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HumMod - Large Scale Physiological Models in ModelicaJiri Kofranek Marek Matejak Pavol Privitzer
Institute of Pathophysiology, First Faculty of Medicine, Charles University U nemocnice 5, 128 53 Praha 2, Czech Republic
[email protected] [email protected] [email protected]
Abstract
Modelica is being used more and more in industrial applications, but Modelica is still not used as much in biomedical applications. For a long time we have mostly been using Matlab/Simulink models, made by Mathworks, for the development of models of physio-logical systems. Recently, we have been using a simu-lation environment based on the Modelica language. In this language, we implemented a large scale model of interconnected physiological subsystems contai-ning thousands of variables. Model is a richly hierar-chically structured, easily modifiable, and “self-docu-menting”. Modelica allows a much clearer than other simulation environments, to express the physiological nature of the modeled reality. Keywords: simulation; physiology; large-scale model
1 Introduction
It is simply amazing how fast the Modelica simulation language adopted various commercial development environments. Modelica is being used more and more in industrial applications. However, Modelica is still not used as much in biomedical applications. The vast majority of biomedical simulation applica-tions are still done in casual, block-oriented environ-ments. These include referencing database develop-ment environments for biomedical models (such as the JSIM language - http://physiome.org/model/doku.php or CellML language - http://www.cellml.org/). A frequently used environment in biology and medi-cine is Matlab/Simulink – monographs dedicated to biomedicine models are usually equipped with additi-onal software used in this environment, but so far wi-thout the use of new acasual or non-casual Simulink libraries, such as [24, 28, 32]. However, already in 2006, Cellier and Nebot [5] poin-ted out the benefits of Modelica, when used for clear implementation of physiological systems descriptions and interpretations. The classic McLeod‘s circulation system model was implemented by PHYSBE (PHYS-
iological Simulation Benchmark Experiment) [25, 26, 27]. The difference is clearly seen, if we compare the Cellier model implementation [5] with the freely downloadable version of the PHYSBE model imple-mentation in Simulink http://www.mathworks.com/products/demos/simulink/physbe/. Haas and Burnhan, in their recently published mono-graph, pointed out the benefits and large potential of the Modelica language used for modeling medically adaptive regulatory systems [9]. The most recent, Brugård [4] talks about work on the implementation of the SBML language (http://sbml.org/) in the Mode-lica language. This would enable us in the future, to simply run models, whose structure is described in the SBML language, on development platforms, based on the Modelica language.
2 Web of physiological regulations
Thirty-nine years ago, in 1972 Guyton, Coleman and Granger published an article in the Annual Review of Physiology [9] which at a glance was entirely diffe-rent from the usual physiological articles of that time. It was introduced by a large diagram on an insertion. Full of lines and interconnected elements, the drawing vaguely resembled an electrical wiring diagram at first sight (Fig. 1). However, instead of vacuum tubes or other electrical components, it showed interconnec-ted computation blocks (multipliers, dividers, adders, integrators and functional blocks) that symbolized mathematical operations performed on physiological variables. In this entirely new manner, using graphi-cally represented mathematical symbols; the authors described the physiological regulations of the circu-latory system and its broader physiological relations and links with the other subsystems in the body – the kidneys, volumetric and electrolyte balance control, etc. Instead of an extensive set of mathematical equa-tions, the article used a graphical representation of mathematical relations. This syntax allowed depicting relations between individual physiological variables graphically in the form of interconnected blocks re-presenting mathematical operations. The whole dia-
gram thus featured a formalized description of phys-iological relations in the circulatory system using a graphically represented mathematical model. Guyton’s model was the first extensive mathematical description of the physiological functions of interco-nnected body subsystems and launched the field of physiological research that is sometimes described as “integrative physiology” today. Just as theoretical physics tries to describe physical reality and explain the results of experimental research using formal me-ans, “integrative physiology” strives to create a for-malized description of the interconnection of phys-iological controls based on experimental results and explain their function in the development of various diseases. From this point of view, Guyton’s model was a mi-lestone, trying to adopt a systematic view of physio-logical controls to capture the dynamics of relations between the regulation of the circulation, kidneys, the respiration and the volume and ionic composition of body fluids by means of a graphically represented ne-twork. Guyton’s graphical notation was soon adopted by
other authors – such as Ikeda et al. (1979) in Japan [13] and Amosov et al. (1977) in the former USSR [2]. However, the graphical notation of the mathematical model using a network of interconnected blocks was only a graphical representation – Guyton’s model and later modifications (as well as the models of other authors that adopted Guyton’s representative notati-on) were originally implemented in Fortran and later in C++. Today the situation is different. Now, there are specialized software simulation envi-ronments available for the development, debugging and verification of simulation models, which allow creating a model in graphical form and then testing its behavior. One of these is the Matlab/Simulink de-velopment environment by Mathworks, which allows building a simulation model gradually from individual components – types of software simulation elements that are interconnected using a computer mouse to form simulation networks. Simulink blocks are very similar to the elements used by Guyton for the formalized representation of
Figure 1: Guyton’s blood circulation regulation diagram from 1972.
