANM

AMK

RFAB

REK

VUDN

KODN

KOD

CKU

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]

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]

Potassium Excretion

VP

VTCLP

DPL

CPI

LPPR

PPD

DPR

PPC

DPC

CPP

DLP

PLASMA PROTEINS DYNAMICS

INTPUTS: VP - plasma volume [l]

VTCLP - rate of leakage of whole plasma through 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] PPD - rate of loss of protein through the pulmonary capillary

membrane [g/min] DPR - rate of loos of protein through the kidney [g/min]

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]

Plasma Protein Dynamics

RFN

GLPC

RFAB

RCPRS

PERITUBULAR CAPILLARIES

INTPUTS: RFN - renal blood flow if kidney is not damaged [l/min]

GLPC - average glomerular plasma colloid osmotic pressure [torr]

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]

Peritubular Capillaries

8

PXTP

1PO2DFF

150PO2AMB

4

PLURCNORM

60

OMM

164.5

O2M

POT ARM

NON MUSCLE LOCAL BLOOD FLOW CONTROL

INTPUT: POT - non-muscle cells PO2 [torr]

OUTPUT:

ARM - vasoconstrictor effect of local blood flow autoregulation in non-muscle tissues

[ratio to normal]

Non-muscle Local Blood Flow Control

0.1NID

PAR

MYOGTAU

TENSGN

MYOGRSAA

MYOGENIC AUTOREGULATION OF AFFERENT ARTERIOLE

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

OUTPUT: MYOGRSAA - myogenic autoregulation effect on vascular resistance

in afferent arteriole [multiplier, ratio to normal effect]

Myogenic Autoregulation of Afferent Arteriole

PA

PC

MYOGTAU

TENSGN

MYOGRS

MYOGENIC AUTOREGULATION


PC - capillary pressure [torr] MYOGTAU - time delay factor of myogenic response

(in normal condition TENSTC= 240 min) TENSGN - factor of effectiveness of myogenic response

OUTPUT: MYOGRS - myogenic autoregulation effect on vascular resistance

in muscle and in non-renal tissue [multiplier, ratio to normal]

Myogenic Autoregulation

PMO AMM

MUSCLE LOCAL BLOOD FLOW CONTROL

INTPUT: PMO - muscle cells PO2 [torr]

OUTPUT:

AMM - vasoconstrictor effect of local blood flow autoregulation in muscles

[ratio to normal]

Muscle Local Blood Flow Control

CNA

GFN

NAPT1

RNAUG1

MACULA DENSA

INTPUTS: CNA - Extracellular sodium concentration [mmol/l]

GFN - glomerular filtration rate if kidney is not damaged [l/min]

OUTPUTS: RNAUG1 - macula densa feedback signal

[ratio to normal effect] NAPT1 - delivery of sodium to the macula densa area

[ratio to normal value]

Macula densa

240

MYOGTAU1

240

MYOGTAU

PLA

PA

AUH

OSA

HSL

HPL

HMD

QLO

QLN

LVM

LEFT HEART PUMPING

INTPUTS: 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] HMD - cardiac depressant effect of hypoxia, shock

and other factors [ratio to normal]

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]

Left Heart Pumping

0.03LPPR

0.06

KID

VTS

DPC

TSP0

PGH

PTC

VTL

DPL

CPI

PTT

PIF

PTS

VIF

VG

TSP

INTERSTITIAL TISSUE FLUIDS, PRESSURES AND PROTEIN DYNAMICS

INTPUTS: VTS - total interstitial fluid volume [l]

DPC -rate of influx protein into the interstitial fluid from plasma [g/min] TSP0 - initial value of total interstitial tissue proteins [g]

OUTPUTs:

PGH - hydrostatic pressure in tissue gel [torr] 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] PTT - total interstitial tissue pressure [torr]

PIF - pressurte in the free interstitial fluid [torr] PTS - solid tissue pressure [torr] VIF - free interstitial fluid volume[l]

VG - tissue gel volume[l] TSP - total interstitial tissue proteins [g]

Interstitial Tissue Fluids, Pressures and Gel Dznamics

PA

QAO

PPA

HSR

HSL

POT

HPR

HPL

HMD



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]

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

Heart hypertrophy or deterioration

AUR

HMD

PRA

QLO

HR

SVO


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]

