PHYSIOLOGICAL MODELLING OF HEMODYNAMIC EFFECTS OF SIMULTANEOUS ADMINISTRATION OF NORADRENALINE AND DOBUTAMINE TO SEPTIC PATIENTS IN CICU

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1 PHYSIOLOGICAL MODELLING OF HEMODYNAMIC EFFECTS OF SIMULTANEOUS ADMINISTRATION OF NORADRENALINE AND DOBUTAMINE TO SEPTIC PATIENTS IN CICU M. Mahfouf 1 M.A. Denaï 1 J.J. Ross 2 1 Dept of Automatc Control & Systems Eng 2 Dept of Anaesthetcs Unversty of Sheffeld Northern General Hosptal Mappn Street, Sheffeld S1 3JD Herres Road, Sheffeld S5 7AV UK UK M.Mahfouf@sheffeld.ac.uk M.Dena@sheffeld.ac.uk J.J.Ross@sheffeld.ac.uk ABSTRACT Septc shock s a medcal emergency whch requres a supportve treatment wth vasoactve agents to restore adequate blood pressure and tssue perfuson. Due to the complex medcal condtons of septc patents, the dentfcaton of the best therapeutc approach remans one of the major challenges for the clncans. Thus, an mproved understandng of the pathophysologcal mechansms of septc shock s needed. A computer model provdes a means of quantfyng the key phenomena nvolved and dentfyng the potental therapeutc targets. Ths paper presents a comprehensve physologcal and pharmacologcal model of the cardovascular system that can smulate the hemodynamc response to vasoactve drugs wth dfferng pharmacologc profles. The model s used to study the nteracton of combned noradrenalne and dobutamne therapy n patents wth septc shock who typcally reman hypotensve despte flud admnstraton. KEY WORDS Sepss, septc shock, cardovascular modelng, pharmacologcal model, noradrenalne, dobutamne. 1. Introducton Septc shock s characterzed by an overwhelmng systemc response to bacteral nfecton and remans the leadng cause of death n the ntensve care unts. Ths medcal emergency (sepss) occurs n three dfferent forms whch are the (1) uncomplcated sepss that results from a known or suspected nfecton (2) severe sepss whch arses when sepss occurs n combnaton wth one vtal organ dysfuncton (3) septc shock occurs when sepss s complcated wth persstent hypotenson that does not respond to flud resusctaton. Patents wth septc shock syndrome are characterzed by severe physologc abnormaltes such as (1) perpheral arterolar vasodlaton whch results n low systemc vascular resstance causng hypotenson (2) ncreased vascular leakage and flud loss from the ntravascular space causng hypovolaema and (3) myocardal depresson wth mpared systolc and dastolc functon, noncomplant, dlated and poorly contractle ventrcles [1]. After flud resusctaton, parallel to reversng the underlyng cause of nfecton, supportve treatment of septc patents wth vaso-actve medcaton s very often requred to restore normal blood pressure and mprove the crculatory performance. The most useful notrope/vasopressor drugs n septc shock are dopamne, dobutamne, norepnephrne and epnephrne. Dobutamne has predomnantly ß 1 effects. It ncreases the contractlty and heart rate and hence the cardac output. It also has ß 2 effects whch cause a mld vasodlataton and thus decreases the afterload. Noradrenalne, on the other hand, s very effectve n rsng arteral blood pressure through ts potent vasoconstrcton. Many clncal studes have reported that dobutamne used n conjuncton wth noradrenalne appears to be the optmal regmen n the therapeutc management of septc shock patents. The am of ths study s to model the nteractons of these two drugs wth the cardovascular system n septc shock condtons. The model developed gves a good understandng of the hemodynamc abnormaltes observed n septc patents and successfully predcts the response to dfferent nfuson rates of noradrenalne and dobutamne. The paper s organsed as follows. Frst, the basc features of the model are presented. The model s subsequently used to smulate three classes of septc patents based on quanttatve descrpton of sepss related hemodynamc abnormaltes. Fnally, the nteracton of the model wth noradrenalne and dobutamne s descrbed. 2. Model Descrpton The physologcal model used n ths study combnes a pulsatle model of the cardovascular mechancs wth a pharmacologcal model whch descrbes drug transport

