Oscillations in Mean Arterial Blood Pressure in Conscious Dogs

Transcription

1 692 Oscillatis i Mea Arterial Bld Pressure i Cscius Dgs STVN G. SHIMADA AND DONALD J. MARSH SUMMARY Oscillatis i mea arterial bld pressure (MABP) with perids ear 1.5 hurs were bserved i cscius male dgs with pressure trasducers implated i their artas. Cardiac utput (CO) was measured with a electrmagetic flw prbe implated abut the ascedig arta, ad ttal peripheral resistace (TPR) was calculated as the rati f MABP t CO. Heart rate (HR) was measured with a carditachmeter. Cherece fuctis were calculated amg the fur variables (MABP, TPR, CO, ad HR) t determie sigificat scillatis at the frequecy f the MABP scillati. Crssspectral calculatis prduced phase relatiships amg the variables. TPR ad CO were bth scillatig at the same frequecy as MABP. Hwever, TPR lagged MABP by 63 degrees, whereas the phase agle fr CO ad MABP was t sigificatly differet frm zer. We ccluded that CO must be prducig the MABP scillatis, ad that the TPR scillatis arse as a reacti t the MABP r CO chages. HR was scillatig i phase with CO, idicatig that COfluctuatiswere iduced i part by HR chages ad that the sympathetic ervus system was prbably drivig the heart. I further experimets, chric dietary sdium chages did t alter the pwer spectra fr MABP. Thus, the rei-agitesi system (RAS) was t respsible fr the scillatis; cversely, the scillatis were t actig as a sigal t the RAS durig sdium-deficiet states, a cditi kw t stimulate the RAS. Circ Res 44; , 1979 CARDIOVASCULAR peridicities have bee kw sice ma first felt his pulse, but the heart beat ad circadia rhythms are the ly frequecies that have attracted much atteti. Rhythms lyig betwee these tw extremes have bee reprted fr a umber f physilgical variables (Kleitma, 1963; Krieger et al., 1971; Lefat, 1967; Okhtes et al., 1974; Yamaji et al., 1972), but t fr the circulati. We speculated, frm very geeral csideratis, that flws ad pressures might fluctuate peridically at a itermediate frequecy (Marsh, 1973), ad the majr purpse f this paper is t reprt bservatis f such scillatis i mea arterial bld pressure (MABP), cardiac utput (CO), heart rate (HR), ad ttal peripheral resistace (TPR) i cscius dgs. The perid legth is 1.5 hurs. A imprtat ureslved questi i the area f fluid vlume regulati is the idetificati f the sigal that triggers reiim release whe extracellular fluid vlume is depleted, as durig dietary NaCl restricti. Arterial bld pressure gvers rei release, at least i part, but MABP remais rmal ver a wide rage f rei secreti rates (Davis ad Freema, 1976). We therefre speculated that a bld pressure sigal that varied i the frequecy Frm the Departmet f Bimedical gieerig, Uiversity f Suther Califria, Ls Ageles, Califria. Supprted by Natial Istitutes f Health Grats AM ad GM 01724, ad Bimedical Supprt Grat RR The preset address fr Dr. Shimada is: The Jh B. Pierce Fudati, 290 Cgress Aveue, New Have, Cecticut Address fr reprits. Dald J. Marsh, M.D., Departmet f Physilgy, Uiversity f Suther Califria Schl f Medicie, 2025 Zal Aveue, Ls Ageles, Califria Received August 22, 1978; accepted fr publicati Octber 31, dmai, rather tha i the amplitude dmai, might cause the chage i rei release whe extracellular fluid vlume varies (Marsh, 1973). We have tested this hypthesis by examiig the effect f dietary NaCl restricti the MABP scillatis. Methds Male mgrel dgs weighig kg were divided it tw grups. The first was used ly fr MABP bservatis, ad the secd prvided data CO, HR, ad TPR, as well as MABP. Surgery I the first grup, csistig f 10 dgs, a straigauge pressure trasducer (Kigsberg Istrumets) was implated thrugh a left flak icisi it the abdmial arta uder sdium petbarbital aesthesia. The trasducer was placed it the arta, 7-8 cm distal t the rigi f the real arteries, after a icisi had bee made i the wall f the arta large eugh t accmmdate the head f the trasducer. The electrical cable frm the trasducer was threaded subcutaeusly alg the spie ad brught ut thrugh a pucture wud i the ski at the back f the eck. The electrical cectr was badaged t the ski ad prtected by a stiff leather cllar. Durig a exi lamet, the cectr was ucvered ad attached t a trasducer amplifier (mdel 3A10, Tektrix), after which the leather cllar was repsitied fr prtecti durig a experimet. Bth a pressure trasducer ad a flw prbe were implated it the fur dgs f the secd grup, agai uder sdium petbarbital aesthesia. The

