A PHYSIOLOGICAL MODL DSCRIBING DOBUTAMIN INTRACTION WITH SPTIC PATINTS: A SIMULATION STUDY M.A. Denaï *, M. Mahfouf * and J.J. Ross ** * Dept of Automatc Control & Systems ng., Unv of Sheffeld, Sheffeld, UK ** Dept of Anaesthetcs, Unv of Sheffeld, Sheffeld, UK M.Dena@sheffeld.ac.uk Abstract: The complex and dynamc pathophysology of sepss make the desgn of the best approach to therapy one of the most challengng tasks n ICU. Ths s due to the large amount of clncal nformaton whch need to be effectvely and safely put nto practce n the management of crtcally ll patents n general and septc shock patents n partcular. The provson of a computer guded treatment strategy based on a comprehensve physologcal model s an attractve approach n the management of septc patents. Ths paper presents prelmnary studes on the non-lnear modellng of the cardovascular system nteracton wth the most routnely used vaso-actve drug n ICU. A case study wth dobutamne s explored to llustrate the nteracton between the cardovascular and pharmacologcal models. Introducton Sepss s the systemc response to bacteral nfectons and s the most common cause of mortalty n the ntensve care unts. Septc shock s assocated wth three major pathophysologcal effects on the cardovascular system : vasodlaton, hypoperfuson and myocardal depresson [1]. The frst prncples of hemodynamc support of patent wth septc shock s to provde adequate flud resusctaton, vasopressor therapy and notropc therapy. After adequate flud resusctaton, most septc patents become hyperdynamc. Despte ths, myocardal contractlty may stll be decreased especally n patents wth preexstng cardac dysfuncton. Inotropc agents are useful f the patent demonstrates a low cardac output state. One such notropc agent whch s frequently used n ntensve care unts s dobutamne. Dobutamne s prmary effect s to ncrease myocardal contractlty by drectly stmulatng β 1 -receptors n the heart. Ths s accompaned by a mnmal chronotropc and vascular effecs. If used n the presence of low blood pressure, the addton of a vasopressor such as noradrenalne s necessary to restore an adequate systemc vascular resstance. The physologcal model used n ths study combnes a pulsatle model of the cardovascular mechancs wth pharmacologcal model whch descrbes drug transport throughout the varous parts of the body. Descrpton of the Physologcal Model The overall model structure s shown n Fgure 1. Changes n parameters ffect Model Drugs CVS Drug concentratons Blood flows Transport Model Fgure 1: Structure of the physologcal model The cardovascular system (CVS) model conssts of fourteen compartments descrbng the systemc, pulmonary, coronary and cerebral crculatons. Fgure shows the model layout. Vena Cava Arteres Rght Ventrcle Bran Capllary Heart Muscle Kdney Tssue Skeletal Muscles Splanchnc Vens Left Ventrcle Aorta Systemc Arteres Fgure : The cardovascular system model structure ach compartment conssts of a complant element (C) and a resstance (R) as shown n Fgure 3.
