J Thorac Cardiovasc Surg 2000;119:1053-1077
© 2000 The American Association for Thoracic Surgery
Macro design, structure, and mechanics of the left ventricle
Henry M. Spotnitz, MD*
From Department of Surgery, Columbia University College of Physicians and Surgeons, New York, NY.
This work was supported in part by US Public Health Service grant HL-48109.
Address for reprints: Henry M. Spotnitz, MD, Department of Surgery, Columbia University College of Physicians and Surgeons, 630 West 168th St, New York, NY 10032.
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Introduction
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The functional anatomy of the left ventricle (LV) has been defined by anatomic dissection,
1 light 2,3 and electron microscopy, 4,5 x-ray contrast angiography, 6,7 two-dimensional echocardiography, 8,9 nuclear magnetic resonance (NMR) tagging, 10,11 implanted radiopaque markers, 12,13 sonomicrometry, 11,14,15 and other methods. 16,17 Early in the history of cardiac surgery, interest in functional anatomy was spurred by inconsistent results of valve replacement 18-20 and ventricular aneurysm surgery and by issues in correction of congenital heart disease. Although some inconsistency could be attributed to problems with myocardial protection or technical errors, other problems appeared to reflect incomplete understanding of LV functional anatomy. The importance of papillary muscle function in mitral valve surgery 21-26 and of ventricular size and shape in LV aneurysmectomy 27,28 have been emphasized in subsequent studies.
Maturation of intraoperative two-dimensional echocardiography further focused surgical interest in acute changes in function. The marked, intraoperative decrease in LV ejection fraction after valve replacement for chronic mitral regurgitation 29 spurred study of valve repair and chordal preservation. 21-26 Improving surgical materials, skill, and knowledge have made novel procedures like cardiomyoplasty, 30 LV volume reduction, 31,32 and patch ventriculoplasty 27 feasible, but they also challenge surgical investigators to define related changes in global and regional function.
Physiologic understanding of LV function can facilitate definition of the appropriate role for new procedures and help explain successes and failures. Thus enthusiasm for LV volume reduction has waxed and waned rapidly with little understanding of why the operation succeeded in some patients and failed in others, leaving uncertainty about who is an appropriate candidate for such surgery. Looking ahead, advances in surgical capacity to remodel and rearrange ventricular anatomy and an avalanche of new tools, including skeletal muscle grafts, mechanical assist devices, maze operations, pacing therapies for heart failure, and molecular and laser approaches to myocardial revascularization, will challenge our ability to understand new surgical tools and define their appropriate clinical role. The ability to meet this challenge begins with functional cardiac anatomy.
This review summarizes current understanding of the relation between structure and function of the LV. Some areas in which such knowledge is incomplete and analytic methods are flawed are discussed. Illustration of how current understanding may contribute to further progress in clinical surgery is an underlying goal.
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Technical issues
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The heart has been described as "a complex three-dimensional and fiber-wound structure with mechanical properties that are nonlinear, anisotropic, time varying, and probably spatially inhomogeneous." 33 The LV, the heart’s most structurally complex region, has proven remarkably resistant to analysis of functional anatomy. Studies have generally been based on quantitative histology or dynamic measurements. Quantitative histology requires fixed tissue that accurately reflects conditions in vivo. Proper relation of sample dimensions to three-dimensional LV architecture is also essential. Dynamic studies are compromised by difficulty defining the location of the endocardial surface when that surface buckles and thickens during systole. When resolution is coarse, as in echocardiography, dynamic techniques provide measurements averaged over a slice several millimeters thick. Such data are not directly comparable with histologic sections, which are a fraction of a millimeter in thickness. Markers or gauges that are implanted on a short-term basis may not move properly with surrounding tissues, and long-term implantation results in scarring that can cause tethering artifacts. Both dynamic and static techniques are troubled by complex movement of muscle bundles in three dimensions, which are difficult to envision and measure with two-dimensional techniques. The sum of all these difficulties is uncertainty about critical measurements like LV wall thickness, reported to increase from 20% to 80% 6 during normal systole. One recent study comparing NMR tagging and sonomicrometry reported values between 21% and 43% for LV wall thickening. 11 Given these difficulties, there is a subjective element to selection of material in this review, favoring a unified view of LV functional anatomy, governed by the same rules of solid geometry that apply to other common three-dimensional structures.