2 BLOOD PRSSUR OSCILLATIONS/Shimada ad Marsh 693 flw prbe was placed arud the rt f the ascedig arta thrugh a icisi i the 4th itercstal space the left side. A pressure trasducer was sew it the descedig arta 3-5 cm distal t the rigi f the left subclavia artery. The cables frm bth the flw prbe ad the pressure trasducer were chaeled subcutaeusly t the back f the eck, where they emerged thrugh a pucture wud i the ski. Durig a experimet, the trasducer was cected t the trasducer amplifier, ad the flw prbe was cected t a electrmagetic flwmeter (mdel BL 610, Bitrex Labratry). A carditachmeter (mdel 2170, Harvard Apparatus) was used t measure HR ad was triggered by the bld pressure sigal. After bth surgical prcedures, a iterval f at least 7 days was allwed fr recvery befre data were acquired. Durig this recvery perid, three r fur ijectis f 1,000,000 U f peicilli G were admiistered subcutaeusly. xperimetal Prcedures Whe recrdigs f data were t beig take, the dgs were hused i a aimal care facility where the lights were tured at 6:00 a.m. ad ff at 6:00 p.m. Feedig (Puria lab chw) tk place ce a day ear 8:00 a.m. O a recrdig day the dgs were allwed t eat that mrig ad were brught t the labratry shrtly thereafter. O the day f a recrdig sessi, the electrical cectrs were expsed ad cected t apprpriate istrumetati. The dgs were tethered by a chai 2 meters lg. Durig the day, they were allwed t sit, lie, r stad as they wished withi the 2-meter radius. Occasially, water was ffered t the dgs durig a experimet. These sessis usually lasted 8.5 hurs. The measuremets were made i a rm apprximately 5 by 5 m. The rm was lit by artificial light ad was air-cditied frm a cetral cmpressr i the buildig. The rm ctaied ly the measuremet ad recrdig equipmet, ad e ivestigatr, wh did t iteract with the dg. N ther perss were admitted. Frm the stadpit f temperature, light, ise, r ther disturbace, we culd detect peridic exteral stimulus. N systematic recrd was kept f the dg's activity durig the recrdig perid. Durig dietary sdium experimets, the dgs were fed either the rmal lab diet r a diet with a lw sdium ctet (Hartrft frmula, Geeral Bichemicals). The rmal diet ctaied 0.5% NaCl by weight, whereas the salt-deficiet diet is listed as havig trace amuts f NaCl. Bth specificatis are the maufacturer's. ach dg was studied first e diet, ad the the ther. The rder f presetati f the diet was varied radmly. The dgs the lw salt diet teded t eat less tha whe they were fed the rmal diet, a respse that reifrced the reducti i salt itake. These diets were fed a miimum f 4 days prir t a recrdig sessi. Urie samples were take by suprapubic pressure after a experimet ad aalyzed fr sdium ad ptassium ccetratis t verify that the dgs were i the desired state f salt balace. The urie sdium levels durig lw ad rmal diets were abut 5 ad 140 mq/liter, respectively. The crrespdig uriary sdium-ptassium ratis fr dgs these diets were apprximately 0.05 ad 1.0 fr lw ad rmal diets, respectively. very dg used i this prti f the study shwed this respse t chages i dietary salt ctet. I additi, we measured plasma rei activity by radiimmuassay i tw f these dgs. Plasma rei activity icreased i e dg by a factr f 4, ad i the secd by a factr f 2.5 whe the lw salt diet replaced the rmal diet. Aalytical Prcedures Arterial bld pressure, CO, ad HR were btaied as aalg vltages frm their respective amplifiers. The aalg data were filtered by a lw pass aalg filter, the digitized by a aalg-t-digital cverter. I mst cases, data pits 20 secds apart were used i the aalyses. TPR was calculated pit by pit as the rati f arterial bld pressure ad CO. ach set f data was prcessed t a frm suitable fr etry it a fast Furier trasfrm (FFT) algrithm. This prcess icluded digital filterig by a lw pass Butterwrth filter, applicati