Subendocardial vascular distortion at small ventricular volumes

JOURK.4L

OF SURGICAL

RESEARCH

17, 114-124 (1974)

Subendocardial at Small

JOE KAZI

R.

UTLEY,

Vascular Ventricular

M.D.,

MOBIN-UDDIN,

AND

and

MICHALSKY, R.

BRYANT,

M.D.

xl-23 - xr13 Xl"13

DC r1 = 2

DC rz = T + Tt then Figure 2 shows V,,/V, plotted as a function of T,/D, by this equation. In portions of the ventricular wall which behave as a sphere, as V, decreases concentric portions the V,, behaves somewhat like concentric laminae (Fig. 3). With this assumption one can determine the changes in thickness of laminae and area at the in-

MODEL

Ta3lr

114 Press, Inc. form reserved.

B.

V, -= VU

From the Division of Cardio-Thoracic Surgery University of Kentucky Medical Center Lexington, Kentucky 40506. This work was supported by the General Research Support Grant No. RR0 5374-11, National Institute of Health Grant No. HL15738-01, Kentucky Heart Grant No. 203-65-7H850-T3829, and the Tobacco and Health Research Institute Grant No. 124-05-83230-24060. Submitted for publication September 9, 1973.

@ 1974 by Academic of reproduction in any

LESTER

Table 1 shows the terms used in this model. For a spherical ventricle (Fig. 1) :

As ventricular volume diminishes during systole the thickness of the ventricular wall increases. Because of spherical ventricle is easiest to model, we used the following equations to determine which portion of the left ventricle behaves most like a sphere.

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Volumes

GWENDOLYN

M.D.,

THE SUBENDOCARDIUM OF THE LEFT VENTRICLE is vulnerable to ischemia and interstitial hemorrhage in a number of pathologic states [l-16]. The presence of subendocardial hemorrhages in many conditions associated with small ventricular volumes suggests that distortion of subendocardial vessels, particularly veins, might cause the hemorrhagic ischemic lesions. A simple mathematical relationship predicts distortion of subendocardial vessels at small ventricular volumes. Observations of coronary vessel geometry at different ventricular volumes confirms the prediction. Histologic study of experimental subendocardial hemorrhagic necrosis shows definite evidence of venous obstruction. MATHEMATICAL

Distortion

1.

Ventricular myocardial volume. Ventricular cavity volume. Diameter of ventricular cavity. Thickness of ventricular wall. Radius of ventricular wall. Radius of ventricular ca.vity plus ventricular wall thickness. 4/3?r. 4*. Thickness of concentric laminae from endocardium to epicardium. Area at interface of concentric laminae from endocardium to epicardium.

UTLEY

ET

AL. : SUBENDOCARDIAL

Fig. i. Drawing showing model of spherical ventricle and the relations of wall thickness to caTi@ diameter. 7, is radius of ventricular cavity; r2 is radius of ventricular cavity + wall thickness; T, is ventricular wall cavity diamctcr.

THICKNESS

thicknrss;

-VOLUME IN

LEFT

and L>, is vent riwl:u

VASCULAR

DISTORTION

Pig. 3. Illustration shows geometry of concmtric laminae of equal mass in the ventricular wall. T is thickness of laminae and A is area at the interface between laminae. The thickness of inner lnminae is greater than that of outer and the area at the interface of inner laminae is much lrss than ouier.

RELATIONSHIPS VENTRICLE

If one assumes T’,,, to be composed of 10 concentric laminae of equal volume (mass) then the thickness of each laminae from endocardium CT,) to epicardium (T,,,) will Iw :

647

4oL

Pig.

2. Computer plot, showing the relationship of to V,/V,. As ventricular cavity volume diminishes, the rulxtionshil~ of n-all thicknrw to rarity diameter increasrs greatly.

