Fiber shortening in the inner layers of the left ventricular wall as assessed from epicardial deformation during normoxia and ischemia

FIBER SHORTENING IN THE INNER LAYERS OF THE.LEFT VENTRICULAR WALL AS ASSESSED FROM EPICARDIAL DEFORMATION DURING NORMOXIA AND ISCHEMIA FRITS W. Departments

PRINZEN,

THEO

of Physiology

ARTS,

GER J. VAN DER VLME

and

ROBERT

and Biophysics. University of Limburg. Maastricht,

S. RENEMAN The Netherlands

Abstract-A mathematical model of left ventricular mechanics predicts that fiber shortening in the inner ) from the magnitude of minimal (e,,,,J and layers of the left \sntricular wall can be estimated (eondo,NIL maximal shortemng (P,,,, D) of the outer surface (= epicardium) of this wall. TO evaluate this prediction, erndu.sl, and G.. o were compared with the shortening in the inner layers approximately along the fiber direction (e,.J as measured d’Irectly, before and during one minute of coronary artery occlusion. Deformation of the epicardium and the inner layers was determined by measuring mutual motion and angulation of three needles pierced into the myocardial wall, using an electromagnetic inductive technique. The proposed linear relations of e,.d.. us,and emin,D with P,.~~ were found to be significant. The needles hardly influenced wall deformation since similar values of epicardial deformation were found in separate, comparable, experiments (n = 13) using a triplet of epicardial coils. So e,.,,, 11,and e,+ o are useful estimates of fiber shortening in the inner layers during normoxia and ischemia. especially when the time course of events is followed in the same animal.

NOMESCLATURE orientation of shortening shortening shortening in the inner layers approximately parallel to the fibers (presently defined at an angle of 0.22 rad with Brnin,.), calculated according to equation (16). fiber shortening in the inner layers as estimated from em,“,o and P,,,, (I according to equation (17) unit vector

circumferential inner layers maximal minimal outer surface (= epicardium) shear base-to-apex

ISTRODUCIION

As a consequence of obstruction of How in a coronary artery, part of the cardiac wall becomes ischemic. Under theseconditions the inner layers of the wall are more severely affected than the outer layers as indicated by transmural gradients in myocardial blood How (Reneman et al., 1975; Bathe et al., 1977) and metabolic variables like lactate, creatine phosphate and glycogen (Griggs t’l al.. 1972; Opie rt nl., 1975) as w#ellas non-esterified fatty acids (Van der Vusse rf al., 1982; Prinzen et al.. 1984). Within 10-20s after onset of occlusion of a coronary artery shortening during the contraction phase of the left ventricle

Ruceid

21 Sep[rmber

1983; in reckedform

5 June

1984.

decreases at the epicardium (Tennant and Wiggers. 1935;Tomoda rl (II., 1971; Bankaand Helfant, 1974)as well as in the inner layers of the wall (Theroux rf NI., 1976). To obtain better insight into the mechanisms involved in inhomogeneities across the myocardial wall, assessment of shortening in the various layers of the myocardial wall is required. Accurate assessment of transmural differences of fiber shortening (which is defined in this paper as: shortening parallel to the muscle fibers) is ditiicult due to limitations of the techniques used. Recently, shortening of segments in the inner and outer layers has been measured simultaneously by implanting pairs of ultrasonic crystals within these layers (Weintraub Ed al., 1981; Gallagher ef al., 1982; Hattori er a(., 1982). Using the latter method, however, the implantation of the crystals may damage the myocardium at the site of measurement and thus may influence the measurement (Theroux rt al., 1974; Hattori et al., 1982). Moreover. this approach requires proper alignment of the transducers with respect to the fiber orientation because of anisotropy of the myocardium (Gallagher er al., 1982). In the present investigation determination of the transmural course of fiber shortening is approached differently. Instead of measuring shortening of one segment only, the transmural course of deformation of P plane in parallel with the wall is determined. This planar deformation is characterized by circumferential shortening (e,,), axial or base-to-apex shortening (e,,) and shear (e,,). Using data on the transmural course of fiber orientation as obtained in anatomical studies (Streeter and Hanna, 1973; Ross and Streeter, 1975), fiber shortening can be calculated from the transmural course of planar deformation. Under normal nonischemic conditions (normoxia) deformation of the outer surface (epicardium) is closely related to defor801

802

FRITSW. PRISZEN.THEOARTS.GER J. VANDERVuss~ and ROBERT S. RESEMAN

layers because shear deformation parallel to the wall is small compared to muscle fiber shortening (Feigl and Fry, 1964). A second. more indirect indication of this shear being relatively small, is based on a mathematical analysis of cardiac wall mechanics (Arts rr (11..1979, 1982). In this analysis the left ventricle is simulated by a cylinder. Torsion of the left ventricular cavity is represented by rotation of the upper cross-section with respect to the lower cross-section of the cylinder around the axis of the cylinder. The amount of torsion is predominantly determined by an equilibrium of torques, directed around the axis of the cylinder, and results from circumferential-axial shear stress components in the wall. The ratio ofaxial to circumferential deformation of the wall of the cylinder is determined by an equilibrium of axial stresses in the wall and left ventricular cavity pressure, which is built up by circumferential stresses in the cylindric wall. In this model it was found that shear deformation between layers parallel to the wall is small, confirming the experimental findings of Feigl and Fry (1964). The validity of the model was indicated by two comparative studies. In one, deformation of the outer surface of the left ventricle as predicted, was found to be close to this deformation as measured directly at the free wall of the left ventricle (Arts rr al., 1982). In a second investigation the ratio of left ventricular circumferential shortening to torsion as measured in the closed-chest dog, using two-dimensional echo-cardiography, was only IO’?, below the value as predicted by the model (Arts PI al.. 1984). Thus, according to the insights into left ventricular mechanics as obtained in the model study, under non-ischemic conditions deformation of the inner layers of the left ventricle can be determined from deformation of the outer surface of the heart with reasonable accuracy. If this is also true during ischemia, determination of epicardial deformation might be a useful method to assess deformation of the inner layers in experimental studies. The aim of the present study was to assess fiber shortening in the inner layers of the wall of the left ventricle from deformation of the outer surface during both normoxia and ischemia. For this purpose deformation of the epicardium and the inner layers was determined simultaneously by measuring mutual motion and angulation of three needles pierced into the myocardial wall. This was achieved by using the inductive method to determine planar deformation as described by Arts and Reneman (1980) at two levels along the needles. Then values of the deformation parameters at the epicardium and within the inner layers, in a plane parallel to the wall surface, were obtained by downward extrapolation of the values of the deformation parameters as measured directly at two different levels above the epicardium. TO investigate possible artifactual inffuences of the needles on deformation of the left ventricular wall, in thirteen experiments epicardial deformation was measured by a triplet of epicardial coils (Arts and Reneman, 1980). mation