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Ventricular geometry and definitions
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The geometry of the normal LV resembles an ellipsoid of revolution (Figs 1-8), 6,7,9,14-16 with its long axis directed from apex to base (Figs 4-7). Short-axis cross sections, perpendicular to the long axis, reveal circular geometry (Figs 1–5). Sections parallel to the long axis (meridional sections) reveal roughly ellipsoidal geometry (Figs 4–8). This concept ignores the presence of the right ventricle, atria, valves, aorta, papillary muscle, trabeculae carneae, and coronary vessels.
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Fig. 1. Cross sections of the human heart at the tip of the mitral valve (75% level) and mid ventricle (50% level). Roughly circular geometry of LV, variable fiber orientation, and irregularities of wall related to papillary muscles and trabeculae are apparent. (Modified from Greenbaum RA, Ho SY, Gibson DG, Becker AE, Anderson RH. Left ventricular fibre architecture in man. Br Heart J 1981;45:248-63. Reproduced with permission from BMJ Publishing Group.)
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Fig. 2. Schematic drawings summarizing angiographic studies of short-axis cross sections from the dog in systole and diastole. Geometry is roughly circular. Normal ejection fraction is associated with systolic wall thickening of 40% to 50%. Exaggerated infolding of the innermost regions of the wall is apparent. Endocardial markers (black circles) are displaced from the inner boundary of the LV in systole by infolding. (Modified from Mitchell JH, Wildenthal K, Mullins CB. Geometric studies of the left ventricle utilizing biplane cinefluorography. Fed Proc 1969;28:1334-43. Reprinted with permission of the Federation of the American Society for Experimental Biology.)
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Fig. 3. Short-axis two-dimensional echocardiograms of normal human LV. Ventricle appears roughly circular, with uniform wall thickness. Normal ejection fraction in these sections is associated with systolic wall thickening of 40% to 50%. (Cabreriza SE, Spotnitz HM, unpublished data.)
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Fig. 4. Upper panel illustrates dimensions of dog LVs weighing roughly 100 g fixed in diastole (left) and systole (right). Systole is associated with a 13% decrease in sarcomere length (SL), a 61% decrease in fixation volume from 52 to 20 mL (V), and a 50% increase in wall thickness (h). Middle panel illustrates hypothesized changes in fiber dimensions, including a 13% decrease in fiber length and a compensatory 13% increase in the cross-sectional area of the fiber (to keep fiber volume constant). A 13% increase in cross section implies a 6% increase in fiber thickness by the geometry of a circle. The lower panel illustrates dimensions calculated for a spherical model with volume and mass similar to the fixed ventricles. The 37% increase in calculated wall thickness of the model and the 15% decrease in midwall circumference (Cm) are similar to measurements in the fixed ventricles. (Spotnitz HM, Sonnenblick EH. Structural conditions in the hypertrophied and failing heart. In: Mason DT, editor. Congestive heart failure. New York: Yorke Medical Books; 1976. p. 13-24.)
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Fig. 5. Ellipsoidal model defines measurement of systolic apical torsion of LV. Torsion displaces the marked point from ED at end-diastole to ES at end-systole. (Modified from Yun KL, Niczyporuk MA, Daughters GT 2d, Ingels NB Jr, Stinson EB, Alderman EL, et al. Alterations in left ventricular diastolic twist mechanics during acute human cardiac allograft rejection. Circulation 1991;83:962-73.)
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Fig. 6. Two-dimensional echocardiograms of canine LV in long-axis (S1A and S2A ) and short-axis (SS) sections. Varying radii of curvature and wall thickness compared with idealized models are apparent. (From Haasler GB, Rodigas PC, Collins RH, Wei J, Meyer FJ, Spotnitz AJ, et al. Two-dimensional echocardiography in dogs: variation of left ventricular mass, geometry, volume, and ejection fraction on cardiopulmonary bypass. J Thorac Cardiovasc Surg 1985;90:430-40. Reprinted with permission of Mosby, Inc.)