f a csie taper t the eds f the data set, remval f liear treds, ad subtracti f the mea value frm each data pit s that the etire data set had a mea value f zer. The data were the Furier-trasfrmed by the FFT, ad the results were used t calculate pwer spectral desities, crss-spectral desities, ad cherece fucti estimates (Bedat ad Piersl, 1971; Otes ad chs, 1972). These calculatis are give i the Appedix. Figure 1 illustrates the data aalysis scheme fr MABP. Aalgus prcedures were used fr CO, TPR, ad HR. Cmputatis were carried ut a PDP 8/1 labratry cmputer. Statistical tests ivlved the calculati f cfidece itervals fr cherece fuctis. Cherece is aalgus t a crrelati, but the cherece fucti is a mre suitable measure fr peridic phemea tha is the crrelati cefficiet. The cherece fucti ca rage frm zer t e, zer idicatig that the tw variables are ucrrelated ad a value f e that the variables are perfectly crrelated. We wated t kw whether ay cherece existed at all, i.e., whether the cherece fucti was differet frm zer. Thus a 95% cfidece iterval was calculated abut the estimated cherece fuctis, ad if the iterval excluded zer, we accepted the cherece fucti as differig sigificatly frm zer. Fr phase relatiships it was als f iterest t kw whether variables were i r ut f phase, i.e., whether the phase agle was differet

3 694 CIRCULATION RSARCH VOL. 44, N. 5, MAY i FIGUR 1 Typical MABP recrd frm a dg receivig a rmal diet. The plt is geerated by cmputer frm the raw data after lw pass filterig, liear tred remval, ad csie taperig. frm zer. Therefre, 95% cfidece itervals were calculated t determie whether the phase agles were sigificatly differet frm zer. Results MABP Oscillati Figure 1 shws a filtered recrdig f MABP recrded frm a dg ver a perid f slightly mre tha 8 hurs. The recrd has bee subjected t liear tred remval ad csie taperig ad csists f 1024 discrete data pits spaced equally i time. Figure 2 shws that the pricipal pwer frm the time series f Figure 1 is i a badwidth with a frequecy f 114 miutes. The results f 33 experimets 10 dgs were averaged t acquire the result pictured i Figure 3. The peak i this spectrum is at miutes, but appreciable pwer is preset i the rage miutes, idicatig that the perid f scillati varies smewhat frm the peak value. Pressure, Flw, ad Resistace xperimets Figure 4 shws data frm e experimet. As befre, these are cmputer-geerated plts f data that have uderge lw pass filterig ad have had csie tapers applied t the eds ad liear treds remved. The fur paels represet MABP, ~ 50- I LJ 20 I II FRQUNCY (cyclet/hr.) FIGUR 2 Pwer spectrum frm the time series f Figure v 20 z Id O cr UJ * FRQUNCY (cycles/hr.) FIGUR 3 semble average pwer spectrum fr 33 MABP experimets. The peak pwer has a frequecy f 0.6 cycle/hr. mea CO, mea TPR, ad mea HR, ad are displayed as percet variatis abut the mea value. Similar sets f data were btaied frm each experimet. Pwer spectra were calculated frm each idividual set f data, ad the the spectra were averaged fr each variable. The averaged pwer spectra fr the fur variables are shw i Figure 5. These spectra are esemble-averaged ver six experimets ad frequecy-averaged ver fur adjacet frequecy bads. The six experimets were perfrmed fur dgs; tw f the aimals were used twice. All spectra have the same geeral appearace, with mst f the pwer at the lw frequecy prti f the spectrum ad little pwer at the higher frequecies. Fr MABP, Figure 5A shws that a large amut f pwer is preset i the frequecy bad cetered at a perid legth f 78.8 miutes. Figure 5B displays the pwer spectral desity fr mea CO, ad it is apparet that the largest amut f pwer is als i a frequecy bad whse perid is 78.8 miutes, althugh there is substatial pwer i the adjacet frequecy bads as well. The HR pwer spectral desity shw i Figure 5C has its peak pwer at a frequecy that is cetered abut a perid f miutes. The TPR pwer spectrum has the greatest amut f pwer at 48.8 miutes, as shw i Figure 5D. I Figure 6, the magitude prti f the crssspectral desity betwee MAPB ad CO, MAPB ad TPR, ad CO ad HR, is illustrated (see als Table 1). The phase agle is shw ly at that frequecy at which MABP is scillatig, amely 78.8 miutes (Fig. 5A). Sice we are iterested i the ctributis f TPR ad CO t the MABP scillatis, the prti f the crss-spectral desities with which we are ccered is that frequecy at which MABP is shwig a fluctuati. Fr MABP ad CO, the magitude f the crss-spec-

