Tissue expansion is a common technique in reconstructive surgery used to grow skin in vivo for correction of large defects. Despite its popularity, there is a lack of quantitative understanding of how stretch leads to growth of new skin. This has resulted in several arbitrary expansion protocols that rely on the surgeon's personal training and experience rather than on accurate predictive models. For example, choosing between slow or rapid expansion, or small or large inflation volumes remains controversial. Here we explore four tissue expansion protocols by systematically varying the inflation volume and the protocol duration in a porcine model. The quantitative analysis combines three-dimensional photography, isogeometric kinematics, and finite growth theory. Strikingly, all four protocols generate similar peak stretches, but different growth patterns: Smaller filling volumes of 30 ml per inflation did not result in notable expander-induced growth neither for the short nor for the long protocol; larger filling volumes of 60 ml per inflation trigger skin adaptation, with larger expander-induced growth in regions of larger stretch, and more expander-induced growth for the 14-day compared to the 10-day expansion protocol. Our results suggest that expander-induced growth is not triggered by the local stretch alone. While stretch is clearly a driver for growth, the local stretch at a given point is not enough to predict the expander-induced growth at that location. From a clinical perspective, our study suggests that longer expansion protocols are needed to ensure sufficient growth of sizable skin patches.

Excessive mechanical stress following surgery can lead to delayed healing, hypertrophic scars, and even skin necrosis. Measuring stress directly in the operating room over large skin areas is not feasible, and nonlinear finite element simulations have become an appealing alternative to predict stress contours on arbitrary geometries. However, this approach has been limited to generic cases, when in reality each patient geometry and procedure are unique, and material properties change from one person to another. In this manuscript, we use multi-view stereo to capture the patient-specific geometry of a 7-year-old female undergoing cranioplasty and complex tissue rearrangement. The geometry is used to setup a nonlinear finite element simulation of the reconstructive procedure. A key contribution of this work is incorporation of material behavior uncertainty. The finite element simulation is computationally expensive, and it is not suitable for uncertainty propagation which would require many such simulations. Instead, we run only a few expensive simulations in order to build a surrogate model by Gaussian process regression of the principal components of the stress fields computed with these few samples. The inexpensive surrogate is then used to compute the statistics of the stress distribution in this patient-specific scenario.

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A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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