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Left ventricular volume and cardiac output of the canine heart

Application of a mathematical two compartment model and a new dye dilution technique

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Abstract

This paper describes a mathematical model of some of the circulatory properties of the heart, and it is demonstrated how information about the volume of the ventricle can be retrieved from dye dilution curves using the value of the volume flow rate, the time for maximum dye concentration to appear at the sampling site, and the mean transit time of the dye.

A nomograph has been developed in order to eliminate the need for mathematical calculations. The validity of the model described is assessed in seven dog experiments by comparing results obtained using the dye dilution technique with results from cineangiocardiographic films taken almost simultaneously of dispersed radiographic contrast fluid. The flow measurements have been checked using a new method employing a suspension of radio-opaque particles.

Sommaire

On présente un modèle mathématique de certaines caractéristiques circulatoires du coeur et l'on décrit une méthode pour estimer le volume ventriculaire en partant de courbes de dilution du colorant et en utilisant la valeur du volume de flot, le temps demandé pour que la concentration maximum puisse apparaître au point d'échantillage, et le temps moyen de transit du colorant.

Un nomographe a été étudié qui peut servir à éliminer le calcul mathématique. La validité de notre modèle est estimée par sept experiénces avec des chiens; les résultats de la méthode de dilution du colorant sont comparés aux resultats obtenus avec des films ciné-angiocardiographiques du liquide radiographique de contraste dispersé, pris à peu près simultanément. Les mesures de la circulation ont été verifiées par une méthode nouvelle se basant sur la suspension de particules radio-opaques.

Zusammenfassung

Dieser Artikel beschreibt ein mathematisches Modell einiger kreislaufbestimmender Eigenschaften des Herzens. Es wird dargetan, wie Informationen über das Volumen der Herzkammer mit Hilfe von Farbstoffverdünnungskurven erhalten werden, wobei der Wert der volumetrischen Abflußgeschwindigkeit, die zum Erscheinen der maximalen Farbstoffkonzentration an der Prüfstelle erforderliche Zeit und die durchschnittliche Laufzeit des Farbstoffs wesentliche Anhaltspunkte sind.

Um mathematische Berechnungen zu erübrigen, wurde ein Nomogramm ausgearbeitet. Die Gültigkeit des beschriebenen Modells wird anhand von sieben Hundeexperimenten geprüft, indem die mit der Farbverdünnungsmethode erhaltenen Resultate mit Resultaten verglichen werden, die mit praktisch gleichzeitig durchgeführter angiokardiografischer Filmaufnahmen einer radiografischen Kontrastdispersion erhalten wurden. Die Strömungsmessungen wurden mit Hilfe einer neuen Methode geprüft, bei der eine für Röntgenstrahlen undurchlässige Teilchensuspension Verwendung findet.

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Abbreviations

V 1 :

volume of the first compartment of the model

V 2 :

volume of the second compartment of the model

V d :

volume causing transport delay of indicator

EDV u :

end-diastolic volume determined by means of radiographic contrast medium

F :

volume flow rate

K 1 :

defined asF/V 1

K 2 :

defined asF/V 2

F D :

volume flow rate determined by means of dye dilution method

F P :

volume flow rate determined by means of radiopaque particles

F U :

volume flow rate determined by means of radiographic contrast medium

S D :

stroke volume determined by means of dye dilution method

S P :

stroke volume determined by means of radiopaque particles

S U :

stroke volume determined by means of radiographic contrast medium

m :

amount of indicator (subscripts 1 and 2 denoting first and second compartment of the model respectively)

m o :

initial amount of indicator

c :

concentration of indicator (subscripts 1 and 2 denoting first and second compartment of the model respectively)

c s :

concentration of sample used for determination of step response

t :

variable time

t M :

time for maximum concentration to occur

t a :

appearance time of indicator

t c :

transport delay in sampling catheter

t d :

transport delay related toV d

t e :

time interval between two successiveR-waves

τ:

time constant

σ:

mean transit time

d j :

diameter of thejth slice of ventricular volume

h :

height of thejth slice of ventricular volume

n :

number of slices

s :

Laplace operator

M :

Laplace transform ofm

f D :

pulse rate during dye dilution procedure

f P :

pulse rate during the use of radiopaque particles

f U :

pulse rate during the use of radiographic contrast material

L 1 :

entrance of the first compartment

L 2 :

site of sampling

L 3 :

site of injection

G :

transfer function

G t :

transfer function of inverting amplifier

G n :

transfer function of noninverting amplifier

R :

resistance of an electrical network

C :

capacitance

r :

coefficient of correlation

s y·x :

standard error of estimate

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Authors and Affiliations

  1. Technical Department of Department of Cardiology, Gentofte Hospital, Copenhagen, Denmark

    Anders Jarløv

  2. Department of Radiology, Gentofte Hospital, Copenhagen, Denmark

    Thorkild Mygind & Erling Dyrskjøt Christiansen

Authors
  1. Anders Jarløv
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  2. Thorkild Mygind
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  3. Erling Dyrskjøt Christiansen
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Advanced Fellow in Academic Radiology of the James Picker Foundation.

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Jarløv, A., Mygind, T. & Christiansen, E.D. Left ventricular volume and cardiac output of the canine heart. Med. & biol. Engng. 8, 221–239 (1970). https://doi.org/10.1007/BF02477240

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