Growing skin: A computational model for skin expansion in reconstructive surgery

Abstract

The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

Figure 1

Tissue expansion for pediatric forehead reconstruction. The patient, a one-year old girl, presented with a giant congenital nevus involving almost 50 percent of the forehead, affecting the hairline and the left eyebrow. Three forehead and scalp expanders were implanted simultaneously for in situ forehead flap growth. For complete resurfacing of the region, serial tissue expansion was performed to successively stretch the previously expanded tissues until the entire nevus could be excised and resurfaced. This technique allows to resurface large anatomical areas with skin of similar color, quality, and texture. The follow-up photograph shows the patient at age three; the initial defect was excised and resurfaced with expanded forehead and scalp flaps.

Figure 2

Schematic sequence of tissue expander inflation and deflation. At biological equilibrium, the skin is in a physiological state of resting tension, left. A tissue expander is implanted subcutaneously between the skin, consisting of the epidermis and dermis, and the hypodermis. When the expander is inflated, the skin is loaded in tension, middle left. Mechanical stretch induces cell proliferation causing the skin to grow. Growth restores the state of resting tension, middle right. Expander deflation reveals the irreversible nature of skin growth associated with growth-induced residual stresses in the skin layer, right.

Figure 3

Tissue expanders to grow skin flaps for defect correction in reconstructive surgery. Typical applications are birth defect correction, scar revision in burn injuries, and breast reconstruction after tumor removal. Devices are available in different shapes and sizes, circular, square, rectangular, and crescent-shaped. They consist of a silicone elastomer inflatable expander with a reinforced base for directional expansion, and a remote silicone elastomer injection dome. Reprinted with permission, Mentor Worldwide LLC.

Figure 4

Tissue expander inflation and deflation. Skin is modeled as a 0.2 cm thin 12 × 12 cm² square sheet, discretized with 3 × 24 × 24 = 1728 trilinear brick elements, with 4 × 25 × 25 = 2500 nodes and 7500 degrees of freedom. We explore the impact of different tissue expander geometries, circular, square, rectangular, and crescent-shaped. The base surface area of all expanders is scaled to 148 elements corresponding to 37 cm2. This area, here shown in light red, is gradually pressurized from underneath while the bottom nodes of all remaining elements, shown in white, are fixed.

Figure 5

Tissue expander inflation. Temporal evolution of fractional area gain and increasing expander volume. Expanders are inflated gradually between t = 0 and t = 4 by linearly increasing the pressure. The pressure is then held constant from t = 4 to t = 50 to allow the skin to grow. Under the same pressure applied to the same base surface area, the circular expander displays the largest fractional area gain, followed by the square, the rectangular, and the crescent-shaped expanders, left. Growth causes the tissue to relax and the expander volume to increase. The expander volume is largest for the circular expander, followed by the square, the rectangular, and the crescent-shaped expanders, right. Both graphs demonstrate the characteristic creep-type growth under constant pressure with a gradual convergence towards the biological equilibrium state.

Figure 6

Tissue expander inflation. Spatio-temporal evolution of growth area stretch ϑ^g for circular, square, rectangular, and crescent-shaped expanders. Under the same pressure applied to the same base surface area, the circular expander induces the largest amount of growth followed by the square, the rectangular, and the crescent-shaped expanders. The color code illustrates the evolution of the growth multiplier ϑ^g, ranging from ϑ^g = 1.0 for the initially ungrown skin, shown in blue, to ϑ^g = ϑ^max = 2.4 for the fully grown state, shown in red. Snapshots correspond to t = 4, t = 12, t = 24, and t = 48, from left to right, corresponding to the labels in Figure 5.

Figure 7

Tissue expander deflation. Spatio-temporal evolution of elastic area stretch ϑ^e for circular, square, rectangular, and crescent-shaped expanders. As the expander pressure is gradually removed, from left to right, the grown skin layer collapses. Deviations from a flat surface after total unloading, right, demonstrate the irreversibility of the growth process. Growth induces compression at the edges of the original base surface area, and tension in the center region. The color code illustrates the evolution of the elastic area stretch ϑ^e, ranging from ϑ^e = 0.9 corresponding to 10% of area compression, shown in blue, to ϑ^e = 1.1 corresponding to 10% of area tension, shown in red. Snapshots correspond to t = 12, t = 13, t = 14, and t = 15, from left to right.

Figure 8

Tissue expander deflation. Spatio-temporal evolution of maximum principal stress σ^max for circular, square, rectangular, and crescent-shaped expanders. As the expander pressure is gradually removed, from left to right, the grown skin layer collapses. Deviations from a flat surface after total unloading, right, demonstrate the irreversibility of the growth process. Remaining stresses at in the unloaded state, right, are growth-induced residual stresses. The color code illustrates the evolution of the maximum principal stress σ^max, ranging from σ^max = 0.0, shown in blue, to σ^max = 0.40, shown in red. Snapshots correspond to t = 12, t = 13, t = 14, and t = 15, from left to right.