physiological relations. The only difference is in their graphical form. This similarity inspired us to use Si-mulink to revive Guyton’s good, classic diagram and transform it into a working simulation model. When implementing the model in Simulink, we used swit-ches that allow us to connect and disconnect indivi-dual subsystems and control loops while the model is running. We strove to keep the appearance of the Simulink model identical to the original graphic dia-gram – the arrangement, wire location, variable na-mes and block numbers are the same. The simulation visualization of the old diagram was not without difficulties – there are errors in the origi-nal graphic diagram of the model! It does not matter in the hand-drawn illustration but if we try to bring it to life in Simulink, the model as a whole collapses immediately. A detailed description of the errors and their corrections is in [23]. Our Simulink implementation of Guyton’s (correc-ted) model (Figs. 2 and 3) is available for download at www.physiome.cz/guyton. Also available at that ad-dress is our Simulink implementation of a much more complex, later model from Guyton et al. There is also
a very detailed description of all applied mathemati-cal relations with an explanation.
3 Block-oriented simulation networks for physiology
Block-oriented simulation languages, of which Simu-link is a typical example, allow assembling computer models from individual blocks with defined inputs and outputs. The blocks are grouped in libraries; when building a model, a computer mouse is used to crea-te individual block instances, with inputs and outputs connected through wires that “conduct” information. A Simulink network can be arranged hierarchically. Blocks can be grouped into subsystems that commu-nicate with their ambient environment through defined input and output “pins”, making “simulation chips” of a sort. A simulation chip hides the simulation network structure from the user, much like an electronic chip hiding the interconnection of transistors and other electronic elements. Then the user can be concerned
Figure 2: The implementation of Guyton’s model in Simulink preserves the original arrangement of elements in Guyton’s graphic diagram.
NON-MUSCLE OXYGEN DELIVERY
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
336
337
338
339POT
PO1
POY
PO2
RC1
RCD
VRC
RKC
RC2VRC
VB
HM
HM2
VIE
VIM
336c
336b
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
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
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
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
1
0
2
2400
1600
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
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
0.01095
0.3229
0.9898
2.86
99.95
1
15.22
0.022555.085
0.09914
3.781
2.782
1.014
2.86
6.822e-008
0.01252
40
-3.994e-010
2
40
0.9897
1
1
1.001
-6.328
11.99
20.17
7.987
5.043
0.038250.001896
0.001897
16.8169.78
0.03838
3.004
5.00416.81
198.7
40
142
5
1.115e-006
1.003
10
1.004
0.9999
0.001001
1.002
0.9456
0.0704
1
1.001
1
2.949
1.001
0.1003
1.211
1.211
0.001007
7.999
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
0.55
40
0.3331.5
0.00092
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
just with the behavior of the chip and does not have to bother about the internal structure and calculation algorithm. The behavior of a simulation chip can be tested by monitoring its outputs using virtual displays or vir-tual oscilloscopes connected to it. This is very useful especially for testing the behaviour of a model and expressing the mutual relations of variables. Simulation chips can be stored in libraries and users can create their instances for use in their models. For example, we created a Physiolibrary for modelling physiological regulations. Hierarchical, block-oriented simulation tools are thus used advantageously in the description of the com-plex regulation systems that we have in physiology. A formalized description of physiological systems is the subject matter of PHYSIOME, an international project that is a successor to the GENOME project. The output of the GENOME project was a detailed description of the human genome; the goal of the PHYSIOME project is a formalized description of physiological functions. It uses computer models as its methodological tool [3, 12]. Several block-oriented simulation tools developed under the PHYSIOME project have been used as a reference database for a formalized description of the structure of complex physiological models. These include JSIM (http://www.physiome.org/model/doku.php) and CellML (http://www.cellml.org).