in the inner

between layers

The thus obtained values of the deformation parameters were compared with those obtained with the needles.

THEORETICAL.\NALYSIS In the wall of the left ventricle, fiber shortening can be calculated from local deformation and fiber orientation. In the analysis below, the wall of the left ventricle is simplified to a thick-walled cylinder as described before (Arts et al.. 1979, 19S2). The coordinates used in this representation are oriented along the radial (r), circumferential (c) and axial 1:) direction. Shortening r is defined by e = -In

(I, :/_)

where I,, and 1, denote length of a segment before after deformation, respectively. If deformation is small as compared to unity, first order approximation deformation can be resented by a tensor D. Shortening e, along a vector k, representing fiber orientation, is cI = k.D.k

(1) and in a repunit

(2)

with

(3) Fortunately, equation (2) can be reduced considerably using properties of cylinder symmetry of the field of deformation. Circumferential gradients in radial and axial displacement and radial gradients in axial and circumferential rotation are considered to be absent (Arts rt a[., 1979,1982). So, the deformation tensor D is simplified to (4) Fortunately, in the wall of the left ventricle, the radial component of k is small (Streeter and Hanna, 1973). Neglecting this component equation (2) may be written as eJ = e,,cosZp~+e,zsin2~,+rz,sin~,cos~,

(5)

where /I/ represents the angle between k and the circumference. Because e,, = 0 (equation 4), err is the same everywhere in the cylinder wall. Using incompressibility of the myocardial material (Hill, 1950) it is found that e,,=

The constants

deformation

-A-B.Rf/r2

(6)

ecc = -A+B.Rz/r’

(71

err = 2A e;, = C r/R,

63) (9)

A, B and C determine the field of of the cylindric wall. R, represents the

803

Epicardial assessment of transmural fiber shortening outer radius of the cylinder and is used as a scaling length. Xleasurement of outer surface deformation of the cylinder enables the solution of ‘4. B and C by A = 1 2 t);;, D

( 10)

B=l

(11)

2
c = YTC. D

(12)

where index o refers to the outer surface. By measuring shortening along the principal directions (e,,,,, and e m,n,,) and the angle (/I,) between the principal e,,,,,, D direction and the circumference, parameters A, B and C can be solved using ezr. D = c,,,, u co? 8, + r,,,, Dsin’ I%

(13)

r cc.0 = r mu-r.0 sin’ p, + em,“,u sin’ fl,,

(14)

J 0 = -2(~,,,..--~,,..)sinp,cosB,. CL<.

(15)

When the ratio of inner to outer radius (R,/R,\ is known, deformation of the inner layers can be calculated using equations (6)-(9). Our main interest is estimating fiber shortening within the wall from deformation measurements performed at the outer surface ofthe left ventricle. Using the results ofa model of left ventricular mechanics (Arts rt al., 1979, 1952). the principal Q,,,~.~,~direction was found to be approximately -0.82 rad deviated from the circumference and lo coincide closely with the fiber orientation in the outer layers (-0.67 rad). Thus, fiber shortening in the outer layers is closely related to r ma.~,O.The angle between the orientation of the muscle fibers in the inner layers and the principal L’,,,,, direction wasapproximately 1.35 rad, which isequal to an angle of - 0.22 rad with the Pmin.Ddirection. In the present analysis, shortening e‘,nJualong the muscle fiber direction in the inner layers is used as an estimate of fiber shortening in these layers. The angle between this direction and the circumference is defined to be /?l.JO, The values obtained from the model, fi_,,, = 0.52 and R,iR, = 0.7. are substituted into L’ endo= G,, , cos* Ando+ crz., sin’Ando

-t el,, i ~0sPendo sin Bend0

116)

where the index i denotes the inner wall. In the model of Arts and colleagues (1979) emin,u = 0.02 r,,,_, Din the control situation. Starting from this situation and using the values of A, B and C as obtained from equations (lo)-(12). a first order estimate of t>c,dOis found by numerical calculation %fo. es, = 1.42 e,in, o + 0.78 emar, “.

(17)

The influence of deviations of PO and R,/R,, from the substituted values is given by the values of the partial derivatives

____ ~(K’R,)

= - 3.73 r,,,, D

In the experimental part of the study. e,.du, cl, as calculated by equation (17) was compared with eendoas measured directly, under normal as well as ischemic conditions. Because r,,,,. appeared to be the main determinant of erndo, the relation between em,,,0 and evnJo was also investigated.