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Fig. 7. Definition of LV myocardial fiber orientation for fixed hearts containing silicone rubber casts. A metal pin was inserted in the long-axis orientation shown. The heart was mounted in an anvil with a knife guide that produced circular cuts coincident with the circumferential (0°) plane. A microscope with a rotating stage was used to estimate mean fiber orientation relative to 0°. Fibers with an angle of 60° run obliquely upward to the right. Fibers with an angle of –60° run obliquely downward to the right. APM, Anterior papillary muscle; PPM, posterior papillary muscle.
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Fig. 8. Longitudinal section of cut surface of immature, unfixed LV on the left (A) and corresponding frozen section on the right (B). Variation in wall thickness and radius of curvature is apparent. Smallest radius and thinnest wall are at the apex. A papillary muscle bulge is apparent at midwall on the left. Cleavage planes appear in the frozen section and contribute a characteristic pattern. These cleavage planes are not seen in the fresh ventricle, suggesting that they are created along intercellular boundaries by processing. (Spotnitz WD, Spotnitz HM, unpublished data.)
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In the idealized ellipsoid, cross sections are circular, with uniform wall thickness (Figs 3
and 4). 34 In the real LV, particularly at end-systole, the endocardial surface is irregular (Figs 1–3 and 6) relative to the epicardial surface, including the origin of papillary muscles and trabeculae. 1,6,7-9 There are important variations in both endocardial radius of curvature and wall thickness (Fig 8). Radius (r) and wall thickness (h) appear related, wall thickness being smallest at the apex (Fig 8), where the radius of curvature is also smallest. Mathematically, the relation of radius to wall thickness, r/h, is a determinant of the relation between pressure and afterload, 7,18,19,35,36 as discussed below.
During systole, the ventricle shortens, narrows, twists, and thickens. 6-17,37 Dimensions within the curved surface of the wall change in three principal directions, defined by polar coordinates. 36 The wall thickens radially, in the direction of radii from the long axis to the epicardial surface. Apex to base shortening occurs along meridians, curved lines parallel to the long axis. Shortening around the waist of the ventricle occurs circumferentially, along curved lines in the short-axis plane.
The apex twists relative to the base during systole, and metrics for torsion have been defined (Fig 5). 10,12,13 Measurement/definition of torsion, cleavage plane angles, and myocardial fiber angle are discussed below.
LV structure
The LV wall is composed predominantly of muscle fibers, also containing connective tissue, fat, arteries, veins, nerves, and lymphatics. 38 The general organization of the muscle fibers resembles a ball of twine in a bath of fluid contained by the epicardium and endocardium. 1,2 The fibers are relatively taut in the midwall and epicardial regions and more loosely wound in the endocardial regions, where inward buckling occurs in systole (Fig 2). 6
Coronary arteries and veins course along the epicardial surface; penetrating vessels run perpendicular to the epicardium and carry the blood supply to the deeper layers. Myocardial capillaries run predominantly parallel to the long axis of the myocytes. 39 Vessels connecting myocardial capillaries to the epicardial arteries and veins pass through many muscle layers and are subject to shearing forces during the cardiac cycle. The shear stresses produce discontinuities of flow and increase resistance during systole.
Ultrastructure
Myocardial fibers are composed of cells, elongated structures with central nuclei and branching attachments (Figs 9–11) that allow serial connections to one or more adjacent cells. 4,5,38,40 The cells are composed predominantly of actin and myosin myofilaments organized into sarcomeres, with an alternating pattern of I bands and A bands (Fig 10). 4,5 Sarcomeres, bounded by Z lines, are stacked end to end to form myofibrils, which resemble cables and run parallel to the long axis of the myocyte (Fig 9). 38 Contraction is triggered by calcium entry into the sarcoplasmic reticulum, which induces actin-myosin interaction, adenosine triphosphate hydrolysis, and release of energy. 41 A change in the angle of myosin cross-bridges results in movement of actin and sarcomere shortening, which in turn shortens the length of the cell. 41,42
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Fig. 9. Photomontages assembled from electron micrographs of dog LV. Cells are from control (A), congestive heart failure due to mitral regurgitation (B), and recovery state after successful mitral valve surgery (C). Recovery from failure is associated with recovery of normal sarcomere architecture, but cells remain enlarged and thickened compared with the control state (From Spinale FG, Ishihra K, Zile M, DeFryte G, Crawford FA, Carabello BA. Structural basis for changes in left ventricular function and geometry because of chronic mitral regurgitation and after correction of volume overload. J Thorac Cardiovasc Surg 1993;106:1147-57. Reprinted with permission of Mosby, Inc.)