2 throughout the varous parts of the body. Drug effects on the cardovascular system are smulated as changes n the physologcal model parameters based on publshed quanttatve data [2]. The overall model structure s shown n Fg. 1. Drugs Fg. 1. Structure of the Physologcal Model. The cardovascular system (CVS) model conssts of fourteen compartments descrbng the systemc, pulmonary, coronary and cerebral crculatons. Fg. 2 shows the model layout. Vena Cava Changes n parameters Effect Model Pulmonary Arteres Rght Ventrcle Fg. 2. Cardovascular System Model Structure. Each compartment conssts of a complant element (C) and a resstance (R) as shown n Fg. 3. P CVS Drug concentratons Bran Pulmonary Capllary Heart Muscle Kdney Tssue Skeletal Muscles Splanchnc Q Q+1 P+1 Blood flows Transport Model Pulmonary Vens Left Ventrcle Aorta Systemc Arteres The relatonshps between pressure (P), flow (Q) and volume (V) n a compartment are gven as follows: P (V V ) / C Q 0 (P P 1 ) / R 1 dv / dt Q Q Where 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 a tme-varyng elastance E(t) modeled wth two Hll equatons. The frst bracket descrbes the ascendng part of E(t) and the second the descendng part of E(t). E(t) E mn E max n1 t n α1t t n 1 α1t n1 1 t n 1 α2t The parameters n 1, n 1, α 1 T and α 2 T expermentally observed elastance. n 2 (1) (2) are obtaned from The mathematcal model of the baroreflex has been adapted from [3]. The model ncludes the afferent carotd baroreflex pathway, the sympathetc and 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. Fg. 4 depcts the structure of the baroreflex model. Carotd Snus Pressure Baroreceptor Sympathetc Vagal Fg. 4. Baroreceptor Frng Pathways. The drug transport model conssts of the same number of compartments as the CVS and s used to calculate drug concentratons n the relevant body compartments. A sngle compartment representaton s shown n Fg. 5. Q C Q +1 C +1 M +1 Elastance Unstressed Volume Perpheral Resstances Heart rate Afferent pathway Efferent pathways Effectors R C Q 0 M +1,0 Fg. 3. Electrc Analog Model of a Compartment. Fg. 5. Drug Transport Model Compartment.

3 Drug mass n each compartment s governed by the followng equaton: dm 1 Q.C - Q.C - M (3) 1 1 1,0 dt where M +1 s the mass of drug n compartment (+1), C and C +1 represent the nflow and outflow concentratons, Q and Q +1 are the nward (leavng the prevous compartment) and outward blood flows respectvely. M +1,0 denotes the mass of drug removed from that compartment. Drug elmnaton from the body s assumed to occur wthn each compartment. The nstantaneous drug concentraton s calculated as follows: C M / V (4) where V denotes the total blood volume (stressed and unstressed) avalable n the relevant compartment. The drug effect model relatng the concentraton of drug n the dfferent compartments to the changes n the correspondng parameters values (resstances, complances, elastances and heart rate) has been descrbed by an exponental functon. The parameters of the exponental functon are optmsed usng the Levenberg- Marquardt algorthm based on the avalable effect data gven for noradrenalne and dobutamne respectvely [2]. 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 transent and return to normal n survvors usually after 7 to 10 days. 4. Smulaton Results The baselne parameters of the CVS model correspond to a human subject of 75 Kg wth a total blood volume of 5.6 lters and a heart rate of 75 beats/mn [6]. For ntegraton the Euler method was used wth a step sze ntally set to sec. and subsequently adjusted wth changng heart rates. 