4 BLOOD PRSSUR OSCILLATIONS/S/iimarfa ad Marsh 695 A MAN ARTRIAL BLOOD PRSSUR as The cherece fucti estimate fr MABP ad TPR at the same frequecy was 0.19 ad fr CO ad HR was We determied 95% cfidece itervals fr all three cherece fucti estimates, ad all three were sigificatly greater tha zer. 100% - 30% 0-30% -100%-» CARDIAC OUTPUT C HART RAT TOr>«t PRIPHRAL RSISTANC TIM (-I.OI..I FIGUR 4 Cmputer-geerated plts f raw data fr e experimet with lw pass filterig, csie taperig, ad liear tred remval applied. The fur paels represet (A) mea arterial bld pressure, (B) cardiac utput, (C) heart rate, ad (D) ttal peripheral resistace. The data are pltted as percet variatis f the mea value. The mea values are (A) 103 mm Hg, (B) 2.7 liters/mi, (C) 118 beats/mi, ad (D) 2.2peripheral resistace uits-secds. trum is the highest at a frequecy badwidth whse perid is cetered at 78.8 miutes. The phase agle is calculated as 33.8 degrees at this frequecy, but the 95% cfidece iterval shwed this is t sigificatly differet frm zer. I Figure 6B, a peak i the crss-spectrum als ccurs at 78.8 miutes fr MABP ad TPR. Here the phase agle is degrees, TPR laggig behid MABP; this result was sigificatly differet frm zer. Fially, the crss-spectrum fr CO ad HR shws a large magitude i the lw frequecy rage, with the peak magitude at a frequecy whse perid is 48.8 miutes. The phase agle at the frequecy f MABP scillati is degrees, HR leadig CO; this was t sigificatly differet frm zer. The cherece fucti fr MABP ad CO at the frequecy f MABP scillati was estimated Dietary Sdium xperimets Figure 7 shws the averaged MABP spectra frm dgs bth rmal ad lw sdium diets. ach spectrum is the average f 10 experimets. Bth spectra shw a strg scillati with a perid ear 90 miutes, but there is sigificat differece betwee them, either i pwer r i the lcati f the badwidth with greatest pwer. There was als differece betwee the tw states whe the cmparis was made a itra-aimal basis. Discussi Our data reveal a persistet free-ruig scillati i HR, CO, MABP, ad TPR, all with perids f abut 90 miutes. Several factrs preclude a mre precise specificati f the frequecy. Prbably the mst imprtat f these is the prblem f cstacy f the scillati, fte referred t as statiarity. Applicati f the time series aalytic methds we have used assumes that the peridic sigal, hwever much crrupted by ise, remais cstat ver the perid f bservati. This durati i ur experimets was ver 8 hurs. Sice there is a circadia activity cycle that affects cardivascular perfrmace, ad sice ur bservati perid lasted e-third f that perid, it is a priri ulikely that the dgs i this study satisfied the criteri f statiarity cmpletely. We have attempted t deal with this prblem by remvig liear treds frm the raw data, but this prcedure assumes that the scillati f primary iterest ad the tred that is beig remved simply add, i.e., that the uderlyig system is liear. The system regulatig cardivascular perfrmace is highly liear, s that if there is a scillatr drivig the fluctuatis we bserved, it will prbably becme etraied i ther rhythms, particularly slwer es, ad the effect will be t brade the peak i the pwer spectrum ver several adjacet badwidths. Ather reas that a precise frequecy cat be give is that we have averaged the pwer spectra frm all the dgs i ur study t arrive at a esemble pwer spectrum fr each variable. Iteraimal variability teds t brade the pwer spectrum. The time series techiques als ctribute t the imprecisi f the estimate f perid legth. The pwer spectrum calculati partitis the variace f the rigial data set it equally spaced frequecy badwidths. Sice the perid legth is simply the reciprcal f frequecy, the legth is shrtest at the high frequecy ed f the spectrum ad lgest (r least precise) at the lw frequecy

