Tissue expansion in pediatric patients

Tissue expansion is a technique used clinically to grow skin in situ to correct large defects. Despite its enormous potential, lack of fundamental knowledge of skin adaptation to mechanical cues, and lack of predictive computational models limit the broader adoption and efficacy of tissue expansion. In our previous work, we introduced a finite element model of tissue expansion that predicted key patterns of strain and growth which were then confirmed by our porcine animal model. Here we use the data from a new set of experiments to calibrate the computational model within a Bayesian framework. Four $10\times 10$ ${\mathrm{cm}}^2$ patches were tattooed in the dorsal skin of four 12 weeks-old minipigs and a total of six patches underwent successful tissue expander placement and inflation to 60cc for expansion times ranging from 1 h to 7 days. Six patches that did not have expanders implanted served as controls for the analysis. We find that growth can be explained based on the elastic deformation. The predicted area growth rate is $k\in [0.02,0.08]$ [${\mathrm{h}}^{-1}$]. Growth is anisotropic and reflects the anisotropic mechanical behavior of porcine dorsal skin. The rostral-caudal axis shows greater deformation than the transverse axis, and the time scale of growth in the rostral-caudal direction is given by rate parameters $k_1\in [0.04,0.1]$ [${\mathrm{h}}^{-1}$] compared to $k_2\in [0.01,0.05]$ [${\mathrm{h}}^{-1}$] in the transverse direction. Moreover, the calibration results underscore the high variability in biological systems, and the need to create probabilistic computational models to predict tissue adaptation in realistic settings.

Tissue expansion is a widely used technique in reconstructive surgery because it triggers growth of skin for the correction of large skin lesions and for breast reconstruction after mastectomy. Despite of its potential, complications and undesired outcomes persist due to our incomplete understanding of skin mechanobiology. Here we quantify the deformation and growth fields induced by an expander over 7 days in a porcine animal model and use these data to calibrate a computational model of skin growth using finite element simulations and a Bayesian framework. The calibrated model is a leap forward in our understanding skin growth, we now have quantitative understanding of this process: area growth is anisotropic and it is proportional to stretch with a characteristic rate constant of $k\in [0.02,0.08]$ [${\mathrm{h}}^{-1}$].

Tissues in vivo are not stress-free. As we grow, our tissues adapt to different physiological and disease conditions through growth and remodeling. This adaptation occurs at the microscopic scale, where cells control the microstructure of their immediate extracellular environment to achieve homeostasis. The local and heterogeneous nature of this process is the source of residual stresses. At the macroscopic scale, growth and remodeling can be accurately captured with the finite volume growth framework within continuum mechanics, which is akin to plasticity. The multiplicative split of the deformation gradient into growth and elastic contributions brings about the notion of incompatibility as a plausible description for the origin of residual stress. Here we define the geometric features that characterize incompatibility in biological materials. We introduce the geometric incompatibility tensor for different growth types, showing that the constraints associated with growth lead to specific patterns of the incompatibility metrics. To numerically investigate the distribution of incompatibility measures, we implement the analysis within a finite element framework. Simple, illustrative examples are shown first to explain the main concepts. Then, numerical characterization of incompatibility and residual stress is performed on three biomedical applications: brain atrophy, skin expansion, and cortical folding. Our analysis provides new insights into the role of growth in the development of tissue defects and residual stresses. Thus, we anticipate that our work will further motivate additional research to characterize residual stresses in living tissue and their role in development, disease, and clinical intervention.

Skin expansion is widely used in reconstructive surgery to obtain supplemental and optimal skin. Enhancing the regenerative capacity of expanded skin is therefore of great interest. Hair follicle bulge-derived stem cells (HFBSCs) located in hair follicle bulges are closely associated with skin; HFBSC transplantation could promote cutaneous wound repair. However, the effects of transplanted HFBSCs on skin regeneration during expansion remain unclear. The aim of the study was to reveal the potential effects of transplanted HFBSCs in the expanded skin and explore its mechanism. Our results showed higher skin area, tissue weight, epidermal thickness, dermal thickness, proliferating cell count, collagen content, microcirculatory blood flow, blood vessels, and lower retraction ratios were observed in HFBSC-injected rats compared to uninjected controls. Moreover, the transplanted HFBSCs directly contributed to tissue regeneration by differentiating into vascular endothelial cells, epidermal cells, and the outer root sheath cells of hair follicle. Higher expression of EGF, VEGF, bFGF, and TGF-β were observed in HFBSC-injected rats. Our research demonstrated the transplanted HFBSCs could promote skin regeneration by differentiating into various types of skin related cells and by up-regulating the expression of growth factors. Our results could form a basis for the development of novel strategies to enhance regeneration in expanded skin by using HFBSCs.

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.

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.

Successful use of tissue expanders depends on the quality of expanded tissue. This study evaluates the impact of anisotropic self-inflating tissue expander (SITE) on the biomechanics of skin. Two different SITE were implanted subcutaneously on sheep scalps; SITE that requires 30 days for maximum expansion (Group A; n = 5), and SITE that requires 21 days for maximum expansion (Group B; n = 5). Control animals (n = 5) were maintained without SITE implantation. Young’s Modulus, D-periodicity, overlap and gap region length, diameter, and height difference between overlap and gap regions on collagen fibrils were analyzed using atomic force microscopy. Histology showed no significant differences in dermal thickness between control and expanded skin of groups A and B. Furthermore, most parameters of expanded skin were similar to controls (p > 0.05). However, the height difference between overlap and gap regions was significantly smaller in group B compared to both control and group A (p < 0.01). Strong correlation was observed between Young’s Modulus of overlap and gap regions of the control and group A, but not group B. Results suggest that a relatively slower SITE can be useful in reconstructive surgery to maintain the biomechanical properties of expanded skin.