From pictorial charts to educational models creating and using

From pictorial charts to educational models: creating and using simulation models in teaching physiology Jiří Kofránek, Stanislav Matoušek, Ondřej Vacek, Jan Rusz, Michal Andrlík 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 chart. Authors brought this large-scale chart to life using a modern tool of simulation – Matlab Simulink. The original lay-out, 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 possibility to study behavior of all variables in time. Autoři popisují svoji technologii tvorby výukových simulačních modelů a simulátorů zahrnující tvorbu modelu v prostředí Matlab/Simulink, s využitím tzv. simulačních čipů. Verifikované modely jsou pak autory vyvinutým softwarovým nástrojem automaticky převáděny do vývojového prostředí Microsoft .NET nebo Control Web, kde jsou vyvíjeny vlastní výukové simulátory. Při jejich tvorbě se využívají interaktivní animované obrázky vyvíjené pomocí Adobe Flash/Flex, které jsou v simulátorech propojeny s jádrem simulačního modelu. Autoři dále formulují požadavky na tvorbu výukových modelů a diskutují problémy, kterým musí čelit jejich tvůrci. Introduction The article (Guyton et al, 1972) published 35 years ago in the Annual Review of Physiology was altogether different from the familiar form physiological articles had in those times. Its central place was occupied by a grand diagram, at first glance resembling of some electronic device’s diagram chart (fig. 1). However, the symbols depicted did not represent electron tubes; instead they represented connected computational blocks (gains, sums, products, integrators, function blocks), symbolizing mathematical operations done with physiological entities. Plexus of interconnecting wires in between the blocks showed instantaneously relationships in between them, in many cases relationships of physiological feedback control. The blocks were grouped into eighteen clusters, each cluster representing individual physiologic subsystem. The central cluster represented the circulatory dynamics – the other blocks generally the subsystems that play role in the feedback regulation of some of its parameters. These clusters represented kidneys, interstitial fluid, electrolytes, regulation by autonomic nervous system and hormones ADH, angiotensin and aldosteron. The author of the article was a famous physiologist Arthur C. Guyton, together with T. C. Coleman and H. J. Grander. The article described a large-scale model of the circulatory system regulation in the wider perspective: The respiratory system is integrated into other subsystems of the organism that can influence its function. Instead of giving the reader 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 the principal graphical chart only (which was, however, fully illustrative), explicatory comments and reasoning for 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 of the reader to understand the meaning of the formalized relationships between the physiological entities. One year later, in 1973, Arthur C. Guyton published a monograph (Guyton et al, 1973) where he explained most of the concepts in more length. The group of A. C. Guyton kept elaborating the model later on, and upon request even afforded the FORTRAN source code of the model realization to the people interested (last time in 1986). Guyton’s model represents the first large-scale mathematical description of the physiological functioning of the interconnected subsystems of the organism. It was a turningpoint that got started research in the field known as integrative physiology. Using the systems 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. Guyton se svými spolupracovníky, především s Thomasem Colemanem, v dalších letech svůj model dále rozšiřoval. Výsledkem práce Guytonovy školy pak byly large-scale integrativní modely komplexních fyziologických regulačních vztahů (Coleman a Randal 1982, Abram a spol. 2007). Pioneers of the systemic approach in physiology Arthur C. Guyton (fig. 2) 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 regulation of circulating volume, osmolarity and ionic composition of bodily fluids. He worked up great many original experimental procedures – for instance, he was the first one to measure the value of pressure in interstitial fluid. However, he was not only 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 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 to control the cardiac output; equally important roles are played by the regulation of tissue perfusion, dependent