OUTPUTS: HR - heart rate [beats/min]

SVO - stroke volume [l]

Heart Rate and Stroke Volume

0.1

HSR

1

HSL

PAR

RFN

AAR

HM

PPC

PXTP

GLFC

REK

GFR

GFN

GLP

GLPC

PFL

GLOMERULUS

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]

GFLC - glomerular filtration coefficient [l/torr/min] REK - percent of normal renal function [ratio to normal]

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]

Glomerulus

0

GLB

0.0208

GFLC1

0

FIS

VP

VTS

VPF

NID

STH

NOD

KID

KOD

AMK

ACLK

VICNorm

VEC

VIC

VTW

VID

NAE

CNA

CKE

KI

CKI

KCD

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]

Extracellular and Intracellular Fluid Electrolytes and Volumes

EARK

RNAUG1

EFARF

ANM

VIM

EAR

EFFERENT ARTERIOLE

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]

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

Efferent Arteriole

VVE

VV6

VV7

VENOUS STRESS RELAXATION

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

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]

Effect of stress relaxation on basic venous volume

1

EXC

0

EFARF

43.333

EARK

278.7

0.003815

23.2

0.09873

11.41

0.6012

0.004489

0.9856

5.687

-4.683

0.104

1.003

0.00119

1.005

0.0007524

0.01242

1

0.809

1

0

0.905

2.945

1

1.152e-005

1.16e-005

40

2

5

0.9503

2321

168.6

0

4.708

37.9

168.2

0.6632

49.93

0.0049651.142

0.5892

0.0006392

1.035

1.167

0.84951.167

1

1

1.001

1

99.85

2.669

407.728

2397

2.856

61.5

61.53

0.6667

7.754

38.09

0.9625

7.119

1.05

0.05863

80.3

-0.4086

1.009

10.81

1.652

1.43

2.915

35.9

96.65

17.67

14.1

0.809

0.809

4.708

4.46

4.708

1.494

0.001962

0.9803

1.01

0.06686

2.267e-006

1.005

0.00119

0.004256

10.5

-2.687

17.67

2.856

2.669

0.2387

1

3.082

4.46

99.85

17.67

-0.4086

14.1

17.67

1.035

0.9625

0.9503

1

0

1.012

1.009

1.142

2.915

4.017

0.9714

0.9714

41.48

50.07 47.44

0.905

6.965

1

1

0.5776

0.06686

0.1353

0.1246

4.002

0.001962

1

0.9969

4.708

1.494

0.9803

0.9714

0.5803

1.161

142.2

5.068

1

0.5776

0.9527

0.3739

0.1246

0.001962

1.01

1.494

0.1246

142.2

1

0.9714

1

1.142

1.047

3.277

0.9714

41.48

1.05

0.9969

47.44

1.047

99.85

30.53

40

99.85

0.7535

50.07

1.047

50.07

1

7.728

7.728

99.85

1.167

142.2

99.85

4.246

5.068

0.9143

7.754

0

1

0.7953

0.7953

0.5776

0.9143

0.9803

21.04

0.7395

0.9714

0.9143

1

1.047

91.54

20.65

0.9783

0.9527

0.001962

0

0.001962

0.2387

34.08

68.97

0.06686

99.85

0.5803

1.161

0.1353

0.1353

1.167

1.05

1.01

0.06686

5.991

33.45

0.1246

1.047

195.5

0.9915

2.669

1.025

4.708

0.3314

14.1

30.53

0.1009

160

4.002

-0.05811

14.98

24.99

1.025

142

3549

5.068

142.2

2131

-0.001555

39.97

0.9915

0.0118

40

4.708

1.025

61.53

168.2

40

0.1393

19.97

-10.71

8.891e-005

8.664e-005

0.9775

3.082

195.5

72.93

-0.007738

2.088

2.957

0.0006743

12.01

-2.687

10.5

0.004256

0.3959

4.017

99.85

OVA

BFN

HM

AOM

O2M

OSV

POV

POT

DOB

MO2

QO2

NON MUSCLE O2 DELIVERY

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]

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]

Delivery of Oxygen to the Non-muscleTtissues

OVA

BFM

HM

AOM

OMM

EXC

OVS

PVO

PMO

RMO

MMO

QOM

MUSCLE O2 DELIVERY

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]