(19)

MATERIALS

AND METHODS

Animal prepcuxtion The experiments were performed on nineteen mongrel dogs of either sex and unknown age, ranging in weight from 20 to 60 kg. The animals were premeditated with Hypnorm (1 ml kg- ’body weight i.m.) as described by Marsboom and colleagues (1964). One ml Hypnorm contains 10 mg fluanisone and 0.315 mg fentanyl citrate. Anesthesia was induced with sodium pentobarbital (10 mg kg-’ body weight i.v.) and, after endotracheal intubation, was maintained with oxygen in nitrous oxide (40”” 02/60”, N20) and a continuous infusion of sodium pentobarbital (2 mg kg-’ h-’ i.v.). Ventilation was kept constant during the experiments with a positive pressure respirator (Pulmonat). During thoracotomy. succinylchoiine (2 mp kg- ’i.m.) was injected to prevent muscle movement caused by electrocoagulation. The chest was opened through the left fifth intercostal space and the pericardium was incised over the antero-lateral aspect of the heart. ECG was recorded from the limb leads. Aortic pressure was measured with an external pressure transducer (Ailtech), connected to a polyethylene catheter in the aortic arch. Left ventricular pressure was measured with a Millar catheter-tip micromanometer, inserted through the left brachial artery. For the measurement of phasic aortic flow, an electromagnetic flow probe (Skalar) was placed on the ascending aorta. The flow probe was connected to a sine-wave electromagnetic flowmeter with a carrier frequency of 600 Hz (Transflow 600; frequency response O-100 Hz, -3 dB). The end-diastolic level of the phasic aortic flow tracing was used as a zero reference. Coronary artery occlusion was induced with an inflatable cu8 which was placed around the left anterior interventricular coronary artery, just distal to rhe diagonal branch. All hemodynamic variables measured and the epicardial deformation variables (see below) were recorded on a multichannel Schuarzer recorder (upper frequency response 280 Hz, - 3 dB) generally at low speed (1.25 mms-‘). but during the measurements at high speeds (50 or 200 mm s- ‘). Assrs.smrnt

of transmural

rl@rtwces

in deformation

In six animals (group I) information about deformation within the wall of the left ventricle was obtained from measurement of mutual motion and angulation of three needles, pierced into the wall of the left ventricle. Mutual motion and angulation was determined from triangulation measurements at two levels above the epicardium. For this purpose two

FRITS W. PRINZEN. THEO ARTS. GER J. VAN DER VL~SSE and

80-t

coils. identical to those used for the determination of epicardial surface deformation (Arts and Reneman, 1980). were placed on each needle 2 and 12 mm above the epicardium, respectively. The needles were positioned at three corners of a rectangle in the perfusion area of the left anterior interventricular coronary artery (Fig. I). The three needles were placed in parallel with each other and perpendicular to the wall in the centre of the triangle. The needle with the magnetic tield generating coil was positioned at the right angled corner. The sides containing the right angle, were parallel to the circumferential and base-to-apex direction. respectively (Fig. 1). The distar?ce between each sensor coil needle and the magnetic field generating coil needle was approximately 15 mm. The stem of each needle consisted of a PVC cylinder (outer diameter 2 mm, length 15 mm). A nonferromagnetic needle (Tungsten; outer diameter 0.6 mm, length 25 mm) was placed underneath this stem. For fixation of the needle within the myocardium, small notches were made in each needle about 2 mm below the PVC cylinder. The deformation variables ccc, e,, and r,, were measured at the two coil levels above the epicardium. The values of r,,, ezLand err at the epicardium and in the inner layers, parallel to the outer surface, were calculated from the deformation variables as measured at the two coil levels by downward linear extrapolation along the needles according to the equation or

= (1 -&/4)p,

+ (dxld,)~,

(20)

where p, = parameter value at level rl,<:d,x = distance (mm) from the upper coil; d, = distance (mm) between

ROBERTS. RENECIAN

upper and lower coils; pu = parameter value at the upper coil level; p, = parameter value at the lower coil level. For the needles used it holds d, = 10 mm. At the epicardium d, = 12 mm and in the inner layers d, = 12 mm + wall thickness. End-diastolic wall thickness was assumed to be proportional to the cube root of the left ventricular weight wall thickness = 2.3 [left ventricular weight]“3 (21) with wall thickness expressed in mm and left ventricular weight in grams. This formula was derived from data as published by McHale and Greenfield (1973) saying left ventricular weight = 129 g and left ventricular wall thickness = 11.6 mm. When using wall thickness as an extrapolation distance, this distance was assumed to be constant during the ejection phase and throughout the experimental period. Thus the accuracy of shortening measurements in the inner layers was limited to a first order approximation. The changes in the three deformation variables were determined during the ejection phase. The period of ejection was considered rather than the whole systolic period, because during the isovolumic phase considerable shape changes of the left ventricle may occur (Rankin er al., 1976) at relatively low levels of muscle fiber stress and with little external generated work. The electronic circuitry used in these experiments was the same as the one used by Arts and Reneman (1980) for planar deformation measurements. So the deformation parameters e,,, err and err as measured during the cardiac cycle, could be registrated directly for only one level of coils at a time. Therefore, the signals from each level were alternatively registrated during 2-5 heart beats, using a switch. For each variable, the values were averaged over 2 or 3 beats. Assessmenr of epicardial

I-circumference

-I

Fig. 1. Assessment of transmural dinerences in deformation. Three needles arc pierced into the myocardial wall parallel to each other. On each needle two inductive coils are placed 2 and I2mm above the epicardium. Mutual movement and angulation of these needles during the ejection phase are measured by determining circumferential shortening, baseto-apex shortening and shear at the two levels above the epicardium (solid lines). The three planar deformation parameters on the epicardium and in the inner layers are calculated by extrapolation (dotted lines).