of the oxygen supply, as well as the filling of the vessels and compliance of great veins. It was A.C. Guyton, who proved that the long-term regulation of blood pressure is done by kidneys (Guyton, 1990). When you study the dynamism of regulatory processes, verbal description and common sense are often not sufficient. Prof. Guyton has realized that 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 a same time, he was engaged in biomedical engineering in times, when this specialization did not yet officially exist. Formalization of physiological relationship description 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. The behavior of a formally described system can then be examined using formal manipulation rules – e.g. solving equations of the mathematical model. Converting these equations to a form of computer program, we can leave “the toil to machines” – this is the quintessence of what simulation modeling is about. Simulation model cannot replace biological experiments, as would propose some of the campaigners against experiments on animals. Yet, giving the possibility to watch the behavior of a complex dynamic system in time as a function of various inputs, a simulation model is a very effective tool for deduction and verification of hypotheses. The criterion for refuting or not refuting a hypothesis is always the comparison of the model behavior with experimentally (empirically) assessed behavior of the biological original. Use of formalization in biological and medical sciences is not at all common and here medicine has a certain handicap as compared to technical sciences, physics or chemistry. Formalization in physics has started already in 17-th century. However, due to the complexity of the examined systems in biological and medical sciences, the same process has only come with the advent of computers. A certain dividing line can be drawn in the beginning of seventies of 20-th century, a period, when progress in computation and programming languages created new possibilities in making and testing models of physiological systems. Beginning with the above mentioned model of Guyton et al., large-scale models began to appear in the scientific literature. They were aimed at depicting the intricate relationships among excretory, respiratory, circulatory and homeostatic regulation with sets of non-linear differential equations. Modeling of nervous tissue interactions also advanced. For the annotation of these models, authors often employed the graphic syntax proposed by Guyton – for example Amosov et al. published a monograph in 1977, where they described an intertwined model of circulation, respiration, excretion, electrolyte homeostasis and thermoregulation. Likewise, Ikeda et al. used this syntax in their model of internal environment published in 1979. Physiome Project for education Bouřlivý rozvoj modelování biologických systémů a jejich formalizovaného popisu přichází zejména koncem dvacátého století v souvislosti s novými možnostmi, které přináší technický pokrok v oblasti výpočetní techniky. Stoupá počet prací využívajících počítačové modely pro vyhodnocování a interpretaci výsledků experimentálních dat. A tak jako teoretická fyzika se snaží interpretovat výsledky experimentálního výzkumu ve fyzikálních vědách, tak i nový fyziologický směr, nazývaný někdy také "integrativní fyziologie", buduje formalizovaný popis vzájemného propojení fyziologických regulací. Metodickým nástrojem jsou zde počítačové modely. Aktivity v této oblasti se snaží koncentrovat mezinárodní projekt Physiome (Bassingthwaighte, 2000, Hunter et al, 2002, Hunter and Borg, 2003, Crampin et al. 2004 ). The Physiome Project is a worldwide public domain effort to provide a computational framework for understanding human and other eukaryotic physiology. It aims to develop integrative models at all levels of biological organisation, from genes to the whole organism via gene regulatory networks, protein pathways, integrative cell function, and tissue and whole organ structure/function relations. Current projects include the development of:  ontologies to organise biological knowledge and access to databases  markup languages to encode models of biological structure and function in a standard format for sharing between different application programs and for re-use as components of more comprehensive models  databases of structure at the cell, tissue and organ levels  software to render computational models of cell function such as ion channel electrophysiology, cell signalling and metabolic