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Cardiovascular Research 2000 47(2):284-293; doi:10.1016/S0008-6363(00)00089-4
© 2000 by European Society of Cardiology
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Copyright © 2000, European Society of Cardiology

Structural basis of regional dysfunction in acutely ischemic myocardium

Reza Mazharia, Jeffrey H Omensa,b, James W Covella,b and Andrew D McCullocha,*

aDepartment of Bioengineering, The Whitaker Institute for Biomedical Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA
bDepartment of Medicine, The Whitaker Institute for Biomedical Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412, USA

* Corresponding author. Tel.: +1-858-534-2547; fax: +1-858-534-6896 amcculloch{at}ucsd.edu

Received 20 December 1999; accepted 4 April 2000


   Abstract
Top
 Abstract
1 Introduction
 2 Methods
 3 Results
 4 Discussion
 References
 
Objective: Impaired systolic function in the normally perfused myocardium adjacent to an ischemic region — the functional border zone — is thought to result from mechanical interactions across the perfusion boundary. We investigated how segment orientation and vessel involved affect regional strains in the functional border zone and whether altered stresses associated with a step transition in contractility can explain the functional border zone. Methods and results: Regional epicardial strain distributions were obtained from measured displacements of radiopaque markers in open-chest anesthetized canines, and related to local myofiber angles and blood flows. The functional border zone for fiber strain was significantly narrower than that for cross-fiber strain and significantly wider for left anterior descending (LAD) than left circumflex (LCx) coronary occlusion (1.23 vs. 0.45 cm). A detailed three-dimensional computational model with a one-to-one relation between perfusion and myofilament activation and no transitional zone of intermediate contractility showed close agreement with these observations and significantly elevated stresses in the border zone. Differences between LAD and LCx occlusions in the model were due to differences in left ventricular systolic pressure and not to differences in perfusion boundary or muscle fiber orientation. The border zone was narrower for fiber strain than cross-fiber strain because systolic stiffness is greatest along the muscle fiber direction. Conclusion: Abnormal regional mechanics in the acute ischemic border arise from increased wall stresses without a transitional zone of intermediate contractility. Perfusion is more tightly coupled to fiber than cross-fiber strain, and a wider functional border zone of fiber strain during LAD than LCx occlusion is primarily due to higher regional wall stresses rather than anatomic variations.

KEYWORDS Regional blood flow; Ventricular function; Contractile function; Hemodynamics


   1 Introduction
Top
 Abstract
 1 Introduction
2 Methods
 3 Results
 4 Discussion
 References
 
It is well known that regional systolic function is impaired in the normally perfused myocardium immediately adjacent to an acutely ischemic region [7]. Estimates of the width of this ‘functional border zone’ in the left ventricular (LV) free wall of dogs and pigs [8,9,17,24,26,29] vary widely with region, segment orientation and vessel involved from less than 2 mm [29] to almost 30 mm [9,17]. The mechanics of the ischemic border has clinical importance because myocardial remodeling and hypertrophy could be affected by altered wall mechanics in the border zone [4], and mechanical heterogeneity may increase dispersion of repolarization via mechanoelectric feedback and provide a substrate for reentrant arrhythmia [6].

Most investigators have concluded that the functional border zone results from mechanical interactions between ischemic and non-ischemic myocardium [26,30]. For example, in their ‘parallel fiber hypothesis’, Wyatt et al. [30] suggested that ischemic muscle fibers adjacent to non-ischemic fibers would impose a greater resistance to shortening when they are in parallel rather than in series across the perfusion boundary [28]. Since epicardial fibers are oriented more tangent to the perfusion boundary of the left anterior descending (LAD) coronary artery than that of the left circumflex (LCx) coronary artery, this hypothesis suggests that the functional border zone for epicardial strain should be wider for LAD than LCx occlusions.

Altered regional wall stress has also been postulated as a mechanism of altered mechanics in the border zone [10]. However, stresses can not be measured directly, and previous mathematical models have been based on highly simplified geometric and material assumptions [2,3]. Therefore, it remains unknown whether mechanical interactions alone are sufficient to explain the mechanics of the border zone and what structural mechanisms govern the regional variations. We hypothesized that a step transition in contractility across the perfusion boundary is sufficient to explain the regional deformations observed in the functional border zone, and that variations in its size could be explained by regional ventricular shape, fiber architecture, and perfusion boundary geometry.

