Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 6669822, 6 pages https://doi.org/10.1155/2021/6669822 Research Article 1 2 2 Pavel Drlík, Vladimír Červenka , and Jan Červenka Central Military Hospital in Prague, Czech Republic Cervenka Consulting s.r.o., Prague, Czech Republic Correspondence should be addressed to Vladimír Červenka; firstname.lastname@example.org Received 5 December 2020; Revised 17 February 2021; Accepted 26 February 2021; Published 15 March 2021 Academic Editor: Qiguo Rong Copyright © 2021 Pavel Drlík et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A pathological disorder of human penile function, known as Peyronie’s disease, is characterized by the formation of plaque particles within the tunica albuginea. The plagues in the shape of rigid plate form in the scars as a result of the imperfect healing process. Due to high stiﬀness, plagues are the source of pain and anomalous deformations during erectile penis function. The authors simulate the biomechanical behavior of the penile structure by a 3D ﬁnite element model. The numerical model is based on the real geometrical shape and the tissue structure with consideration of large nonlinear deformations. The penile erection is modeled by the initial strains imposed on the corpus cavernosa. The stress analysis is performed in a case study of various plague locations. The Peyronie’s syndrome manifested by the penis angular deviation simulated by the analysis is compared with the clinical data. The computational simulations provide a rational explanation for the clinical observations on patients. The objective is to apply the proposed modeling approach for the development and validation of treatment methods based on the application of shock waves. 1. Introduction sidered. In this model, the tunica albuginea was the only lig- ament forming the resisting structure. The corpus cavernosa Peyronie’s disease is characterized by a ﬁbrous rigid scar (pla- was not represented by solid elements but substituted by the que) or indurated area in the tunica albuginea causing penile internal pressure acting inside on the tunica albuginea. Timm pain and penile curvature during erection, reducing the pos- et al.  used a model based on 3D geometry and the internal sibility of intercourse. Physical manifestation includes penile pressure in the corpus cavernosa with the aim to simulate the curvature, hinging, narrowing, shortening, and painful erec- buckling strength of the penis (stability limit). The mechanics tions. Attempts to explain the pathogenesis and etiology of of the Peyronie’s disease and the eﬀect of the ﬁbrotic plague have not been extensively studied by 3D models. this frustrating disease are dated from the 13th century. This disease was named after François de la Peyronie , who The authors of this paper have investigated the question worked on the study of induratio penis plastica, and recom- of the eﬀect of a rigid plague on the behavior of the soft tissue mended therapeutic approaches in the treatment of this dis- structure of the penis. They have developed a 3D structural ease. The etiology of this disease is currently not completely model reﬂecting the real penile structure. The penile anat- understood. Only a few studies have high merit of credibility, omy is quite complex in detail, but only some of its constitu- and the remaining studies had a low level of evidence. ents are relevant for the problem of the Peyronie’s disease The recent advances in biomechanics oﬀer a rational sci- investigated here. The cross-section of the penis in the com- entiﬁc approach to its treatment by the mechanical modeling putational model is shown in Figure 1. It includes the corpus of the erectile process based on the structural analysis. Gefen cavernosa as a driving agent of the erection and the tunica et al.  and Gefen et al.  developed a computational albuginea as a resisting ligament. The skin is just a cover layer model and investigated the stress states of the penis with with a negligible structural eﬀect, and the glans tissue is Peyronie’s plague. Their model was a 2D representation, in needed to provide a pressure closure of the corpus cavernosa. which the stress analysis of the penis cross-section