4 From Simulink to Modelica in mo-deling of large-scale physiological systems
We have been using Matlab and Simulink for years to create and develop models of physiological systems [16, 17, 23] and have also been developing the rele-vant application Simulink library – the Physiolibrary (http://www.physiome.cz/simchips). We have also developed the relevant software tools that simplify the transfer of models implemented in Simulink over to development environments (Contro-lWeb and Microsoft .NET), where we create tutorial and education simulators [18, 22]. Our development team gained invaluable experience in previous years working with the Matlab/Simulink development en-vironment made by the renown company MathWorks. On the other hand, we were also attracted by the acau-sal development environments using the Modelica language. In the Modelica language environment the essence of physiological regulation is much clearer than in Simulink causal network (see Figures 3 and 4). We were facing a decision whether to continue with the development process of physiological system models in Simulink (using new acasual libraries), or to make a radical decision and switch to the new Modelica lan-guage platform. Our decision was affected by our efforts to imple-
Figure 3: Circulatory dymamics - more detailed cent-ral structures of the Simulink implementation of Gu-yton’s model, representing flows through aggregated parts of the circulatory system and the activity of the heart as a pump.
Figure 4: The same model structure as is shown in figure 3 implemented in Modelica. The structure of the model in Simulink corresponds to the structure of computational steps, while the Structure of Modelica model reflects the structure of the modeled physiolo-gical reality.
ment a large model made by Guyton’s disciples and followers. Their Quantitative Human Physiology model is an extension of a tutorial simulator called the Quantitative Circulatory Physiology (QCP) [1]. Quantitative Human Physiology (QHP) simulator [10], which is now distributed as “HumMod” [11], represents today’s most comprehensive and largest model of physiological functions.
The HumMod model contains more than 4000 vari-ables and at the present time, it probably represents the largest and most extensive model of physiologi-cal regulations. It enables the user to simulate a wide range of pathological stages and statuses, including the effects of the relevant applied therapy. The authors developed a special block-oriented simulation system to represent the complex model structure. Compared
Figure 5: All necessary files of the Quantitative Human Physiology tutorial simulator (called the HumMod by the authors in the last version). This simulator has been designed for the Windows operating system and does not require special installation. Only zip files must be unzipped into a selected folder. After you click the Hummod.exe icon, the translator translates the source text embedded within hundreds of directories and more than two thousand files and initiate its own simulator. Even though the source text of the simulator and the entire mathematical model on the background is offered as an open source (and in theory, the user may modify the model), the navigation through thousands of mathematical relations and viewing thousands of XML and interconnected files is rather difficult.
