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Modelling the biomechanics and control of sphincters

Marcel Heldoorn^1,*, Johan L. Van Leeuwen² and Jan Vanderschoot³

¹ Department of Neurosurgery, Leiden University Medical Center (LUMC), Wassenaarseweg 62, PO Box 9604, NL-2300 RC Leiden, The Netherlands,
² Experimental Zoology Group, Wageningen Institute of Animal Sciences (WIAS), Wageningen University, Marijkeweg 40, PO Box 338, NL-6700 AH Wageningen, The Netherlands and
³ Department of Medical Informatics, Leiden University Medical Center (LUMC), Wassenaarseweg 62, PO Box 2086, NL-2301 CB Leiden, The Netherlands

View larger version (9K): [in a new window]   Fig. 1. Diagram of the muscle units used in sphincter models: (A) as in Van Duin et al. (1998, 1999); (B) as in Bastiaanssen et al. (1996a,b); (C) as in Usui and Hirata (1995). CE, contractile element; EE, elastic element; VE, viscous element. Arrows show directions of external forces on the systems.

View larger version (22K): [in a new window]   Fig. 2. Diagram of the model sphincter: a two-dimensional system of point masses. (A) The masses were assumed to be interconnected by tensile elements (with zero cross-sectional area) thought to represent the circularly arranged muscle fibre bundles and the radially oriented connective tissue. (B) Detail of the shaded portion in A. The masses were connected to either four (corner point) or two (mid point) tensile elements, with the exception of the corner point masses on the inner or outer border, which are connected to only three tensile elements. The tensile elements were assumed to have a constant curvature along their length, as determined by the locations of two adjacent corner points and one intermediate mid point. Fluid elements were enclosed by the tensile elements through four corner points and four mid points. The pressure was assumed to be constant in any one element. The motion of the masses was calculated by application of Newton’s second law. The acceleration of each mass was calculated from the forces in the connecting tensile elements (red arrows) and the forces due to the pressure in the adjacent fluid compartments (blue arrows). (C) Mapping of the neurons in the neural network to the muscle elements in the sphincter. The neurons in the neural network (labelled a–j in the upper square) correspond to the muscle elements in the sphincter. The vertical columns of neurons innervate the circular layers of the muscle, starting from the outside, whereas the horizontal rows innervate the radial segments of the muscle, starting at the 09:00 h position and proceeding in a clockwise direction.

View larger version (45K): [in a new window]   Fig. 3. Simulation experiments with the neuromuscular sphincter model. (A–D) The results of the partial activation experiment at various points in time (0, 350, 700 and 1050 ms, respectively); (E) the state of the uniformly activated model at 1050 ms as a control. The normalised network activity is shown in the top row. The normalised active state, the fibre strain, the pressure and the fibre stress in the sphincter are depicted in the subsequent rows. The colours in the graphs represent values indicated by the accompanying colour scales. In the pressure graph, the circular lines represent the muscle fibres, while the radial lines represent passive connective tissue fibres. In the pressure panel, the lumen is coloured, indicating the pressure in the lumen of the sphincter; the lumen has no value for strain, stress or active state.