was con- Remaining components of the penis anatomy, such as corpus 2 Applied Bionics and Biomechanics ρ t+Δt Tunica albuginea i ðÞ ðÞ i ðÞ i tþΔt t ðÞ i t S = x τ x , ð2Þ t ij tþΔt mn tþΔt tþΔt i,m j,n Skin Corpus cavernosa i i i i i ðÞ ðÞ ðÞ ðÞ ðÞ tþΔt tþΔt tþΔt tþΔt tþΔt ð3Þ ε = u + u + u u , t ij t i,j t j,i t k,i t k,j t t+Δt where ρ/ ρ is a ratio of material density at the time t and t t+Δt tþΔt tþΔt tþΔt Figure 1: Geometry of the model cross-section. t + Δt, ρ= ρ det ð F Þ; F = x is the defor- t t t ij ij i,j tþΔt mation gradient tensor to a position at the time t; τ is mn tþΔt the Cauchy stress tensor at the time t + Δt; x is the t i,m spongiosum, urethra, artery, veins, and nerves, are omitted in derivative of point coordinates at the time t + Δt to the con- the numerical model since due to a low tissue stiﬀness they tþΔt t+Δt t ﬁguration at the time t; and u = x − x is the i-th ele- are not signiﬁcant for the penis mechanical response. t i i i ment of a vector of displacement increments at the time In the computational model, the erectile function demar- t + Δt. cated by the penis deformation is driven by the volume tþΔt expansion of the corpus cavernosa, considered as a loading R represents the virtual work of the external forces at eﬀect by the imposed initial strain. This approach is diﬀerent the time t + Δt. This formulation assumes incremental load- from the other approaches described in the literature ([2, 3], ing in time intervals Δt. The energetic conjugate quantities of Timm et al. 2008 ). It represents a robust approach and 2nd Piola-Kirchhof and Green-Lagrange strain tensors allows to control the deformation behavior of the model enable to simulate load increments with large translations reﬂecting a real behavior. The numerical simulation was and rotations. made using the commercial software ATENA (Cervenka The boundary conditions are applied as displacement et al. ). constraints ﬁxed on the penile base surface in the axial direc- tion Z. Besides, spring supports representing the reaction of 2. Computational Model the abdominal structure were applied on the base surface in X and Y directions, at 1 N/mm The ﬁnite element model of the penis is illustrated in The loading is applied through imposing the initial Figure 2. The penis length in the placid state is assumed to strain on the volume of the corpus cavernosa (Figure 2) by be 68 mm. The external dimensions of the cross-section are the value 0.7 in the axial direction Z and 0.4 in radial direc- 23:6×17:5mm (width × thickness). The size of each corpus tions X and Y. cavernosa is 9×11:7mm, the thickness of the tunica albugi- The choice of the material model is the result of a nea is 1.2 mm, and the skin on the sides is 1 mm. The dimen- research study in which existing data from the literature were sions are chosen to correspond on average to the real considered. In the ﬁrst attempt, the corpus cavernosa was conditions of the penis anatomy. modeled as a soft material with internal pressure due to the The ﬁnite elements used for the penis body are the qua- blood represented by the initial stress. The model was similar dratic isoparametric brick elements with 20 nodes. For the to Gefen et al.  and Timm et al.  in which the tunica glans, quadratic tetrahedral elements with 10 nodes (each albigunea is inﬂated by the blood pressure from the corpus node is with 3 DOF) were used. These high-order elements cavernosa. However, such a model does not properly reﬂect assume a linear strain distribution within the element, which the mechanical action of the corpus cavernosa, namely, a enables a relatively accurate simulation of real stress and penis deviation due to plague. Therefore, an alternative strain states. In the case of the elastic material, it means a lin- approach was chosen, in which the erectile action is simu- ear stress distribution within the element. The updated lated by the imposed strains on the corpus cavernosa body. Lagrangian approach is used for the modelling of this geo- This allows modeling a penis bending but requires suﬃcient metrically highly nonlinear problem. This means that all stiﬀness of the corpus cavernosa body. The linear elastic coordinates are updated, and all mechanical tensors