Numerical simulation of breast reduction with a new knitting condition

Abstract

Breast reduction is one of the most common procedures in breast surgery. The aim of this work is to develop a computational model allowing one to forecast the final breast geometry according to the incision marking parameters. This model can be used in surgery simulators that provide preoperative planning and training, allowing the study of the origin of the errors in breast reduction. From the mathematical point of view, this is a problem of calculus of variations with unusual boundary conditions, known as knitting conditions. The breast tissue is considered as a hyperelastic material, discretized with three-dimensional finite elements for the body, whereas the skin is modelled with two-dimensional finite elements on the curved surface. Although the model is of low precision, we show that it is sufficient for a satisfactory prediction of breast reduction surgery results, allowing an analysis of errors frequently performed during the surgery and giving an understanding of how to avoid or correct them. Copyright © 2016 John Wiley & Sons, Ltd.

Parameters identification method for breast biomechanical numerical model

“…The domain is parameterised with the radius R of the sphere while H < R represents the non-truncated length as displayed in Figure 2. The cap which is placed in the torso plane corresponds to a circle of radius r which is smaller than R. We could use a more complex shape such as a super-ellipsoid as in [17], but this shape was proven to be representative as it was shown in [4,20]. The final and more realistic shape of the breast is obtained by determining the effect of gravity on the breast tissues as observed in figure 3.…”

“…To prescribe the boundary condition and compute the energy associated to the skin, we introduce the following notations, reproduced on Figure 3: Γ B is the back side plane of the breast which attaches to the torso, Γ F represents the surface associated to the skin of the breast and γ D is the arc of the inframammary fold. Like in [4,20] we use the γ D as a fixation boundary in order to allow breast mobility. The hyperelastic neo-Hookean compressible relations [5] equipped with the so-called Chassaignac space represent a well-accepted model for biomechanical soft tissues [4].…”

“…For the particular case of breast, we differentiate the skin from the core assuming a couple of coefficients for each material. Moreover, an additional goal of the present model is to develop a numerical method that runs on a mid-range laptop and produce results within a few minutes (see also [20]). The key ideas are, on the one hand, the introduction of a simple set of in vivo breast measures easy to achieve (avoiding the use of medical imaging technology), and on the other hand, the introduction of a four-parameters non-linear mechanical model defining on a simplified two-parameters reference configuration (breast in a free stress state).…”

Computational modelling to determine the physical characteristics of biological tissues for medical diagnosis

“…A separate and independent task is the construction of 3D models of internal and general structure of biological tissues. It must be pointed out, however, that such 3D models are also important for various medical tasks, including preoperative planning and evaluation of oncoplastic surgery [34], cosmetic surgery [15], including the establishment of safety criteria for MRI research [17].…”