Tt/D,

&face of concentric laminae as T’, decreases. Ventricular mall thickness (Tt I can be determined from T’,?, and T’, according to the following formula: Tt =

at the interface hetn’ecn The arca lxminae from cndocardium (A,) to epicnrdium (A,,,) can also be calculated:

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2

As= Y

A,0 =

RESEARCH,

3 v, + o.9vm 2 (Y ) X

The ratio of thickness of laminae to square root of area between laminae (T/VIA) is an index of regional myocardial distortion in two dimensions. This relationship (T/dx) as a function of V,/V, is shown in Fig. 4. A scale drawing of the dimensional changes of regional myocardial geometry as

DISTORTION

VS VENTRICULAR

VOLUME

zoo ,60 I60

Fig. 4. T/r/?? is an index of the two-dimensional distortion as ventricular volume changes. The com.-putcr plot shows the relation of Z’/ I/A in the inner laminae (upper line) and the outer laminae (lower line) as ventricular volume diminishes. Distortion is greater in the inner layers of the ventricular wall.

Fig. 5. Illustration shows the change in the geometry of the inner and outer laminae as ventricular volume diminishes.

a function of ventricular volume based on this mathematical model is shown in Fig. 5. This model predicts greater distortion of the subendocardium than subepicardium as ventricular volume changes. ANATOMIC

STUDIES

The relation of wall thickness to cavity diameter at different V,,,,/V, ratios was studied to determine which portion of the left ventricle behaves most like the wall of a sphere. Four dog hearts were fixed in formalin at different vent,ricular volumes. The variations in ventricular volume were produced by distending the heart at different pressures after occluding pulmonary veins, aorta, and pulmonary artery. After the right ventricular wall was removed V, and V, were determined for each heart. V, included left ventricle and septum. Four equidistant sections were made perpendicular to the long axis of the left ventricle from base (level 1) to apex (level 4). Five determinations of wall thickness and cavity diameter were made at each level in the four hearts. Figure 6 shows the ratio of wall thickness to cavity diameter (at the four levels) compared to the ratio of wall volume to cavity volume in the four hearts.

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ET

AL.:

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THICKNESS-VOLUME IN LEFT

VASCULAR

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RELATIONSHIPS VENTRICLE

Fig. 6. Ratio of wall thickness to cavity diameter (T!/D,) as a function of ventricular volume (V,/V,) at four levels in four hearts fixed at different ventricular volumes. Level 1, 2, 3, and 4 are perpendicular to the axis of the left ventricular cavit and equidistant between base and apex. Level 1 is nearest the base, and Level 4 is nearest the apex of the heart. The solid line represents the theoretical line derived from the mathematical model. This relationship shows that level 1 behaves like the theoretical line and therefore the wall of the left, ventricle behaves as the contracting wall of a sphere near the base of the heart.

Level one agrees best with the mathematical model. Thus the base of the left ventricle appears to behave as a contracting sphere with changes in ventricular volume. The variations from the spherical model in the apex of the vcntriclc appeared to be due to greater buckling of the endocardium. The regional geometry of coronary vessels was then studied a~ a function of ventricular volume. Dog 1 \vas sacrificed by injecting 5 g of calcium chloride intravenously. The heart was removed and the coronary arteries injected with a fine dyed suspension of barium sulfate.” The heart was then fixed in 10% formalin. Dog 2 was sacrificed by injecting five g of potassium chloride intravenously. The coronary arteries were similarly injected with barium suspension. The pulmonary veins were ligated and the great vessels clamped. The left ventricle was distended with 80 cm of water pressure via a catheter * Chromopaque, Hers, England.

Damaney

and Co. Ltd,

Ware-

in the left atrium and fixed in 107; formalin. The hearts were then sectioned perpendicular t#o the long axis of the left ventricle one fifth the distance from the base to apex. The hearts were frozen and 100 Frn sections made with a Sartorium Werke sliding microtome. Sections were examined and photographed with a Wild Heerbrug dissecting microscope. Figures 7 and 8 shows the geometry of the ventricular wall of the two hearts. V,/V, was 59 cc/4 cc for Dog 1 and 110 cc/51 cc for Dog 2. Figures 9 and 10 shows photomicrographs of the subendocardial and subepicardial vessles of two hearts. The subepicardial and subendocardial vessels of the distended ventricle (Dog 2) are relatively straight and parallel to the ventricular surface. The subepicardial vessels of dog 1 are similarly parallel and not distorted. The subendocardial vessels of the small ventricle (Dog 1) are distorted, not parallel and without consistent relationshp to the ventricular surface