pathways, transport, motility, the cell cycle, etc. in 2 & 3D graphical form software for displaying and interacting with the organ models which will allow the user to move across all spatial scales An important goal of the project is to develop applications for teaching physiology (see www.physiome.org). Spojení multimediálního prostředí sloužícího jako grafické a zvukové uživatelské rozhraní se simulačními modely umožňuje demonstrovat složité regulační procesy (a jejich poruchy) formou interaktivní simulační hry - výstupy těchto modelů jsou v multimediálním programu vizualizovány pomocí křivek v grafech nebo změnou obrazů, pohybem objektů apod. Jsou proto ideální kombinací zejména pro vysvětlování příčinných zákonitostí a průběhu složitých procesů. Počítačové modely z oblasti medicíny a biologie proto nyní nacházejí přímé praktické uplatnění ve výukových programech a zejména v lékařských simulátorech, jejichž význam s rozšiřováním a zvyšováním grafického a numerického výkonů počítačů a rozvojem broad-band Internetu dále poroste. Two types of problems Two types of problems are usually to resolve when creating educational simulation games and simulators: 1. Simulation model designing – a theoretical physiology based research work describing formalized physiological relations expressed in mathematical formulas, construction, testing and verification of model (behavior of model is compared with behavior of human organism). 2. Designing of final multimedia simulator – designing of an educational application using simulation games is an application of theoretical results. The foundations of the simulator are verified mathematical models. Each of the problems is specific and it has proved effective to use appropriate development tool for each step of this process. For simulation models design jsou dnes k dispozici nástroje usnadňující návrh, testování chování, ladění a verifikaci simulačních modelů. Krom řady komerčních nástrojů jsou pro vývoj modelů dostupné i Open Source nástroje - např. JSIM dostupný na adrese http://physiome.org/jsim (Miller et all, 1997, Raymond et all, 2003), nebo DEMaker a DESolver, vyvinutý Guytonovým spolupracovníkem Thomasem Colemanem - viz http://physiology.umc.edu/themodelingworkshop. Pro tvorbu simulačních modelů byl vyvinut i speciální programovací jazyk Modelica, jehož překladač, krom komerčních licencí, je rovněž dostupný i jako Open Source (http://www.modelica.org/). Guyton's diagram brought to life V naší laboratoři pro tvorbu simulačních modelů využíváme prostředí Matlab/Simulink od firmy Mathworks (http://www.mathworks.com). Simulink block diagrams are very similar to the thirty five years old notation used in the above mentioned large-scale model of the Guyton team. This inspired us to bring the chart to life, using this modern software tool. We tried to keep the external aspect as close to the original chart as possible – layout of the blocks and connecting wires, names of variables and even numbering of the blocks is same as in the original diagram (fig. 3). The only visible difference is that of symbolic representation of some blocks (fig. 4). Besides these graphical details, we have introduced one change, designed for the convenience of the user. We have introduced switches to the wires though  which run the input and output variables of the individual subsystems. Thus, it is possible to connect and/or disconnect the individual subsystems and regulatory loops even during the runtime of the model. The realization of the old diagram might not be as smooth as it seems at the first sight, for there are errors in the original scheme. They do no matter so much in the original paper chart, but if you try to vivify the chart in Simulink, the errors manifest themselves either as a non-adequate model behavior or even as instability of the entire model. The errors are small – swapped signs, division in place of a product, swapped connection between two blocks, missing decimal point in a constant, etc. However, they are significant enough for the model not to run correctly. If you have some knowledge of physiology and system analysis, you could find them with a bit of effort. It is interesting that although the diagram was reprinted and cited many times, nobody has made an effort to patch the errors. Well, the diagram was made in times, when no computer design tools existed and manual redrawing of a complicate chart is certainly not easy. Maybe the authors did not even want to correct the errors – if you made the effort to analyze the model, you could easily find out the typing