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Fig. 10. Electron micrograph of adult LV canine myocardium. 4,45 Long axes of several cells cross the figure from left to right. Arrows mark the location of boundaries between adjacent cells. Large open spaces are capillaries perfused with fixative. Alternating band patterns from left to right are sarcomeres, consisting of a wide, dark central A band and a light I band on each end. Each I band is divided into two halves by a central, dark Z-line that defines the end of the sarcomere. Two light lines in the center of each A band are part of the M-L complex. Rounded and/or elongated structures between rows of sarcomeres are mitochondria, sites of oxidative phosphorylation. (From Spotnitz WD, Spotnitz HM, Truccone NJ, Cottrell TS, Gersony W, Malm JR, et al. Relation of ultrastructure to function: sarcomere dimensions, pressure volume curves, and geometry of the intact left ventricle of the immature canine heart. Circ Res 1979;44:679-91. Reprinted with permission of Lippincott Williams & Wilkins.)
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Fig. 11. Schematic illustration of substructure of the connective tissue matrix of the myocardium (From Weber K. Cardiac interstitium in health and disease: the fibrillar collagen network. Reprinted with permission from the American College of Cardiology J Am Coll Cardiol 1989;7:1637-52.)
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In the transverse direction, across the shorter dimensions of the myocyte, the myofilaments are arranged in a precise, repetitive hexagonal array defined by stearic requirements for myosin cross-bridges to interact with active sites on the actin filaments. 43 The cardiac myocyte is believed capable of active contraction only in the direction of the long axis. Dimension changes perpendicular to the long axis of the cell must be passive in nature or, alternatively, must reflect energy stored in elastic elements. 38,44
Mitochondria are also prominent in cardiac cells and are more abundant in cardiac myocytes than in skeletal muscle myocytes (Fig 10). Mitochondria are factories for adenosine phosphorylation. Glycogen particles, an important substrate for anaerobic metabolism, and tubules of the sarcoplasmic reticulum providing calcium transport are visible in high-resolution electron micrographs. 45 Synthesis of myofilaments and synthesis of sarcomeres can also be seen in appropriately selected tissue. 45
The extracellular matrix of the myocardium has a complex and extensive structure of its own, consisting of intricate networks of noncontractile filaments oriented both transversely and parallel to the long axis of cardiac myocytes (Fig 11). Changes in this matrix have been described in LV hypertrophy and failure. 38
Although a great deal is known about the ultrastructure of the myocardium, many issues are incompletely understood, and many structural elements that are believed to exist on the basis of experimental evidence from other sources remain to be defined. Thus the classic Hill model of the contractile element requires parallel elastic components that produce force during diastole and series elastic components that stretch during isovolumic systole. 46 The concept of "myocardial slippage" or "creep" during chronic volume overload, infarction, or stunning requires relaxation of elements of the ventricular wall. 47,48 Also, it is extremely difficult to stretch myocardial sarcomeres beyond 2.3 µm, 4 whereas this is easily achieved in skeletal muscle. The structural correlate of this resistance to stretch is undefined. 44 Finally, the remarkable uniformity of sarcomere length along and across the individual myocyte, as well as in adjacent myocytes (Figs 9 and 10), implies the presence of elastic elements that are not visible in standard electron micrographs. Many of these functions presumably are provided by collagen elastin and other elements of the extracellular matrix (Fig 11). 38,44 Titin filaments, which connect Z lines to M bands, may prove important sources of diastolic forces and structural stability of the sarcomere. 44
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Sarcomere length during the cardiac cycle
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Myosin filaments that form the dark A band in the center of the sarcomere are 1.5-µm long and are not believed to shorten appreciably during systole. The maximum functional length of the myocardial sarcomere under physiologic stretch is about 2.25 µm, and the minimum length allowed by the myosin filaments is about 1.5 µm. 4,5,41 All cardiac function is therefore based on an engine with an effective shortening capacity of only 0.75/2.25 or 33%. In reality, 10% to 20% sarcomere shortening appears to power the heart under all but the most extreme conditions. The sliding filament hypothesis of striated muscle suggests that optimum preload for force generation is 2.0 to 2.2 µm and has been most elegantly supported experimentally in isolated skeletal muscle. In the dog heart, a midwall sarcomere length of 2.2 µm corresponds to a fixation pressure of 10 mm Hg (Fig 12).