To test these hypotheses, we measured regional epicardial strains in the anterior left ventricular wall of canine hearts and found that the functional border zone of systolic fiber strain is wider than that for cross-fiber strain and narrower for LCx than LAD occlusions. A three-dimensional (3-D) anatomically detailed computational model based on the assumption that there is a one-to-one relation between regional myocardial blood flow and myofilament activation agreed well with the experimental measurements, and showed how variations in ventricular shape and fiber architecture, perfusion boundary geometry and hemodynamics contribute to altered wall stresses in the border zone.


   2 Methods
Top
 Abstract
 1 Introduction
 2 Methods
3 Results
 4 Discussion
 References
 
2.1 Experimental preparation
Animal care and use adhered to guidelines in the Institute of Laboratory Resources Guide for the Care and Use of Laboratory Animals (National Research Council, 1996), and experimental protocols were approved by the University of California, San Diego Animal Subjects Committee. Fourteen mongrel dogs of either sex weighing 19–30 kg were anesthetized with intravenous sodium pentobarbital (30 mg/kg), intubated and ventilated with 100% oxygen.

The heart was exposed by a median sternotomy and lateral thoracotomy, and suspended in a pericardial cradle. The LAD and LCx coronary arteries were isolated distal to the first main and marginal branches, respectively. Ultrasonic blood flow probes (T206, Transonic Systems Inc., Ithaca, NY) were placed around each vessel adjacent to a snare to be used as the occluder. To measure LV pressure (LVP), a fluid-filled catheter was introduced via the right femoral artery and a high fidelity micromanometer (Königsberg P-20) was inserted through the left atrial appendage. Electrocardiogram, all hemodynamic measurements, the first derivative of the LVP, and coronary flows were recorded on a strip chart.

An array of 42 1-mm radiopaque markers was sutured to the anterior LV epicardium so that seven circumferential rows of six markers each spanned the anterior margins of the LAD and LCx perfusion beds [29]. Using biplane fluoroscopy (General Electric DXD-525II) with synchronized video cameras (COHU 4915, San Diego, CA), anterior/posterior and lateral views of the marker motion were recorded for 3–4 s with the respirator turned off at end-expiration onto two Pentium microcomputers (one per view) using video analog-to-digital converters (Data Translation DT3155, Marlboro, MA). Video frame-sync signals were recorded so that frames could be registered to phase of the cardiac cycle.

2.2 Experimental protocol
Video and hemodynamic data were recorded during: (1) control with left ventricular end-diastolic pressure (LVEDP) elevated to 10 mmHg (to match the anticipated value during ischemia), (2) approximately 3 min after occlusion of either the LAD or LCx randomly chosen, (3) after 15–20 min reperfusion, and (4) approximately 3 min after occlusion of the contralateral vessel. Occlusions typically lasted less than 6 min to avoid necrosis and reperfusion injury. LVEDP was adjusted by intravenous infusion of 70% warmed dextran or blood withdrawal. Regional transmural blood flows were measured using 10-µm fluorescent microspheres (Molecular Probes, Eugene, OR) before and 4 min after coronary occlusion [11]. A total 3.3 million microspheres were injected into the left atrium and an arterial reference blood sample was withdrawn from the right femoral artery for 60 s (at 30 ml/min starting 5 s prior to microsphere injection) [21]. At the end of the study, the animal was sacrificed by anesthetic overdose (60 mg/kg). The LAD or LCx coronary artery was cannulated distal to the occlusion site and monastral blue was infused to demarcate the ischemic region.

2.3 Post-mortem measurements
Using techniques described previously [20], LV epicardial geometry, marker locations, major coronary vessel geometry and the sites of occlusion, and the perfusion boundary (demarcated by the blue dye) were acquired with a 3-D digitizing probe (Immersion Corporation, Palo Alto, CA). Epicardial myofiber orientations were recorded with the probe, using the LV long-axis as a reference direction (±90°). A prolate spheroidal finite element model [20,22] was fitted to the epicardial geometric points, fiber angles and regional blood flows values, as described previously [20].