5 ISN 696 CIRCULATION RSARCH VOL. 44, N. 5, MAY 1979 A. MAN ARTRIAL 35-1 BLOOD PRSSUR 35-i B CARDIAC OUTPUT hr.j > H (ft Z UJ cc I 50- ~ -^ HART RAT M g >- 1 ONSI' cc UJ Q_ \ L 0 TOTAL PRIPHRAL RSISTANC FIGUR 5 Average pwer spectra fr (A) mea arterial bld pressure as (mm Hg) 2 /hr~ l ; (B) cardiac utput as (liters/mif/hr''; (C) heart rate as (beats/mi) 2 /hr~ l ; ad (D) ttal peripheral resistace as (peripheral resistace uits-secds) 2 / K 3 cc a. *-* cc 50- LU a cc UJ * J 0 r 1 pl L FRQUNCY (cycle»/hr ) FRQUNCY (cycles/hr) ed. We culd have btaied better estimates by prlgig the legth f the bservati, but such a decisi wuld have made the statiarity prblem eve mre serius. The 8.5-hur bservati therefre represets a cmprmise betwee these tw cflictig demads. Measuremet ise prbably ctributed little t the imprecisi f the estimates, particularly i the MABP determiati. The trasducers we used drifted less tha 1 mm Hg ver 8 hurs whe placed i salie, ad the drift was t peridic. Of the fur variables we examied, TPR is prbably the mst susceptible t measuremet ise, because it is calculated as the qutiet f tw variables, ad therefre ctais the ise f bth. The phase agle relatiships permit us t reach certai cclusis abut the cause f the scillatis. Because f the lw frequecy f these chages, there shuld be phase lag betwee MABP ad whichever f CO ad TPR is causal. Sice there is a sigificat lag betwee TPR ad MABP, we reject scillatis i TPR as the cause f MABP fluctuatis. O the ther had, we culd detect phase lag betwee CO ad MABP, ad TABL 1 Summary f Phase Agles ad Cherece Fucti stimates Phase agle 95% cfidece iterval fr phase agle Cherece fucti estimate 95% cfidece iterval fr cherece fucti Preasure-CO spectrum Pressure-TPR spectrum CO-HR spectrum (7.4) «: <t> < (-0.88) (15.69) < Y 2 «: stimates are cmputed at the frequecy where arterial pressure is scillatig (perid 78J miutes). The equivalet time perids fr the phase agles (i miutes) are give i paretheses (-13.7) «.#>« (-24.76) (-2.72) < y 2 « (1.32) «$ : (-11.96) (9.32) < Y 2 «0.4004

6 BLOOD PRSSUR OSCILLATIONS/SAimada ad Marsh I 79 I 90 I 29 I 00 7» t ~ 20H W x O «J (u * O a e betwee HR ad CO. These phase relatiships suggest that scillatis i CO, pssibly caused i part by scillatis i HR, prvide the primary cause f the MABP fluctuati. Oe plausible iterpretati f the TPR scillatis is that they represet a autregulatry adjustmet t the variable peripheral flw caused by the MABP scillatis Jl NORMAL DIT SODIUM DFICINT DIT I 79 I 90 I 29 I I 79 I 90 - I 29 - I t 4 10 It 14 > It 10 FRCOUCNCY (CfCl««/fir) FIGUR 6 Average crss-spectra betwee mea arterial bld pressure ad cardiac utput as (mm Hg) (liters/mi)/hr~\ mea arterial bld pressure ad ttal peripheral resistace as (mm Hg) (peripheral resistace uits-secds)/hr~\ ad cardiac utput ad heart rate as (liters/mi) (beats/mi)/hr~'. The phase agle is shw i each spectrum at the frequecy at which mea arterial bld pressure is scillatig (Fig. 5A). I FRQUNCY (cycles/hr.) FIGUR 7 Average pwer spectra fr mea arterial bld pressure fr rmal sdium ad chric lw sdium dietary cditis. It seems ulikely that variatis i HR ale, as might be caused by variatis i vagal efferet activity, culd cause MABP t vary as much as it did i these experimets. Variable cardiac sympathetic activity that wuld iduce bth itrpic ad chrtrpic effects culd prduce the bserved MABP scillatis. There is thig i ur data t rule ut simultaeus ad cmplemetary chages i bth cardiac vagal efferet ad cardiac sympathetic activity. The sigificat phase lag betwee TPR ad the ther variables des suggest that if peridically varyig cardiac sympathetic firig des ccur, there is ccmitat variati i peripheral sympathetic vasmtr activity. The si-artic barreceptr system is either bypassed durig the geesis f these scillatis r is ieffective i prevetig them. I respse t a risig pressure, cardiac slwig ad a reducti i CO wuld be the expected respses f the barreceptr reflex system. This behavir is t see; MABP ad CO rise i uis. Thus, chages i MABP due t hydrstatic chages, such as ecutered i pstural shifts (Lamberti et al., 1968), which are mediated by the barreceptrs, are t ivlved i the