simulátor Hummod
fragment of XML source code
Compiler and launcher of Hummod simulator
Source code files of HumMod simulator
RunningHumMod simulator
with the previous QCP simulator, whose mathemati-cal background is hidden from the user in its source code written in C++, the HumMod simulator uses a different approach. The HumMod authors decided to separate the simulator implementation and descrip-tion of the model quotations, in order to make the structure of the model more clear and apparent for the larger scientific community. In 1985 the architect of this model, Thomas Coleman, had already created a special language used to write the model structure, as well as the element definiti-ons into the simulator user interface. The language is based on modified XML notation. The model is then written by using XML files. A special converter/de-coder (DESolver) converts XML files into executable simulator code. A detailed description of this language and DESolver converter, as well as the relevant educational tutorial, is freely accessible on the web page of the University of Mississippi (http://physiology.umc.edu/themode-lingworkshop). The new HumMod model is written
in the XML language as well. Its structure with all de-tails may be found at (http://HumMod.org), published as an open source. Therefore, the user can modify this model as he wishes. However, the model description has been divided into more than three thousand XML files in more than thousand directories, from which the spe-cial solver creates and executes the simulator (Figure 5). The entire structure of the model and following links and references are not easily identifiable. That is why the international research and development team in its SAPHIR project (System Approach for Physiological Integration of Renal, cardiac and respiratory control) decided to use the old Guyton models from 1972 [9] and the Ikeda model from 1979 [13] for the creation of its new and extensive model of physiological func-tions instead of the freely available QHP model. The source codes of the QHP model appeared unclear or hard-to-understand to those involved in this project [31].
VascularCompartments QHPViewSpla
nchn
icVein
s
Equations
Figure 6: Visualization tool QHPView, created by us, simplifies viewing of the QHP/HumMod simulator structure, containing more than two thousand XML files, scattered in thousands of directories, where quotati-ons and links between them may not be apparent.
We have been able to create a special software tool called QHPView (Figure 6), which is able to create a clear and legible overview of mathematical relations and connections from thousands of source codes. We are offering this tool as an open source on the web page at (http://physiome.cz/HumMod). First, we tried to implement the QHP/HumMod model in the Simu-link environment. The model contains a wide range of relations that of-fer solutions for implicit equations. That is why the implementation of this block-oriented model (outputs from one block are used as inputs for the next blocks) is very difficult and as the implementation got more and more complex, the transparency of this model went down quickly. The use of new acasual Simulink libraries in this complex model proved to be proble-matic and the transparency of the model improved only a little bit. Therefore, we decided to stop using the Simulink implementation and began to implement in Modeli-ca language (using the Dymola environment). Very quickly we discovered that the implementation of a large and extensive model in Modelica is much more effective than using acasual libraries in Simulink. When we compared the Simulink and Modelica im-plementations we also discovered a significant diffe-rence. Mainly due to the fact that the new acasual lib-raries are only acasual superstructure of Simulink and not an objectively oriented modeling language based on equatations, as the Modelica language is. Therefore, if we compare the development environ-ments based on the simulation language Modelica with the Matlab/Simulink development environments made by Mathworks, we may say the following: • contrary to Simulink, the model implemented in
Modelica much better reflects the essentials and base of the modeled reality and the simulation models are more clear, readable and less error prone;
• the object architecture in Modelica enables the user to build and tweak models with an hierar-chical structure gradually, while using reusable element libraries;
• contrary to Simulink (which is the industrial stan-dard from Mathworks), Modelica is a non pro-prietary programming language and therefore, it may contain various commercial and non-co-mmercial developing environments competing between each other. This language is used for specific problem solutions originating in various application fields (for commercial and non-co-
mmercial specialized libraries); • in Modelica it is possible to combine causal
(mostly signals) and acasual links; and unlike in Simulink, it is also possible, (within interconne-cted blocks) to create algebraic loops - Modelica compiler uses symbolic manipulations to resolve the loops automatically (when possible) and the-refore the disconnection of algebraic loops is the task for the development environment and not for the programmer.
The above specified reasons led us to use, as the main implementation tool for the model creation, the Mo-delica language and we also gradually stopped using the Matlab/Simulink environment [20].