dejormation

by a triplet ofcoils

Deformation of the epicardium was determined with a triplet ofcoils. The threecoils were placed on the free wall of the left ventricle, in the perfusion area of the left anterior interventricular coronary artery. The coils were attached to the epicardium by suction (under-pressure approximately - 25 kPa) in a rectangularly triangular array as described previously (Arts and Reneman, 1980). The coil at the right angled corner transmits a rotating magnetic field which is sensed by the other two coils. The amplitude of the voltages induced in both sensor coilscontains information about the distance between these coils and the magnetic field generating coil (MFGC), while the phase angle between both voltages determines the angle between the sensor coils as seen from the MFGC (Fig. 2). In this way the deformation variables e,,., e==,0 and err. 0 were determined during the ejection phase in 13 experiments (group 2). Experimental

protocol

After a control registration period, the left anterior interventricular coronary artery was occluded during

Epicardial

assessment of transmural

805

fiber shortening

icircumferential

shortening(Q

Fig. 2. Measurement of epicardial deformation parameters with a triplet of coils. In the open-chest preparation three inductive coils (one field generating coil and two sensor coils) are sucked on the epicardium in the perfusion area of the left anterior interventricular coronary artery (LAICA). Blood Row through this artery can be obstructed by the occluder placed around this vessel. LCCA = left circumflex coronary artery.

Fig. 3. Schematic representation of the relation between circumferential shortening (e,,), axial (= base-to-apex) shortening (e,,) and shear (e,,) with principal minimal shortening (emi.). principal maximal shortening (e,,,) and the orientation of minimal shortening (/Imin). During the ejection phase a square, assumed to be present at the onset of ejection, is deformed into a parallelogram, the form of which is determined bye,,, err and e,,. The inscribed circle of the square is

deformed

one minute by rapid inflation of the occluder cuff around this artery in both experimental groups. A second period of occlusion of one min was performed only in group 1 (needle measurements) after a time interval of at least 15 min, which was considered to be sufficient for recovery of the myocardium from the previous occlusion. The values of all continuously registrated variables were calculated just before and 5, 10, 20, 40 and 60 s after coronary artery occlusion. Each experiment was terminated by killing the dogs with an overdose of the anesthetic. The heart was excised and the weight of the left ventricle was determined. Dnru ana1p.si.s From the values of r,,, err and ezc the values of emor and emin (Fig. 3) were calculated according to r m.zr.

e,,f err

ml”

kc -

=-+

2

-

[

1

ezz)* + kA* “’ 4

into an ellipse, the form of which is determined emox, emin and IL..

by

variables was evaluated by comparing the values during occlusion with those just before occlusion (time t = 0 s). Differences between the values of the various variables were evaluated for statistical significance by applying Wilcoxon’s matched pairs signed-ranks test (two-tailed probability). The relationship between emin.Dand eenda.er, on the one hand and ePndoon the other, was investigated by linear regression techniques and tested for significance by Spearman’s signed-rank correlation test. The data are presented as median values and 95 p/;, confidence limits. A value of p
(22)

which can be derived from equations (13)-(15). The thus obtained e,,,X, D and CJ,,,~“. o were used to estimate fiber shortening in the inner layers (eendo,_,) according to equation (17). Shortening in the inner layers approximately along the fiber direction (e,,,,) was assessed by calculation of the deformation of the inner layers, using equation (20), and by subsequent calculation of shortening in the /?rn,lodirection using equation (16). Since the model predicts that fi,,,rn,u - benJo = 0.22 rad (see above), in the experiments Pendo was calculated as /?min,0 - 0.22 rad. Information about the effect of acute coronary artery occlusion on regional myocardial mechanical performance was obtained by using the animal as its own control. The effect of ischemia on the various

In Fig. 4 a registration of the variables of transmural deformation during normoxia is shown. At the two coil levels circumferential shortening, base-to-apex shortening and shear are registrated. The ejection phase was determined from the phasic aortic flow tracing as indicated by the dots. The values of the three deformation variables at the epicardium (ccc.o, err. Dand ez,. ,) and in the inner layers (e,,.i, e:.-.i and e:,.i) d uring normoxia and 1 min of coronary artery occlusion are shown in Table 1. After onset of coronary artery occlusion eC_ and e,,,, (significant after 10 s) as well as e,,. i and err. i (significant after 20 s) decreased. Within 40 s of occlusion err, ~ decreased in two experiments (four occlusions) and increased in the remaining four experiments (eight occlusions; Table 1). The changes in ezC,i showed even larger variations between the experiments than the changes in err, 0. The angle fimin.o (= orientation of

FRITS W. PRINZEN, THEO ARTS, GER J. VAN DER VUSSE and ROBERT S. RENEMAN

806

Shortening

LOWER

COILS

:

UPPER

20

COILS

I see base-to-apex rhorten,ng clrcumferenflal shorfenmg

shear

-/ ---A’

‘-

?‘.-_* ..’

q

.,

, ,.

\.‘..-._,

.-._v.‘,

!

fi, flow

_J

i

,J

p-. \;

,-

jZO%

IO -L..-L~~,

.

-J:--

‘/ 4

aort,c

,_.:-*

A,-

-2.’

--

_

:I-

i.,’

Ti

.__

i i

20%

,* 0.2

ra4

0

fi; ai_ i

.

‘r-

,.ee,do,est .______________;,~___________I_

\.