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]

Delivery of Oxygen to the Muscles

0

DR

0DPR

1

DIURET

VB

QRO

QLO

VVS0

VAS0

VRA0

VPA0

VLA0

CAS

CV

CRA

CPA

CLA

RSN

RSM

RPT

RR

VIM

FIS

PA

PVS

PRA

PPA

PLA

VAS

VVS

VVE

VRA

VPA

VLA

QAO

QVO

QPO

BFN

BFM

RBF

FISFLO

RTP

VT0

VE0

MCP

CIRCULATORY DYNAMICS - FLOWS AND PRESSURES

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]

OUTPUTS:

PA - arterial (aortic) pressure [torr] PVS - average venous pressure [torr]

PRA - right atrial pressure [torr] PPA - pulmonary arterial pressure [torr]

PLA - left atrial mpressure [torr] VAS - volume in systemic arteries [l]

VVS - systemic venous vascular volume [l] VVE - excess blood volume in the veins [l]

VRA - right atrial volume [l] VPA - volume in pulmonary arteries [l]

VLA - volume in left atrium [l] 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]

BFN - blood flow in non muscle and non renal tissues [l/min] BFM - blood flow in muscles [l/min]

RBF - renal blood flow [l/min] FISFLO - blood flow through a fistula [l/min]

RTP - total systemic peripheral resistance [torr min /l] VT0 - total unstressed blood volume [l]

VE0 - total excess volume of blood in the vasculature [l] MCP - mean circulatory pressure [torr]

Circulatory Dynamics - Flows And Pressures

PC

PPC

PGH

PTC

VTL

TVD

VUD

DFP

VID

CFC

VPN

VTSN

VP

VTCLP

VTS

CFILTR

VTC

VPREL

VTSREL

CAPILLARY MEMBRANE FLUID DYNAMICS

INTPUTS: PC - systemic capillary pressure [torr]

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] 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] 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:

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] 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]

Capillary Membrane Fluid Dynamics

0.0825

CV0.005

CRA

72

CPP

0.0003

CPF0.0048

CPA0.01

CLA

0.01167

CFC

0.00355

CAS

HM VIM

BLOOD VISCOSITY

INTPUT: HM - hematocrit [%]

OUTPUT:

VIM - blood viscosity [ratio to normal]

Blood viscosity

PA

POT

PMO

EXC

ANUBR

AUZ

AU

AUH

AUR

VVR

AUP

AOM

AUM

AVE

AUTONOMIC CONTROL OF THE CIRCULATION

INTPUTS: PA - systemic arterial pressure torr

POT - non-muscle cell PO2 [torr] PMO - muscle cells PO2 [torr]


ANUBR - direct effect of angiotensin on vasomotor center ["virtual" torr]

AUZ - overall sensitivity of autonomic control [ratio to normal]

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

[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] 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

[ratio to normal]

Autonomic Contorl of the Circulation

AARK

MYOGRSAA

RNAUG1

ANM

AUM

VIM

AAR

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]

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

Afferent Arteriole

1AUZ

0

ATRVFBM

0

ATRRFBM

-0.2

ANY

0

ANXM

0

ANUVM1

0ANUBRM

0

ANG

0

ALD

1ALCLK

0AHMRM

0

ADH

40

AARK

12

PA

PA

PA

PPA

PPA

HMD

HMD

HM

HM

HSL

HSL

BFN

OSA

RR

ANM

ANM

ANM

ANM

ANU

ANC

AHC1

AHRMAHRM

Fig 10. Simulink implementation of a Guyton-Coleman model from 1986.

models running in the background can enable students to "play" with this physiological subsystem and monitor its response to various inputs.

Simulation models in the background of teaching programs are therefore very effective educational tools that facilitate the comprehension of complex regulation relations in the human organism and pathogenesis of their malfunction.

From the pedagogical perspective it is advantageous, according to our experiences, if we allow disconnection of individual regulation loops temporarily, and study reaction of the individual subsystems separately, which contributes to better understanding of the dynamics of physiological regulations [12].

During the creation of teaching applications with the use of simulation games, it is necessary, on one hand, to resolve the creation of the simulation model, and on the other hand the creation of our own simulator. These are two different tasks, whose effective solution facilitates the use of various developmental tools [14].

