Tissue expansion (TE) is an indispensable technique for breast reconstruction after mastectomy and for reconstruction of large skin defects such as nevi (a type of congenital birthmark) [1], [2], [3]. In TE, a balloon-like device is inserted subcutaneously and gradually inflated over a period of weeks to months up to several hundreds of milliliters. The principle underpinning TE is skin’s ability to adapt to sustained supra-physiological stretch by growing, i.e. through permanent increase in area from cell proliferation and extra-cellular matrix (ECM) deposition [4], [5], [6]. Using a porcine animal model, we have measured the dynamics of skin growth in response to a variety of injection volumes, inflation times, and expander shapes [7], [8], [9]. With these data, we have established and calibrated a theoretical and computational modeling framework [10]. However, it remains untested whether the biomechanics and mechanobiology parameters of growing skin in the swine model constitutes an adequate prior probability for the prediction of human patient skin growth after TE. Unfortunately, despite its widespread use, TE can lead to complications such as tissue necrosis [11], as well as sub-optimal outcomes, e.g. asymmetric or unnatural breast shape [12].

TE was introduced in 1957 to reconstruct an ear [13], [14]. Since then, the most prevalent use of TE has become post-mastectomy breast reconstruction. This is because breast cancer is the most common cancer in women, with 1 in 8 women suffering from breast cancer over their lifetime [15]. Surgical treatment of breast cancer is recommended in almost all cases, with the two options being breast conserving surgery or lumpectomy, and total breast removal or mastectomy. Nearly 40% of patients undergo mastectomy, and nearly 65% of this population undergoes breast reconstruction with TE [2], [16]. While TE has been refined over the past few decades, complication rates remain high, between 8% and 37% [17]. Complications include wound dehiscence, contracture, expander leakage, infection, hematoma, seroma, lymphedema, and necrosis [17], [18]. Moreover, even in the absence of complications, poor aesthetic outcomes -related to breast size, shape and symmetry- are prevalent and reduce quality of life of breast cancer survivors [19], [20], [21]. The skin is stretched, depending on breast size, with expanders that are regularly filled in the [400,500]cc range, depending on the pre-operative breast volume. The volume and rate of inflation remains controversial [22], [23], [24]. Expanders also come in different shapes in order to match the natural contour of the breast; however, the best choice of expander for a given patient is not well defined [25]. Thus, there is a significant need for patient-specific pre-operative tools to plan safe TE and achieve better cosmetic outcomes.

Reconstruction of large skin defects in the pediatric population is another important application of TE [26]. Even though the technique is very similar to the breast reconstruction case, there are also some notable differences. Expanders for pediatric patients are available in a much wider range of volumes and shapes, including rectangular, circular, and crescent-shaped expanders, from a few milliliters to hundreds of milliliters [27]. They are also placed in various anatomical locations, not just the chest wall, but commonly in the lower abdomen, followed by head and neck area, lower extremities, and less commonly on the upper limbs [28]. The variability of expander selection is due to the variability of size and anatomical location of the skin defects that need to be corrected. There are also clinical differences between pediatric and adult skin. In terms of mechanical properties, adult skin is stiffer [29], [30], [31]. In terms of its mechanobiological adaption, it is not clear to what extent pediatric skin adaptation dynamics differ from adult skin growth during TE [26], [32]. Nonetheless, independently of TE, it is clear that pediatric skin grows continuously to accommodate for the growing body of the child, which is reflected in increased cellularity and ECM turnover in the younger population compared to adults [33], [34]. Complication rates in pediatric TE are up to 40%, which is much higher than those reported for breast reconstruction [11], [26], [28]. Similar to the breast reconstruction case, the volume and timing of inflations remains controversial for the pediatric population [27], [32]. Thus, personalized predictive models for TE in the context of pediatric reconstruction could change the treatment paradigm toward a more widespread and safer use of TE in children.

In our previous work we established theoretical, computational and experimental frameworks for studying skin growth in TE [9], [35]. We modeled skin growth using finite volume growth within continuum mechanics, a theory akin to plasticity introduced by Rodriguez et al. [36]. The key assumption for modeling tissue growth is to decompose the deformation gradient into growth and elastic contributions [37]. The elastic part explains how the tissue deforms in response to applied forces, while the growth portion describes addition of mass by permanent changes in volume at constant density, either from cell division or ECM deposition [38]. Other theoretical frameworks for tissue growth and remodeling include reactive mixture models [39], [40]. For skin, within the finite volume framework, we posed a growth deformation tensor that captured permanent area changes in response to applied stretch [35]. Thus, the two kinds of parameters for the theory are either related to the elastic deformation and stress, or to the accumulation of area growth in response to deformation. Computationally, we implemented the model into finite element software Abaqus through user material subroutines, and showcased the simulation of both idealized and patient specific geometries [10], [41]. To inform the theoretical model and gain fundamental understanding of how skin grows in TE we conducted a series of animal experiments and measured area deformation and total area grown at the end of TE under different protocols, varying volume, expander shape, and timing of inflation [7], [8], [9]. With these data and using the computational model, we were able to do Bayesian inference and calibrate the mechanical and biological parameters [9]. We learned that the best model to explain skin growth in the pig was a linear relationship between the elastic deformation and the rate of skin growth, with a characteristic time constant [9]. These findings were in line with other work characterizing growth and remodeling of skin and skin-equivalent tissue engineered constructs [42], [43].

Motivated by the success calibrating finite element (FE) models of skin growth to the porcine data, here we translate the theoretical and computational framework to the human clinical setting, following a similar data collection and simulation pipeline as we did in the porcine model, and using the biological parameters for the pig as priors for the human model. For the mechanical parameters we rely on extensive characterization of human-specific material properties available in the literature [44], [45], [46]. Digital twins in biomedical applications are virtual representations of a biological system including the internal state and its observable outcomes [47], [48]. In our case, the system of interest is the skin, and its state includes the observed deformation and geometry, as well as the stress field and biological growth field, which are not necessarily observable or might be observed only at a small number of locations and/or time points. We initialize the digital twin using 3D photography at the start of TE. As more 3D geometries are used, the digital twin is calibrated to yield accurate models of skin deformation and growth in a patient-specific setting, addressing the existing gap in predictive modeling of TE for human patients. The calibration framework is posed as a Bayesian inference problem [49], [50], [51]. Sampling of the posterior distribution requires many function evaluations, which is not feasible if the detailed physics solvers are used [52]. Machine learning surrogates such as artificial neural networks and Gaussian process surrogates have gained attention in the biomechanics field as accurate metamodels to replace the computational expensive finite element models [53], [54], [55]. In this work we leverage Gaussian process surrogates [56].