Sarcomere lengths in cardiac tissue have been measured by quantitative electron microscopy, by light or laser diffraction techniques, and by optical magnification. 4,5,45,47-53 Diffraction studies require muscle samples in which sarcomeres lie in register across the sample, as in papillary muscles and trabeculae. Quantitative electron microscopy requires carefully fixed tissue and meticulous sectioning of carefully oriented blocks. In dog hearts fixed to represent conditions of normal diastole, sarcomere length is most reproducible at midwall and can be related to fixation pressure (Fig 12). 4 Changes in sarcomere length with filling volume are qualitatively smallest in the epicardial third of the wall, intermediate at midwall, and largest at the endocardial surface (Fig 13). Average LV midwall sarcomere length in hearts fixed by coronary perfusion during systole is 1.81 µm and 2.07 µm in hearts fixed to replicate diastole (Figs 4 and 14). 4 With active contraction, sarcomere length is linearly related to changes in circumference of the fixed LV (Fig 14). 5,47 These data imply that 13% midwall sarcomere shortening is all that is needed to power the normal canine LV through ejection fractions greater than 50% and systolic increases in wall thickness of 30% to 49% (Figs 4 and 19). Preload is currently believed to influence force generation in cardiac muscle through effects on calcium transport, as well as through effects on actin-myosin overlap in the sarcomere. 51 The gradient of sarcomere lengths and strains across the LV wall during changes in volume has been contested on the basis of contradictory data from numerous sources 50 and should be regarded as incompletely defined.
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Fig. 13. Relation of sarcomere length to fixation pressure for three myocardial layers in LV of the dog. The data suggest that a wider range of sarcomere lengths occurs at the inner third than is observed in the outer third, consistent with geometric models of the LV. (From Spotnitz HM, Sonnenblick EH, Spiro D. Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure volume curves of intact left ventricles of the dog and cat. Circ Res 1966;18:49-66. Reprinted with permission of Lippincott Williams & Wilkins.)
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In passively fixed hearts, shortened sarcomeres are difficult to demonstrate (Figs 12 and 13). During systole, the endocardial layers buckle inward (Fig 2). Negative pressure is required to completely empty the LV, and the volume of the arrested LV open to the atmosphere is greater than zero, averaging 12 mL in the dog. 4 Internal stresses in the LV wall appear to keep sarcomeres extended in the absence of electrical activation. The source of these internal stresses resides in part in the complex fiber weave of the ventricular wall, which will now be described.
Fiber angles
Quantitative myocardial histology requires accurate relation of the three-dimensional, orthogonal reference system used to position tissue blocks for sectioning to the polar reference system of the intact ventricle (Fig 7). Ideally, the ventricle is fixed with chamber pressure and volume controlled to reflect the physiologic conditions observed in vivo. Next, the ventricle is mounted in an apparatus facilitating cuts parallel to the circumferential plane. Two such cuts produce a ring of tissue. Two vertical cuts in such a ring produce a roughly rectangular block whose surfaces consist of epicardium, endocardium, two circumferential cuts, and two meridional cuts.
This general method has been used to study the orientation of the LV myocardial fibers. The results can be described in reference to the circumferential plane, which has a fiber angle of zero. 2 Predominant orientation of myocardial fibers varies with wall thickness, and the pattern is reminiscent of multiple concentric layers of hoops (Figs 4 and 15–17). At midwall, halfway between the epicardium and endocardium, the fibers lie in the circumferential plane, aligned with short-axis sections perpendicular to the long axis. In the 10% of wall thickness closest to the endocardial surface, fibers course upward to the right, averaging +60° oblique to the circumferential plane (Figs 15–17). In the 10% of wall thickness closest to the epicardial surface, the fiber angle is downward to the right, averaging –60° oblique to the circumferential plane and overlapping the endocardial fibers at a 120° angle. At the endocardial and epicardial surfaces, fibers are vertical in some areas, parallel to the long axis. All intervening fiber angles are represented, and fiber orientation varies gradually with depth within the wall between the limits described. 2 An observer facing an upright LV with its apex pointed toward the floor and its base toward the ceiling would observe fibers on the epicardial surface coursing obliquely downward and to the right.