5 HumMod in Modelica
The implementation of the HumMod model clearly shows the benefits of the model creation process when done in the Modelica language. If we compare the complex structure of the HumMod model by using the visualization option in QHPView (Figure 5) with examples of implementations done in the simulation language Modelica, shown in Figures 7-13, we can see that the acasual implementation done in Modelica creates a transparent and legible model structure and
Figure 7: Structure of Hummod model. Model con-sist of cardiovascular component (CVS), nutritient and metabolism component, water and osmolarity component, proteins component, O2, CO2 and acid--base regulation component, electrolyte component, nervous regulation component, hormone regulation component, status of virtual pateint component and setup component. All components ar connected wtih bus connectors.
therefore offers easier model modifications. The HumMod model implemented in Modelica is be-ing currently modified and extended. Modifications and extensions of HumMod were par-tially taken from our original model Golem [16, 17] and further modified according to newest findings and experiences. Our modifications are mainly extensions, which improve the usability of the model during the modeling of difficult disorders in acid-base, ionic, vo-lume and osmotic homeostasis of inner environments, which is very important for urgent medicinal statuses. Our modification of the HumMod model is based mainly on the process of re-modeling the subsystem of acid-base balance, which is based in the original QHP on the so-called Stewart acid-base balance theo-
ry. Simply put, the so-called “modern approach“ of Stewart [30] and his followers (e.g. Fencl et al. [8], Sirker et al. [29] ) explaining disorders in the acid--base balance, uses mathematical relations calculating the concentration of hydrogen ions [H+] from partial pressure CO2 in plasma (pCO2), total concentration ([Buftot]), weak (partially dissociated) acids ([HBuf]) and their base ([Buf-]), where:
[Buftot]=[Buf-]+[HBuf] and from the difference between the concentration of fully dissociated cations and fully dissociated anions in SID (strong ion difference):
[H+]=Function (pCO2, SID, Buftot ) The problem of this approach is that the precision of acid-base calculations in the model depends on the
Figure 11: Structure of splanchnic circulation compo-nent (SplanchnicCirculation class).
Figure 9: Structure of systemic circulation component (SystemicCirculation class).
Figure 10: Structure of systemic peripheral circulati-on component (Peripheral class).
Figure 8: Structure of cardiovascular component (CVS class).
precision of the SID calculation, that is the difference between the concentration of fully dissociated cations (that is mainly sodium and potassium) and fully di-ssociated anions (mostly chlorides). Imprecision that is created during the modeling of sodium, potassium and chlorides intake and excretion are transferred and reflected by the imprecision in the modeling process of the acid-base status. Even though Hester et al. [11], significantly improved the modeling of reception and excretion of sodium, potassium and chlorides in kidneys in his HumMod model, if we model a long-term status (when nothing is happening with the virtual patient), the virtual pa-tient (in the current model version) has a tendency to fall into slight and steady metabolic acidosis after one
month of the simulated time. Our evaluative approach towards the modeling and evaluation of disorders in acid-basic balance [14, 15, 21] is based on the modeling and evaluation of two flows – the creation and excretion of CO2 and the creation and excretion of strong acids, connec-ted through the purification systems of each part of the bodily fluids. This approach, according to our opinion, better explains the physiological causality of acid-base regulations, rather than direct mode-ling of acid-base disorders through the balancing of accompanying electrolytes. Besides, the fidelity and truthfulness of the modeling process is getting better; mainly in mixed (acid-base and electrolyte) disorders in inner environments. Another important modification of the HumMod, is the fact that the model was extended by adding the dependency of the potassium flow on the intake of glucose as a result of insulin, which enables us to model (besides other things), the influence of pota-ssium solution infusions with insulin and glucoses, which are distributed in acute medicine for treating potassium depletions. We have been using this “balancing and evaluation” approach [18] towards the modeling of acid-base ba-lance in our old “Golem” simulator [17]. The exten-ded HumMod model serves as the base for the educa-tional simulator „eGolem“, used in medical tutoring in clinical physiology of urgent statuses which is be-ing currently developed. On the webpage http://physiome.cz/HumMod you may find the updated and current structure of our implementation of the HumMod model („HumMod--Golem edition“). In collaboration with M. Tiller we are preparing a detailed description of this model with extensive descriptions of the various physiological regulatory circuits.