2.4 Strain analysis
Using strain analysis methods described previously [20], the 3-D coordinates of each bead reconstructed from the biplane image pairs were mapped on to the ex vivo model and used to compute epicardial strain distributions. In Mazhari et al. [20] Fig. 9 shows an example of the resulting strain maps. During baseline and ischemia systolic strains were computed from the displacements of the beads between end-diastole and end-systole (determined in time from ECG and LVP recordings). Since changes in these systolic strains during the experiment reflect changes in the end-diastolic configuration as well as the end-systolic state, end-diastolic and end-systolic acute ‘remodeling strains’ were also computed using the changes in bead position from baseline to ischemia at matching phases of the cardiac cycle. We use ‘remodeling strain’ to describe changes in regional 3-D segment geometry at end-systole or end-diastole associated with acute alterations in material properties and loading conditions between baseline and ischemia [20]. Positive end-systolic remodeling strain therefore reflects lengthening of end-systolic segments during ischemia independent of the acute diastolic remodeling which is described by the end-diastolic strain. Strains were then resolved with respect to the measured local fiber axes to obtain strains in fiber and cross-fiber orientations. For each dog, strains were averaged along contours of equal distance d from the perfusion boundary, as described by Mazhari et al. [20]. The resulting strain–distance relationships in turn were averaged across all animals for each perfusion bed.

2.5 Mathematical model of the systolic ventricle
A 3-D finite element model of LV mechanics based on comprehensive measurements of canine geometry and myofiber architecture [22] was used to simulate filling and ejection using the measured mean diastolic and systolic LV pressures. Systolic stresses were computed from the sum of passive and active stresses in fiber coordinates [12]. Active isometric tension was a function of sarcomere length and intracellular calcium concentration [15]. In this model, transverse systolic stresses (Txx) were a function of developed fiber stress (Tff) and fiber and transverse extension ratios ({lambda}f and {lambda}x, respectively) according to Eq. (1), which matches recent biaxial test results of Lin and Yin [18] ({alpha}=0.4):

Formula (1)
To model ischemia, myofiber calcium sensitivity was reduced by increasing the intercellular calcium concentration that results in 50% maximal activation (C50 of Hunter et al. [15]) in the ischemic region from 4.2 to 7.9 µM, with a step transition across the perfusion boundary [1].

2.6 Statistical methods
Analysis of variance was used for statistical analysis, with P<0.05 indicating statistical significance.


   3 Results
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
4 Discussion
 References
 
3.1 Exclusions
Two dogs were excluded because the images did not permit accurate reconstruction of the markers. Another dog was eliminated from analysis due to ventricular fibrillation during the first occlusion. Recordings during the second coronary occlusion were only included subject to three a priori criteria: (1) no ventricular fibrillation occurred; (2) LV systolic pressure recovered to within 25% of control following reperfusion; and (3) mean coronary flows recovered to within 25% of control during reperfusion. Using these criteria, LAD occlusion was first in five dogs and second in two (n=7, LAD group), LCx occlusion was first in six dogs and second in two (n=8, LCx group).

3.2 Hemodynamics
LVSP fell significantly during LCx occlusion (P<0.05), but there was no significant difference between LAD and LCx occlusions (P=0.056). However, the power for this latter difference was low (β=0.23) because the variations between subjects was high (Table 1) and sample was not very large. Mean transmural myocardial blood flow during ischemia relative to baseline varied significantly (P<0.001) with distance from the perfusion boundary (Fig. 1). The mean ratio of regional myocardial blood flow during coronary artery occlusion relative to control was 13% lower during left circumflex occlusion than LAD occlusion (P=NS).


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  		Table 1 Measured hemodynamicsa

 

Figure 1
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  		Fig. 1 Myocardial blood flow (MBF) during left anterior descending (LAD, {square}) and left circumflex (LCx, {circ}) coronary artery occlusions relative to control values, with respect to the distance from the perfusion boundary (d=0 cm). Values are mean±S.D. IS, ischemic; NIS, non-ischemic.