errors yourself, if you just wanted to copy it bluntly, you were ill fated. After all, upon request, the authors did even send the FORTRAN source code to the interested – so, if one just wanted to test the model behaviour, there was no need to implement it. Our implementation of the (corrected) Guyton model is available at your free disposition at site http://www.physiome.cz/guyton. There is also an implementation of a much more complex sequel of the model from 1986. From the computational web towards simulation chips The complex intricate web of the computational blocks of the Guyton's model is at first glance impressive, but the work with it is rather complicated. Today, we are not trying to build a hive of blocks thick-sawn with the connection wires, where the user (and indeed even the author) gets easily lost. Instead, we are trying to decompose the model into transparent parts whenever possible. An advantage can be drawn from the possibility to arrange the parts of the computational web into hierarchical subsystems with user defined inputs and outputs; the mask of the subsystem can be used for a brief description of the inputs and outputs. On a click, even a comprehensive documentation of the subsystem can be made accessible, as well as the theoretical background of the subsystem. At first sight, this concept of the subsystems evokes electronic integrated circuit, at the pins of such "simulation chips: are the particular inputs and outputs. The pins can be used to connect the simulation chip with other blocks or/and subsystems (fig. 5). It should be noted that the simulation chips are functional units, whose internal structure can be entirely hidden to the user. For instance, using Simulink, we can bring constant or varying inputs to the chip; the output can be connected with other block, inspected in numerical or graphical form or recorded. Only thing which the user has to know is which input or output variable the given pin represents. Simply dragging with the mouse, the simulation chip can be taken out of the particular library and incorporated into the model being built. The behaviour of a "simulation chip" can easily be tested. It suffices to bring defined courses of variables to its inputs and visualize its outputs with scopes (Kofránek et al. 2002). Every chip can contain other simulation chips inside. Thus, a large-scale model can have a multi-layer hierarchy. As already mentioned, simulation chips can be stored in libraries and re-used. The construction of simulation chips in biomedical sciences is often a team work. On one side stands the system analyst – expert in formalization and model making. On the other side stands the physiologist or even a clinician – generally no expert in using differential equations for the description of the studied system. However, an erudite physiologist or medical doctor can tell whether or not the behavior of the simulation chip corresponds with the biological reality. Thus, a consistent use of simulation chips can vitally improve the understanding in between the two groups of specialists while building the simulation model. From simulation model to multimedia simulator V sedmdesátých letech Guyton used his scheme printed on a sheet of paper to teach medical students, because computers were not able to visualize the simulation blocks directly at the time. Dnes, v prostředí Matlab/Simulink, na PC můžeme při simulačních hrách s modelem se studenty bezprostředně sledovat chování všech proměnných modelu a graficky vizualizovat jejich průběh s využitím virtuálních osciloskopů, které jsou standardní součástí prostředí Matlab/Simulink. Implementace Guytonova modelu v tomto prostředí využíváme pro výuku fyziologických regulačních systémů pro studenty biomedicínského inženýrství. Matlab users are primarily the engineering specialists, while it is not so easy for the medical students "to play with". Krom toho, regulační schemata v Simulinku, připomínající elektrické obvody, jsou srozumitelná studentům bioinženýrství, pro studenty medicíny však mnohdy představují složitou a nesrozumitelnou hádanku. Medici potřebují uživatelské rozhraní připomínající spíše schematické obrázky, obdobné jako v obrázkových atlasech fyziologie nebo patofyziologie (Silbernagl a Lang, 2000, Despopoulos a Silbernagl, 2003), doplněné o grafickou vizualizaci průběhu hodnot jednotlivých veličin a nejlépe provázené interaktivními animacemi. Mnohé implementace medicínských výukových simulačních modelů toto multimediální rozšíření opomíjí. For example, one of the implementations of the