6 From a model to the simulator
A simulation model, implemented in a sophistica-ted development environment, cannot be used for education as is alone. It is the implementation of the formalized description of the modeled reality that enables testing of the behavior of the mathematic model during various input values and the search for model quotations and parameters, which within the established precision range, can ensure the sufficient compatibility of the behavior of the model with the modeled system (model identification). Even after this goal is reached, there is still a long
Figure 12: Structure of gastrointestinal vascular resi-stance component (GITract class).
Figure 13: Structure of component calculating influ-ence of alpha receptors stimulation on gatrointestinal vascular resistance (AlphaReceptors class).
road ahead from the identified model to the educatio-nal or tutorial simulator. It is a very demanding deve-lopment work, which requires the combination of ide-as and experiences of teachers who create the script of the tutorial application, the creativity of art designers who create the multimedia components interconnec-ted with the simulation model in the background, as
well as the efforts of programmers who finally “sew up” the final masterpiece into its final shape. We have used a special web simulator creation technology for creation of educational simulators [20]. To automate the model debugging transfer from the simulation development environment (previously using Simulink and nowadays using Modelica) into
Figure 15: Our new solution of creative interconne-ction of tools and applications, used for the creation of simulators and tutorial programmes using simu-lation games. The base of an e-learning program is still a high-quality script, created by an experienced pedagogue. The creation of animated figures is done by artists who create interactive animations in Expre-ssion Blend. To create and test animations that will be controlled by the simulation model, art designers use the Animtester software tool, developed by us. The core of simulators is the simulation model, created in the Modelica simulation language environment. Wi-thin the project Open Modelica Source Consortium, we are in the process of creating a tool which is able to generate the source code from Modelica to C# lan-guage. This enables us to generate a component from .NET used in the final application on the Silverlight platform, which enables to distribute the simulator as a web application, running in the internet browser (even on computers with various operating systems).
Figure 14: The original solution of creative interco-nnection of tools and applications, used for the crea-tion of simulators and tutorial programmes using si-mulation games. The base of an e-learning program is a high-quality script, created by an experienced pedagogue. The creation of animated pictures is done by artists who create interactive animations in Adobe Flash. The core of simulators is the simula-tion model, created with special development tools, designed for the creation of simulation models. For a long time, we have been using Matlab/Simulink made by Mathworks for the development of models. The simulator development process is a demanding pro-gramming work. To make this task easier, we have developed special programmes that simplify the au-tomatic transfer process of simulation models created in Matlab/Simulink over to ControlWeb or over to the Microsoft .NET environment.
the development environment where the development application is programmed, specialized software tools (developed by us) are used. We have been creating tu-torial simulators in Microsoft .NET and Adobe Flash environments (Figure 14). Recently, we began using the Microsoft Silverlight platform (Figure 15), which enables distribution of simulators over the internet and may be executed directly into the internet brow-ser environment (even on computers running various operating systems).
7 Conclusions
Nowadays, the old Comenius motto – “schola ludus,“ or “playful school” [6], has found a modern use in interactive educational programs that use simulation games. Connection of the multimedia environment, serving as an audio-visual user interface, with simula-tion models, gives the studied problem a much more tangible feeling. A simulation game offers the possi-bility to test, without any risk, the simulated object’s behavior. The behavior of individual physiological subsystems can be appreciated in a simulation game, both under normal conditions and in the presence of a disorder. Complex integrative simulators of human physiolo-gy can be of large importance when teaching patho-physiology or studying pathogenesis of varied medi-cal conditions and syndromes using virtual patients. Such simulators include models of not only individual physiological subsystems but also of their mutual co-nnection into more complex units. Modelica is a very convenient developing tool for design of those com-plex hierarchical models.
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AcknowledgementWork on the development of medical simulators has been supported by the grants MPO FR-TI3/869, MSM 0021620806 and by Creative Connections s.r.o.