Fig. 4. Registration of base-to-apex shortening, circumferential shortening and shear by the lower and upper coils. Onset and

(%I

-10

end of the ejection phase are indicated by dots on the aortic flow tracing.

emin..) was about 1.Orad. Ten and 20 s after the onset of occlusion /Jmin.o increased slightly, but significantly. The increase in Prni... (pooling of all data obtained during ischemia) was 0.26 (0.17433) rad (median value and 95 “, confidence limits; p < 0.05). The orientation of minimal shortening in the inner layers (/lmi.. i) was not significantly different from &.. o. Figure 5 shows the time course of eenda,pI,, emi,. Dand E,..~,,as assessed in this experimental set-up. Both emin.o and c,,do had low positive values during normoxia. Coronary artery occlusion caused a rapid decrease of both variables. From 10 till 60 s of occlusion the values of emi,, ,, and %du were generally negative, indicating lengthening in their direction at the epicardium and in

6

i-

1’0

2’0

4’0 go Time (9

Fig. 5. Shortening in the inner layers approximately parallel to the direction of the fibers (e,,,.) and epicardial minimal shortening (emi,_ ?? ) as determined from transmural deformation measurements, and fiber shortening in the inner layers as estimated from epicardial deformation parameters (ernoO,_, 1 min of acute coronary artery A), before and during occlusion. Median values and 95 oAconfidence limits of twelve occlusions in six animals (group I) are shown.

the inner layers, respectively, during the ejection phase. Maximum lengthening was reached after about 20s of occlusion. During the normoxic and the ischemic period no significant difference between c,,,~,,0 and &Jo

Table I. Deformation parameters at the epicardium and in the inner layers as well as orientation* of minimal shortening at the epicardium and in the inner layers before and during coronary artery occlusion. Median values and 95 % confidence limits of twelve occlusions in six animals are shown Coronary Control Epicardium ecc.0

5

artery

occlusion

Time (s) 20

10

40

10.4 6.0-12.3 1.3 3.7-15.6 0.054 0.04OXl.092 0.86 0.20-1.37

9.6 6.2-13.1 6.5 5.0-9.0 0.067 0.038-0.088 1.11 0.75-1.45

4.9t (- 1.3)-l 1.4 - 0.7+ (- 3.7)-3.7 0.092 ( - 0.032j-O. 120 1.07+ 0.86-1.44

2.9* - 0.2+ (- 1.8)-3.5 (- 2.4)-6.8 0.6+ - 5.8’ (- 14.0)-( - 1.5) (- 3.2)-9.4 0.118 0.108 0.024-O. 128 0.048~.158 1.03 1.06+ 0.90-1.18 0.65-1.34

Wad)

10.6 7.8-15.1 9.9 1.1-23.2 0.07 1 0.006-0.137

12.2 8.0-17.2 6.8 4.5-9. I 0.058 O.GW-O.116

8.6 0.8-12.5 1.4 (- 2.6-6.2 0.049 (-0.07O)-O.155

4.2’ (- 1.5)-10.1 2.8’ (-O.lP.3 0.105 0.033-0.250

2.0’ (- 0.3)-3.6 3.0+ (-2.1)-14.0 0.115 0.01 l-O.249

k:;

0.19-1.10 0.73

0.75-1.41 0.96

0.86-1.71 1.06

0.91-1.19 1.06

0.65-1.10 0.12

( “cl

e:<, 0

(rad) L. 0 @ad)

Inner layers e,. i

( 7”) e::. i ( %) e:,. I

?? Orientation with respect to the circumferential + p < 0.05 as compared with time 0 s.

direction.

60

- 0.9’ ( - 2.2)-0.8 0.4+ ( - 1.2)-2.8 0.046 0.010-0.108 0.67 0.44-1.36 0.1+ (- 1.7)-1.8 1.0’ (- 1.3)-6.9 0.054 (-0.026fl.316 0.66 0.00-1.12

Epicardial

assessment of transmural

could be detected. During normoxia the values of r rnJ,,.r,r uereabout 16”,,. hipher than the values of eenllu and P,,,,~,“. After onset of coronary artery occlusion tlend,,,,.sI decreased to negative values within 20 s. For each individual experiment ecndowas plotted as a function of t’,,_ and of z,.~~. cI,. using the values obtained during normoxia and 1 min of coronary a:tery occlusion. Figure 6 shows a typical example of the relations found. In all six experiments. the relation between eYndoand t~,,,~“. ,, was significant (p < 0.05) with correlation coefticients in the six individual experiments of 0.70. 0.7% 0.86. 0.95, 0.98 and 0.99. The relation betkveen Y,,,, ,, and r,,,, could be described by linear reeression C’,.do=

m em,“, ,, + b

bvith m = 1.OY (0.45 to 1.61) and b = 1.6 (-0.6 to + 3.7)“,, (median values and 95 ‘I<,confidence limits). The relation between c’_,,, and L’,.~~,cs, was also

e endo

fiber shortenmg

significant coefficients correlation

in all six experiments with correlation of 0.60,0.70. 0.91, 0.93. 0.93 and 0.97. This could be described by tJrnJu = me mJo.
(0.31 to 0.70) and b = - 2.2 I - 12.8 to Since analysis of covariance showed that the regression lines of the six individual experiments were significantly ditferent. no calculations were made on the basis of pooled data. Figure 7 ivas constructed from the median talues of the deformation variables e,,. zzz and oz; at the epicardium and in the inner layers during normal perfusion. Circles at the epicardium (left panel) and in the inner layers (right panel) deform into ellipses, the ellipse in the inner layers being narrower. The direction of the fibers at the epicardium and in the middle of the inner third layer according,to Streeter and Hanna ( 1973)is depicted as well. Shortening in the direction

with

+

m = 0.55

1.1)““.

