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578 References

1 Bonow RO,BacharachSL, GreenMV, et al. Impaired leftventricular diastolicfillinginpatients with coronary artery disease: assessment with radionuclide angiogra- phy.Circulation 1981; 64:315-23.

2 RedutoLA,WickemeyerWJ,Young JB, et al. Left ven- triculardiastolic performance at rest and during exercise in patients with coronary artery disease. Assessment with first-pass radionuclide angiography.Circulation 1981;63:

1228-37.

Correspondence 3 Mancini GBJ, Slutsky RA,Norris SL,BhargavaV, Ash- burn WL, Higgins CB. Radionuclideanalysis of peak fillingrate,fillingfraction and time topeakfillingrate.

Response to supine bicycle exercise in normal subjects andpatientswithcoronary disease. AmJ Cardiol 1981;

51: 43-51.

4 Nichols AB, Strauss HW, Moore RH, et al. Acute changes in cardiopulmonary blood volume during uprightexercise stress testing in patients with coronary heart disease.Circulation 1979; 60: 520-30.

Analysis of circadian blood pressure rhythms

Sir,

We read with interest the observation by Davies et al (1984; 52: 93-8) on the circadian rhythm of blood pressure. The authors state that Millar-Craig et al reported a second peak of blood pressure in the early evening.' Weconsider that this is not a correct cita- tion, as Millar-Craiget al reported that ". . . blood pressurefellprogressively during the day and rose in theearly hours of the morning."

Davies et al mention the difficulties in quantifying variations in the blood pressure. Some of the basic work onrhythmic blood pressure changes (summar- isedin2) dealswith theproblemsof recording,repro- ducibility, and analysis of blood pressure patterns.

Usingcosinoranalysis, first introduced by Halberget al3 might improve the accuracy of analysis. It pro- vides an exact calculationof rhythm variables such as mesor, amplitude, and acrophase of circadian rhythmic changes.4-6 It would be interesting to evaluatethecarefullydocumented data ofDaviesetal bycosinoranalysis.We wonderwhether this method ofanalysis would confirm thereportedtwohourdif- ference between the nadir of thepacedgroupand the control group.

Theauthorsalsopointoutthat theamplitudeof the cirdacian patternwaslower in thepacedthan in the hypertensivegroup. Judgingfrom thedata inFig. 1 of their article this seems notunlikely. Quantitative evaluationoftheamplitudes, however,isnotreported butmightbe donebycosinoranalysis. Furthermore, cosinor analysis might allow abetter comparisonof circadianheartrateand bloodpressurevarations.

Alexander L Gerbes,*

Ekkehard

Haen,t

Bernhard

Arbogast.4

*Medizinische Klinik II,

KlinikumGrosshadern derUniversitatMunchen.

tlnstitute

of

Pharmacology,

Universitat Munchen.

*Bavarian

Reinsurance

Company,

D-8000Munich 22,

FederalRepublicofGermany.

References

1 Millar-Craig MW, Bishop CN, Raftery EB. Circadian variationof blood-pressure. Lancet 1978; i: 795-7.

2 Halberg F. Quo vadis basic and clinical chronobiology:

promiseforhealthmaintenance.AmJ Anat1983; 168:

543-94.

3 Halberg F, Tong YL, Johnson EA. Circadian system phase-an aspect of temporal morphology; procedures andillustrativeexamples. In: Von Mayersbach H, ed.

Thecellularaspectofbiorhythms. Berlin:Springer, 1967:

20-48.

4 Bingham C,ArbopstB, GuillaumeGC, LeeJK,Hal- bergF.Inferential statisticalmethodsforestimatingand comparing cosinorparameters.Chronobiologia 1982;11:

397-439.

5 GerbesAL, Arbogast B, Schick P, Messerschmidt0.

Acuteradiationinjuryofmice and the influenceofsud- den timeshift. RadiatRes 1984;99: 285-93.

6 Haen E, Halberg F, Cornelissen G. Cortisol marker rhyimometryinpediatrics andclinicalpharmacology.

Annual ReviewofChronopharmacology 1984,in press.

This letter was shown to theauthors, whoreply as follows:

Sir,

We thank Drs Gerbes etal for their interest in our paper on circadianrhythmsof blood pressure in paced patients. Theycorrectly cite ouroriginal description ofthe broad 24 hourpattern of blood pressure'; how- ever,mostofourdata on closerinspectionshoweda subsidiarylateafternoon rise ofloweramplitudethan thatseenafterwaking.This isvisible inFigs. 1and 3 oftheoriginal publication.'