P Q Q +1 P +1 R C Q 0 P = (V V Q = (P dv / dt P = Q + 1 0 ) / C Q ) / R + 1 Fgure 3: lectrc analog model of a compartment Where P=pressure, Q=flow and V=volume. V 0 denotes the unstressed volume of the relevant compartment. Flow nto the crculaton s mantaned by a pulsatle cardac pump where the rght and left hearts are descrbed by the followng tme-varyng elastance model [3]. ( t ) = dast dast + + syst syst dast t 1 cos( π ) t 1 + cos( π ) dast dast 0 t T sys 3 t T 3 t T (1) Where dast and syst represent the end-dastolc and end-systolc elastance values respectvely, T s the cardac cycle and T syst defnes the systolc nterval and s gven by T syst (t) 0.3 T(t -1). The mathematcal model of the baroreflex has been adapted from [4]. The model ncludes the afferent carotd baroreflex pathway, the sympathetc and the vagal efferent actvtes. The effector stes of these nerve stmulatons are the left and rght ventrcular maxmum elastances, the heart perod and the dfferent perpheral arteral resstances. Fgure 4 s depcts the structure of the baroreflex model. lastance sys C = M / V (3) Where V denotes the total blood volume avalable n the relevant compartment (stressed and unstressed). The drug effect model relates the concentraton of drug n the dfferent compartments to the changes n the correspondng parameters values. An exponental functon has been employed to descrbe ths relatonshp. The parameters of the exponental functon are optmsed usng the Levenberg-Marquardt algorthm based on the avalable effect data gven for dobutamne. Cardac Dysfuncton n Sepss Sepss stmulates the release of multple nflammatory medators whch nduce mportant effects on vascular smooth muscles and compromse the cardac functon by causng myocardal depresson. Ths results n a rse n the left ventrcle complance and a severely depressed ejecton fracton [5]. However ths s most commonly masked by an elevated cardac output. Smlar patterns have been observed n the rght ventrcle. The theoretcal pressure-volume loops correspondng to normal and septc patents are plotted n Fgure 5. syst represents the slope of the end systolc pressure volume relatonshp and s assmlated to the ventrcle contractlty. In survvors of severe sepss, an adequate stroke volume s mantaned n the early stage by an ncrease n the end dastolc volume. In nonsurvvors, falure to ncrease the end dastolc complance results n nablty to mantan the same stroke volume [5]. These alteratons n ventrcular functon and sze are transents and return to normal n survvors after 7 to 10 days n general. Carotd Snus Pressure Baroreceptor Sympathetc Unstressed Volume Perpheral Resstances syst normal syst severe spess Vagal Heart rate Afferent pathway fferent pathways ffectors Pressure Fgure 4: Baroreceptor frng pathways The drug transport model conssts of the same number of compartments as the CVS and s used to calculate the drug concentratons n the relevant body compartments. Drug concentraton n each compartment s calculated by applyng the followng mass balance equaton : dm / dt = Q.C - Q.C - M.ln/τ () n n out Where M s the mass of drug n the compartment, C n and C out represent the nflow and outflow concentratons, Q n and Q out are the nward (leavng the prevous compartment) and outward blood flows respectvely and τ s the drug half-lfe. The nstantaneous drug concentraton s calculated as follows out Volume Fgure 5: Pressure-volume loops for a normal patent (sold lne), survvors (dotted lne) and non-survvors (dashed lne) of severe sepss Smulaton Results The parameters of the CVS model correspond to a human subject of 75 Kg wth a total blood volume of 5.6 ltres and a heart rate of 75 bpm []. For ntegraton the uler method was used wth a step sze of 0.005 sec.
Intal compartment volumes have been calculated for each compartment as the sum of the unstressed volume and the volume gven by the ntegraton procedure (.e. the stressed volume). Intal smulatons results are presented for a healthy patent under normal condtons. The steady-states hemodynamc varables are shown n Fgures 6-8. reduces the afterload whch s relfected by a lower mean arteral pressure (MAP) as shown n Fgure 10. The result s an elevated cardac output despte a reducton n the ventrcle contractltes. Fgure 9: Left ventrcle pressure, volume and flow n sepss Fgure 6: Left ventrcle pressure, volume and flow Fgure 7: Rght ventrcle pressure, volume and flow Fgure 10: Rght ventrcle pressure, volume and flow n sepss Fgure 8: Hemodynamc parameters Vascular dlaton has been smulated as a 40% decrease n all systemc resstances. Myocardal depresson n the early stage of sepss was smulated as 30% decrease n left and rght ventrcular systolc elastance. The results are shown n Fgure 9-11. A decrease n the systemc vascular resstance (SVR) Fgure 11: Hemodynamc parameters n sepss Both PV loops are plotted n Fgure 1 for comparson. The PV loops for the left and rght ventrcles have moved to the rght n the septc case owng to a decrease n the slope of the end systolc pressure volume relatonshp characterstc. The slght ncrease n the end dastolc volume s the result of
