Abstract
The left ventricle (l.v.) is represented as a shell of muscle whose performance is characterised in terms of the chamber pressure and stress/strain in the ventricular wall; the effective elastic modulus of the l.v. relates these peerformance variables, and hence represents the transfer function of the left ventricular physiological system. A method is presented for indirectly determining the effective modulusE for the left ventricle. The method employs a thick-walled mathematical model of the l.v. having a homogeneous isotropic medium. Instantaneous values ofE are determined for subjects with heart diseases of varied etiologies, in order to assess the responses of the l.v. to chronic overloads of pressure and volume. Resulting values forE are used diagnostically to characterise the physiological state of the l.v. Normal values ofE, at systole, indicate that the strength of contraction exercised by the l.v. is normal, and hence is an indication of the l.v. having adjusted to the heart disease.
Sommaire
Le ventricule gauche (VG) est représenté par une enveloppe musculaire dont la performance est caractérisée par la pression de la chambre et la contrainte et la déformation sur la paroi ventriculaire; le module d'élasticité ventriculaire effectif du VG décrit la relation entre ces variables de la performance et représente donc la fonction du transfer du système physiologique du ventricule gauche. On présente une méthode de détermination indirecte du module effectifE du ventricule gauche. La méthode fait usage d'un modèle mathématique à paroi épaisse du VG et ayant un milieu isotropique homogène. On détermine des valeurs instantanées deE pour des sujets atteints de maladies cardiaques à étiologies variables, de façon à évaluer la réponse du VG aux surcharges chroniques de pression et de volume. Les valeurs résultantes deE sont utilisées diagnostiquement pour caractériser l'état physiologique du VG. Des valeurs normales de,E à la systole indiquent que la force de la contraction exercée par le VG est normale et qu'il s'est donc ajusté à la maladie cardiaque.
Zusammenfassung
Das linke Ventrikel (LV) wird als Muskelschale dargestellt, dessen Leistung durch Kammerdruck und Beanspruchung der Ventrikulärwand beschrieben wird. Das effektive elastische Modul des LV bringt diese Leistungsvariablen aufeindander in Bezug und stellt daher die Ubertragungsfunktion des linken physiologischen Ventrikelsystems dar. Es wird ein Verfahren zur indirekten Bestimmung des effektiven Moduls (E) für das linke Ventrikel dargestellt. Das Verfahren verwendet das starkwandige mathematische Modell eines LV mit einem homogenen isotropen Medium. Sofortige E-Werte werden für Fälle mit Herzkrankheiten verschiedener Ursachen betimmt, um die Reaktion des LV auf chronische Überbelastung durch Druck und Volumen zu beaurteilen. Die sich für E ergebenden Werte werden diagnostisch dazu verwendent, den physiologischen Zustand des LV zu bestimmen. Normale Werte für E bei Systole bedeuten, daß die vom LV ausgeführte Kontraktion normal stark ist, was bedeutet, daß sich das LV auf die Herzkrankheit eingestellt hat.
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Abbreviations
- L.V.:
-
left ventricle
- L, W, H :
-
maximum length, calculated width and measured wall thickness of the left ventricular chamber—data quantities
- P :
-
pressure in the cavity of the left ventricle
- d 1 :
-
W/2, for the analytic model
- d 2 :
-
(W/2)+H, for the analytic model
- t :
-
time during a cardiac cycle
- (x, y, z):
-
Cartesian co-ordinates
- (r, y, w):
-
cylindrical co-ordinate system withy as the axis of rotation
- \(\bar x,\bar r,\bar y\) :
-
x/a, r/a, y/a
- a :
-
half the length along which point dilatations are distributed
- R :
-
ratio of\(\bar y\) to\(\bar r\) intercept of a stress trajectory
- (\(\bar r_1 ,\bar y_1 \)) and (\(\bar r_2 ,\bar y_2 \)):
-
intercepts of the stress trajectories of the inner and outer surfaces of the geometrically similar model with the\(\bar r\) and\(\bar y\) axes
- R1,R2:
-
\(\left( {\bar y_1 /\bar r_1 } \right),\left( {\bar y_2 /\bar r_2 } \right)\), shape parameters of the model
- σ1,ε1:
-
stress and strain for line dilatation
- σ2,ε2:
-
stress and strain for a uniform hydrostatic stress system
- B :
-
strength or intensity factor for a uniform hydrostatic stress system (= magnitude of the uniform hydrostatic stress)
- C :
-
strength or intensity factor for a line dilatation system
- E :
-
instantaneous effective modulus of the left ventricle
- v :
-
Poisson's ratio
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Ghista, D.N., Vayo, W.H. & Sandler, H. Elastic modulus of the human intact left ventricle—determination and physiological interpretation. Med. & biol. Engng. 13, 151–161 (1975). https://doi.org/10.1007/BF02477722
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DOI: https://doi.org/10.1007/BF02477722