The problems inherent in describing ambulatory intra-arterial bloodpressure patternshave been rec- ognised by several groups of workers. We find it difficult to accept that Halberg's cosinor analysis would be able to providesufficient accuracy in this case. As weunderstandit, thetechniqueconsists of fittingasingle24 hourcosinecurvetothe datausing the method of least squares. Variables such as the amplitude,mesor(averagevalue),andacrophase (tim-

(2)

Correspondence

ingof the peak relative to an arbitrary time origin) are then measured from the fitted curve. The pattern of blood pressure is not symmetrical within a 24 hour cycle;for example, a single cosine function would be a very poor fitto the systolic data in Fig. 1 of our paper.

Thisobservation appears to be confirmed by the work ofMurnaghauret al in their study of blood pressure in pregnancy.2 The single cosinor technique failed to givesufficient resolution to describe other than gross features of the blood pressure patterns. Walsh and

Goldberg

also found thatsignificantcomponents were present at higher frequencies.3 Detailed studies by Sayers4 indicate the presence of several concurrent patterns, posing severe problems in any detailed statistical analysis 'acrosspatients. More recently, the same grouphas suggested a setof procedures for pat- ternanalysis ofthese records, relying more on meas- urementsfromeach record than on a priorimodels.5 These procedures are at present being applied to bloodpressure datafromavariety ofsources.

In active untreated subjects the timing of the acrophase must beheavily dependent on the time of waking sincethis is the event which hasthegreatest effectonbloodpressure.This would tend toplace the acrophase at approximately 14 hours before waking-that is,at 1800 orso, and this hasbeen the finding of several workers.36 It is hard to see how this wouldprovideanyillumination ofourobserved shifts in the nadir ofblood pressure at around 0100-0300.

Forcritical studies we now compile our data relative towakingtimeaswellastoabsolute clock time.

Weare thereforeunconvinced thatcosinoranalysis would clarify our observations ofambulatory intra-

579 arterial blood pressure unless applied in a complex formtaking account of many pattern features andfre- quencies, in which case conventional Fourier analysis seems tooffermorepossibilities.

E BRaftery, P MMCashman,

Departmentsof Cardiology and Bioengineering, Northwick ParkHospital,

Harrow,

Middlesex HAI

3UJ.

References

1 Millar Craig MW,Bishop CN, Raftery EB. Circadian variation of bloodpressure.Lancet 1978; i:795-7.

2 MumaghanGA,MitchellRH, Ruff SC.Bloodpressure rhythms innormotensiveandpre-eclampticpregnancy.

In:StottFD,RafteryEB, Goulding L, eds.Proceedings ofISAM1979.London:Academic Press, 1980: 157-66.

3 Walsh JT, Goldberg AD. The analysis of prolonged records of continuous intra-arterial blood pressure-a softwareapproach.In:Stott FD, Raftery EB, Goulding L, eds. Proceedin of ISAM 1979. London:Academic Press,1980: 451-5.

4 SayersBMcA. Analysis ofintra-arterial blood pressure records. In: Stott FD, Raftery EB, Goulding L, eds.

Proceedins of ISAM 1979. London: Academic Press, 1980: 513-35.

5 Sayers BMcA, Cicchiello LR, Raftery EB, Mann S, Green HL. Theassessment ofcontinuous ambulatory bloodpressurerecords.MedInf(Lond) 1982; 7:93-108.

6 Halberg F. Quo vadis basic and clinicalchronobiology:

promisefor health maintenance.AmJAnat 1983; 168:

543-94.

Delayed recovery of left ventricular function after anti- thyroid treatment

Sir, been treated for their

thyrotoxicosis. Nevertheless,

as

Forfaretal(1984;52:215-22)suggest that inhyper- shown inthe Table

below, using

datatakenfrom their thyroidism left ventricular function is reversibly ownpaperit may becalculatedthatisometric exercise depressed. Theit conclusions are based on actually caused

directionally opposite changes

in haemodynamic measurements performed on 15

peripheral

vascular resistance

during

the thyrotoxic hyperthyroid subjects before and during isometric and

euthyroid

states.

Peripheral

vascular resistance is

exercise,

andthosemeasurements wererepeatedafter amajor determinant of theimpedanceofferedtothe the subjects had been rendered euthyroid. The outflow of blood from the left ventricle. In thestudy authorsstressthat

hyperthyroidism

involves

changes

of Forfar etal the

thyrotoxic heart,

faced with an intrinsic not only tothe heart itself but alsoto the increased

peripheral

resistance

during

isometricexer-

peripheral circulation. They assume,

however,

that

cise,

did not function as well as it did at rest. In the

performance

ofastandardisedisometric exercise contrast, the

euthyroid

heart experienced a large taskproducedthesamechangesin the

peripheral

cir- reduction in calculated

peripheral

vascular resistance culation in both

hyperthyroid

and

euthyroid

states

durig

isometric exercise and showednodeterioration and,

therefore,

that exercise caused thesame

changes&

inlfundtkn.

in cardiac loading beforeand after the subjects

had&-

--Thuy would appear that

peripheral

resistance is

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