The modeling of physiological control systems
via mathematical equations reflects the calculation procedure
more than the structure of the real system modeled, and several
simulation environment have been used so far for this
task. Nevertheless, object-oriented modeling is spreading in
current simulation environments through the use of the individual
components of the model and its interconnections to
define the underlying dynamic equations. In this paper we
describe the use of the MODELICATM simulation environment
in the object-oriented modeling of the cardiovascular control
system. The performance of the controlled system has been
analyzed by object-oriented simulation in the light of existing
hypothesis and physiological data used here for validation
purposes

Barbancho Concejero, Julio

Fernández de Cañete Rodríguez, Francisco Javier

Luque Rodríguez, Joaquín

Muñoz Martínez, Víctor Fernando

English

idUS. Depósito de Investigación Universidad de Sevilla

 L.M. Roa Romero (ed.), XIII Mediterranean Conference on Medical and Biological Engineering and Computing 2013,  IFMBE Proceedings 41,  923DOI: 10.1007/978-3-319-00846-2_228, © Springer International Publishing Switzerland 2014  Object-Oriented Modeling and Simulation of the Arterial Pressure Control System by Using MODELICA J. Fernandez de Canete1, J. Luque2, J. Barbancho2, and V. Muñoz1 1 Dpt. System Engineering and Automation, Andalucia-Tech University, Malaga, Spain  2 Dpt. Electronics, Andalucia-Tech University, Sevilla, Spain    Abstract—The modeling of physiological control systems via mathematical equations reflects the calculation procedure more than the structure of the real system modeled, and sev-eral simulation environment have been used so far for this task. Nevertheless, object-oriented modeling is spreading in current simulation environments through the use of the indi-vidual components of the model and its interconnections to define the underlying dynamic equations. In this paper we describe the use of the MODELICATM simulation environ-ment in the object-oriented modeling of the cardiovascular control system. The performance of the controlled system has been analyzed by object-oriented simulation in the light of existing hypothesis and physiological data used here for  validation purposes. Keywords—Object-Oriented Modeling, MODELICATM  Simulation Language, Cardiovascular System, Pressure  Control. I. INTRODUCTION There are a considerable number of specialized and gen-eral-purpose modeling software applications available for biomedical studies, which are commonly divided into struc-ture-oriented and equation-oriented. Most of them follow a causal modeling approach and require explicit coding of mathematical model equations or representation of systems in a graphical notation such as block diagrams, which is quite different from common representation of physiologi-cal knowledge. The object-oriented approach can offer many advantages in biomedical research both for the building of complex multidisciplinary models when dynamics are given by a set of differential algebraic equations [1]. The object-oriented approach has been made possible by using the modeling environment MODELICATM [2] among others, which al-lows the system, subsystem, or component levels of a whole physiological system to be described in increasing detail. While the MODELICATM environment has been used for a long time in different fields of engineering [3] there are few results in biomedical system modeling [4-5] particularly in cardiovascular modeling and control.   Cardiovascular modeling and control present a particular challenge and require both a multi-scale and a multi-physics approach [6-7]. Several mathematical models of the closed loop cardiovascular system have been developed [8-9] and software tools based on hierarchical block diagrams have also been applied to the description of cardiovascular  systems [10-11].  The regulatory control of the cardiovascular system has been studied intensively, more than any other physiological system. In fact, the high rate of cardiovascular diseases is certainly one of the main reasons for its analysis. The con-trol mechanisms responsible for maintaining arterial blood pressure may be divided into short-term processes, which are effective over a period of seconds to hours, and long-term processes that operate over days to weeks. The former are largely neural based, utilizing receptors in the heart and blood vessels to sense blood pressure and the autonomic nervous system (ANS) to regulate the cardiac function and diameter of resistance vessels.  