During the creation of simulation models it is advantageous to use developmental tools designated for creating and identification of simulation models – for example Matlab/Simulink from the Mathworks company. In this environment, we have also created a special library of physiological models - Physiology Blockset for Matlab/Simulink, open source software library. 1st Faculty of Medicine, Charles University, Prague, available at http://physiome.cz/simchips.

Creating simulation models is closely related to issues of creating formalized description of biological reality, which is the content of the worldwide PHYSIOME project [3, 10].

Creating our own teaching simulators is done in the environment of classic developmental tools for computer programmers (for example Microsoft Visual Studio, etc.) and tools facilitating the creation of interactive animated pictures, used in user interface of teaching programs (for example Adobe Flash, Adobe Flex). The future probably lies in simulators available on the web and on the accessibility of e-learning educational environment [15, 19]..


13

7 From Simulation Games to Medical Simulators Thirty five years ago, when A. C. Guyton et al. published his large-scale model, the only

possibility to study the behaviour of the model was on large computers that often occupied an entire room. Nowadays it is possible to run even very sophisticated models on a PC. Moreover, today’s technology allows us to add on a graphical attractive user-friendly interface to these models.

From the technological standpoint there are no obstacles that would prevent PCs from running learning simulators for practicing medical decision-making. The basis for a pilot's simulator during training pilots is the model of the plane. Similarly, one of the prerequisites when creating a medical simulator is the extensive simulation model of a human organism. This simulation model must include all significant physiological subsystems – circulation, respiration, kidney function, water, osmotic and electrolyte homeostasis, acid-base regulation, etc. – which have to be interconnected into the model. Therefore, now is the time of a renaissance in the formation of large integral models of human organism, and of the concept of integrative physiology, that Guyton came up with years ago. At the present time the practical fulfillment is being achieved.

For example, at the present time, Thomas Coleman, one of the co-authors of the legendary article by prof. Guyton from 1972 [6], together with Guyton’s disciples, created a simulator Quantitative Human Physiology (QHP), whose theoretical basis is a new mathematical model of integrative human physiology which contains more than 4000 variables of biological interactions. A review edition of this simulator is freely available for download at http://physiology.umc.edu/themodelingworkshop/.

The simulator consists of two software packages.

The first is the equation solver, named QHP 2007.EXE. This is the executable file, prepared for the Windows operating system (2000, xp, Vista).

The second is an XML document that defines the model, the solution control and the display of results. This document is distributed over a large number of small files in the main folder and several subfolders. The XML schema used is described in a preliminary fashion in another section of this modeling workshop.

The XML document is parsed at program startup. Parsing progress is displayed in the status bar at the bottom of the program’s main window.

All of the XML files are both machine and human readable. You only need a text editor (such as Notepad, WordPad).

Unfortunately, the orientation in the structure of such a large model is difficult, due to a large number of variables (more than 4000).

Standardized notation of the model structure in XML is easily understandable for the machine, but for a human it is necessary to provide a graphic depiction of the structure of the physiological regulation relations.

Thus, the suggestions that prof. Guyton et al. sparked, thirty five years ago, by his legendary article (the concept of integrative physiology, the creation of large-scale models of physiological subsystems interconnected in an integrative way, and an effort to graphically depict the structure of physiological regulation relations), nowadays return in a new form and with new possibilities.

References

[1] S. R. Abram, Hodnett, B. L., Summers, R. L., Coleman, T. G., Hester R.L.: Quantitative Circulatory Physiology: An Integrative Mathematical Model of Human Physiology for medical education. Advannced Physiology Education, 31 (2), 202-210, 2007.

[2] N. M. Amosov, Palec B. L., Agapov, B. T., Jermakova, I. I., Ljabach E. G., Packina, S. A., Solovjev, V. P.: Theoretical Research of Physiological Systems (in Russian). Kiev: Naukova Dumka, 1977

[3] J. B. Bassingthwaighte: Strategies for the Physiome Project. Annals of Biomedical Engeneering 28, 1043-1058, 2000


14

[4] T. G. Coleman, Randall, J. E.: HUMAN. A Comprehensive Physiological Model. The Physiologist 26, 15-21, 1982

[5] P. Fritzson: Principles of Object-Oriented Modelling and Simulation with Modelica 2.1, Wiley-IEEE Press, 2003

[6] A. C. Guyton, Coleman T. A. , & Grander H. J.: Circulation: Overall Regulation. Annual Review of Physiology, 41, 13-41, 1972.