 
3.3 Regional epicardial strains
Acute ischemia resulted in significant changes in fiber and cross-fiber end-systolic strains (P<0.05) in central ischemic, border, non-ischemic, and remote non-ischemic regions (Table 2). While baseline strain was similar in all regions, ischemic zone dysfunction was more severe for LAD than LCx occlusion; non-ischemic zone hyperkinesis was more pronounced during LCx than LAD occlusion. End-diastolic segment lengths did not change significantly from control to coronary artery occlusion (i.e. end-diastolic remodeling strains in fiber and cross-fiber directions were not significantly different from zero) (data not shown here).


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  		Table 2 Mean regional end-systolic strains during control and coronary occlusiona

 
End-systolic remodeling strains (relative end-systolic segment lengths during occlusion to control) varied significantly with distance (P<0.001) for both vascular beds and both strain components (fiber and cross-fiber) (Fig. 2). However, the gradient of both strain components across the perfusion boundary was not different between the two occlusions. At all distances, mean end-systolic remodeling strain was significantly lower (shorter end-systolic segment lengths) during LCx than LAD occlusion both for fiber and cross-fiber components (P<0.001); this indicates less dysfunction in the ischemic zone and more hyperfunction in the non-ischemic region (Fig. 2) during LCx than LAD ischemia.


Figure 2
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  		Fig. 2 End-systolic remodeling strains (mean±S.E.M.) for fiber (A) and cross-fiber (B) segments across the perfusion boundary (d=0 cm). Strains were greater during LAD (n=7) occlusion ({square}) than LCx (n=8) occlusion ({circ}), consistent with a narrower border zone and greater hyperfunction in the non-ischemic (NIS) region during LCx occlusion.

 
The functional border zone — defined as the region between the perfusion boundary and the contours of zero end-systolic remodeling strain (i.e. similar segment length during occlusion and control) (Fig. 2) — was significantly wider (P<0.01) for cross-fiber segments than for fiber segments during both occlusions (Fig. 3). It was also significantly wider (P<0.001) during LAD than LCx occlusion in fiber direction (1.2±0.2 vs. 0.4±0.1 cm), but not for cross-fiber direction (2.3±0.2 vs. 2.2±0.2 cm).


Figure 3
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  		Fig. 3 Width of the functional border zone (FBZ) for fiber (A) and cross-fiber segment function (B) during LAD (filled bars) and LCx (open bars) occlusions at basal (Base), mid-ventricular (Mid), and apical (Apex) region of the anterior wall of the LV; comparison for all regions pooled (All) are shown also (statistical correction was made for repeated measurements).

 
3.4 Computational model
The LV model was passively inflated to 10 mmHg to simulate end-diastole, then activated to contract against systolic pressures of 150 mmHg (control), 130 mmHg (LAD occlusion) or 110 mmHg (LCx occlusion). In good agreement with the experimental observations, end-systolic strain was greater for LAD than LCx occlusion in the ischemic region for fiber (0.141 vs. 0.090) and cross-fiber (0.150 vs. 0.080) segments, and in the non-ischemic region (fiber: –0.012 vs. –0.020, cross-fiber: –0.002 vs. –0.007, LAD vs. LCx, respectively) (Fig. 4, see Table 2 for comparisons to experimental mean values). Also in agreement with the experimental findings, the functional border zone for strains in the fiber direction obtained from the model was wider for LAD than LCx occlusion (1.3 vs. 0.8 cm), and narrower than that for the cross-fiber direction in both regions (LAD: 1.3 vs. 1.8 cm; LCx: 0.8 vs. 2.6) (Fig. 4). Comparison of end-systolic remodeling strains as a function of distance to the experimental values is also shown in Fig. 5 (see Fig. 2 for mean experimental values). Regional fiber stresses were 2.2-fold higher in the ischemic and the border region for both ischemic models compared with control, while cross-fiber stresses were increased 4.7-fold.


Figure 4
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  		Fig. 4 Subepicardial end-systolic strains in the anterior view of the left ventricle from the 3-D computational model for fiber (left panels) and cross-fiber (right panels) during control (top panels), LAD (middle panel) and LCx occlusion (bottom panels). Functional border zone widths (in cm, blue) are also shown along with experimental values (mean±S.E.M., black). Regional fiber orientations (vectors) and perfusion boundaries of each occluded vessel (dashed line) are superimposed on the 3-D geometry.

