Numerical simulation of the damage evolution in the pelvic floor muscles during childbirth
Introduction
Childbirth-related pelvic floor damage is an issue that has been much studied mainly due to the dysfunctions that can arise from childbirth-related traumas, such as urinary and/or anal incontinence, and pelvic organ prolapse (Goldberg, 2007, Heit et al., 2001). These are very debilitating conditions, affecting approximately 50% of women older than 50 years (Wilson et al., 2001). In this sense, the fear of developing some type of dysfunction leads pregnant women to choose Cesarean section, which appears to protect against it (Tegerstedt et al., 2006). Childbirth-related pelvic floor damage is a fact, however, it remains necessary to understand if this type of trauma is common or severe enough to require a change in clinical practice, since, there are nulliparous with pelvic floor dysfunction (PFD) (Rortveit et al., 2001) and women who delivered vaginally without it (DeLancey et al., 2003).
During childbirth, the pelvic floor muscles (PFM), specially the puborectalis-pubococcygeus complex, can stretch beyond a permissible length, damaging mechanically and nervously (Li et al., 2009). Since vaginal delivery is one of the main risk factors for the development of PFD (Goldberg et al., 2005, Hendrix et al., 2002, Peyrat et al., 2002), further research is needed concerning the contribution of vaginal delivery to the PFM damage.
As in vivo experimental work cannot be performed due to clinical, technical and ethical reasons, biomechanical models have been applied to estimate the mechanical changes on PFM during delivery (Hoyte et al., 2008, Noritomi et al., 2013, Parente et al., 2008), analyze the fetus descent (Buttin et al., 2013) and also the effect of the fetal head molding on the PFM mechanical behavior (Silva et al., 2015a). The purpose of this work is to simulate a vaginal delivery and study its influence on the pelvic floor damage. Therefore, the PFM were modeled using a material model that describes the mechanical behavior in the failure region. Studying damage mechanics will contribute to determine the conditions for the initiation of the first damage event, predict its evolution, characterize, quantify and analyze its effect on material response. However, convergence issues often accompany such simulations, caused by the strain-softening and loss of strong ellipticity phenomena that occurs at the onset of damage (Bažant and Jirásek, 2002). To regularize the localization problems, Arc-Length, Newton-Raphson and Stabilization methods are used as common static methods within the finite element tools (Taylor et al., 2015).
The overall goal of this paper is to better understand the mechanisms of birth-related injuries, comprehending the nature and cause of PFD. To further improve the clinical practice, enhancing women׳s health and lifestyle and reducing medical costs.
Section snippets
Material model
The material model used in this work encompasses the quasi-incompressible transversely isotropic hyperelastic constitutive model previously used by (Parente et al., 2008) and the directional damage model proposed by (Calvo et al., 2007). The constitutive equation defines the strain energy density function per unit volume of the reference configuration,
is the strain energy stored in the isotropic matrix embedding the muscle fibers, defined as:
Damage model evaluation
To evaluate the damage model adopted, a numerical simulation of a thin perforated plate subjected to cyclic stretching along its longitudinal axis was performed (Calvo et al., 2007). A periodic triangular displacement profile was used to cycle the specimens between a tensile and compressive strain at a strain rate of (1), (2) and (3) for the uniaxial test (Fig. 1) and for the biaxial test (Fig. 2). The uniaxial and biaxial tests lasted for and , respectively. In
Establishment of the material and damage parameters
Mechanical data from PFM were analyzed to validate the model (Nagle et al., 2014). To identify the material and damage parameters, the constitutive model was fit to the experimental data using the fmincon function from MATLAB® (MathWorks, Inc., Natick, MA, USA). To analyze the effectiveness of the adjustment, the coefficient of determination () (12) and the root mean square error () (13) values were calculated.
Damage parameters have
Conclusions
Vaginal delivery is a known risk factor for the development of PFD. Although these disorders become apparent only years later, birth-related injuries may occur immediately during the second stage of labor. The computational model presented in this work envisages that in a normal vaginal delivery occur tear of more than 10% of muscle fibers. That is, even an apparently uneventful delivery inflicts injuries to the PFM due to the large deformations to which they are subject in order to allow the
Conflict of interest statement
The authors declare that there is no financial, professional or other personal interest of any nature or kind in any product, service and/or company that could be constructed as influencing the position.
Acknowledgments
Funding for this work was provided by Fundação para a Ciência e a Tecnologia, Portugal Grants SFRH/BD/80110/2011 and IF/00159/2014, and research project UID/EMS/50022/2013.
References (32)
- et al.
Biomechanical simulation of the fetal descent without imposed theoretical trajectory
Comput. Methods Programs Biomed.
(2013) - et al.
Biological variability in biomechanical engineering research: Significance and meta-analysis of current modeling practices
J. Biomech.
(2014) - et al.
The appearance of levator ani muscle abnormalities in magnetic resonance images after vaginal delivery
Obstet. Gynecol.
(2003) - et al.
Delivery mode is a major environmental determinant of stress urinary incontinence: results of the Evanston-Northwestern Twin Sisters Study
Am. J. Obstet. Gynecol.
(2005) - et al.
Pelvic organ prolapse in the Women׳s Health Initiative: gravity and gravidity
Am. J. Obstet. Gynecol.
(2002) - et al.
Quantity and distribution of levator ani stretch during simulated vaginal childbirth
Am. J. Obstet. Gynecol.
(2008) - et al.
Passive biomechanical properties of human cadaveric levator ani muscle at low strains
J. Biomech.
(2014) - et al.
Virtual Modeling of a Female Pelvic Floor and Hypothesis for Simulating Biomechanical Behavior During Natural Delivery
Procedia CIRP
(2013) - et al.
The influence of the material properties on the biomechanical behavior of the pelvic floor muscles during vaginal delivery
J. Biomech.
(2009) - et al.
Computational modeling approach to study the effects of fetal head flexion during vaginal delivery
Am. J. Obstet. Gynecol.
(2010)