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Fig. 15. Serial sections across the LV wall illustrate fiber orientation. The long edge of each section was cut parallel to the circumferential plane as indicated in Fig 7. Sections in the region between deciles 4 and 5 reveal circumferential fiber orientation at an angle of 0° relative to the reference plane. Fiber angle increases gradually in opposite directions in sections approaching the epicardial and endocardial surfaces. Sections close to the surface in this example reveal fiber angles of 90°. (From Streeter DD Jr, Spotnitz HM, Patel DP, Ross J Jr, Sonnenblick EH. Fiber orientation in the canine left ventricle during systole and diastole. Circ Res 1969;24:339-47. Reprinted with permission of Lippincott Williams & Wilkins.)
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Fig. 16. Idealized, three-dimensional segment of the LV wall illustrates mean fiber orientation. The apex-base direction is vertical in this figure, and the horizontal edges of the block are parallel to the circumferential plane. (Data from reference 2.)
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Fig. 17. LV myocardial fiber angles, averaged for 10% increments (deciles) across the wall. Fibers halfway between the endocardium and epicardium are circumferential, at a fiber angle of 0°. Fibers at the endocardial and epicardial surface overlap at a 120° angle and form opposite 60° angles with circumferential midwall fibers. Fiber angles vary gradually between these extremes. More than 60% of fibers lie within ±22° of circumferential orientation. 5 A minimal effect of systolic contraction on the distribution of fiber angles is illustrated and is consistent with a twisting motion of the anterior wall in systole. These hearts were arrested during systole by coronary injection. (From Streeter DD Jr, Spotnitz HM, Patel DP, Ross J Jr, Sonnenblick EH. Fiber orientation in the canine left ventricle during systole and diastole. Circ Res 1969;24:339-47. Reprinted with permission of Lippincott Williams & Wilkins.)
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Fiber angle in systolic contraction
Systole has little effect on the array of fiber angles across the wall, but all angles are decreased by an increment of 10° to 15° that suggests torsion of the entire wall relative to the long axis (Fig 17). 2 The array of force vectors suggests that systolic activation constricts the LV more powerfully circumferentially than in the (meridional) direction of the long axis. Although contraction of fibers oriented 60° toward the apex tends to shorten the LV in the apex-base direction, some force is also exerted in the circumferential direction. 2,54 When all the fiber directions and force vectors in the LV wall are summed, circumferential shortening is favored. Experimentally, systolic contraction narrows the circumference of the LV more than its length. 6,7,14-16,54,55 In the normal LV the long axis/short axis ratio is less than 2:1 at end-diastole and more than 2:1 at end-systole. 6,7,16 In the dog heart, nearly 90% of stroke volume is due to minor axis (circumferential) shortening, and variation of LV shape during the cardiac cycle is a function of end-diastolic volume. 14,15
Fiber angle and physiologic studies
Physiologically, the directions of greatest interest in the LV wall are (1) coincident with principal local fiber direction and (2) perpendicular to it, the "cross-fiber direction." 3,56 Myocardial cells are optimized to shorten along their long axis; this drives systolic contraction. Dimension changes or "strains" coincident with fiber orientation can be understood in terms of sarcomere length, which is physiologic preload. 4,50 Fiber direction must be known to orient sections properly for measurement of sarcomere length.
Fiber shortening and extension parallel to fiber orientation is intuitive and easy to understand. Conversely, shortening in the cross-fiber direction is counterintuitive, difficult to understand, and physiologically very important. The analysis of cross-fiber movement and the anatomic structures that facilitate such movement requires meticulous attention to the proper sectioning planes, and many planes are required. NMR tagging is particularly versatile in tracking strains over a large number of vectors in three-dimensional space. 10,11 However, as will be discussed, myocardial strains are average deformations, so that components both larger and smaller than the mean may be present and go undetected.
