$346 Journal o f Biomechanics 2006, Vol. 39 (Suppl 1) Oral Presentations

have sacrificed some increase in penile second moment of area to ensure that semen can move through the penis during copulation.

5360 Tu, 12:15-12:30 (P20) A three-dimensional model o f the penis for analysis o f tissue stresses dur ing erect ion

E. Linder-Ganz 1 , A. Gefen 1 , J. Chen 2, D. Elad 1 . 1Department of Biomedical Engineering, Tel Aviv University, Israel, 2Department of Urology, Tel Aviv Medical Center, Israel

Approximately half of the males between the ages of 40-70 years suffer from erectile dysfunction. Since adequate mechanical interactions in the penis are necessary for developing functional erection it is important to analyze me- chanical stresses in the erect penis. Recent publications demonstrated many of the mechanical characteristics of the structural elements of the penis, but the models were limited to the geometry of a two-dimensional cross-section. In this work we developed a three-dimensional model that allowed for structural analysis of normal erection as well as a variety of erectile dysfunction condi- tions. The model was constructed from the Visible Human digital anatomical database and included the skin, deep and superficial fascia, tunica albuginea, corpus cavernosa and the corpus spongiosum. The mechanical properties of each tissue component were extracted from our previous works. Stresses and deformations during penile erection were analyzed by implementing the model into the commercial finite elements solver of Nastran. Penile erection was simulated by simultaneously raising blood pressure in the three corporal bodies and weighing the counteracting tractions by trabecular smooth muscle stretching, which produced effective erectile pressure of 6.3 kPa (-47 mmHg). In a patient with diabetes the collagen-rich tissues (e.g., tunica albuginea and deep fascia) were stiffened by a factor of 3. Simulations of a normal erection, from tumescence to rigidity demonstrated maximal von Mises stresses in the tunica albuginea and deep fascia of 120kPa and 95kPa, respectively. The corresponding stresses in the diabetic patient were 10% and 5% higher, respectively. In the diabetic tunica albuginea and deep fascia larger areas were exposed to maximal stresses. This rise in mechanical stresses, though mild, may further decrease blood perfusion in the penis, which, in turn, may further deteriorate the erectile dysfunction condition.

16.7. Sperm Propulsion 6264 Tu, 14:00-14:30 (P22) Sperm moti l i ty: a re-emphasis on hydrodynamics D. Woolley. Department of Physiology, School of Medical Sciences, University of Bristol, UK

The re-emphasis will deal with two topics: how hydrodynamic factors influence sperm trajectories; and how they might dictate the flagellar oscillation itself. In relation to trajectories, the tendency of spermatozoa to accumulate at surfaces will be explained in terms of sperm-head-geometry in some instances and in terms of flagellar-envelope-geometry in others. This study leads on to explanations of the circular trajectories that sperm often follow at solid or air boundaries. In relation to the more fundamental question of the flagellar oscillation, it will be argued that the direction of new bends alternates because of the automatic alternation in the direction of the thrust applied to the proximal flagellum by the last-formed, propagating bend. This thrust, being applied obliquely to the long axis of the waveform, will constitute a bending stress. The result of this, a passively induced bend, is assumed to trigger an active propagating state in the dyneins - probably by the concomitant inter-doublet shear in the direction of force generation. This scheme is based on an analysis of two-dimensional meander-waves formed in viscous media by an exceptionally long avian sperm flagellum. The critical observation concerning these waves is that subtle irregularities in the frequency can be correlated with irregularities in the direction of the thrust elicited by the last bend. It is shown also that the site of origin of the oscillation can be anywhere on a 9+2 flagellum; there is not a unique 'pacemaker' site. The notion that the flagellar oscillation requires no specialized control system unifies the phenomenon with the oscillations that can be displayed by individual microtubules when they become impeded during translocation over surfaces.