 

Figure 5
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  		Fig. 5 End-systolic remodeling strains in the fiber direction as a function of distance from the perfusion boundary (d=0 cm), obtained from the models of LAD ({square}) and LCx ({circ}) occlusions with systolic pressures matched to mean experimental values. Compare with corresponding mean experimental relations in Fig. 2A.

 
Since there is a stronger coupling between blood flow and systolic fiber strain than between blood flow and cross-fiber strain [21], we investigated the mechanism behind the difference in border zone size for fiber versus cross-fiber segments by perturbing the level of anisotropy of systolic stress development in the model. Increasing the ratio of cross-fiber to fiber systolic stress (Eq. (1)) from 40 to 55%, decreased the width of the cross-fiber strain border zone (to 1.5 cm for LAD ischemia) and increased the width of the border zone for fiber strain (to 2.3 cm for LAD ischemia).

The ‘parallel fiber hypothesis’ [30] implies that the LAD border zone may be wider than that for LCx occlusions because epicardial myofibers have a greater component parallel to the LAD perfusion boundary. The mean angle between the fiber axis and perfusion boundary axis was 24±21° at the LAD perfusion boundary compared with 47±19° at the left circumflex boundary (P<0.05). To examine the role of perfusion boundary orientation relative to the muscle fiber architecture, we reoriented the perfusion boundary in the model of LAD ischemia from a mean orientation of –60° to –78° without changing the size of the ischemic region. Rather than decreasing the width of the border zone, this actually increased it from 1.3 to 1.6 cm.

Another difference between the models of LAD and LCx occlusion was the systolic blood pressure which was matched to the experimental means (134±21 and 111±41 mmHg, respectively). Increasing systolic LV pressure in the circumflex model to 135 mmHg widened the border zone to 1.4 cm, and decreasing systolic pressure in the LAD model narrowed the border zone to 0.7 cm.

To test the conclusions of these models against the experimental data, we performed a multiple regression on the effects perfusion boundary orientation, regional fiber angle, LV systolic pressure, and relative myocardial blood flow on the measured width of the border zone for fiber strain. Unlike relative myocardial blood flow, perfusion boundary angle, and fiber angle, LV systolic pressure was the only variable that had a significant positive correlation with the width of the functional border zone (P=0.02).


   4 Discussion
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
References
 
During acute coronary artery occlusion, there is a sharp transition in blood flow across the perfusion boundary [13], with correspondingly steep gradients in tissue ATP, creatine phosphate, and lactate [14]. The distribution of wall motion abnormalities, however, does not directly follow the distribution of perfusion. This finding has been confirmed in many studies in anesthetized and conscious animals, though estimates of the width of the functional border zone have varied ten-fold averaging about 1 cm [7–9,17,24,26,29]. Most researchers have attributed the functional border zone to mechanical interactions or ‘tethering’ between normal and ischemic muscle rather than to a transitional region of impaired contractility [7,9,24,26,29], though evidence for this is scant. In an attempt to define these mechanical interactions more precisely some investigators have suggested that wall stress is amplified in the border zone [7,10] and mathematical models of ventricular mechanics support this interpretation [2,3] though these models were too simplified to reproduce many specific details of mechanics observed in the border zone.

In this study, we found that the functional border zone of fiber strain is narrower for LCx than LAD occlusion, but substantially wider for cross-fiber segments than fiber segments. We also found more end-systolic lengthening in the central ischemic region during LAD occlusion than circumflex occlusion; hyperfunction was also seen in the remote non-ischemic region during circumflex occlusion. A sharp step transition in regional myofilament activation across the perfusion boundary was sufficient to explain these observations in a 3-D computational model. Stresses were substantially elevated in the border zone region compared with control. Decreasing systolic anisotropy decreased the width of the cross-fiber segment border zone and increased the width of the fiber segment border zone, indicating that the border zone is narrower for fiber segments because perfusion is more tightly coupled to fiber tension than cross-fiber tension. Increasing the perfusion boundary angle did not decrease the width of the functional border zone but increasing systolic blood pressure did. Thus the differences between the border zones for LCx and LAD occlusion are related more to the differences in regional stresses that result than to anatomic factors.