[7] A. C. Guyton, Jones C. E., Coleman T. A.: Circulatory Physiology: Cardiac Output and Its Regulation. Philadelphia: WB Saunders Company, 1973

[8] A. C. Guyton, Taylor, A. E, Grander, H. J.: Circulatory Physiology II: Dynamics and Control of the Body Fluids. Philadelphia: WB Saunders Company, 1975.

[9] Guyton A. C.: The Suprising Kidney-Fluid Mechanism for Pressure Control – Its Infinite Gain!. Hypertension, 16, 725-730, 1990. [10] P. J. Hunter, Robins, P., Noble D.: The IUPS Physiome Project. Pflugers Archive-European Journal of Physiology, 445,1–9, 2002. [11] N. Ikeda, Marumo F. , Shirsataka M.: A Model of Overall Regulation of Body Fluids. Annals

of Biomedical Engeneering, 7, 135-166, 1979. [12] J. Kofránek, Anh Vu, L. D., Snášelová, H., Kerekeš, R., Velan, T.: GOLEM – Multimedia

Simulator for Medical Education. In Patel, L., Rogers, R., Haux R. (Eds.). MEDINFO 2001, Proceedings of the 10th World Congress on Medical Informatics. London: IOS Press, 1042-1046, 2001, available at http://physiome.cz/Guyton.

[13] J. Kofránek, Andrlík, M., Kripner, T., Mašek, J.: From Simulation Chips to Biomedical Simulator. In Amborski K, Meuth H, (eds.): Modelling and Simulation 2002, Germany 2002, Proceeding of 16th European Simulation Multiconference, Germany, Darmstadt, 431-436, 2002, available at http://physiome.cz/Guyton.

[14] J. Kofránek, Andrlík M., Kripner T., Stodulka P.: From Art to Industry: Development of Biomedical Simulators. The IPSI BgD Transactions on Advanced Research 2. 62-67, 2005, available at http://physiome.cz/Guyton.

[15] J. Kofránek, Matoušek, S., Andrlík, M., Stodulka, P. Wünsch, Z. Privitzer, P., Hlaváček, J., Vacek O.: Atlas of Physiology - Internet Simulation Playground. In Proceedings of EUROSIM 2007, Ljubljana, Vol. 2. Full Papers (CD). (B. Zupanic, R. Karba, S. Blažič Eds.), University of Ljubljana, MO-2-P7-5, 1-9, 2007, available at http://physiome.cz/Guyton.

[16] J. A. Miller, Nair, R. S., Zhang, Z., Zhao, H.: JSIM: A JAVA-Based Simulation and Animation Environment, In Proceedings of the 30th Annual Simulation Symposium, Atlanta, Georgia, 31-42, 1997.

[17] G. M. Raymond, Butterworth E, Bassingthwaighte J. B.: JSIM: Free Software Package for Teaching Physiological Modeling and Research. Experimental Biology 280, 102-107, 2003.

[18] S. Silbernagl, Lang, F.: Color Atlas of Pathophysiology, Stuttgart: Thieme Verlag, 2000. [19] P. Stodulka, Privitzer, P., Kofránek, J., Tribula, M., Vacek, O.: Development of WEB

Accessible Medical Educational Simulators. In Proceedings of EUROSIM 2007, Ljubljana, Vol. 2. Full Papers (CD). (B. Zupanic, R. Karba, S. Blažič Eds.), University of Ljubljana, MO-3-P4-2, 1-6, 2007, available at http://physiome.cz/Guyton.

Acknowledgement This research was supported by MŠMT aid grant No. 2C06031 and BAJT servis s.r.o company.

Jiří Kofránek, M.D., Ph.D. Laboratory of Biocybernetics, Dept. of Pathophysiology, 1st Faculty of Medicine, Charles University, Prague U Nemocnice 5, 128 53 Praha 2, Czech Republic e-mail: [email protected]

guyton's diagram brought to life after revision -...

Documents