6083 Tu, 14:30-14:45 (P22) The Geometr ic Clutch as a work ing hypothes is for future research C.B. Lindemann. Dept. of Biological Sciences, Oakland University, Rochester, Michigan, USA

The Geometric Clutch hypothesis contends that the forces transverse to the flagellar axis (t-forces) act on the axonemal scaffold to regulate flagellar beating. T-forces develop as the product of the curvature and the accumulated tension or compression on the doublet microtubules. In this respect, t-force is a mediator of self-organizing behavior. It arises from the collective action of the assemblage of dynein motors on the structural components of the axoneme

and, in turn, imparts order to the sequence of activation and deactivation of the dynein. At the switch point of the flagellar beat, the magnitude of the t- force per micron of flagellum is approximately equal to the sum total of dynein force that can be generated per micron of flagellum. This suggests that the t- force could directly overcome the force-producing dynein bridges and terminate their action. However, many questions remain to be answered concerning the behavior of the axonemal scaffold under stress. Little is known of the force bearing capacity of the radial spokes and the central pair projections. The properties of these structures will determine how t-force is distributed within the axoneme. The mechanical and elastic properties of the dynein arms and nexin links need to be better understood in order to determine how they respond to the application of t-force. In the framework of the Geometric Clutch hypothesis these are the issues that are most important to explore if we are to understand how the flagellum works. Supported by N.S.E Grant MCB-0516181.

7186 Tu, 15:30-15:45 (P22) Fluid dynamic models o f f lagel lar and ci l iary beating

L. Fauci 1 , R. Dillon 2, X. Yang 1 . 1Department of Mathematics, Tulane University, New Orleans, LA, USA, 2Department of Mathematics, Washington State University, Pullman, WA, USA

There are no better illustrations of complex fluid-structure interactions than those that occur during the process of reproduction. Mammalian fertilization requires the motility of spermatozoa, muscular contractions of the uterus and oviduct, as well as ciliary beating. Although the patterns of flagellar movement are distinct from those of ciliary movement, and the flagella are typically much longer than cilia, their basic ultrastructure is identical. We present a mechanical model of a eukaryotic axoneme that represents its passive elastic structures, along with a discrete representation of individual dynein molecular motors. This mechanical model is coupled to a viscous, incompressible fluid. The mathematical and computational model is based upon the immersed boundary method - a general method developed to study the interactions of elastic objects with an incompressible fluid. This framework can incorporate a variety of dynein activation models, and the resulting motility behavior can be measured. We will present simulations of flagellar motility in fluids of different viscosities, as well as simulations that demonstrate metachronal coordination of neighboring cilia.

7737 Tu, 15:00-15:15 (P22) Flagel lar axonemes: the moti le machinery o f sperm for the movement in micro-environmental f ield K. Inaba. Shimoda Marine Research Center, University of Tsukuba, Japan

Sperm motility is generated by a highly organized, microtubule-based structure, called the axoneme, which is constructed from approximately 250 proteins. Recent studies have revealed the molecular structures and functions of a number of axonemal components, including the motor molecules, the dyneins, and regulatory substructures, such as radial spoke, central pair, and other accessory structures. The force for flagellar movement is exerted by the sliding of outer-doublet microtubules driven by the molecular motors, the dyneins. Dynein activity is regulated by the radial spoke/central pair apparatus through protein phosphorylation, resulting in flagellar bend propagation. Prior to fertilization, sperm exhibit dramatic motility changes, such as initiation and activation of motility and chemotaxis toward the egg. These changes are triggered by changes in the extracellular ionic environment and substances released from the female reproductive tract or egg. After reception of these extracellular signals by specific ion channels or receptors in the sperm cells, intracellular signals are switched on through tyrosine protein phosphorylation, Ca 2+ , and cyclic nucleotide-dependent pathways. All these signaling molecules are closely arranged in each sperm flagellum, leading to efficient activation of motility.

7922 Tu, 14:45-15:00 (P22) Fluid dynamic models o f f lagel lar and ci l iary beating with viscoelasticity

R. Dillon 1 , Z. Yang 2, L. Fauci 2. 1Department of Mathematics, Washington State University, Pullman, WA, USA, 2Department of Mathematics, Tulane University, New Orleans, LA, USA

The complex fluid-structure interactions that occur during the process of reproduction take place in a fluid environment that includes viscoelasticity. In this talk we present a method for extending an existing immersed boundary model for flagellar and ciliary motion to include this viscoelasticity. We will present simulations of flagellar motility and ciliary motion in this viscoelastic medium.