Gallagher et al. [9], in a preliminary report, also observed a wider border zone of wall thickening during LCx occlusion than during LAD occlusion in open-chest canines. Some workers have suggested that the orientation of the perfusion boundary relative to the local myofiber direction determines the width of the functional border zone [26]. In the ‘parallel fiber hypothesis’ [30], myofibers in the ischemic region may impede the shortening of parallel fibers in the non-ischemic region unlike fibers in series with each other. In our experiments, the mean angle between the perfusion boundary and the epicardial fibers was 23° greater for LAD than LCx ischemia so the parallel fiber hypothesis predicts a wider border for LAD occlusions as observed. However, the myocardium is three-dimensional and fiber orientations vary through the ventricular thickness. Contrary to expectation, making the LAD perfusion boundary more longitudinal in the model actually increased the width of the border zone for fiber strain, rather than decreasing it as predicted by the parallel fiber hypothesis.

There was a difference in mean LV systolic pressures of about 20 mmHg between LAD and LCx occlusions. Although our experimental sample did not have sufficient power to achieve statistical significance, inferior wall ischemia (LCx) has been reported to stimulate vagal afferents preferentially, producing reflex hypotension, whereas anterior wall ischemia produces a reflex sympathetic response and hypertension [19]. In the model simulations, the measured mean difference in systolic pressure was large enough to explain the differences observed in mean regional strains and border zone widths. Using matched systolic pressures in the model essentially eliminated the differences between the two regions. Likewise, Gallagher et al. [10] reported that substantially increasing systolic pressure by aortic constriction widened the functional border zone of systolic radial strain during LCx occlusion. To test this conclusion, we looked for a direct correlation between systolic pressure and border zone width in the experimental measurements. Accounting for the variance due to differences in regional myocardial blood flow, fiber angle, and perfusion boundary geometry, the multiple regression analysis showed that systolic ventricular pressure was the only significant determinant of the width of the fiber strain border zone. These results suggest that hemodynamic rather than anatomic differences between LAD and LCx ischemia are primarily responsible for differences in regional fiber strain distributions during acute ischemia. This conclusion could have important implications for therapeutic interventions after myocardial ischemia. An increase in regional stress may increase the region of ischemic dysfunction and contribute to ventricular dilation and increase in oxygen demand. Therefore, interventions that achieve afterload reduction may help to minimize acute dysfunction and reduce the risk of chronic dilatation.

We also saw that the functional border zone of cross-fiber strain was wider than that of fiber strain. This is consistent with a report by Prinzen et al. [24], who found that systolic area changes were depressed over a wider region than reductions in fiber strain. In contrast, Van Leuven et al. [29] during LCx occlusion in pigs, found no difference in the width of the epicardial border zone comparing circumferential with longitudinal segments. However, strains along those axes get similar contributions from fiber and cross-fiber strains, so this result is not inconsistent. The narrower border zone of fiber strain is consistent with a tighter coupling between local perfusion and fiber function than cross-fiber function, which is also influenced by fiber stress in adjacent regions [21]. To test this hypothesis, we altered the anisotropy of active tension in the model. Recent biaxial tests show that systolic stress in the transverse direction is about 40% of that in the fiber direction [18]. Increasing this ratio decreased the width of the functional border zone for cross-fiber segments and increased it for fiber segments. Therefore, differences in the functional border zone between fiber and cross-fiber strains are associated with the systolic anisotropy of cardiac muscle.

Regional elevation of myocardial stresses in the ischemic and border regions has been shown by previous mathematical models [2,3]. These authors proposed that stress concentration is the main determinant of systolic dysfunction in the border zone region. However, these models were based on simplified geometric and material assumptions and could not reproduce experimentally observed strain distributions. For example, the model of Bogen et al. [2] was an isotropic spherical membrane with a symmetric apical infarct. The thick-walled model of Bovendeerd et al. [3] had more realistic strain distributions, but these authors assumed a gradual transition in contractility across the ischemic boundary. The present model was fully three-dimensional and based on detailed measurements of ventricular geometry, fiber anatomy and perfusion boundaries. This enabled us to investigate systematically the effects of several structural mechanisms thought to affect the interactions between ischemic and non-ischemic myocardium. The simulations showed that no transition zone of intermediate contractility is needed and that stresses are substantially elevated in the ischemic and border zones, especially the transverse stresses.

