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Eur J Cardiothorac Surg 2005;28:363-364
© 2005 Elsevier Science NL
Letter to the Editor |
a Department of Biomedical Engineering, Texas A&M University, MS: 3120, College Station, TX 77843-3120, USA
b Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA
Received 21 March 2005; accepted 22 April 2005.
* Corresponding author. Tel.:+1 979 845 5428; fax: 1 979 845 4450. (Email: jccriscione{at}tamu.edu).
Key Words: Cardiac Anatomy • Cardiac Microstructure • Cardiac Mechanics • Computer Modeling • Continuum Mechanics
We read with great interest the three recent review articles on cardiac structure in the February 2005 issue [1–3]. Yet, we were dismayed that there was no direct discussion of the continuum approach advocated by Hunter and Smaill [4], which is used by most biomechanical engineers. It is significant that Lunkenheimer et al. [1] uses syncytium to describe myocardium, because it has the same connotation as continuum. Perhaps Lunkenheimer is suggesting a continuum approach despite some disagreements about LeGrice's work (with Hunter, Smaill and others [5]). Note that much has been done since LeGrice's 1995 article [6–8]. Our measurements support LeGrice's initial finding that the helical myocardial fibers within the ventricular mass are arranged in syncytial fashion and assemble into transmural branching laminar sheets, or myolaminae, but our recent results indicate that the myolaminae are highly discontinuous and thus begin and end many times between the inner wall and the outer wall [8]. No "radial septation of the ventricular wall by connective tissue" is hypothesized in our view, and thus its lack of existence does not invalidate a myolaminar based architecture—a primary criticism levied by Lunkenheimer et al. [1].
Admittedly, the continuum approach is not simple, yet neither is the self-assembly and mechanical behavior of millions of myocytes and their extracellular matrix. There are many ways to convey this concept, but given the Baltimore roots of the first author, consider the words of H.L. Mencken: "For every problem there is one solution that is simple, neat, and wrong." The word ‘wrong’ provides vibrancy, yet the word ‘incomplete’ would be more pertinent for this discussion. It is our contention that the ventricular myocardial band (VMB) hypothesis is, at the very least, incomplete because of its simplicity. At worst, VMB is counterproductive in its intended purpose—to explain cardiac function and guide surgical treatment [9–10].
For those who have tried to do a quantitative, mechanical analysis in 3D space, complexity is expected and simplicity is not considered. An example is the gravitational three-body problem—it is the simplest 3D problem because the two-body problem can be reduced to 2D. This ‘simplest’ problem, however, is notoriously difficult. Although mathematicians such as Euler, Lagrange, Jacobi, and Poincaré have tried to solve it, the gravitational three-body problem can only be simulated or modeled. Fortunately for Newton, he had two-body systems, because when even just one corruptor is introduced (i.e. one more body) a simulation is necessary to verify Newton's law of gravitation.
In cardiac mechanics, there are many corruptors or complexities—e.g. heterogeneous tissue properties, heterogeneous activation, anisotropic behavior, mechano-electric feedback, variable preload, variable afterload and variable heart rate. This list is larger; and so, like the gravitational three-body problem, a simulation or model is necessary to verify the mechanics of our hypotheses on heart development, growth and remodeling, filling, synergy and timing of contraction, twisting, etcetera. As our knowledge of cell growth, fiber structure, and electrical propagation improve, our models will become better representative and more enlightening.
In our opinion, the most useful approach to defining cardiac structure and function is a continuum approach because the laws of dynamics can be satisfied forthwith. It is indisputable that the heart must satisfy the basic balance law for linear moment: F=ma (where F is the sum of the forces, m is the mass, and a is the acceleration of the centroid). Although, less well known (but more important because it is a stricter condition), all subregions of the heart must also satisfy the balance law for linear moment. Pointwise, this law is expressed as: div(T)=
a (where div(T) is the divergence of the stress tensor, is the density, and a is the acceleration). Toward satisfying the laws of dynamics for subregions or elements, solution procedures for complicated geometrical bodies have been developed (e.g. finite element analysis). Moreover, electrical wave propagation, excitation–contraction coupling, mechano-electric feedback, and growth and remodeling laws are quantifiable within continuum models.