I

‘;mc

a,,’

(%) ,’

;’ ,’ I’ ,’

Fig. 6. Example of the relationship of epicardial minimal shortening (emm.,J and estimated fiber shortenins in the inner layers (e cnJo.n,) with shortening approximately parallel to the fiber direction in the inner layers (P,.J just before and during ischemia in one experiment. The linear regression equation and the correlation coefficient are indicated. The numbers inside the circles denote the time after onset of coronary arter) occlusion in seconds.

EPICARDIUM

807

INNER

LAYERS base

base

t

I

apex

apex

Fig. 7. Direction and magnitude of shortening at the epicardium and in the inner layers as derived from transmural deformation measurements. As a result of shortening during the ejection phase, in both layers circles are deformed to ellipses. For the sake of clearness the real shortening has been multiplied by a factor of two in all directions.

808

FRITSW. PRINZEN,THEO ARTS,GER J.

VAN

DER VIXE and

ROBERT S. RE?;EMAS

Table 2. Epicardial minimal and fiber shortening in the inner layers

maximal shortening and the derived estimation of (emdo..,,). Comparison between the values, obtained with needles pierced into the myocardial wall and those obtained with coils attached to the epicardium. The median values and 95 Ybconfidence limits are presented Coronary artery occlusion Time (s) 10 20 40

Control

60

emin.o(9,) Needles Coils

3 2-6 3 (-2)-7

(ylO)-(-4)

;-‘I 1)-( -4)

(t59)-( - 1)

(:13)-O

Significance

NS

NS

NS

NS

p < 0.05

emZlehL;

12 9-18 15 9-19

7 O-8 IO l-13

4 l-11 7 (-1)-11

4 o-5 6 2-9

3 o-5 3 l-5

Significance

NS

NS

NS

NS

NS

e..;erd/e$)

16 9-23 12 6-19

6 ( - 8)-8

(&9l4,-o

(139)-l

(t35)-l

Coils

Coils Significance

;-:)-(

- 1)

(I41 5)-l p < 0.05

NS

(:*l5)-( - 5) (L48)-0

(136)-( - 1)

(1816)-1

;-zs)-( - 1)

(c13)-4

NS

NS

NS

Differences between the groups 1 and 2 were evaluated for statistical significance by applymg Wicoxon’s rank-sum test.

close to the short axis of the ellipse (e,,,,,) is larger in the inner layers than at the epicardium (Fig. 7). However, in the direction close to the long axis of the ellipse, which is the flmi. direction, only minor differences in shortening between these two layers could be detected. In Table 2 the values of e,,,,,,0, e,,,,, 0 and esndo,eS,as obtained with the transmural needles (group 1) are compared with those obtained with a triplet of epicardial coils (group 2). Generally, for the three variables no significant difference could be detected between the values obtained by the coils and the needles. Exceptions are the value of e,,,,,.0 after 60 s, being less negative than the value obtained with the needles, and

Shortening

(%)

the value of eend,,.eS,after 10 s of occlusion, being lower than the value obtained with the needles (Table 2). Measurements with the coils and with the needles revealed that before &hernia the values of eendo,eS,were not significantly different from those of ema_ (Table 2). After onset of occlusion eendo._, and emi,,D decreased rapidly to negative values, whereas the decrease in e,,,,,.. was more gradual. With use of the epicardial coils the time course of these three variables during coronary artery occlusion (Fig. 8) could be determined with higher temporal resolution than using the needles (Fig. 5), since the latter technique requires switching between the two coil levels (see methods). Throughout the ischemic period the values of e,,,,,. o remained aligned in the outer two thirds of the myocarening during the ejection phase at the epicardial surface along the fiber direction (Fig. 8, Table 2).

’51 DISCUSSION Theoretical analysis

0

2

4

6

8

IO

20

:-

30

40

50

60

Time ($1

Fig. 8. Epicardial minimal (e,+ o ?? )and maximal shortening (e,,. 0 m) as well as fiber shortening in the inner layers, calculated from enril.0 and e,,,,. .,, (ernd..??,, 0). as determined by measurements with epicardial coils, before and during one min of acute coronary artery occlusion. Only the median values are presented (n = 13, group 2). For the 95% confidence limits at some sample times see Table 2.

The theoretical analysis is mainly based on a model study of left ventricular mechanics (Arts et al., 1979, 1982) which presumes cylinder symmetry. In the normal healthy heart deformations as predicted by the model are in agreement with experimental results on epicardial deformation (Arts et al., 1982) and twodimensional echocardiography (Arts et al., 1984). Although during ischemia the cylindrical geometry is disturbed, the findings in the present study indicate that the relation between epicardial and inner wall deformation can be applied to the latter situation too, albeit with limited accuracy. Generally, deformation is small enough to be rep-