are material was chosen for all components of the penis structure assembled at time t. The ﬁnite element simulation system with the geometrically nonlinear formulation of Green- ATENA  that was used throughout this study is based Lagrange strains (3) to accommodate large deformations. A on the following governing equations in the weak form over linear elastic material is assumed in this study for all mate- the domain V for the time interval Δt and iteration ðiÞ in the rials. The parameters of the plague are according to Mente nonlinear iterative process: and Lewis . The elastic modulus for the tunica albuginea was experimentally determined by Bitsch et al.  to be about 12 MPa. The list of material parameters used in the study is i i ðÞ ðÞ tþΔt tþΔt t+Δt S ∂ ε dV= R, ð1Þ shown in Table 1. The material properties of the glans are t t ij ij V not signiﬁcant in this analysis, and elastic modulus was assumed to be 10 MPa and Poisson’s ratio 0.4. The elastic properties for the corpus cavernosa are relatively high mainly ðiÞ ðiÞ where S is the 2nd Piola-Kirchoﬀ stress tensor and ε is the due to the adopted initial strain approach, which requires a ij ij Green Lagrange strain tensor at iteration i which take the fol- higher stiﬀness value to recover the expected behavior. These lowing forms: properties should correspond to the average properties of the Applied Bionics and Biomechanics 3 Glans Skin Tunica albuginea Corpus cavernosa Figure 2: Mesh discretization of the penis model. Table 1: Material parameters. 4. Confirmation by Clinical Investigation Material E (MPa) Poison’s ratio (-) The ﬁrst author performed an investigation of the Peyro- Tunica albuginea 12.0 0.4 nie’s symptoms, Drlik , within the research of treatment Corpus cavernosa 10.0 0.0 by the shock waves. The measurement of penis angular deviation due to Peyronie’s disorder was performed on a Skin 0.5 0.4 group of 125 patients. The result of the clinical study is Glans 10.0 0.4 illustrated by the histogram of penile deviations shown in Plague 320.0 0.2 Figure 7. The range of deviation was from 5 to 90 degrees with the mean value at 49.6 degrees and the coeﬃcient of corpus cavernosa in the state of erection and do not consider variation 0.42 indicating a rather high random variability. its detailed complex ﬁbrous-ﬂuid microstructure. Simulation Case A corresponds to the average of the clini- cal data. The results of the simulations are depicted by red marks. In general, the experimental data conﬁrm the 3. Case Study mechanical behavior documented in this study. Of course, This computational study is aimed at simulating the eﬀect of due to the reduced extent of the numerical study limited plagues located within the tunica albuginea. The plaque size to four cases, a wide range of clinical behavior was not cov- was 5 × 20 mm (tangentially × axially) and partially occupied ered. The signiﬁcant variability of deviations observed in the ligament volume. It was positioned at a distance of 10 mm the clinical investigation can be attributed to a large vari- from the penis base. The variety of plague positions in the ability of the parameters, namely, the plague size and loca- radial orientation is indicated in Figure 3. Case 0 is without tion, and material properties of tissues. Furthermore, the plague and serves as a reference to healthy conditions. Case present study does not include a disease stage with the pla- A with two plagues is a frequently observed clinical case. gue extending into the corpus cavernosa, which could fur- Cases B to D are representing diﬀerent plague locations. ther increase the scatter of the results. Figure 4 shows the simulation of the penile deformations of all studied cases in the real scale 1 : 1. Deformations are accompanied by the stress ﬁelds and can be described by 5. Clinical Application Von Mises stresses, typically used for the assessment of the material failure. By comparing Figure 5 (Case 0 normal) Although a conservative therapy, which includes an applica- and Figure 6 (Case A with plague), a plague eﬀect on the tion of Xiapex (clostridial collagenase) and shock pulses stress distribution can be observed. In the normal condition, applied to the scar plagues, developed by the