As a caveat, we are not saying that models should be trusted outright. Like statistics and statisticians, one must be skeptical of models and their makers. Models have the potential to lead reasoning, and they have the potential to mislead it as well.
Nevertheless, for all theories of heart function the laws of dynamics must be satisfied. Currently, a finite element model is the only approach that we know of to verify whether or not the laws of dynamics are satisfied for the VMB ‘systolic filling’ hypothesis [2,3], and we suspect that this hypothesis violates the laws of dynamics. We disagree with the statement in [3], "Analysis of Fig. 8 shows that Torrent-Guasp's concept of systolic ventricular filling is fully supported by this sonomicrometer data, as the ascending segment continues to shorten 
90ms after shortening stops in the descending segment". A careful inspection of the data in Fig. 8 of [3] reveals that most (80%) of the shortening of the ascending segment occurs during ejection, and the remaining 20% of shortening likely occurs before LVP falls below LAP. If the heart has not yet started filling at the end of the ascending segment contraction, how can the idea of systolic filling (via anterior segment contraction) be fully supported by these sonomicrometer data? LAP is not graphed, but it is our reading of the presented data that ascending contraction is overwhelmingly associated with ejection, isovolumic relaxation slightly, and early filling hardly at all.
A simple, elegant solution or mechanism is attractive, but it would be prudent to first know the complexities before they are excluded in a pursuit of heuristic simplification. The danger of accepting an incomplete fallacy is that a more complicated truth might not be sought. In this regard, note that the statement "The ancient enigma of myocardial architecture is finally solved" from Torrent-Guasp et al. [2] is troubling because it seeks to finalize or quench our search for deeper understanding. We are just beginning our quest for understanding cardiac structure—a quest that should eventually yield the processes responsible for cardiac development, function, growth and remodeling.
References
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  S. H. Gilbert, A. P. Benson, P. Li, and A. V. Holden Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure Eur. J. Cardiothorac. Surg., August 1, 2007; 32(2): 231 - 249. [Abstract] [Full Text] [PDF]
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F. Dorri, P. F. Niederer, K. Redmann, P. P. Lunkenheimer, C. W. Cryer, and R. H. Anderson An analysis of the spatial arrangement of the myocardial aggregates making up the wall of the left ventricle Eur. J. Cardiothorac. Surg., March 1, 2007; 31(3): 430 - 437. [Abstract] [Full Text] [PDF]
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 H. Ashikaga, B. A. Coppola, B. Hopenfeld, E. S. Leifer, E. R. McVeigh, and J. H. Omens Transmural Dispersion of Myofiber Mechanics: Implications for Electrical Heterogeneity In Vivo J. Am. Coll. Cardiol., February 27, 2007; 49(8): 909 - 916. [Abstract] [Full Text] [PDF]
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P. P. Sengupta, J. Korinek, M. Belohlavek, J. Narula, M. A. Vannan, A. Jahangir, and B. K. Khandheria Left Ventricular Structure and Function: Basic Science for Cardiac Imaging J. Am. Coll. Cardiol., November 21, 2006; 48(10): 1988 - 2001. [Abstract] [Full Text] [PDF]
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M. J. Kocica, A. F. Corno, F. Carreras-Costa, M. Ballester-Rodes, M. C. Moghbel, C. N.C. Cueva, V. Lackovic, V. I. Kanjuh, and F. Torrent-Guasp The helical ventricular myocardial band: global, three-dimensional, functional architecture of the ventricular myocardium Eur. J. Cardiothorac. Surg., April 1, 2006; 29(Suppl_1): S21 - S40. [Abstract] [Full Text] [PDF]
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R. H. Anderson, S. Y. Ho, K. Redmann, D. Sanchez-Quintana, and P. P. Lunkenheimer The anatomical arrangement of the myocardial cells making up the ventricular mass Eur. J. Cardiothorac. Surg., October 1, 2005; 28(4): 517 - 525. [Abstract] [Full Text] [PDF]
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