models which show the current state-of-the-art is the implementation of the successor the Gyuton's model as Quantitative Human Physiology available at: http://physiology.umc.edu/themodelingworkshop/index.html . The model is much more complex and physiologically accurate then the original model from 1972. Although it is definitely the top of the current development from the point of view of integrative physiological model, it does not offer any visualization besides graphs, neither it is very easy to start the application (for the inexperienced user), nor does it suggest to the user what to do with the model – and the possibilities are many. Pro zvýšení pedagogické efektivity při mvýuce medicíny zpravidla nestačí strohé, technicky vyhlížející prostředí vývojových nástrojů pro tvorbu simulačních modelů. Je vhodné využít ještě další technologie a simulační model konvertovat do multimediálního simulátoru. For creation of user interfaces for an educational simulator, it is very useful to visualize the simulator as an animation. That is why we interconnect the simulation model with a multimedia animation created with the help of Macromedia Flash/Flex. The animations can be then controlled by outputs from the implemented simulation model and the meaning of numerical values can be represented graphically – i.e. a schematic picture of a vein can dilate or compress, an air sack can breathe more or less deeply, a device pointer can move and continuously display values of an output variable of the model, which is being read from the running simulation model in the background. Conversely, various inputs can be entered into the simulation model with the help of visual components (various kinds of buttons, knobs, draw bars etc.). For simulator creation, we use the Microsoft .NET platform. So that it is not necessary to create the Simulink model in Visual Studio .NET manually once again, we have created a special software tool which automatically converts the Simulink model into the target platform - this tool automatically generates a simulation model in .NET assembly from Simulink (Kofranek et. al, 2005) - see fig. 6 . Another platform in which the simulation games can be run is the environment Control-Web, originally meant for being able to easily create a visual design of controlling and measuring devices for industry with use of a PC, equipped with a special measuring/controlling card (see http://www.mii.cz). V tomto prostředí byl například implementován náš simulátor Golem (Kofránek et. al. 2001) Simulační jádro simulátorů (ať již v prostředí Control Web či v prostředí .NET) je v simulátorech propojeno animovanými obrázky, vytvořenými pomocí Adobe Flash/Flex. Flashové animace jsou pak řízeny podle výstupů simulačního modelu – fig.7,8 Teaching physiology with the web-based simulation games - Guytonian dream? V současné době se na internetu objevují interaktivní simulátory jednotlivých fyziologických subsystémů – např. AIDA: freeware diabetic software simulator program of blood glucoseinsulin interaction (http://www.2aida.net). Objevují se i webové simulátory rozsáhlých fyziologických systémů – např. webová implementace Colemanova a Randalova modelu Human (Coleman a Randal 1982): web-Human Physiology Teaching Simulation (Physiology in Health, Disease and During Treatment) available at http://placid.skidmore.edu/human/index.php. Moderní výukové simulátory by měly být šiřitelné prostřednictvím Internetu – to mimo jiné umožní jejich integrální propojení s webovými e-learningovými programy a zjednoduší jejich aktualizaci. Therefore, another task to solve was to find a way to embody simulators into the Internet e-learning applications. There are several ways to do that. One is to run model on a server and send only the outputs to the client’s workstation. But that means one model instance started for each connected client, apart from slow time response. That’s why we’re using client-based models (Stodulka et al. 2007). Simple models may use Flash ActionScript (fig. 9), but complicated models must be provided with more sophisticated simulator background. Složitější modely využívají prostředí Microsoft .NET. Jejich distribuce po Internetu je v prostředí operačních systémů Microsoft snadná. First step is the .NET framework installation, in case user doesn’t already have it. The ClickOnce technology which is part of the Microsoft .NET environment, elegantly allowing the user to download, open and run the model on his/her computer with just one click on the webpage. Windows Vista or .NET Framework 2.0 are needed for the ClickOnce technology to run properly. Naše simulátory využívající prostředí Control Web si nejprve přes síť stáhnou a nainstalují Control Web runtime that ensures the simulator execution. Current and future development in the field With the current technology, it seems possible to aim at the following goals: 1) The model – simulator should be Internet diffusible and it should not require special computer skills nor programs to be uploaded and started – ideally just one click should be enough to start the simulation. 