Epicardlal assessment of transmural by a tensor. Second order disturbing terms are in the order of the square root of occurring deformations and appear to be much smaller than the accuracy of the measurements. The use of properties of symmetry to reduce the deformation tensor to a simpler form seems to be allowed in the free wall of the normal left ventricle. not too close to the apex. Feigl and Fry (1964) experimentally found that the tensor components err and P,, are close to zero (mean value of (t,I:; + t!;<)’ 2 < 0.02) in the hearts of open-chest anesthetized dogs. They measured the angulation of a needle pierced perpendicularly into the wall of myocardium. Closer to the apex and in case of ischcmia, this deformation tensor probably becomes more complex. introducing discrepancies between the mechanical changes in the real situation and those predicted by the model of ventricular deformation. Besides the attachment of the papillary muscles to the wall of the left ventricle, close to the site of measurement, may also disturb epicardial deformation. In the mathematical model of left ventricular mechanics (Arts t’l al., 1979, 1982) the angle between the principal t’,,,, u direction and the circumference was predicted to be -0.82 rad. In experiments this angle was found to be - 0.78 rad (Fenton rt al., 1978), - 0.71 (present study, Table I) and -0.62 rad (Arts cr al., 1982). lngels and co-workers (1971) showed myocardial wall shortening to be maximal approximately perpendicular to the direction of the left anterior interventricular coronary artery, which is also the direction of the epicardial muscle fibers (Streeter and Hanna, 1973). The angle between the fibers in the outer layer (epicardium) and the circumference was found to be - 1.08 rad in the dog (Streeter and Hanna, 1973) and -0.85 rad in the macaque (Ross and Streeter, 1975). From these studies it may be concluded that epicardial fiber orientation is slightly steeper than the principle emar. Ddirection, but this difference in orientation is so small that epicardial fiber shortening is represented quite well by 0.93 em,,<,0. The fibers in the middle of the inner third layer (subendocardium) form an angle of 0.49 rad (Streeter and Hanna, 1973) and 0.40 rad (Ross and Streeter, 3975) with the circumference. The angle between the principal em_ Ddirection as measured and subendocardial fiber orientation is approximately 1.2 rad, which is slightly smaller than the model prediction (1.35 rad). SO the principal e,,, Ddirection, which is perpendicular to the G,,, D direction, is quite close to the fiber orientation in the inner third layer of the left ventricle. resented

PJeasurrmm~

of transmural

dlyerences in dtformarion

During deformation of the wall of the left ventricle, the value of the deformation parameters in a plane in parallel with the outer wall surface generally depends on the distance from the epicardium. Measurement of epicardial deformation is sufficient to describe wall deformation provided that deformation is homogeneous across the wall. With the present measuring setup wall deformation can also be described when the

809

fiber shortening

values of the related deformation variables vary linearly across the wall. However, when these values ‘vary non-linearly across the wall, the needles of the transducers would be forced to bend. This bending does not occur because of the stiffness of the needle. So. non-linear components in the course of deformation across the wall are not detected with the present device. Several findings support the idea that the major part of wall deformation is detected by such a linear approach. If deformation across the wall varies nonlinearly, the values of epicardial minimal and maximal shortening are expected to be different when determined by the needles and the single epicardial coil triplet. This does not seem to occur (Table 2). Fenton and co-investigators (1978) positioned linear arrays of lead spheres in the myocardium of the dog, equidistantly along lines perpendicular to the epicardial surface. During deformation of the heart this array remained aligned in the outer two thirds of the myocardial wall, indicating that bending deformation is relatively small in the major part of the wall of the left ventricle. The significant bending deformation in the inner third layer of the ventricular wall (Fenton el al., 1978) may be caused by the trabecular structures and the papillary muscles. Inaccuracy of the present measuring technique as introduced by inertia of the needles is probably small since during systole the stiffness of the myocardium is increased, thus improving the mechanical contact of the needles with the surrounding tissue. The minor importance of the inertia of the needles is indicated by the short rise time found in the deformation signals (< 16 ms, indicating a frequency response up to at !east 21 Hz).

Epicardinl

estimation

ofjher

shortening

in [he inner

layers

The present results indicate that minimal (emin,.) and maximal shortening at the epicardium (e,,,, ,) can be used to estimate shortening in the inner layers approximately along the fiber direction (eenda), since statistically significant linear relationships were found between emin,Dand ePndo,and between eenda,es, (the value calculated from emor.D and emi_; equation 17) and e endo, both during normoxia and ischemia (Fig. 6). Shortening eendois closely related to the fiber shortening in these layers because of their approximate coincidence of orientation (Fig. 7). The observed relationships between emin,o and epnJo and between indicate that the effect of shear eendo. cs, and eendo between the myocardial layers (e,< and e,,) is relatively small, under the conditions studied. This is in agreement with earlier findings on normoxic hearts (Feigl and Fry, 1964). An estimate of fiber shortening in the inner layers by eendo. es, is advantageous over the use of emin,o, because during normoxia its absolute value is probably close to the actual magnitude of fiber shortening. The model of left ventricular mechanics predicted that fiber shorten-

810

FRITS W. PRWZEN. THEN ARTS. GER J. VAN DER VUSSE and ROBERT S. REXEM*&

ing is approximately wall

(Arts

uniform

across the left ventricular

rf a[., 1979. 1982). In agreement

prediction.

no

significant

difference

with

was

ing

this

observed

between eonJo.pII and 0.93 emal, 0, which is considered be the value of epicardial However.

advantages

of fiber shortening

fiber shortening

in the inner

of the linearized

When shortening found

layers over the use of coefficient

relation

occurred,

to be systematically

although

deviation

from

by

were expected

to

for this discrepancy

is

in the inner- layers the

value

this orientation

change in the magnitude

of

is inac-

ficnJO. A small

causes a considerable

of measured

the

shortening

eynrlv

direction direction.

Improper

For example, layers

in

direction

inner

layers

and

the

principle

directions

of

beforehand.

measurement

the

of devices used for one

of shortening

circumferential

errors,

in the inner

instead

of

ditferent

the

liber

character

of

I and 2).