Cross-fiber shortening
During systole, LV ejection fraction (50%-70%) and increases in wall thickness (30%-50%) vastly exceed circumferential strains and sarcomere shortening (10%-20%) (Figs 4, 18, and 19). This dimensional divergence reflects an ingenious natural implementation of basic solid geometry. 3 Simple models illustrate what aspects of this are straightforward and where obfuscation and uncertainty remain.
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Fig. 19. Data from x-ray contrast angiograms for diameter and wall thickness in the LV of the normal dog during the cardiac cycle. Wall thickness increases more than 40% during systole, whereas epicardial diameter increases less than 10%. (Modified from Mitchell JH, Wildenthal K, Mullins CB. Geometric studies of the left ventricle utilizing biplane cinefluorography. Fed Proc 1969;28:1334-43. Reprinted with permission of the Federation of the American Society for Experimental Biology.)
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Fig. 18. Calculations based on a spherical model for effect of changing volume on LV dimensions. The left panel demonstrates increasing midwall circumference (Cm), decreasing wall thickness (h), and decreasing area of equatorial myocardial ring (A) as LV volume increases. The right panel indicates calculated changes in fiber distribution. All fibers are assumed perpendicular to the cut surface, presenting as transected cylinders. Diameter and cross-sectional area of the fibers change in accordance with the mean change in cell length (circumference of ventricle). As volume increases and the wall thins, the number of fibers perpendicular to the circumference (Nc) increases and the number aligned across the wall (Nh) decreases, whereas the total number of fibers (Nt) does not change. (From Spotnitz HM, Spotnitz WD, Cottrell TS, Spiro D, Sonnenblick EH. Cellular basis for volume related wall thickness changes in the rat left ventricle. J Mol Cell Cardiol 1974;6:317-31. Reprinted with permission of Academic Press, Ltd.)
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Modeling techniques
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The simplest geometric model is two concentric spheres, one for the endocardial shell and one for the epicardial shell. 3 Dimension changes during the cardiac cycle are symmetrical around the center of mass and can be calculated with a spreadsheet. An alternate model, an ellipsoid of revolution with a 2:1 long axis/short axis relation, is closer to reality. 34 Calculations are relatively simple for an ellipsoid, if it is assumed that wall thickness is uniform and that dimension changes are symmetrical along the long axis and the two principal short-axis diameters. Tapering wall thickness and asymmetric contraction add more complexity than can be handled by simple calculations. The true physiologic situation, in which radius of curvature, sarcomere length, fiber orientation, wall thickness, and electrical activation vary widely with location within the ventricular wall 36 and from moment to moment, require advanced techniques like finite element analysis 57 and powerful supercomputers. Even so, the problem becomes overwhelming if detail is extensive. Geometric, finite element, and multiple compartment elastance models 57 have been defined to analyze the effect on global LV function of addition or resection of normally functioning or akinetic wall segments (Figs 20 and 21).
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Fig. 20. Calculated effects of changing patch size on function, derived from a spherical LV model. The model is assumed to remain spherical regardless of patch size, and the area change of the normal surface is assumed to remain constant, although these idealized conditions cannot be achieved in reality. The calculations indicate that both stroke volume and wall stress increase, while ejection fraction decreases, with increasing patch size. Theoretically, any desired level of stroke volume could be achieved by adding a patch of sufficient size. The limitation, however, is that when wall stress become high enough, afterload mismatch will result and the ventricle will fail. Patch repair LV aneurysmectomy and LV reduction surgery seek to move the LV from right to left in this diagram, reducing wall stress without making stroke volume too small. SV, Stroke volume; LVP, left ventricular pressure; EDV, end-diastolic volume. (From Nicolosi AC, Weng Z-C, Detwiler PW, Spotnitz HM. Simulated left ventricular aneurysm and aneurysm repair in swine. J Thorac Cardiovasc Surg 1990;100:745-55. Reprinted with permission of Mosby, Inc.)
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Fig. 21. Calculated effects of volume reduction on LV function. Resection of normal myocardium increases elastance (Ees), ejection fraction (EF), and diastolic stiffness (K) while LV end-diastolic volume (LV EDV) decreases. Data are based on finite element analysis. (From Dickstein ML, Spotnitz HM, Rose EA, Burkhoff D. Heart reduction surgery: an analysis of the impact on cardiac function. J Thorac Cardiovasc Surg 1997;113:1032-40. Reprinted with permission of Mosby, Inc.)