2) The information should not be given just in form of number outputs. Visualization is needed to achieve good learning results - graphs are already good, but multimedia animations that would behave like puppets on the stings of the model outputs are better. Not only the changes of shape, but also the speed of change can transmit the adequate information. 3) The model diffused should be modular, giving possibility to disconnect and connect various parts the similar way as in our implementation of the Guyton's model to Simulink nebo v implementaci našeho simulátoru Golem (Kofránek et al., 1982) 4) It should be fun to play with the model; ideally it can resemble a computer game. We should suggest the student which parameters can be changed and what pathological state it resembles. We should encourage him to see the response with and without the regulation taking place. 5) Podle našich zkušeností je z pedagogického hlediska vhodné, aby simulační model byl doplněn i multimediální výkladovou částí. Kombinace interaktivního výkladu provázeného multimediálními animacemi a simulačními hrami je i podstatou námi postupně vytvářeného "atlasu fyziologie a patofyziologie" (Kofránek et al. 2007), který, prozatím ovšem jen v české verzi, je dostupný na internetové adrese http://www.physiome.cz/atlas. Though the authors believe it is possible to reach all four goals today, it is nevertheless demanding. Creation of modern educational software represents a challenging and complicated project, requiring team cooperation of various professionals:  Skilled teacher - prepares the scenario (including the basic design of pictures and interactive animations) and tests the final products as a teaching aid  System analyst – an expert that designs, formalizes and tunes the simulation models, in cooperation with a physiologist. The means of mutual communication are simulation chips of Matlab/Simulink environment. Graphic designer - designs and constructs graphic components for interactive animations in Macromedia Flash/Director Programmer - utilizes Control Web or Microsoft .NET as a container for the simulation model (in Control Web via a driver of a virtual input/output card, in Microsoft .NET as a special assembly) and connects it with the interactive animations and other multimedia features and programs the actual educational application And last but not least – the student, for whom the whole product is intended and whose comments after testing the program are of high interest to the teacher and the developers.    It is clear, that convenient developer’s tools save time and money. Appropriate developing tools have to be available to allow the interconnection of aforementioned professionals. But, to master the design tools requires certain time and effort. To keep the whole interdisciplinary design cycle fast and efficient, it is necessary to use specialized development tools with sufficient technical support at every stage of the design. Only such tools allow us to tie the respective parts of the simulator together according to the given scenario, forming a compact union. To our knowledge and in our experience, the call for reliable support from the software producer is crucial, that’s why we prefer proven commercial development tools to “open source” tools of the academic domain. It seems, the time of only small groups of educational software enthusiasts is coming to a close. The authoring of multimedia educational programs is getting closer to an industrial procedure. This doesn’t mean that the invention and teaching experience of the scenario creators or the creativity of a graphic designer or the skills of a programmer are becoming less important. 