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). Fg. 7 shows the smulated left and rght ventrcle pressures and the aortc and pulmonary pressures related to a normal subject. 3. Pathophysologcal Mechansms of Sepss Sepss stmulates the release of potent nflammatory medators nto the crculaton whch nduce vasodlataton of vascular smooth muscles and compromse the cardac functon by causng myocardal depresson [4]. The theoretcal pressure-volume loops correspondng to normal and septc patents are plotted n Fg. 6. Fg. 7. Smulated left and rght ventrcles, aortc and pulmonary pressures of a normal subject. Pressure Emax Normal Emax Severe sepss Under normal condtons, the compensatory response to hypotenson s medated by a sympathetc actvaton of the heart and perpheral vessels whch restores the arteral blood pressure to ts normal value. The onset of severe sepss s accompaned by an mparment of the autonomous nervous system leadng to a compromsed baroreflex functon wth a deregulaton n the sympathetc and parasympathetc actvtes. Therefore, to better llustrate the nteracton between drugs and the physologcal model, the baroreflex has been excluded n ths smulaton study. Volume Fg. 6. Pressure-volume loops for normal patent (bold), survvors (dotted) and non-survvors dashed) [5]. E max represents the slope of the end systolc pressure volume relatonshp and s assmlated to the ventrcle For smulaton purposes, the model has been parameterzed to descrbe three categores of septc patents: mld, moderate and severe. The smulated pressure-volume curves under mld, moderate and severe sepss condtons are plotted n Fg. 8. The pressurevolume loops are lowered as a result of a decreasng afterload (vasodlataton) and shfted to the rght as a

4 result of a decreased contractlty (myocardal depresson). The three hypothetcal models of septc patents are consdered separately to evaluate the nteracton of combned nfusons of noradrenalne and dobutamne. consequently ths result s a fall n stroke volume. At ths stage, all hemodynamc varables have reached reasonable steady-state values. The notropc effect of dobutamne s expected to ncrease the cardac output through ts drect effect on the ventrcle contractlty. It also causes an ncrease n the heart rate and a mld vasodlataton. Fg. 10 shows the left ventrcle pressure and aortc blood pressure durng smultaneous nfuson of the two drugs. Fg. 8. Left ventrcle pressure-volume loops related to the three classes of smulated septc patents. In the subsequent smulatons noradrenalne and dobutamne half-lves have been taken equal to 90 sec and 120 sec respectvely. Noradrenalne nfuson s started at tme 200 sec whle dobutamne nfuson begns at 1000 sec. A tme delay of 30 sec has been assumed between the commencement of nfuson and the onset of acton, ths beng deemed to be reasonable. 4.1 Mld Sepss Noradrenalne and dobutamne nfusons rates were set to 0.15g/kg/mn and 5g/kg/mn respectvely. The results are shown n Fg. 9. Fg. 10. Left ventrcle pressure and aortc pressure related a subject wth a mld sepss. 4.2 Moderate Sepss Vasodlataton and hypotenson are more pronounced for ths category of smulated septc patent hence requrng a hgher dose of noradrenalne. The nfuson rates were set to 0.25g/kg/mn for noradrenalne and 2.5g/kg/mn for dobutamne. The results obtaned are shown n Fg. 11. All the hemodynamc parameters were normalzed accordngly. Fg. 9. Hemodynamc response of a subject under mld sepss. Noradrenalne produces a marked ncrease n the SVR due to ts vasoconstrctng potency whch results n an mproved MAP. The heart rate s ncreased and Fg. 11. Hemodynamc response of a subject wth moderate sepss.