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Compressibility of the LV wall
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Most LV models postulate that the LV wall is incompressible, so that LV mass and wall volume remain constant during the cardiac cycle. Components of the LV wall that may be compressible under physiologic conditions are primarily the vasculature and lymphatics, which compose less than 10% of LV mass. 39 Experimental data based on large numbers of dynamic sections support the view that LV mass remains constant during the cardiac cycle. 9,14 Reactive hyperemia and myocardial edema can occur suddenly and may produce measurable changes in LV mass over a few minutes. 37,58 These phenomena are not believed to render LV mass susceptible to variation during the cardiac cycle. The discussion that follows assumes that LV wall volume is constant.
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Thick-wall geometry
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In a soap bubble, a 50% decrease in volume requires a 21% decrease in radius and circumference. Because wall thickness is trivial to begin with, changes in thickness are not important. A thick-walled sphere differs qualitatively, because when wall volume is a significant fraction of total volume (wall plus chamber), the mass of the wall becomes an increasing fraction of the whole as chamber volume decreases. Stated another way, as chamber volume decreases, the surface area over which wall volume is distributed diminishes and wall volume must be distributed over a shrinking surface. This requires large increases in wall thickness. 7,14-16,29,37
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Assumptions
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Modeling this behavior incorporates the following characteristics, definitions, and assumptions: The LV wall volume is constant and is numerically similar to chamber volume. LV wall thickness is similar to chamber radius. The volume of the myocardium is roughly equal to its mass (the specific gravity of myocardium is 1.055). Calculations are based on the normal dog LV with a mass of 100 g and LV end-diastolic volume of 50 mL, for comparison with relevant experimental data. In normal human beings, LV end-diastolic volume averages 100 to 125 mL and LV mass averages 150 g. 7,59
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Calculations
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The endocardial radius (Ri) can be calculated simplistically from a 100-mL sphere as 50 = (4/3)(
Ri3). The epicardial radius (Ro) can similarly be calculated from the geometry of a 50(end-diastolic volume) + 100(LV wall) = 150-mL sphere. If the ejection fraction is 60%, end-systolic endocardial radius (Ri) will be given by a 20-mL sphere and end-systolic epicardial radius (Ro) by a 20 + 100 = 120-mL sphere. During systole, the epicardial volume will decrease by 60/100 = 60%, while the chamber volume determining the endocardial radius will decrease by 60/150 = 40%. Corresponding changes in radius and circumference are as follows: epicardial 7%, midwall 15%, and endocardial 26%. 4,8 Calculated wall thickness increases 36%. Any given change in chamber volume will produce a much larger change in radius and circumference at the endocardium than at the midwall and epicardium 4 (Fig 22).
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Fig. 22. Relation between radii and chamber volume calculated for a 100-g spherical model of the LV. Curves are drawn for the endocardial surface, epicardial surface, and midwall. The distance between the epicardial and endocardial curves at any given volume represents wall thickness. Percentage changes in wall thickness are larger than percentage changes in radius for any given increment of volume. Thick-wall geometry requires largest changes in radius at the endocardial surface. Conversely, small dimension changes at the epicardial surface can produce large changes in wall thickness and chamber volume. (From Spotnitz HM, Antunes ML. Effect of aortic and mitral regurgitation on left ventricular structure and function. Adv Card Surg 1991;2:85-116. Reprinted with permission of Mosby, Inc.)
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Thus amplification of 15% fiber shortening to an ejection fraction of 60% and an increase in wall thickness of 36% (Fig 19) results directly from the laws of solid geometry and conservation of mass. These results are essentially unchanged when calculations are based on an ellipsoid of revolution. 34
Solid geometry readily explains how 15% circumferential sarcomere shortening can produce large changes in wall thickness and chamber volume. 3,34 However, other issues are not resolved by modeling or experimental data. In particular, how exactly do dimensional changes in the cross-fiber direction occur? This is discussed further in the next section.
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Mechanisms of wall thickening/cross-fiber thickening
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