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(2007) Atlas of physiology - internet simulation playground. In Proceedings of EUROSIM 2007, Ljubljana, ****dokončit citaci - stránky***** Miller J. A, Nair, R. S., Zhang, Z. & Zhao, H. (1997). JSIM: A JAVA-Based Simulation and Animation Environment, In Proceedings of the 30th Annual Simulation Symposium, Atlanta, Georgia, 31-42. Raymond G. M, Butterworth E, & Bassingthwaighte J. B. (2003). JSIM: Free software package for teaching physiological modeling and research. Experimental Biology 280,102-107 Silbernagl, S. & Lang, F. (2000). Color Atlas of Pathophysiology, Stuttgart: Thieme Verlag, 2000. Stodulka, P., Privitzer, P., Kofránek, J., Tribula, M., Vacek, O.: Development of WEB accessible medical educational simulators. In Proceedings of EUROSIM 2007, Ljubljana, ****dokončit citaci - stránky ***** Acknowledgement This research was supported by aid grant MŠMT 2C06031 and BAJT servis s.r.o company. Fig. 1 A. C. Guyton (1919-2003) – one of the founders of the integrative approach to the physiological regulations Fig. 2 Circulation: Overall regulation model original scheme by A.C.Guyton et al., 1972 NON-MUSCLE OXYGEN DELIVERY 260 57.14 OSV 261 POV 5 258 268 POT 262 226 POV 39.85 RDO 512 267 u^3 P40^3 MUSCLE BLOOD FLOW CONTROL AND PO2 1 s 1 xo 0.7 259 227 RMO 5 PK1 2500 PM1^2 u^2 BFM 228 PK2 800 240 PMO PM3 1 lower limit .001 245 AU 254 AMM 1 s xo 237 PK3 02A 0.15 246 1 253 1 02M 168 269 1 270 VASCULAR STRESS RELAXATION 200 65 1 s VV7 KIDNEY DYNAMICS AND EXCRETION RR 205 GFN 206 GFR 218 VUD lower limit 0.0003 208 VUD 0.001103 THIRST AND DRINKING 8 POT 192 193 STH 194 TVD 229 239 0.125 0.00781 EVR STH 1.031 8.25 Z10 AHM 0.01 4 Z11 190 191 lower limit 0 199 64 AAR AAR 51.66 18 PFL 0.8 212 TRR 1000 219 217 1 230 257 5 238 QOM 1 s xo 236 PM4 -1 247 TVD 0.0009088 0.009 0.25 SRK 252 33 VV6 POE 8 AOM lower limit .005 61 248 1 251 62 VV1 VV2 63 VV7 2688 263 OVA 198.5 BFM 198 PPC 1 GLP 5 209 lower limit 50 5 225 OVA 231 1 s xo 0.7 235 2400 Xo P2O 1 P2O 31.67 VV7 0.01044 197 1 VIM VIM GF3 203 GF4 210 AM 189 220 211 216 0.9882 AH2 187 10u DOB 264 266 P4O MO2 8.0001 265 u^3 POT^3 256 5 2400 224 OSA 1 PVO OVA 223 200 PM5 2.8 122 0.5 VPF PMO 8 HM 40 233 DVS upper limit 8 241 232 57.14 RMO 234 242 P3O^3 u^3 188 AH4 6 186 AHC 1 s 158A AHM 8.0001 60 P3O 244 1 POM 0.08 243 PDO 249 512 EXC 1 PVO lower limit 0.35 PA 40 0.3 195 1.5 ARF 1 lower limit 0 201 RFN 0.301 VVE 250 0.5 202 1 AAR PA APD 1 NOD 0.0785 AH1 6 185 271 1 s xo 271 HM 255 215 GF3 221 upper limit 15.0 lower limit 0.4 AM AHM 6 CNY AHM 196 BFN 40 CNZ 175 NOD 0.1112 222 CNR 139 142 CNA 1 CN8 AH lower limit 3 176 182 0.3333 183 upper limit P1O POT 272 0.00333 QO2 0.14 184 207 213 214 POT 7.992 0.0125 AOM RBF RBF 1.213 RFN 1.213 0.001 0.025 2.5 CNX 0 PRA 177 AHZ 178 179 180 1 s AHY 0.9984 1 AMM AUM AOM 1 100 AH7 1 AHM 10 CNE 2 181 1 AM 1 lower_limit_0 AU AH8 0.0007 1.001 28 PPC REK 1 NON-MUSCLE LOCAL BLOOD FLOW CONTROL 278 1 s AR1 277 276 POB 275 274 POD 1 40 POV 273 1 lower limit 0.95 POK ANM AVE 1 POR 40 290 ARM 0.9763 96.3 ARM AR1 AR3 ARM VIM 1 ANU VIM 1 RAR 30.5 RAR AUM 1 284 PA 100.4 284b 31 0.33 0.495 0.00355 33 1 s 0.85 xo PVS VAS3 DAS 60 VAS PA 29 30 QAO QLO PLA QLO 5.069 0.02593 0 PLA 27 44 1 0 LVM = f(PA2) 260 QLN HSL LVM QLO QLN HMD HPL LVM PA2 PVS 46 45 0.002 QLO PR1 0.6 QRF PVS 10 PPC VP AM 0.9926 AM 1 ANM 164 4 1 PLA QLN 1.24 EXC Z12 1 VLA 25 VLA 0 QLO 1 s xo -4 QLN = f(PLA) 1 56 RPV lower limit 0 1 307 DLA 24 DAU AUK 0.0005 304 AU2 308 AUH 1 PLA 0.4 0.0357 55 RVM 16 PP2 AUH PPA PR1 0 -4 QRN = f(PRA) PPA 0 AU8 AUZ 309 Z8 6 23 QPO PLA RPT PGL 22 21 PPA VPE 20 VPA 1 s xo 0.38 15.18 19 QPO 18 QRO PRA 0.101 VTL 0.002 VTC xo 1 83 87 20 0 AUJ^AUZ VID VTD 0.9895 AUL AU VV9 3.159 313 AUD 0.7 315 0.9968 AUH AUM VVR 2.951 AUH 15 136 PPA VVR PLA 0 70 0.4667 28 146 PPC 0.55 AVE 0.9955 138 AVE 137 0.000225 147 PPD PPN PCP PPC 139 POS PPI 2 PRA 0 140 CPF 0.0003 11 VRC 40 333 1 141 PFI PPI 143 PLF DFP 2-(0.15/u) PPI = 2 - (0.15/VPF) -2.429e-008 VB DFP 0.0125 xo 1 s 142 VPF 0.01252 5 VPF VRC 2 VRC 1 xo 344 1 s 349 1 s HMD HPR 100 RC2 334 1 57 HYL VG 89 CHY PRM -5.9 24.2 12 VTS 3 VP 90 91 0.0000058 RKC 335 144 PLF 145 0.0003 PLF 152 PPO 1 s HM HM 39.95 HMD PTS PIF 92 0.0125 57600 343 348 RCD 332 xo 2 342 336b 1600 148 PPD POS 331 RC1 40 336c HM2 336 1 s xo 347 u^0.625 PA4^0.625 u^0.625 PP3^0.1 1 42 41A 40 2.9 RVS 66 1.6379 0.2 CAPILLARY MEMBRANE DYNAMICS DP0 PVG 67 3.7 PVS 85 CPR LPK 0.00047 16.65 PC 62 PPC VP 61 CPP PRP VP 0.4 CPP CFC 0.007 69 73 u^3 ANTIDIURECTIC HORMONE CONTROL xo 1 AK1 1 lower limit 0.2 1 0.06 1 ANU AMM VIM RAM AUM 36 38 1.79 RSM RVS 43 RV1 RV1 0.0212 CN2 41 17 3 37 PGS BFM 2.774 17 PPD 0 77 78 DLP 79 0.007 DPL 0.04 DPP ANM 163 AN5 162 3.3 160 AN2 10u CN7 2.8 39 BFN 285 1 s AR2 282 281 POA 280 279 35 RAM PC 17 VB 72 VRC 2 5.007 VB 68 xo 1 A2K 20 lower limit 0.5 1 PON 0.1 80 1 s 1.004 ANM xo 210 lower limit 0.7 4.0 REK 153b 153a