Structural Model of Penile Erection

Amit Gefen1, Chen1,2, David Elad1

1 Tel Aviv University and 2 Tel Aviv Sourasky Medical Center

Erectile dysfunction (ED) is defined as the inability to achieve and maintain an erection adequate for satisfactory intercourse. It is a common problem among approximately 50% of men between the ages of 40 and 70, which is stressful to both the affected individual and his partner. Biomechanical models provide tools to study the structural factors involved in normal and pathological erectile conditions. A realistic structural model that considers the different tissue components of the penis (e.g., tunica albuginea, skin, dorsal blood vessels and the urethral channel) is shown in Fig. 1. The symmetrical two-dimensional (2D) geometry of the model was extracted from an anatomical schematic section through the middle of the penis and scaled to conform to averaged dimensions. The model was solved for the internal stress distribution within its different tissue components during erection by using commercial finite element software.

The boundary conditions included 4 constraints on the lateral and dorsal-plantar aspects of the penis, allowing its expansion as a result of inflation by an equivalent erectile pressure Ρe = Ρa- σcc. The erectile pressure, Ρe, reflected the resistance stress σcc of the spongy corpus cavernosa tissue to inflation pressure Ρa = 100 mmHg caused by arterial blood flow into the cavities of the penis. As the penis becomes erect, blood is supplied to the corpus cavernosa until the full erection corporal volume reaches VE which is the total corporal capacity (TCC). When blood drains and the penis becomes flaccid, the corporal volume reduces up to VF = 35% TCC. Assuming that the corpus cavernosal tissue is unstressed at VF, the characteristic stretch ratio λmax from flaccid to full erection is given by the generally accepted relationship λ= (VE/VF)1/3 and equals 1.42. It is further assumed that the mechanical characteristics of the corpus cavernosal tissue is similar to those of the lung parenchyma, hence, σcc=7 KPa at λmax=1.42. The penile soft tissues were assumed to be homogenous, isotropic, and linear elastic materials.

The simulation of stress distribution in the normal penis indicated that most of the load bearing during inflation is carried by the dorsal part of the tunica albuginea, where stresses are in the range of 5-30 KPa (Fig. 1b). Since this site contains several nerves, it is most vulnerable to intensified mechanical stresses. The skin appeared to bear a negligible load. Inflation of the neutral, elliptical cross-sectional shape of the cavernosum during erection yielded a more circular corporal profile as well as lateral expansion of the cross-sectional shape of the penis (Fig. 1). This modeling approach allows simulation of stress distributions in various pathologic conditions of the penis (e.g., diabetes, Peyronie’s disease) by altering the geometry and material properties of its components.

References

  1. Gefen A, Chen J, Elad D. Stresses in the normal and diabetic human penis following implantation of an inflatable prosthesis. Medical & Biological Engineering & Computing, 37: 625-631, 1999.
  2. Gefen A, Chen J, Elad D. Optimization of design and surgical positioning of inflatable penile prostheses. Annals of Biomedical Engineering, 28: 619-628, 2000.
  3. Gefen A, Chen J, Elad D. A biomechanical model of Peyronie’s disease. Journal of Biomechanics, 30: 1739-1744, 2000.
  4. Gefen A, Chen J, Elad D. Computational tools in rehabilitation of erectile dysfunction. Medical Engineering & Physics, 23: 42-55, 2001.

Figure 1. The normal penis model: (a) anatomical scheme, (b) the cross-sectional geometry of the model, (c) the finite elements mesh, (d) the distribution of von Mises stresses during simulation of full erection. The indices MX and MN mark the locations of the maximal and minimal stress values, respectively.