One limitation of these experiments is that strain was only measured at the epicardium and only on the anterior LV wall. Therefore, caution must be exercised in extrapolating the present conclusions to the whole heart. It is well known that ischemic dysfunction tends to be more severe on the subendocardium. But, when function is resolved with respect to the fiber direction, the flow-function relation was independent of transmural position in a recent study of three-dimensional strains [21]. Recent advances in cardiac MRI and other three-dimensional imaging modalities are improving the ability to map regional strains in patients. Simulations with a fully three-dimensional model suggest that the present conclusions should also apply to three-dimensional measures of regional function. Another possible limitation of these studies was that we measured function only 3 min after coronary ligation. This short duration was chosen to minimize confounding effects of factors that contribute to phenomena such as stunning, which could take place after 10–15 min of ischemia and reperfusion.

For comparison with measured strains, model strains were interpolated at the subepicardium, approximately 1 mm beneath the epicardium, to coincide with the outermost layer of numerical integration points, where the computational solutions should be most accurate. In the anterior wall of the anatomic model (derived from the earlier measurements of Nielsen et al. [22]), fiber angles were approximately –50° on the epicardium compared with approximately –40° at the depth where solutions were computed. Fortuitously, this coincided better with the mean epicardial fiber angles that were measured during the present studies in the LAD and LCx regions (–42±11° and –39±12°, respectively).

Although the computational model included considerable three-dimensional structural detail, it did necessarily include numerous simplifying assumptions, which may have affected our conclusions. Material properties were quasi-static; none of the well-documented length–history dependent properties of myocardium such as viscoelasticty [23], the force–velocity relation or shortening deactivation [27] were included in the constitutive law. Therefore, model comparisons were confined to end-diastole and end-systole, where the time-varying elastance assumption [25] is usually recognized as a reasonably reliable approximation [12], and where inertial effects and ventricular pressure gradients are negligible. Material properties were assumed to be transversely isotropic with respect to the muscle fiber axis, but recent studies suggest that the laminar sheet arrangement of muscle fibers may affect wall thickening and transverse shearing strains during systole [5,16]. Hence, we concentrated on strains in planes parallel to the epicardium. Important structures such as the pericardium, papillary muscles, right ventricle and atria were not modeled. While the model results seemed to agree well with measurements in the open-chest pericardiectomized preparation, it is possible that these omissions would limit applying the present model to myocardial ischemia in vivo.

In summary, we found that the functional border zone of fiber segments is narrower for LCx than LAD occlusion, and narrower than that for cross-fiber segments. A step transition in regional myofilament activation across the perfusion boundary was sufficient to explain these findings in a computational model without the need for a transitional zone of intermediate contractility. We conclude that the functional border zone is caused by increased wall stress arising from mechanical interaction between ischemic and non-ischemic myocardium with a one-to-one relation between regional perfusion and myofilament activation. The functional border zone for strains in the fiber direction is narrower than that for strains in the cross-fiber direction, because of the anisotropy of systolic tension development. And a wider functional border zone of fiber shortening during LAD than LCx occlusion was primarily due to hemodynamic rather than anatomic variations.

Time for primary review 31 days.


   Acknowledgements
 
This work was supported by NIH Grant HL41603 and NSF Grant BES 9634974. Computational modeling was supported in part by the National Biomedical Computation Resource (NIH grant RR08605). R. Mazhari was partially supported by NIH pre-doctoral training grant HL07089. The authors would like to thank Dr. Dale Baker for his assistance with blood chemistry measurements during the experiments. The authors would also like to thank Richard Pavelec, Babak Fazeli for their technical help and expertise.


   References
Top
 Abstract
 1 Introduction
 2 Methods
 3 Results
 4 Discussion
 References
 

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