AUM PAM AUM AN3 161 PAM 34 100 1.022 1.2 BFM RBF 4 QAO 5 VBD RSN PGS 2 BFN BFN 2.833 QVO 3.25 xo DVS 1 s 6 RVS VVE 0.322 0 VV7 PVS VVR 2.95 7 VVS VVE 8 VV8 lower limit 0.0001 VVS QVO 9 PVS 5 0.0825 CV 3.776 -6.3 0.042 159 1 s xo PIF 1.2 10 RFN (1.2/u)^3 (1.2/RFN)^3 287 POC 286 283 ANC 1 POJ 69.75 74 75 CP1 74 CPI DPC 70 71 VPD 3 xo 1 s VP 20 27.9 3.007 0.03705 DPC CPP 142 PTC CNE 154 CNA CNE 155 ANM 156 AN1 157 158 288 11520 A3K lower limit 0.3 0.3 1 POZ if (POD<0) {POJ=PODx3.3} 32 VAS VAE PA 1 289 1 s AR3 VTC 0.001657 PC^3 1.6283e-007 CPK TVD 152 0.1 15 ANT 1 xo VVS 0.001 VB 0.001 59 1 1.4 58 VLA VUD DFP 0 VTL 5 VPA VRA ANGIOTENSIN CONTROL 292 8 291 POQ POT 8 upper limit 8 PA lower limit 4 100 20.039 174 AM5 173 19.8 172 10u 294 POQ 3 8 293 296 P2O 0.1 26 0.4 8 295 28 VLE 47 15 CPA 54 53 sqrt 20 RPA PP1 50 1.4 HMD HMD HPR 1 48 1 49 AUH RVG 2.738 AM2 AM3 171 RVM 11 100 HSR 1 QVO VTL 12 QRO PTC DPL 0.1 PTC 105 xo 109 -6.381 VRA 1 s 0.25 VRA 15 PRA 0.005 0.04 DPC 102 DPL 0.1 GPD DPI 12 103 1 s 110 IFP VIF PIF PTT 5.109 lower limit 5 108 CPI 20.44 CPI 142 0.001717 0.03509 DPL 107 VTL 0.004 106 PIF 7.8 5 CKE CNA PLD 0.00352 298 EXE 297 PA 167 AMP AM1 168 -0.017 0 0 AMP = f(PA) 166 KN1 200 AMR AMT 60 169 AUC CALCULATION PA1 PA1 when PA1<40: AUC=1.2 when 40>PA1<80: AUC=0.03*(80-PA1) when PA1>=80: AUC=0 AUC calculation AUC AUC 165 1 s AMC lower limit 6 9 170 xo 302 AU6 A1B 301 u^3 AUB CALCULATION when PA1<40: AUB=1.85718 PA1 AUB when 40>PA1<170: AUB=0.014286*(170-PA1) when PA1>=170: AUB=0 AUB 1 s xo AUB^3 305 303 20 57 PL1 52 0 0 RVM = f(PP2) RPT 0.026 51 50 1 15 DRA 13 1 QRN PRA ALDOSTERONE CONTROL 104 GP1 20 lower limit 4 AUB calculation 14 xo -2.489e-005 VID 135 AUN CALCULATION PA1 when PA1<50: AUN=6 when 20>PA1<50: AUN=0.2*(50-PA1) when PA1>=50: AUC=0 AUN AUN 310 311 AU v u AUJ 1 s 1 0.0048 0.30625 VPA CKI GP2 0.0005 111 VIC PIF 12 VIF PTS 88 171 112 xo 0 0 PTS = f(VIF) 86 VG VG 113 10 1 s GPD 132 133 CCD 134 VID CNA 0.01 25 xo 1 s VIC CIRCULATORY DYNAMICS 84 xo 1 s 8 150 CPP PPR VPF 1 s xo POY 0.375 5.124e-006 330 0.00092 341 PPA4 346 PP3 351 0.0025 464e-7 0.4 151 lower limit 0.2375 VIE 337 CPN PO1 8.25 PO2 0.333 338 1.5 100 HSL 15 100 340 HSR PPA 15 350 345 PTT = (VTS/12)^2 6 PTT (u/12)^2 POT 8 11.94 VTS 85 0.9889 POT 329 VIM 339 VIM VTS AUN calculation 317 316 AU9 0.85 0.15 314 AUV 0.3 131 KI 1 s xo 3550 KCD 130 KIE 129 128 KIR 2850 KE1 0.013 127 CKE 5.001 140 1 AM 0.00014 1 s KE 123 CKE 124 KCD 0.21 312 GPR 1 318 AUY 0.5 319 1 320 0.991 AUM 149 101 1 s xo PA 121 KED 75 122 0.0028 11.4 97 KID xo AUTONOMIC CONTROL VGD 100 0.013332 120 KOD 98 126 125 0.00042 HPL 1 HPR 1 DHM 352 xo 1 s 1 V2D 0.1 96 u^2 CHY^2 NOD REK 117 NED 2130 116 xo 1 s NAE 118 119 CNA CNA 142.2 0.07061 SVO SVO 327 HR 323 32 322 328 93 0.4 PGR 94 PGC 95 PG2 99 PIF 0.25 0.1 QLO 326 325 324 321 57600 upper limit 1 PGP PTC PGH 1 STH NID 0.1 VIC VPF 114 VEC VTW VTW 115 39.93 HMD 5 0.5 1 1 1 AU HPL 1 xo HEART RATE AND STROKE VOLUME PULMONARY DYNAMICS AND FLUIDS RED CELLS AND VISCOSITY HEART HYPERTROPHY OR DETERIORATION TISSUE FLUIDS, PRESSURES AND GEL ELECTROLYTES AND CELL WATER Fig. 3 Circulation: Overall regulation model implemetation in Matlab/Simulink. The layout and block numbering is exactly the same as in the original Guyton's scheme (Fig.1). The difference is, that this scheme is also a fully functional simulation model. Available for download at www.physiome.cz/guyton. Fig. 4 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. Fig. 5 A model fragment assembled using simulation chips. The chip structure is more user friendly as opposed to the raw simulation blocks. The reusable chipsets are stored in Simulink libraries. Automatic build of Control Web virtual driver virtual driver (model) Control Web Automatic build of .NET assembly Model development and testing in Matlab/Simulink .NET assembly (model) Control layer Creating of flash animation Development of simulator application Flash animations Flash animations Control Web simulator .NET simulator Deployment Testing in Education Scenarious and scripting Fig.6 Development cycle of educational simulator application Fig. 7 An example of a simulator user interface combining custom MS .NET controls (bar graphs) with Flash animations (alveoli) in educational program on ventilation-to perfusion abnormalities. Fig. 8 An example of a simulator user interface combining Control Web controls (bar graphs) with Flash animations (glomerulus) in first prototype of renal simulator Fig. 9 An example of pure Flash simulator (simulation game in e-learning lecture on muscle physiology).