Computer simulation of cervical tissue response to a hydraulic dilator device
© Filipovic et al.; licensee BioMed Central Ltd. 2013
Received: 14 June 2013
Accepted: 29 October 2013
Published: 6 November 2013
Classical mechanical dilators for cervical dilation are associated with various complications, such as uterine perforation, cervical laceration, infections and intraperitoneal hemorrhage. A new medical device called continuous controllable balloon dilator (CCBD) was constructed to make a significant reduction in all of the side effects of traditional mechanical dilation.
In this study we investigated numerically the cervical canal tissue response for Hegar and CCBD using our poroelastic finite element model and in-house software development. Boundary conditions for pressure loading on the tissue for both dilators in vivo were measured experimentally. Material properties of the cervical tissue were fitted with experimental in vivo data of pressure and fluid volume or balloon size.
Obtained results for effective stresses inside the cervical tissue clearly showed higher stresses for Hegar dilator during dilation in comparison with our CCBD.
This study opens a new avenue for the implementation of CCBD device instead of mechanical dilators to prevent cervical injury during cervical dilation.
KeywordsCervix dilation Hydraulic balloon dilator Finite element simulation
Cervical dilation is used not only for childbirth but also for diagnostic and therapeutic procedures [1, 2]. Mechanical dilation is characterized by an increase of the cervical diameter until dilation procedure in completed. The use of mechanical dilator induces significant forces, which could damage cervical tissue and affect the fertility [3, 4] or cause complications . Several attempts have been made to reduce the force for cervical dilation by using pharmacological agents, which, however, can cause bleeding and cramping prior to the surgical procedure . In order to avoid damage of cervical tissue, it is important to understand the structure and biomechanical behavior of this complex tissue.
Cervical tissue consists of less than 15% of smooth muscle cells and an extracellular matrix (ECM) rich in collagen . The biomechanical strength of connective tissue is determined by the collagen concentration of collagen types (predominantly types I and III, IV) [7, 8], the proteoglycans decorin and biglycan which affect collagen fibrillogenesis [9, 10], the amount and types of collagen cross-links [11, 12], the orientation of collagen fibers  and the concentration of elastin and water .
While the anatomy of cervical tissue is known, it is important to note that biomechanical models are not widely examined. A nonlinear response of cervical tissue in vivo conditions is observed but not quantified. Ex vivo analysis was used to quantify mechanical properties of the cervix . Several finite element studies with anisotropic visco-hyperelastic of female pelvic modeling were described in [16–18]. To our knowledge, there is no literature data for finite element studies on cervical dilation.
In our previous pilot study  we introduced a continuous controllable balloon dilator (CCBD)  in order to achieve a smoother mechanical cervical dilation, as well as a significant reduction of the side effects observed when traditional mechanical dilation is applied . Also, we presented a unique system of in vivo measurement which can determine the pressure which acts directly on cervical tissue.
In this study we analysed numerically effective wall stress response from cervical tissue and compared the results from traditional Hegar and hydraulic CCBD where boundary conditions for pressure are measured from in vivo patient data. We analysed the cervix as a porous hydrated soft tissue with a simplified geometrical tube deformable model. The innovative part of this study is the comparison of traditional Hegar and hydraulic CCBD using a computational porous model for cervical tissue which we developed.
where terms with m denote the mass matrix, terms with c denote damping, terms with k denote stiffness matrix, terms with f denote force vector for full dynamics system of displacements, pressures and fluid velocities equations. More details about all variables in eq. (1) are given in .
The above equations are further assembled and the resulting FE system of equations is integrated incrementally, with time step Δt, transforming this system into a system of algebraic equations. A Newmark integration method is implemented for the time integration.
We analyzed the dynamic response of cervical canal. An imposed loading pressure on cervical tissue elicits an effective stress. Our model assumes formulation of a small deformation. The corresponding material constants in finite element model are modulus of elasticity E and permeability coefficient k. These material constants were fitted by standard least square method and the obtained values are E = 0.15 MPa , k = 3●10-15 m4/Ns . Geometry model represents a simple cervical canal as a porous tube which is inflated. Boundary conditions are prescribed uniform pressures along the cervical canal tissue for both dilators in the zone of dilator-tissue contact. Time step used for simulation was Δt = 0.1 s which is enough to track dynamical changes during dilation process over 1 minute .
Basic difference between Hegar and CCBD is a total flexibility for CCBD during the opening of the cervical canal. Displacement results clearly show a different radial opening of the cervical canal for Hegar and CCBDs. A very low resistance to penetration for CCBD could reduce damage of cervical tissue. Measurement of the pressure during CCBD process with precise pressure control on the cervical canal gives far more opportunities for future dilation procedure.
Effective stress inside cervical tissue during the dilation procedure in vivo is not possible to be measured. There are some in vitro measurements which investigate separately the cervical tissue sample. Obviously, CCBD induces a continuous radial displacement position with reduced effective stress during the dilation process. Computational simulations can give insight into this complex dilation procedures and open new avenues for implementing the CCBD device in the current medical practice.
This study was funded by a grant from Serbian Ministry of Education, Science and Technological Development III41007.
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