bventrcular dlaton whch accompanes the myocardal depresson. Fgure 1: Left ventrcle PV loops for normal and septc patents Dobutamne s a potent notrope. It works at a number of dfferent receptor stes n the body, however t mostly acts on beta-receptors n the heart to ncrease the force of myocardal contracton wth relatvely mnor chronotropc and vascular sde effects. Baroreflex control has been removed n the subsequent smulatons n order to emphasze the dose related effects of dobutamne on the contractlty. Dobutamne nfuson s started at tme 00 sec. and the onset of effect s delayed by 30 sec. The results of Fgure 13 show a marked ncrease n the cardac output as a results of the notropc effects of dobutamne. There s a small decrease n SVR. For larger doses, there s a sgnfcant ncrease n heart rate and consequently a slght fall n stroke volume. Fgure 14: Left ventrcle PV loops for dfferent doses of dobutamne The baroreflex compensates for a decrease n the MAP by adjustng the parameters of the CVS model (Fgure 4). On the other hand and accordng to the data used n ths smulaton study, dobutamne s controlled parameters are the ventrcle contractltes, the heart rate and the muscle arterolar resstance. The next smulaton results are ntended to llustrate the nteracton of dobutamne wth overall CVS model ncludng baroreflex control. Dobutamne nfuson rate has been set to 10 µg/kg/mn wth baroreflex control ncluded. Fgure 15 shows the response of the dfferent hemodynamc varables. Baroreflex control frst compensates for the changes nduced n SVR and contractlty n order to restore an adequate MAP as seen n the ntal stage of the smulaton. After drug nfuson has been ntated, a second counteracton s exerted by the baroreflex n response to dobutamne effects on the crculatory parameters. Fgure 13: Hemodynamc responses to dfferent dobutamne doses Fgure 15: Hemodynamc responses wth baroreceptor Fgure 14 shows the left ventrcle PV loops related to dfferent dosage of dobutamne. The curves are shfted to the left as a result of an mproved myocardal contractlty. Usually, dobutamne s accompaned wth a vasoconstrctor to mprove the SVR and hence the afterload. One such vasoactve agent whch s frequently used wth dobutamne s noradrenalne.
References [1] KUMAR A., HARY C. and PARILLO J.. (001): Myocardal Dysfuncton n Septc Shock: Part I. Clncal Manfestaton of Cardovascular Dysfuncton, J Cardoth and Vascul Anesth, Vol 15, 3, pp. 364-376 Fgure 16: Changes n the ventrcles elastances [] MASUZAWA T., FUKUI Y. and SMITH N.T. (199): Cardovascular Smulaton Usng a Multple Modelng Method on a Dgtal Computer Smulaton of Interacton Between the Cardovascular System and Angotensn II, J. of Cln. Montorng, Vol 8, pp. 50-58 [3] HLDT T., SHIM.B., KAMM R.D. and MARK R.G. (199): Computatonal Modelng of the Cardovascular Response to Orthostatc Stress, J Appl. Physol, pp. 139-154 [4] URSINO M. (1998): Interacton between Carotd Baroregulaton and the Pulsatng Heart: A Mathematcal Model, Am J Physol Heart Crc Physol, 75, pp. H1733-H1747 [5] DHAINAUT J.F., CARIOU A. and LAURNT I. (000): Myocardal Dysfuncton n Sepss, Sepss, 4, pp. 89-97 Acknowledgement The authors gratefully acknowledge the fnancal support for ths project from the UK ngneerng and Physcal Scences Research Councl (PSRC) under Grant GR/S94636/1. Fgure 17: Changes n the controlled CVS model resstances and unstressed volume Conclusons In ths paper the nteracton of vasoactve drugs, such as dobutamne, wth the cardovascular system n patents wth sepss nduced myocardal dysfuncton has been modelled and analysed. The physologcal model has successfully predcted how the cardovascular hemodynamcs are affected by dfferent drug doses of dobutamne. The model can also be extended to smulate multple drug therapy gven the quanttatve nformaton about the drect actons of these drugs on the relevant cardovascular parameters. It s hoped to conduct such a comprehensve study n the future.