The present results emphasize that proper alignment of the devices ofa single distance measurement is more critical in the inner than in the outer layers. This is caused by the larger difference

more information

in the

the value of

may cause systematic

the time course (Tables

obtain

about fiber orientation

directions.

be known

results in a significantly

shortening

to

not

alignment

measurements

differences

required

all

will not influence

of emin,” must

mural

are

in

device with respect to the

which is the case when distance is measured in only one

minimal

deformation

surface

the principal shortening parameters c,,,, Dand P,,,, ,,as measured. SO in positioning the measuring devices. the

in the inner layers (Fig. 7). Further investigations, including measurement of fiber orientation and transin

epicardial

of the measuring

axes of the left ventricle

distance

lower than those of eenrlo,esl,

the fiber orientation estimated

ezndo.

the values of eendowere

be equal. A possible explanation that

and a lower

with

the values of these variables

curately

(see above).

of the use of rmi,, (I as an estimate

pen,,,,.es, are a higher correlation intercept

to

of

Orientation

shortening

between

in the former

maximal

fact that, in the inner layers the direction does

direction.

not

coincide

at all

as is approximately

and

layers and by the of maximal

with

the fiber

the case in the outer

layers (Fig. 7).

deformation. Using

ultrasonic

crystals

to measure

changes

in

segment length, changes up to 0.05 mm can be detected (Theroux

er (I/., 1974; Crozatier

means that during

normoxia

ef (I/., 1978). which

shortening

withanabsoluteaccuracyof0.5”,,.

In thepresent

the value of cc.,,,, could be estimated a standard emin. n

error

errorofthe

crystals

the direct

implanted

back of the estimation between

estimation data

assessment

However,

rather

than

preferentially shortening

from

vantageous

be

within

epicardial

used

within

dium and less damage is to be expected

adjacent

tissue

because

influence is dimcult independent method with

1974; Hattori

Using

the large

may not only injure the (Theroux

of function

of damage

These possible disadvantages

parison

in the area, the

the relatively

1 mm zone of myocardium

1974), but also cause impairment remote

is easier

the myocar-

has to be determined. method,

wall

is ad-

The positioning

of transducers

crystals (about 2 mm diameter)

study

of inner

than implantation

transit-time

to

measurements

devices on the epicardium

of which

this

the same animal.

over direct measurements.

ultrasound

in the

quantitative

of three measuring

function

draw-

Therefore,

in several aspects estimation

deformation

ultrasonic

were observed

these three variables.

should in fiber

may be less

with

are recognized,

et al., in more

of blood

vessels. but their

to assess because there is no of sufficient accuracy for com-

the ultrasound

(Theroux

et al.,

er al., 1982). A second advantage

of our

approach

concerns

Shortening

is not measured in one single direction,

in three directions

the

method triangular

which is sufficient

The early decline in shortening artery

occlusion

investigators

after acute coronary

is in agreement

with lindings

(Banka and Helfant,

1976; Crozatier pronounced

measurement. but

to derive shorten-

after

Ed (I/., 1978). The

earlier

onset

of coronary

The variable various

artery

more

cr al.. 1972; Bathe

the inner than the

r( al., 1977).

response of shear to ischemia

by its dependence

the mathematical

model

shear are directly

in the

wall. According

to

(Arts PI al., 1982) chang.es in

related to left ventricular

hence are determined

may be

on fiber shortening

layers of the left ventricular

shortening.

with the idea that

occlusion

more severely by ischemia

layers (Griggs

explained

L’I ul..

and

decline in ecadO._,. emin.D and c,.,,,, than in

layers are affected outer

of other

1974: Theroux

em,,_ (Figs 5 and 8) is in agreement

of eendOfrom e,,,i,, o or eenda,_, is differences

gives qualitative

and

changes

estimation

in the inner layers. Another

that interindividual relation

from erndu,_, with

mean of0.5-l.O”;,,so

in this respect the epicardial than

study

of the mean of 0.7-1.3 “<, and from

withastandard

accurate

is determined

by the transmural

torsion

and

course of fiber

A decrease in fiber shortening

only in the

inner layers will result in an increase of shear (observed in four

out of six experiments).

understood During

This increase can be

from an earlier analysis

cardiac

orientation

contraction

(Arts ef al.. 1979).

the left

handed

of the muscle fibers in the outer

the left ventricular equilibrium

wall causes a torque

with

the opposite

torque

helical layers of

which

is in

caused by the

right handed helical orientation

of the muscle fibers in

the inner

In

torsion inner

layers

occurs layers.

diminishes, outer

in favor When

wall.

contraction

decreases,

the normal

of the outer

the counteraction

layers

torsion,

of that

of the inner to the torque

resulting

decrease

shear may convert six experiments). less ratio

shortening.

in overall

fiber

When shortening

of the

a slight

this increase

In this case, however, shortening

of

decrease in

adding

to a decrease (observed

of circumferential

the

layers

in an increase

despite the presence ofa significant

circumferential

heart.

layers over

of

in two out of

the dimensionto torsion

is

Epicardial

expected control

to decrease state.

which

considerably

with

was indeed

observed.

assessment

respect

of transmural

to the

CONCLUSIOS

As predicted ventricular

by

a mathematical

wall mechanics

during

model normoxia,

of

left

the pre-

sent experimental results show that just before and during acute ischemia epicardial shortening parallel to the direction of minimal shortening is closely related to shortening in the inner layers in a direction close to the fiber direction. Therefore, epicardial minimal and maximal shortening can be used to estimate shortening parallel to the fibers in the outer as well as in the inner layers. Since the triangular measurement (Arts and Reneman, 1980) enables the calculation of shortening in all directions, variations due to differences in orientation of the measuring devices with respect to the circumference

of the

This is a significant measurements.

left ventricle

advantage

are

excluded.

over single distance

Ar~no~~lrdyrmmrs-We are greatly endebted to I. SimonsAchterberg, R. Kruger, Th. van der Nagel and C. Verlaan for their biotechnical assistance and to M. L. Coenen for her help m preparing the manuscript. This investigation was supported by the Foundation for Medical Research (FUNGO), which is subsidized by the Netherlands Organization for the Advancement of Pure Research (ZWO).

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