author, is rela- the stress ﬁeld is quite uniform on average 10 MPa. In con- tively highly successful (in about 70-75% of patients), for a trast, with a plague, the stress ﬁeld is irregular with maxima certain group of patients, an improvement is not observed, up to 30 MPa in concentrations, indicating an increase by and a surgery is oﬀered. The surgeries are aimed at the factor 3 within the tunica albuginea. In the plague, the stress adjustment of penis angulation and at the restoring of a sat- reaches the values of more than 50 MPa, indicating a stress isfactory sexual intercourse. It is always necessary to discuss intensity increase factor of about 5. with the patients the course of surgery and potential risks For brevity, a presentation of the detailed results of all involved. The speciﬁc problems associated with this therapy cases is not shown. However, a summary of the results is are penis shortening, erectile and sensitivity malfunctions, given in Table 2, from which general conclusions can be recurrence of angulation, palpable stitches, and often a neces- drawn. The consequences of plague extent and location on sity to perform a circumcision within the surgery. Serious the pathologic deformations are quite evident. The penile complications can arise due to inﬂammatory states and a deviation from the normal state is in the radial direction of development of cavernous scars in the erectile bodies. This the plague location. The more extensive plague size produces can lead to serious malfunctions and an inability of satisfac- a larger deviation and a shorter penis elongation. tory intercourse. 4 Applied Bionics and Biomechanics OA B C D Figure 3: Cases of plague locations in the study. Displacement X (2) [m] (a) (b) –2 –2 Deformation (c) (d) Figure 4: Deformed state of the penis in scale 1 : 1. Von mises stress Sigmav [MPa] 20.0 18.3 16.7 15.0 12.0 9.0 6.0 3.0 0.0 Time: 40.0 Figure 5: Von Mises stress distribution in tunica albuginea in normal condition. Case 0. In this therapy, two classes of surgical methods are recog- erection before a surgical correction, which conﬁrmed the nized. In the ﬁrst method, referred as “shortening,” a resec- simulated predictions shown in Figure 4. Figure 9 shows a tion is applied to the concave side of penis. In the second state after resection before a patch implantation. method, referred as “lengthening,” a plague scar is resected Based on our experience, a 3D model of penis anatomy is and replaced by a patch gained from the patient’s own mus- very supportive and helpful in planning a surgery of the spe- cle. An example of the later method performed by the ﬁrst ciﬁc patient. A mechanical model of penis angular deforma- author in a surgical procedure is illustrated in Figures 8 and tion during the erection and its detail shape and direction 9. Figure 8 shows the deformed penis under the artiﬁcial provides a virtual simulation platform for the planning of Applied Bionics and Biomechanics 5 Von mises stress Sigmav [MPa] 100.0 87.5 75.0 62.5 50.0 37.5 25.0 12.5 0.0 Time: 40.0 Figure 6: Von Mises stress distribution in tunica albuginea with plague. Case A. Table 2: Summary of simulation results. Tip displacement Von Mises (mm) Case Deviation (degree) stress (MPa) Δ Δ Δ x y z 0 0.0 0.0 32.3 0.0 10.0 A 0.0 42.6 24.8 40.2 30.0 B -12.6 6.4 28.7 15.6 17.7 C -12.6 -6.4 28.7 15.6 17.7 D -9.3 -16.3 27.9 20.4 19.5 50 Count = 125 Coefficient of variation = 0.42 (5, 20) (20, 35) (35, 50) (50, 65) (65, 80) (80, 95) Figure 8: Angulation and rotation of penis at artiﬁcial erection before surgical correction (Drlik ). Clinic measurements Simulations Figure 7: Histogram of penis deviation from the clinical research of Drlik . surgery and enables to choose optimal parameters and pre- dict the resulting eﬀects. It supports the important decisions to be made in the planning phase of the therapy. 