fluctuatis. Ay chages iduced by TPR chages ca be excluded als, sice TPR chages appear t be secdary t MABP fluctuatis rather tha casual. This cclusi is at variace with the idea that CO is determied primarily by the sum f peripheral tissue eeds (Clema et al., 1974). At this pit we ca ly speculate abut the rigi f these scillatis. The questi remais pe as t whether they are itrisic sptaeus scillatis f the bld pressure-regulatig system r the result f etraimet by ather system iteractig i the cetral ervus system with the bld pressure-regulatig system. A rest-activity cycle with a perid f ear 90 miutes that ctiues 24 hurs a day has bee prpsed i ma (Kleitma, 1963). Cyclical rapid eye mvemet

7 698 CIRCULATION RSARCH VOL. 44, N. 5, MAY 1979 sleep is a reflecti f this cycle durig sleep, whereas, durig wakefuless, activity waxes ad waes als with a perid f ear 90 miutes. This rhythm culd reside i r be trasmitted t the autmic ervus system, where sympathetic ad/r parasympathetic ctrl f the heart culd iduce peridic CO chages that culd affect MABP. Ideed, a scillati i huma HR with a perid f ear 90 miutes has bee reprted previusly (Orr ad Hffma, 1974). Sice systematic bservatis were made f aimal behavir durig ur experimets, we are uable t crrelate a restactivity cycle with ur MABP scillatis. Other causal pssibilities iclude: (1) a effect f chagig reticular activatig system drive t skeletal muscles, which wuld alter vascular capacity; (2) peridic chages i vaspressi secreti, which ca be a sigificat pressure ctrller uder sme circumstaces (Cwley et al., 1978); ad (3) a effect f sympathetic drive, primarily capacitace vessels. Ne f these pssibilities excludes the thers, ad all appear t be csistet with ur data. Whatever the cause f the scillati, hwever, we wish t emphasize that these fluctuatis affect flw ad impige pressure-sesitive receptrs everywhere, icludig thse that mediate rei release. Whether the fluctuatis i MABP affect rei release wuld deped the frequecy respse f the real barreceptr. Other hrmes are released at similar frequecies (Krieger et al., 1971; Yamaji et al., 1972). The last series f experimets tested the pssibility that variati i the frequecy dmai f MABP culd prvide a sigalig pathway t the rei-agitesi system durig chric sdium deficiecy. The frequecy ctet f the MABP pwer spectral desity was cmpared durig a rmal diet ad a sdium-deficiet diet. N sigificat differece i the respective pwer spectra culd be detected. Thus, whatever the sigal may be that alters rei release durig the chage i sdium states, it des t ivlve a alterati i ay aspect f the bld pressure we have examied. Altered respsiveess f the real barreceptr might be respsible, s that bld pressure might still be the sigal, but the prblem the remais t determie what alters receptr sesitivity. Appedix The time series aalysis we perfrmed t characterize the data icluded cmputati f pwer spectral desities, crss-spectral desities, ad cherece fuctis. A fast Furier trasfrm (FFT) algrithm was used t calculate pwer spectral desity ad crss-spectral desity estimates, ad these, i tur, were used t derive cherece fuctis. The data were first btaied i aalg frm ad put thrugh aalg lw pass filters. The filters used fr the MABP ad CO sigals were furth-rder, tw-stage, active filters. The crer frequecy fr these filters was ear 0.06 Hz, s that higher frequecies i the sigal were atteuated. These filters were desiged t remve variatis due t cardiac ad respiratry cycles. Aliasig errrs were elimiated by these filters s lg as the samplig iterval did t exceed 5 secds. HR was filtered by usig the aalg filter supplied with the carditachmeter. The filtered aalg sigals were sampled every 5 secds by aalg-t-digital cverters. By selectig every th pit f a data set, the samplig iterval culd be chaged t 5 secds. Varyig the samplig iterval, i tur, altered the rage f frequecies bserved later i the spectral aalysis. Thus, the chice f samplig was depedet the frequecies t be ivestigated. Whe we were cfidet that a scillati existed with a perid ear 1-2 hurs, a samplig iterval f 30 secds was used; every sixth data pit was