The mid-term control is basically hormonal while the renal system plays the central role at long-term [6]. In this paper we describe the use of the MODELICATM simulation environment in the object-oriented modeling of the cardiovascular regulatory system considering the short, medium and long-term mechanisms. For this task we have followed an acausal hierarchical structure whose validity has been previously assessed to represent the cardiovascular dynamics as a multi-compartmental system. The results have been obtained under both physiological and pathologi-cal conditions, namely, hypertension due to either increased values of peripheral resistance, heart rate or intravascular volume, and hypotension due to either decreased heart  rate or severe hemorrhage, assuming the validation tests previously performed with physiological data. II. MODELING THE CARDIOVASCULAR  CONTROL SYSTEM The cardiovascular model here used can be represented with a set of nonlinear equations describing its dynamics [8]. Nevertheless, the present paper focuses on the multi-compartmental acausal approach so that the whole system will be described by eight compartments, namely, the four cardiac chambers (auricles and ventricles), the pulmonary circulation (arterial and venous) and the systemic circula-tion (arterial and venous) (Fig. 1). 924icainpto t   whdef   whadmmaimwhrepregelaof witrepuriscr  Fig. 1 ComEach compartml relationship ut flowrate he ith compartile flowrate ined by                ere  and ittance of cox , 0  is useportant to highich exhibits eaThe short-termresented by thulate the hearstance and thethe mean aortih transfer funcThe long-termresented by thne. In order tibed in [13] t  partmental Modelent will be mbetween pre and outpment given as      betwee  stand respectmpartment i, d in case of fllight the tempch of the ventr mechanism te baroreceptort rate, the ve peripheral syc pressure valtion  an mechanism te renal systemo model this hat there is a of the Circulatoryodeled by usinssure , vut flowrate  -                n compartmen  ively for the cwhile the funcowrate througoral dependenicular comparo control artes, which as dentricular elaststem resistancue through a fd a dead zone o control arter through the effect it is a linear relatioIFMBE P  System g a mathemat-olume  relative            (1)            (2)ts i and j is            (3)            (4)ompliance andtion limh a valve. It isce tments. rial pressure isscribed in [12ance, the cavae as a functionirst-order filter(Fig. 2). ial pressure iselimination ossumed as den between theroceedings Vol.  ,                    ]     f - renal exc stat     where constant flow undfor the plplasmaticvolume applying FThe wintegratiolong-termIII. THMODEject-orienphysical and is prstatementmeaning objects fr 41 retion flowrated as  ,  and for dehydratioer normal conasmatic volum volume  of each the hematocritig. 2 Diagram of thole cardiovasn of the circul arterial pressuE MODELICALICATM [3] ited language systems for thimarily based s. It also has that model coom several dJ. F  e  and t  represent n and overhydition respectie under physi is calculated of the const factor.  he Baroreceptor Rcular control atory system, re control moTM MODELIs in general afor modelinge purpose of on equations multi-domainmponents corrifferent domaernandez de Canhe plasmatic  ,    ,  a measured edration and thvely while ologic conditioby aggregatioitutive compaegulatory Systemsystem is obtathe short-termdules describeNG APPROAn equation-ba continuous ccomputer siminstead of ass modeling caesponding to ins can be dete et al.volume      (5)     xcretion e urine  stands ns. The n of the rtments   ined by  and the d.  CH sed ob-omplex ulation, ignment pability, physical escribed  Object-Oriented Modeling and Simulation of the Arterial Pressure Control System by Using MODELICA 925  IFMBE Proceedings Vol. 41     and connected. MODELICATM is an object-oriented  language whose basic construct is class (model, block,  function, type,…), which facilitates reuse of components and evolution of models.  