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Fig. 7. Cross section of the c~ontr:xct,c~d lcft yc-n1ric.k :tftclr injection of ihr co~onnry nrtflries drmonsiratw thcl thick n-all and ~m:dl w\-ity of this Ircart. Src.liol:s of entio~:rrdium and epicardium of t.llis heart we shoxn in Fig. 9.

HISTOLOGIC

STUDIES

A loo-kg calf ins plarcd on complete iopulmonary bypass and the left atrii urn was opened and vented and the ventricl e was fibrillated. One gram of calcium was given every hour during 4 hr of bypass. The heart became very hard, small and cont,racted after the calcium infusions. The hear % was removed after four hours of bypass; and sectioned transverscIy near the base: (Fig. 11 J. Subendocardial hemorrhagic necr *osis was present throughout the left Cal-d

ventricle. Xicroscopic sections of the subel)icnrdinl muscle showed no abnormality (Fig. 12). Sections of the subendocardial muscle showed venous distention and interstitial hemorrhage (Fig. 13). This picture is most consistent with venous obstruction due to vascular distort’ion in the sma11, cont’ractcd ventricle.

Greater distortion of subcndocardial vessels at small ventricular volumes may exI’lnin the hemorrhagic am1 isrhemic lesions

UTLEY

ET

AL. : SUBENDOCARDKAL

VASCULAR

DISTORTION

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7ig. 8. Cross section of the ventricle fixed at a large wntricular \rolumc after injection If coronary arteries. Sections of endocardium and ep&rdium of this heart are &own in Zig. 10.

obser *ved in many conditions associated with small ventricular volumes. The resistanct : to blood flow through distorted blood vesse ,ls is increased and is related to the loss of kLinetic energy with flow directional chani ges and increased vessel wall friction.

The thin walled veins would under :go greatest distortion. The presence of subt ?ndocardial hemorrhagic necrosis in ma ,ny conditions of small ventricular volume is explained on the basis of venous obstructil The conditions associated with subenc;:-

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Fig. 9. Anatomy of the coronary vessels in the subepicardial and subendocardial regions of the contracted left ventricle is shown. The sub-epicardial I-essels shows a configuration which is parallel to the epicardial surface of the ventricle and no significant distortion of the vessels. In the subendocardial area however, there is great distortion of vessels, and vessels are running in many directions, both perpendicular and parallel to the cndocardial surface. This great distortion of vasculature was only in the subendocardium of the small ventricle.

cardial hemorrhages and necrosis include cardiopulmonary bypass [ 1, 21 isoprotereno1 infusion [3, 41 cervical sympathetic ganglion stimulation [5], trauma [6], hemorrhagic shock [ 7-131, and pericardial tamponade [14]. The only factor common to all those conditions may be small ventricular volume. The prevention of subendocardial hemorrhage and necrosis by increasing ventricular volume has been demonstrated by Martin et al. in dogs during hemorrhagic shock [ 71 Subendocardial hemorrhages and zonal lesions consistently occurred following hemorrhagic shock.

They were prevented by producing complete heart block or by Beta- sympathetic blockade with Pronethalol. Biplane cineangiocardiography showed that both interventions produced increases in ventricular volume in hemorrhagic shock. Martin showed by separation of the cardiac circulation from the systemic circulation with cardiopulmonary bypass that the subendocardial lesions occurred only when the heart was in “shock” and were not caused by changes in the systemic circulation [ 71. Sugisita et al. have shown that isoproterenal produces diminished flow to the sub-

UTLET

ET

BL.:

YUBENDOCARDIAL

VASCULAR

DISTORTION

121

Fig. 10. Swtions of subepicardium and subendocnrdium of dilntcd wntriclc show nondistorted parallel vessels in both subcndocardium and eubcpicardium. So distoltion of the vessels occurred dcspitc distention of the ventricle.

endocardium compared to the subepicardium [15]. Greater distortion of subendocardial vessels at small ventricular volumes induced by isoproterenol might explain these observations. The prevention of isoprotereno1 induced subendocardial lesions by Beta blockade, pot’assium, and antithyroid drugs may be due to effects of ventricular volume

[161The greater distortion of subendocardial muscle at low ventricular volumes may affect intramyocardial pressure at low ventricular volumes. Many observers have found a gradient of intramyocardial pressure from epicardium to endocardium in the beating working heart and in the empty heart [ 17, 181. Salisbury found intramyo-

cardial pressure to be a complex function of contractile force, left ventricular pressure and volume 1191. Baird and Salisbury used similar methods to measure intramyocardial pressure. They measured the pressure necessary to perfuse a collapsible vessel placed in the myocardium. Pressures required for perfusion of these vessels at low ventricular volumes may have been a result of distortion and not due directly to changes in pressure. Increased intramyocardial pressure would decrease flow by decreasing the effective pressure across the vascular bed and raising critical opening pressure. Increased intramyocardial pressure may also imply changes in regional oxygen demand whereas increased resis-

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Fig. 11. Concentric hemorrhagic monary bypass is shown.

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necrosis in a calf hcwt

t,ancc due to distortion of vessels does not imply changes in regional oxygen needs. The concept of intramyocardial pressure may be inappropriate with distorted myocardium, especially when intramyocardial pressure is measured through vessels implanted in the heart muscle. Armour and Randall measured intramyocardial pressure with subminiature implanted pressure transducers and found that increased inotropic effect by stellate ganglion stimulation by increased intrawas accompanied myocardial pressure relative to intraventricular pressure. Similarly, distortion of tissue will affect implanted transducers of finite size. Theoretically measurement of pressure at a infinitesmal point in the myocardium would be necessary to avoid the effects of tissue distortion.

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4 hr hypercalcemic

cardiopul-

Estes reported that the subendocardial vessels did not fill with a radio-paque injection following calcium injections, We have shown that hypercalcemia produces small ventricular volumes in the fibrillating heart. The present study shows prominent subendocardial hemorrhagic necrosis and venous distention in the subendocardium following hypercalcemic cardiopulmonary bypass. The practical importance of these observations is that pharmacologic interventions which decrease ventricular volume may be important determinants of regional vascular dist’ortion as well. If greater subcndocardial vascular distortion occurs with greater V,/V, ratios then patients with aortic stenosis would be more likely to develop subendocardial hemorrhagic necrosis than patients with aortic insufficiency.

UTLEY

ET

AL. : SUBENDOCARDIAL

Fig 12. SutJc,l-)ic:rrdiurII~~lrdi~lt~l muscle from calf heart and ! lack of hemorrhage, edcmn, or necrosis.

Fig 13. Subendocardial ant 1 the distention of disf ;ortion.