6. Concluding Remarks The plague occurrence aﬀects the increase in stress and strain intensity. Within the region of tunica albuginea adjacent to the plague, the increase factor of Von Mises stress was 3; in Figure 9: State after resection by “lengthening” method before the plague, it was more than 5. The high stress intensity can patch implantation (Drlik ). be attributed to the pain symptoms of Peyronie’s disease. The high local stress intensity is caused by the signiﬁcant adjusted to reﬂect the clinical observations and the chosen modeling strategy. stiﬀness diﬀerence between the tunica albuginea and the pla- The results can be applied for the treatment of Peyronie’s gue. The material parameters in this study were based on lit- erature data, which are limited in general. The material condition in which the rigidity of the plague is reduced by shock pulses. The eﬀect of changes in mechanical parameters properties of the tunica albuginea and corpus cavernosa were Count (number) 6 Applied Bionics and Biomechanics of the plague induced by the treatment can be rationally  A. Gefen, J. Chen, and D. Elad, “A biomechanical model of Peyronie’s disease,” Journal of Biomechanics, vol. 33, investigated using numerical simulations. pp. 1739–1744, 2000. The numerical simulation presented in this report has a  A. Gefen, D. Elad, and J. Chen, “Biomechanical aspects of potential application in the diagnosis of Peyronie’s disease Peyronie’s disease in development stages and following recon- and similar disorders. The numerical model can reﬂect in structive surgery,” International Journal of Impotence Research, detail the anatomy of the tissue structure with malforma- vol. 14, pp. 389–396, 2002. tions. The graphical visualization can improve understand-  G. W. Timm, S. Elayaperumal, and J. Hegrenes, “Biomechanical ing and communication with patients. The process is not analysis of penile erections: penile buckling behaviour under invasive and well suited for analysis in the diagnosis phase. axial loading and radial compression,” BJU international, Parametric studies can be made to identify the eﬀects of pla- vol. 102, no. 1, pp. 76–84, 2008. gue size and location in speciﬁc situations.  V. Cervenka, L. Jendele, and J. Cervenka, “ATENA program documentation,” Praha, 2019, 2019. Data Availability  P. L. Mente and J. L. Lewis, “Elastic modulus of calciﬁed carti- lage is an order of magnitude less than that of subchondral The data on clinical studies on Peyronie’s disease used to sup- bone,” Journal of Orthopaedic Research, vol. 12, no. 5, port the ﬁndings of this study are available from the ﬁrst pp. 637–647, 1994. author upon request. Please contact: MUDr Pavel Drlík, Cen-  M. Bitsch, B. Kromann-Andersen, J. Schou, and E. Sjontoft, tral Military Hospital in Prague, U Vojenské nemocnice 1200 “The elasticity and tensile strength of the tunica albuginea,” Praha 6-Střešovice, 16200, Czech Republic, email: pavel.drli- Journal of Urology, vol. 143, pp. 642–645, 1990. email@example.com. Data on ATENA numerical models supporting  P. Drlik, Aplikace rázových vln na destrukci biomateriálů, PhD the results of the presented study are available upon request Thesis. CTU Prague, Czech, 2020. from the corresponding author. Please contact: Ing. Vladimir Cervenka, PH.D., Cervenka Consulting s.r.o., Na Hrebenkach 55, 150 00, Praha 5, email: firstname.lastname@example.org. Additional Points Attestation of Investigator Independence/Accountability/First Publication. The authors had full access to all study data, take full responsibility for the accuracy of the data analysis, and have authority over manuscript preparation and decisions to submit the manuscript for publication. The manuscript, including related data, ﬁgures, and tables, has not been previ- ously published and is not under consideration elsewhere. Code Availability. The numerical simulation was performed with the code ATENA, which is owned by the second author. Conflicts of Interest The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper. Authors’ Contributions Pavel Drlik contributed to the conceptualization and experi- mental investigation. Vladimir Cervenka contributed to the formal analysis and writing the original draft. Jan Cervenka contributed to the software development. Acknowledgments The research was funded privately by the authors. References  F. La Peyronie, “Sur quelques obstacles qui s’opposent á l’ejacu- lation naturele de la semence,” Mémoires de l'Académie royale de chirurgie, vol. 1, pp. 425–434, 1743.
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Published: Mar 15, 2021