The most important difference with regard to the tradi-tional block-oriented simulation tools is in the different way of connecting components. So, a special-purpose class con-nector as an interface defines the variables of the model shared with other sub-models, without prejudicing any kind of computational order. In this way the connections can be, besides inheritance concepts, thought of as one of the key features of oriented-object modeling, enabling effective model reuse. The basic idea of implementation in MODELICATM is to decompose the described system into components that are as simple as possible and then to start from the bottom up, connecting basic components (classes) into more compli-cated classes, until the top-level model is achieved. The default integration method is the DASSL code as defined by [14], nevertheless some other methods are available as Runge-Kutta and BDF based.   Fig. 3 MODELICATM Block Diagram of the Systemic Circulation The arterial pressure control system was simulated using MODELICATM including each of the circulatory compart-ments above mentioned together with the control mechan-isms. The MODELICATM block diagrams of any of the compartments are illustrated in Fig. 3, while the barorecep-tor control system and the renal control system program-ming are also depicted in Fig. 4 and Fig. 5.   Fig. 4 MODELICATM Block Diagram of the Baroreceptor Mechanism  Fig. 5 MODELICATM Block Diagram of the Renal Control Mechanism IV. RESULTS In order to test the performance of the pressure control system several experiences have been accomplished, both under physiologic conditions by varying resis-tance,elastance or heart rate reference values in the barore-ceptor control module and by considering liquid intake, hemorrhage and blood transfusion as external flowrates entering the circulatory system. The results have been   926obtperspoaorFisligthesysingabnFilonsio  ained by asformed with pIn Fig. 6 it is nse to a systetic pressure reg. 6 Baroreceptor In Fig. 7 it is ht hemorrhag system circultemic pressure the ability oformal situatiog. 7 Renal responsml/min durinAn object orig- term arterialogical and pa     suming the hysiological ddepicted the sm resistance igulation to a cresponse to a suddtance at t shown the lone combined wation compart value is resto the renal sysns. e to an hemorrhagg 10 min at t = 10V. CONCLUented computl pressure conthological convalidation tesata by [8]. hort-term conncreasing showonstant referenen 30% change in= 20 s g-term controith a transfusment. It can bred after the ttem to compee and subsequent s and t = 30 s resSIONS er model of trol system undition is presenIFMBE Pts previouslytrol system reing the meance level.  the system resis-l response to aion applied toe observed theransient shownsate for these transfusion of 10 pectively the short- andder both phyted.  roceedings Vol.    -     -   -The whthe MODhierarchicunderstanThe dethe teachiFutureapproach going hemMODELIcardiovasconstructi1. Hakmamodell17. 2. Mattssling w3. Tiller MODE4. Celliermedicipp 33-5. Fernanmodeliand he6. GuytonEdition7. Berne Louis.8. AvanzsimulaCompu9. Rotheactive Educ. 10. RaymoFree ssearch11. Abram(2007)ical mmedica12. Kline Press, 13. GyengModeland Hy14. 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Object-oriented mSimulation Confe  Del Saz Huangolute exchange inions. Comput. Bio996). Textbook  New York, NY. 997). Cardiovasc, Cappello A, C-loop cardiovascu(2002). Cardiovasmatical model, Aorth E, Bassingthfor teaching phys02-107. L, Summers RL,ulatory physiologathematical mode Physiol. Educ. 31ook of biomedic, Reed RK, Beration of Fluid anions. Acta AnaestL, Petzold LR (2 differential algeb ernandez de Cand and simulatenment, which aids to a qua also a valuable medical studtion of the pce of a patienthe developmy for the buills is currentl riented biomedicds Programs Biom8). Physical syste 6:501-510. physical modelodeling in the rence, Beijing, Ch P. (2010). First- the human durinl. Med. 40:740-75of medical physioular physiology, Mevenini G (1988)lar system. Int. Jcular interactionsm. J. Physiol. Advwaighte JB (200iological modelin Coleman TG, Hy. An integrative ml of human phys:202–210. al engineering. t JL (2003). Mad Small Ions dur. Scand. 47:127-1011). 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Object-Oriented Modeling and Simulation of the Arterial Pressure Control System by Using MODELICA

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Object-Oriented Modeling and Simulation of the Arterial Pressure Control System by Using MODELICA

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