muscle arteries

VASCULAR

demonstrating

from calf heart demonstrating and veins suggesting venous

DISTORTION

normal

histologic

a~~I~c;lr~anW

the interstitial hemorrhage obstruction due to vascular

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SUMMARY Greater distortion of subendocardial vessels compared to subepicardial vessels with decreasing ventricular volume was predicted from a simple mathematical model. The left ventricular wall near the base bchaves as the wall of a sphere with changing ventricular volumes. Photomicrographs of barium injected coronary vessels at different ventricular volumes demonstrates the distortion of subendocardial vessels at small ventricular volumes. Venous obstruction was observed in the subendocardium of the contracted fibrillating heart following cardiopulmonary bypass. Small ventricuIar voIume appears to predispose the heart to subendocardial hemorrhagic lesions. BIBLIOGRAPHY 1. Buckberg, G. D., Towers, B., Paglia, D. E., Mulder, D. G., and Maloney, J. V. Subendocardial ischemia after cardiopulmonary bypass. J. Thor. Cardiovas. Surg. 64:669, 1972. 2. Najafi, H., Henson, D., Dye, W. S., Javid, J., Hunter, J. A., Callaghan, R., Eienstein, R., and Julian, 0. C. Left ventricular hemorrhagic necrosis. Ann. Thor. Surg. 7:550, 1969. 3. Ferrand, V. J., Hibbs, R. G., Black, W. C., and Weilbaecher, D. ‘G. Isoproterenol-induced myocardial necrosis. A histochemical and electron microscopic study. Amer. Heart J. 68:71, 1964. 4. Szakacs, J. E., and Cannon, A. I-Norepinephrine Myocarditis. Amer. J. Clin. Path. 30:425, 1958. 5. Kaye, M. P., McDonald, R. H., and Randall, W. C. Systolic hypertension and subendocardial hemorrhages produced by electrical stimulation of the stellate ganglion. Circ. Res. 9:1164, 1961. 6. Light, F. W., and Benbrook, S. C. Subendocardial hemorrhages of the left ventricle following trauma in goats. Arch. Path. 65:407, 1958. 7. Martin, A. M., Hackel, D. B., Entman, M. L., Capp, M. P., and Spach, M. S. Mechanisms in the development of myocardial lesions in hemorrhagic shock. Ann. New York Acad. Sci. 156:79, 1969.

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8. Martin,

A. M., Hackel, D. B., and Kurtz, S. M. The ultrastructure of zonal lesions of the myocardium in hemorrhigic shock. Amer. J. Path. 44:127, 1964. 9. Martin, A. M., and Hackel, D. R. An electron microscopic study of the progression of myocardial lesions in the dog after hemorrhagic shock. Laboratory Investigation X:243, 1966. 10. Martin, A. M., and Hackel, D. B. The myocardium of the dog in hemorrhagic shock. Laboratory Investigation 12:77, 1963. 11. Hackel, D. B., and Catchpole, B. N. Pathologic and electrocardiograhic effects of hemorrhagic shock in dogs treated with 1-Norepi7:358, 1958. nephrine. Laboratory Investigation 12. Hackel, D. B., Martin, A. M., Spach, M. S., and Sieker, H. 0. Hemorrhagic shock in dogs. Arch. Path. 77:575, 1964. 13. Hamilton, W. F., Dow, P., and Hamilton, W. F. Measurement of volume of dog’s heart by X-ray: Effect of hemorrhage, of Epinephrine infusion, and of buffer nerve sections. Amer. J. Physiol.

161:466, 1950.

14. Wertheimer, N. Bloom, S., and Hugher, R. K. Myo ardial effects of pericardial tamponade. Ann. Thor. Surg. 14:494, 1972. 15. Sugishita, Y., Sigckoto, K., Yasuda, H, Iio, M., Murao, S., and Ueda, H. Myocardial distribution of blood flow in the dog studied by the labeled microsphere. Jap. Heart. J. 12:60, 1971.

16. Zbinden, G., and Moe, R. A. Pharmacological studies on heart muscle lesions induced by Isoproterenol. Ann. New York Acad. Sci. 156:294, 1969. 17. Brandi, G., and McGregor, M. Intramural pressure in the left ventricle of the dog. Cnrdiovasc. Res. 3:472, 1969. 18. Baird, R. J., Goldbach, M. M., and de la Rocha, A. Intramyocardial pressure. b. Thor. Cardiovusc. Surg. 64:635, 1972. 19. Salisbury, P. F., Cross, C. E., and Rieben, P. A. Intramyocardial pressure and strength of left ventricular contraction. Circ. Res. 10:608, 1962. 20. Armour, J. A., and Randall, W. C. Canine left ventricular intramyocardial pressures. Amer. J. Physiol. 220:1833, 1971. 21. E&es, E. H., E&man, M. L., Dixon,

H. B.,

and Hackel, D. B. The Vascular supply of the left ventricular wall. Amer. Heart J. 71:58, 1966.