used fr aalysis. A ttal f 1024 data pits were aalyzed frm each experimet. Frm the data, w i the frm f a set f discrete pits, each separated by a cstat time iterval, TPR was calculated, pit by pit, frm the MABP ad CO data pits. This prcedure geerated a ew time series, s that i all there were w fur sets f pits, e each fr MABP, CO, TPR, ad HR. Sice the aalg filter culd prevet abasig ly if the samplig iterval was t mre tha 5 secds, a digital lw pass filter was applied t prevet aliasig with the large samplig itervals. A third-rder Butterwrth filter was emplyed fr this purpse (Rader ad Gld, 1967). Liear tred remval, a prcedure that applies a frm f high pass filterig, was ext applied t the data. A liear tred i the data is viewed as a small prti f a cycle whse perid is large relative t the data recrd legth. If t elimiated, such treds distrt the spectral aalysis i the lw frequecy rage. Sice the mea value f a data recrd des t affect the spectral aalysis, the data are cverted t zer mea t save cmputati time durig FFT calculatis. We used a liear leastsquares fit t the data ad the subtracted this fit frm the data t create a data set with zer mea ad zer slpe. A csie taper was applied t the first ad last 10% f the data t alleviate leakage i the spectral aalysis. Durig spectral aalysis, the data are viewed as a ifiitely lg recrd multiplied by a bxcar fucti which has a value f uity durig the time the data recrd exists ad zer at all ther times. Whe the data ad the bxcar fucti are subject t Furier trasfrmati, the sharp disctiuities at the eds f the bxcar cause leakage; pwer that shuld be attributed t e frequecy becmes spread ut t adjiig frequecies. Thus, if the disctiuities were t smthed by taperig, the resultat pwer spectrum might lead t a spurius result. Althugh leakage cat be

8 BLOOD PRSSUR OSCILLATIONS/S/iimada ad Marsh 699 ttally elimiated, because the data recrd has fiite legth, taperig reduces this leakage csiderably. The data were subject t Furier trasfrmati with a FFT algrithm. The Furier cmpets, X k, are defied as: X k = 2 x(i)exp -j 1-1 _ ii j where x(i) = ith data pit, j = V 1, ad = 1024 data pits. These cmpets are defied at the frequecies: where h = samplig iterval. The particular FFT rutie used cmputed Xk frm the data pits, x(i), by carryig ut the fllwig cmputatis: S(D = i xw, s(k) = V x(i) cs.-i [ h k = 2, 3,, k - -, s(k) x = v x(i) /-v sm f2wi(k-/2 + l)] desity is calculated betwee tw variables, x(i) ad y(i). Bth sets f variables are subject t Furier trasfrmati t create X k ad Y k. Frm these tw, the crss-spectral desity estimates are calculated: G, y (f k ) = [XfYk], where Xjf = cmplex cjugate f Xk. G xy (fk) are cmplex umbers f the frm: G iy (fk) =- C iy (f k ) - jq iy (f k ). The crss-spectral desity has a magitude ad a phase agle determied by: Magitude - G xy (f k ) = VC^y(f k ) + Oj y (fk), 360 rq* Phase agle = <f>(fk) = -pr arc ta 1 was als multiplied by the factr, 0.875' t crrect fr csie taperig. semble ad frequecy averagig were used t characterize the ppulati t imprve the spectral estimates. semble averagig csists f cmbiig spectral estimates cmputed frm differet time segmets. I ur studies, data recrded frm differet experimets were averaged tgether. If Gk,, are the spectral estimates frm i differet experimets, the the averaged estimate, Gk, is: X k are the cmputed frm s(k): X k = s(k) + js(k + 2 k = 2, 3, -..,-. G k = [Gk,i + Gk,2 + + Gkji]. where = umber f time segmets averaged. Frequecy averagig is averagig ver adjacet frequecy bads i the pwer spectrum. The resultig averaged spectral estimate is w the value fr a ew frequecy bad which cvers all the frequecy bads averaged. If m differet frequecy bads are averaged, the ew estimate becmes: Frm these valus f Xk, the pwer spectral estimates, Gk, were frmed: r _ 2h i Y 12 <Jk = Xk. Gk is the average pwer ver the frequecy bad,, cetered at a frequecy fk. These values were h multiplied by the factr 0.875, t cmpesate fr the lss f variace due t the csie taperig applied earlier. The pwer spectral desity plt, r peridgram, is a graph f Gk pltted as a fucti f frequecy, fk. Crss-spectral