maps – to morphologists, and provide them with somedata they could compare to their own. The correspon-dence with microdissected specimens is almost direct forthe sub-epicardial fibres, which have been well studiedand illustrated by Anderson et al. (1980), Greenbaum etal. (1981), and Fernandez-Teran and Hurle (1982). Forexample, there is a striking resemblance between themaps of the diaphragmatic face of the heart (Fig. 3 bot-tom) and the images provided by these authors. For thedeepest fibres, the correspondence is indirect, but oncethe full significance of fibre elevation and azimuth hasbecome clear, the pictures are mostly self-explanatory,and provide new insights into some of the more compli-cated areas of the ventricular mass.

The second aim was to give an account of the overallarchitecture of the fibres in the fetal heart at mid gesta-tion. Our studies show that the “flattened-rope analogy”of Torrent-Guasp (1975) and Streeter (1979) is inade-quate to describe the fibre architecture at this develop-

mental period. The inconsistencies of this model have al-ready been discussed by Lunkenheimer et al. (1997).But, at least during the fetal period, one major inconsis-tency obliges us to discard it. In this model, the purport-edly continuous band stretched between the two outflowtracts is said to follow a preferential pathway that, at thelevel of the base of the diaphragmatic face of the ventric-ular mass, is located between the fibres of the right ven-tricle and the left ventricle (Fig. 1B). This is not the pref-erential pathway observed in our study, where the latitu-dinal fibres of the diaphragmatic face of the right ventri-cle merge preferentially with the latitudinal fibres of theseptum.

The description of the ventricular mass based on lay-ers is less inadequate than the “flattened rope analogy”,but it, too, gives an excessive simplification of the fibrearchitecture. This is mostly because, as shown in our re-sults, the fibres of the ventricular walls and the septumrun constantly from one layer to the other. The azimuth

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Fig. 9 Schematic descriptionof the fibre architecture of thewhole ventricular mass. Thelines in green symbolize thegeodesic trajectories of the fibres on the nested “pretzels”.Wedges have been cut out ofthe right and left ventricularwalls, in order to show the innermost hulls

peskincs

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Numerical Solution of the Fiber Architecture Equations of the Aortic Valve David M. McQueen and Charles S. Peskin

peskincs

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Numerical Solution of the Fiber Architecture Equations of the Aortic Valve. David M. McQueen & Charles S. Peskin

Detailsareinthefollowingpapers:Peskin CS and McQueen DM: Mechanical equilibrium determines the fractal fiber architecture of the aortic heart valve leaflets. American Journal of Physiology 266: H319-H328, 1994 http://ajpheart.physiology.org/content/266/1/H319 Stern JV and Peskin CS: Fractal dimension of an aortic heart valve leaflet. Fractals - Complex Geometry Patterns and Scaling in Nature and Society 2(3): 461-464, 1994 http://dx.doi.org/10.1142/S0218348X9400065X Peskin CS: Fiber architecture of the left ventricular wall: an asymptotic analysis. Communications on Pure and Applied Mathematics 42: 79-113, 1989 http://dx.doi.org/10.1002/cpa.3160420106