5 The left ventrcle and aortc pressures are shown n Fg. 12. Fg. 14. Left ventrcle pressure and aortc pressure related a subject wth a severe sepss. Fg. 12. Left ventrcle pressure and aortc pressure related a subject wth a moderate sepss. 4.3 Severe Sepss The same protocol s appled to ths category of smulated septc patent. The nfuson rates used for noradrenalne and dobutamne are 0.8g/kg/mn and 2g/kg/mn respectvely. The results of Fg. 13, show an mproved MAP trace followng noradrenalne nfuson. There s a marked ncrease n the cardac output and hgh tachycarda due to the chronotropc effects of these two drugs. Table 1 Steady-state hemodynamcs after noradrenalne and dobutamne nfusons Patent CO HR SV MAP SVR Where CO=cardac output (l/mn), HR=heart rate (beats/mn), SV= stroke volume (ml/beat), MAP=mean arteral pressure (mmhg) and SVR=systemc vascular resstance (dynes/mn/l). The pressure-volume curves related to the three septc patent models consdered n ths study are plotted n Fg. 15 (see Fg. 8). The results of Fg. 15 reflect a successful reversal of the hemodynamc abnormaltes charactersng septc shock. A further mprovement of the hemodynamc status requres returnng the heart rate to normal usng addtonal medcaton. Fg. 13. Hemodynamc response of a subject wth severe sepss. Fg. 14 shows the left ventrcle and aortc pressures n the case of a severe sepss. Fg. 15. Left ventrcle pressure-volume curves related to the three classes of septc patents after drug nfusons.

6 5. Concluson The physologcal model descrbed n ths research study succeeded n smulatng the hemodynamc response of a wde range of patents wth sepss and assess the pharmacologcal effects of varous vasoactve drugs. The classes of patent models consdered here have been parameterzed based on the (the 3 rd author) clncan s quanttatve descrpton of the key features of septc shock. The models successfully reproduced the therapeutc effects of noradrenalne and dobutamne observed n clncal practce. It s envsaged to valdate the model usng real-tme clncal data n the near future. [8] C.Martn, X. Vvand, M. Leone, X. Thron, Effect of norepnephrne on the outcome of septc shock, Crt Care Med, 28, 2000, [9] E.J. Brdges, M.S. Dukes, Cardovascular aspects of septc shock: Pathophysology, montorng and treatment, Crtcal Care Nurse (25), 2005, [10] P. Segun, E. Bellssant, Y.Le Tulzo, B. Lavolle, Y. Lessard, R. Thomas, and Y. Malledant, Effects of epnephrne compared wth the combnaton of dobutamne and norepnephrne on gastrc perfuson n septc shock, Clncal Pharmacology and Therapeutcs (71), 2002, Acknowledgements The authors gratefully acknowledge the fnancal support for ths project from the UK Engneerng and Physcal Scences Research Councl (EPSRC) under Grant GR/S94636/1. References [1] J.E. Parllo, The cardovascular pathology of sepss, Ann. Rev. Med., 40, 1989, [2] C.V. Greenway, Mechansms and quanttatve assessment of drug effects on cardac output wth a new model of the Crculaton. Pharm. Revews, 33, 1982, [3] M. Ursno, Interacton between carotd baroregulaton and the pulsatng heart: A Mathematcal Model. Am J. Physol Heart Crc Physol, 275, 1998, H1733-H1747. [4] J.F. Dhanaut, A. Carou and I. Laurent, Myocardal dysfuncton n sepss, Sepss, 4, 2000, [5] A. Kumar, C. Haery and J.E. Parllo, Myocardal dysfuncton n septc shock, Part I. Clncal manfestaton of cardovascular dysfuncton..j Cardoth and Vascul Anesth, 15(3), 2001, [6] T. Masuzawa, Y. Fuku Y. and Smth N.T., Cardovascular smulaton usng a multple modelng method on a dgtal computer Smulaton of nteracton between the cardovascular system and angotensn II. J. of Cln. Montorng, 8, 1992, [7] C. Martn, X. Vvand, S. Arnaud, R. Valet and T. Rougnon, Effects of norepnephrne plus dobutamne or norepnephrne alone on left ventrcular performance of septc shock patents, Crt. Care Med., 27(9), 1999,