desities were als cmputed frm the utput f the FFT rutie. A crss-spectral Gk = [Gk + Gk+i + + Gk+m-i], m where m = umber f frequecy bads averaged. The ew frequecy bad which results frm fre-. m quecy averagig is. h A cherece fucti, yj y (fk), was calculated betwee a iput, x(t), ad a utput, y(t), f a system. I these studies, the utput was csidered t be MABP scillatis ad the pssible iputs t the system, CO ad TPR scillatis. I additi, HR scillatis were viewed as a pssible iput t CO variatis. The cherece fucti represeted the fracti f the variace i the utput that was due t variace i the iput. If the cherece fucti was zer, e f the utput variace was due t the assumed iput, ad thus this iput was i

9 700 CIRCULATION RSARCH VOL. 44, N. 5, MAY 1979 fact t a iput t the system. Cversely, a cherece fucti with a value f 1.0 meat that all f the utput variace was accuted fr by the iput variace. The cherece fucti was calculated frm the crss-spectrum betwee the iput ad utput ad the pwer spectra f the idividual iput ad utput: &&) = «I ic \ I 2 where G iy (fk) = crss spectrum betwee x ad y, G IX (fk) = pwer spectrum f x, ad G yy (fk) = pwer spectrum f y. The statistical testig i this study ivlved the cmputati f cfidece itervals. A primary ccer was whether the cherece fucti betwee CO ad MABP r TPR ad MABP equaled zer. If either was zer, CO r TPR culd be excluded as beig a ctributig factr tward the scillatis i MABP. Thus 95% cfidece itervals were estimated. If zer was excluded frm this iterval, the cherece fucti was accepted as beig sigificatly differet frm zer, ad vice versa. A trasfrmati was used t facilitate a cfidece iterval calculati: w(f) = Yx y (f) where y xy (f) = Jyl y (f) The variable w(f) has a apprximately rmal distributi. Thus, a 100 (1 a)% cfidece iterval fr the cherece fucti is: tah{w(f) - ( - 2)" 1 - a w z<, /2 } < Y*y(f) < tah{w(f) - ( - 2)~' + a w z,, /2 }, where = degrees f freedm, a 2 w = ( 2)~' = variace f w(f), z,, = 100a percetage pit f the stadard rmal distributi. A cfidece iterval fr the crss-spectrum phase agle was als calculated. Fr a 100 (1 a)% cfidece iterval, the quatity f(f) was first determied (Bedat ad Piersl, 1971): Gyy(f) l- 2w [ where = degrees f freedm, ad F 2jl - 2j, = 100a percetage pit f F distributi with i = 2 ad 2 = 2 degrees f freedm. The quatity, A^>(f), is the fud: =sm - where f(f), ad H(f) ~ -. The cfi- ( dece iterval fr the real phase agle, <j>(f), was derived frm the estimated crss-spectrum, phase agle, </>(f), ad A^> (V- Refereces Bedat JS, Piersl AG: Radm Data: Aalysis ad Measuremet Prcedures. New Yrk, Wiley, 1971 Clema TG, Maig RD, Nrma RA, Guyt AC: Ctrl f cardiac utput by regial bld flw distributi. A Bimed g 2: , 1974 Cwley AW Jr, Ms, Guyt AC: Iteracti f vaspressi ad the barreceptr reflex system i the regulati f arterial bld pressure i the dg. Circ Res 34: , 1974 Davis JO, Freema RH: Mechaisms regulatig rei release. Physil Rev 56: 1-56, 1976 Kleitma N: Sleep ad Wakefuless. Chicag, Uiversity f Chicag Press, 1963 Kreiger DT, Alle W, Rizz F, Krieger HP: Characterizati f the rmal tempral patter f plasma crticsterid levels. J Cli dcril Metab 32: , 1971 Lamberti J, Urquhart J, Siewers RD: Observatis the regulati f arterial bld pressure i uaesthetized dgs. Circ Res 23: , 1968 Lefat C: Time depedet variatis f pulmary gas exchage i rmal ma at rest. J Appl Physil 22: , 1967 Marsh DJ: Tempral hierarchies i the regulati f mammalia fluid ad electrlyte balace. Tras ASM J Dy Sys Meas Ctrl 95: , 1973 Okhtes M, Marsh DJ, Smith SW, Bergma RN, Yates F: Fluctuatis f plasma glucse ad isuli i cscius dgs receivig glucse ifusis. Am J Physil 226: 9919, 1974 Orr WC, Hffma HJ: A 90 miute cardiac birhythm: Methdlgy ad data aalysis usig mdified peridgrams ad cmplex demdulati. I Tras Bimed g 21: , 1974 Otes RK, chs L: Digital Time Series Aalysis. New Yrk, Wiley, 1972 Rader CM, Gld B: Digital filter desig techiques i the frequecy dmai. I Prc 55: , 1967 Yamaji T, Dierschke DJ, Bhattacharya AN, Kbil : The egative feedback ctrl by estradil ad prgestere f LH secreti i the variectmized rhesus mkey. dcrilgy 90: , 1972