title: Biomechanical analysis of penile erections: penile buckling behaviour under axial loading and radial compression.
abstract: OBJECTIVE
  To characterize the biomechanics of erectile function, as contrary reports have modelled the penis as an isotropic material and state that only axial buckling tests can effectively predict penile rigidity; that assumption is questioned and an alternative structure proposed and validated.
  
  
  METHODS
  Three experimental physical cylindrical models of diameters 1.9, 2.54 and 3.81 cm were fabricated and the relationship between axial loading and radial compression was measured for cylindrical pressures of 8-20 kPa. A finite element analysis (FEA) computer model of the penis was constructed to simulate the response of the corpora cavernosa to axial and radial loading for differing diameters and lengths of the penile shaft. The stresses developed in the tunica albuginea of the corporal bodies of the penis during buckling were assessed using a mathematical analysis.
  
  
  RESULTS
  From the analysis of surface stresses under variable axial loading, as the angle of an applied load changes on an isotropic shaft, the magnitude of surface stresses varies up to 50 kPa, and for a pressure vessel the magnitude of surface stresses varies up to 100 kPa. The FEA model showed that nodal displacements were greatest around a ring under radial compression, and for the axially loaded model displacements were greatest at the vessel tip under the force gauge. All displacements were 0.1-1.0 mm. There was an exponential relationship between internal pressure and the axial force required to cause buckling in a thin-walled pressure vessel. There was a nearly constant relationship between circumferential displacement and internal pressure under uniform radial compression. The displacement values on the FEA analysis were approximately equal outside of the areas of high stress which were under the load of the external device (compressive ring or force gauge) in both cases. Physical modelling shows that when a pressurized vessel is under either axial or radial load the internal pressure increases. Vessels at high internal pressure require more force to cause buckling than vessels at lower internal pressure. The circumferential displacement of a vessel under radial compression is higher in vessels of lower internal pressure and less in vessels of high internal pressure. The size of a vessel also contributes to its ability to be buckled. Smaller vessels buckle under smaller load, but the ratio of force required to buckle vs. diameter of the cylinder remained constant.
  
  
  CONCLUSIONS
  The computer simulations show that with slight deviations from perfectly aligned axial loading the stresses felt on the walls of cylindrical columns vary considerably, whether they are isotropic beams or pressurized vessels. The material properties of the tissues within the corpora cause it to behave as a thin-walled pressurized vessel, in which the hoop stress and axial stress have a constant relationship independent of the length to diameter ratio rather than as an isotropic beam where this relationship varies. Patient discomfort and high operator dependency further contribute to the inconsistencies of axial loading methods to determine penile buckling. Based on the constant relationship between hoop stress and axial stress in thin-walled pressurized vessels this study confirms the validity and desirability of using radial compression methods to assess penile rigidity in lieu of axial loading methods.
authors.affiliation: Department of Urologic Surgery, University of Minnesota, Minneapolis, MN, USA. timmx025@tc.umn.edu
authors.forename: Gerald W
authors.initials: GW
authors.lastname: Timm
authors.forename: Santhi
authors.initials: S
authors.lastname: Elayaperumal
authors.forename: Jami
authors.initials: J
authors.lastname: Hegrenes
mesh_terms: D001696:Biomechanical Phenomena / Q000295:instrumentation; D003198:Computer Simulation; D003950:Diagnostic Techniques, Urological / Q000295:instrumentation*; D006801:Humans; D018783:Impotence, Vasculogenic / Q000175:diagnosis* / Q000503:physiopathology; D008297:Male; D010410:Penile Erection / Q000502:physiology*; D010413:Penis / Q000098:blood supply* / Q000503:physiopathology